Characterization and Modeling of the SpinCasting of Polymer Nanocomposite Films S. Schwarz, J. Li, V

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Characterization and Modeling of the Spin-Casting
of Polymer Nanocomposite Films S. Schwarz, J.
Li, V. Shapovalov, M. Isakova, S. Schiffman, S.
Bhupinder, D. Kapoor, M. Rafailovich, and J.
Sokolov Queens College Department of Physics,
Flushing, NY, and SUNY Dept. of Materials
Science, Stony Brook, NY
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Spin-cast film thicknesses depend on the
evaporation rate (drying) and viscosity
(spreading). The evaporation rate varies with
spin rate and concentration. The
viscosity varies with shear rate and
concentration. Cloisite 6A exfoliates in the
spin-casting process, but induces a strong radial
dependence of film thickness. We employ an ARES
rheometer in the cone-plate geometry to measure
viscosity at different clay concentrations for
various polymers. We employ mass loss
measurements for evaporation. A Dektak surface
profilometer measures the depth of a razor blade
scratch along its length. A simple numerical
model is used to fit the data.
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AFM topographic (left) and friction force (right)
images, and corresponding cross-section plot of
height variation, for a PS (690K) spin-cast film
(2500rpm, 30s, 0.4 mg/ml).
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Equivalent film thicknesses of spin-cast dPS
(690K, 2000rpm, 30s) films vs. concentration in
toluene, as determined by SIMS (for
concentrations less than 10 mg/ml) and by
ellipsometry (for the two highest
concentrations).
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A simple standard model of the spin casting
process suggests that film thickness h depends on
density ?, spin rate ?, viscosity ?, and
evaporation rate ê, according to
?h/?t (2/3) (??2h3/?) ê.
The dependence of viscosity, evaporation rate,
and density on the concentrations of PS and clay
must be determined in order to employ this model.
After each time iteration, a new concentration
is calculated, and the corresponding viscosity
and evaporation rate are employed.
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EXPERIMENT AND RESULTS The viscosities of PS/clay
solutions in toluene were determined in the
cone-plate geometry on an ARES rheometer, at room
temperature in air. The cone-plate fixture was
machined with a lip to prevent leakage and
evaporation, and was calibrated to a glycerol
standard. Viscosities were measured over a range
of shear rates, and are shown below for a shear
rate of 100/s, corresponding to a typical value
in spin cast films.
Viscosities of PS (180K) in toluene vs. clay/PS
weight fraction at a shear rate of 100/s.
Numbers in inset indicate mg of PS added to 1 ml
toluene.
Viscosities vs. shear rate for 480 mg PS in 1 ml
toluene with 0 mg or 40 mg clay added. Repeated
measurements completed after the times shown in
the inset indicate the effect of evaporation
during the measurement.
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Evaporation rates were measured in still air, and
correspond closely to the evaporation rate of
pure toluene when the concentration of PS/clay is
low. When evaporation ceases at high
concentrations, remnant toluene is trapped in the
gel, The evaporation rate during the spinning
process is substantially increased, and is known
to vary in proportion to the square root of the
spin rate ?. In the model, the evaporation rate
is accelerated by the factor (? /?o)1/2, where
the constant ?o has been determined to be 4 rpm
from the literature for the solvent ethanol.
Evaporation rate determined by weight loss in
still air for PS (280K) in toluene with weight
fractions () of clay shown in the inset. The
model fit is proportional to V2/3, where V is the
volume fraction of free toluene.
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Empirical fits to the viscosity and evaporation
rate data are employed in the computer model.
Data from the aforementioned Shapovalov reference
for thickness vs. concentration and molecular
weight (spin times of 30 s at 2000 rpm)are fit,
where the known Mark-Houwink parameter is
employed to describe the expected variation of
viscosity with molecular weight. The model
yields reasonable fits as shown here
PS/toluene with molecular weights listed in the
inset is spin cast for 30 s at 2000 rpm. The
computer model, employing the viscosity and
evaporation rate data provides a good description
of MW and concentration dependence.
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Thickness data for spin cast films containing
clay is shown below. The time dependence data
indicates that the evaporation rate has been
significantly reduced, possibly due to crust
formation. Thus the model predictions of
thickness are poor for high clay concentrations.
Improved fits are obtained by reducing the
evaporation rate, however, as evidenced below,
the low shear rates also require modification of
the viscosity formula used in the model
Time dependence of spin cast film thickness 60
mg/ml PS. The weight of added clay (mg) and spin
rate (rpm) are shown in the inset
Thickness vs. spin rate for PS (280K, 60 mg/ml),
with clay weight in mg shown in the inset, and
with fits for 0 mg and 40 mg clay shown.
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At high clay concentrations, the low shear rates
affect viscosity, and the model must be modified
to account for the dependence of viscosity on
radial distance and shear rate according to the
following formulas from the standard model
?h/?t (1/3) (??2/ ? r) ( ?(r2h3) /?r ) ê. ? ?
/?t ?rh?2/ ? (at Si surface)
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The figure below demonstrates a very strong
dependence of film thickness on distance from the
spin axis. The model must be modified to allow
evaporation to continue after rotation ceases,
and predicts a weaker dependence. The
discrepancy may well be due to the fact that the
viscosity falls as the clays platelets align with
the silicon surface. The model does provide a
good prediction of the thickness at the center of
the sample.
Spin cast film thickness for PS (60 mg/ml), clay
(40 mg/ml), spin cast at 2000 rpm for 30 s, along
with the model prediction.
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smoothed exp. data 60 mg PS (280K) _ mg
Cloisite 6A 2000 rpm, 30 s
PMMA/ Cloisite/ Chlorobenzene 2000 rpm, 30 s
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Conclusions Addition of clay results in a strong
radial dependence of spin-cast film thickness
due to the dependence of viscosity on shear
rate. A simple numerical model provides a
reasonable description of the observed behavior,
but cannot account for crust formation, changing
platelet orientation, 3-D shear rate variations,
. . . Work continues on Cloisite vs. Laponite in
various polymers (PS, PMMA, PB).