Micrometer-sized ice particles for planetary-science experiments - I. Preparation, critical rolling friction force, and specific surface energy

Abstract

Coagulation models assume a higher sticking threshold for micrometer-sized
ice particles than for micrometer-sized silicate particles. However, in
contrast to silicates, laboratory investigations of the collision properties of
micrometer-sized ice particles (in particular, of the most abundant water ice)
have not been conducted yet. Thus, we used two different experimental methods
to produce micrometer-sized water ice particles, i. e. by spraying water
droplets into liquid nitrogen and by spraying water droplets into a cold
nitrogen atmosphere. The mean particle radii of the ice particles produced with
these experimental methods are $(1.49 \pm 0.79) \, \mathrm{\mu m}$ and $(1.45
\pm 0.65) \, \mathrm{\mu m}$. Ice aggregates composed of the micrometer-sized
ice particles are highly porous (volume filling factor: $\phi = 0.11 \pm 0.01$)
or rather compact (volume filling factor: $\phi = 0.72 \pm 0.04$), depending on
the method of production. Furthermore, the critical rolling friction force of
$F_{Roll,ice}=(114.8 \pm 23.8) \times 10^{-10}\, \mathrm{N}$ was measured for
micrometer-sized ice particles, which exceeds the critical rolling friction
force of micrometer-sized $\mathrm{SiO_2}$ particles ($F_{Roll,SiO_2}=(12.1 \pm
3.6) \times 10^{-10}\, \mathrm{N}$). This result implies that the adhesive
bonding between micrometer-sized ice particles is stronger than the bonding
strength between $\mathrm{SiO_2}$ particles. An estimation of the specific
surface energy of micrometer-sized ice particles, derived from the measured
critical rolling friction forces and the surface energy of micrometer-sized
$\mathrm{SiO_2}$ particles, results in $\gamma_{ice} = 0.190 \, \mathrm{J \,
m^{-2}}$.

Full text

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Micrometer-sized ice particles for planetary-science experiments - I. Preparation, critical
rolling friction force, and specific surface energy
B. Gundlacha, S. Kiliasa, E. Beitza, J. Bluma
aInstitut f¨ ur Geophysik und extraterrestrische Physik, Technische Universit¨ at Braunschweig,
Mendelssohnstr. 3, D-38106 Braunschweig, Germany
Abstract
Coagulation models assume a higher sticking threshold for micrometer-sized ice particles than for micrometer-sized silicate parti-
cles. However, in contrast to silicates, laboratory investigations of the collision properties of micrometer-sized ice particles (in par-
ticular, of the most abundant water ice) have not been conducted yet. Thus, we used two different experimental methods to produce
micrometer-sized water ice particles, i. e. by spraying water droplets into liquid nitrogen and by spraying water droplets into a cold
nitrogen atmosphere. The mean particle radii of the ice particles produced with these experimental methods are (1.49 ± 0.79)µm
and (1.45 ± 0.65)µm. Ice aggregates composed of the micrometer-sized ice particles are highly porous (volume filling factor:
φ = 0.11 ± 0.01) or rather compact (volume filling factor: φ = 0.72 ± 0.04), depending on the method of production. Furthermore,
the critical rolling friction force of FRoll,ice = (114.8 ± 23.8) × 10−10N was measured for micrometer-sized ice particles, which
exceeds the critical rolling friction force of micrometer-sized SiO2particles (FRoll,SiO2= (12.1±3.6)×10−10N). This result implies
that the adhesive bonding between micrometer-sized ice particles is stronger than the bonding strength between SiO2particles. An
estimation of the specific surface energy of micrometer-sized ice particles, derived from the measured critical rolling friction forces
and the surface energy of micrometer-sized SiO2particles, results in γice= 0.190Jm−2.
Keywords: Ices, mechanical properties, Interplanetary dust, Origin, Solar System, Comets, nucleus
1. Introduction
Coagulationofmicrometer-sizedparticlesplaysanimportant
role in molecular clouds (Ossenkopf, 1993; Weidenschilling
and Ruzmaikina, 1994; Ormel et al., 2009) and protoplane-
tary disks (Blum and Wurm, 2008; Zsom et al., 2010). In both
environments, the dominating dust materials are silicates, car-
bonaceous material, and ices. A wide variety of experimental
investigations of the coagulation and fragmentation of aggre-
gates composed of micrometer-sized dust particles, mostly sil-
icates, have been performed (Blum and Wurm, 2008; G¨ uttler
et al., 2010). Micrometer-sized silicate grains stick to one an-
other for collision velocities ? 1ms−1(G¨ uttler et al., 2010).
Dust collisions can lead to fragmentation of the dust aggre-
gate if the collision velocity exceeds the fragmentation thresh-
old for aggregates, which is expected for velocities in the range
of ∼ (1−100)ms−1, depending on grain size and material. This
effecthasbeeninvestigatedinthelaboratoryforsilicatesbutnot
for ices.
Water ice obviously played an important role in planet for-
mation of our own Solar System as can be seen by the high
H2O-ice abundances in the planetary bodies of the outer Solar
System. It is generally assumed that the increased stickiness
of water-ice particles over the refractory materials plays a cru-
cial role in the rapid formation of the giant planets and their
satellite systems. Unfortunately, most of the planetary bodies
Email address: b.gundlach@tu-bs.de (B. Gundlach)
of the outer Solar System lost memory of their formation pro-
cesses, due to sintering, melting, or high-pressure effects. An
exception are probably the comets, which never experienced
enhanced pressures or temperatures since their formation in the
outer reaches of the solar nebula (but see also Levison et al.
(2010) for an extrasolar formation of part of the comets). Here,
we expect the building blocks of the planetary bodies to be
preserved in their original state. The first direct evidence for
micrometer-sized ice particles on a cometary nucleus was given
by the Deep Impact mission, when the ejected particles of the
comet9P/Tempelwere observedin theinfrared (Sunshineet al.,
2007). Recently, A’Hearn and coleagues (pers. comm.) found
evidence for larger icy bodies (presumably aggregates of micro-
scopic ice grains) during the flyby of comet Hartley 2. Thus, we
believe that understanding the collision and adhesion behavior
of ice particles and the subsequent formation of ice aggregates
can help to better understand the physical processes which led
to the formation of the ice-dominated bodies of the outer Solar
System.
In contrast to silicates, the collision properties of ices (and,
in particular, of the most abundant water ice) are largely unde-
termined. Coagulation models assume a higher surface energy
and therefore a higher sticking threshold for ice particles (Wada
et al., 2007; Wada et al., 2008) as compared to silicates. How-
ever, experimental investigations of the specific surface energy
of water ice are scarce. Furthermore, experiments on the coag-
ulation or fragmentation behavior of microscopic ice particles
under astrophysical conditions have not been conducted yet.
Preprint submitted to IcarusApril 21, 2011
arXiv:1102.0430v3 [astro-ph.EP] 20 Apr 2011

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Figure 1: Design of the two different experimental setups (A and B), which
were established to produce micrometer-sized ice particles.
Figure 2: Temperature distribution of the dry gas environment (squares) and the
cold target (cross) inside the experimental chamber of setup B. The solid lines
are included to guide the eye.
Laboratory experiments with macroscopic ice particles in the
cm- to dm-regime were performed by Hatzes et al. (1988),
Hatzes et al. (1991), Supulver et al. (1997), and Heißelmann
et al. (2010). In all these experiments, no sticking of the ice par-
ticles was observed, even at velocities below 0.1mms−1. The
existence of a frost layer increased the sticking threshold of the
macroscopic ice particles to observable values. However, it is
questionable whether these experiments can be used to derive
the collision properties of microscopically small ice particles.
In this paper, we will present two experimental methods to
produce micrometer-sized ice particles and ice aggregates (see
Sect. 2). In Sect. 3, the size distribution of the produced
micrometer-sized ice particles, the volume filling factor of the
ice aggregates, the critical rolling friction force and the specific
surface energy of the micrometer-sized ice particles are investi-
gated. Finally, asummaryoftheobtainedresultsandanoutlook
on future experiments are given in Sect. 4.
2. Preparation of micrometer-sized ice particles
Two different experimental setups (A and B, see Fig. 1) were
developed to produce ice particles with diameters ranging from
sub-micrometer-size to several micrometers (see Sect. 3.1). In
both experiments, liquid water was dispersed by a commercial
droplet dispenser (1, in Fig. 1). For instant cooling to ∼ 77K
(setup A), the dispersed water was directly sprayed into liquid
nitrogen (2), which was stored in a dewar vessel (3). After-
wards, separation of the produced ice particles from the liquid
nitrogen was conducted by filtration or by evaporation of the
liquid nitrogen.
The second experiment (setup B) was performed by spraying
the dispersed water droplets into a dry, cold gas environment
(4). Liquid nitrogen was filled into the experimental setup be-
fore the production of the ice particles was started in order to
cool the aluminum walls (5) of the experimental setup. The dry
coldgasenvironmentwasgeneratedbytheevaporatednitrogen,
which was kept cool by the aluminum walls after the nitrogen
had fully evaporated. A gas outlet (6) was incorporated into the
experimental setup to enable the escape of the nitrogen vapor.
Due to the strong upward directed gas flux of the evaporating
nitrogen, the production of the ice particles was started after
the liquid nitrogen had evaporated. For safety reasons, the cold
experiment was thermally isolated by a polystyrene mantle (7).
Temperature sensors (8) were positioned inside the experiment
to monitor the vertical temperatures of the gas environment. A
typical temperature distribution inside the experimental cham-
ber during an experiment is shown in Fig. 2. The measured
temperature of the cold target is lower than the temperature of
the gas environment, due to (a) the connection of the cold target
with the cold aluminum walls of the experimental chamber and
(b) the heat deposition of the warm water droplets to the gas.
Formation of ice particles occurred during sedimentation of
the water droplets inside the dry, cold gas environment. The
falling speed of micrometer-sized particles at atmospheric pres-
sure is about 300µms−1. Thus, the duration of sedimentation
inside the dry, cold gas environment is much longer than the
required time to freeze the dispersed water. Two windows (9)
were incorporated into the aluminum wall, 31cm beneath the
droplet dispenser, to illuminate and observe the sedimenting ice
particles with a long-distance microscope together with a high-
speed camera (10). For the measurement of the critical rolling
friction force of micrometer-sized ice particles (see Sect. 3.3),
a cold target (11) was positioned in the field of view of the
long-distance microscope. After sedimentation, the ice parti-
cles were stored on a cold plate (12) at the bottom of the cham-
ber, 53cm beneath the droplet dispenser, for further investiga-
tions.
3. Characterization of the produced micrometer-sized ice
particles
3.1. Size distribution
The size distributions of the produced ice particles were in-
vestigated for both experimental methods. For the size estima-
tion of the ice particles produced with setup A, a light micro-
scope was used. The ice particles were positioned on a cooled
object slide. To avoid condensation of moisture (frost) on the
ice particles as well as on the optical components, the light mi-
croscope was positioned inside a glove box which was filled
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Figure 3: Ice particles produced with setup A and observed with the light mi-
croscope.
with dry nitrogen gas. The prevention of water vapor conden-
sation is very important, because the formation of frost on ice
particles can have a strong influence on their sticking proper-
ties, like e.g. on the coefficient of restitution (see e. g. Heißel-
mann et al. (2010); Hatzes et al. (1988)). To avoid melting of
the ice particles during the measurements, the sample holder of
the microscope was cooled and the illumination of the micro-
scope was modified by an infrared filter to block the infrared
radiation, due to the strong light absorption of water ice in the
infrared. Fig. 3 shows ice particles produced with setup A and
observed with the light microscope.
The measured cumulative size distribution of the ice parti-
cles is visualized in Fig. 4a (solid curve). Ice particles pro-
duced with setup A have an arithmetic mean radius of a0A =
(1.49 ± 0.79)µm (dashed line), the error indicates the standard
deviation of the measured radii (dashed dotted line). The parti-
cle radii range from aA,min= 0.24µm to aA,max= 6.07µm.
An estimation of the size distribution of the ice particles pro-
duced with setup B was carried out using the long-distance mi-
croscope (see Sect. 2). The measurement of the size distribu-
tion was performed at the height of the cold target. Fig. 4b
shows the cumulative size distribution of the ice particles pro-
duced with setup B (solid curve). The particle radii range from
aB,min= 0.24µm to aB,max= 5.52µm. Furthermore, the arith-
metic mean radius of the ice particles produced with setup B is
a0B= (1.45±0.65)µm (dashed line), with the error of the mea-
surement given by the standard deviation of the measurement of
radii (dashed dotted line). Both experimental setups produced
very similar micrometer-sized ice particles, due to the usage of
the same commercial droplet dispenser. Examples of sediment-
ing ice particles, observed with the long-distance microscope,
are shown in Fig. 6.
3.2. Volume filling factor of ice aggregates composed of
micrometer-sized ice particles
Ice aggregates composed of micrometer-sized ice particles
were produced with both experimental setups (A and B). Fig.
5 shows examples of different ice aggregates produced by the
two setups. Measurements of the volume filling factor of these
Figure 4: Cumulative size distributions of the ice particles produced with setup
A (a, solid curve) and produced with setup B measured at the position of the
cold target (b, solid curve). The arithmetic mean radii of the particles (dashed
lines), which were produced using the different setups, are very similar: a0A=
(1.49±0.79)µm (setup A) and a0B= (1.45±0.65)µm (setup B). The errors of
both measurements are given by the standard deviations of the measurements
(dashed dotted lines).
aggregates were conducted, determining the mass as well as the
occupied volume of the aggregates before and after melting.
Figure 5: Images of ice aggregates composed of micrometer-sized ice particles.
Ice aggregates, produced with setup A, were separated from the liquid nitrogen
by evaporation of the liquid nitrogen or by filtration. The images are showing
ice aggregates before and after evaporation of the liquid nitrogen (a and b) and
ice aggregates after filtration (c and d). An ice aggregate produced with setup
B is shown in image (e).
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Figure 6: Sedimenting ice particles and ice aggregates during formation (setup B), observed with the long-distance microscope. The general structure of these
very porous aggregates, φB= 0.11 ± 0.01, is shown in a. This high porosity is caused by the ”hit-and-stick” behavior of micrometer-sized particles at low impact
velocities. Examples of two ”hit-and-stick” collisions between micrometer-sized ice particles are shown in the image sequences b-e and f-j.
A volume filling factor of φA = (0.72 ± 0.04) was mea-
sured for five ice aggregates, which were produced by spraying
the dispersed water into liquid nitrogen (setup A). The error is
given by the statistical variation of these measurements. The
determined value is close to the volume filling factor of hexag-
onal close packed material: φhcp=∼ 0.74. Thus, ice aggregates
produced with setup A are relatively compact, due to the sed-
imentation and rearrangement of the ice particles in the liquid
nitrogen.
However, ice aggregates produced with setup B, are highly
porous, φB = 0.11 ± 0.01.
filling factor of ice aggregates produced with setup B, we de-
posited the ice particles on a cooled metal plate (with dimen-
sions 45mm × 45mm) inside the experimental chamber. The
occupied volumes of 15 ice aggregates were determined by
measuring the heights of the deposited ice aggregates with the
long-distance microscope (see Sect. 2) and taking the cross-
section area of the metal plate into account. Afterwards, the
ice aggregates were rapidly weighted to avoid condensation of
frost and the volume filling factors of the ice aggregates were
calculated by comparing the mass of an individual ice aggregate
with the mass of solid water ice occupying the same volume as
the ice aggregate at the same temperature.
An example of the grown ice aggregates, observed with the
long-distance microscope, is shown in Fig. 6a. This image
demonstrates the high porosity of the ice aggregates, which can
be explained with ”hit-and-stick” behavior of the sedimenting
micrometer-sized particles at low impact velocities. Two dif-
ferent ”hit-and-stick” collisions of micrometer-sized ice parti-
cles with the grown ice aggregate are shown in the image se-
quences 6b-e and 6f-j. Sticking at the first point of contact of
micrometer-sized particles was also found in previous works
with similar setups (Blum and Wurm, 2000), in which the stick-
ing properties of micrometer-sized SiO2particles, with a radius
of a0= 0.95µm, were investigated.
To calculate the mean volume
3.3. Critical rolling friction force and specific surface energy
The critical rolling friction force between two adhering par-
ticles is an important quantity for the characterization of their
collisional properties and of the restructuring of particle aggre-
gates in contact (Dominik and Tielens, 1995; Heim et al., 1999;
Blum and Wurm, 2000; Wada et al., 2008). An expression for
the critical rolling friction force between two spheres was cal-
culated by Dominik and Tielens (1995),
FRoll = 6πγξ,
(1)
where γ is the specific surface energy of the material and ξ is
the critical rolling displacement of the particle, which is the
distance one sphere may roll over the other before irreversible
rearrangement in the contact zone occurs. The critical rolling
friction force of uncoated monodisperse silica particles of a0=
0.95µm radius was experimentally investigated by Heim et al.
(1999), by pulling on chainlike aggregates with an AFM tip
and testing their resistance to a forced oscillating motion on
one end of the chain, while the other end was fixed. From this
experiment, a mean critical rolling friction force of FRoll,SiO2=
(8.5 ± 1.6) × 10−10N was found for uncoated SiO2particles.
Another experimental approach for the estimation of the crit-
ical rolling friction force of monodisperse SiO2particles with
the same size was performed by Blum and Wurm (2000). In
this work, the SiO2particles were coated with a silicon-organic
mantle (dimethyldimethoxysilane, (CH3)2Si(OCH3)2), to guar-
antee a nonpolar, hydrophobic surface layer. They found that
the additional mantle enhanced the specific surface energy of
the SiO2particles by a factor of 1.35. Thus, the obtained critical
rolling friction force of the coated SiO2particles was corrected
by this factor for a comparison with uncoated SiO2particles.
The critical rolling friction force was estimated by observing
severalcollisonsbetweenSiO2particlesandagglomeratescom-
posed of individual SiO2particles, in which gravitational re-
structuring was manifested through a slow morphological tran-
sition within the aggregate layer. In this case, the critical rolling
friction force can be calculated as follows,
FRoll = mg0acm
a0
where m is the mass of the restructuring aggregate, g0 =
9.81ms−2is the gravitational acceleration of the Earth, a0
is the mean particle radius and acm is the horizontal projec-
tion of the distance from the center of gravity of the rotat-
ing aggregate to the point of contact about which restructur-
ing occurs. The analysis of several temporally resolved restruc-
turing events yielded a mean critical rolling friction force of
FRoll,SiO2= (5.0 ± 2.5) × 10−10N for the coated SiO2particles,
,
(2)
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Figure 7: Examples of time resolved restructuring events of aggregates composed of micrometer-sized SiO2particles (a-d) or H2O ice particles (e-h). The restruc-
turing events were initiated by the addition of an impacting particle or cluster. The images were taken every 0.03s (a-d) and every 0.02s (e-h).
which was corrected to FRoll,SiO2= (3.7 ± 1.9) × 10−10N for a
comparison with the results for uncoated SiO2particles.
To test the capability of our experimental setup, we mea-
sured the critical rolling friction force of uncoated, monodis-
perse SiO2particles of a0 = 0.75µm, using the experimental
setup B (see Sect. 2) together with the procedure introduced by
Blum and Wurm (2000). In this case, the dust was dispersed by
a commercial dust-disperser and sprayed into the experimental
chamber. An analysis of the size distribution of the dispersed
dust showed that the dust is mostly dispersed into single grains
(∼ 75%) and into cluster of two particles (∼ 15%) as well as
of three particles (∼ 10%). Our measurements yielded a criti-
cal rolling friction force of FRoll,SiO2= (12.1 ± 3.6) × 10−10N,
which is relatively close (within one standard deviation) to the
quantity measured by Heim et al. (1999), but slightly further
away from the corrected value obtained by Blum and Wurm
(2000). Fig7a-dshowanexampleofatime-resolvedrestructur-
ing event of an aggregate composed of micrometer-sized SiO2
particles. A comparison of the different measured quantities is
given in Table 1. However, a better reproduction of the previ-
ously published values is not possible, due to the uncertainty of
the mass estimation of the restructuring particle chains, which
have occurred in this work as well as in the previous work con-
ducted by Blum and Wurm (2000). Nevertheless, the obtained
critical rolling friction force is in the expected range between
5 × 10−11N and 4 × 10−9N (Heim et al., 1999).
For comparison, the critical rolling friction force of the pro-
duced micrometer-sized ice particles was also investigated with
the same method. In total, 23 temporally resolved restructur-
ing events (see Fig.7e-h) of ice particles on the cold tar-
get were analyzed. The critical rolling friction force of the
ice particles was then calculated, taking a mean radius of
a0B = 1.45µm, a mean cross section of a single ice sphere
of S = (8.90 ± 0.24) × 10−12m2and a mean mass of m =
(2.65±0.13)×10−14kg of the ice particles into account. These
Figure 8: Normalized cumulative count of the critical rolling friction force
measured for micrometer-sized SiO2particles (dashed curve) as well as for
micrometer-sized ice particles (solid curve).
forces of FRoll,SiO2= (12.1 ± 3.6) × 10−10N and of FRoll,ice= (114.8 ± 23.8) ×
10−10N were measured for the micrometer-sized SiO2and ice particles, respec-
tively.
Mean critical rolling friction
values were derived from the cumulative size, cross section and
mass distributions of the ice particles. A critical rolling friction
force of FRoll,ice = (114.8 ± 23.8) × 10−10N was derived for
the ice particles, in which the uncertainty of the measurement
is given by the statistical error of the mean value. The tem-
perature of the cold target during the measurements was in the
range between 189K and 226K, which is relatively high, com-
pared to the temperature in molecular clouds or protoplanetary
discs. Therefore, future experiments should be carried out at
lower temperatures in order to estimate the temperature depen-
dence of the attractive bonding between micrometer-sized ice
particles.
5