Microphase Separation In Cross-Linked Polymer Blends (original) (raw)
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Physical Review Letters, 2000
In order to investigate the origin of the often invoked nanoheterogeneities in miscible polymer blends, we have performed quasielastic neutron scattering experiments on the component dynamics within the miscible polymer blend polyisoprene͞polyvinyl ether including the pure components as a reference. We find that the apparent local heterogeneities observed by spectroscopic techniques originate from the chain specific crossover properties between entropy driven and local chain dynamics and are, thus, a purely dynamical phenomenon. PACS numbers: 61.41. + e, 61.12.Ex, 61.25.Hq The study of thermodynamic and structural properties of polymer blends is a very active field in polymer physics. Recently also dynamical aspects like the socalled "dynamic miscibility," i.e., the question how the chain dynamics is altered upon blending, came into focus . Mainly on the basis of results from spectroscopic techniques many workers have invoked the existence of nanoheterogeneities in thermodynamically miscible blends and disordered block copolymer systems [2-6]. Among the different materials studied, the miscible blend of polyisoprene and polyvinyl ether (PI͞PVE) has been investigated particularly well and can be considered as a model system . 2D NMR revealed [3] that, though the system is homogeneous (Flory Huggins parameter x , 0), the two polymers exhibit significantly different mobilities. By dielectric spectroscopy several groups have found two separate relaxations in the miscible regime (e.g., ). This finding is supported by recent quasielastic neutron scattering (QENS) studies, where at large momentum transfers distinctly different QENS patterns are observed for the two components . Such findings are not restricted to PI͞PVE system but have been observed also in several other miscible polymer blends (e.g., ). Finally, studies by forward recoil spectroscopy [10] on polystyrene͞poly(xylenyl ether) blends resulted in grossly different component diffusion coefficients, indicating very different friction coefficients for the two components in this particular blend.
Glassy correlations and microstructures in randomly cross-linked homopolymer blends
The Journal of Chemical Physics, 2006
We consider a microscopic model of a polymer blend that is prone to phase separation. Permanent crosslinks are introduced between randomly chosen pairs of monomers, drawn from the Deam-Edwards distribution. Thereby, not only density but also concentration fluctuations of the melt are quenched-in in the gel state, which emerges upon sufficient crosslinking. We derive a Landau expansion in terms of the order parameters for gelation and phase separation, and analyze it on the mean-field level, including Gaussian fluctuations. The mixed gel is characterized by thermal as well as time-persistent (glassy) concentration fluctuations. Whereas the former are independent of the preparation state, the latter reflect the concentration fluctuations at the instant of crosslinking, provided the mesh size is smaller than the correlation length of phase separation. The mixed gel becomes unstable to microphase separation upon lowering the temperature in the gel phase. Whereas the length scale of microphase separation is given by the mesh size, at least close to the transition, the emergent microstructure depends on the composition and compressibility of the melt. Hexagonal structures, as well as lamellae or random structures with a unique wavelength, can be energetically favorable.
Critical microphase properties of crosslinked polymer blends with quenched random impurities
European Physical Journal E, 2011
We extend published works dealing with microphase separation in crosslinked polymer blends to the case where these are surrounded by random impurities. To study their influence on critical microphase properties, from a static and kinetics point of view, we first assume that the (real) disorder caused by impurities is quenched. Second, the replica theory is used to study such critical properties, upon the impurities concentration and their interaction strength. More precisely, we compute the spinodal temperature and structure factor. We find that the spinodal temperature is shifted towards its lower and higher values, for attractive and repulsive impurities, respectively. The obtained expression for the static structure factor suggests that, contrarily to repulsive impurities, the crosslinked mixture scatters better in the presence of attractive ones. Thereafter, the study is extended to kinetics of microphase separation, when the mixture is impregnated by small random impurities. Kinetics is investigated through the growth rate, and in particular, we demonstrate that the latter is increased by the presence of repulsive impurities. This is natural, since these play a stabilizer role. Finally, the discussion is extended to crosslinked polymer blends immersed in a good solvent, which induces drastic changes of the critical microphase properties.
Fluid Phase Equilibria, 2003
Blending (or mixing) of macromolecules is widely used to tailor the properties of polymeric materials and small-angle neutron scattering (SANS) has provided detailed information at the molecular level on the ability of different polymer species to mix or segregate at various thermodynamic conditions. For two decades, SANS data have been analyzed via the de Gennes "random phase approximation" (RPA) [P.-G. de Gennes, Scaling Concepts in Polymer Physics, second ed., Cornell University Press, Ithaca, London, 1979], which is based on the assumption that the dimensions of polymer chains remain unchanged on mixing for all concentrations and temperatures. Here we investigate the effect of temperature and concentration on the dimensions of macromolecules in blends using SANS and high-concentration labeling methods and construct a generic phase diagram, which specifies the range of validity of the RPA. Using scaling arguments, we demonstrate a parallel between the structure-property relationships in blends and solutions of polymers in small molecule solvents and reveal the impact of the chain length of the polymeric solvent on the phase behavior of polymer blends. The results offer new insights into the universality of the thermodynamic properties and structure of macromolecules in polymeric, liquid and supercritical solvents.
Journal of Polymer Science Part B-polymer Physics, 2004
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
Theory of heterogeneities in polymer networks
Polymer Science Series A, 2016
Following Edwards' ideas we present main experimental results and the theory of random heterogeneities in neutral and charged networks obtained by instantaneous as well as chemical cross-linking of a melt and semidilute solution of linear chains. We study how random monomer density patterns in such networks change after swelling and stretching. We also describe main features of monomer density correlation functions, which determine the neutron and light scattering on spatial heterogeneities. We show that largescale cross-link density patterns written into network structure in the melt or semidilute state, can be revealed upon swelling by monitoring the monomer density patterns. We demonstrate that while isotropic deformations in good solvent yield magnified images of the original pattern, anisotropic deformations distort the image. We study how the monomer density image changes under different solvent conditions and discuss the difference between deformations of the density images in gels and ordinary solids. Possible tests of our predictions and some potential applications are proposed.
Incorporating Fluctuations and Dynamics in Self-Consistent Field Theories for Polymer Blends
Advances in Polymer Science, 2005
We review various methods to investigate the statics and the dynamics of collective composition fluctuations in dense polymer mixtures within fluctuating-field approaches. The central idea of fluctuating-field theories is to rewrite the partition function of the interacting multi-chain systems in terms of integrals over auxiliary, often complex, fields, which are introduced by means of appropriate Hubbard-Stratonovich transformations. Thermodynamic averages like the average composition and the structure factor can be expressed exactly as averages of these fields. We discuss different analytical and numerical approaches to studying such a theory: The self-consistent field approach solves the integrals over the fluctuating fields in saddle-point approximation. Generalized random phase approximations allow to incorporate Gaussian fluctuations around the saddle point. Field theoretical polymer simulations are used to study the statistical mechanics of the full system with Complex Langevin or Monte Carlo methods. Unfortunately, they are hampered by the presence of a sign problem. In dense system, the latter can be avoided without losing essential physics by invoking a saddle point approximation for the complex field that couples to the total density. This leads to the external potential theory. We investigate the conditions under which this approximation is accurate. Finally, we discuss recent approaches to formulate realistic dynamical time evolution equations for such models. The methods are illustrated by two examples: A study of the fluctuation-induced formation of a polymeric microemulsion in a polymer-copolymer mixture, and a study of early-stage spinodal decomposition in a binary blend.
Phase Diagram of Random Heteropolymers
Physical Review Letters, 2004
We propose a new analytic approach to study the phase diagram of random heteropolymers, based on the cavity method. For copolymers we analyze the nature and phenomenology of the glass transition as a function of sequence correlations. Depending on these correlations, we find that two different scenarios for the glass transition can occur. We show that, beside the much studied possibility of an abrupt freezing transition at low temperature, the system can exhibit, upon cooling, a first transition to a soft glass phase with fully broken replica symmetry and a continuously growing degree of freezing as the temperature is lowered. PACS numbers: 81.05.Lg, 64.70.Pf, 36.20.Ey
50th Anniversary Perspective: Phase Behavior of Polymer Solutions and Blends
Macromolecules, 2017
We summarize our knowledge of the phase behavior of polymer solutions and blends using a unified approach. We begin with a derivation of the Flory− Huggins expression for the Gibbs free energy of mixing two chemically dissimilar polymers. The Gibbs free energy of mixing of polymer solutions is obtained as a special case. These expressions are used to interpret observed phase behavior of polymer solutions and blends. Temperature-and pressure-dependent phase diagrams are used to determine the Flory−Huggins interaction parameter, χ. We also discuss an alternative approach for measuring χ due to de Gennes, who showed that neutron scattering from concentration fluctuations in one-phase systems was a sensitive function of χ. In most cases, the agreement between experimental data and the standard Flory−Huggins−de Gennes approach is qualitative. We conclude by summarizing advanced theories that have been proposed to address the limitations of the standard approach. In spite of considerable effort, there is no consensus on the reasons for departure between the standard theories and experiments.
Networklike pattern formation in phase separating polymer solutions: a molecular dynamics study
1998
The dynamics of phase separation of a quenched polymer solution is studied using a stochastic molecular dynamics simulation. At early times, the elastic nature of the polymer chains generates a networklike domain morphology for sufficiently dense polymer solutions. However, at late times, this network structure breaks up into disconnected polymer-rich domains to minimize the interfacial energy. Our simulations explain why different experiments carried out to different time regimes seem to produce contradictory results, and strongly indicate that the true late-time growth kinetics of quenched polymer solutions belong to the same universality class of small molecular mixtures. [S0031-9007(97)04972-7]