Kinetics of phase separation in polymer mixtures: A molecular dynamics study

Nonuniversality of Aging during Phase Separation of the Two-Dimensional Long-Range Ising Model

We investigate the aging properties of phase-separation kinetics following quenches from T=∞ to a finite temperature below T_{c} of the paradigmatic two-dimensional conserved Ising model with power-law decaying long-range interactions ∼r^{-(2+σ)}. Physical aging with a power-law decay of the two-time autocorrelation function C(t,t_{w})∼(t/t_{w})^{-λ/z} is observed, displaying a complex dependence of the autocorrelation exponent λ on σ. A value of λ=3.500(26) for the corresponding nearest-neighbor model (which is recovered as the σ→∞ limit) is determined. The values of λ in the long-range regime (σ<1) are all compatible with λ≈4. In between, a continuous crossover is visible for 1≲σ≲2 with nonuniversal, σ-dependent values of λ. The performed Metropolis Monte Carlo simulations are primarily enabled by our novel algorithm for long-range interacting systems.

Growth kinetics and morphology characterization of binary polymeric fluid under random photo-illumination

We present a comprehensive study using dissipative particle dynamics simulations to investigate phase separation kinetics (PSK) in three-dimensional (3d) polymeric fluids under random photo-illumination. We consider two scenarios: polymer blends with active radicals at one end of each immiscible chain and block copolymer (BCP) melts with photosensitive bonds linking incompatible blocks. The phase separation (PS) is induced by temperature quench of the initial homogeneously mixed system. Simultaneously, the system experiences random photo-illumination, simulated by two concurrent random events: (a) the recombination of active radicals in polymer blends and (b) the breaking of photosensitive bonds in BCP chains. Variations in the bond-breaking probability, Pb, mimic the change in light intensity. The length scale follows power law growth, R(t) ∼ tϕ, where ϕ represents the growth exponent. Increasing Pb results in a gradual transition in growth kinetics from micro-PS to macro-PS, accompanied by corresponding transition probabilities for both systems. Micro-PSK dominates the evolution process at low Pb values. The scaling functions exhibit data overlap for most scaled distances, indicating the statistical self-similarity of evolving patterns. Our study enhances the understanding of PSK in polymeric fluids, revealing the impact of photosensitive bonds and active radicals. Furthermore, it suggests the potential for designing novel polymeric materials with desired properties.

Effect of amphiphilic polymers on phase separating binary mixtures: A DPD simulation study

We present the phase separation dynamics of a binary (AB), simple fluid (SF), and amphiphilic polymer (AP) mixture using dissipative particle dynamics simulation at d = 3. We study the effect of different AP topologies, including block copolymers, ring block copolymers (RCP), and miktoarm star polymers, on the evolution morphologies, dynamic scaling functions, and length scale of the AB mixture. Our results demonstrate that the presence of APs leads to significantly different evolution morphologies in SF. However, the deviation from dynamical scaling is prominent, mainly for RCP. Typically, the characteristic length scale for SF follows the power law R(t) ∼ tϕ, where ϕ is the growth exponent. In the presence of high AP, we observe diffusive growth (ϕ → 1/3) at early times, followed by saturation in length scale (ϕ → 0) at late times. The extent of saturation varies with constraints imposed on the APs, such as topology, composition ratio, chain length, and stiffness. At lower composition ratios, the system exhibits inertial hydrodynamic growth (ϕ → 2/3) at asymptotic times without clearly exhibiting the viscous hydrodynamic regime (ϕ → 1) at earlier times in our simulations. Our results firmly establish the existence of hydrodynamic growth regimes in low surfactant-influenced phase separation kinetics of binary fluids and settle the related ambiguity in d = 3 systems.

Mechanical Slowing Down of Network-Forming Phase Separation of Polymer Solutions

Phase separation is a fundamental phenomenon leading to spatially heterogeneous material distribution, which is critical in nature, biology, material science, and industry. In ordinary phase separation, the minority phase always forms droplets. Contrary to this common belief, even the minority phase can form a network structure in viscoelastic phase separation (VPS). VPS can occur in any mixture with significant mobility differences between their components and is highly relevant to soft matter and biomatter. In contrast to classical phase separation, experiments have shown that VPS in polymer solutions lacks self-similar coarsening, resulting in the absence of a domain-coarsening scaling law. However, the underlying microscopic mechanism of this behavior remains unknown. To this end, we perform fluid particle dynamics simulations of bead-spring polymers, incorporating many-body hydrodynamic interactions between polymers through a solvent. We discover that polymers in the dense-network-forming phase are stretched and store elastic energy when the deformation speed exceeds the polymer dynamics. This self-generated viscoelastic stress mechanically interferes with phase separation and slows its dynamics, disrupting self-similar growth. We also highlight the essential role of many-body hydrodynamic interactions in VPS. The implications of our findings may hold importance in areas such as biological phase separation, porous material formation, and other fields where network structures play a pivotal role.

Segregation of fluids with polymer additives at domain interfaces: a dissipative particle dynamics study

This paper investigates the phase separation kinetics of ternary fluid mixtures composed of a polymeric component (C) and two simple fluids (A and B) using dissipative particle dynamics simulations with a system dimensionality of d = 3. We model the affinities between the components to enable the settling of the polymeric component at the interface of fluids A and B. Thus, the system evolves to form polymer coated morphologies, enabling alteration of the fluids' interfacial properties. This manipulation can be utilized across various disciplines, such as the stabilization of emulsions and foams, rheological control, biomimetic design, and surface modification. We probe the effects of various parameters, such as the polymeric concentration, chain stiffness, and length, on the phase separation kinetics of the system. The simulation results show that changes in the concentration of flexible polymers exhibit perfect dynamic scaling for coated morphologies. The growth rate decreases as the polymeric composition is increased due to reduced surface tension and restricted connectivity between A- and B-rich clusters. Variations in the polymer chain rigidity at fixed composition ratios and degrees of polymerization slow the evolution kinetics of AB fluids marginally, although the effect is more pronounced for perfectly rigid chains. Whereas flexible polymer chain lengths at fixed composition ratios slow down the segregation kinetics of AB fluids slightly, varying the chain lengths of perfectly rigid polymers leads to a significant deviation in the length scale and dynamic scaling for the evolved coated morphologies. The characteristic length scale follows a power-law growth with a growth exponent ϕ that shows a crossover from the viscous to the inertial hydrodynamic regime, where the values of ϕ depend on the constraints imposed on the system.

Hydrodynamic effects in kinetics of phase separation in binary fluids: Critical versus off-critical compositions

Via hydrodynamics-preserving molecular dynamics simulations we study growth phenomena in a phase-separating symmetric binary mixture model. We quench high-temperature homogeneous configurations to state points inside the miscibility gap, for various mixture compositions. For compositions at the symmetric or critical value we capture the rapid linear viscous hydrodynamic growth due to advective transport of material through tubelike interconnected domains. For state points very close to any of the branches of the coexistence curve, the growth in the system, following nucleation of disconnected droplets of the minority species, occurs via a coalescence mechanism. Using state-of-the-art techniques, we have identified that these droplets, between collisions, exhibit diffusive motion. The value of the exponent for the power-law growth, related to this diffusive coalescence mechanism, has been estimated. While the exponent nicely agrees with that for the growth via the well-known Lifshitz-Slyozov particle diffusion mechanism, the amplitude is stronger. For the intermediate compositions we observe initial rapid growth that matches the expectations for viscous or inertial hydrodynamic pictures. However, at later times these types of growth cross over to the exponent that is decided by the diffusive coalescence mechanism.

Facile Stratification-Enabled Emergent Hyper-Reflectivity in Cholesteric Liquid Crystals

Cholesteric liquid crystals (CLCs) are chiral photonic materials with selective reflection in terms of wavelength and polarization. Helix engineering is often required in order to produce desired properties for CLC materials to be employed for beam steering, light diffraction, scattering, and adaptive or broadband reflection. Here, we demonstrate a novel photopolymerization-enforced stratification (PES)-based strategy to realize helix engineering in a chiral CLC system with initially one handedness of molecular rotation throughout the layer. PES plays a crucial role in driving the chiral dopant bundle consisting of two chiral dopants of opposite handedness to spontaneously phase separate and create a CLC bilayer structure that reflects left- and right-handed circularly polarized light (CPL). The initially hidden chiral information therefore becomes explicit, and hyper-reflectivity, i.e., reflecting both left- and right-handed CPL, successfully emerges from the designed CLC mixture. The PES mechanism can be applied to structure a wide range of liquid crystal (LC) and polymer materials. Moreover, the engineering strategy enables facile programming of the center wavelength of hyper-reflection, patterning, and incorporating stimuli-responsiveness in the optical device. Hence, the engineered hyper-reflective CLCs offer great promise for future applications, such as digital displays, lasing, optical storage, and smart windows.

Photo-induced bond breaking during phase separation kinetics of block copolymer melts: a dissipative particle dynamics study

Using a dissipative particle dynamics (DPD) simulation method, we study the phase separation dynamics in block copolymer (BCP) melts in d = 3, subjected to external stimuli such as light. An initial homogeneous BCP melt is rapidly quenched to a temperature T < T_c, where T_c is the critical temperature. We then allow the system to undergo alternate light "on" and "off" cycles. An on-cycle breaks the stimuli-sensitive bonds connecting both the blocks A and B in the BCP melt, and during the off-cycle, the broken bonds recombine. By simulating the effect of light, we isolate scenarios where phase separation begins with the light off (set 1); the cooperative interactions within the system allow it to undergo microphase separation. When the phase separation starts with the light on (set 2), the system undergoes macrophase separation due to bond breaking. Here, we report the role of alternate cycles on domain morphology by varying the bond-breaking probability for both set 1 and set 2, respectively. We observe that the scaling functions depend upon the conditions mentioned above that change the time scale of the evolving morphologies in various cycles. However, in all the cases, the average domain size respects the power-law growth: R(t) ∼t^φ at late times, where φ is the dynamic growth exponent. After a short-lived diffusive growth (φ∼ 1/3) at early times, φ illustrates a crossover from the viscous hydrodynamic (φ∼ 1) to the inertial hydrodynamic (φ∼ 2/3) regimes at late times.

Power-law coarsening in network-forming phase separation governed by mechanical relaxation

A space-spanning network structure is a basic morphology in phase separation of soft and biomatter, alongside a droplet one. Despite its fundamental and industrial importance, the physical principle underlying such network-forming phase separation remains elusive. Here, we study the network coarsening during gas-liquid-type phase separation of colloidal suspensions and pure fluids, by hydrodynamic and molecular dynamics simulations, respectively. For both, the detailed analyses of the pore sizes and strain field reveal the self-similar network coarsening and the unconventional power-law growth more than a decade according to ℓ ∝ t1/2, where ℓ is the characteristic pore size and t is the elapsed time. We find that phase-separation dynamics is controlled by mechanical relaxation of the network-forming dense phase, whose limiting process is permeation flow of the solvent for colloidal suspensions and heat transport for pure fluids. This universal coarsening law would contribute to the fundamental physical understanding of network-forming phase separation.

Gelation Impairs Phase Separation and Small Molecule Migration in Polymer Mixtures

Surface segregation of the low molecular weight component of a polymeric mixture is a ubiquitous phenomenon that leads to degradation of industrial formulations. We report a simultaneous phase separation and surface migration phenomena in oligomer-polymer ( O P ) and oligomer-gel ( O G ) systems following a temperature quench that induces demixing of components. We compute equilibrium and time varying migrant (oligomer) density profiles and wetting layer thickness in these systems using coarse grained molecular dynamics (CGMD) and mesoscale hydrodynamics (MH) simulations. Such multiscale methods quantitatively describe the phenomena over a wide range of length and time scales. We show that surface migration in gel-oligomer systems is significantly reduced on account of network elasticity. Furthermore, the phase separation processes are significantly slowed in gels leading to the modification of the well known Lifshitz-Slyozov-Wagner (LSW) law ℓ ( τ ) ∼ τ 1 / 3 . Our work allows for rational design of polymer/gel-oligomer mixtures with predictable surface segregation characteristics that can be compared against experiments.

Role of a polymeric component in the phase separation of ternary fluid mixtures: a dissipative particle dynamics study

We present the results from dissipative particle dynamics (DPD) simulations of phase separation dynamics in ternary (ABC) fluids mixture in d = 3 where components A and B represent the simple fluids, and component C represents a polymeric fluid. Here, we study the role of polymeric fluid (C) on domain morphology by varying composition ratio, polymer chain length, and polymer stiffness. We observe that the system under consideration lies in the same dynamical universality class as a simple ternary fluids mixture. However, the scaling functions depend upon the parameters mentioned above as they change the time scale of the evolution morphologies. In all cases, the characteristic domain size follows l(t) ∼ tφ with dynamic growth exponent φ, showing a crossover from the viscous hydrodynamic regime (φ = 1) to the inertial hydrodynamic regime (φ = 2/3) in the system at late times.

Effect of bond-disorder on the phase-separation kinetics of binary mixtures: A Monte Carlo simulation study

We present Monte Carlo (MC) simulation studies of phase separation in binary (AB) mixtures with bond-disorder that is introduced in two different ways: (i) at randomly selected lattice sites and (ii) at regularly selected sites. The Ising model with spin exchange (Kawasaki) dynamics represents the segregation kinetics in conserved binary mixtures. We find that the dynamical scaling changes significantly by varying the number of disordered sites in the case where bond-disorder is introduced at the randomly selected sites. On the other hand, when we introduce the bond-disorder in a regular fashion, the system follows the dynamical scaling for the modest number of disordered sites. For a higher number of disordered sites, the evolution morphology illustrates a lamellar pattern formation. Our MC results are consistent with the Lifshitz-Slyozov power-law growth in all the cases.

Phase separation in ternary fluid mixtures: a molecular dynamics study

We present detailed results from molecular dynamics (MD) simulations of phase separation in ternary (ABC) fluid mixtures for d = 2 and d = 3 systems. Our MD simulations naturally incorporate hydrodynamic effects. The domain growth law is l(t) ∼ t(ϕ) with dynamic growth exponent ϕ. Our data clearly indicate that a ternary fluid mixture reaches a dynamical scaling regime at late times with a gradual crossover from ϕ = 1/3 → 1/2 → 2/3 in d = 2 and ϕ = 1/3 → 1 in d = 3 resulting from the hydrodynamic effect in the system. These MD simulations do not yet access the inertial hydrodynamic regime (with l(t) ∼ t(2/3)) of phase separation in ternary fluid mixtures in d = 3.