Statistical thermodynamics of polymer crystallization

A survey was made on the recent development of the mean-field lattice theory of polymer solutions to predict the properties of equilibrium melting points of bulk polymers. The interaction parameters were identified for several real polymers.     

Simulation of heterogeneous end-coupling reactions in polydisperse polymer blends

The influence of polydispersity on the interfacial kinetics of end-coupling and microstructure formation in the melt of immiscible polymers was studied using dissipative particle dynamics simulations. The irreversible reaction started at a flat interface between two layers, each of which contained polymer chains of two different lengths with functionalized or unreactive end groups. As in the case of fully functionalized monodisperse reactants [A. V. Berezkin and Y. V. Kudryavtsev, Macromolecules 44, 112 (2011)], four kinetic regimes were observed: linear (mean field coupling at the initial interface), saturation (decreasing the reaction rate due to the copolymer brush formation or reactant depletion near the interface), autocatalytic (loss of the initial interface stability and formation of a lamellar microstructure), and terminal (microstructure ripening under diffusion control). The interfacial instability is caused by overcrowding the interface with the reaction product, and it can be kinetically suppressed by increasing chain length of the reactants. Main effects of polydispersity are as follows: (i) the overall end-coupling rate is dominated by the shortest reactive chains; (ii) the copolymer concentration at the interface causing its instability can be not the same as in the lamellas formed afterwards; (iii) mean length of the copolymer product considerably changes with conversion passing through a minimum when a microstructure is just formed.     

Statistical thermodynamics of polymer crystal and melt

A crystalline-state theory recently developed by Midha and Nanda is commented on and applied to the isobars of polyethylene, poly(vinylidene fluoride), and poly(chlorotrifluoroethylene) at atmospheric pressure, and to an isotherm of polyethylene. Satisfactory agreement with experiment results. This includes the volume change at the melting point T_m and the volume difference ΔV between crystal and melt below T_m, when crystal and the earlier liquid-state theory are combined. A similar agreement is noted with respect to the results at high pressure. The scaling parameters obtained indicate the approximate role of melt temperature and volume as reducing quantities. An inverse proportionality between T_m and α_l, the expansivity of the melt at T_m, derived much earlier for low-molecular-weight solids, is recovered with an identical numerical coefficient. The thermodynamic functions of polyethylene are investigated in both phases. For this purpose contributions of internal harmonic modes are considered within the framework of the equivalent s-mer model. One or, at most, two average frequencies are adequate to represent the temperature dependence of the excess free energy and entropy over the value at absolute zero, when the external contributions are included for the crystal. A similar representation of the hard modes can be adopted for the melt. However, the free energy of segmental disorientation computed either from a constant entropy for the s-mer or a rotational isomeric state model for the isolated chain does not appear to be an adequate representation over a sufficient temperature range. An additional temperature-dependent term in the entropy and free energy is introduced and tentatively attributed to a volume- and temperature-dependent short-range ordering. Good agreement with experiment, including the entropy and temperature of fusion, ensues.     

Reaction-induced phase separation of pseudo-interpenetrating polymer networks in polydisperse polymer blends: a simulation study

We develop a minimal model for the process of reaction-induced phase separation in a polydisperse polymer blend. During the reaction, one component undergoes polymerization, leading to phase separation via spinodal decomposition. The effect that changing the final degree of polymerization has on the phase-separation process is studied. Finally an elastic energy term is included mimicking the cross-linking process and the generation of a semi-interpenetrating polymer network. We show that the scaling of the dominant lengthscale with time varies according to the reaction conditions.     

Statistical thermodynamics evaluation of polymer–polymer miscibility

The Simha and Somcynsky (S–S) statistical thermodynamics theory was used to compute the solubility parameters as a function of temperature and pressure [δ = δ(T, P)], for a series of polymer melts. The characteristic scaling parameters required for this task, P*, T*, and V*, were extracted from the pressure–temperature–volume (PVT) data. To determine the potential polymer–polymer miscibility, the dependence of δ versus T (at ambient pressure) was computed for 17 polymers. Close proximity of the δ versus T curves for four miscible polymer pairs: PPE/PS, PS/PVME, and PC/PMMA signaled the usefulness of this approach. It is noteworthy, that the tabulated solubility parameters (derived from the solution data under ambient conditions) propounded the immiscibility of the PVC/PVAc pair. The computed values of δ also suggested miscibility for polymer pairs of unknown miscibility, namely PPE/PVC, PPE/PVAc, and PET/PSF. In recognizing the limitations of the solubility parameter approach (the omission of several thermodynamic contributions), these preliminary results are auspicious because they indicate a new route for estimating the miscibility of any polymeric material at a given temperature and pressure. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2909–2915, 2004     

Depletion interaction mediated by a polydisperse polymer studied with total internal reflection microscopy

Total internal reflection microscopy (TIRM) was applied to measure depletion forces between a charged colloidal sphere and a charged solid wall induced by dextran, a nonionic nonadsorbing polydisperse polysaccharide. The polymer size polydispersity is shown to greatly influence the depletion potential. Using the theory for the depletion interaction due to ideal polydisperse polymer chains, we could accurately describe the experimental data with a single adjustable parameter.     

Nematic-isotropic phase behaviours of polydisperse polymer/liquid crystal systems: Applicability of continuous thermodynamics

Phase behaviours of polydisperse polystyrene (PS)/nematic liquid crystals (LCs) P-ethoxy-benzylidene-p-n-butylaniline (EBBA) are investigated by thermo-optical analysis (TOA) technique. In this study, to describe nematic-isotropic transition of the polydisperse PS/EBBA systems, a continuous distribution function to obtain the composition of polydisperse polymers is considered precisely. We apply these molar mass distributions to the extended Flory–Huggins model. The proposed semi-empirical model gives a remarkable agreement with experimental data for the model systems.     

Determination of pair interaction parameters for multicomponent polymer blends

Pair interaction parameters for multicomponent polymer blends were found to be determined by analyzing the sorption isotherms of common solvent.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2494–2496, November, 2004.     

Theory of polydisperse reacting polymer systems

The kinetics of irreversible reactions between polymer chains of different molecular weights are studied, with emphasis on the case of highly reactive end groups. We calculate the rate constant k(N, M) for reaction between chains of lengths N and M respectively, in dilute and semi-dilute solutions and in the melt. In all cases, k(N, M) is dominated by the shortest chain: the limit k(N) ≡ k(N, ∞) is well-defined and scales as if both chains were of length N. In dilute solutions k(N, M) obeys mean field theory, being proportional to the equilibrium reactive group contact probability. For melts and concentrated solutions, k(N, M) follows diffusion-controlled laws: k(N, M) ≈ (R/τ_N)ƒ(M/N) where R_N and τ_N are the coil size and relaxation time of the shortest chain N, and ƒ(M/N) is a cross-over function describing the approach to the asymptotic form k(N) for M/N ≫ 1. We calculate the leading contributions to this cross-over function, which has universal forms depending on the concentration regime. The implications of these results for high-conversion free-radical polymerization are discussed.     

Role of crystal-amorphous interaction in phase equilibria of crystal-amorphous polymer blends

A self-consistent theory has been developed for determination of phase diagrams of a crystalline polymer solution. Although the original Flory diluent theory captures the liquidus line, the theory is incapable of accounting for the solidus line due to the inherent assumption of complete immiscibility of solvent in the solid crystal. The present theory considers all possible interactions involving amorphous-amorphous and crystal-amorphous interactions. The self-consistent solutions predict various phase diagrams involving liquid-liquid, pure solid, and liquid-solid coexistence regions bound by liquidus and solidus lines. In the limit of complete insolubility of solvent in neat solid crystal, the original Flory diluent theory is recovered.     

Crystallization and structure formation in polymer blends with strong intermodular interactions: blends of poly(ethylene oxide) and styrene-hydroxystyrene copolymers

Time-resolved synchrotron wide- and small-angle X-ray scattering experiments were used to investigate crystallization behavior and microstructure development of a nearly monodisperse poly(ethylene oxide) [PEO] (M_w = 53,500), and its melt-miscible blends with two fractionated styrene - hydroxystyrene random copolymers [SHS]. PEO crystallization rates decrease significantly in the presence of the melt-miscible SHS copolymers. All low and high molecular weight SHS blends exhibit a crystallization process at relatively short times characterized by large Avrami exponents (n), followed by a dominant process with n near that of neat PEO. A model for the crystallization of these blends is proposed.     

Scanning electron microscopy methods for studying interfacial interaction in polymer blends

The scanning electron microscopy method in combination with the selective etching technique for polymer blends have been used to evaluate interfacial interaction in natural rubber and low density polyethylene blends. The morphology of the polymer blends, studied under externally applied strain, has been investigated to understand the role of interface adhesion between natural rubber and polyethylene phases, for two separate crosslinking systems, i.e. sulphur and peroxide.

Externally induced strain which facilitates phase separation in sulphur cured blends by initiating cracks at the interface; peroxide curing prevents separating out of the polyethylene phase from the natural rubber matrix. In the latter case, induced stress is distributed predominantly by developing fine flaw paths in the rubber matrix.

The method which has been developed for natural rubber and polyethylene blend systems may be used to evaluate the degree of interfacial adhesion between the dispersed phase and the dispersion medium for other kinds of polymer-polymer, polymer-filler as well as polymer-fibre composites.     

Statistical thermodynamics in the framework of the lattice fluid model, 2. Binary mixture of polydisperse polymers of special distribution

In this paper, the Gibbs free energy, the equation of state and the chemical potentials of polydisperse multicomponent polymer mixtures are derived. For general binary mixtures of polydisperse polymers, we also give the Gibbs free energy, the equation of state and the chemical potentials and derive the stability criteria and spinodal. Furthermore, binary polydisperse polymer mixtures of special distribution, i.e., Flory distribution, uniform distribution and Schulz distribution, are discussed and the influence of polydispersity on the interaction energy parameter is considered. For these special-distribution systems, the spinodal curves are simulated and the influence of chain length and polydispersity on the spinodal curves is discussed. The results suggest that the spinodal temperature of the mixture with a given volume fraction of one component decreases with increasing polydispersity and the extent of the shift decreases with increasing degree of polymerization when η = M̄_w/M̄_n is given. In addition, the variations of the spinodal curves with polydispersity and chain length are shown and they are qualitatively compared with the experimental results.     

Reactive polymer blends with thermoplastic polyurethan

The paper presents the concept of reactive coupling of thermoplastics and describes the technological preconditions and the present state of development. The examples of developments of blends of thermoplastic polyurethan (TPU), and polyethylene terephthalate (PET) serve to show that different mechanisms of reactive coupling of the blend components permit to produce high-quality blends.     

Depletion interaction mediated by polydisperse rods

The interaction between a colloidal hard sphere of radius R and a wall or between two spheres in a dilute suspension of infinitely thin rods of length L is calculated numerically. The method allows the study of depletion potentials for any value of LR and, consequently, the influence of rod length polydispersity can be investigated. It was observed that both the depth and the range of the potential increase drastically if the relative standard deviation sigma of the length distribution is larger than 0.25, while the potential is virtually indistinguishable from that caused by monodisperse rods, if sigma < or similar to 0.1.     

The Correlation between segment interaction parameter and interface width of polymer blends

The correlation between the segment interaction parameter and the interface width of incompatible polymer blends can be used to obtain information on the segment interaction of incompatible polymers via an accurate measurement of the narrow interface width by neutron reflectometry. Several model systems are discussed including polystyrene/poly(cyclohexyl acrylate-stat-n-butyl methacrylate), polystyrene/ poly (styrene- stat-p-bromo styrene) and poly styrene/poly(methyl methacrylate).