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     

Temperature‐dependent polymer–polymer interactions in polystyrene–polyethylene blends

The effect of the temperature on the interaction between the components of an immiscible polystyrene–polyethylene blend has been analyzed with different techniques. Lap‐shear‐strength data and morphological observations indicate an enhanced interaction between the polymeric phases at elevated temperatures, at which dispersive forces are known to predominate. This raises the degree of compatibility of the polymeric components. Rheological measurements also justify the concept of increased adhesion between the components of the blend when it is processed at very high temperatures. Differential scanning calorimetry analysis lends support to an improved homogeneity of the blend at an elevated temperature; this is again consistent with an improved interaction between the blend phases. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2545–2557, 2004     

Photoaddition of maleic anhydride to unsaturated polymers in homogeneous solution,solid polymer–solution,and solid polymer–vapor systems

Photoreactions of maleic anhydride (MAH) with unsaturated olefinic polymers such as 1,2-polybutadiene, 1,4-polybutadiene, block copolymer of styrene and butadiene, polystyrene, poly(styrene-co-isoprene), and poly(styrene-alt-methyl methacrylate) were investigated in air. When the polymers have olefinic unsaturation, the addition of MAH to the polymers in homogeneous solutions proceeded efficiently by a chain mechanism, and the quantum yield of the photoaddition of MAH was greater than unity under irradiation at λ > 310 nm. From the effects of solvent and photosensitizer, a radical chain mechanism involving crosslinking of the polymers by MAH molecules was suggested. Together with the spectroscopic results, the reaction mechanism was discussed. The photoaddition reaction was then applied to the surface photomodification of polymer films. Photoreactions were conducted at the interphase between solid polymer and acetone solution of MAH and also at the interphase between solid polymer and gaseous MAH. Irradiation by a 300-W high-pressure mercury lamp could bring about considerable modification of the surface properties of the polymers, which then show improved wettability and dyeability. From the oxygen permeation experiments, the present interfacial phototreatment was shown to provide a double-layered polymer film in which one side of the film is polar and hydrophilic while the other side is nonpolar and hydrophobic.     

A TSC investigation of polymer–polymer contact charging

The transfer of charge across the interface between two materials brought into contact was studied by measuring the small currents produced when layered films composed of two dissimilar films were first heated and then held under isothermal conditions. It was found that, given a fixed electrode orientation, the polarity of the current generally reversed when the relative position of the films were reversed. The sense of the current was in agreement with that expected from the polymer work functions. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2901–2912, 1997     

Growth and decay of concentration fluctuations in polymer–polymer mixtures

A computer simulation based on the Cahn–Hilliard nonlinear diffusion equation, developed in the field of metallurgy, is applied to the demixing behavior of a polymer–polymer mixture. The simulation is a one-dimensional version. Spatially periodic concentration fluctuations appear at a very early stage and evolve with the wave number almost constant. Later some waves are absorbed into neighboring ones, resulting in a decrease in the average wave number of the concentration fluctuation. Thus, characteristic phenomena in the demixing are successfully described by the computer simulation. Furthermore, the simulated time variation of wave number agrees with experimental results in the literature. The analysis is extended to two-step quenching: after a homogeneous mixture undergoes the first temperature-jump from the single-phase region to the two-phase region of the phase diagram, the system is allowed to demix isothermally for a time, and then the demixed system undergoes the second jump to deeper or shallower quench. When the quench depth of the second jump (ΔT₂) is smaller than half the first depth (ΔT₁), the concentration fluctuation as developed under ΔT₁ decays with time after the second jump. When ΔT₂ is between ΔT₁ and (ΔT₁/2), the fluctuation decays slightly after the second jump and then increases. When the second jump is to a deeper quench (ΔT₂ > ΔT₁), a new fluctuation of short wavelength is superimposed on the previously developed one.     

Evaluation of polymerization rate by chain length dependence on polymer–polymer termination and primary radical termination in radical polymerization

In order to analyze the polymerization rate at high initiation rate and/or low monomer concentration, the rate equations are derived by a rate formulated previously for polymer–polymer termination and another rate for primary radical termination, which is formulated here (both rates depend on chain length of polymer radical). Such equations would be applicable to the kinetic data in the polymerizations of styrene and methyl methacrylate. This shows that the assumption that both rates are independent of chain length overestimates the rate of primary radical termination.     

Effect of the polymer matrix on the formation of silver nanoparticles in polymer–silver salt complex membranes

When polymer–silver salt complex membranes were exposed to UV irradiation, the separation performances of both the permeance and selectivity for propylene–propane decreased, which was primarily attributed to the reduction of the silver ions in the membranes to silver nanoparticles. Here, the effect of the polymer matrix on the formation of silver nanoparticles in the polymer–silver salt complex membranes was investigated. This effect was assessed for the complexes of two kinds of silver salts (AgBF₄ and AgCF₃SO₃) with several polymeric ligands containing three different carbonyl groups, including poly(vinyl pyrrolidone) (PVP) with an amide group, poly(vinyl methyl ketone) (PVMK) with a ketone group, and poly(methyl methacrylate) (PMMA) with an ester group. UV–vis spectra and transmission electron microscopy (TEM) images clearly indicated that the reduction rate of the silver ions has the following order in the various polymer matrices: PVP > PVMK > PMMA, whereas the size and the distribution of the nanoparticles exhibited the reverse order. The tendency to form silver nanoparticles was explained in terms of the differences between the comparative strengths of the interactions of the silver ions with the different carbonyl oxygens in the matrices, as well as that of the silver ions with counteranions, which was characterized by X‐ray photoelectron spectroscopy (XPS) and FT‐Raman spectroscopy. It was concluded that when the concentration of free silver ions was low due to weak polymer–silver ion and strong silver ion–anion interactions, as found with PMMA, the reduction rate of silver ions to silver nanoparticles was slow. Therefore, the PMMA–silver complex membranes were less sensitive to decreases in separation performance upon UV irradiation than compared to the PVP membranes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1168–1178, 2006     

Selective adsorption behavior of polymer at the polymer–nanoparticle interface

Coarse‐grained molecular dynamics simulations are used to investigate the adsorption behavior of monodisperse and bidisperse polymer chains on the nanoparticle (NP) surface at various polymer–NP interactions, chain lengths, and stiffness. At a strong polymer–NP interaction, long chains preferentially occupy interfacial region and squeeze short chains out of the interfacial region. Semiflexible chains with proper stiffness wrap NPs dominantly in a helical fashion, whereas fully flexible chains constitute the surrounding matrix. As chain stiffness increases, the results of the preferential adsorption are the opposite. The chain‐length or chain‐stiffness‐induced selective adsorption behavior of polymer chains in the polymer–NP interfacial region relies on a delicate competition between entropic and enthalpic contributions to the total free energy. These results could provide insights into polymer–NP interfacial adsorption behavior and guide the design of high‐performance nanocomposites. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1829–1837     

Model for the fracture energy of glassy polymer–polymer interfaces

The increase in the interfacial fracture energy (G_c) with increasing interfacial width (a_i) goes through a transition at a critical value of a_i that is unique to each polymer–polymer system. This transition point does not scale with the bulk entanglement spacing (d_t) for different systems, implying that the role of chain friction in reinforcing these interfaces is more important than previously thought. A theoretical model has been developed to calculate G_c as a function of the interfacial stress transfer due to individual polymer chains. When including the effects of chain friction only, the model reproduces the nonuniversal behavior of G_c with respect to a_i/d_t but yields poor fits for a_i/d_t > 1. The effects of entanglements are then added by calculating the fraction of entangled chains as a function of a_i/d_t. This contribution, although not material specific, matches the qualitative behavior of G_c for large values of a_i/d_t. When both contributions are included in the model, excellent fits are obtained for all data sets. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2377–2386, 2002     

Functional monomers and polymers. LXIII. A study on the polymer–polymer interaction between nucleic acid base-substituted poly-L-lysines

A study of polymer-polymer interaction was made on several poly-L -lysines that contained pendant nucleic acid bases substituted on the N′ position. Conformation and interaction of these polypeptides were studied in solution by spectroscopic measurement. The results obtained suggest that the high-molecular-weight polymers form polymer complexes in a helical conformation by specific adenine-thymine base pairing. On the other hand, no interaction could be observed for the low-molecular-weight polymers, which existed in a random coil structure.     

Free energy of an inhomogeneous polymer–polymer–solvent system. II

A complete expression for the enthalpy of mixing of inhomogeneous polymer–polymer–solvent systems applicable for small as well as large concentration fluctuations has been developed. This is used to express the free energy of inhomogeneous polymer–polymer–solvent systems in an extended form of the Landau-Ginzburg functional. The gradient energy parameters obtained here are consistent with the published results. The free energy functional has been applied to develop a generalized continuity equation for spinodal decomposition in polymer–polymer systems. A linearized version of this continuity equation has been used to study the effect of the gradient terms on the dominant wavelength during spinodal decomposition.     

Effect of correlations in the interaction along polymer chain on the globule structure

A special potential for interaction between polymer chain units, whose energy decreases with increasing distance s between the units as s ^–1, was introduced for the first time. According to Monte Carlo simulation, interactions of this type result in the formation of a globule with an equilibrium packing of domains in space. The radius of gyration of a chain segment in these globules varies with segment length according to the scaling law typical of crumpled globules.     

Electric field dependence of lower critical phase separation behavior in polymer–polymer mixtures

The electric field dependence of the cloud point temperature of a poly(vinyl methyl ether)–polystyrene mixture has been experimentally measured in a laser light scattering experiment. It is found that the cloud point temperature is depressed linearly with the square of the applied electric field. A thermodynamic derivation of the electric field dependence of the spinodal temperature for polymer–polymer mixtures is also presented. A large disagreement between the experimental and theoretical findings is noted and possible explanations for this discrepancy are discussed.     

Thermodynamic characterization of polymer‐polymer interfaces

The properties of multiphase polymer blends are determined in part by the nature of the polymer‐polymer interface. The interfacial tension, γ, influences morphology development during melt mixing while interfacial thickness, λ, is related to the adhesion between the phases in the solid blend. A quantitative relation between the thermodynamic interaction energy and these interfacial properties was first proposed in the theory of Helfand and Tagami and has since been correlated with experimental measurements with varying degrees of success. This paper demonstrates that the theory and experiment can be unified for polymer pairs of some technological importance: copolymers of styrene and acrylonitrile (SAN) with poly (2, 6‐dimethyl‐1, 4‐phenylene oxide) (PPO) and with bisphenol‐A polycarbonate (PC). For each pair, the overall interaction energy was calculated using a mean‐field binary interaction model expressed in terms of the interactions between repeat unit pairs extracted from blend phase behavior. Predictions of γ and λ as a function of copolymer composition made by combining the binary interaction model with the Helfand‐Tagami theory compare favorably with experimental measurements.     

Phase equilibria in polymer–liquid–liquid systems

The phase equilibria in polymer–liquid 1–liquid 2 ternary systems have been calculated on the basis of the Flory-Huggins theory of polymer solutions. A new approximation method based on the “cluster” concept has been introduced for mixed solvents comprising a solvent and a nonsolvent. This concept has been verified with polystyrene–solvent–methanol systems.     

Effects of composition drift on the effectiveness of random copolymer reinforcement at polymer–polymer interfaces

Random copolymer layers are surprisingly effective at reinforcing polymer–polymer interfaces. One hypothesis is that composition drift during synthesis can account for the higher than expected toughening. To test this hypothesis, we polymerized a series of poly(d‐styrene‐r‐2‐vinylpyridine) (dPS_f‐r‐PVP_1?f) copolymers with various fractions (f) of deuterated styrene to only 10% completion to avoid composition drift. The fracture energies (G_c) of polystyrene/dPS‐r‐PVP/poly(2‐vinylpyridine) interfaces with relatively thick layers of dPS‐r‐PVP were measured. G_c decreased relative to interfaces reinforced with composition‐drifted dPS‐r‐PVP. Conversely, G_c increased when two or more copolymers were blended together. In such samples, the copolymers form distinct layers with multiple interfaces characterized by the difference in f (Δf) between adjacent layers. We find that G_c is governed by Δf_max, the largest difference in adjacent compositions, and, therefore, by the width of the narrowest interface (w_min). G_c increases strongly as w_min increases from 3 to 5 nm. Remarkably, these w_min values are about half the entanglement spacing in bulk polystyrene. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2363–2377, 2001     

Diffusion behavior in polymer–clay nanocomposites

This paper reviews our previous studies on the diffusion behavior in polymers clay nanocomposites. A geometric model for predicting the effective diffusivity through this type of systems as a function of clay sheets orientation, volume fraction, polymer clay interaction, and aspect ratio is proposed. Model predictions are compared to the effective diffusivity generated using random walk simulations as well as with predictions obtained from already existing theoretical models. Fair agreement is found between the model prediction and the results of numerical simulations. With respect to the already existing theoretical models, the present mathematical derivation seems more adequate to describe diffusion behavior in conventional nanocomposites systems (i.e. when fillers present very low values of volume to surface ratio). Experimental diffusion tests are discussed and interpreted with the aid of the proposed model. In addition to the aspect ratio and clay concentration, the polymer clay interactions as well as the sheets orientation are the factors controlling the barrier properties of polymer‐layered silicate nanocomposites. Good agreement was found in the case of samples containing exfoliated clay, whereas the model fails in the case of micro‐composites, in which the inorganic lamellae are agglomerated in clusters. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 265–274, 2006     

Role of chain interpenetration in layer-by-layer deposition of polyelectrolytes

The effects of temperature, pH, and salt concentration on the layer-by-layer (LBL) deposition of sodium poly(styrene sulfonate) (PSS)/poly[2-(dimethylamino)ethyl methacrylate] (PDEM) were investigated by use of a quartz crystal microbalance with dissipation (QCM-D). At pH 4, the frequency change (Deltaf) gradually decreased to a constant, indicating that the polyelectrolyte complexes of the layer were not dissolved. As the layer number increased, the -Deltaf oscillatedly increased, indicating that the thickness of the multilayer increased. At the same time, the dissipation change (DeltaD) oscillatedly increased with the layer number, indicating the chain interpenetration or complexation that led to the alternative swelling-and-shrinking of the outermost layer. For the same layer number, as the temperature increased, the amplitude of DeltaD increased, indicating that the chain interpenetration increased. The thickness also increased with temperature. Further increasing the pH to 7 led to a thicker layer, reflected in the larger amplitude of DeltaD. At pH 10, the polyelectrolytes no longer formed multilayers on the surface because of the lack of electrostatic interactions. On the other hand, the addition of NaCl also led to a thickness increase. The amplitude in DeltaD increased with NaCl concentration, indicating that the chain interpenetration increased. Our experiments indicated that the LBL deposition of polyelectrolytes was dominated by the chain interpenetration. Also, the polyelectrolyte complexes in the layer can redissolve into solution from the surface at a high temperature or a high salt concentration.