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 $z(N)\phi_{A}\phi_{B}$, 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 $N$-dependence, and predict that $z(N) = z^{\infty}[1 + \beta \bar{N}^{-1/2}]$, where $\bar{N}$ is an invariant degree of polymerization, and $\beta=(6/\pi)^{3/2}$. 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 $N \to \infty$. We show that a renormalized one-loop theory contains a quantitatively correct description of the $N$-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 $H(z_1,z_2;\Delta x)$ together with its projections, is computed. It is demonstrated that the shape fluctuations follow the (extended) capillary-wave theory expression $S(q)=kT/(D+\gamma q^2 +\kappa q^4)$ for sufficiently small wave vectors $q$. We find $\kappa$ {\it negative}, $\kappa <0$ . At $q=2\pi$ 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 $m$, 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 ($33 \le m \le 115$), 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