Kinetics of phase separation in polymer mixtures: A molecular dynamics study

We present detailed results from a molecular dynamics (MD) simulation of phase-separation kinetics in polymer mixtures. Our MD simulations naturally incorporate hydrodynamic effects. We find that polymeric phase separation (with dynamically symmetric components) is in the same universality class as segregation of simple fluids: the degree of polymerization only slows down the segregation kinetics. For d = 2 polymeric fluids, the domain growth law is L(t) similar to t(phi) with phi showing a crossover from 1/3 -> 1/2 -> 2/3. For d = 3 polymeric fluids, we see the crossover phi = 1/3 -> 1. Our MD simulations do not yet access the inertial hydrodynamic regime (with L similar to t(2/3)) of phase separation in 3-d fluids. (C) 2014 AIP Publishing LLC.

Studies on coarsening of microdomains in binary polymer mixtures by Lattice Boltzmann methods

An improved free energy approach Lattice Boltzmann model(LBM) is proposed by introducing a forcing term instead of the pressure tensor. This model can reach the proper thermodynamic equilibrium after enough simulation time. On the basis of this model, the phase separation in binary polymer mixtures is studied by applying a Flory-Huggins-type free energy. The numerical results show good agreement with the analytic coexistence curve. This model can also be used to study the coarsening of microdomains in binary polymer mixtures at the early and intermediate stages.

What has brought on the effects of number-average molecular weight on the spinodals in polymer mixtures?

On the basis of the thermodynamics of Gibbs, the spinodal for the quasibinary system was derived in the framework of the Sanchez-Lacombe lattice fluid theory. All of the spinodals were calculated based on a model polydisperse polymer mixture, where each polymer contains three different molecular weight subcomponents. According to our calculations, the spinodal depends on both weight-average ((M) over bar (w)) and number-average ((M) over bar (n)) molecular weights, whereas that of the z-average molecular weight is invisible. Moreover, the extreme of the spinodal decreases when the polydispersity index (eta = (M) over bar (w)/(M) over bar (n)) of the polymer increases. The effect of polydispersity on the spinodal decreases when the molecular weight gets larger and can be negligible at a certain large molecular weight. It is well-known that the influence of polydispersity on the phase equilibrium (coexisting curve, cloud point curves) is much more pronounced than on the spinodal. The effect of M, on the spinodal is discussed as it results from the infuluence of composition temperatures, molecular weight, and the latter's distribution on free volume. An approximate expression, which is in the assumptions of v* v(1)* = v(2)* and 1/r --> 0 for both of the polymers, was also derived for simplification. It can be used in high molecular weight, although it failed to make visible the effect of number-average molecular weight on the spinodal.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMER MIXTURES

A statistical thermodynamics theory of polydisperse polymer blends based on a lattice model description of a fluid is formulated. Characterization of a binary polydisperse polymer mixture requires a knowledge of the pure polymer system and the interaction energy. It is assumed that the intrinsic and interactive properties of polymer (for example, T*, P*, rho*, and epsilon(ij)*) are independent of molecular size. Thermodynamic properties of ternary and higher order mixtures are completely defined in terms of the pure fluid polymer parameters and the binary interaction energies. Thermodynamic stability criteria for the phase transitions of a binary mixture are shown. The binodal and spinodal of general binary systems and of special binary systems are discussed.

DYNAMIC SCALING AND FRACTAL BEHAVIOR OF SPINODAL PHASE-SEPARATION IN POLYMER MIXTURES OF POLY(METHYL METHACRYLATE) WITH POLY(STYRENE-CO-ACRYLONITRILE)

Dynamic scaling and fractal behaviour of spinodal phase separation is studied in a binary polymer mixture of poly(methyl methacrylate) (PMMA) and poly(styrene-co-acrylonitrile) (SAN). In the later stages of spinodal phase separation, a simple dynamic scaling law was found for the scattering function S(q,t):S(q,t) approximately q(m)-3S approximately (q/q(m)). The possibility of using fractal theory to describe the complex morphology of spinodal phase separation is discussed. In phase separation, morphology exhibits strong self-similarity. The two-dimensional image obtained by optical microscopy can be analysed within the framework of fractal concepts. The results give a fractal dimension of 1.64. This implies that the fractal structure may be the reason for the dynamic scaling behaviour of the structure function.

Computer simulation of rod-coil block copolymers and tetrapod,polymer mixtures

In this thesis I present a new coarse-grained model suitable to investigate the phase behavior of rod-coil block copolymers on mesoscopic length scales. In this model the rods are represented by hard spherocylinders, whereas the coil block consists of interconnected beads. The interactions between the constituents are based on local densities. This facilitates an efficient Monte-Carlo sampling of the phase space. I verify the applicability of the model and the simulation approach by means of several examples. I treat pure rod systems and mixtures of rod and coil polymers. Then I append coils to the rods and investigate the role of the different model parameters. Furthermore, I compare different implementations of the model. I prove the capability of the rod-coil block copolymers in our model to exhibit typical micro-phase separated configurations as well as extraordinary phases, such as the wavy lamellar state, percolating structuresrnand clusters. Additionally, I demonstrate the metastability of the observed zigzag phase in our model. A central point of this thesis is the examination of the phase behavior of the rod-coil block copolymers in dependence of different chain lengths and interaction strengths between rods and coil. The observations of these studies are summarized in a phase diagram for rod-coil block copolymers. Furthermore, I validate a stabilization of the smectic phase with increasing coil fraction.rnIn the second part of this work I present a side project in which I derive a model permitting the simulation of tetrapods with and without grafted semiconducting block copolymers. The effect of these polymers is added in an implicit manner by effective interactions between the tetrapods. While the depletion interaction is described in an approximate manner within the Asakura-Oosawa model, the free energy penalty for the brush compression is calculated within the Alexander-de Gennes model. Recent experiments with CdSe tetrapods show that grafted tetrapods are clearly much better dispersed in the polymer matrix than bare tetrapods. My simulations confirm that bare tetrapods tend to aggregate in the matrix of excess polymers, while clustering is significantly reduced after grafting polymer chains to the tetrapods. Finally, I propose a possible extension enabling the simulation of a system with fluctuating volume and demonstrate its basic functionality. This study is originated in a cooperation with an experimental group with the goal to analyze the morphology of these systems in order to find the ideal morphology for hybrid solar cells.

A study of the mechanism of radiation-induced gelation in monomer-polymer mixtures : report for the period May 1, 1961 - October 31, 1962 /

"October 31, 1962."

A study of the mechanism of radiation-induced gelation in monomer-polymer mixtures : report for the period May 1, 1961 - October 31, 1963 /

"November 31, 1963."

Thermodynamical study on pressure-induced compatibility in UCST polymer-containing mixtures

The present calculations were performed on the basis of the Sanchez-Lacombe lattice fluid theory and the new combinatorial rules for block copolymer according to the experimental results on the pressure-induced compatibility in poly(ethylene oxide) (PEO) and poly(ethylene oxide-b-dimethylsiloxane) (P(EO-b-DMS)) mixtures with UCST behavior. The study on enthalpy, combinatorial entropy, vacancy entropy and Gibbs energy upon mixture shows that Sanchez-Lacombe fluid theory and the new combinatorial rules could describe the pressure-induced compatibility (PIC) of polymer mixtures with UCST behavior well.

Thermodynamics of phase behavior in PEO/P(EO-b-DMS) homopolymer and block co-oligomer mixtures under pressure

The cloud-point temperatures (T-cl's) of poly(ethylene oxide) (PEO) and poly(ethylene oxide)-block-polydimethylsiloxane (P(EO-b-DMS)) homopolymer and block-oligomer mixtures were determined by turbidity measurements over a range of temperatures (105 to 130degrees), pressures (1 to 800 bar), and compositions (10-40 wt.-% PEO). The system phase separates upon cooling and T-cl was found to decrease with an increase in pressure for a constant composition. In the absence of special effects, this finding indicates negative excess volumes. Special attention was paid to the demixing temperatures as a function of the pressure for the different polymer mixtures and the plots in the T-phi plane (where phi signifies volume fractions). The cloud-point curves of the polymer mixture under pressures were observed for different compositions. The Sanchez-Lacombe (SL) lattice fluid theory was used to calculate the spinodals, the binodals, the Flory-Huggins (FH) interaction parameter, the enthalphy of mixing, and the volume changes of mixing. The calculated results show that modified P(EO-b-DMS) scaling parameters with the new combining rules can describe the thermodynamics of the PEO/P(EO-b-DMS) system well with the SL theory.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMER BLENDS WITH STRONG INTERACTION

A statistical thermodynamics theory of polydisperse polymer mixtures with strong interaction between dissimilar components based on a lattice fluid model is formulated. Expressions for the free energy, equation of state, phase stability and spinodal for a polydisperse, binary polymer mixture with strong interaction are derived.

Phase behavior of mixtures of colloidal platelets and nonadsorbing polymers

The phase behavior of a model system of colloidal platelets and nonadsorbing polymers is studied using computer simulations and perturbation theory. The equation of state for the pure platelet reference system is obtained by Monte Carlo simulations, and the free volume fraction accessible to polymers is measured by a trial insertion method. The free volume fraction is also calculated using scaled particle theory. Subsequently, the phase diagram for platelet-polymer mixtures is calculated. For a platelet aspect ratio L/D=0.1 and a polymer to platelet size ratio d/D>0.2, we observe coexistence between two isotropic phases with different densities. For smaller polymers d/D

Mixtures of colloidal rods and spheres in bulk and in confinement

When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. Monte Carlo simulations were performed to study the phase diagram of such rod-polymer mixtures. The colloidal rods were modelled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while overlap of polymers and rods is forbidden. In this thesis the emphasis was on the depletion effects caused by the addition of spheres on the isotropic phase of rod-like particles. Although most of the present experimental studies consider systems close to or beyond the isotropic-nematic transition, the isotropic phase with depletion interactions turns out to be a not less interesting topic. First, the percolation problem was studied in canonical simulations of a system of hard rods and soft spheres, where the amount of depletant was kept low to prevent phase separation of the mixture. The lowering of the percolation threshold seen in experiment is confirmed to be due to the depletion interactions. The local changes in the structure of the fluid of rods, which were measured in the simulations, indicated that the depletion forces enhance local alignment and aggregation of the rods. Then, the phase diagram of isotropic-isotropic demixing of short spherocylinders was calculated using grand canonical ensemble simulations with successive umbrella sampling. Finite size scaling analysis allowed to estimate the location of the critical point. Also, estimates for the interfacial tension between the coexisting isotropic phases and analyses of its power-law behaviour on approach of the critical point are presented. The obtained phase diagram was compared to the predictions of the free volume theory. After an analysis of the bulk, the phase behaviour in confinement was studied. The critical point of gas-liquid demixing is shifted to higher concentrations of rods and smaller concentrations of spheres due to the formation of an orientationally ordered surface film. If the separation between the walls becomes very small, the critical point is shifted back to smaller concentrations of rods because the surface film breaks up. A method to calculate the contact angle of the liquid-gas interface with the wall is introduced and the wetting behaviour on the approach to the critical point is analysed.