Kinetics Of Phase Separation Research Articles

Domain growth kinetics in active binary mixtures.

We study motility-induced phase separation in symmetric and asymmetric active binary mixtures. We start with the coarse-grained run-and-tumble bacterial model that provides evolution equations for the density fields ρi(r⃗,t). Next, we study the phase separation dynamics by solving the evolution equations using the Euler discretization technique. We characterize the morphology of domains by calculating the equal-time correlation function C(r, t) and the structure factor S(k, t), both of which show dynamical scaling. The form of the scaling functions depends on the mixture composition and the relative activity of the species, Δ. For k → ∞, S(k, t) follows Porod's law: S(k, t) ∼ k-(d+1) and the average domain size L(t) shows a diffusive growth as L(t) ∼ t1/3 for all mixtures.

Segregation kinetics of miktoarm star polymers: A dissipative particle dynamics study.

We study the phase separation kinetics of miktoarm star polymer (MSP) melts/blends with diverse architectures using dissipative particle dynamics simulation. Our study focuses on symmetric and asymmetric miktoarm star polymer (SMSP/AMSP) mixtures based on arm composition and number. For a fixed MSP chain size, the characteristic microphase-separated domains initially show diffusive growth with a growth exponent ϕ∼1/3 for both melts that gradually crossover to saturation at late times. The simulation results demonstrate that the evolution morphology of SMSP melt exhibits perfect dynamic scaling with varying arm numbers; the timescale follows a power-law decay with an exponent θ≃1 as the number of arms increases. The structural constraints on AMSP melts cause the domain growth rate to decrease as the number of one type of arms increases while their length remains fixed. This increase in the number of arms for AMSP corresponds to increased off-criticality. The saturation length in AMSP follows a power-law increase with an exponent λ≃2/3 as off-criticality decreases. Additionally, macrophase separation kinetics in SMSP/AMSP blends show a transition from viscous (ϕ∼1) to inertial (ϕ∼2/3) hydrodynamic growth regimes at late times; this exhibits the same dynamical universality class as linear polymer blends, with slight deviations at early stages.

Oil-in-water emulsion stabilized by hydrolysed black soldier fly larvae proteins: Reproduction of experimental data via phase-field modelling

A phase field model based on the Cahn-Hilliard equation was validated experimentally by comparison of the numerical data with experimental data of emulsions of oil in water stabilized with Black Soldier Fly Larvae Proteins (BSFLP) and protein hydrolysates. Among the model parameters, the surface tension was determined by the pendant drop method, and the mobility by two different experiments, one based on the Turbiscan Stability Index, and another one based on the history of the average d3,2, both of them throughout a 48 h period. The initial condition was built from an experimental droplet size distribution measured prior to phase separation. Results show that the model is able to quantitatively reproduce the phase separation kinetics, and provide an intuitive graphical representation of the droplet growth. Application of this procedure to other systems will allow the generalization of phase field modelling as a predictive tool for food applications.

Dynamics of phase separation of metastable crystal surfaces by surface diffusion: A phase-field study.

A new phase-field approach is designed to model surface diffusion of crystals with strongly anisotropic surface energy. The model can be shown to asymptotically converge toward the sharp-interface equationfor surface diffusion in the limit of vanishing interface width. It is employed to investigate the dynamical evolution of a thermodynamically metastable crystal surface. We find that nucleation and growth by surface diffusion of the newly formed surface induce the formation of additional stable surfaces at its wake. This induced nucleation mechanism is found to produce domains composed of several stable surfaces of prescribed width. The domains propagate on the crystal surface and then coalesce to form a hill-and-valley structure. The resulting morphology is more regular than the typical hill-and-valley surface produced by random thermal nucleation, i.e., when motion-by-curvature controls the phase separation dynamics. Moreover, the induced nucleation mechanism is found to be peculiar to surface diffusion and to dominate the phase separation at high degree of metastability. Once the hill-and-valley structure is formed, coarsening operates by motion and elimination of facet junctions, points where two facets merge to form one and we find the following scaling law L∼t^{1/6}, for the growth in time t of the characteristic length scale L during this coarsening stage. The density of junctions is found to exhibit a t^{-2/3} regime. Our results elucidate the role of the induced nucleation mechanism on the dynamics of interfacial phase separation and corroborate surface faceting experiments on ceramics.

Noise-Induced Phase Separation and Time Reversal Symmetry Breaking in Active Field Theories Driven by Persistent Noise.

Within the Landau-Ginzburg picture of phase transitions, scalar field theories develop phase separation because of a spontaneous symmetry-breaking mechanism. This picture works in thermodynamics but also in the dynamics of phase separation. Here we show that scalar nonequilibrium field theories undergo phase separation just because of nonequilibrium fluctuations driven by a persistent noise. The mechanism is similar to what happens in motility-induced phase separation where persistent motion introduces an effective attractive force. We observe that noise-induced phase separation occurs in a region of the phase diagram where disordered field configurations would otherwise be stable at equilibrium. Measuring the local entropy production rate to quantify the time-reversal symmetry breaking, we find that such breaking is concentrated on the boundary between the two phases.

Balancing thermodynamic stability, dynamics, and kinetics in phase separation of intrinsically disordered proteins.

Intrinsically disordered proteins (IDPs) are prevalent participants in liquid-liquid phase separation due to their inherent potential for promoting multivalent binding. Understanding the underlying mechanisms of phase separation is challenging, as phase separation is a complex process, involving numerous molecules and various types of interactions. Here, we used a simplified coarse-grained model of IDPs to investigate the thermodynamic stability of the dense phase, conformational properties of IDPs, chain dynamics, and kinetic rates of forming condensates. We focused on the IDP system, in which the oppositely charged IDPs are maximally segregated, inherently possessing a high propensity for phase separation. By varying interaction strengths, salt concentrations, and temperatures, we observed that IDPs in the dense phase exhibited highly conserved conformational characteristics, which are more extended than those in the dilute phase. Although the chain motions and global conformational dynamics of IDPs in the condensates are slow due to the high viscosity, local chain flexibility at the short timescales is largely preserved with respect to that at the free state. Strikingly, we observed a non-monotonic relationship between interaction strengths and kinetic rates for forming condensates. As strong interactions of IDPs result in high stable condensates, our results suggest that the thermodynamics and kinetics of phase separation are decoupled and optimized by the speed-stability balance through underlying molecular interactions. Our findings contribute to the molecular-level understanding of phase separation and offer valuable insights into the developments of engineering strategies for precise regulation of biomolecular condensates.

Genetically-encoded phase separation sensors for intracellular probing of biomolecular condensates.

Biomolecular condensates are dynamic membraneless compartments with enigmatic roles across intracellular phenomena. Intrinsically-disordered proteins (IDPs) often function as condensate scaffolds, fueled by their liquid-liquid phase separation (LLPS) dynamics. Intracellular probing of these condensates relies on live-cell imaging of IDP-scaffolds tagged with fluorescent proteins. Conformational heterogeneity in IDPs, however, renders them uniquely sensitive to molecular-level fusions, risking distortion of the native biophysical properties of IDP-scaffolds and their assemblies. Probing epidermal condensates in mouse skin, we recently introduced genetically encoded LLPS-sensors that circumvent the need for molecular-level tagging of skin IDPs. The concept of LLPS-sensors involves a shift in focus from subcellular tracking of IDP-scaffolds to higher-level observations that report on the assembly and liquid-dynamics of their condensates. Towards advancing the repertoire of intracellular LLPS-sensors, here we demonstrate biomolecular approaches for the evolution and tunability of epidermal LLPS-sensors and assess their impact in early and late stages of intracellular LLPS dynamics. Benchmarking against scaffold-bound fluorescent reporters, we found that tunable ultraweak scaffold-sensor interactions are key to the sensitive and innocuous probing of nascent and established biomolecular condensates. Our LLPS-sensitive tools pave the way for the high-fidelity intracellular probing of IDP-governed biomolecular condensates across biological systems.

Emergence and growth dynamics of wetting-induced phase separation on soft solids

Liquid droplets on soft solids, such as soft polymeric gels, can induce substantial surface deformations, leading to the formation of wetting ridges at contact points. While these contact ridges have been shown to govern the rich surface mechanics on compliant substrates, the inherently divergent characteristics of contact points and the multiphase nature of soft reticulated gels pose great challenges for continuum mechanical theories in modeling soft wetting phenomena. In this study, we report experimental characterizations of the emergence and growth dynamics of the wetting-induced phase separation. The measurements demonstrate how the migration of free chains prevents the stress singularities at contact points. Based on the Onsager variational principle, we present a phenomenological model that effectively captures the extraction process of free chains, including a crossover from a short-term diffusive state to a long-term equilibrium state. By comparing model predictions with experimental results for varied crosslinking densities, we reveal how the intrinsic material parameters of soft gels dictate phase-separation dynamics. Published by the American Physical Society 2024

Lie symmetry analysis, closed-form solutions and dynamics for the kinetics of phase separation in iron (Fe–Cr–X (X=Mo, Cu)) based on ternary alloys

Lie symmetry analysis, closed-form solutions and dynamics for the kinetics of phase separation in iron (Fe–Cr–X (X=Mo, Cu)) based on ternary alloys

Shape Memory Polymers with Patternable Recovery Onset Regulated by Light.

Shape memory polymers (SMPs) show attractive prospects in emerging fields such as soft robots and biomedical devices. Although their typical trigger-responsive character offers the essential shape-changing controllability, having to access external stimulation is a major bottleneck toward many applications. Recently emerged autonomous SMPs exhibit unique stimuli-free shape-shifting behavior with its controllability achieved via a delayed and programmable recovery onset. Achieving multi-shape morphing in an arbitrary fashion, however, is infeasible. In this work, a molecular design that allows to spatio-temporally define the recovery onset of an autonomous shape memory hydrogel (SMH) is reported. By introducing nitrocinnamate groups onto an SMH, its crosslinking density can be adjusted by light. This affects greatly the phase separation kinetics, which is the basis for the autonomous shape memory behavior. Consequently, the recovery onset can be regulated between 0 to 85min. With masked light, multiple recovery onsets in an arbitrarily defined pattern which correspondingly enable multi-shape morphing can be realized. This ability to achieve highly sophisticated morphing without relying on any external stimulation greatly extends the versatility of SMPs.

Preparation and size control of epoxy resin multilevel structures with SiO2 particles

In the process of preparing porous epoxy materials using reaction-induced phase separation (RIPS), the introduction of an appropriate amount of SiO2 particles enables the control of the phase separation behavior of the system and its ultimate phase structure. This study examined the role of SiO2 particles in the preparation and size control of epoxy resin multilevel structures by analyzing the phase separation and reaction kinetics in an epoxy resin blend system and characterizing the ultimate phase structure. It was found that fumed SiO2 particles (0–3 wt%) added to the DGEBA/DDCM/PEG200 blends resulted in significant interfacial stabilization, delaying phase separation. With an increase in the fumed SiO2 particle content, the phase structure stopped evolving at an earlier stage of phase separation. In addition, the fumed SiO2 particles dispersed in the porogen-enriched phase helped to stabilize the system, i.e., preventing or slowing down the segregation and aggregation of the components in the system, which may inhibit secondary phase separation in the porogen-enriched phase. When 350 nm SiO2 particles were used, an increase in the particle size resulted in a larger phase structure. The SiO2 particles were dispersed within the pore-forming agent phase, increasing the proportion of the pore-forming agent and exerting an occupancy effect, which diminished with decreasing SiO2 particle size and increasing hydrophobicity. Notably, the surface of the epoxy porous material skeleton was decorated with small pits formed by the acid etching of the SiO2 particles, and this multilevel structure contributed to the specific surface area. The multilevel structure can be precisely controlled by adjusting the size, content, and wettability of the SiO2 particles. The results of this study are universal and instructive for the preparation of porous materials using a phase separation method in combination with solid particles.

Convergence and stability analysis of energy stable and bound‐preserving numerical schemes for binary fluid‐surfactant phase‐field equations

AbstractIn this article, we develop stable and efficient numerical schemes for a binary fluid‐surfactant phase‐field model which consists of two Cahn–Hilliard type equations with respect to the free energy containing a Ginzburg–Landau double‐well potential, a logarithmic Flory–Huggins potential and a nonlinear coupling entropy. The numerical schemes, which are decoupled and linear, are established by the central difference spatial approximation in combination with the first‐ and second‐order exponential time differencing methods based on the convex splitting of the free energy. For the sake of the linearity of the schemes, the nonlinear terms, especially the logarithmic term, are approximated explicitly, which requires the bound preservation of the numerical solution to make the algorithm robust. We conduct the convergence analysis and prove the bound‐preserving property in details for both first‐ and second‐order schemes, where the high‐order consistency analysis is applied to the first‐order case. In addition, the energy stability is also obtained by the nature of the convex splitting. Numerical experiments are performed to verify the accuracy and stability of the schemes and simulate the dynamics of phase separation and surfactant adsorption.

Diels-Alder Network Blends as Self-Healing Encapsulants for Liquid Metal-Based Stretchable Electronics.

Two dynamic covalent networks based on the Diels-Alder reaction were blended to exploit the properties of the dissimilar polymer backbones. Furan-functionalized polyether amines based on poly(propylene oxide) (PPO) FD4000 and polydimethylsiloxane (PDMS) FS5000 were mixed in a common solvent and reversibly cross-linked with the same bismaleimide DPBM. The morphology of the phase-separated blends is primarily controlled by the concentration of backbones. Increasing the PDMS content of the blends results in a dilute droplet morphology at 25 wt %, with a growing size and concentration of droplets and the formation of two separate PPO- and PDMS-rich layers at 50 wt %. Further increasing the PDMS content to 75 wt % leads to larger droplets and a thicker layer of the secondary phase. The hydrophobic PDMS phase creates a barrier against water, while the more hydrophilic PPO phase enhances the resistance against oxygen diffusion. Lowering the maleimide-to-furan stoichiometric ratio resulted in a decrease in cross-link density and thus more flexible and stretchable encapsulants. Changes in the stoichiometric ratio also affected the phase morphology due to resulting changes in phase separation and network formation kinetics. Lowering the stoichiometric ratio also resulted in enhanced self-healing properties of 96% at room temperature as a consequence of the increased chain mobility in the blended networks. The self-healing blends were used to encapsulate liquid metal circuits to create stretchable strain sensors with a linear electro-mechanical response without much drift or hysteresis, which could be efficiently recovered by 90% after the damage-healing cycles.

Smart Electrolytes for Lithium Batteries with Reversible Thermal Protection at High Temperatures

Battery safety is a multifaceted concern, with thermal runaway standing out as a primary issue. In this work, we introduce a novel temperature‐responsive, self‐protection electrolyte governed by the phase separation dynamics of poly (butyl methacrylate) (PBMA) in lithium salt/tetraglyme (G4) blends. This innovation effectively mitigates the risks associated with thermal runaway in lithium batteries. Our electrolyte exhibits a temperature‐responsive‐recovery characteristic, imparting intelligent capabilities to lithium batteries. At temperatures of >105oC, the electrolyte transitions from a homogeneous phase to a segregated state, comprising a PBMA‐rich phase with low conductivity and a high conductivity phase containing dissolved lithium salt in G4. The deposition of the PBMA‐rich phase on the electrode surface obstructs ion transport, thereby averting thermal runaway. Subsequently, upon returning to room temperature of 25oC, the electrolyte reverts to its homogeneous, highly conductive state, with battery capacity resuming at approximately 94%. Thus, our electrolyte offers robust, reversible, smart self‐protection for batteries. Additionally, it demonstrates exceptional cycling performance at room temperature. Our findings open new avenues for thermo‐reversible and self‐protective electrolytes, advancing the safe and widespread adoption of lithium‐ion batteries.

Finite-size scaling in kinetics of phase separation in certain models of aligning active particles.

To study the kinetics of phase separation in active matter systems, we consider models that impose a Vicsek-type self-propulsion rule on otherwise passive particles interacting via the Lennard-Jones potential. Two types of kinetics are of interest: one conserves the total momentum of all the constituents and the other does not. We carry out molecular dynamics simulations to obtain results on structural, growth, and aging properties. Results from our studies, with various finite boxes, show that there exist scalings with respect to the system sizes, in both the latter quantities, as in the standard passive cases. We have exploited this scaling picture to accurately estimate the corresponding exponents, in the thermodynamically large system size limit, for power-law time dependences. It is shown that certain analytical functions describe the behavior of these quantities quite accurately, including the finite-size limits. Our results demonstrate that even though the conservation of velocity has at best weak effects on the dynamics of evolution in the thermodynamic limit, the finite-size behavior is strongly influenced by the presence (or the absence) of it.

Phase separation dynamics in a symmetric binary mixture of ultrasoft particles.

Phase separation plays a key role in determining the self-assembly of biological and soft-matter systems. In biological systems, liquid-liquid phase separation inside a cell leads to the formation of various macromolecular aggregates. The interaction among these aggregates is soft, i.e., they can significantly overlap at a small energy cost. From a computer simulation point of view, these complex macromolecular aggregates are generally modeled by soft particles. The effective interaction between two particles is defined via the generalized exponential model of index n, with n = 4. Here, using molecular dynamics simulations, we study the phase separation dynamics of a size-symmetric binary mixture of ultrasoft particles. We find that when the mixture is quenched to a temperature below the critical temperature, the two components spontaneously start to separate. Domains of the two components form, and the equal-time order parameter reveals that the domain sizes grow with time in a power-law manner with an exponent of 1/3, which is consistent with the Lifshitz-Slyozov law for conserved systems. Furthermore, the static structure factor shows a power-law decay with an exponent of 4, consistent with the Porod law.

Facile Characterization of Isothermal Crystallization and Microphase Separation Kinetics of Polyamide 6 (PA6)‐Based Thermoplastic Elastomers

AbstractThe facile characterization of isothermal microphase separation kinetics in polyamide 6 (PA6)‐based thermoplastic elastomers (TPAE‐6) has long posed a challenge for the development of suitable melt spinning processes. In this study, this challenge is addressed through differential scanning calorimetry (DSC) measurements. It is assumed that the enthalpy changes of TPAE‐6 during the isothermal process are a linear superposition of enthalpy changes associated with microphase separation and crystallization of PA6 in hard phases, resembling that of TPAE‐6 without soft segments (TPAE‐6‐0). The study reveals that, as the concentration of soft segments in TPAE‐6 increases, the accelerated dynamics of phase separation become stronger than the dilution of soft segments to PA6 segments during isothermal process, resulting in an increase in the microphase separation rate of TPAE‐6. Furthermore, despite microphase separation, the overall crystallization rate of TPAE‐6 decreases with rising isothermal temperature and varies with increasing soft segment content at different temperatures. Additionally, the crystallization mode of TPAE‐6 follows two‐dimensional, three‐dimensional, or a combination of both crystal growth mechanisms, accompanied by a heterogeneous nucleation mechanism.

Colloid phase separation dynamics driven by chiral turbulent flows

Hydrodynamic interactions significantly influence phase-ordering kinetics in complex fluids. While passive fluid phase separation is well studied, the impact of active components remains relatively unexplored. We examine pure- and quasi-two-dimensional mixtures of attractive colloids and self-rotating particles in a solvent. Varying rotor rotational speed and area fraction yield diverse dynamic patterns such as percolated networks and round droplets composed of passive colloids alone. At intermediate rotation speeds, inertial chiral flows, accompanied by the inverse energy cascade, lead to self-similar power-law coarsening with a growth exponent of 1/2. The flows spontaneously organize within fluid domains, exhibiting turbulent and chiral characteristics. Surprisingly, these turbulent flows can sustain hexatic order hydrodynamically stabilized by the Magnus force under certain conditions. Conversely, at higher speeds, nonlinear hydrodynamic interactions impede phase separation. Our findings illuminate the intriguing dynamic interplay between phase separation and chiral turbulence, effectively bridging the realms of phase ordering and turbulent physics. Published by the American Physical Society 2024

Combinatorial entropy determines the early stages of nucleation

AbstractBiomolecular phase separation, a complex phenomenon within living systems, has garnered significant interest due to its diverse roles in cellular organization and function. Despite its importance, studying phase separation dynamics experimentally, particularly in the early stages, poses challenges. Our study investigates the dynamics of biomolecular phase separation using a graph‐based simulation module, particularly emphasizing its early stages. Through a simplified model, we dissect the influences of various factors on collective behavior, highlighting the crucial role of combinatorial entropy in percolation dynamics. This study offers valuable insights into the fundamental principles governing biomolecular phase separation, with implications for understanding cellular processes and disease mechanisms.

Pattern dynamics of density and velocity fields in segregation of fluid mixtures.

We present comprehensive numerical results from a study of model H, which describes phase separation kinetics in binary fluid mixtures. We study the pattern dynamics of both density and velocity fields in d = 2, 3. The density length scales show three distinct regimes, in accordance with analytical arguments. The velocity length scale shows a diffusive behavior. We also study the scaling behavior of the morphologies for density and velocity fields and observe dynamical scaling in the relevant correlation functions and structure factors. Finally, we study the effect of quenched random field disorder on spinodal decomposition in model H.