Temperature Gradients Induced Phase Separation in a Miscible Polymer Solution

Giant Casimir Nonequilibrium Forces Drive Coil to Globule Transition in Polymers

We develop a theory to probe the effect of nonequilibrium fluctuation-induced forces on the size of a polymer confined between two horizontal, thermally conductive plates subject to a constant temperature gradient, ∇ T. We assume that (a) the solvent is good and (b) the distance between the plates is large so that in the absence of a thermal gradient the polymer is a coil, whose size scales with the number of monomers as N^ν, with ν ≈ 0.6. We find that above a critical temperature gradient, ∇ T_c ≈ N^-5/4, a favorable attractive monomer-monomer interaction due to the giant Casimir force (GCF) overcomes the chain conformational entropy, resulting in a coil-globule transition. Our predictions can be verified using light-scattering experiments with polymers, such as polystyrene or polyisoprene in organic solvents in which the GCF is attractive.

Solvent coarsening around colloids driven by temperature gradients

Using mesoscopic numerical simulations and analytical theory, we investigate the coarsening of the solvent structure around a colloidal particle emerging after a temperature quench of the colloid surface. Qualitative differences in the coarsening mechanisms are found, depending on the composition of the binary liquid mixture forming the solvent and on the adsorption preferences of the colloid. For an adsorptionwise neutral colloid, the phase next to its surface alternates as a function of time. This behavior sets in on the scale of the relaxation time of the solvent and is absent for colloids with strong adsorption preferences. A Janus colloid, with a small temperature difference between its two hemispheres, reveals an asymmetric structure formation and surface enrichment around it, even if the solvent is within its one-phase region and if the temperature of the colloid is above the critical demixing temperature T_{c} of the solvent. Our phenomenological model turns out to capture recent experimental findings according to which, upon laser illumination of a Janus colloid and due to the ensuing temperature gradient between its two hemispheres, the surrounding binary liquid mixture develops a concentration gradient.

Simulation of phase separation with temperature-dependent viscosity using lattice Boltzmann method

This paper presents an exploration of the phase separation behavior and pattern formation in a binary fluid with temperature-dependent viscosity via a coupled lattice Boltzmann method (LBM). By introducing a viscosity-temperature relation into the LBM, the coupling effects of the viscosity-temperature coefficient [Formula: see text] , initial viscosity [Formula: see text] and thermal diffusion coefficient [Formula: see text] , on the phase separation were successfully described. The calculated results indicated that an increase in initial viscosity and viscosity-temperature coefficient, or a decrease in the thermal diffusion coefficient, can lead to the orientation of isotropic growth fronts over a wide range of viscosity. The results showed that droplet-type phase structures and lamellar phase structures with domain orientation parallel or perpendicular to the walls can be obtained in equilibrium by controlling the initial viscosity, thermal diffusivity, and the viscosity-temperature coefficient. Furthermore, the dataset was rearranged for growth kinetics of domain growth and thermal diffusion fronts in a plot by the spherically averaged structure factor and the ratio of separated and continuous phases. The analysis revealed two different temporal regimes: spinodal decomposition and domain growth stages, which further quantified the coupled effects of temperature and viscosity on the evolution of temperature-dependent phase separation. These numerical results provide guidance for setting optimum temperature ranges to obtain expected phase separation structures for systems with temperature-dependent viscosity.

Universal scaling effects of a temperature gradient at first-order transitions

We study the effects of smooth inhomogeneities at first-order transitions. We show that a temperature gradient at a thermally driven first-order transition gives rise to nontrivial universal scaling behaviors with respect to the length scale l_{t} of the variation of the local temperature T_{x}. We propose a scaling ansatz to describe the crossover region at the surface where T_{x}=T_{c}, where the typical discontinuities of a first-order transition are smoothed out. The predictions of this scaling theory are checked, and get strongly supported, by numerical results for the two-dimensional (2D) Potts models, for a sufficiently large number of states to have first-order transitions. Comparing with analogous results at the 2D Ising transition, we note that the scaling behaviors induced by a smooth inhomogeneity appear quite similar in first-order and continuous transitions.

A theoretical study of biological membrane response to temperature gradients at the single-cell level

Recent experimental studies provide evidence for the existence of a spatially non-uniform temperature field in living cells and in particular in their plasma membrane. These findings have led to the development of a new and exciting field: thermal biology at the single-cell level. Here, we examine theoretically a specific aspect of this field, i.e. how temperature gradients at the single-cell level affect the phase behaviour and geometry of heterogeneous membranes. We address this issue by using the Onsager reciprocal relations combined with a simple model for a binary lipid mixture. We demonstrate that even small temperature variations along the membrane may introduce intriguing phenomena, such as phase separation above the critical temperature and unusual shape response. These results also suggest that the shape of a membrane can be manipulated by dynamically controlling the temperature field in its vicinity. The effects of intramembranous temperature gradients have never been studied experimentally. Thus, the predictions of the current contribution are of a somewhat speculative nature. Experimental verification of these results could mark the beginning of a new line of research in the field of biological membranes. We report our findings with the hope of inspiring others to perform such experiments.

Polymer Microstructures Self-Assemble on Single-Walled Carbon Nanotube Thin Films

The formation of self-assembled microstructures of anionic polyelectrolyte, poly(acrylic acid) salts, on the surface of single-walled carbon nanotube thin films was studied by a fast phase separation process that filtrated a mixed dispersion composed of single-walled carbon nanotubes and poly(acrylic acid) derivatives on a membrane filter. The resulting microstructures of poly(acrylic acid) self-assembly were characterized by scanning electron microscopy, energy-dispersive X-ray spectroscopy, element mapping, and diffuse reflectance Fourier transform infrared spectroscopy. The influence factors including substrate, ion species, single-walled carbon nanotubes, and different kinds of carbon nanotubes were discussed comprehensively for the formation of microstructures of PAA self-assembly by a liquid-liquid phase separation.

Effect of temperature gradient on liquid-liquid phase separation in a polyolefin blend

We have investigated experimentally the structure formation processes during phase separation via spinodal decomposition above and below the spinodal line in a binary polymer blend system exposed to in-plane stationary thermal gradients using phase contrast optical microscopy and temperature gradient hot stage. Below the spinodal line there is a coupling of concentration fluctuations and thermal gradient imposed by the temperature gradient hot stage. Also under the thermal gradient annealing phase-separated domains grow faster compared with the system under homogeneous temperature annealing on a zero-gradient or a conventional hot stage. We suggest that the in-plane thermal gradient accelerates phase separation through the enhancement in concentration fluctuations in the early and intermediate stages of spinodal decomposition. In a thermal gradient field, the strength of concentration fluctuation close to the critical point (above the spinodal line) is strong enough to induce phase separation even in one-phase regime of the phase diagram. In the presence of a temperature gradient the equilibrium phase diagrams are no longer valid, and the systems with an upper critical solution temperature can be quenched into phase separation by applying the stationary temperature gradient. The in-plane temperature gradient drives enhanced concentration fluctuations in a binary polymer blend system above and below the spinodal line.

The Soret effect in dilute polymer solutions: influence of chain length, chain stiffness, and solvent quality

Thermal diffusion in dilute polymer solutions is studied by reverse nonequilibrium molecular dynamics. The polymers are represented by a generic bead-spring model. The influence of the solvent quality on the Soret coefficient is investigated. At constant temperature and monomer fraction, a better solvent quality causes a higher affinity for the polymer to the cold region. This may even go to thermal-diffusion-induced phase separation. The sign of the Soret coefficient changes in a symmetric nonideal binary Lennard-Jones solution when the solvent quality switches from good to poor. The known independence of the thermal diffusion coefficients of the molecular weight is reproduced for three groups of polymers with different chain stiffnesses. The thermal diffusion coefficients reach constant values at chain lengths of around two to three times the persistence length. Moreover, rigid polymers have higher Soret coefficients and thermal diffusion coefficients than more flexible polymers.

Thermal patterning of a critical polymer blend

Utilizing the Soret effect, we have employed a moderately focused laser beam (30 microm, 20 mW) to write spatial composition patterns into layers of the critical polymer blend poly(dimethyl siloxane)/poly(ethyl-methyl siloxane) (PDMS/PEMS, M(w)=16.4/22.8 kg/mol) both in the one- and in the two-phase region a few degrees above and below the critical temperature T(c)=37.7 degrees C. Because of the critical divergence of the Soret coefficient, moderate temperature gradients are sufficient to induce composition modulations of large amplitude. In the two-phase regime the spinodal demixing pattern can be locally manipulated in a controlled way. 2D simulations based on a modified Cahn-Hilliard equation are able to reproduce the essential spatial and temporal features observed in the experiments.

Convection-driven pattern formation in phase-separating binary fluids

Using a thermal-lattice Boltzmann model, we examine the rich phase behavior that develops when partially miscible fluids evolve in the presence of a vertical temperature gradient, which encompasses the critical temperature T(c) of the mixture. In particular, a binary AB fluid is confined between two plates in a gravitational field. The upper plate is fixed below T(c) and hence, the nearby fluid phase separates into A-rich and B-rich domains. The lower plate is fixed above the temperature T(c), and the surrounding fluid is in the homogeneous phase. A coupling between convection (driven by the temperature gradient) and phase separation gives rise to unique pattern formation. A number of regimes are identified: regularly spaced stripes, convective steady-state columns, the periodic disturbance of these columns, and finally, chaotic dripping from the upper surface. These results highlight dynamical behavior in partially miscible mixtures.

Filler-induced composition waves in phase-separating polymer blends

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 particles. The linearized CHC model is used to estimate the number of composition oscillations emanating from isolated filler particles. In far-off-critical composition blends, an "encapsulation layer" grows at the surface of the filler rather than a target pattern. The results of these simulations compare favorably with experiments on filled phase-separating ultrathin blend films in which the filler particles are immobilized on a solid substrate.