Chemistry Reference
In-Depth Information
molecular interpretation of how such dispersed phases reinforce elasto-
mers. The approach taken enabled estimation of the effect of the excluded
volume of the filler particles on the network chains and on the elastic
properties of the networks. In the first step, distribution functions for the
end-to-end vectors of the chains were obtained by applying Monte Carlo
methods to rotational isomeric state representations of the chains.
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Conformations of chains that overlapped with any filler particle during
the simulation were rejected. The resulting perturbed distributions were
then used in the three-chain elasticity model
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to obtain the desired
stress-strain isotherms in elongation.
In one application, a filled PDMS network was modeled as a composite
of cross-linked polymer chains and spherical filler particles arranged on a
cubic lattice.
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The filler particles increase the non-Gaussian behavior of
the chains and increase the moduli. It is interesting to note that compos-
ites with such structural regularity have actually been produced
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and
mechanical properties have been reported.
387,
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In a subsequent study, the reinforcing particles were randomly dis-
tributed within the PDMS matrix.
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One effect of the filler was to in-
crease the end-to-end separation of the chains. These results on the
chain-length distributions are in agreement with some subsequent neu-
tron scattering experiments on silicate-filled PDMS.
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The polymers
contained silica particles that were surface treated to make them inert to
the polymer chains, as was implicitly assumed in the simulations. These
experimental results also indicated chain extension when the particles
were relatively small, and chain compression when they were relatively
large.
Two issues need to be addressed by simulations regarding the molecu-
lar origin of reinfocement: increases in modulus with loading and upturns
in the modulus with increasing deformation. Results are typically ex-
pressed as the reduced-nominal or engineering stress as a function of de-
formation. The area under such curves up to the rupture point then gives
the energy of rupture, which is the standard measure of the toughness of
a material.
42
The stress-strain isotherms in elongation
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from simulated
distributions showed substantial increases in modulus that increased
with increase in filler loading, as expected. Additional increases would be
expected by taking into account other mechanisms for reinforcement
such as physisorption, chemisorption, and so on.
Simulations have also been carried out on ellipsoidal particles such as
the polystyrene prolate and oblate ellipsoids. For example, oriented pro-
late particles
390
showed that the anisotropy causes the modulus in the lon-
gitudinal direction to be significantly higher in the transverse direction.
