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ROGER BOSCOVICH
THE FOUNDER OF MODERN SCIENCE
DRAGOSLAV STOILJKOVICH
Translated by: Roger J Anderton
Roger Boscovich
The founder of modern science
Dragoslav Stoiljkovich
Translated and edited by
Roger Anderton
Petnica Science Center
2010 (Serbian edition)
2014 (English edition)
2015 (English edition corrected)
Translated from Serbian edition:
Petniĉke sveske broj (Petnica's Papers No.) 65
ISBN 978-86-7861-043-1
ISSN 0354-1428
Urednik (Editor): Branislav Savić
RUĐER BOŠKOVIĆ - UTEMELJIVAĈ SAVREMENE NAUKE
Autor (Author): Dragoslav Stoiljković
Recenzenti (Reviewers):
Dr Slobodan Jovanović
Dr Nikolai Ostrovski
Dr Radmila Radiĉević
Dr Radoslav Dimitrić
Dr Aleksandar Tomić
Lektura i korektura (Proofreading): Dušica Boţović
Direktor (Director): Vigor Mojić
Štampa (Printed by): Valjevoprint, Valjevo
Izdavaĉ (Publisher): Istraţivaĉka stanica Petnica (Petnica Science Center)
Valjevo, 2010.
CONTENT
FOREWORD OF ENGLISH EDITION I
FOREWORD OF SERBIAN EDITION I
1. LIFE OF ROGER BOSCOVICH 1-1
2. ACTIVITIES OF ROGER BOSCOVICH 2-1
3. BOSCOVICH'S "THEORY OF NATURAL PHILOSOPHY" 3-1
3.1. A unique law of forces that exist in nature 3-1
3.2. Orbitals in Boscovich's Theory 3-2
3.3. Quantum meaning of Boscovich's Theory 3-3
4. CONTRIBUTION OF BOSCOVICH'S THEORY TO MODERN
COMPREHENSION OF THE STRUCTURE OF MATTER 4-1
4.1. Common view of the historical journey for the discovery
of structure of atoms, molecules and macromolecules 4-1
4.2. Contribution of Boscovich's Theory to the discovery of
the structure of atoms 4-2
4.3. Boscovich's comprehensions of elementary points,
atoms and molecules 4-5
4.4. Macromolecular hypothesis of Boscovich 4-9
4.5. Nano-tubes, diamond and graphite 4-10
4.6. Boscovich's signposts to neutrino, gluons and quarks 4-11
5. CONFIRMATIONS OF BOSCOVICH'S FORCE LAW
IN MODERN SCIENCE 5-1
5.1. Relation of force and energy dependence
on the distance between particles 5-1
5.2. Interaction of atoms 5-2
5.3. Interaction of molecules 5-3
5.4. Interaction of nano-particles 5-5
5.5. Interaction of macromolecules 5-5
5.6. Interaction of colloidal particles 5-6
5.7. Fission of heavy atomic nuclei 5-7
5.8. Energy of atomic nucleus 5-8
5.9. Interaction between nucleons and Λ hyperon 5-9
5.10. Conclusion concerning the validity of Boscovich's curve 5-9
6. COMPRESSION OF MATTER - REFLECTIONS OF
BOSCOVICH'S THEORY IN SAVICH-KASHANIN THEORY 6-1
6.1. Introduction 6-1
6.2. Material density changes according to Boscovich's opinion 6-1
6.3. Material density changes according to Savich-Kashanin theory 6-2
6.4. Relation between Boscovich's opinion and
opinion of Savich and Kashanin 6-3
6.5. Density change in the compression of matter by the model
of Savich and Kashanin 6-5
6.6. Mean densities of planets in Solar system calculated by model
of Savich-Kashanin 6-7
6.7. Adaptation of stepwise mathematical model
by actual empirical data 6-7
7. APPLICABILITY OF BOSCOVICH'S THEORY 7-1
7.1. Introduction 7-1
7.2. Meaning of critical volumes of matter 7-1
7.3. Characteristic volumes of matter 7-3
7.4. Physico-chemical state and polymerization
of compressed ethylene gas 7-6
7.5. Effect of pressure on polyethylene melting point 7-9
7.6. Structure of fluids based on Boscovich's Theory
and Savich-Kashanin's Theory 7-11
7.7. Polymerization of methyl methacrylate 7-14
8. PHILOSOPHICAL FOUNDATION OF BOSCOVICH
COMPREHENSIONS 8-1
8.1. Introduction 8-1
8.2. Attraction and repulsion
– Comprehensions of Boscovich, Hegel and Engels 8-1
8.2.1. Boscovich's comprehension 8-2
8.2.2. Hegel's comprehensions 8-2
8.2.3. Engels' comprehension 8-3
8.2.4. Distinctions and similarities of Boscovich,
Hegel and Engels comprehensions 8-7
8.2.5. Analysis of Boscovich's comprehension of attractive
and repulsive forces 8-8
8.2.6. Differentiation of matter 8-10
9. ROGER BOSCOVICH – THE FOUNDER OF MODERN SCIENCE 9-1
9.1. Influence of Boscovich's Theory
on the contemporaries and followers 9-1
9.2. Resurrection of Boscovich's Theory 9-2
REFERENCES
Note about author
FOREWORD OF ENGLISH EDITION
The English edition of this monograph is almost identical to the Serbian edition
published in 2010 by Petnica Science Center, however, revised, extended and
corrected. A new Chapter 7.6. titled "Structure of fluids based on Boscovich's Theory
and Savich-Kashanin's theory" was added. The Chapters 7.4. and 7.7. are slightly
extended, all in order to clarify the applicability of Boscovich's Theory. Table 8-2 and
corresponding explanation are added, too.
The author is very grateful to Roger Anderton for translating and editing this book.
Author,
April, 2014
FOREWORD OF SERBIAN EDITION
It's been two and a half centuries since Roger Boscovich published his
monumental work "A Theory of natural philosophy reduced to a one unique law of
forces that exist in nature". The Theory has had a major impact on Boscovich's
contemporaries, scholars of the 18th century, and this resulted in many followers in
the 19th and at the beginning of the 20th century. It was studied in many educational
institutions all over the world, and was present in many textbooks, books,
encyclopaedias.
And then suddenly everything went silent. Today it is no longer present in the
curricula of schools and colleges. Apart from the few individuals, our contemporaries,
even highly educated people, know almost nothing about Boscovich. They knew
hardly anything about who he was, when he lived and what he did, and why many
streets and other institutions carry his name.
In the last century in our (Serbian) language there has been published several
monographs and a number of professional articles on Roger Boscovich which shows
his life and scientific activity, his scientific and philosophical views, as well as his
influence on contemporaries and followers. These topics are dealt with briefly and
succinctly in this monograph (Chapters 1 and 2).
However, scholars and interpreters of Boscovich's life and creativity have
completely missed some of his concepts or have only partially processed them, and
sometimes completely misrepresented them. Therefore, it is the basic purpose of this
monograph to shed light on those issues which the existing literature has not devoted
enough attention. I
It is almost unnoticed that his Theory is actually the first quantum theory. He was
the first one to draw the orbitals by which a particle moves around particles located in
a centre and explain that by transition from one orbital to another a particle either
gains or loses a certain amount (quantum) of energy. Having summarized his Theory
in Chapter 3, then we present Boscovich's orbitals and interpret the quantum meaning
of his Theory.
Little is popularly known about Boscovich's contribution to the contemporary
understanding of the structure of matter. His primary undoubted contribution was to
the discovery of the structure of atoms of chemical elements. Boscovich's
understanding of elementary points, atoms and molecules are usually incomplete and
misinterpreted by scholars. Also the scholars of Boscovich's work have completely
missed that he was on his way, with his vocabulary, pointing to the possibility of
existence of macromolecules (i.e. polymers) and nano-tubes. He described the
structure of these materials and their basic properties, and also the structure of
diamond and graphite. Following the signposts (of his line of thought), the ideas of
neutrino, quarks and gluons can be reached. These topics are dealt within Chapter 4
of this monograph.
The foundation of Boscovich's Theory is the well-known (to some academics)
Boscovich's curve that describes the change in force between the particles of matter
depending on the distance between them. It is striking that the investigators of his
work have never asked themselves whether the curve is scientifically confirmed. This
question was never considered, and hence the answer was not sought. Therefore, in
Chapter 5 we list a dozen examples that confirm the validity of Boscovich's curve at
several levels in the hierarchy of matter - of nucleons in atomic nucleus to the
colloidal particles.
Serbian famous scientists, Savich and Kashanin, in the middle of the last century
presented a theory about the behaviour of matter at high pressures. Among other
things, it can be applied to calculate the mean density of the planets in the Solar
system. Although they do not refer to Boscovich, there is obviously a real connection
with his Theory. With some adaptation of the mathematical model, we can obtain a
significantly more accurate calculation for the results of planet density (Chapter 6).
The value of Boscovich's Theory is reflected in the multitude of ideas that sprout
from it and that can be used to solve some of the problems of modern science. Using
his directions we approached an original interpretation of the meaning of a critical
point, and gave a mathematical model to calculate the volumes of matter at critical
point conditions and in some other characteristic states of matter. His Theory was also
a signpost to the interpretation of the mechanism and kinetics of the polymerization
of ethylene and methyl methacrylate. This topic is devoted to Chapter 7.
II
There is a plenty of writings concerning the philosophical views of Boscovich. It is
written that, from his perception, the attractive and repulsive forces are the essence of
the behaviour of matter. However, it is missed that Kant, Hegel, Engels and many
other philosophers had similar views. A comparison of Boscovich's understanding of
attractions and repulsions with the understanding of these other philosophers is stated
in Chapter 8.
Bearing in mind the influence of Boscovich's Theory on contemporaries and
subsequent scholars we derive the conclusion that his Theory directly, and sometimes
indirectly, have been built into the foundations of modern science.
Everything we have written in this book has been already published in scientific,
professional and philosophical journals and presented in a number of scientific
meetings. However, in each of them only some particular issues of Boscovich's life
and work are considered. All these considerations are scattered in many national and
international journals and conference proceedings. This book is arisen as a need to
collect them into one place, to interconnect those ideas and then to give readers a
complete view of Boscovich's contributions to modern science. Only then, can it be
seen to what extent his Theory has been built into the foundations of contemporary
science, and thus reveal how far he was ahead of his time, and according to some
beliefs he is ahead of our present time.
Initial Chapters of the book are written in a popular and interesting way to be
understood by those whose knowledge of natural science is not their strong point.
Other Chapters are slightly more complicated. In order to understand them it requires
some knowledge of physics, chemistry and science of polymeric materials.
The author thanks the reviewers, and also, Dr. Matilda Lazich, for very useful
suggestions and comments, which have contributed to the quality of the monograph.
The author is also grateful to the Petnica Science Center, which accepted this
monograph for publication.
Author,
2010
III
Roger Boscovich
The founder of modern science
1. LIFE OF ROGER BOSCOVICH
In the past decade there has been published several books /1-7/ which describe in
great detail the life of Roger Boscovich. The reader is referred to the literature cited,
and here we will only briefly point out the main themes of his life that are important
for the creation and development of his scientific and philosophical thoughts.
Boscovich was born on May 18th, 1711 in Dubrovnik, as the eighth of nine
children of a father Nikola and mother Pavla. Nikola was born in the Herzegovinian
village Orahov Do, and the mother of Pavla came from a family of Betera in Bergamo
in northern Italy. Roger attended the Jesuit College of Dubrovnik where his
exceptional talent was observed. To continue his education, in 1725 he went to the
Roman Jesuit College where he studied rhetoric, logic, philosophy, mathematics,
astronomy and theology. In 1733, he became a teacher of grammar, and in 1740 he
was professor of mathematics at the Roman College. In Rome he remained until in
1759 during which period he developed his scientific and philosophical concepts. He
published a number of papers among those which are significant are "De viribus
vivis" ("The Living Forces" in 1745) and "De Lumine" ("The Light", 1748), along
with many works on astronomy, and his most important work "Philosophiae naturalis
theoria redacta ad unicam legem virium existentium in natura" ("A Theory of natural
philosophy reduced to a one unique law of forces that exist in nature") /8/. The first
edition of the Theory was printed in Vienna in 1758, and the second edition 1763 in
Venice, which was then in Austria. (Editor's note: There have been many boundary
changes of countries over the centuries.)
Boscovich was a member of the Catholic order of the Jesuits (Society of Jesus),
whose important role was to defend the church from heretical teachings. At that time
the church taught that the Earth was the centre of the universe and that the Sun and
planets revolve around it (geocentricism). On the list of banned books were
heliocentric teachings, according to which the Earth and the other planets revolve
around the Sun. Although it was already in full development (in England), on the list
of undesirable teachings was also Newtonian mechanics. The part of Newtonian
mechanics, which refers to the movement of the planets around the sun, was banned
by the church.
Although a Jesuit, Boscovich had convinced himself to be a Newtonian. He
advocated the acceptance of Newton's teaching, but also feared that he might come
under attack by the Jesuits, to which he belonged. His Theory was therefore published
in Austria, where there was less Jesuit influence. He realized, however, that too
conservative a point-of-view ruled in the Roman College and that this was not the
environment to keep pace with the latest scientific and philosophical achievements,
thus Rome was not the place to develop and present such views.
1-1
Therefore, in 1759, he went on a long study trip to Europe, without any desire to
return to Rome. He went first to Paris, where as a corresponding member of the Royal
Academy of Sciences (admitted on May 6th, 1748) he attended meetings of the
Academy. There he met many famous encyclopaedists, and became introduced to
their ideas. He went to London in 1760, where on January 15th, 1761, he became a
member of The Royal Society; the Royal Society represents English academy of
sciences. After England, from about 1760 to 1763, he visited many well-known
scientific and public institutions and individuals in the areas that now form parts of
Netherlands, Belgium, Germany, Austria, Turkey, Bulgaria, Moldova and Poland.
Upon completion of his travels, he refused to go back to the Roman College, but in
1764 accepted professorship of mathematics in the small town of Pavia near Milan,
which was then within Austria. In 1765, he accepted the invitation to establish an
astronomical observatory in Milan, together with the Jesuits from Brera. Brera is a
district that still exists in the centre of Milan (Figure 1-1). All his intellectual forces
and financial funds he invested in the construction of the observatory (Figure 1-2),
and in 1770, he moved to Milan, to be professor of astronomy and optics. Until in
1772, he was the head of the observatory, together with Abbot Le Grange.
Figure 1-1. The entrance to the Brera (Milan, recorded 2003)
Figure 1-2. Photo models of the Boscovich observatory
1-2
In Brera there is still the Astronomical Institute founded by Boscovich. The name
of the founder Roger Boscovich is still prominent on the board at the entrance of the
Institute (Figure 1-3). In the lobby of the Institute, there is a bust of Boscovich
(Figure 1-4), as well as the telescope from the period of his work in Brera. On the
roof of Brera, in a place where once there was Boscovich's observatory, today is a
modern observatory (Figure 1-5).
Figure 1-3. The board at the entrance of the Astronomical Institute in Brera, which
reads Boscovich as founder of the Institute
Figure 1-4. Bust of Boscovich at Astronomical Institute in Brera
1-3
Figure 1-5. Modern observatory in Brera is located
where once was Boscovich's Observatory
Due to disagreements with Abbot Le Grange as well as with other Jesuits in Brera,
Boscovich left Milan in 1772. He was then an elderly man of 61 years, left with no
income and no savings after using them to establish the observatory. Unfortunately
for Boscovich, in 1773 the Jesuit order was abolished so that even from them he
could not expect help. Therefore in 1773, he accepted the offer of the Ministry of the
Navy of France to be their director of the Department of optics. He moved to Paris
and took French citizenship.
To prepare for printing his works on optics, in 1782 he obtained leave to reside in
Milan, where in 1785 his book was published "Opera pertinentia ad opticam et
astronomiam" ("Acts relating to optics and astronomy"). Exhausted from work, and
mentally ill, Roger Boscovich died in Milan on February 13th, 1787.
He was buried in the church of St. Mary Podone, which is located on the piazza
Boromeo in down-town of Milan (Figure 1-6). At the entrance to the church is a relief
of Boscovich (Figure 1-7) where still can be read the letters "...CO ...VI..." as part of
his last name, written in Latin. Boscovich's body was placed in a recess in the wall of
the church. The church was unfortunately destroyed in the bombing during World
War II /1, p. 1041/. After its restoration, Boscovich's burial place was sealed off. At
the Milan cemetery in the Pantheon called "Famedio" there is a memorial plaque with
only Boscovich's name and the years 1711 - 1787.
1-4
Figure 1-6. Church of St. Mary Podone in the centre of Milan
where Roger Boscovich was buried (recorded 2011)
Figure 1-7. Relief of Boscovich at the entrance to the church of St.Mary Podone
(recorded 2011)
Boscovich was a celebrity in his time, a member of several academies of sciences
(English, French, Russian...), renowned as an astronomer, physicist, mathematician
and philosopher. The impressiveness of the versatile activities of this great scientist is
perpetuated in the "heart" of his scientific activity, in magnificent Milan. One street in
the centre of Milan even bears Boscovich's name (Figure 1-8) with a memorial plaque
dedicated to him (Figure 1-9).
1-5
Figure 1-8. Street in Milan, named after Roger Boscovich
Figure 1-9. Memorial plaque in the street of Roger Boscovich in Milan
1-6
2. ACTIVITIES OF ROGER BOSCOVICH
Boscovich's versatile activities were in many different scientific fields. Here in this
chapter we will only briefly outline his scientific and philosophical activities. A more
detailed account of his life and work can be found in the books of domestic /1-5, 9/
and foreign authors /6, 7/. The books by Markovich /1/, Dimitrich /4/ and White /6/
give lists of more than one hundred works by Boscovich.
Basic scientific and philosophical concepts, which Boscovich dealt with include:
continuity and discontinuity of matter, space, time and motion /10, 11/; issues of
divisibility and combinability of particles of matter, the forces that govern between
these particles, the nature and use of infinitely large and infinitely small sizes.
Although to these issues he devoted specific works, their unified representation, as
well as their elaboration and implementation are given in the most important of
Boscovich's work "Philosophiae naturalis theoria redacta ad unicam legem virium
existentium in natura" ("The theory of natural philosophy reduced to one unique law
of forces that exist in nature") /8/. In that work the basic issues of the structure of
matter are considered: starting from elementary points, via the atoms, molecules,
macromolecules and so up to the celestial bodies. (A more detailed presentation of the
Theory is given in Chapter 3. of this book.) Boscovich's Theory suggests a unique
law of forces between the particles, as follows: at the large distance between the
particles there is an attractive (gravitational) force, and with decreasing distance a
repulsive force arises, then again becomes attractive... And so on several times until at
small distances there arises a large repulsive force that prevents contact of the
particles (or bodies). The unique law of forces Boscovich displayed as an oscillating
"force-distance" curve in which the attractive and repulsive arches turn alternately (so
called Boscovich's curve, Figure 3-1). This law of forces, Boscovich applied to the
interpretation of various phenomena in physics, mechanics, optics, chemistry and
astronomy, which were known in his time. (Confirmation and implementation of
Boscovich's law of forces in modern science are presented in Chapter 5 to 7 of this
book).
A large part of Boscovich activities was related to many theoretical and practical
issues in the field of astronomy. He elaborated theoretically the construction of
astronomical instruments and assessed their reliability. He constructed a ring
micrometer and achromatic telescope.
Applying the theory of gravity, he considered the movements of bodies in the
Solar system and what emerges as consequences of these movements (tidal sea, the
shape and structure of the Earth).
2-1
In 1760, he published in London, in the form of a poem, a work on the eclipses of
the Sun and the moon, which was reprinted in 1761 in Venice and in 1767 in Rome;
in 1779 it was printed in Paris in the French language. Recently, the poem, which is
about 300 pages with 1550 verses, was published in Serbian /12/. Contrary to Euler,
Boscovich suggested that the moon has no atmosphere. While using data from shifts
in sunspots, and applying his own method, Boscovich determined the rotation time of
the Sun.
He developed an original method for determining the orbits of the planets and
comets. When the English astronomer Herschel in 1781 discovered a new celestial
body in the Solar system it was initially thought to be a comet. Boscovich, it could be
said, was among the first who accurately determined the path of the body and
concluded that it was not a comet but a new planet, which is now known as Uranus
/1, 2/.
As a great scientist he paid special attention to the theoretical interpretation and
application of optical issues: nature of light, its propagation, diffraction and
scattering, improving optical instruments.
In mathematics Boscovich made major contributions. He hollowed out (i.e.
defined and explained) many mathematical concepts and provided original solutions
of mathematical problems, primarily in the area of geometry. He also developed
spherical trigonometry. It is also interesting to point out that Boscovich first
developed a theory for analysis of measurement errors (long before Gauss and
different from Gauss) /4/.
There are reports of Boscovich's contributions in the field of engineering, civil
engineering, architecture, hydraulic engineering, as well as contributions to
archeology.
It is also worth mentioning his famous diary of his journey from Constantinople to
Poland in 1762. This was the "literary and scientific work of the first order, with
French, German and Polish translations occurring before the Italian originals and
were snapped up by readers so fast that even Boscovich could not get copies."
(Preface of D. Nedeljkovich the Serbian edition of the diary /13/).
2-2
3. BOSCOVICH'S "THEORY OF NATURAL
PHILOSOPHY"
3.1. A unique law of forces that exist in nature
Boscovich's comprehension of nature is partly based on the ideas of Leibniz and
Newton, and partly deviates from them. From Leibniz he accepts the assumption that
the basic elements of matter are tiny dots (monads), which do not have size (non-
extended) and are indivisible. However, Boscovich does not accept Leibniz's
assumption that the points can touch each other. Instead, he believes that the points
are distanced from each other over some space, which can infinitely increase or
decrease, but not completely disappear. From Newton, he accepts the existence of
mutual forces between these points. Unlike Newton, who believes that at very short
distances there is strong attractive force between the particles, Boscovich believes
that there is a strong repulsive force, which becomes greater as the distance becomes
less. This is similar to the views of Empedocles that there are forces of love and
forces of strife, where Boscovich believes that force can be attractive or repulsive,
and which alternates depending on the distance between points (Figure 3-1).
(a)
(b)
(c)
Figure 3-1. General (a) and special shapes of Boscovich curve show the
change of attractive and repulsive forces (lower and upper ordinate,
respectively) with the change of the distance (abscissa) between the
elementary points of matter /8, Figure 1/
3-1
Boscovich accepted Newton's notion that assembling points together in collections
forms more complicated particles of the first order, connecting these first order
particles together then forms particles of the second order, then the third order and so
on, and by further assembling atoms are formed which are not themselves elementary
particles but consist of parts. He considered that molecules are even larger assemblies
of particles. Moreover, Boscovich in 1758 was the first to put forward the suggestion
that the macromolecules could exist as series of atoms, and he describes their spiral
structure and properties! However, today it is commonly said that the macromolecular
hypothesis was first proposed by Staudinger in 1920!? (This is described in more
detail in Chapter 4.)
According to Boscovich, there are individual stages (ranks) in the hierarchy of
matter, i.e. elementary points, then particles of first order, then second order, atoms,
molecules, and even the entire Solar system. Boscovich indicates that "all worlds of
smaller dimensions, taken together, were like a single point in relation to the larger"
world. (The forces acting among the lower orders of the particles are larger than the
forces between the particles of higher orders /8, Section 424/.) He believes that his
curves shown in Figure 3-1 are valid for each pair of particles at any level of the
hierarchy of matter. The number of arches, their size and shape, however, can be
different: curve with one attractive and repulsive arch (Figure 3-1b), two attractive
and repulsive two arches (Fig. 3-1c), as well as with a number of arches (Fig. 3-1a).
Boscovich especially points out that there are distances (E, G, I, L, N, P, and R in
Figure 3-1a) at which the repulsive and attractive force are equal. The particles are in
balance if they are at such distances. However, there are two types of cases. In some
cases (E, I, N and R) by increasing the distance the attractive force increases, and by
reducing the distance the repulsive force increases. In this case, the particles are in a
stable equilibrium, for if the distance between the particles is accidentally increased,
then it creates an attractive force, and brings them back to the previous distance. If,
however, the distance is reduced, then the resulting repulsive force brings them back
to the previous distance. These distances (from A to E, I, N and R) are called the
limits of cohesion.
In other cases, if the distances are corresponding to the positions G, L and P, the
particles are in an unstable equilibrium because you either have (a) a small increase
leading to the appearance of the repulsive force and to an even greater separation of
the particles, or (b) a small decrease in distance leading to the appearance of the
attractive force and to an even greater approach of the particles. These positions
Boscovich called the limits of non-cohesion.
3.2. Orbitals in Boscovich's Theory
When considering the mutual effects of three points, Boscovich indicates a
"beautiful theory about the point placed on the ellipse, while the other two points
occupy the foci of the ellipse" /8, Sections 230-235/. Specifically, if the two points (or
3-2
particles) located at focal points A and B near the centre of D, then the third point
may be located at anywhere on the ellipse at a distance corresponding to the limits of
cohesion (Figure 3-2). Accordingly, there are as many ellipses as there are cohesion
limits.
Figure 3-2. Orbitals in Boscovich's Theory /8, Figure 33/
3.3. Quantum meaning of Boscovich's Theory /14, 15/
Boscovich indicates that "in mechanics it is known that for a curve, whose
abscissas represent distances and ordinates represent forces, then the area (delimited
by the curve and abscissa) represents the increase or decrease of the square of
velocity" of the particles that move mutually /8, Sections 118, 176, 191/. (In this
book, Chapter 5-1 in Figure 5 it is shown that F = dE/dr; wherein: force F, distance r,
and the kinetic energy E of a particle of mass m moving at a speed v is E = mv2/2.
Hence it follows that the area below or above the arches of the abscissa in Figure 3-1
represent energy.). Therefore, the individual areas, delimited by abscissa and
(repulsive and attractive) arches, are a measure of the increase or decrease of the
square of speed of the particles as they approach (or separate from) each other. The
two particles upon approaching will remain at a distance apart, the size of which
depends on their initial rates and the area delimited by attractive and repulsive arches.
Boscovich explains that if the areas delimited by repulsive arches are less than the
attractive areas, the particles will reach the first limit of cohesion (position E in
Figure 3-1) by a speed that is proportional to the surface delimited by the first
attractive arch (EFG) and moving on a circle having radius of AE will continuously
oscillate around that limit.
Moreover, Boscovich indicates that it stems from his Theory that as a particle
approaches another particle, and when it passes from one to the other limits of
cohesion, it will lose or gain exactly a certain amount of energy. That "quantum
energy", as it is now called, between the two limits of cohesion is equal to the
difference between areas delimited by repulsive and attractive arches.
3-3
Hence, Boscovich's Theory is actually the very first quantum theory. He described
what a century later was merely assumed by Planck. Reviewing the quite extensive
literature on Roger Boscovich available to us, we find that no other authors (except A.
Tomic /16/) observed that Boscovich's Theory is indeed a quantum theory and that
Boscovich laid the foundation stone for the discovery and development of 20th
century quantum theory, which followed a century and a half later. Unfortunately,
even the originators (Planck, Einstein and Bohr) of 20th century quantum theory and
the latter scholars seemed mostly unaware of Boscovich's foundation.
3-4
4. CONTRIBUTION OF BOSCOVICH'S THEORY TO
MODERN COMPREHENSION OF THE
STRUCTURE OF MATTER
4.1. Common view of the historical journey for the discovery of
structure of atoms, molecules and macromolecules
It is often said that the ancient Greek philosophers Leucippus and Democritus first
came to idea that all was made of atoms, tiny indivisible particles. Their thought was
religiously prohibited and dormant for more than 1500 years. During this period,
there were a few people who thought about the atomic structure, but in the period
to19th century, there was a great preparation that formed the basis for further work on
it. It is often said, that John Dalton at the beginning of the 19th century came up with
the idea that each chemical element has its smallest particles. Believing that these
particles are indivisible, Dalton, following the example of the Greeks, called them
atoms (Scheme 4-1.).
Scheme 4-1. A common view of the historical journey of discovery
structure of atoms, molecules and macromolecules
4-1
The Greek term
of atoms
(Leucippus and
Democritus,
5 century BC)
Dalton's term
of atoms
(Early 19th c.)
Contemporary theory
of atoms
(Thomson, Rutherford,
Bohr, the beginning of the
20th c.)
Molecules
(Avogadro and Cannizzaro,
the beginning of the
19th c.)
Macromolecules
(polymers)
(Staudinger in 1920)
A little later it turned out that these Dalton atoms must be divisible, i.e. the atom
had a structure, and the atom was made up of smaller particles, the atomic nucleus
and electrons. This truth of atoms was revealed in the 19th and 20th century and
many famous scientists contributed to finding out the structure of atoms are usually
named as: Faraday, Maxwell, William Thomson (better known as Lord Kelvin), J. J.
Thomson, Rutherford and Bohr. The remarkable contributions of the last three
scientists are emphasized; according to the usual contemporary story for the historical
journey of the discovery of the atomic structure looks like shown in scheme 4-1.
Then, usually are listed the names of A. Avogadro and A. Cannizzaro who in 19th
century indicated that atoms are combined into molecules, and then its stated that H.
Staudinger in 1920 first introduced the hypothesis that the molecules combine into
even larger entities - macromolecules.
However, it was not quite so. A part of the story was left out. It is undeniable that
these scientists contributed highly to the interpretation of the structure of matter. It is
important to note, however, that these achievements are based on the ideas of Roger
Boscovich, which is not known enough to the wider scientific community.
Earlier in western literature it was regularly cited the importance of Boscovich to
the discovery of the structure of atoms, but since 1920, his name is usually omitted
/6a/. It is commendable that some of our scholars in Serbia and Croatia typically cite
the name of this great scientist, but unfortunately do not give enough information on
his impact on the discovery of the structure of atoms. Therefore, we would like here
to briefly introduce the reader to the contribution of Boscovich to the discovery of
atomic structures, and more detailed views can be found in the literature /2, 6a, 7, 15,
17, 18/.
4.2. Contribution of Boscovich's Theory to
the discovery of the structure of atoms
At the end of the 19th century, the more mature conviction (i.e. point-of-view) was
that Dalton's atoms of chemical elements were still divisible and consisted of
positively charged particles and negatively charged electrons. The question was - how
were these particles located in the atom.
At the end of the 19th century, J. J. Thomson (from Cavendish Laboratory in
Cambridge) discussed various models of atoms. According to one of them, which is
most frequently cited in contemporary literature as by Thomson, is that of positive
charge filling the entire atom forming a ball, where negative electrons are deployed
like plum grains in pudding. (Hence, it is named "plum-pudding model" as well as
"Thomson model".) However, Lord Kelvin, in the period 1902-1907, published
several works which emphasized his belief that the issue of atomic structure can be
resolved by Boscovich's Theory and proposed a "planetary model of the atom".
4-2
J. J. Thomson also thoroughly discussed the "planetary model of the atom", under
which the positive charge is located in the nucleus of atom and the electrons orbit the
nucleus /2, 7/. Seeking a theoretical foundation for the idea that electrons can move
only at certain paths around the nucleus of atoms, Thomson concluded that for this
purpose only Boscovich's Theory would serve. In 1907 Thomson wrote in his work
"The corpuscular theory of matter" /90/: "Suppose we regard the charged ion as a
Boscovichian atom exerting a central force on a corpuscle which changes from
repulsion to attraction and from attraction to repulsion several times... such a force,
for example, as is represented graphically in Figure 4-1 where the abscissa represent
distances from the atom, and the ordinates the forces exerted by the atom on a
corpuscle...” It is obvious that Figure 4-1 actually combines Boscovich's curve (Fig.
3-1) and Boscovich's orbitals (Fig. 3-2).
Figure 4-1. Left curve as stated by Thomson /90/: A positively charged nucleus
of the atom is at coordinate's origin and the positions of electron orbits are at
bolded part of the curve. Following Thomson's opinion, Gill /7/ presented
"permissible" (solid line) and "forbidden" (dashed line) orbitals (right curve).
The abscissa shows the distance of the electron from nucleus and the ordinates
show the force: repulsive (below) and attractive (above) /7/.
The doubt, over what model of the atom was correct, the "plum-pudding" or
"planetary", was solved by Rutherford, who was a former student and collaborator to
Thomson. Rutherford in 1907 transferred to the Department of Physics, University of
Manchester, and in the next year confirmed that alpha particles are actually helium
nuclei, i.e. positively charged particles which are composed of two protons and two
neutrons. Thin sheets of metal were bombarded with alpha particles, and thus
Rutherford in 1911 experimentally confirmed the "planetary model of the atom". This
model is commonly called a "Rutherford model".
In 1912, after seven months spent with Thomson in Cambridge and four months
spent with Rutherford in Manchester /19/, Niels Bohr in 1913 calculated the possible
paths of electrons, taking into account that electrons can move from one orbital to
another only if they receive or lose a certain amount of (quantum) energy - as
Boscovich said a century and a half earlier (Section 3.3). Today, this model of the
atom is called "Bohr model", which is not fully justified to call it that.
4-3
During the celebration of the two hundredth anniversary of the publication of
Boscovich's Theory, held in Dubrovnik, Niels Bohr wrote: "Boscovich's ideas exerted
a deep influence on the work of the next following generation of physicists... Our
esteem for the purposefulness of Boscovich's great scientific work, and the inspiration
behind it, increases the more as we realize the extent to which it served to pave the
way for the later developments" /5, p. 8 and 184/.
Therefore Supek /5, p. 184/ rightly asks whether Niels Bohr was really referring to
himself when he emphasized the impact of Boscovich on the next generation of
physicists. "When I repeatedly talked to him, the answer was never clear. Perhaps
such clarity was not in the father of modern physics. If then he did not know Roger's
work, he had to have known the Thomson atom which probably makes the influence
indirect."
Therefore, bearing in mind that in the period 1903-1907 "J. J. Thomson deducted
his hypothesis directly from the Theory and curve of Boscovich, and showed that the
notion of 'allowed' and 'forbidden' orbits follows from it", Gill /7/ points out that
Boscovich made an "essential element of the modern concept of the atom" and
"where Boscovich planted two hundred years ago others have reaped." Hence, Gill
called this model "The Boscovich-Thomson" atom and indicates that "when the
history of atomic theory is being written, it is right that the part played by Father
Roger Boscovich should not be overlooked".
Taking into account the contribution of Boscovich, the actual history of the
discovery of atomic structure is shown in Scheme 4-2.
Scheme 4-2. The actual historical path of discovery of the structure of atoms
4-4
Empedocles:
The forces of
love and strife
(5th century BC)
Newton:
The forces
and particles
(17th century)
Modern
theory of
atoms
(Thomson,
Rutherford,
Bohr,
(20th century)
Leibniz
points
(monads)
(17th century)
Boscovich's
Theory
(18th
century)
Leucippus and
Democritus:
matter =
atoms + void
(5th century BC)
4.3. Boscovich's comprehension of elementary points,
atoms and molecules
In many descriptions of Boscovich's Theory his comprehension of elementary
points are incompletely, and even wrongly interpreted, which leads to the fact that his
views in terms of atoms and molecules can be completely ignored. To properly
understand his comprehension of elementary points, atoms and molecules, it is first
necessary to clarify some basic contemporary concepts in terms of matter and atoms.
In many scientific and popular articles /20/ it is often said that today we can be
absolutely sure that matter is composed of atoms. Afterwards it is stated that Greek
philosophers Leucippus and Democritus came to this idea in 5th century BC.
However, the modern understanding of the term "atom" and the term "mater" is
essentially different from the understanding of Leucippus and Democritus. For these
philosophers, atoms are the smallest particles of matter, which have no parts, and thus
they cannot to be further divided. The word "atom" comes from the Greek word
meaning "indivisible". In fact, according to the ancient Greeks there are many types
of atoms, which are different in size and shape.
The contemporary understanding of the term "atom" is more recent and comes
from an English scientist Dalton who early 19th century showed that the chemical
elements are composed of tiny particles that enter into mutual chemical reaction.
Dalton believed that these particles did not have parts and he named them "atoms",
like the Greeks did. However, Dalton was wrong in terms of their indivisibility, since
in the late 19th century it became known that these chemical atoms still have parts
inside them, as it was confirmed in the 20th century. The modern concept of the atom
means that they are composed of identical electrons (negatively charged), which
range around the atomic nucleus, and the nucleus of an atom consists of identical
protons (positively charged) and identical neutrons (not charged). Moreover, it is well
known that the protons and neutrons also consist of still smaller particles.
The ancient Greeks would never have called the smallest particles of chemical
elements as "atoms”, because they are divisible and consisting of smaller particles,
but modern science does call them "atoms". Therefore, when the scientific and
philosophical works speak of "atoms" and "atomistic" it should clearly be
distinguished if what is meant is as per what the Greeks referred to atoms (as the
smallest indivisible particles), or the modern concept of atoms, as complex and
divisible particles.
In addition, there are misconceptions when describing Leucippus and Democritus
in their comprehension of the concept of matter: "Well, of atoms, these tiny particles,
it was all done by Democritus" – it was recently stated in an article /20/. It is
customary to say that the ancient Greeks believed that matter is composed of atoms.
But something like that they have never claimed! In fact, Leucippus and his associate
Democritus held the belief that the elements are composed of fullness and the void;
they call them being and not-being, respectively. Being is full and solid; not-being is
4-5
void and rarefied. Since the void exists no less than does the body, it follows that not-
being exists no less than being. The two together are the material causes of
existing things /21/. When Democritus says atoms touch, the touch is called the
mutual proximity of atoms over short distance, because they certainly can be
dismantled. In other words, in their view it is not possible for atoms to touch even in a
collision, because there must remain at least a small gap between them.
So, they thought that the matter is inseparable unity of fullness and VOID
(emptiness). We repeat: the VOID! According to them, the atoms are only one part of
matter (fullness), and the second part is the void (emptiness). The atoms + void, only
taken both together, constitute matter.
This is reflected in the structure of chemical atoms, as we know it today. No matter
that it is a very small particle, the atom is "a nearly infinite nothingness with little
substance concentrated in the nucleus and even less in the electrons swarming around
far, far away on the horizon... Imagine a few grains of sand in the middle of a football
playing field and several smaller grains that are rushing around the playground - it is
[analogous to] an atom increased several times. An emptiness with a few grains, but
imbued with forces" /20/.
It can also be easily imagined that in the space from the centre to the rim of the
field can accommodate more tons and tons of sand - because the space on the field is
really almost empty. (It was calculated that atomic nucleus and electrons occupy only
0.000000000001 % of total volume of an atom, and the residual 99.999999999999 %
is void.)
However, despite the relatively large distance between the nucleus of the atom and
the surrounding electrons, there cannot be placed even a single electron. Nothing can
be placed there. Is it empty space, when nothing else can be settled? Moreover, as
long as they are together, the nucleus and the electrons do not leave room in the space
between them for anything else. It is possible only to place the electrons in orbitals at
the perimeter of the atom, and the same orbital can accommodate a maximum of two
electrons only if they synchronize their movements so that their spins are opposite
(anti-parallel). And when that happens the orbital is completely filled, nothing more
can be located in it /22/. [Translator's note: Only 2 electrons with anti parallel spins
can be placed in some orbital, whatever its energy level. However, level 1 can
accommodate 2 electrons since it has only one 1S orbital; level 2 can accommodate 8
electrons since it has four orbitals: 2S, 2Px, 2Py, 2Pz; etc.]
Nucleus, electrons, space between them and the space that is formed in the orbitals
are one entity, which is now called the atom. If the atom is moved it is as a whole, its
inner space is moved, too. Whither it is - there is its inner space, too.
But, to be able to move an atom, you need a space between the atoms. Even the
ancient Greeks knew that. Also the outer space between atoms is a prerequisite of
their independent existence. And that space is an integral part of the matter in which
the atoms are moving independently. Matter at the atomic level consists of atoms and
the space in and around them.
4-6
The extent to which an atom jealously guards its inner space is shown by the fact
that it does not give it up even if it is forced to be joined with other atoms. Both
atoms will give off some external electrons, and its outer orbitals transform into
common inter-atomic or molecular orbitals. However, the inner orbitals and the space
in-between the nuclei and electrons in each of the connected atoms will be preserved,
perhaps slightly modified.
And then the story gets repeated, but this time at the molecular level. Again, it can
be seen that the molecules does not consist only of atoms, but also consist of the
space between atoms and within atoms, and matter at the molecular level must also
include the intermolecular space.
Therefore, when we ask "What is all this is made off?" we should keep in mind not
only the particles, i.e. electrons, protons, neutrons, nuclei, atoms, molecules... Since
that is just a part of the matter, namely its "fullness". But the matter is not only the
"fullness", but the void (emptiness), too. Thus the real answer requires that for each
particle we take into account the space in it and around it.
Consider now Boscovich's comprehension of the structure of matter. According to
him, the smallest parts of matter are elementary points, which are indivisible and
without size, i.e. non-extended. All of these points are identical; they do not differ for
each other. Boscovich said that the idea of non-extended and indivisible elementary
points was taken from Leibniz. These are actually the monads of Leibniz. But unlike
Leibniz, who held that monads touch each other and therefore matter is continuous,
Boscovich believed that the points can not touch, and one point interacts with another
by the attractive and repulsive forces according to the law presented in Figure 3-1.
Between two points there must always exist at least some very small space.
Therefore, Boscovich's elementary points are different from the concept of atoms
of the Greek philosophers, and also from the contemporary understanding of the
concept of the chemical atoms (Table 4-1). Hence, it is wrong that some authors call
Boscovich's elementary points as "Boscovich's atoms". Boscovich never called his
points as atoms.
Table 4-1. The main features of ancient Greek and modern atoms
and Boscovich's elementary points
Divisibility
Shape and size
Versatility
Possibility of
combining
Atoms of
Leucippus and
Democritus
Indivisible
Different shape
and size
Various
Combine
without contact
Boscovich's
elementary
points
Indivisible
Non-extended
Identical
Combine
without contact
Contemporary
understanding of
atoms
Divisible
Different shape
and size
Various
Combine
without contact
4-7
However, Boscovich in his Theory also considers atoms /8, Section 440/. The term
"atom" Boscovich implies for a particle that is composed of parts, and these parts
remain together in an atom owing to the force described by his curve. It should be
noted that Boscovich indicates that the atoms have parts, a half century before
Dalton!
By Boscovich, atoms are combined into larger particles. "In the case of two
particles of which one has approached the other with a very great velocity, there
arises a fresh connection of great strength, that is, one so strong that there is no
rebound of the particles from one another. For instance, it may be said that the hook
of the one is introduced into an opening in the other..."/8, Section 440/. If he had that
"hook" of an atom named as electron, and the "hole" of the other atom as an
incomplete filled atomic orbital, then it would fully correspond to the modern
interpretation of the chemical bond.
Boscovich also uses the term "molecule" and suggests that it can be seen by micro-
scope /8, Section 188/. (We now know that the particles that modern science calls
"molecules" can not be seen by optical microscopes, which existed in Boscovich's
time.) It is important to note that the particles that Boscovich means by molecule are
larger compared to atoms. It is also important to note that Boscovich suggests the
existence of molecules, but more than half a century before Avogadro and a century
before Cannizzaro, who are usually attributed to the discovery of molecules!
By Boscovich, a molecule is a particle of higher order then atoms. He indicates
that the particles of higher orders may be different. First difference comes from the
number of points that make up the particle /8, Section 419/; then, because of the
different disposition of points /8, section 420/. From these differences in the number
and distribution of points the other important differences emerge that influence a
large variety of bodies and natural phenomena / 8 Section 421 /. This primarily refers
to the force that one particle has acting on another. So, there are particles which are
attracted, or which are repelled, or which are inert /8, Section 422/. Today it is now
known that particles with the same charge repel but with different charges attract one
another and also there are uncharged particles that are inert.
Another important difference among the forces of these particles is that one side of
some particles are able to attract a second particle, while the other side will repel /8,
section 423/.
Boscovich's description of the behaviour of higher order particles is in line with
the modern description of the behaviour of molecules. It is now known that many
kinds of molecules do not have a uniform distribution of positive and negative charge,
due to the fact that some of the atoms in a molecule more strongly attract electrons
and some do so weaker. Therefore, the molecules are polarized, i.e. are dipoles - on
one side of the molecule is partially positive, and on the other side partially negative
charge. It is known that two dipoles mutually repel each other if they approach each
other with their sides having the same type of charges. Two dipoles are attracted to
each other if one positive charged side of the dipole approaches the negative charged
side of another. 4-8
4.4. Macromolecular hypothesis of Boscovich /23-25/
Today it is a widely accepted view that the German Herman Staudinger was the
creator of the hypothesis of the existence of macromolecules (i.e. polymers) and he
first presented the hypothesis in 1920. However, this view was not widely accepted
before 1930, and there were conflicting opinions in the coming decades.
In this section we want to show that Boscovich was actually the first who
announced the possibility of the existence of macromolecules in 1758, in his Theory
/8, Section 440/. Bearing in mind his curve, Boscovich suggests that atoms can link
(together): "In such a way atoms might be formed like spirals; and, if these spirals
were compressed by a force, there would be experienced a very great elastic force or
propensity for expansion". Furthermore he stated that "a force being produced at
each distance, the figure might suffer some change; and by a very slight change of
each of the distances in a very long series of points there might be obtained a
bending of the figure of comparatively large amount, due to a large number of
these slight bendings." In those statements it highlights some of Boscovich's ideas
that deserve to be further considered and interpreted in the light of modern concepts
in the science of macromolecules.
Boscovich indicates "a long series of points" and "spirals of atoms". That is
identical with the modern comprehension about the existence of macromolecules as
the chains of chemical bonded atoms. Furthermore, he indicates that these chains
could be "very long" and could have "a large number of bendings". Using
contemporary scientific words, Boscovich is indicating that there may be a high
degree of polymerization. (Under the polymerization degree is meant the number of
molecules that are linked to a macromolecular chain.)
By Boscovich, these arrays of atoms may be "spiral" shaped, which represents the
polymer chain conformation. In modern science of polymers it is well known that
some natural and synthetic polymers do have a spiral (helical) conformation (Figure
4-2).
a
b
c
Figure 4-2. The spiral structure of some natural and synthetic macromolecular
chains (a
proteins, b
deoxyribonucleic acids, i.e. DNA, c
polyolefins)
4-9
Boscovich also indicates that "...by a very slight change of each of the distances in
a very long series of points there might be obtained a bending of the figure of
comparatively large amount, due to a large number of these slight bendings." In
contemporary scientific words - conformation of the whole chain can be changed by
bending a large number of chemical bonds between the atoms in the chain.
In his statement that these series of atoms can have a huge "elastic force to the
expansion" one may recognize a hint of the high elasticity of polymer materials,
which is one of the basic features of most polymers.
Obviously, Boscovich pointed to all the basic features of macromolecules: chain
structure, a high degree of polymerization, the possibility of helical conformation of
the chain, conformation change due to bending of chemical bonds, and even the
elastic properties of macromolecular materials. Boscovich suggested this almost two
centuries before Staundiger introduced his macromolecular hypothesis.
4.5. Nano-tubes, diamond and graphite
Boscovich points out /8, Section 440/ that it is possible that there are atoms whose
force curve is as shown in Figure 3-1b. Point C on the curve represents the stable
distance of such atoms. There could be "inscribed a continuous series of little cubes,
and points are situated at each of their corners". That series would have great
persistence in maintaining its shape. Speaking in modern terms, this would be a nano-
tube of square cross-section.
If the particles were deployed in the tack of proper pyramid (tetrahedron) and at a
distance that corresponds to the limit of cohesion then the body will be "an
unbreakable and impermeable solid" with infinite resistance and inflexibility /8,
Sections 239, 363 and 419/. But if the particles are not deployed in the tack of the
pyramid, or if they are not at the appropriate distances, we cannot then speak of the
great strength of the body. If these particles were in one plane, then it would be a
flexible material and "could even be folded in spirals after the manner of ancient
manuscripts (i.e. rolled scrolls)" /8, Section 362/.
The hardness of diamond and graphite softness is the confirmations of these
perceptions by Boscovich. H. Davy (1778-1829) went with the Boscovichian
atomistic idea to explain the structure of molecules, different crystal forms, as well as
to solve the problem of the structure of the diamond /5, p. 153/. Both diamond and
graphite are composed of the same kind of atoms - carbon atoms. But in the diamond
these carbon atoms are deployed in the tack of the tetrahedron, while in graphite are
in the plane (Figure 4-3), and this is the main cause of their different hardness.
4-10
Figure 4-3. The structure of diamond (a) and graphite (b)
4.6. Boscovich's signposts to neutrino, gluons and quarks
"Also, in some of these classes (of particles), the absence of any force may be
admitted; then the substance of one of these classes will pass perfectly freely through
the substance of another without any collisions" /8, Section 518/. We only need to call
these particles "neutrinos", and then Boscovich's idea is the same as contemporary
understanding.
P. M. Rinard /26/ indicates that Boscovich's Theory can be linked to the modern
theory of quarks, which is described by Dadich /2, p. 128-130/. Also Boscovich's
Theory is important in relation to contemporary theory of elementary particles /6b/
and gluons /27/.
In 1993, Nobel Prize laureate Leon Lederman wrote that Boscovich "had an idea,
completely crazy for the eighteenth century (and possibly any other)... Boscovich
argues, no less, that matter is composed of the particles have no dimensions! We
found a particle just a couple of decades ago that fits such a description. It's called a
quark" /83, p. 103/.
4-11
5. CONFIRMATION OF BOSCOVICH'S FORCE LAW
IN MODERN SCIENCE /23, 40/
5.1. Relation of force and energy dependence on the distance
between the particles
By Boscovich, the elementary points, particles of first order, then of the second
and third order, atoms, molecules, series of atoms... are only certain levels in the
hierarchy of matter. According to him all worlds of smaller dimensions are like a
single point in relation to the larger world. It is believed that for every pair of
particles in any level of the hierarchy of matter applies some form of curves as shown
in Figure 3-1.
In order to check if Boscovich's Theory is correct, the crucial question is: Has
modern science confirmed that the interaction between particles at different
levels of the hierarchy of matter is really described by Boscovich's curve? By
overview of the many papers on Boscovich's life and works /1-7/ we did not find that
anyone asked that question, or has tried to give the answer. (A few examples of
correctness of Boscovich's curve are stated by Dadich /2/, but these examples he took
from the author of this monograph.) If the results of modern science do not confirm
the validity of Boscovich curve – then we can speak about Boscovich's Theory only
as a transient phase in the history of science, though taking into account he is our
countrymen. If modern science confirms that it is correct, then we need a different
approach to this Theory (than treating it as merely transient).
Therefore, we examined the way in which modern science interprets the
interaction of particles depending on their distance. While for Boscovich the
interaction presents the change of attractive and repulsive forces, in the current
literature that interaction usually is presented as a change of potential energy with
the distance of particles. However, bearing in mind that the force (F) is actually a
negative value of differential change in energy (E) with distance (r), i.e. F = - dE/dr,
both curves are oscillating and are very similar (Figure 5-1), and can be derived from
each other. The distinction is that the stable and unstable distances (limits of cohesion
and non-cohesion, i.e. intersections with the abscissa on Boscovich curve, Figure 5-1,
below) correspond to minima and maxima of potential energy (Figure 5-1, above),
which are stable and unstable distances according to contemporary interpretation.
Therefore, by observing the change of potential energy with distance between the
particles, one can infer that the change in force, and thus check the validity of
Boscovich's curve.
5-1
Figure 5-1. The change of the potential energy (E) and force (F) depending
on the distance (r) in the chemical reaction of the two atoms /28/
5.2. Interaction of atoms
In Fig 5-1 it is actually displayed the change in the potential energy of a chemical
reaction of two atoms. We see that the curve has a similar shape as Boscovich's curve
(Figure 3-1c).
Interaction of atoms may not be chemical, but can be physical in nature. In this
case, modern science has confirmed that this interaction is presented by a curve
shown in Figure 5-2 such as in the case of sodium. In addition to liquid sodium,
similar examples of argon and aluminium atoms are listed in Croxton's book /29/.
Figure 5-2. The change in potential energy with the change in distance
between atoms of liquid sodium /29/: Solid lines are theoretical curves,
and the points are the experimental data
5-2
Portnoy et al /30/ obtained similar results and showed the similar oscillatory curve
for boron, magnesium, sodium, lead and aluminium. The fact that authors put that
curve on their book cover (Figure 5-3) suggests to which extent the authors give
significance to these findings.
Figure 5-3. Book cover of Portnoy et al /30/ (The curve represents the change
in potential energy with the change in the distance between the atoms.)
Croxton and Portnoy in their books do not call it Boscovich's Theory. Probably
they are not familiar with it. However, it is obvious that these curves are generally
identical with Boscovich's curve (Figure 3-1).
5.3. Interaction of molecules
Because molecules are formed by combining atoms, the molecules are at a higher
level of the hierarchy of matter with respect to the atoms. According to Boscovich's
Theory, the same law of force should be valid. Modern science has many examples
that confirm this. Usually it is presented by a curve as in Figure 5-4, which fully
corresponds to the curve of Boscovich in Fig 3-1b. Although this form of curve
Boscovich showed since 1745, in his work "On the live forces" ("De viribus vivis"),
today almost nobody mentions him. The exception is Kaplan, who indicates that
Boscovich was the first who gave the law of interaction between particles /31/.
5-3
Figure 5-4. The curve of the potential energy Eint depending on the distance R
between the two molecules of ethylene /31/. (Curves 1 and 2 are calculated
theoretically by different methods. Eint is in atomic units (AU), where AU =
2.6253x106 kJ/mol, the R has units a0, where a0=5.2918x10-7cm.)
In the adsorption of molecules on a solid surface, first occurs physical and then
chemical adsorption. This change is attributed to the different interactions of the
support's molecule with the adsorbing molecule, represented by a curve in Figure 5-5,
which is the same as Boscovich's curve in Figure 3-1c.
Energy (kcal)
Distance (Å)
Figure 5-5. The transition of the physical to the chemical adsorption
/32/; at the abscissa is the distance of adsorbing from the surface of
the carrier, and the ordinate is the change of potential energy; (1kcal =
4.184 kJ, 1Å = 10-8 cm)
5-4
5.4. Interaction of nano-particles
Particles having a size of several tens to several hundreds of nano-metres are
denoted as nano-particles. These are complex particles, formed by connecting
together atoms or molecules. According to size and complexity nano-particles surpass
that of the molecules; hence, they represent a higher level in the hierarchy of matter
compared to the lower level of molecules. Pure nano-materials have great properties,
and when added to other materials (atomic or molecular structure) significantly alter
the properties of these materials, which has caused a great deal of attention in those
working in the science and technology of materials.
Boscovich in his Theory pointed to the possible existence of such particles (section
4.5.). If someone could ask him how he would describe the interaction of these nano-
particles, he would presumably say: "Well, by my curve!" Indeed, a recently
published theoretical analysis and computer simulation /33/ showed that Boscovich
was right (Figure 5-6).
Figure 5-6. Effective interaction potential energy (U) between identical charged
nano-particles against the distance (r/d) between the centres of particles. (d is the
particle diameter; individual curves refer to different values of charge.) /33/
5.5. Interaction of macromolecules
A macromolecule is formed by chemical coupling of a large number of small
molecules. The number of small molecules can be a few hundred to several millions.
These also pose a particular level in the hierarchy of matter.
5-5
Boscovich in his Theory pointed to the possible existence of macromolecules
(Chapter 4.4.). If someone could ask him to show what the interaction of
macromolecules would look like, presumably he would again reply: "Well, by my
curve!" Indeed, the results of modern science confirm /34/ and show that Boscovich
would have been right (Figure 5-7).
Figure 5-7. The change in entropy (Sij) and the enthalpy (Uij) with distance (Rij)
between two macromolecular chains (i and j) /34/
5.6. Interaction of colloidal particles
Interaction of colloidal particles (Figure 5-8) /35/ is also described by a form of
Boscovich's curve (Figure 3-1c). The interaction of two clay particles can serve as an
example (Figure 5-9) /36/.
Figure 5-8. Potential energy change with distance of two charged
colloidal particles /35/
5-6
Figure 5-9. Potential energy depending on the distance between
the two particles of clay /36/
5.7. Fission of heavy atomic nuclei
We have shown that in modern sciences the interactions of particles at different
levels of the hierarchy of matter from atoms, molecules, nano-particles, macro-
molecules and up to colloids are described by Boscovich curves. In this and
subsequent chapters we consider interactions of particles at the lower level of the
atom.
The fission of heavy nuclei has the change of potential energy curve as an
oscillatory shape (Figure 5-10) similar to Boscovich's curve. But, at high deformation
of nuclei the potential energy has no horizontal asymptote as that which is shown in
Boscovich's curve in Figure 3-1. However, Boscovich predicted such a possibility
(/8/, Figure 14) as shown in Figure 5-11.
Potential energy
Fission
Fission "below
threshold"
Fission of
isomeric
state
Spontaneously fission
Potential barrier for
spherical nuclei
Deformation
Figure 5-10. Change of potential energy by fission of heavy nuclei of atoms /37/
5-7
Figure 5-11. One shape of Boscovich's curve similar to the curve in Figure 5-10.
5.8. Energy of atomic nucleus
The dependence of atomic nucleus energy on its relative density in some cases
may have an oscillatory shape (Figure 5-12) /38/. Taking into account that the
distance between the nucleons is inversely proportional to density, it is clear that the
presentation of nucleons interaction as an oscillatory shape is in line with Boscovich's
curve.
Figure 5-12. The dependence of potential energy of atomic nucleus,
on the ratio of actual density (n) to equilibrium density (n0) /38/
5-8
5.9. Interactions of nucleons and Λ° hyperon
Λ° hyperons are particles that belong to the baryons; they are uncharged with mass
2184 times that of the electron, spin ½, and lifetime 2.5•10-10 seconds. By interaction
of nucleons and Λ° hyperons there is an attractive force at large distances, but with a
decrease in the distance it becomes a repulsive force and then attractive again, and at
smaller distance it again becomes a repulsive force /39/. Curve for this interaction is
not shown in /39/, but according to this description, it is exactly as described by
Boscovich's curve (Figure 3-1c).
5.10. Conclusion concerning the validity of Boscovich's curve
In the previous sections we have discussed the way in which modern science
describes interactions of particles at several levels in a hierarchy of matter. We have
listed a few examples for each level (Table 5-1). In addition to the examples
mentioned in this monograph, there are many others. In all cases, it has been shown
to correct with Boscovich's curve.
Table 5-1. Outline of examples that confirm the validity of Boscovich curve
Interactions in the hierarchy of matter
Level
Particles
Figures
1
Colloidal particles
5-8. and 5.9.
2
Macromolecules
5.7.
3
Nano-particles
5.6.
4
Molecules
5.4. and 5.5.
5
Atoms
5.1., 5.2. and 5.3.
6
Nucleus and electrons
4.1.
7
Fission of heavy nuclei
5.10.
8
Λ hyperon and nucleons
Description in Chapter 5.9.
9
Nucleons in nucleus
5.12.
Boscovich's Theory by its philosophical approach therefore made a great
contribution to the development of modern science. By elaboration of his approach to
the structure of matter and clarifying concepts in the hierarchy of matter, many
natural laws have become very simple and generally applicable.
5-9
6. COMPRESSION OF MATTER
REFLECTIONS OF BOSCOVICH'S THEORY
IN SAVICH-KASHANIN THEORY /41/
6.1. Introduction
There was a gap of two centuries since the creation of Boscovich's "Theory of
natural philosophy" and the emergence of Savich-Kashanin theory /42-44/. The first
Theory is based on Leibniz's monads, the law of continuity and the principles of
classical Newtonian mechanics, improving and complementing them where
Boscovich thinks it is necessary. The second of these theories has its basis in quantum
mechanics, which it might seem very distant from Boscovich's Theory. And when
taken into account that Boscovich applies his law of forces to the primary elements of
matter (that are non-extended indivisible points), as well as to the particles of the first
and second order (which are comprised of the primary elements), whereas Savich and
Kashanin focussed their observations on particles "from the atom to the celestial
bodies" /44/, then it might appear that the subjects of these two theories are
completely different. We are left to wonder: is the Slavic origin of these authors the
only link between the two theories?
No, it is not so. There is much common to both theories. First of all, there is the
dialectical base of both theories, which we previously reported /45/. Here we only
point out the similarities of these theories in interpreting compressing substance. To
this purpose, we will just briefly outline some key postulates of both theories and
compare them.
6.2. Material density changes according to Boscovich's opinion
The density of matter is the relationship between the mass and volume of a body.
The definition applies in the case when there is a very large number of material
particles, which occupy a certain space. Even then, Boscovich's force law has
relevance; each set of two particles obeys his force law. If we consider the
compression of dispersed points of matter, then, by Boscovich, the density of the
body gradually changes without any jumps /8, Section 51/. Bouncy density change
is not possible, because "if a given density persists for an hour, and then is changed in
an instant of time into another twice as great, which will last for another hour; then in
that instant of time which separate the two hours, there would have to be two
densities at one and the same time, the simple and the double..." /8, section 52/. The
body, that has two densities, is inconceivable. So, by Boscovich, there is no abrupt
change in density.
6-1
To what extent can the compression of matter go? Boscovich argues that "as there
is no limit to increase of rarity, so there are no limits to increase of density" /8,
Section 89/.
6.3. Material density changes according to Savich-Kashanin theory
In contrast to Boscovich views, Savich and Kashanin believe that by the
compressing of matter, it alternates between intervals of gradual and abrupt changes
in density (Figure 6-1) /44/. The density of matter is gradually changed from d10 to
d1* in the pressure range from p0* to p1*. Then at the pressure p1*, there is a jump in
the change of density from d1* to d20. Again, up to the pressure p2* there is the
interval of gradual change of density, and again there is a jump of density, etc...
Substances can only have those values of density that correspond to intervals of 1, 2,
3, 4... Each interval corresponds to one phase state of matter. The density is gradually
changing within a definite phase state. The transition from one phase to another is
like a jump in terms of changes in density.
Figure 6-1. Changes of density of matter (d) with the change of pressure (p)
according to Savich-Kashanin theory /44/
For the causes of these alternating stepwise and gradual changes in the density of
matter, Savich and Kashanin looked to the combination of the type of quantum-
mechanical phenomena, which describes the structure and properties of atoms. When
atoms approach each other, there arises the moment when the atoms are close enough
to each other that their outer electron orbits "touch" (Figure 6-2). Further compression
is possible only if the electrons leave its former path and rebound from the atoms
seeking a new space for their movement. Atoms, stripped due to these runaway
electrons, can further approach each other until again "touch" the remaining outer
electrons. 6-2
Figure 6-2. Showing stepwise (i.e. act of leaping) atoms
approaching each other under pressure where it is observed
a stepwise change of the radius of action (ai0 > ai+10) /44/
"Excitation and ejection of electrons under the influence of pressure leads to a
number of new phenomena in macro-systems. We see (Figure 6-2) that large and
ultra-high pressure disrupts the inner micro-structure of the electron shells of
chemical elements by pushing and ejecting electrons from them. Since the electrons
are deployed by discrete, spaced levels, which are sharply separated from each
other..., their ejection under this pressure will be in jumps. Accordingly, material
densities under pressure must be changed in jumps or sharp transitions from
one value to another. Due to the layered structure of the electron shells, by the
displacement and ejection of electrons by the pressure, densities of the materials, as
well as the properties of the macro-systems of particles, must exhibit abrupt changes"
/44, p. 70/.
6.4. Relation between Boscovich's opinion and
the opinion of Savich and Kashanin /41/
The density of a body is gradually changed without any jumps - claims Boscovich.
Densities of the material under pressure must be change in jumps - claim Savich and
Kashanin.
Boscovich, as 18th century citizen, built his comprehension of Nature on the law
of continuity and classical Newtonian physics. Savich and Kashanin, our
contemporaries, find support in modern quantum mechanics, which almost
completely squeezes out the law of continuity and Newtonian mechanics from the
micro-world. Therefore, Savich and Kashanin do not call on Boscovich's Theory,
although they knew it /46/. Which of them is right – Boscovich or Savich and
Kashanin? 6-3
Boscovich discovered his force law by reasoning, analyzing collisions between
bodies (as well as other natural phenomena). However, he did not know the real cause
why there was alternating turns in repulsive and attractive forces.
The above observations, however, indicate that there are missing links between the
seemingly contradictory theories. The relation between Boscovich's force law and
Bohr's model of the atom is accomplished through the works of Thomson, Rutherford
and Bohr (Chapter 4.2.). This is the first link of Boscovich to Savich, as the Bohr
model of the atom served for Savich as a display for the interpretation of abrupt
changes of densities. The second link is calculation of the potential energy change
when two atoms approach each other, a calculation based on a quantum-mechanical
model of the atom. Next, the third link is the application of the results of this
calculation for the prediction of properties of different phase states of matter made up
by the atoms. These last two links are described in the books of Croxton /29/ and
Portnoy /30/, although the authors do not cite papers of Boscovich, Savich and
Kashanin. However, it can be seen that the change of potential energy as the distance
changes between two atoms, with respect their discrete quantum-mechanical structure
(the phenomena that Savich and Kashanin take into account), is described by the
curve (Figure 5-2 and 5-3), which is identical with Boscovich's curve (Figure 3-1).
Thus, the path from Boscovich, through Thomson, Rutherford and Bohr up to
Savich and Kashanin is connected completely. Moreover, Boscovich carefully
analyzes his curve (Figure 3-1) and observes the intervals in which the particles
spontaneously condense and the intervals in which the condensation is only possible
if there is external pressure /8, Sections 190-194/. For example, if two atoms are at
distance R (Figure 3-1), a further rapprochement of these atoms is possible only if it
is exerted by external pressure, which is high enough to overcome the repulsive arch
RQP. When the atoms come closer than P, there is attractive force acting on them.
These atoms are still spontaneously and rapidly approaching and require no additional
external pressure. When they come at distance less then N, again there appears a
repulsive force, and again an outside pressure is necessary for the compression of
matter. Boscovich's curve undoubtedly shows that the intervals of spontaneous and
forced approach of particles are alternated.
There is an obvious similarity in the sense of Boscovich's curve (Figure 3-1) with
Figure 6-1 of Savich and Kashanin. The ordinate of the first one (i.e. force)
corresponds to the abscissa of the other (pressure, i.e. force over unit of surface area).
The abscissa of the first one (i.e. distance) corresponds to the ordinate of the other
(i.e. density, which is inversely proportional to distance). Furthermore, characteristic
points on the Boscovich's curve (E, G, I, L, N, P, R), the so-called limits of cohesion
and non-cohesion, are nothing else but the beginnings and endings of some steps in
the diagram of Savich and Kashanin. Hence, to every arch of the Boscovich's curve
there is a corresponding step in the diagram of Savich and Kashanin. A repulsive
arch of Boscovich curve corresponds to gradual change (in density), but an attractive
arch corresponds to a jump in density changes.
6-4
Then, does it not seem that Boscovich was wrong when he claimed that the change
of density of matter must be a continuous, without jumping? Actually not! Nowadays
it is known that the density of a substance significantly changes in the transition from
solid to liquid or from liquid to a gaseous state (first-order phase transitions). But
there are also known examples of phase changes of the second and higher order, in
which the density is gradually changing when going from one phase state to another
phase state, passing through all intervening values. But in both cases, the change of
phase state is achieved as small fractions of the matter pass from one to another phase
state. (The cloud does not condense entirely at once, but drop by drop.) On the micro-
level the change is abrupt, like a jump. And that is what we describe by the Boscovich
curve and diagram of Savich and Kashanin. But at the macroscopic level, the density
change is gradual. Therefore, as to the question posed in this chapter, who is right,
Boscovich or Savich and Kashanin, there is a dialectical answer: both Boscovich and
Savich and Kashanin.
6.5. Density change in the compression of matter
by the model of Savich and Kashanin
Savich and Kashanin in the form of a staircase diagram show the function, which
describes the change in density of matter at the beginning and at the end of certain
phases (Figure 6-3).
Ordinal of phase
Densities at the end of phases
Densities at the beginning of phases
Figure 6-3. The density at the beginning of di0 at the end di* of individual
phases (i = 1, 2, 3...) according to the Savich-Kashanin theory /44/
6-5
Law of Savich and Kashanin for the stepwise change of density is not directly
derived from the quantum-mechanical model of the atom, but it was only assumed
that abrupt changes in the macro system are caused by the stepwise changes in
microsystems. It should be noted that Savich and Kashanin empirically come to the
law that the density of matter (d) at the end of individual phases (i) changes abruptly,
according to the expression (6-1a). Densities at the beginning of the individual phases
(i) are calculated by multiplying the density at the end of a certain phase with
parameter α, where α = 3/5 and α = 5/6 for the even and the odd phases, respectively
(6-1b and 6-1c).
di-1* = 2 di* (6-1a)
di0 = α ∙ di* (6-1b)
α = 3/5 and α = 5/6 for the even and the odd phases, respectively (6-1c)
Savich and Kashanin calculated these values of parameter α by taking into account
the van der Waals equation of state for real gases (6-2).
(P + a/V2) (V b) = RT (6-2)
P, V and T are the pressure, volume, and absolute temperature of gas, respectively,
a and b are the so-called van der Waals constants, R is the universal gas constant.
It follows from equation (6-2) that the constant b, so-called "covolume", is the
volume V0, which a gas would have at absolute zero (T = 0 K). It is also known that it
follows from this equation that covolume b is equal to one third of critical volume Vc,
for given material at critical point (6-3). (V0 and Vc are characteristic points in P-V-T
diagram, Figure 7-1a.) Respecting the van der Waals equation of state, Savich and
Kashanin took into account the relationship (6-3) and calculated the values of
parameter α as in equation (6-1c). It should be noted that this relationship (6-3) is one
of the important assumptions built into obtaining the mathematical model of Savich
and Kashanin (Figure 6-3).
b = V0 = Vc/3 (6-3)
It should be borne in mind that the specific volume of matter (V) is equal to the
reciprocal of the density (d) (6-4), so it is easy to calculate the value of one of them if
the other is known.
V = 1/d (6-4)
Another important assumption of Savich and Kashanin used to derive their
mathematical model is that matter at the end of the zero-phase has volume, or density,
which corresponds to the critical point (6-5).
d0* = 1/Vc (6-5)
6-6
6.6. Mean densities of planets in Solar system
calculated by model of Savich-Kashanin
Savich and Kashanin applied the above mathematical model (Figure 6-3) to
calculate the mean density of planets in the Solar system and the results of their
calculations they compared with astronomical data available in that time. According
to their calculations some planet should have a density of 0.67 g/cm3, which
approximately corresponds to the density of Saturn (0.65 g/cm3). For one group of
planets the calculated density was 1.33 g/cm3; that corresponds to Jupiter (1.34
g/cm3), Uranus (1.36 g/cm3) and Neptune (1.32 g/cm3). For the second group of
planets the calculated density was 5.33 g/cm3; that which corresponds to Earth (5.52
g/cm3), Venus (5.21 g/cm3) and Mercury (5.6 g/cm3). The agreement of calculated
and measured values is very good. A large discrepancy is only in the case of Mars: the
calculated value is 5.33 g/cm3, while the empirically estimated value is 3.94 g/cm3.
Savich and Kashanin believed that their calculation was correct, and the discrepancy
with the observed value of the density indicated a possible error of astronomical data
for the radius of Mars.
6.7. Adaptation of stepwise mathematical model
by actual empirical data
Analyzing the mathematical model of Savich and Kashanin we noticed that some
of their assumptions are not consistent with recent empirical data.
Empirical data show that the relations given by (6-3) are not correct, but that the
volume of material at critical point (Vc) is twice the value of covolume (b) /47/, a
four-fold higher value than the volume of matter at absolute zero temperature (V0)
/48/ (6-6).
Vc = 2 b = 4 V0 (6-6)
Analysis of the compressed gaseous ethylene showed that the different phases are
indeed formed /53/. However, the density of ethylene at the critical point corresponds
to the end of first phase, but not to the end of zero phase, as it is proposed by Savich
and Kashanin in relation (6-5).
In the theory of Savich and Kashanin the initial state of matter is the rarefied gas
that is condensed into forming Sun and planets. This means that the beginning of the
zero phase should have a density which is close to zero. However, in their staircase
model (Figure 6-3) the density at the beginning at the zero phase has some definite
value higher then zero, i.e. d00=(3/5) d0*>>0.
6-7
Due to these empirical facts, it was necessary to adapt the mathematical model so
that it will be consistent with these empirical facts. This adaptation and theoretical
derivation of our model is presented in /49/ which the ratio of the characteristic
volumes of matter to the critical volume is shown (Chapter 7). The same model can
be represented by the density of the matter, which is the reciprocal of the volume (6-
4). Based on the above, the theoretical mathematical model was obtained that shows
the relationship of mean density of the planet to mean density of the Sun (see Figure
6-4).
According to our staircase model, the condensation starts with the gaseous matter
where the density is close to zero and then the density increases in the phase
transition from zero to the first phase, then to the second, then to the third phase and
so on. The coefficients α that describe the ratio of density of the beginning and end of
some phases (6-7) are not 3/5 or 5/6, as in Savich-Kashanin theory (6-1c), but in
some stages have the values according to the formula (6-8).
α (i) = di0/di* (6-7)
α (i) = 2-1/i (6-8)
Where the number of the phase is i = 1, 0, 1, 2, 3...
Beginning, ordinal and end of phase
Saturn
Sun
Asteroids
Mercury
Venus
Earth
Jupiter, Uranus,
Neptune, Pluto
Mars
Initial state
of rarified
gas
Figure 6-4. Our theoretical staircase model
the ratio of mean density
of the planets with that of the Sun (ds = 1.41 g/cm3) /50/
6-8
Bearing in mind that the mean density of the Sun is equal to 1.41 g/cm3, the values
of mean density of the planets can be calculated by our model (Figure 6-4) /50/.
Agreement with empirical data /51/ was very good (Table 6-1). In addition, unlike the
staircase model of Savich and Kashanin (Figure 6-3), our model shows that mean
density of Mars should be about 4 g/cm3, which is close to the empirical data.
Table 6-1. Mean density of planets in the Solar system
Planet
Mean density (g/cm3)
Empirical
data /51/
Calculated using our staircase
model (Figure 6-4) /50/
Mercury
5.4
5.64
Venus
5.2
5.64
Earth
5.5
5.64
Mars
3.9
4.00
Jupiter
1.3
1.41
Saturn
0.7
0.71
Uranus
1.6
1.41
Neptune
1.7
1.41
Based on our staircase model, a celestial body (or bodies) with mean density 2.8
g/cm3 could exist in the Solar system. Indeed, it corresponds to the asteroids whose
density is in the range of 2.0 to 3.5 g/cm3.
Although Pluto was recently removed from the list of planets, we also calculated
by our model that its mean density would be 1.41 g/cm3 which is in accordance with
empirical data, i.e. 1.75 g/cm3 (though in the literature one can find other very
different values).
The trend of densification is indicated by an arrow in Figure 6-4. If Saturn
followed the same trend, then there will be no condensation, but instead a state of
spreading rarefied gas. In other words, according to our model, planet Saturn can not
be condensed (i.e. is mostly a ball of gas).
There is a hypothesis that the Sun has a twin star, which is called Nemesis. Mean
density of Nemesis would be 79.21 g/cm3 /52/. It can be calculated by extrapolation
of our staircase model that there could be a body with density of 80.63 g/cm3, which
is in good agreement with the above data for Nemesis.
6-9
7. APPLICABILITY OF BOSCOVICH'S THEORY
7.1. Introduction
Boscovich pointed to numerous diverse application of his Theory in mechanics
and physics. He considered the following phenomena: pressure in fluids, the speed of
the fluid flow out of a container; equality of action and reaction; gravitation;
cohesion; solid and fluid state; non-flexible, flexible, elastic and brittle rods;
viscosity; fluid resistance; elasticity and softness; ductility and malleability; chemical
operations; nature of fire; light and its properties; tastes and smells; sound; cold and
heat, electricity and magnetism. These considerations were supported by scientific
knowledge that existed in the 18th century, but which in many cases today is
surpassed. So, some of Boscovich's considerations are therefore outdated and
surpassed. However, by evaluation of his interpretations, always we should be
cautious and ask ourselves: "Maybe Boscovich was right?"
Very important is the question: "Is Boscovich's Theory applicable and useful in
modern science?" This question is quite reasonable when one takes into account that
modern science has only recently confirmed the validity of Boscovich's force law
(Chapter 5). Maybe Boscovich's Theory can not provide a solution of some scientific
problems, but it can be a good clue and signpost to finding solutions by modern
scientific methods.
The author of this monograph has several times used Boscovich as road signs to
successfully find the answers to some open scientific questions. In this chapter there
will be only a short summary, and a more detailed explanation is given in the cited
published papers.
7.2. Meaning of critical volume of matter /49, 53/
Boscovich suggested the possibility that "it may happen that two points
approaching one another from a long way off, but not exactly in the straight line
joining them... then the points will not reverse their motion and recede, but will
gyrate about a motionless middle point of space for ever more, always remaining very
near to one another, the distance between them not being appreciable by the senses".
/8, Section 201/. In this case, the repelling centrifugal force equals to the attractive
centripetal force, and the distance of these rotating pair of points should correspond to
the outermost cohesion limit (position R in Figure 3-1a), The two particles by their
gyration will occupy a sphere, wherein the diameter of the sphere corresponds to a
cohesion limit.
7-1
It is known that molecules in the gaseous state of matter have such large initial
distance. If they approached each other they can form a rotating molecular pair at a
distance that corresponds to the limit of cohesion (by Boscovich), i.e. corresponds to
the minimum potential energy (according to the modern terminology). The volume of
the sphere in which the pair rotates can be calculated using a simple equation (7-1):
Vp = (2/3) π re3 N (7-1)
where Vp is the volume of sphere occupied by the rotating molecular pair, calculated
on one mole; re is equilibrium distance between the molecules; π = 3.14; N is the
Avogadro's number (6.022x1023 molecules per mole).
If almost all the gas molecules were coupled as rotating molecular pairs at a
distance re corresponding to the outermost cohesion limit (point R in Figure 3-1a),
then this would be a very characteristic state of matter in the pressure-temperature-
volume thermodynamic diagram, presented in Figure 7-1a. One characteristic state is
critical point above which it is not possible to condense vapor to liquid.
Triple
point,
Vt,s
Vo
Vc
Vc
Figure 7-1a. Characteristic points of matters, i.e. critical point, triple point
and absolute zero temperature with corresponding volumes (Vc, Vt,s and VO),
presented in a typical pressure-volume-temperature diagram of substances.
There is empirical data for equilibrium distance re for many substances and it is
possible to calculate Vp by equation (7-1). Also, there is empirical data for critical
7-2
volume Vc for many substances. We have proved for 92 substances that the volumes
of rotating molecular pairs Vp is equal to Vc (Figure 7-1b). It means that the volumes
of rotating molecular pairs at outermost cohesion limit (position R in Figure 3-1a)
corresponds to their volumes Vc at critical point.
Figure 7-1b. Equality of critical volume Vc and the volume Vp occupied by two
rotating molecules at outermost cohesion limits (R in fig. 3-1a) /49, 53/. (
empirical data for 92 substances; ― Regression; ---- Expected; ····· Confidence
limits. Standard error of 60.1 cm3/mol; Correlation coefficient 0.94)
7.3. Characteristic volumes of matter /49, 54/
It can be concluded that the outermost limits of cohesion has a certain physical
meaning and corresponds to a certain distinctive state of matter, i.e. the critical point.
It is reasonable to ask whether other limits of cohesion and noncohesion on the
Boscovich's curve have some physical meaning. It was explained (Chapter 6) that
each step in the diagram of Savich and Kashanin (Figure 6-3) corresponds to a
repulsive and an attractive arch of the Boscovich curve (Figure 3-1). Based on the
empirically established relationship (6-6) it can be concluded that the specific
volumes of matter at the end of first, second and third phases correspond to the
critical volume, covolume (van der Waals's constants b) and volume of matter at
absolute zero. Once the adjustments of the coefficients α(i) are performed (equations
6-8), the volumes of the end of phases are multiplied by α(i) to obtain the volumes at
the beginning of the phases (Figure 7-2).
7-3
Cohesion limits
Non-cohesion limits
Covolume
Critical
volume
Zero
tempe-
rature
Hard
sphere
Triple point
Rotating
molecule
V→
→
Ideal
gas
Figure 7-2. The relationship between the specific volumes of matter in
characteristic states and the critical volume Vc, i.e. our staircase mathematical
model /49, 54/
It has been shown that the volumes at the beginnings of a certain phases have some
definitive physical meaning: VM is volume occupied by the rotation of individual
molecules; b0 is the hard sphere volume, occupied by the two molecules for the
distance at which the potential energy is equal to zero; Vt,s is the volume of the solid
phase at the triple point. Agreement of calculated values with experimental value for
specified volume is very good (Figure 7-3).
Although the gravitational and intermolecular forces are different nature of forces,
the mathematical models presented in staircase diagrams in Figures 6-4 and 7-2, are
completely identical. (They differ only in that the first diagram presents the
calculation of density, while the second diagram presents the calculation of specific
volume, i.e. the reciprocal value of density.) This identity of mathematical models
confirms Boscovich's opinion that there is a one unique law of forces that exist in
nature (Figure 3-1).
7-4
Characteristic volume
Critical volume
Figure 7-3. The relationship between the critical volume Vc and other
characteristic volumes: hard sphere volume b0, covolume b, the volume of
the solid phase in the triple point Vt,s, volume of matter at absolute zero V0.
Lines represent the theoretical expected values based on our model (Figure
7-2), and points are experimentally determined values taken from the
literature for the 143 substances: metals, inert gases, elements, saturated
and unsaturated hydrocarbons, aromatic hydrocarbons, organic or
inorganic compounds of oxygen, nitrogen, sulphur and halogens /49, 54/.
The law of nature, according to which the density of matter at the end of certain
phases is related to the expression di+1* = 2 di* (6-1) was spotted by Savich and
Kashanin when analyzing the density of the planets in the Solar system; it has a much
deeper meaning than mentioned by these authors. Interpreting the abrupt changes in
the density of matter by step-transition of electrons from one orbit to another, Savich
and Kashanin, unknowingly, in their theory built in Boscovich's law of interaction of
particles of matter. Each step in the diagram of Savich and Kashanin corresponds to
an arch of the Boscovich curve. This similarity and common dialectical-materialistic
core of both theories, give to them such a type of universality, which is attributive
only to those general laws of nature, on which foundations rests the magnificent
edifice of modern science. Boscovich's Theory evolved from the interaction of "non-
extended material points" leading to the quantum model of the atom, and this is
carried on by the Savich-Kashanin theory, leading to describing how these atoms
make up the celestial body and Solar system.
7-5
Hence, it is not surprising that our attempt was fruitful in incorporating the
molecular and supra-molecular particles into Savich-Kashanin's steps and
Boscovich's arches. So, we get the volumes at the beginning and end of each phase
representing the characteristic volumes of matter. These are universal states of matter,
unequivocally determined by the nature of matter itself and by Boscovich's unique
law of forces existing in nature.
7.4. Physico-chemical state and polymerization
of compressed ethylene gas /53, 55/
Ethylene molecule has a double bond and can be polymerized by a free-radical
mechanism: the initial radical R• binds to a molecule of ethylene CH2=CH2 by
breaking the double bond and a new radical is formed on just combined ethylene
molecule (7-2). Then the next molecule of ethylene is bonded, and again the next, and
so a few hundred or thousand times, resulting in a macromolecular chain of bonded
molecules of ethylene. The resulting plastic mass, composed of such macromolecules,
is referred to as polyethylene:
R• + CH2=CH2 → R-CH2CH2• (7-2)
The process was discovered in 1933, by Imperial Chemical Industry Company.
The peculiarity of this simple polymerization is that it can be done only if the gaseous
ethylene is compressed to very high pressure. Typical polymerization conditions in
industrial plants are in the range 1000-3000 bar and 150-300 °C. Since its discovery,
in the following decades the unresolved question was - why is it necessary to have
such high pressure. Hunter /56/ observed that the density of compressed ethylene gas
at the polymerization conditions is approximately 0.46 g/cm3. This value exceeds the
density of the randomly packed ethylene molecules which is 0.28 g/cm3. The
calculated average distance between the molecules of ethylene under polymerization
conditions is 0.4-0.5 nm, which is less than the diameter of the molecule (0.5 nm).
Hunter concluded that in these conditions the ethylene molecule is regularly packed,
suitably oriented and distorted. He concluded that the compression achieves certain
molecular organization of ethylene, which is a prerequisite for successful
polymerization. However, he did not explain how the molecules are packed, oriented
and distorted.
The interaction of most molecules, including ethylene molecules, is usually
presented by Lennard-Jones's potential (Figure 5-4) published in 1924, which is
similar to Boscovich's curve (Figure 3-1b) published in 1745. The empirical value for
the distance between the centers of two molecules of ethylene at a minimum potential
energy is re = 0.466 nm. Thus, rotating molecular pairs of ethylene are formed.
The volume occupied by rotation of a pair is 127.6 cm3/mol calculated by equation
(7-1). 7-6
At shorter distances a strong repulsive force is expected, according to Figure 5-4.
Ethylene, with its molecules at that distance, has density 0.22 g/cm3. This value is two
times lower than the density of ethylene in the polymerization conditions. This means
that the molecules of ethylene may come towards each other at a distance less than
0.466 nm.
Therefore, we assumed /53, 55/ that instead of Lennard-Jones's potential (Figure 5-
4), it is more appropriate (and hence correct) to apply Boscovich's curve as shown in
Figure 3-1a. We supposed that the distance between the two paired molecules
corresponds to position R in Figure 3-1a. Once the free volume between the
molecular pairs is exhausted by compression, the additional compression is possible
on account of space that exists between the two molecules in a pair. These already
paired molecules come more closely towards each other, thus forming a rotating
bimolecule. Van der Waals's constant b corresponds to the volume occupied by two
molecules that have touched. Hence, constant b is named "covolume". Therefore, we
proposed that a rotating bimolecule occupies volume b=57.1 cm3/mol, which is the
empirically determined value of ethylene covolume.
By additional compression, more and more molecules are transformed into
bimolecules. The density of ethylene composed of bimolecules is db=M/b=0.49
g/cm3, where M=28 g/mol is molar mass of ethylene. This density corresponds to that
in ethylene polymerization conditions, mentioned above. Consequently, the formation
of bimolecules is a clue to the prerequisite of successful polymerization.
Bimolecules rotate about all three axes, i.e. they have three degrees of freedom
(3D). A further condensation is possible by cooling, which reduces the degree of
freedom to one (1D). As a consequence, bimolecules are combined and linear
oligomolecules are formed, which rotate around the longitudinal axis. As the
dimensions of ethylene molecule and distance between two of these molecules is
known, it is easy to calculate that the molar volume occupied by rotation of
oligomolecule is 37.8 cm3/mol.
On the basis of these assumptions the supra-molecular organization of compressed
ethylene was proposed (Figure 7-4).
The existence of these particles and phase transitions of the second and third
orders in compressed ethylene have been confirmed by thermodynamic, physical and
spectroscopic methods /53, 55/. The phase transition from α to β phase occurs under
conditions when the volume of ethylene is equal to critical (V/Vc=1), transition from
β to γ phase is when entropy of ethylene is equal to the critical ethylene entropy
(S/Sc=1).
We have shown that the polymerization of ethylene is only possible in the β and γ
phase, and it has the highest rate at phase transition β-γ, when ethylene from less
ordered β phase transforms to the more ordered quasi-crystalline γ phase.
7-7
Figure 7-4. The phase state of molecular particles and their volumes
(empirical values) of compressed ethylene /53, 55, 57-60, 62-65/
The ethylene supra-molecular particles have a decisive influence on the
mechanism and kinetics of polymerization, as well as the structure and properties of
the polyethylene. Crystalline polyethylene with regularly packed macromolecules
originates in the ordered γ phase, while less crystalline polyethylene with disordered
macromolecules originates in disordered β phase.
This interpretation, that has emerged thanks to Boscovich's roadmap, and its
application in explanation of the polymerization of ethylene have been published in
dozens of scientific papers /57-65/ and is of great importance for a better
understanding and managing of the industrial polymerization process.
7-8
7.5. Effect of pressure on polyethylene melting point
The product of the industrial polymerization of ethylene by free-radical
mechanism is a plastic material called low density polyethylene, which is in the form
of solid partially crystalline granules. These granules are heated and melted in
machines for making different products: electrical cable insulation, films and sheets,
bottles, canisters, drums... At atmospheric pressure polyethylene melts at 115-120 °C.
However, in the machine that melts polyethylene it is subjected to pressures from
several hundred to several thousand bars. There is a danger that the melted substance
solidifies at the increased pressure and causes damage to the machine or gives a
defective product. Therefore, the melted substance should be warmed up well above
120 °C. Once, we (in Chemical industry "Panchevo") urgently required a proposal for
the temperature at which to warm the melted substance, so that it did not harden at
elevated pressures. At that moment in time, we did not have empirical data on the
effect of pressure on the melting temperature of polyethylene.
However, in response to the above request, we found the signpost in Boscovich's
Theory, i.e. his interpretation of the law of continuity /10, 11/. The law was first
expressed by Leibniz, and Boscovich elaborated it in more detail. One of the
consequence of this law is that "whenever the two variable quantities, which of
course can change magnitude, are interconnected, then by the magnitude of one it can
be determined the magnitude of the other" /10, section 102/.
We know that two such related quantities are: the degree of order of compressed
ethylene (numerically presented by the entropy) and the degree of crystallinity of
polyethylene, which is experimentally determined.
Furthermore Boscovich continues: "...let's imagine the two magnitudes of the first"
(e. g. Ei and Em in Figure 7-5) "and two magnitudes of the second quantity..." (e. g.
Pi and Pm) and "if the first quantity by a constant change passes from the first
magnitude to the other, passing through all the [possible values of] magnitudes..."
(Ej...Ek ...El), then "it will happen also with the other quantity", i.e. it will pass
through the proper magnitudes (Pj...Pk...Pl). If by Ei we denote the γ phase, and by
Em the β phase of ethylene, then Pi and Pm represents polyethylene, which is
obtained by polymerization of the corresponding phases of ethylene. If Ek is a
transition from the γ to β phase of pure ethylene, i.e. "melting" of quasi-crystalline γ
phase at a temperature which depends on the pressure, then Pk must represent the
corresponding phase transition, i.e. melting of polyethylene crystalline domains,
which must occur at the same temperature and pressure. In other words, quasi-
crystalline γ ethylene and partially crystalline polyethylene should melt at the same
temperature and the same pressure.
7-9
Figure 7-5. Explanation of the application of the law of continuity
on example of ethylene(E) and polyethylene (P) /53/
We knew that γ ethylene at elevated pressures "melts" at a temperature at which
the entropy is equal to the critical (S/Sc=1), the exact values of the temperature are
known from thermodynamic data. We also concluded that the polyethylene should
melt at the same temperatures as ethylene. The experimental data, collected
afterwards, fully confirmed this conclusion (Figure 7-6) /25, 53, 62/.
Figure 7-6. Phase transition conditions β-γ in pure ethylene(line S/Sc=1)
correspond to that of melting point of polyethylene (points)
at elevated pressure /25, 53, 62/
7-10
7.6. Structure of fluids based on Boscovich's Theory
and Savich-Kashanin's theory
A huge problem in modern physics is a consequence of the fact that it can not
accurately describe the structure of fluids, i.e. liquids and real compressed gases, in
which plenty of very important physical, chemical, biological and other processes are
performed. It is generally accepted that fluids have an amorphous structure;
molecules in them are irregularly arranged. However, some short range local order is
experimentally confirmed, i.e. some molecules are regularly arranged as consequence
of different kinds of intermolecular forces acting between them. According to the
comprehension of Eyring and Marchi, a liquid consists of two phases, a "gas-like"
and the other phase that of "crystal like" domains /68/, but there is no explanation
what is the fraction (percentage) of these domains, and how molecules are arranged in
them.
Let's look at how Boscovich interpreted the interaction of particles in fluids.
According to him /8, 71/ it can be described by the curve similar to Figure 3-1a, but
instead of the outmost attraction arch, which represents gravitational force, there
should be a repulsive arch since the gases have tendency to spread, i.e. there are
repulsive forces between the molecules in gases. According to that description, S.
Paushek-Bazhdar drew a solid oscillating curve (Figure 7-7) /84, 85/.
Rotating
molecular pair
Rotating
bimolecule
Rotating
oligomolecule
Bundle Rotating
molecule
Critical point
Covolume
Triple point
Aps. zero
Translating
molecule
Particles
Characteristic
points and
volumes
Boscovich’s
curve for
fluids
Vo Vts bVc
Ideal gas
V=
Real (compressed) gas
Liquid
Solid
Distance
Force
Phase state
VM
b0
Hard sphere Rotating molecule
Figure 7-7. Boscovich's curve for fluids /84, 85/ completed with supra-molecular
particles, characteristic volumes of matter and phase states
7-11
Previously, we explained that for every arch of the Boscovich's curve there is a
corresponding step in the diagram of Savich and Kashanin (Chapter 6.4.). It was
concluded that the molecules situated at cohesion and noncohesion limits on
Boscovich's curve contribute to some characteristic state of matter that can be
calculated by our staircase model (Figures 7-2 and 7-3). It was confirmed for 92
substances that the outermost cohesion limit corresponds to the critical point (Chapter
7-2). The anterior (i.e. earlier than the critical point) cohesion limit corresponds to the
van der Waals constant b, i.e. covolume. Consequently, in Figure 7-7, we denoted the
characteristic volumes of matter and the corresponding cohesion and noncohesion
limits.
It was shown for 143 different substances that the same mathematical model can
be used to describe the changes in characteristic volumes during condensation from
ideal gas state (characterized by individual molecules having the highest mobility and
freedom) to absolute zero temperature (where molecules are interconnected and
totally immobilized) (Figures 7-2 and 7-3). If the same mathematical model can be
used to describe these changes, the next two consequences can be logically drawn
/49, 54/:
(A) All substances are exposed to the same structural changes by passing from
one characteristic state to another. Otherwise, if the structural changes are not the
same, the changes of volume for different substances could not be described by a
common mathematical model.
(B) All substances have the same supra-molecular structure in the same
characteristic states. This second conclusion is a logical consequence of the
previous conclusion. If all substances are exposed to the same structural changes as
they go from one characteristic state to another, it is quite reasonable to suppose that
all substances have the same supra-molecular structure in the initial characteristic
point, and some other structure in the subsequent characteristic point.
Next logical question is: What are these supra-molecular structures? The answer
can be found in the case of compressed ethylene, and then can be generalized to other
substances.
Based on our mathematical model (Figure 7-2), critical volume, covolume and
volume of solid phase at triple point of ethylene were calculated: 127.6, 63.8 and 40
cm3/mol, respectively. These values are very close to the empirically determined
values of the volumes necessary for rotation of supra-molecular particles of ethylene,
i.e. molecular pairs, bimolecules and oligomolecules: 127.6, 57.1 and 37.8 cm3/mol,
respectively. Hence, the supra-molecular structure of ethylene at critical point
corresponds to molecular pair, since their volumes are equal, i.e. Vc=Vp=127.6
cm3/mol. According to consequences (A) and (B), the same should be valid for other
substances, i.e. supra-molecular structure of all substances at critical point should
correspond to molecular pairs, and both volumes should be equal i.e. Vc=Vp. Indeed,
it was confirmed that Vc=Vp for 92 substances (Figure 7-1).
7-12
Also, the consequences (A) and (B) are valid for the beginning of phase 0 in
staircase model (Figure 7-2), i.e. the structure of ideal gas, which is equal for all
substances: chaotic movement of individuals molecules; average distance between
molecules is the same for all substances, at same pressure-temperature-volume
conditions (Avogadro-Ampere's law); all substances have the same energy equal P•V
and all obey the unique equation of state, i.e. P•V=RT, where R is universal gas
constant common for all gases.
The phase state and supra-molecular particles of compressed ethylene gas are
presented in Figure 7-4, but only in supra-critical conditions, i.e. above critical
temperature and above critical pressure. But, what is structure of liquid ethylene? It
can be imagined by cooling and depressurizing of phase of ethylene. Consequently,
the liquid ethylene should be a dynamic equilibrium of bimolecules and
oligomolecules, the former rotating around three axes and the second around one
axis, the former dominating at high temperatures, the latter prevailing at low
temperatures. Bimolecules vanish at melting point. Indeed, Rytter and Gruen /86/
investigated the ethylene transition gas→liquid→solid by infrared spectra and
interpreted data in terms of monomer→dimer→aggregate→crystal scheme.
According to consequences (A) and (B), liquids of other substances should have
the same structure as liquid ethylene.
Indeed, Korolev et al /70/ have confirmed for 8000 organic compounds that their
liquids consist of ordered and disordered domains: by cooling gas at the temperature
of condensation the individual molecules pass into liquid as dimers. By further
cooling linear oligomers are formed, and at even lower temperatures the molecules
are all mutually connected forming a continuous associative structure.
Also according to Eyring and Marchi, liquid consists of two phases, a "gas-like"
phase and a "crystal like" phase /68/. According to our conceptions, the "gas-like"
domains consist of 3D-rotating bimolecules. The "crystal-like" domains consist of
1D-rotating linear oligomolecules. There is a dynamic equilibrium between these
phases, i.e. bimolecules are transformed into oligomolecules and vice versa.
It should be noted, however, that Lennard-Jones's potential (Figure 5-4), which is
usually used to represent the interaction of molecules in liquid, is not appropriate: two
molecules at equilibrium distance re occupy the volume equals to critical volume Vc
(Figure 7-1). The minimum volume that can be achieved according to this potential is
bo, i.e. so called 'hard sphere volume' which is equal to 0.71 Vc (Figures 7-2 and 7-3).
However, the actual volumes of liquids are much smaller, i.e. 0.3-0.5 Vc. Hence, the
rotating molecular pairs at distance re, according to Lennard-Jones's potential, cannot
represent dimers in liquid, that were found by Korolev et al. Molecules in dimers
have to be at shorter distance where the volume is equal to van der Waals's constant b,
i.e. covolume.
Consequently, the positions of molecular and supra-molecular particles in
Boscovich's curve for fluids are as presented in Figure 7-7.
7-13
We applied very successfully this concept of liquid structure to interpret:
polymerizations of liquids: methyl and higher alkyl methacrylates /64, 66, 72, 73, 87/,
propylene /64/, styrene /88/ and styrene modified with nano-silica /89/. Here we shall
now deal with the polymerization of methyl methacrylate.
7.7. Polymerization of methyl methacrylate
The molecule of methyl methacrylate (MMA), H2C=C(CH3)COOCH3 has a
double bond (C=C), and can be polymerized by free radical mechanism in same way
like ethylene (7-2). Liquid MMA can polymerize at atmospheric pressure and at room
temperature up to 90 °C. The polymethylmethacrylate (PMMA) is derived as a
material for the production of organic glass (i.e. plexiglass), dental fillings and
various other products. It is thought that this simple reaction may be explained by the
generally accepted theory of the radical polymerization, which needs to be fast at the
beginning of the reaction, and later to slow down as MMA is consumed by the
reaction. However, the reaction is not realized just as theory predicts. Initially, the
reaction is really fast, and then it slows. But after some time, the reaction begins to
accelerate, than it reaches a large value, and then abruptly decelerates and stops
completely. This is not in line with theoretical expectations, which also causes some
problems in MMA polymerization. Such reaction acceleration is undesirable. It
should be prevented. In order to achieve this, we need to know its cause.
Since 1930, a dozen "theories" were proposed attempting to explain the cause of
the acceleration /66/. But, there was no success. In the 1960s Kargin and Kabanov
/67/ suggested a hypothesis based on the assumption that the liquid MMA, like any
other liquid, is partially an ordered system where some molecules are regularly
arranged, and some are not. Therefore, they argued that the theory of polymerization
of organized monomers systems should be used to interpret the MMA polymerization.
However, this hypothesis has never been checked.
Sasuga and Takehisa /69/ have experimentally confirmed that the liquid MMA is
actually composed of domains in which the molecules are regularly arranged, and
domains of randomly arranged molecules. Korolev and al /70/ have confirmed this for
the liquid MMA, and also for 8000 other liquids; the existence of ordered and
disordered domains that consists of molecular dimers and linear oligomers.
Based on these and many other studies it can be concluded that the liquid MMA is
a partially organized system, but no study has proposed a method to determine the
fractions (percentage) of molecules that are in ordered and disordered domains. This
can, however, be very easily achieved using Boscovich's concept of liquid structure
(Figure 7-7).
There is empirical data for specific volume of the liquid MMA (Vt): it is
V25°C=106.7 cm3/mol at 25 °C and increases up to V75°C=113.9 cm3/mol at 75 °C.
7-14
Knowing that the critical volume of MMA is Vc=315 cm3/mol, covolume b and
volume Vt,s can easily be calculated by the staircase model in Figure 7-2. Hence, b =
157.5 cm3/mol and Vt,s =99.2 cm3/mol.
Specific volume of liquid MMA Vt is less than b, but greater than Vt,s i.e.
(b>Vt>Vt,s), (Figure 7-2). In the theory of Savich and Kashanin there is an interval of
abrupt change in density (Figure 6-1) and this corresponds to the repulsive arch in
Boscovich's curve for fluids (Figure 7-7). Molecules can not exist at that distance;
they have to be either on the lower non-cohesion limit or on the higher cohesion limit.
Therefore, it is reasonable to assume that the liquid MMA is a mixture of two micro
phases: disordered "gas-like" phase consisting of 3D-rotating bimolecules with
specific volume that corresponds to covolume b, and ordered "crystal-like" phase
consisting of 1D-rotating linear oligomolecules with specific volume that corresponds
to Vt,s .The specific volume Vt of liquid MMA, as a mixture of two micro phases,
depends on the fractions (percentages) of these phases according to equations (7-3).
Xb + Xt,s = 1 (mass fraction) (7-3a)
Vt = Xb b + Xt,s Vt,s (7-3b)
Yb + Yt,s = 1 (volume fraction) (7-3c)
Yb = Xb b/Vt (7-3d)
Yts = Xts Vts/Vt (7-3e)
Here, Yb and Yt,s are volume fractions, and Xb + Xt,s are mass fractions of
bimolecules and oligomolecules, respectively. The fractions of disordered and
ordered micro-phases are the only unknown terms in equations (7-3), and can be
easily calculated.
These fractions depend on temperature. By heating, 1D-rotating oligomolecules
disintegrate to 3D-bimolecules. Hence, with the increase of temperature the fraction
of bimolecular disordered micro phase increases, and fraction of ordered
oligomolecular micro phases decreases. Since b>Vt,s, specific volume of liquid MMA
increases with temperature.
Based on the known values of Vt, b and Vt,s, we calculated the fractions of
individual phases in liquid MMA (Figure 7-8). To test the feasibility of these concepts
and the accuracy of the calculations, we polymerized MMA and experimentally
determined the fractions of PMMA that have been originated in these phases /49, 72,
73/.
There is a very good agreement between the theoretically calculated and
experimentally determined values. Furthermore, many other details concerning
mechanism and kinetics of polymerization, as well as the molecular structure of
PMMA were interpreted using Boscovich's roadmap.
7-15
Figure 7-8. Calculated fractions of ordered (upper line) and disordered phase
(lower line) of liquid MMA; experimentally determined fractions of PMMA
obtained in ordered (squares) and disordered (triangles) phase /49, 72, 73/
7-16
8. PHILOSOPHICAL BASIS OF BOSCOVICH'S
COMPREHENSIONS
8.1 Introduction
Many authors have discussed Boscovich's philosophical comprehensions /74-77/.
In the literature, there are a number of articles about Boscovich's epistemology,
philosophy of mathematics, force and matter, space and time. Since there are very
thoroughly processed philosophical views on Boscovich, the reader is referred to the
literature cited.
Here we want to consider a more detailed look at Boscovich's understanding of
forces of attractions and repulsions, which play an essential role in the behaviour of
materials. It is not only him, but many of his predecessors, contemporaries and
subsequent thinkers have had a similar understanding: Leucippus, Democritus,
Heraclites, Aristotle, Empedocles, Toland, Holbach, Newton, Kant, Hegel, Engels...
Some of them (Kant, Hegel and Engels) believed that the attraction and repulsion
are the essence of matter. We emphasis again - the essence of matter! Therefore it
is astonishing that almost none of our contemporaries, philosophers and naturalists,
paid attention to it. Hegel and Engels works, written in 19th century, were widely
read in 20th century by philosophers and scientists, which wrote plenty of articles and
books about Hegel's and Engels' philosophy. We have read hundreds of these articles
and books, but we did not find a single text that even mentioned something about
Hegel's and Engels' comprehensions of attraction and repulsion.
Dealing with these aforementioned big thinkers, from the ancient Greeks onwards,
about what they thought in terms of attraction and repulsion would be too broad and
beyond the scope of this book. Here we shell consider and compare only the concepts
of Boscovich, Hegel and Engels in terms of attraction and repulsion.
8.2. Attraction and repulsion
Comprehensions of Boscovich, Hegel and Engels /78/
Hegel was quite right in saying that the essence
of matter is attraction and repulsion.
(Engels, "Dialectics of Nature")
The very fact that the great thinkers Boscovich, Hegel and Engels devoted so
much attention to attraction and repulsion suggests that the issue is important.
Therefore, our goal is to underline their basic understandings about the meaning of
attraction and repulsion. We will show the importance of the analysis of attraction and
repulsion for the interpretation of certain phenomena in nature.
8-1
8.2.1. Boscovich's conception of the attraction and repulsion
Boscovich's Theory of natural philosophy /8/ was based on attraction and
repulsion. He believed that the basic elements of matter are non-extended and
indivisible points, scattered in the infinite vacuum. The distance between points of
matter can be infinitely increased or decreased, but it can not completely disappear.
If two points approach each other, then, there is a cause that leads to a deceleration
or acceleration of their movements. At certain distances two points are determined to
be approaching, and at other distances they move away. That cause, which changes
the state of the body concerning its motion and state of rest /8/, i.e. this determination
to move away or towards is named by Boscovich as repulsive or attractive forces. The
law of the force is such that repulsion and attraction alternate as the points approach
each other (known as Boscovich's curve, Figure 3-1).
When points come to a negligible distance, repulsive force is infinitely large and
can destroy any chance of them meeting, no matter how large the speed at which a
point comes closer to the other point; making it impossible for the distance between
the points to completely disappear.
And as the points of matter move away from each other, the repulsive force
reduces, until at greater distance it becomes attractive, and then farther out the force
again becomes repulsive and so on alternatively, until it becomes permanently
attractive at a large mutual distance between the points.
According to Boscovich, attraction and repulsion are forces. However, it is wrong
to understand the attraction and repulsion as two types of forces. "Both kinds of force
belong to the same species; for one is negative with regards to the other, and a
negative does not differ in species from positives. That the one is negative with regard
to the other is evident from the fact that they only differ in direction, the direction of
one being exactly opposite of the direction of the other; for in the one there is a
propensity to approach, in the other a propensity to recede... /8, Section 108/."
The result of the action of these forces is a movement comprised of approaches
inward or recessions outward. Since the quantity of motion in the Universe is
maintained as always the same, Boscovich indicates the sum of all the attractive
movements is equal to the sum of all recessive movements in each moment /8,
Sections 261, 264/.
By Boscovich, transformation of attraction to repulsion and vice versa is possible,
and fulfilled at so-called limits of cohesion and non-cohesion (Chapter 3.1.).
8.2.2. Hegel's conception of the attraction and repulsion
For Hegel, rrepulsion is the fragmentation of one into the many ones /79, 80/.
This is a negative reference of the one to itself. This repulsion generates many ones
and it enables the existence of ones as the one.
8-2
For old Greek atomists, the matter consists of atoms and void. Hegel concludes
that the void, which is assumed as the complementary principle to the atoms, is
repulsion and nothing else, presented under the image of the nothing existing between
the atoms. (See comment at the end of chapter 8.2.4)
The ideality will, however, be realized in attraction. This self-positing-in-a-one of
the many ones is attraction. Repulsion passes over into attraction, the many ones
into one. Both, repulsion and attraction are at first distinguished from each other,
repulsion as the reality of the ones, attraction as their posited ideality.
Although negative, repulsion is nonetheless essentially connection. Attraction
refers to repulsion by having it for a presupposition. Repulsion delivers the material
for attraction. If there were no repelled ones, there would be nothing to attract.
The one is, however, ideality that has been realized, posited in the one; it attracts
through the mediation of repulsion; it contains in itself this mediation as its
determination. It thus does not swallow the attracted ones within it as into one point.
Since it contains repulsion in its determination, the latter equally preserves the ones
as many within it.
As thus determined, they (i.e. attraction and repulsion) are inseparable... Thus,
repulsion is the positing of the many; attraction the positing of the one.
Hegel noticed that attraction and repulsion, as is well known, are usually regarded
as forces. He does not agree with the practice in natural science to explain the
phenomenon with forces. The nature of force itself is unknown and only its
manifestation apprehended. Hence, the explanation of a phenomenon by a force is a
mere tautology.
He noticed that Kant famously constructed matter from the forces of repulsion and
attraction. "Now even if such a so-called construction of matter had at most analytical
merit, however diminished because of a flawed exposition, the thought on which it is
based, namely that matter must be made out to be from these two opposing
determinations as its fundamental forces, must always be highly esteemed."
8.2.3. Engels' comprehension of attraction and repulsion
Engels' comprehension of attraction and repulsion is outlined in his unfinished
work "The Dialectics of Nature" /81/, which is made up of articles, scraps and
fragments written in the period from the 1873 up to 1886 (Table 8-1). Attitudes about
the attraction and repulsion are woven into the whole work and represent the basis for
Engels' dialectics of nature.
Engels started from an attitude that motion, in the most general sense, is conceived
as the mode of existence of matter, comprehending all changes and processes in the
universe, from mere change of place right up to the process of thinking /81, p. 74/.
There is no matter without motion, and there is no motion without matter. The matter
as well as the motion can not be created nor destroyed.
8-3
Table 8-1. Attraction and repulsion in Engels' "Dialectics of Nature" /81/
Chapters and issues interpreted
by attraction and repulsion
Page
Year of
writing
1.
Outline of the part plan
- Transfer of motion, the conservation of energy law
17
1880
2.
Basic forms of motion
- The interaction of two bodies
- The planet's rotation
- Earth mechanics
- Heat
- Electricity and magnetism
- Chemical processes
- Changing one form of motion to another
- The importance of Solar energy for processes on
Earth
- The concept of force
- Origin of the Solar system
74-93
76-78
78
80
82
83
83
84
86
87-93
90-93
90-93
1880-81
3.
Dialectics. General questions of dialectics.
The fundamental laws of dialectics.
- Magnetism, electricity, chemical processes
239
1875
4.
Forms of motion of matter. Classification of the
sciences.
- General concepts of attraction and repulsion
- Repulsion in the tails of comets and gas
- Attraction and gravitation
- Dissipation and condensation of matter
- Transformation of attraction into repulsion
and vice versa
- Origin of the Solar system
- Thermal expansion and repulsion
- Motion and equilibrium
- Differentiation of matter
- Motion of the heavenly bodies
- Motion on one heavenly body
- Conversion of one form of motion into another
275
275
276
276
276
277
277
278-279
278-279
179-280
279-280
280
279-280
280
1874
1874
1874
1874
1874
1880
1880
1880
1880
1880
5.
Physics
- The concept of force
- Repulsion is active, attraction is passive
- Transformation of attraction to repulsion in gases
320
324
325
1880
1880
1873
8-4
The movement of each material carrier (particle or body) is bound up with some
change of place. This change of place can consist only in coming together or
separation. "Hence the basic form of all motion is approximation [see note] and
separation, contraction and expansion - in short, the old polar opposites of attraction
and repulsion". According to Engels, it is expressly to be noted that attraction and
repulsion are not regarded here as so-called "forces" but as simple forms of
motion
approximation [see note] and separation. (And his comprehension of the
forces Engels outlined later in the "Dialectic of nature" and we will look at it.) [Note
of translator: It is more appropriate to say "getting closer together" than
"approximation."]
"All motion consists in the interplay of attraction and repulsion. Motion, however,
is only possible when each individual attraction is compensated by a corresponding
repulsion somewhere else. Otherwise in time one side would get the preponderance
over the other and the motion would finally cease. Hence all attractions and all
repulsions in the universe must mutually balance one another. Thus the law of
indestructibility and uncreatability of motion is expressed in the form that each
movement of attraction in the universe must have as its complement an equivalent
movement of repulsion and vice versa; or, as earlier philosophy long before the
natural-scientific