97 research outputs found
Field-theoretical approach to a dense polymer with an ideal binary mixture of clustering centers
We propose a field-theoretical approach to a polymer system immersed in an
ideal mixture of clustering centers. The system contains several species of
these clustering centers with different functionality, each of which connects a
fixed number segments of the chain to each other. The field-theory is solved
using the saddle point approximation and evaluated for dense polymer melts
using the Random Phase Approximation. We find a short-ranged effective
inter-segment interaction with strength dependent on the average segment
density and discuss the structure factor within this approximation. We also
determine the fractions of linkers of the different functionalities.Comment: 27 pages, 9 figures, accepted on Phys. Rev.
Elasticity of highly cross-linked random networks
Starting from a microscopic model of randomly cross-linked particles with
quenched disorder, we calculate the Laudau-Wilson free energy S for arbitrary
cross-link densities. Considering pure shear deformations, S takes the form of
the elastic energy of an isotropic amorphous solid state, from which the shear
modulus can be identified. It is found to be an universal quantity, not
depending on any microscopic length-scales of the model.Comment: 6 pages, 5 figure
Strain-dependent localization, microscopic deformations, and macroscopic normal tensions in model polymer networks
We use molecular dynamics simulations to investigate the microscopic and
macroscopic response of model polymer networks to uniaxial elongations. By
studying networks with strands lengths ranging from to 200 we cover
the full crossover from cross-link to entanglement dominated behavior. Our
results support a recent version of the tube model which accounts for the
different strain dependence of chain localization due to chemical cross-links
and entanglements
Scaling of Entropic Shear Rigidity
The scaling of the shear modulus near the gelation/vulcanization transition
is explored heuristically and analytically. It is found that in a dense melt
the effective chains of the infinite cluster have sizes that scale sub-linearly
with their contour length. Consequently, each contributes k_B T to the
rigidity, which leads to a shear modulus exponent d\nu. In contrast, in phantom
elastic networks the scaling is linear in the contour length, yielding an
exponent identical to that of the random resistor network conductivity, as
predicted by de Gennes'. For non-dense systems, the exponent should cross over
to d\nu when the percolation length becomes much larger than the
density-fluctuation length.Comment: 4 pages, 2 eps figure
Goldstone fluctuations in the amorphous solid state
Goldstone modes in the amorphous solid state, resulting from the spontaneous
breaking of translational symmetry due to random localisation of particles, are
discussed. Starting from a microscopic model with quenched disorder, the broken
symmetry is identified to be that of relative translations of the replicas.
Goldstone excitations, corresponding to pure shear deformations, are
constructed from long wavelength distortions of the order parameter. The
elastic free energy is computed, and it is shown that Goldstone fluctuations
destroy localisation in two spatial dimensions, yielding a two-dimensional
amorphous solid state characterised by power-law correlations.Comment: 7 pages, 2 figure
Glassy states and microphase separation in cross-linked homopolymer blends
The physical properties of blends of distinct homopolymers, cross-linked
beyond the gelation point, are addressed via a Landau approach involving a pair
of coupled order-parameter fields: one describing vulcanisation, the other
describing local phase separation. Thermal concentration fluctuations, present
at the time of cross-linking, are frozen in by cross-linking, and the structure
of the resulting glassy fluctuations is analysed at the Gaussian level in
various regimes, determined by the relative values of certain physical
length-scales. The enhancement, due to gelation, of the stability of the blend
with respect to demixing is also analysed. Beyond the corresponding stability
limit, gelation prevents complete demixing, replacing it by microphase
separation, which occurs up to a length-scale set by the rigidity of the
network, as a simple variational scheme reveals.Comment: 7 pages, 6 figure
Solution of the local field equations for self-generated glasses
We present a self-consistent local approach to self generated glassiness
which is based on the concept of the dynamical mean field theory to many body
systems. Using a replica approach to self generated glassiness, we map the
problem onto an effective local problem which can be solved exactly. Applying
the approach to the Brazovskii-model, relevant to a large class of systems with
frustrated micro-phase separation, we are able to solve the self-consistent
local theory without using additional approximations. We demonstrate that a
glassy state found earlier in this model is generic and does not arise from the
use of perturbative approximations. In addition we demonstrate that the glassy
state depends strongly on the strength of the frustrated phase separation in
that model.Comment: 11 pages, 3 figure
Statistical mechanics of permanent random atomic and molecular networks: Structure and heterogeneity of the amorphous solid state
Under sufficient permanent random covalent bonding, a fluid of atoms or small
molecules is transformed into an amorphous solid network. Being amorphous,
local structural properties in such networks vary across the sample. A natural
order parameter, resulting from a statistical-mechanical approach, captures
information concerning this heterogeneity via a certain joint probability
distribution. This joint probability distribution describes the variations in
the positional and orientational localization of the particles, reflecting the
random environments experienced by them, as well as further information
characterizing the thermal motion of particles. A complete solution, valid in
the vicinity of the amorphous solidification transition, is constructed
essentially analytically for the amorphous solid order parameter, in the
context of the random network model and approach introduced by Goldbart and
Zippelius [Europhys. Lett. 27, 599 (1994)]. Knowledge of this order parameter
allows us to draw certain conclusions about the stucture and heterogeneity of
randomly covalently bonded atomic or molecular network solids in the vicinity
of the amorphous solidification transition. Inter alia, the positional aspects
of particle localization are established to have precisely the structure
obtained perviously in the context of vulcanized media, and results are found
for the analogue of the spin glass order parameter describing the orientational
freezing of the bonds between particles.Comment: 31 pages, 5 figure
‘‘Lozenge’’ contour plots in scattering from polymer networks
We present a consistent explanation for the appearance of “lozenge” shapes in contour plots of the two dimensional scattering intensity from stretched polymer networks. By explicitly averaging over quenched variables in a tube model, we show that lozenge patterns arise as a result of chain material that is not directly deformed by the stretch. We obtain excellent agreement with experimental data
Dynamical signatures of the vulcanization transition
Dynamical properties of vulcanized polymer networks are addressed via a
Rouse-type model that incorporates the effect of permanent random crosslinks.
The incoherent intermediate scattering function is computed in the sol and gel
phases, and at the vulcanization transition between them. At any nonzero
crosslink density within the sol phase Kohlrausch relaxation is found. The
critical point is signalled by divergence of the longest time-scale, and at
this point the scattering function decays algebraically, whereas within the gel
phase it acquires a time-persistent part identified with the gel fraction.Comment: 4 page
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