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.     

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.     

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.     

The influence of nanoparticle architecture on latex film formation and healing properties

We present a study of chain interdiffusion in films formed by specially architectured PBMA nanoparticles by Förster Resonance Energy Transfer – FRET. Polymer nanoparticles contained linear chains with narrower molecular weight distributions than other previous reports, allowing a more detailed study. Apparent fractions of mixing and diffusion coefficients, determined from the quantum efficiency of energy transfer, were used to characterize the interdiffusion mechanism in the different films. The resistance of the films to dissolution by a good solvent was finally correlated with the interdiffusion results, in order to get information about film healing. We concluded that whenever interdiffusion occurs between nanoparticles containing linear chains and fully cross-linked nanoparticles, healing becomes more effective in spite of showing slower interdiffusion. We also observed that particles with longer chains are more effective for film healing. Finally, we concluded that interdiffusion occurs both ways across interfaces in blends formed by particles swollen with linear chains of different molecular weights.     

Calculation and experimental verification of concentration profiles for selected species at the interphase generated by diffusion in polymer pairs

A method for calculating diffusion rates for individual species in concentrated regime is outlined. The effects of monomeric friction coefficient, Flory–Huggins thermodynamic interaction parameter, individual species molecular weights, local molecular weights distribution, and local T_g are precisely calculated. The method is used to calculate individual concentration profiles generated by diffusion of multicomponent polymer blends, and experimentally tested. Polystyrene with a bimodal molecular weight distribution is allowed to diffuse in a blend of polyphenylene oxide and polystyrene. Local physical properties change markedly along the interdiffusion path and, therefore, this is a demanding test for the proposed calculation method. The simulated concentration profiles are compared with results obtained by using two independent experimental techniques: Raman spectroscopy and dynamic mechanical analyzer (DMA). The total polystyrene (PS) concentration profiles, calculated using the proposed method, agree well with Raman spectroscopy results. Simulated DMA results—which are sensitive to the PS species molecular weight distribution—obtained using the concentration profiles, calculated for each PS molecular weight species agree well with the experimental DMA results. Calculations based on average molecular weights give incorrect results. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3097–3107, 1999     

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.     

Molecular dynamics simulations of a chemical reaction; conditions for local equilibrium in a temperature gradient

We have examined a simple chemical reaction in a temperature gradient; 2F <==> F2. A mechanical model was used, based on Stillinger and Weber's 2- and 3-body potentials. Equilibrium and non-equilibrium molecular dynamics simulations showed that the chemical reaction is in local thermodynamic as well as in local chemical equilibrium (delta(r)G = 0) in the supercritical fluid, for temperature gradients up to 10(12) K m(-1). The reaction is thus diffusion-controlled. The velocity distributions of both components were everywhere close to being Maxwellian. The peak distributions were shifted slightly up or down from the average velocity of all particles. The shift depended on the magnitude of the temperature gradient. The results support the assumption that the entropy production of the reacting mixture can be written as a product sum of fluxes and forces. The temperature gradient promotes interdiffusion of components in the stationary state, a small reaction rate and an accumulation of the molecule in the cold region and the atom in the hot region.     

PHASE INVERSION AND ITS MECHANICAL MODEL STUDIES FOR THE TWO-PHASE POLYMER BLEND SYSTEMS (Ⅱ)——DYNAMIC VISCOELASTIC RESPONSE

The dynamic viscoelastic response of the two-phase polymer blend systems shows the characteristics of the thermorheologically complex materials. In this paper theoretical equations for describing the dynamic viscoelastic response of such polymer blend systems have been established by means of the mechanical modeling technique. The dynamic viscoelastic response of the blend systems at any blend composition can be predicted theoretically by using the equations established, provided that the dynamic viscoelastic response of the two pure components and the mechanical model parameters are known in advance. Thus, we provide an effective method for studying the dynamic mechanical properties and the molecular relaxation characteristics of the two-phase polymer blend systems.     

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.     

A calorimetric study of normal high density and ultra-high molecular weight polyethylene blends

The melting and the crystallization of blends of ultra-high molecular weight polyethylene (UHMWPE) and polyethylene high density with normal molecular weight (NMWPE) are investigated by means of differential scanning calorimetry (DSC). Mixing the components at a temperature below the flow temperature of UHMWPE (215 °C) results in segregated melting and crystallization. The segregated melting and crystallization temperatures of both components do not depend on composition of the blend. The extreme enthalpy dependence on blend composition is explained in terms of mutual influence exhibited by the components with respect to each other. It is due to the inner stresses in nonflowing UHMWPE characterized with a lot of entangled tie molecules. Mixing the components above the flow temperature of UHMWPE results in only one peak of melting and crystallization respectively. Complete mixing and probably co-crystallization between the components takes place on mixing NMWPE with flowing UHMWPE.     

Influence of Competition Between Binary Pairwise Interactions on the Phase Behavior in Ternary Blends

There are three binary pairs in a ternary blend and competition exists among these pairwise interactions owing to the asymmetry of the interaction energies between these binary pairs, which will determine the overall phase behavior of the blend. The influence of molecular weight of the components on the asymmetry of the interactions was discussed based on a ternary copolymer blend poly(styrene-co-acrylonitile)/poly(styrene-comethylmethacrylate/poly(methyl methacrylate-co-acrylonitile) (SAN/SMMA/MAN). It has been demonstrated that the asymmetry of the interactions between different binary polymer pairs is driven not only by the difference of interaction parameters, i.e. the so-called Δξ effect, but also by the difference of chain length between different components in the mixture. If the two effects are coincident with each other, the asymmetry of the interactions will be intensified, promoting phase separation. On the other hand, the compatibility of the system may be improved remarkably as the two factors are in opposite directions. It implies that a miscible ternary blend may be available simply by exchanging the order of the molecular weight between the different components against the asymmetry direction caused by their corresponding interaction parameters, which is easier to do in many experimental conditions. © 1997 John Wiley & Sons, Ltd.     

Thermoplastic blend demixing by a high‐pressure,high‐temperature process

The analysis of a thermoplastic polymer blend requires a precise separation of the blend components, which is usually performed by selective solvent extraction. However, when the components are high‐molecular‐weight polymers, a complete separation is very difficult. The use of fluids in near critical and supercritical conditions becomes a promising alternative to reach a much more precise separation. In this work, a method to separate reactive and physical blends from high‐molecular‐weight commercial polymers is proposed. Polyethylene (PE)/polystyrene (PS) blends were separated into their components with n‐propane, n‐pentane, and n‐heptane at near critical and supercritical conditions. The selectivity of each solvent was experimentally studied over a wide range of temperatures for assessing the processing windows for the separation of pure components. The entire PE phase was solubilized by n‐pentane and n‐heptane at similar temperatures, whereas propane at supercritical conditions could not dissolve the fraction of high‐molecular‐weight PE. The influence of the blend morphology and composition on the efficiency of the polymer separation was studied. In reactive blends, the in situ copolymer formed was solubilized with the PE phase by chemical affinity. The method proposed for blend separation is easy, rapid, and selective and seems to be a promising tool for blend separation, particularly for reactive blends, for which the isolation of the copolymer is essential for characterization © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2361–2369, 2005     

聚合物熔体界面分子链扩散的流变学研究

以2种完全相容的多分散的聚合物树脂为研究对象,利用动态流变学手段实现了界面分子链扩散过程的实时检测.研究结果发现,完全相容的聚合物树脂之间的扩散动力学参数α具有相对分子质量差异的依赖性,两者之间相对分子质量差异越大,α值越大.通过流变学参数还可获得另一扩散动力学参数—特征时间tc,从而得以计算出组分之间扩散系数,研究结果表明所获得的扩散系数具有频率依赖性.     

Viscoelastic properties of blends of “entangled” polymers

The effect of molecular weight distribution on the viscoelastic properties of “entangled” polymers has been examined with blends of narrowly distributed polystyrene and broadly distributed polydimethylsiloxane. It is shown that blending laws established for nonentangled polymers do not apply to high molecular weight systems. The steady-state shear compliance of a blend is examined as a function of its molecular weight and the molecular weight of its components, and an approximation is given for the longtime viscoelastic response of entangled blends.     

Molecular basis of healing and fracture at polymer interfaces

The interdiffusion of polymer chains across a polymer–polymer interface, and subsequent fracture to re-create the interface is reviewed. In particular, films formed via latex coalescence provide a very large surface area. Of course, latex film formation is a very important practical problem. Healing of the interface by interdiffusion is treated using the de Gennes reptation theory and the Wool minor chain reptation model. The self-diffusion coefficients of polystyrene and the polymethacrylates obtained by small-angle neutron scattering, SANS, direct non-radiative energy transfer, DET, and other techniques are compared. Reduced to 150,000 g/mol and 135°C, both polystyrene and poly(methyl methacrylate) have diffusion coefficients of the order of 10^?16?10^?17 cm²/sec. Variations in the diffusion coefficient values are attributed to the experimental approaches, theoretical treatments and molecular weight distribution differences. An activation energy of 55 kcal/mol was calculated from an Arrhenius plot of all polystyrene data reduced to a number-average molecular weight of 150,000 g/mol, using an inverse square molecular weight conversion method. Interestingly, this is in between the activation energies for the α and β relaxation processes in polystyrene, 84 and 35 kcal/mol, respectively. Fracture of polystyrene was considered in terms of chain scission and chain pull-out. A dental burr apparatus was used to fracture the films. For low molecular weights, chain pull-out dominates, but for high molecular weights, chain scission dominates. At 150,000 g/mol, the energy to fracture is divided approximately equally between the two mechanisms. Above a certain number average molecular weight (about 400,000 g/mol), the number of chain scissions remains constant at about 10²⁴ scissions/m³. Energy balance calculations for film formation and film fracture processes indicate that the two processes are partly reversible, but have important components of irreversibility. From the interdiffusion SANS data, the diffusion rate is calculated to be about 1 Å/min, which is nine orders of magnitude slower than the dental burr pull-out velocity of about 0.8 cm/sec.     

Development of a simple experimental method to measure interphase composition profiles generated by diffusion in polymers. Further results and comparison with Raman spectroscopy

Composition profiles generated by interdiffusion in the concentrated regime between poly(phenylene oxide)-polystyrene (PPO-PS) blend pairs are experimentally determined by two techniques. Three-point bending moment measurements over a convenient temperature range (DMA (dynamic mechanical analysis) method) are used to determine interphase composition profiles. Confocal micro-Raman spectroscopy is also used to measure local compositions along a direction which is perpendicular to the original interface. The study includes some limiting cases, to test accuracy, precision and flexibility of the “DMA method”. Excellent agreement is found between results obtained by both independent methods.