Spatially uniform electric fields have been used to induce instabilities in liquids and polymers, and to orient and deform ordered phases of block-copolymers. Here we discuss the demixing phase transition occurring in liquid mixtures when they are subject to spatially nonuniform fields. Above the critical value of potential, a phase-separation transition occurs, and two coexisting phases appear separated by a sharp interface. Analytical and numerical composition profiles are given, and the interface location as a function of charge or voltage is found. The possible influence of demixing on the stability of suspensions and on inter-colloid interaction is discussed.
Colloidal suspensions with free polymer coils which are larger than the colloidal particles are considered. The polymer-colloid interaction is modeled by an extension of the Asakura-Oosawa model. Phase separation occurs into dilute and dense fluid phases of colloidal particles when polymer is added. The critical density of this transition tends to zero as the size of the polymer coils diverges.
We study polymer-polymer phase separation in a common good solvent by means of Monte Carlo simulations of the bond-fluctuation model. Below a critical, chain-length dependent concentration, no phase separation occurs. For higher concentrations, the critical demixing temperature scales nonlinearly with the total monomer concentration, with a power law relatively close to a renormalization-group prediction based on "blob" scaling arguments. We point out that earlier simulations and experiments have tested this power-law dependence at concentrations outside the validity regime of the scaling argu…
The cellular cytoplasm is organized into compartments. Phase separation is a simple manner to create membrane-less compartments in order to confine and localize particles like proteins. In many cases these particles are bound to fluctuating polymers like DNA or RNA. We propose a general theoretical framework for such polymer-bound particles and derive an effective 1D lattice gas model with both nearest-neighbor and emergent long-range interactions arising from looped configurations of the fluctuating polymer. We argue that 1D phase transitions exist in such systems for both Gaussian and self-a…
We study theoretically a model system of a transient network of microemulsion droplets connected by telechelic polymers and explain recent experimental findings. Despite the absence of any specific interactions between either the droplets or polymer chains, we predict that as the number of polymers per drop is increased, the system undergoes a first order phase separation into a dense, highly connected phase, in equilibrium with dilute droplets, decorated by polymer loops. The phase transition is purely entropic and is driven by the interplay between the translational entropy of the drops and …
Phase separation in mixtures of polymers and alkanes is investigated with the aid of a recently developed lattice model, based on the Born-Green-Yvon (BGY) integral equation approach to fluids. The system-dependent parameters of the BGY lattice model for binary mixtures are deduced from those of its pure components, which in turn are determined from a comparison with experimental data. The lower critical solution temperatures (LCST's) for polyethylene in various n-alkanes were predicted from the BGY lattice model and compared with experimental data. While the model underestimates the LCST's fo…
We model a melt of monodisperse side-chain liquid crystalline polymers as a melt of comb copolymers in which the side groups are rod-coil diblock copolymers. We consider both excluded volume and Maier-Saupe interactions. The first acts among any pair of segments while the latter acts only between rods. Using a free energy functional calculated from this microscopic model, we study the spinodal stability of the isotropic phase against density and orientational fluctuations. The phase diagram obtained in this way predicts nematic and smectic instabilities as well as the existence of microphases …
We consider polymers attached to the tip of a cone, and the resulting force due to entropy loss on approaching a plate (or another cone). At separations shorter than the polymer radius of gyration R_g, the only relevant length scale is the tip-plate (or tip-tip) separation h, and the entropic force is given by F=A kT/h. The universal amplitude A can be related to (geometry dependent) correlation exponents of long polymers. We compute A for phantom polymers, and for self-avoiding (including star) polymers by epsilon-expansion, as well as by numerical simulations in 3 dimensions.
We numerically investigate viscoelastic phase separation in polymer solutions under shear using a time-dependent Ginzburg-Landau model. The gross variables in our model are the polymer volume fraction and a conformation tensor. The latter represents chain deformations and relaxes slowly on the rheological time giving rise to a large viscoelastic stress. The polymer and the solvent obey two-fluid dynamics in which the viscoelastic stress acts asymmetrically on the polymer and, as a result, the stress and the diffusion are dynamically coupled. Below the coexistence curve, interfaces appear with …
The number of configurations of a polymer is reduced in the presence of a barrier or an obstacle. The resulting loss of entropy adds a repulsive component to other forces generated by interaction potentials. When the obstructions are scale invariant shapes (such as cones, wedges, lines or planes) the only relevant length scales are the polymer size R_0 and characteristic separations, severely constraining the functional form of entropic forces. Specifically, we consider a polymer (single strand or star) attached to the tip of a cone, at a separation h from a surface (or another cone). At close…
We study the thermodynamics of binary mixtures with the volume fraction of the minority component less than the amount required to form a flat interface and show that the surface tension dominated equilibrium phase of the mixture forms a single macroscopic droplet. Elastic interactions in gel-polymer mixtures stabilize a phase with multiple droplets. Using a mean-field free energy we compute the droplet size as a function of the interfacial tension, Flory parameter, and elastic moduli of the gel. Our results illustrate the role of elastic interactions in dictating the phase behavior of biopoly…
We use Brownian dynamics simulations and advanced topological profiling methods to characterize the out-of-equilibrium evolution of self-entanglement in linear polymers confined into nano-channels and under periodic compression. We distinguish two main forms of entanglement, geometrical and topological. The latter is measured by the number of (essential) crossings of the physical knot detected after a suitable bridging of the chain termini. The former is instead measured as the average number of times a linear chain appears to cross itself when viewed under all projections, and is irrespective…
Polymeric materials that couple deformation and electrostatics have the potential for use in soft sensors and actuators with potential applications ranging from robotic, biomedical, energy, aerospace and automotive technologies. In contrast to the mechanics of polymers that has been studied using statistical mechanics approaches for decades, the coupled response under deformation and electrical field has largely been modeled only phenomenologically at the continuum scale. In this work, we examine the physics of the coupled deformation and electrical response of an electrically-responsive polym…
We study theoretically the equilibrium phase behaviour of a mixture of polydisperse hard-sphere colloids and monodisperse polymers, modelled using the Asakura-Oosawa model within the free volume approximation of Lekkerkerker et al. We compute full phase diagrams in the plane of colloid and polymer volume fractions, using the moment free energy method. The intricate features of phase separation in pure polydisperse colloids combine with the appearance of polymer-induced gas-liquid coexistence to give a rich variety of phase diagram topologies as the polymer-colloid size ratio and the colloid po…
Phase transition kinetics of aqueous hydroxypropyl cellulose solution was studied by using turbidimetric monitoring and mathematical modelling techniques. Based on the nonlinear Cahn-Hilliard equation with a mobility depending on the component concentration, the phase separation has been modeled on a simple one-dimensional Flory lattice. For value set of the interfacial energy parameter, data were obtained on the changing of the average values of the cluster sizes, their mass and concentration. The simulation results allow us to distinguish three stages of the spinodal decomposition: early, in…
Loop expansion in polymer field theory: application to phase separation
School of Physics, Korea Institute for Advanced Study（韩国高等科学研究院物理学院）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences（理化学研究所跨学科理论与数学科学中心）；RIKEN Pioneering Research Institute（理化学研究所先锋研究院）；RIKEN Center for Biosystems Dynamics Research（理化学研究所生物系统动力学研究中心）
The structure and thermodynamic state of a system changes under the influence of external electric fields. Neutral systems are characterized by their dielectric constant epsilon, while charged ones also by their charge distribution. In this Colloquium several phenomena occurring in soft-matter systems in spatially uniform and nonuniform fields are surveyed and the role of the conductivity sigma and the linear or nonlinear dependency of epsilon on composition are identified. Uniform electric fields are responsible for elongation of droplets, for destabilization of interfaces between two liquids…
We study analytically a continuum model for phase-separation in binary polymer blends based on the Flory-Huggins-De Gennes free energy, by means of the self-consistent large-$n$ limit approach. The model is solved for values of the parameters corresponding to the weak and strong segregation limits. For deep quenches we identify a complex structure of intermediate regimes and crossovers characterized by the existence of a time domain such that phase separation is pinned, followed by a preasymptotic regime which in the scalar case corresponds to surface diffusion. The duration of the pinning is …
We investigate the properties of a system of semi-diluted polymers in the presence of charged groups and counter-ions, by means of self-consistent field theory. We study a system of polyelectrolyte chains grafted to a similarly, as well as an oppositely charged surface, solving a set of saddle-point equations that couple the modified diffusion equation for the polymer partition function to the Poisson-Boltzmann equation describing the charge distribution in the system. A numerical study of this set of equations is presented and comparison is made with previous studies. We then consider the cas…
Constitutive modeling of dielectric elastomers has been of long standing interest in mechanics. Over the last two decades rigorous constitutive models have been developed that couple the electrical response of these polymers with large deformations characteristic of soft solids. A drawback of these models is that unlike classic models of rubber elasticity they do not consider the coupled electromechanical response of single polymer chains which must be treated using statistical mechanics. The objective of this paper is to compute the stretch and polarization of single polymer chains subject to…
We show here a general model of phase separation in isotropic condensed matter, namely, a viscoelastic model. We propose that the bulk mechanical relaxation modulus that has so far been ignored in previous theories plays an important role in viscoelastic phase separation in addition to the shear relaxation modulus. In polymer solutions, for example, attractive interactions between polymers under a poor-solvent condition likely cause the transient gellike behavior, which makes both bulk and shear modes active. Although such attractive interactions between molecules of the same component exist u…
Microphase separation in polymeric systems provides a bottom-up strategy to fabricate nanostructures. Polymers that are reported to undergo microphase separation usually include block copolymers or polyelectrolytes. Neutral homopolymers, which are comparatively easy to synthesize, are thought to be incapable of microphase separation. Here, using a minimal model that accounts for ion solvation, we show that microphase separation is possible in neutral homopolymer blends with sufficient dielectric contrast, upon a tiny amount of salt-doping. The driving force for the microphase separation is the…
The influence of immobile filler particles (spheres, fibers, platelets) on polymer blend phase separation is investigated computationally using a generalization of the Cahn-Hilliard-Cook (CHC) model. Simulation shows that the selective affinity of one of the polymers for the filler surface leads to the development of concentration waves about the filler particles at an early stage of phase separation in near critical composition blends. These "target" patterns are overtaken in late stage phase separation by a growing "background" spinodal pattern characteristic of blends without filler particl…
Polymer-Residue Accessibility Shapes Sequence Dependence of Critical Temperatures for Phase Separation
Omenn-Darling Bioengineering Institute, Princeton University（普林斯顿大学奥曼-达林生物工程研究所）；Department of Chemical and Biomolecular Engineering, University of California, Los Angeles（加州大学洛杉矶分校化学与生物分子工程系）；Princeton Center for Theoretical Science, Princeton University（普林斯顿大学普林斯顿理论科学中心）；Department of Chemical and Biological Engineering, Princeton University（普林斯顿大学化学与生物工程学系）；Department of Mechanical and Aerospace Engineering, Princeton University（普林斯顿大学机械与航空航天工程学系）
We study the motion of long polymers (eg DNA) in a gel under the influence of an external force acting locally on small segments of the polymer. In particular, we examine the dependence of the drift velocity on the position where the force acts and the length of the polymer. As an application, we discuss the possibility of gel magnetophoresis - the size-separation of long polymers by the attachment of a magnetic bead at an arbitrary position along the length of the polymer. We show that there is a regime where the separation of such polymers with this `random-position beading' is possible.
In this paper we show that the virial expansion up to third order for the osmotic pressure of a dilute polymer solution, including first-order perturbative corrections to the virial coefficients, allows for a scaling description of phase-separation data for polymer solutions in reduced variables. This scaling description provides a method to estimate the Theta-temperature, where demixing occurs in the limit of vanishing polymer volume fraction $ϕ$ and infinite chain-length $N$, without explicit assumptions concerning the chain-length dependence of the critical parameters $T_c$ and $ϕ_c$. The s…
We present a new computational methodology for the investigation of gel electrophoresis of polyelectrolytes. We have developed the method initially to incorporate sliding motion of tight parts of a polymer pulled by an electric field into the bond fluctuation method (BFM). Such motion due to tensile force over distances much larger than the persistent length is realized by non-local movement of a slack monomer at an either end of the tight part. The latter movement is introduced stochastically. This new BFM overcomes the well-known difficulty in the conventional BFM that polymers are trapped b…
Surface segregation of the low-molecular weight component in a polymeric mixture leads to degradation of industrial formulations. We report a simultaneous phase separation and surface migration phenomena in oligomer-polymer and oligomer-gel systems following a temperature quench. We compute equilibrium and time varying migrant density profiles and wetting layer thickness using coarse grained molecular dynamics and mesoscale hydrodynamics simulations to demonstrate that surface migration in oligomer-gel systems is significantly reduced due to network elasticity. Further, phase separation proces…
Phase separation of sequence-disordered liquid crystalline polymers, a promising class of technological and biological relevance, is studied by field theory, and thermodynamic mechanisms responsible for orientational ordering observed in experiments, are discussed. The theory developed predicts that chemical disorder marginally affects the nematic/isotropic biphasic coexistence width, but strongly impacts ordering; above a critical chemical disorder threshold orientational ordering is precluded.
