127 research outputs found
On the chain length dependence of local correlations in polymer melts and a perturbation theory of symmetric polymer blends
The self-consistent field (SCF) theory of dense polymer liquids assumes that
short-range correlations are almost independent of how monomers are connected
into polymers. Some limits of this idea are explored in the context of a
perturbation theory for mixtures of structurally identical polymer species, A
and B, in which the AB pair interaction differs slightly from the AA and BB
interaction, and the difference is controlled by a parameter alpha Expanding
the free energy to O(\alpha) yields an excess free energy of the form alpha
, in both lattice and continuum models, where z(N) is a
measure of the number of inter-molecular near neighbors of each monomer in a
one-component liquid. This quantity decreases slightly with increasing N
because the self-concentration of monomers from the same chain is slightly
higher for longer chains, creating a deeper correlation hole for longer chains.
We analyze the resulting -dependence, and predict that , where is an invariant degree of
polymerization, and . This and other predictions are
confirmed by comparison to simulations. We also propose a way to estimate the
effective interaction parameter appropriate for comparisons of simulation data
to SCF theory and to coarse-grained theories of corrections to SCF theory,
which is based on an extrapolation of coefficients in this perturbation theory
to the limit . We show that a renormalized one-loop theory
contains a quantitatively correct description of the -dependence of local
structure studied here.Comment: submitted to J. Chem. Phy
Extended Capillary Waves and the Negative Rigidity Coefficient in the d=2 SOS model
The solid-on-solid (SOS) model of an interface separating two phases is
exactly soluble in two dimensions (d=2) when the interface becomes a
one-dimensional string. The exact solution in terms of the transfer matrix is
recalled and the density-density correlation function
together with its projections, is computed. It is demonstrated that the shape
fluctuations follow the (extended) capillary-wave theory expression
for sufficiently small wave vectors .
We find {\it negative}, . At there is a strong
nearest-neighbor peak. Both these results confirm the earlier findings as
established in simulations in d=3 and in continuous space, but now in an
exactly soluble lattice model.Comment: file.tex plus 4 (four) figures in Postscrip
Plasticization and antiplasticization of polymer melts diluted by low molar mass species
An analysis of glass formation for polymer melts that are diluted by
structured molecular additives is derived by using the generalized entropy
theory, which involves a combination of the Adam-Gibbs model and the direct
computation of the configurational entropy based on a lattice model of polymer
melts that includes monomer structural effects. Antiplasticization is
accompanied by a "toughening" of the glass mixture relative to the pure
polymer, and this effect is found to occur when the diluents are small species
with strongly attractive interactions with the polymer matrix. Plasticization
leads to a decreased glass transition temperature T_g and a "softening" of the
fragile host polymer in the glass state. Plasticization is prompted by small
additives with weakly attractive interactions with the polymer matrix. The
shifts in T_g of polystyrene diluted by fully flexible short oligomers are
evaluated from the computations, along with the relative changes in the
isothermal compressibility at T_g to characterize the extent to which the
additives act as antiplasticizers or plasticizers. The theory predicts that a
decreased fragility can accompany both antiplasticization and plasticization of
the glass by molecular additives. The general reduction in the T_g and
fragility of polymers by these molecular additives is rationalized by analyzing
the influence of the diluent's properties (cohesive energy, chain length, and
stiffness) on glass formation in diluted polymer melts. The description of
glass formation at fixed temperature that is induced upon change the fluid
composition directly implies the Angell equation for the structural relaxation
time as function of the polymer concentration, and the computed "zero mobility
concentration" scales linearly with the inverse polymerization index N.Comment: 12 pages, 15 figure
Hyperparallel tempering Monte Carlo simulation of polymeric systems
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Random, blocky and alternating ordering in supramolecular polymers of chemically bidisperse monomers
As a first step to understanding the role of molecular or chemical
polydispersity in self-assembly, we put forward a coarse-grained model that
describes the spontaneous formation of quasi-linear polymers in solutions
containing two self-assembling species. Our theoretical framework is based on a
two-component self-assembled Ising model in which the bidispersity is
parameterized in terms of the strengths of the binding free energies that
depend on the monomer species involved in the pairing interaction. Depending
upon the relative values of the binding free energies involved, different
morphologies of assemblies that include both components are formed, exhibiting
paramagnetic-, ferromagnetic- or anti ferromagnetic-like order,i.e., random,
blocky or alternating ordering of the two components in the assemblies.
Analyzing the model for the case of ferromagnetic ordering, which is of most
practical interest, we find that the transition from conditions of minimal
assembly to those characterized by strong polymerization can be described by a
critical concentration that depends on the concentration ratio of the two
species. Interestingly, the distribution of monomers in the assemblies is
different from that in the original distribution, i.e., the ratio of the
concentrations of the two components put into the system. The monomers with a
smaller binding free energy are more abundant in short assemblies and monomers
with a larger binding affinity are more abundant in longer assemblies. Under
certain conditions the two components congregate into separate supramolecular
polymeric species and in that sense phase separate. We find strong deviations
from the expected growth law for supramolecular polymers even for modest
amounts of a second component, provided it is chemically sufficiently distinct
from the main one.Comment: Submitted to Macromolecules, 6 figures. arXiv admin note: substantial
text overlap with arXiv:1111.176
Effective Soft-Core Potentials and Mesoscopic Simulations of Binary Polymer Mixtures
Mesoscopic molecular dynamics simulations are used to determine the large
scale structure of several binary polymer mixtures of various chemical
architecture, concentration, and thermodynamic conditions. By implementing an
analytical formalism, which is based on the solution to the Ornstein-Zernike
equation, each polymer chain is mapped onto the level of a single soft colloid.
From the appropriate closure relation, the effective, soft-core potential
between coarse-grained units is obtained and used as input to our mesoscale
simulations. The potential derived in this manner is analytical and explicitly
parameter dependent, making it general and transferable to numerous systems of
interest. From computer simulations performed under various thermodynamic
conditions the structure of the polymer mixture, through pair correlation
functions, is determined over the entire miscible region of the phase diagram.
In the athermal regime mesoscale simulations exhibit quantitative agreement
with united atom simulations. Furthermore, they also provide information at
larger scales than can be attained by united atom simulations and in the
thermal regime approaching the phase transition.Comment: 19 pages, 11 figures, 3 table
Intrinsic profiles and capillary waves at homopolymer interfaces: a Monte Carlo study
A popular concept which describes the structure of polymer interfaces by
``intrinsic profiles'' centered around a two dimensional surface, the ``local
interface position'', is tested by extensive Monte Carlo simulations of
interfaces between demixed homopolymer phases in symmetric binary (AB)
homopolymer blends, using the bond fluctuation model. The simulations are done
in an LxLxD geometry. The interface is forced to run parallel to the LxL planes
by imposing periodic boundary conditions in these directions and fixed boundary
conditions in the D direction, with one side favoring A and the other side
favoring B. Intrinsic profiles are calculated as a function of the ``coarse
graining length'' B by splitting the system into columns of size BxBxD and
averaging in each column over profiles relative to the local interface
position. The results are compared to predictions of the self-consistent field
theory. It is shown that the coarse graining length can be chosen such that the
interfacial width matches that of the self-consistent field profiles, and that
for this choice of B the ``intrinsic'' profiles compare well with the
theoretical predictions.Comment: to appear in Phys. Rev.
Self-assembly of artificial microtubules
Understanding the complex self-assembly of biomacromolecules is a major
outstanding question. Microtubules are one example of a biopolymer that
possesses characteristics quite distinct from standard synthetic polymers that
are derived from its hierarchical structure. In order to understand how to
design and build artificial polymers that possess features similar to those of
microtubules, we have initially studied the self-assembly of model monomers
into a tubule geometry. Our model monomer has a wedge shape with lateral and
vertical binding sites that are designed to form tubules. We used molecular
dynamics simulations to study the assembly process for a range of binding site
interaction strengths. In addition to determining the optimal regime for
obtaining tubules, we have calculated a diagram of the structures that form
over a wide range of interaction strengths. Unexpectedly, we find that the
helical tubules form, even though the monomer geometry is designed for
nonhelical tubules. We present the detailed dynamics of the tubule
self-assembly process and show that the interaction strengths must be in a
limited range to allow rearrangement within clusters. We extended previous
theoretical methods to treat our system and to calculate the boundaries between
different structures in the diagram.Comment: 15 pages, 11 figure
The kinetic fragility of liquids as manifestation of the elastic softening
We show that the fragility , the steepness of the viscosity and relaxation
time close to the vitrification, increases with the degree of elastic
softening, i.e. the decrease of the elastic modulus with increasing
temperature, in universal way. This provides a novel connection between the
thermodynamics, via the modulus, and the kinetics. The finding is evidenced by
numerical simulations and comparison with the experimental data of glassformers
with widely different fragilities (), leading to a
fragility-independent elastic master curve extending over eighteen decades in
viscosity and relaxation time. The master curve is accounted for by a cavity
model pointing out the roles of both the available free volume and the cage
softness. A major implication of our findings is that ultraslow relaxations,
hardly characterised experimentally, become predictable by linear elasticity.
As an example, the viscosity of supercooled silica is derived over about
fifteen decades with no adjustable parameters.Comment: 7 pages, 6 figures; Added new results, improved the theoretical
sectio
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