Critical Shear Rate - the Instability Reason for the Creation of Dissipative Structures in Polymers

Abstract

Based on part 1 of the non-equilibrium theory of dispersion, here in part 2 of the theory, the critical parameter which drives the multiphase systems from the equilibrum to the non-equilibrium space, is discussed. It will be deducted that the shear rate is this critical parameter, and that dispersions are only prepared if the system is put under turbulent conditions.

Full text

Zeitschrift
für
Physikalische
Chemie,
Bd.
191,
S.
119-135
(1995)
©
by
R.
Oldenbourg
Verlag,
München
1995
Critical
Shear
Rate
-
the
Instability
Reason
for
the
Creation
of
Dissipative
Structures
in
Polymers
By
B.
Weßling
Zipperling
Kessler
&
Co.,
Kornkamp
50,
D-22926
Ahrensburg,
Germany
(Received
September
9,
1992;
accepted
February
23,
1995)
Multiphase
polymer
systems
I
Dispersion
I
Dissipative
structures
I
Instability
I
Melt
fracture
The
thermodynamical
description
of
non-equilibrium
phenomena
of
heterogeneous
poly-
mer
systems,
recently
presented
by
the
author,
is
currently
being
improved
by
the
analysis
of
the
critical
parameter.
First
results
are
presented.
The
theory
might
become
useful
for
colloidal
systems
in
general,
or
microemulsions
in
particular.
Die
thermodynamische
Beschreibung
von
Nichtgleichgewichts-Phänomenen
heterogener
Polymersysteme,
die
kürzlich
vom
Autor
vorgelegt
wurde,
wird
verbessert
durch
die
Analyse
des
kritischen
Parameters.
Erste
Ergebnisse
werden
präsentiert.
Die
Theorie
könnte
ebenfalls
erfolgreich
bei
anderen
kolloiden
Systemen,
v.
a.
bei
Mikroemulsionen,
angewendet
werden.
1.
Introduction
In
our
daily
life
we
are
dealing
with
an
innumerable
amount
of
different
polymer
systems.
Only
very
few
of
them
(e.g.
clear
polycarbonate
for
com-
pact
discs,
clear
polyacrylates
for
optical
fibres,
or
more
simple,
clear
poly-
styrene
for
beer
cups
at
an
outdoor
popular
festivity)
are
straight
single
phase
systems.
Most
real
polymers
consist
of
at
least
two
phases.
Sometimes,
the
two
phases
are
chemically
"identical",
e.g.
in
polyethylene
or
polypropylene,
where
crystalline
phases
are
embedded
in
an
amorphous
matrix.
But
more
often,
other
materials
or
other
polymers
are
incorporated,
in
order
to
modify
the
properties
of
the
polymer
basis.
If
a
polymer
(B)
is
mixed
with
the
polymer
(A),
mainly
for
improving
impact
resistance,
such
heterogeneous
polymer
systems
are
called
"polymer

120
.
Weßling
blends".
Other
materials
"B",
like
pigments,
stabilizers,
fillers,
halogen-
organic
materials,
conductive
carbon
black
or
intrinsically
conductive
poly-
mers,
are
being
used
for
colouring,
stabilizing,
increasing
stiffness,
improv-
ing
flame
retardant
properties
or
rendering
the
polymer
systems
conductive,
resp.
Such
systems
are
often
called
(polymer)
"compounds"
or
(polymer)
"composites".
They
are
used
as
computer
housing,
food
packaging,
fuel
tanks,
car
bumpers,
skis,
heat
insulation,
battery
membranes,
electrodes,
or
in
millions
of
other
products
in
our
daily
life
and
work.
"Polymer
blends"
and
"polymer
compounds"
are
manufactured
in
so-
called
"extruders"
(heated
cylindrical
apparatuses,
in
which
two
intermesh-
ing
screws
are
melting,
pumping
and
kneading
the
highly
viscous
polymeric
mixture).
All
of
these
two-
or
multiphase
polymer
systems
can
be
considered
being
a
dispersion
of
a
phase
in
a
matrix
A.
Eventually,
dispersion
aids
(surfactants)
are
being
used.
The
size
of
the
dispersed
phase
is
generally
about
1
µ
or
smaller.
Such
systems
are
in
no
principle
parameter
different
from
any
other
colloidal
system
with
colloidal
particles
being
dispersed
in
a
medium,
like
oil
(B)
in
water
(A),
eventually
using
surfactants.
In
particular,
microemulsions
should
be
looked
at
as
being
analogous
systems,
which
could
be
deeper
understood
using
our
approach
[14].
For
most
of
them,
many
surprising
and
non-linear
phenomena
are
well-
known,
and
are
the
objects
of
continuous
work
since
decades.
Especially
the
resulting
properties,
as
for
instance
impact
modification,
viscosity
and
conductivity,
are
depending
upon
a
given
parameter
in
a
non-linear
way.
The
property/parameter
relationship
can
be
described
by
an
S-shaped
curve.
For
explaining
these
phenomena,
theories,
which
are
in
principle
based
on
equilibrium
thermodynamical
considerations,
have
been
developed
and
are
currently
being
used.
These
theories
include
the
"Flory-Huggins-Theory"
[1],
the
"Percolation
Theory"
[2],
the
"Nearest-Neighbour-Model"
[3],
but
also
the
constitutive
and
related
equations
for
the
description
of
rheological
phenomena
[4].
Starting
from
the
interest
to
understand
and
predict
the
conductivity
jump
at
a
critical