Symmetric Polymer Blends Research Articles

Liquid–liquid demixing in a binary polymer blend driven solely by the component-selective crystallizability

On the basis of an extended Flory–Huggins expression for the mixing free energy of the long-chain binary polymer blend, we showed that liquid–liquid demixing can be driven solely by the propensities of crystallization differing with respect to components. Demixing prior to crystallization on cooling was demonstrated by dynamic Monte Carlo simulations of the lattice model for a symmetric polymer blend where only one component is crystallizable. We discussed the implications of this principle to several experimental observations including the (in)compatibility of polymer chains with different stereochemical compositions, the memory effect of polymer crystallization, and the spinodal decomposition at an early stage of polymer crystallization.

Liquid‐liquid equilibria of binary polymer blends: molecular thermodynamic approach

AbstractWe extended and simplified the modified double‐lattice model to binary polymer blend systems. The model has two model parameters, Cβ and Cγ. Those are not adjustable parameters but universal functions. In comparison with Ryu et al.'s simulation data for symmetric polymer blend with various chain lengths (r1 = r2 = 8, 20, 50, 100), Cγ is determined. Our results show that Cβ is negligible for symmetric polymer blend systems. The proposed model describes very well phase behaviors of weakly interacting polymer blend systems.

Molecular thermodynamics approach for liquid–liquid equilibria of the symmetric polymer blend systems

We extended and simplified the modified double-lattice model for polymer solution systems to binary polymer blend systems. The model has three model parameters, C β and C γ in a primary lattice and C a in a secondary lattice. Those are not adjustable parameters but universal constants. In comparison with Müller's Monte-Carlo simulation data for symmetric polymer blend ( r 1=32 and r 2=32), C γ is determined and C β is negligible for symmetric polymer blend systems. Also, C a is obtained from comparing with Panagiotopolous’ Monte-Carlo simulation data. In addition, oriented interactions between polymer segments are considered based on the secondary lattice concept. The proposed model describes very well phase behaviors of ordinary and oriented polymer blend systems.

Bulk and interfacial shear thinning of immiscible polymers.

Nonequilibrium molecular-dynamics simulations are used to study the shear-thinning behavior of immiscible symmetric polymer blends. The phase-separated polymers are subjected to a simple shear flow imposed by moving a wall parallel to the fluid-fluid interface. The viscosity begins to shear thin at much lower rates in the bulk than at the interface. The entire shear-rate dependence of the interfacial viscosity is consistent with a shorter effective chain length s(*) that also describes the width of the interface. This s(*) is independent of chain length N and is a function only of the degree of immiscibility of the two polymers. Changes in polymer conformation are studied as a function of position and shear rate. Shear thinning correlates more closely with a decrease in the component of the radius of gyration along the velocity gradient than with elongation along the flow. At the interface, this contraction of chains is independent of N and consistent with the bulk behavior for chains of length s(*). The distribution of conformational changes along chains is also studied. Central regions begin to stretch at a shear rate that decreases with increasing N, while shear induced changes at the ends of chains are independent of N.

Symmetric binary polymer blends confined in thin films between competing walls: Interplay between finite size and wetting behavior

The phase behavior and structure of a symmetric binary polymer blend confined between two hard impenetrable walls is studied, assuming also short range forces between the monomers and the walls. Phenomenological considerations are elaborated with the self-consistent field theory of Gaussian chains, and also some Monte Carlo simulations of the bond-fluctuation model. In the case of “antisymmetric” walls (right wall attracts component A with the same strength as does left wall component B) the phase diagram is symmetric around volume fraction ϕ = 1/2. For very thin films (or very weak surface fields) one finds a single critical point at ϕc = 1/2, as in the bulk. For thicker films, or stronger surface fields, the phase diagram exhibits two critical points and two concomitant coexistence regions, down to a triple point Tt, while below the triple point there is a single coexistence region. When the film thickness D → ∞, the two coexistence regions for T>Tt shrink into the prewetting lines, while Tt approaches the wetting transition temperature. Asymmetric surface forces are also considered, studying the smooth crossover from “ antisymmetric walls” to “ symmetric walls” (that both attract the A component with the same strength). The resulting crossover between capillary-type behavior (i.e., a single critical point of the thin film) and the above behavior with two critical points is analyzed. Particular attention is paid to the behavior of interfaces between coexisting phases.

Symmetric polymer blend confined into a film with antisymmetric surfaces: interplay between wetting behavior and the phase diagram

We study the phase behavior of a symmetric binary polymer blend that is confined in a thin film. The film surfaces interact with the monomers via short-range potentials. We calculate the phase behavior within the self-consistent field theory of Gaussian chains. Over a wide range of parameters we find strong first-order wetting transitions for the semi-infinite system, and the interplay between the wetting/prewetting behavior and the phase diagram in confined geometry is investigated. Antisymmetric boundaries, where one surface attracts the A component with the same strength as the opposite surface attracts the B component, are applied. The phase transition does not occur close to the bulk critical temperature but in the vicinity of the wetting transition. For very thin films or weak surface fields one finds a single critical point at straight phi(c)=1 / 2. For thicker films or stronger surface fields the phase diagram exhibits two critical points and two concomitant coexistence regions. Only below a triple point there is a single two-phase coexistence region. When we increase the film thickness the two coexistence regions become the prewetting lines of the semi-infinite system, while the triple temperature converges toward the wetting transition temperature from above. The behavior close to the tricritical point, which separates phase diagrams with one and two critical points, is studied in the framework of a Ginzburg-Landau ansatz. Two-dimensional profiles of the interface between the laterally coexisting phases are calculated, and the interfacial and line tensions analyzed. The effect of fluctuations and corrections to the self-consistent field theory are discussed.

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory-Huggins theory becomes quantitatively correct in the long chain length limit, when the χ parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the χ parameter from small-angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like √χ/(ρb3) for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self-consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1/√N. Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non-additive monomer shapes, one has a large positive chain-length-independent entropic contribution to the χ parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the χ parameter of the order 10–3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non-entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End-functionalized homopolymers of different species react at the interface instantaneously and irreversibly to form diblock copolymers. The initial reaction rate for small reactant concentrations is time dependent and larger than expected from theory. At later times there is a depletion of the reactive chains at the interface and the reaction is determined by the flux of the chains to the interface. Pertinent off-lattice simulations and analytical theories are briefly discussed.

Single-Chain Conformations in Symmetric Binary Polymer Blends: Quantitative Comparison between Self-Consistent Field Calculations and Monte Carlo Simulations

Single-chain properties in a symmetric binary polymer blend are studied by self-consistent field calculations and Monte Carlo simulations. Within the self-consistent field scheme, the statistical mechanics of a cluster of neighboring polymers is solved. Interactions among the polymers of a cluster and composition fluctuations within a cluster are incorporated exactly, a mean field approximation is invoked for intercluster interactions and long-range fluctuations. The results are compared to large scale Monte Carlo simulations for a broad range of chain lengths. While we find nearly quantitative agreement for single chain propertiese.g., the reduction of the chain dimensions of the minority componentonly qualitative agreement is achieved for thermodynamic quantitiese.g., the critical temperature. The temperature and composition dependence of the chain conformations are attributed to a balance between the entropy loss upon contraction and the exchange of intermolecular and intramolecular contacts. The calculations suggest that the relative reduction of the spatial extension of the minority chains depends on the parameter χ for not too large incompatibilities χ. The scaling limit is, however, approached only for very long chain lengths N.

Wetting and Capillary Condensation in Symmetric Polymer Blends: A Comparison between Monte Carlo Simulations and Self-Consistent Field Calculations

We present a quantitative comparison between extensive Monte Carlo simulations and self-consistent field calculations on the phase diagram and wetting behavior of a symmetric, binary (AB) polymer blend confined into a film. The flat walls attract one component via a short range interaction. The critical point of the confined blend is shifted to lower temperatures and higher concentrations of the component with the lower surface free energy. The binodals close the the critical point are flattened compared to the bulk and exhibit a convex curvature at intermediate temperatures -- a signature of the wetting transition in the semi-infinite system. Investigating the spectrum of capillary fluctuation of the interface bound to the wall, we find evidence for a position dependence of the interfacial tension. This goes along with a distortion of the interfacial profile from its bulk shape. Using an extended ensemble in which the monomer-wall interaction is a stochastic variable, we accurately measure the difference between the surface energies of the components, and determine the location of the wetting transition via the Young equation. The Flory-Huggins parameter at which the strong first order wetting transition occurs is independent of chain length and grows quadratically with the integrated wall-monomer interaction strength. We estimate the location of the prewetting line. The prewetting manifests itself in a triple point in the phase diagram of very thick films and causes spinodal dewetting of ultrathin layers slightly above the wetting transition. We investigate the early stage of dewetting via dynamic Monte Carlo simulations.

Monte Carlo simulations of symmetric polymer blends. I. Characterization of the interface

A new method is presented for the simulation of the interface between nearly immiscible amorphous polymer phases. Strictly speaking, two independent interfaces are developed whose positions remain fairly in place during the whole simulation process. The interface is characterized by its thickness, by the excess number of contacts between segments of different type in the interface region (a quantity being characteristic of cavities that contain the other type of polymer) as well as by the fractal dimension and the relative surface enlargement (compared to a totally flat interface) similar to the methods introduced earlier for polymer surfaces. Further quantities that are used for a proper description of the interface are density profiles of polymer segments as well as of end segments and centers of mass. A variation of the repulsive energy between the two types of polymers on the one hand and a variation of the (average) chain length on the other hand reveals that the roughness of the interface decreases with increasing immiscibility (increasing energy parameter) and decreasing chain length (when the product of energy parameter and chain length is kept constant).

Monte Carlo simulations of symmetric polymer blends. II. Chain properties in interface regions

Making use of a previously introduced lattice model for binary polymer blends of limited miscibility Monte Carlo simulations have been performed in order to investigate the influence of different thermodynamic conditions on mass segregation and global structure as well as on microstructure of homopolymers when passing from one bulk phase through the interface to the other. The calculations show an enrichment of shorter chains at the interface as well as a decreasing miscibility with decreasing average chain length (at constant bulk density) of the polymer matrix on the one hand and relate the compression of the coils at the interface to the observed orientation and deformation effects on the other. Surprisingly, an additional expansion of the polymer coils (belonging to the minority component) can be found at some distance from the actual interface due to attractive interactions between pairs of chains in rather “diluted” layers. Furthermore, all phenomena are discussed from two different viewpoints: (i) The average chain length is kept constant while the energy parameter is varied, and (ii) the chain length is varied and the bulk densities are held constant by use of identical relative energy parameters.

Surface Segregation of the Higher Surface Free Energy Component in Symmetric Polymer Blend Films

ADVERTISEMENT RETURN TO ISSUEPREVCommunication to the...Communication to the EditorNEXTSurface Segregation of the Higher Surface Free Energy Component in Symmetric Polymer Blend FilmsTisato Kajiyama, Keiji Tanaka, and Atsushi TakaharaView Author Information Department of Materials Physics & Chemistry, Graduate School of Engineering, Kyushu University, 6-10-1 Hazozaki, Higashi-ku, Fukuoka 812-8581, Japan Cite this: Macromolecules 1998, 31, 11, 3746–3749Publication Date (Web):May 8, 1998Publication History Received18 August 1997Revised9 March 1998Published online8 May 1998Published inissue 1 June 1998https://doi.org/10.1021/ma971247sCopyright © 1998 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views618Altmetric-Citations45LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit Read OnlinePDF (74 KB) Get e-AlertsSUBJECTS:Annealing (metallurgy),Free energy,Organic compounds,Polymer chains,Polymer films Get e-Alerts

Reactions at Polymer Interfaces: A Monte Carlo Simulation

Reactions at a strongly segregated interface of a symmetric binary polymer blend are investigated via Monte Carlo simulations. End functionalized homopolymers of different species interact at the interface instantaneously and irreversibly to form diblock copolymers. The simulations, in the framework of the bond fluctuation model, determine the time dependence of the copolymer production in the initial and intermediate time regime for small reactant concentration $\rho_0 R_g^3=0.163 ... 0.0406$. The results are compared to recent theories and simulation data of a simple reaction diffusion model. For the reactant concentration accessible in the simulation, no linear growth of the copolymer density is found in the initial regime, and a $\sqrt{t}$-law is observed in the intermediate stage.

Computer Simulations of the Static Scattering from Model Polymer Blends

To understand the unusual composition and wave vector, q, dependent Flory interaction parameters, χ, obtained from small angle neutron scattering (SANS), we have calculated the three partial structure factors for symmetric binary polymer blends with relatively strong interactions between dissimilar monomers using molecular dynamics simulations. In agreement with past work we find that the radii of gyration of the chains are altered on blending. The following new results emerged from our simulations. The single-chain form factors in the blends follow Gaussian statistics at all distances larger than a monomer diameter, confirming the Flory−de Gennes conjecture that correlations in condensed polymer phases are screened over short length scales. The Rg's deduced from these form factors are in agreement with simulation-determined values and illustrate conclusively that the single chain term in the incompressible random-phase approximation (i-RPA) is altered on blending. The three partial structure factors obtained from the simulations, each of which follows an Ornstein−Zernike behavior, have different q dependences and extrapolate to different values in the thermodynamic limit. The different q dependences can be explained qualitatively by a compressible RPA formalism proposed by Tang and Freed. We then show that any form chosen to combine these partial structure factors into a single total scattering function will, in general, not have a q dependence that is describable by the incompressible RPA. This explains the experimentally observed q dependence of the χ parameter derived from the i-RPA. Finally, a thermodynamic analysis on the zero wave-vector limit of the partial structure factors shows that their absolute values are different from each other due to the effects of density fluctuations, as well as the different partial molar volumes of the two species in the blend. These results serve to emphasize the important role played by compressibility on the scattering obtained from simple polymer mixtures with large excess volumes on mixing.

Optimized cluster theory of structurally symmetric polymer blends

The thermodynamic properties of model structurally symmetric polymer blends were calculated using a recently developed theory that is a generalization of the optimized cluster theories for atomic mixtures and single component molecular systems. Within this approach, cluster expansions for the Helmholtz free energy and pair correlation functions were developed for a mixture of polymer chains modeled using the interaction site formalism. A series of topological reductions was then performed to render an approximate expression for these quantities. The theory was previously shown to be equivalent to a set of diagrammatically proper integral equations. The critical temperature was determined to scale linearly with chain length in agreement with neutron scattering measurements and computer simulations. The critical temperature was also found to be suppressed with respect to the mean-field value due to composition fluctuations. The effective interaction parameter, χs, at the critical composition was well represented by the functional form, χs=A/T+B, where A and B are constants that depend on the chain length and total segment density. Deviations from random mixing were found to extend well beyond monomeric length scales and increased substantially as the critical temperature was approached.

Chain correlations in symmetric binary polymer blends

The many chain problem of two polymers is studied through the summation of the series of the one-loop diagrams between different polymer chains. The free energy of the polymer blend is found revealing that chain correlations affect the phase separation behavior of polymer chains of finite lengths N. The parameter χeff related with the scattering form factor is found to overestimate the composition and molecular weight dependence of the strength of the interactions of the two different polymers expressed by the generalized Flory–Huggins parameter χ. The composition dependences of both parameters are affected by the proximity to the critical region in accord with recent neutron scattering experiments and in the manner Monte Carlo simulations indicate. These dependences become stronger as the system comes close to the critical point either from the one phase or from the two phase region. The dependence of χeff on the molecular weight is not monotonic and is related with the composition of the system. The critical value of χ is found to present a positive deviation of the order of N−1/2 from the mean field prediction taking the classical value χc=2/N only at the limit of large molecular weights.

Phase Separation of Ternary Mixtures: Symmetric Polymer Blends

The dynamics of phase separation of ternary mixtures into two and three phases are analyzed numerically by solving the nonlinear spinodal decomposition equations in two dimensions. We find interesting interface effects during the decomposition process. Between any two α + β phases rich in components I and J respectively, the third component K segregates in the interface between α and β. We study the interface segregation effects in symmetric ternary polymer blends (i.e., with equal Flory interaction parameters between each pair of monomers and equal degrees of polymerization). This segregation phenomenon influences strongly the growth of a third phase with lowest equilibrium volume fraction. In the absence of hydrodynamics, the kinetics of the minority phase is determined by the topology of the segregation pattern initiated by the decomposition of the most unstable phases. Coarsening of the minority phase occurs at the junction of four or more majority phase domain boundaries. We examine the dynamical scaling and the growth laws for the late stages of separation into two and three phases. The growth law R(τ) ∼ τ 1/3 is always obeyed even when the structures are not self-similar. The self-similar regime is achieved very slowly in ternary systems.

Fluctuation phenomena in structurally symmetric polymer blends

Polymer reference interaction site model theory with the new molecular closures is employed to numerically and analytically study structurally and interaction potential symmetric binary blends. Both the compressibility and free energy routes to the thermodynamics are studied and the issue of thermodynamic consistency is addressed. A variety of non-Flory–Huggins effects, or ‘‘fluctuation phenomena,’’ are found. These include nonuniversal renormalization of the critical temperature and effective chi-parameter from their mean field values, composition-dependent chi-parameters, and nonlinear dependence of the inverse osmotic compressibility on inverse temperature. All these fluctuation effects depend on degree of polymerization, N, chain length asymmetry, polymer density, range and precise form of the attractive tail potentials, chain stiffness, and proximity to the phase boundary. Some of the fluctuation effects are intrinsic, i.e., survive in the long chain N→∞ limit, while others are finite size effects which arise from chain-connectivity-induced coupled local density and long wavelength concentration fluctuations. Due to the multiple sources of the fluctuation effects, even asymptotic finite size effects can appear ‘‘intrinsic’’ over extended ranges of N. Comparison with lattice Monte Carlo simulations of Deutsch and Binder shows good agreement with the theoretical predictions. All the fluctuation effects can be understood in simple terms by examining the enthalpy of mixing and local interchain correlations. The key physical process is thermally driven local interchain rearrangements corresponding to the formation of diffuse interfaces and clusters or droplets. Analytic results are derived using the Gaussian thread model, which provides a simple physical understanding of the origin of the numerically determined fluctuation effects. In the long chain limit the predictions for the thread blend are shown to be exactly thermodynamically consistent which is a unique circumstance for liquid state theories. The relation of the blend fluctuation stabilization process to the corresponding diblock copolymer problem is briefly discussed.

The wetting transition for polymer mixtures

The location of the wetting transition in symmetric polymer blends is calculated as a function of the degree of incompatibility and the difference in surface energy between the pure components, using mean-field (square-gradient) theory, coupled with a lattice model for the bare surface energy. The conditions for second-order wetting are discussed.

Phase transitions in thin films of symmetric binary polymer mixtures

We report lattice and off-lattice computer simulation studies on the phase coexistence of symmetric polymer blends confined between two hard walls to which neither component is preferred energetically. We find that the phase diagrams for thin films are always ‘inside’ those for thicker films. While one reason for this is the loss of neighbours due to the presence of the wall, another important factor is the somewhat surprising surface segregation of the minority blend component.