Modern problems of the theory of macromolecular reactions in polymer blends

The main task of the theory of macromolecular reactions in polymer blends is to describe an evolution of the blend structure under the concerted action of the reaction and interdiffusion. For a polymeranalogous reaction proceeding with autoacceleration in a compatible blend, the task has been solved by methods of linear non-equilibrium thermodynamics. The set of reaction-diffusion equations derived permits to describe the blend structure in details, including the parameters characterizing compositional heterogeneity and units' distribution of the reacting chains in any local region of the blend. For incompatible blend of two homopolymers, the competition between a phase separation and the reaction of end-coupling with a formation of diblock-copolymer has been considered. The peculiarities of the processes mentioned as well as the actual problems in this field are discussed.     

Macromolecular reaction and interdiffusion in a compatible polymer blend, 2. The role of H‐bonding

A theory describing slow macromolecular reaction and interdiffusion in a compatible polymer blend is extended to consider H‐bonding. The known treatments of H‐bonding influence on the free energy of mixing and chains' mobilities are combined to calculate mutual diffusion coefficients in the framework of linear non‐equilibrium thermodynamics. Numerical calculations are performed for a blend of two random copolymers AC and BC to reveal the effect of H‐bonding (between A and B, B and B units) on the interdiffusion profiles. Then, the transformation of A units into B ones is included and the reaction‐diffusion equations are solved with the parameters corresponding to the blend of poly(tert‐butyl acrylate‐co‐styrene) with poly‐(acrylic acid‐co‐styrene) in which the thermal decomposition of tert‐butyl acrylate units takes place. The numerical calculations show that this system is suitable for the experimental verification of theoretical predictions concerning the interplay between macromolecular reaction and interdiffusion in polymer blends.     

A control of primary structure in the products of macromolecular reactions

Basing on the theory of macromolecular reactions, an influence of various factors on a units' distribution (UD) of the forming macromolecules is considered. In diluted solutions UD is determined by a competition between external reagent and intrachain interaction of reacted and unreacted units, first by neighbor effect. Should accelerating action of remote units is commensurable with that of nearest neighbors, such a conformational effect enlarges the formation of alternating sequences. In a melt, interchain effect shifts UD to a random one. In a polymer blend consisting of reacting and non-reacting but influencing the reactivity components, UD of transforming macromolecules is formed under concerted action of the reaction and interdiffusion. Thus modern achievements of the theory permit to analyze peculiarities of a wide set of reaction systems and facilitate a choice of optimal conditions for the preparation of tailor-made macromolecules.     

Interchain exchange and interdiffusion in blends of poly(ethylene terephthalate) and poly(ethylene naphthalate)

The interchain exchange and interdiffusion in blends of poly(ethylene terephthalate) and poly(ethylene naphthalene-2,6-dicarboxylate) are investigated with reprecipitated commercial samples (M _η ～ 10⁴) and samples containing no polycondensation catalyst (M _η ～ 10³) synthesized in the course of this study. The kinetics of multiblock copolymer formation and gradual reduction of the mean block length in quasi-homogeneous blends were shown to fit a simple theoretical model of a second-order reaction. The increase of the reaction-rate constants on the transition from commercial samples to synthesized ones revealed a significant role of chain ends in interchain exchange. The detected activation energy of the interchange in the absence of catalysts (97 kJ/mol) was noticeably less than that previously reported for the polymer pair under study (120–170 kJ/mol). The obtained data were applied for analysing the interdiffusion between melts of the same polymers accompanied by the interchain exchange. By means of the microinterference method, the interdiffusion in the synthesized samples was shown to be much faster than that in the reprecipitated commercial samples, a result that may be due to the better compatibility of the initial polyesters as their molecular mass decreased. In later stages of the process in both systems, the interpenetration of components was slower than that predicted by Fick’s law, owing to formation of copolymer species that diminished the thermodynamical factor of mixing.     

Interplay of chemical and physical factors in reacting polymer blends. Theoretical considerations

Various effects produced by copolymers in polymer blends are discussed, with an emphasis on the role of interchain interactions. Simple theoretical models are considered to study the following problems: the interplay of diffusion and macromolecular reaction in compatible and incompatible blends, the stabilizing effect of premade diblock copolymer on the system of minor phase particles in incompatible blends, the kinetics of transesterification in a homogeneous blend. The effect of diblock copolymer on the Ostwald ripening in a polymer blend is stated in more details; the possibility of narrowing the size distribution of minor phase particles is predicted.     

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.     

Light-scattering studies on phase separation in a binary blend with addition of diblock copolymers

Time-resolved light-scattering measurements have been conducted to investigate the influence of a diblock copolymer additive on the phase boundaries and the kinetics of the phase separation of a polymer blend. The blend studied was a polystyrene-d₈/polybutadiene (PSD/PB) mixture with a diblock copolymer composed of the same homopolymers. It was observed that the critical temperature of the blend, which has an upper critical solution temperature (UCST), decreased with increasing copolymer content and the kinetics of the phase separation via a spinodal decomposition mechanism slowed down in the presence of the copolymer. The features of the spinodal peak position and intensity as a function of time with and without copolymer additive were analyzed for near and off-critical compositions in various temperature jumps. The intermediate and late-stage growth rates do not follow a universal scaling function with the addition of diblock copolymers. © 1995 John Wiley & Sons, Inc.     

Macromolecular reaction and interdiffusion in a compatible polymer blend

A theory describing slow macromolecular reaction and interdiffuion in a compatible polymer blend is suggested based on the linear non-equilibrium thermodynamic principles. A simple model system is considered. In a blend consisting initially of homopolymers A and B, the transformation A → B proceeds with the B units accelerating the reaction. A system of diffusive-reaction equations for relevant macroscopic variables is derived. The randomness of the reacting chains' structure gives rise to a new interdiffusion mode in addition to the reacting polymer-homopolymer B interdiffusion. Numerical calculations reveal that the diffusive intermixing of reacting chains of different composition may significantly affect the reaction rate and the local compositional heterogeneity as well. It is possible to discriminate the fast- and the slow-mode theories of interdiffusion using reaction kinetics data. Under certain conditions, the reaction may proceed in a non-trivial autowave-like regime.     

Monte carlo simulation of copolymerization by ester interchange reaction in miscible polyester blends

The effects of reaction variables on the degree of randomness in copolymers formed by ester interchange reaction in miscible polyester melt blends were systematically investigated using a Monte Carlo method. Three reaction variables such as the molecular weight difference between two component polymers, the blend ratio, and the reaction ratio of end attack to bond flip, were particularly considered on the cubic lattice model. Ester interchange reactions were assumed to take place during reptational chain motions. It was found that the copolymerization was dependent upon the molecular weight difference and reaction ratio: As the molecular weight difference becomes smaller and when both end attack and bond flip reactions are involved simultaneously, the copolymerization is accelerated. However, the blend ratio does not affect the copolymerization process. This result is discussed in relation to the polymer chain conformation for the ester interchange reaction. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1637–1645, 1998     

Scaling tests of late stages of spinodal decomposition in PC/PMMA blends

Time-resolved light scattering studies were undertaken to elucidate the kinetics of phase separation in polycarbonate (PC)/polymethyl methacrylate (PMMA) blends. The 40:60 PC/PMMA blend undergoes thermally induced phase separation through spinodal decomposition. Temperature jump experiments were carried out from a single-phase to a two-phase temperature region. The general trend of spinodal decomposition in this blend system is nonlinear in character and obeys the power laws. The time evolution of scattering curves was analyzed in accordance with dynamical scaling laws for self-similarity and the shape of scaled structure functions.     

Formation and dissolution of phase-separated structures in ultrathin blend films

The phase separation of ultrathin polymer blend films of deuterated poly(styrene)/poly(vinylmethylether) leads to a variety of film morphologies, depending on polymer composition. Phase-separation measurements are made at a constant temperature difference from the critical temperature, leading to a bicontinuous spinodal decomposition pattern for near-critical blend compositions and to “mounds” and “holes” for PVME-rich and dPS-rich off-critical mixtures, respectively. Reverse temperature jumps of the phase-separated blend films into the one-phase region result in dissolution of the undulating surface patterns, confirming the phase-separation origin of the film patterns. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 191–200, 1998     

Does coarsening begin during the initial stages of spinodal decomposition?

The initial stages of spinodal decomposition were studied by subjecting a critical blend of model polyolefins to a pressure quench and monitoring the evolution by time-resolved small angle neutron scattering. Contrary to the predictions of the widely accepted Cahn-Hilliard-Cook theory, we demonstrate that coarsening of the phase-separated structure begins immediately after the quench and occurs throughout the initial stages of spinodal decomposition.     

The effect of copolymer composition on the dynamics of random copolymers in a homopolymer matrix

The effect of copolymer composition on the dynamics of random copolymers in a homopolymer matrix is studied using computer simulations within the framework of the bond-fluctuation model on blends containing low concentrations (10%) of A-B copolymers, where A and B are two different types of monomers, dispersed in a homopolymer matrix of chains with only A-type monomers. Four copolymer compositions were studied, phi(A)=0.33, phi(A)=0.5, phi(A)=0.66, and phi(A)=0.82, while maintaining a statistically random sequence distribution. For this study, we have only included intermolecular interactions between A and B monomers. Our results indicate, in agreement with experimental data, that copolymer composition has an impact on system dynamics. Analysis of the structure reveals that copolymers with majority A content are expanded in the homopolymer matrix, have fewer interchain copolymer-copolymer contacts, and are well dispersed in the homopolymer matrix. On the other hand, copolymers with lower A content form a more compact structure, have more interchain contacts, and form aggregates that are short lived. This in turn leads to slower system dynamics. Both the radius of gyration (Rg) and copolymer end-to-end vectors (Re) increase with increasing A content until phi(A)=0.66 and then decrease. Copolymers with lower A content form more compact structures as the repulsive interactions between unlike species are minimized by the copolymers folding back on themselves and forming aggregates of copolymer chains. Thus, these results provide insight into the variation of copolymer dynamics with composition in the system by documenting the correlation between the thermodynamics of this mixture, the conformation of a copolymer chain in a homopolymer matrix, and the dynamics of both components in this blend.     

Early Stages of Interchange Reactions in Polymer Blends

Summary: Simple models are studied for better understanding of the early stages of interchange reactions in polymer blends. For a homogeneous blend of homopolymers A and B, parameters of copolymer AB formed at the reaction beginning are explicitly calculated. It is shown that the analysis of the copolymer composition can help to establish the prevailing interchange mechanism. For a bilayer blend of immiscible homopolymers A and B, the reactive compatibilization through interchange is studied by continual Monte Carlo modeling. The analysis of the local distribution in block length shows that the interdiffusion of blend components may start only after the formation of rather short copolymer blocks in the course of interchange.     

Phase separation in poly(tert-butyl acrylate)/polyhedral oligomeric silsesquioxane (POSS) thin film blends

Phase separation in thin film blends of poly(tert-butyl acrylate) (PtBA) and a polyhedral oligomeric silsesquioxane (POSS), trisilanolphenyl-POSS (TPP), is studied as functions of annealing temperature and time, using reflected light optical microscopy, atomic force microscopy, and X-ray photoelectron spectroscopy. The results demonstrate that the PtBA/TPP blend system confined to thin films ( approximately 90 nm) exhibits lower critical solution temperature (LCST) behavior with a critical temperature of approximately 70 degrees C and a critical composition of 60 wt % PtBA with insignificant dewetting at the phase boundary. Off-critical spinodal behavior is observed for 58 and 62 wt % PtBA blend films. Phase separation by nucleation and growth is observed for all compositions outside the window between 58 and 62 wt % PtBA. The temporal evolution of spinodal decomposition in 60 wt % PtBA blend films is explored at annealing temperatures of 75, 85, 95, and 105 degrees C. The morphological evolution in 60 wt % PtBA blend films is similar for all experimental temperatures (75, 85, 95, and 105 degrees C) with the expected shorter time scales for phase evolution at higher annealing temperatures. Fast Fourier transforms of optical micrographs reveal that these blend films immediately undergo phase separation by spinodal decomposition during temperature jump experiments. Power law scaling for the characteristic wavevector with time (q approximately t(n) with n approximately -1/4 to -1/3) for domain growth during the early stages of phase separation yields to domain pinning at the later stages for 60 wt % PtBA blend films annealed at 75, 85, and 95 degrees C. In contrast, domain growth is pinned over the entire experimental time scale for 60 wt % PtBA blend films annealed at 105 degrees C.     

Scattering Function and Spinodal Transition of Linear and Nonlinear Block Copolymers Based on a Unified Molecular Model

This work uses a block copolymer architecture [(A'B)_n A_2]_m to unify the scattering function and spinodal transition of typical AB-type block copolymers. The key roles of block number, junction points and asymmetry ratios of block length are(1) to determine the form factor of each block copolymer at the molecular scale;(2) to affect the entropy loss across the spinodal transition and may result in deflection of spinodal curves. The common features are validated in typical linear and nonlinear block copolymers, including AB diblock, asymmetric A'BA triblock,miktoarm stars of AB_n, A_n B_n,(AB)_n,(A'B)_n A, A'BA_m, and multi-graft combs of(B_n A_2)m and [(A'B)_n A_2]_m. The explicit scattering functions and form factors of various block copolymers can be directly applied in radiation experiments(i.e. neutron or X-ray scattering) to unravel the effect of molecular architecture in solution and microphase separation in disordered melt. The molecular model used in this study is also helpful to guide the chemical synthesis to explore more potentially interesting block copolymers.     

Prediction of phase separation behaviour from thermodynamic measurements in the one phase region

When a polymer blend is heated to within the unstable region of the temperature - composition diagram spinodal decomposition may be observed using small angle neutron scattering. In the one phase region scattering has been used to obtain the temperature and composition dependence of the second derivative with respect to composition of the Gibbs free energy of mixing. Correlation of these two types of measurement not only tests the current theories of spinodal decomposition, but provides insight into the molecular parameters controlling domain morphology in phase separation blends.     

Effect of random and block copolymer additives on a homopolymer blend studied by small-angle neutron scattering

Small-angle neutron scattering (SANS) has been employed to study a blend of polystyrene and polybutadiene modified by copolymer additives. SANS data from the one-phase region approaching the phase boundary has been acquired for blends modified by random and diblock copolymers that have equal amounts of styrene and butadiene monomers as well as a random copolymer with an unequal monomer composition. The binary blend is near the critical composition, and the copolymer concentrations are low at 2.5% (w/w). The data have been fitted with the random-phase approximation model (binary and multicomponent versions) to obtain Flory–Huggins interaction parameters (χ) for the various monomer interactions. These results are considered in the context of previous light scattering data for the same blend systems. The SANS cloud points are in good agreement with previous results from light scattering. The shifts in the phase boundary are due to the effects of the additives on the χ parameter at the spinodal. All the additives appear to lower the χ parameter between the homopolymers; this is in conflict with the predicted Flory–Huggins behavior. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3191–3203, 2004     

Lamellar morphology induced by two-step surface-directed spinodal decomposition in binary polymer mixture films

A novel process for obtaining ordered morphology on the basis of two-step surface-directed spinodal decomposition is numerically investigated. The formation mechanism and evolution dynamics of this process are also discussed in detail. The calculated results of the chemical potential demonstrate that the equilibration state at the first quench affects the competition between the surface potential and the chemical potential in the bulk, leading to a surprising lamellar structure at the second further quench. It is also found that the lamella formation obeys the logarithmic growth. These results could provide a new approach for fabricating ordered structure of polymer materials and stimulate experimental studies based on this subject.     

Monte Carlo simulation of a polymer-analogous reaction in a polymer blend

The autocatalytic polymer-analogous reaction A → B in a blend composed of two contacting layers of compatible homopolymers A and B is studied by numerical simulation using the dynamic continuum Monte Carlo method. The evolution of the numerical density of units A and units initially belonged to the chains of homopolymer A is investigated in the course of the reaction and interdiffusion. Local characteristics of the distribution of the homopolymer with respect to its composition and blocks A and B with respect to their length are calculated at different times. The dispersions of the above distributions are appreciably higher than the corresponding dispersion of the Bernoullian copolymer of the same average composition, despite the random character of the reaction. This effect can be provided by changes in the composition of the blend on the scale of the reacting chain as well as by the diffusive mixing of the above chains. For the products of the polymer-analogous reaction, the broadening of the compositional distribution is predicted also by the theoretical model, which describes interdiffusion in the reacting system on scales that are markedly greater than the size of a polymer chain.