Density functional theory for nonuniform polymer melts: Based on the universality of the free energy density functional

A density functional theory is proposed for nonuniform freely jointed tangential hard sphere polymer melts in which the bonding interaction is treated on the basis of the properties of the Dirac δ-function, thus avoiding the use of the single chain simulation in the theory. The excess free energy is treated by making use of the universality of the free energy density functional and the Verlet-modified (VM) bridge function. To proceed numerically, one of the input parameters, the second-order direct correlation function of a uniform polymer melt is obtained by solving numerically the Polymer-RISM integral equation with the Percus-Yevick (PY) closure. The predictions of the present theory for the site density distribution, the partition coefficient and the adsorption isotherm, near a hard wall or between two hard walls are compared with computer simulation results and with those of previous theories. Comparison indicates that the present approach is more accurate than the previous integral equation theory and the most accurate Monte Carlo density functional theories. The predicted oscillations of the medium-induced force between two hard walls immersed in polymer melts are consistent with the experimental results available in the literature. Received 18 April 2000     

Modeling oxygen Ion transport of molten oxide membranes based on V<Subscript>2</Subscript>O<Subscript>5</Subscript>

A polymer model for oxygen ion transport in molten oxide membranes (MOM) based on V₂O₅ was developed. The model adapts Wagner’s theory for molten oxides and provides an interpretation of oxygen mobility in the oxide melts. Within the framework of this model, the values of oxygen permeation fluxes through the MOM were calculated and compared with experimental data. The calculated and experimental values are of the same order of magnitude which shows an adequacy of the model. A dynamic polymer chain concept is proposed. It is shown that the transference of oxygen ions in the oxide melts may occur by a mechanism of “connection–disconnection” of the polymer chains.     

Stress distributions in diblock copolymers

We demonstrate how a generalized self-consistent field theory for polymer melts that includes elastic stress and strain fields can be applied to the study of AB diblock copolymers melts. By obtaining the stress distributions for volume conserving strain loadings where lamellar and hexagonal morphologies are stable, we show that the local stress is reduced at the domain interface but slightly enhanced in the immediate vicinity of the interface. The overall stress profile is the result of the combined effects of chain connectivity across the interface, which yields a positive contribution, and the immiscible nature of the monomers, which leads to a stress reduction because of interfacial tension.     

Stress relaxation in entangled melts of unlinked ring polymers

Stress relaxation in unlinked ring polymer melts poses an important challenge to our theoretical understanding of entangled polymer dynamics. Recent experiments on entangled unlinked ring melts show power-law stress relaxation with no hint of a rubbery plateau, usually the hallmark of entangled polymers. Here we present a theory for stress relaxation in rings analogous to the successful approach for star polymers. We augment our theory with mesoscale Monte Carlo dynamics simulations of equivalent "lattice animal" configurations. We find a stress relaxation function G(t)～t(-α) with α≈1/2 consistent with experiment, emerging ultimately from the disparate relaxation times of more- and less-central portions of ring conformations.     

BSO晶体生长固/液边界层结构的实时观测研究

实时测量BSO晶体水平区熔法生长过程中,研究固/液边界层以及边界层两侧的晶体和熔体的显微拉曼光谱,晶体生长固/液边界层以及边界层两侧的熔体和晶体的结构特征, 生长基元结构从熔体结构经边界层过渡到晶体结构的变化过程。结果显示, BSO熔体中存在Bi₃O₄和[SiO₄]的键合结构; Bi₃O₄分子基团在固/液边界层聚合形成[BiO₇]八面体单体、多聚体,与[SiO₄]结构基团联结,在通过固／液边界层时进入格位。     

Generic van der Waals equation of state for polymers, modified free volume theory, and the self-diffusion coefficient of polymeric liquids

In this paper, a molecular theory of self-diffusion coefficient is developed for polymeric liquids (melts) on the basis of the integral equation theory for site-site pair correlation functions, the generic van der Waals equation of state, and the modified free volume theory of diffusion. The integral equations supply the pair correlation functions necessary for the generic van der Waals equation of state, which in turn makes it possible to calculate the self-diffusion coefficient on the basis of the modified free volume theory of diffusion. A random distribution is assumed for minimum free volumes for monomers along the chain in the melt. More specifically, a stretched exponential is taken for the distribution function. If the exponents of the distribution function for minimum free volumes for monomers are chosen suitably for linear polymer melts of N monomers, the N dependence of the self-diffusion coefficient is N⁻¹ for the small values of N, an exponent predicted by the Rouse theory, whereas in the range of 2.3?lnN?4.5 the N dependence smoothly crosses over to N⁻², which is reminiscent of the exponent by the reptation theory. However, for lnN?4.5 the N dependence of the self-diffusion coefficient differs from N⁻², but gives an N dependence, N^−2−δ(0<δ<1), consistent with experiment on polymer melts in the range. For polyethylene δ≈0.48 for the parameters chosen for the stretched exponential. Because the stretched exponential function contains undetermined parameters, the N dependence of diffusion becomes semiempirical, but once the parameters are chosen such that the N dependence of D can be successfully given for a polymer melt, the temperature dependence of the self-diffusion coefficient can be well predicted in comparison with experiment. The theory is satisfactorily tested against experimental and simulation data on the temperature dependence of D for polyethylene and polystyrene melts.     

Ring polymers in melts and solutions: scaling and crossover

We propose a simple mean-field theory for the structure of ring polymer melts. By combining the notion of topological volume fraction and a classical van der Waals theory of fluids, we take into account many-body effects of topological origin in dense systems. We predict that although the compact statistics with the Flory exponent ν=1/3 is realized for very long chains, most practical cases fall into the crossover regime with the apparent exponent ν?2/5 during which the system evolves toward a topological dense-packed limit.     

Structural relaxation and dynamic heterogeneity in a polymer melt at attractive surfaces

Molecular dynamics simulations of polymer melts at flat and structured surfaces reveal that, for the former, slow dynamics and increased dynamic heterogeneity for an adsorbed polymer is due to densification of the polymer in a surface layer, while, for the latter, the energy topography of the surface plays the dominant role in determining dynamics of interfacial polymer. The dramatic increase in structural relaxation time for polymer melts at the attractive structured surface is largely the result of dynamic heterogeneity induced by the surface and does not resemble dynamics of a bulk melt approaching T(g).     

A phase-field model for simulating various spherulite morphologies of semi-crystalline polymers

A modified phase-field model is proposed for simulating the isothermal crystallization of polymer melts. The model consists of a second-order phase-field equation and a heat conduction equation. It obtains its model parameters from the real material parameters and is easy to use with tolerable computational cost. Due to the use of a new free energy functional form, the model can reproduce various single crystal morphologies of polymer melts under quiescent conditions, including dendritic, lamellar branching, ring-banded, breakup of ring-banded, faceted hexagonal, and spherulitic structures. Simulation results of isotactic polystyrene crystals demonstrate that the present phase-field model has the ability to give qualitative predictions of polymer crystallization under isothermal and quiescent conditions.     

Effects of counterion fluctuations in a polyelectrolyte brush

We investigate the effect of counterion fluctuations in a single polyelectrolyte brush in the absence of added salt by systematically expanding the counterion free energy about Poisson-Boltzmann mean-field theory. We find that for strongly charged brushes, there is a collapse regime in which the brush height decreases with increasing charge on the polyelectrolyte chains. The transition to this collapsed regime is similar to the liquid-gas transition, which has a first-order line terminating at a critical point. We find that, for monovalent counterions, the transition is discontinuous in theta solvent, while for multivalent counterions, the transition is generally continuous. For collapsed brushes, the brush height is not independent of grafting density as it is for osmotic brushes, but scales linear with it.Received: 26 November 2003, Published online: 11 May 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.     

模耦合理论计算纳米粒子在聚合物熔体中的含时扩散系数与常规扩散常数 (cited: 2)

分析和计算了纳米粒子在聚合物熔体中的含时扩散系数与常规扩散常数. 采用广义朗之万方程描述扩散动力学,并通过模耦合理论计算摩擦记忆内核.为简单起见,只考虑了来自两体碰撞和溶剂密度涨落耦合作用两类微观因素对摩擦记忆内核的贡献. 采用聚合物参考作用点模型以及Percus-Yevick闭合条件计算了聚合物-纳米粒子复合溶液的平衡态结构信息函数;详尽分析了纳米粒子的尺寸与聚合物链的尺寸对扩散动力学的影响. 揭示了结构函数、摩擦记忆内核以及扩散系数等随着纳米粒子半径和聚合物链长的变化关系. 结果表明,对于小尺寸的纳米粒子或者短链的聚合物,短时间的非马尔可夫扩散 动力学特征比较显著,含时扩散系数需要更长的时间弛豫到常规扩散常数. 微观因素对扩散常数的贡献随着纳米粒子尺寸的增加而减小,却随着聚合物链长的增加而增大. 此外,模耦合理论得到的扩散常数与Stokes-Einstein关系的预测值进行比较,发现对于小尺寸的纳米粒子或者长链的聚合物,微观因素对扩散常数的的贡献占主导地位. 相反,当纳米粒子较大或者聚合物链长较短时,流体力学的贡献会发挥重要作用.     

Non-linear osmotic brush regime: Simulations and mean-field theory

We investigate polyelectrolyte brushes in the osmotic regime using both theoretical analysis and molecular dynamics simulation techniques. In the simulations at moderate Bjerrum length, we observe that the brush height varies weakly with grafting density, in contrast to the accepted scaling law, which predicts a brush thickness independent of the grafting density. We show that such behavior can be explained by considering lateral electrostatic effects (within the non-linear Poisson-Boltzmann theory) combined with the coupling between lateral and longitudinal degrees of freedom due to the conserved polymer volume (which are neglected in scaling arguments). We also take the non-linear elasticity of polyelectrolyte chains into consideration, which makes significant effects as chains are almost fully stretched in the osmotic regime. It is shown that all these factors lead to a non-monotonic behavior for the brush height as a function of the grafting density. At large grafting densities, the brush height increases with increasing the grafting density due to the volume constraint. At small grafting densities, we obtain a re-stretching of the chains for decreasing grafting density, which is caused by lateral electrostatic contributions and is controlled by the counterion-condensation process around polyelectrolyte chains. These results are obtained assuming all counterions to be trapped within the brush, which is valid for sufficiently long chains of large charge fraction.Received: 14 May 2003, Published online: 11 November 2003PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 36.20.-r Macromolecules and polymer molecules - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.     

On the dynamics and disentanglement in thin and two-dimensional polymer films

We present results from molecular dynamics simulations of strictly two-dimensional (2D) polymer melts and thin polymer films in a slit geometry of thickness of the order of the radius of gyration. We find that the dynamics of the 2D melt is qualitatively different from that of the films. The 2D monomer mean-square displacement shows a t^8/15 power law at intermediate times instead of the t^1/2 law expected from Rouse theory for nonentangled chains. In films of finite thickness, chain entanglements may occur. The impact of confinement on the entanglement length N_e has been analyzed by a primitive path analysis. The analysis reveals that N_e increases strongly with decreasing film thickness.     

Dynamical theory of polymer melt morphology

A general kinetic equation of the monomer density variables for polymer blends and block copolymer melts is obtained which describes slow morphology variations. The general theory is applied to a polymer blend adopting the biased reptation model of a polymer chain under mean field. We obtain an equation of motion of interfaces in a phase-separated polymer blend, which contains an interface reaction term for length scales shorter than l_c ≡ R²_G/ξ, where R_G is the gyration radius of a polymer chain and ξ the interfacial width. We also discuss some problems associated with the incompressibility requirement for phase separation kinetics of binary systems not limited to polymers. For length scales greater than l_c the interface dynamics involves diffusion in bulk pure phases even in the strong segregation limit in a way different from that for the usual time-dependent Ginzburg-Landau equation for the conserved order parameter. Implications of the existence of the new term on the late stage phase separation kinetics of polymer blend are discussed.A phenomenological model to study morphology dynamics not relying on the reptation model is also proposed.     

Spontaneous breakup of extended monodisperse polymer melts

We apply continuum mechanical based, numerical modeling to study the dynamics of extended monodisperse polymer melts during the relaxation. The computations are within the ideas of the microstructural "interchain pressure" theory. The computations show a delayed necking resulting in a rupture, as a result of small initial sample imperfections. These ruptures agree with experimental observations.     

Commentary on "Solid-like rheological response of non-entangled polymers in the molten state" by H. Mendil et al

We discuss the rheology experiments on classical and liquid crystal polymer melts by Mendil et al., in the light of the old and new piezorheometry experiments we have carried out on both types of melt. The mechanical behavior we have observed in the linear and non-linear regimes are independent of the melt studied (classical or liquid crystal), and of their nature (siloxane-type, acrylate-type and styrene-type). In the linear regime, the mechanical behavior of the melts presents two components: the first one is the conventional contribution. It is due to polymer chains, and is independent of sample thickness. The second one, which can be observed only when a strong interaction between the compound and the substrate exists, is associated with the glass transition. This component displays an elastic response depending on the sample thickness, and disappears at high temperature. It can be explained by assuming the presence of long-range density fluctuations, which are associated with the glass transition, and frozen at the frequencies used in the experiments. The experiments as a function of the applied strain show that the value of the elastic component decreases when the applied strain increases. This slipping transition occurs progressively, which highlights the heterogeneous nature of the anchoring. The results on the classical polymer by Mendil et al. can be considered to be consistent with ours. In contrast, their results on the liquid crystal polymer differ markedly from ours, showing that the elastic response of this sample has not the same origin.     

Arm retraction potential of branched polymers in the absence of dynamic dilution

We study the stress relaxation of model polymer networks containing low contents of star shaped and linear dangling polymers. As compared with their melts, the behavior of star and dangling polymers leads to a dynamic response with unprecedented large relaxation times. By comparing data of star melts with those corresponding to stars and dangling chains residing in polymer networks, we were able to identify the effects of dynamic dilution clearly. Since in polymer networks the dynamic dilution effect is suppressed, we were able by the first time to experimentally test the validity of the potential for arm retraction proposed by Pearson and Helfand.