Kinetics Of Phase Separation Research Articles

Chromatin mechanics dictates subdiffusion and coarsening dynamics of embedded condensates

DNA is organized into chromatin, a complex polymeric material that stores information and controls gene expression. An emerging mechanism for biological organization, particularly within the crowded nucleus, is biomolecular phase separation into condensed droplets of protein and nucleic acids. However, the way in which chromatin impacts the dynamics of phase separation and condensate formation is poorly understood. Here we utilize a powerful optogenetic strategy to examine the interplay of droplet coarsening with the surrounding viscoelastic chromatin network. We demonstrate that droplet growth dynamics are directly inhibited by the chromatin-dense environment, which gives rise to an anomalously slow coarsening exponent, β ≈ 0.12, contrasting with the classical prediction of β = 1/3. Using scaling arguments and simulations, we show how this arrested growth can arise due to subdiffusion of individual condensates, predicting β ≈ α/3, where α is the diffusive exponent. Tracking the fluctuating motion of condensates within chromatin reveals a subdiffusive exponent, α ≈ 0.5, which explains the anomalous coarsening behaviour and is also consistent with Rouse-like dynamics arising from the entangled chromatin. Our findings have implications for the biophysical regulation of the size and shape of biomolecular condensates and suggest that condensate emulsions can be used to probe the viscoelastic mechanical environment within living cells. Biomolecules in the cell nucleus form condensates at a rate slower than that predicted by the theory of droplet growth. Experiments on living cells attribute this anomalous coarsening behaviour to subdiffusive dynamics in the crowded nucleus.

A variant of stabilized-scalar auxiliary variable (S-SAV) approach for a modified phase-field surfactant model

In this article, we develop a new linear, decoupled, second-order accurate, and energy stable numerical method for a modified phase-field surfactant model (Xu et al., 2020). The proposed scheme is a simple and efficient variant of stabilized-scalar auxiliary variable (S-SAV) method. The proposed scheme not only retains all advantages of S-SAV method but also simplifies the solution algorithm. The phase-field, surfactant, and auxiliary variables are totally decoupled in time, thus we can solve the whole system in a step-by-step manner. The phase-field function ϕ and surfactant ψ can be separately updated by solving two linear semi-implicit systems with constant coefficients and then the auxiliary variable is directly updated in an explicit way. We analytically prove the energy stability and the unique solvability of the proposed method. The numerical experiments show the desired temporal accuracy and energy stability. We numerically investigate the proper stabilization coefficients for the present scheme with specific parameters. Furthermore, various two- and three-dimensional benchmark tests are performed to study the dynamics of surfactant-laden phase separation.

Phase separation dynamics in aqueous solutions of thermoresponsive polymers

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, intermediate and final. It was found that for the intermediate stage, the kinetics of the cluster mass growth is described by a dependence that is characteristic of the usual diffusion mass transfer; the change in the average cluster size can be represented by a scaling function with an exponent close to 1/3, typical of the systems with a conserved scalar order parameter. It is shown that the concentration of clusters at the final stage is determined by the temperature dependence of the interfacial energy.

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 < Tc, where Tc 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) ∼tφ 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.

Phase separation dynamics of the C. elegans PGL-1 P granule protein in oocytes are sensitive to heat stress.

Phase separation has emerged as a widespread process of organizing the cytoplasm of diverse eukaryotic cells. In C. elegans oocytes, several RNA binding proteins are condensed into germ granules called P granules. Prior studies studying the phase transitions of RNA binding proteins in response to increased temperature have suggested that PGL-1 decondenses in oocytes in response to heat. Here, we confirm this finding with a new reporter strain and demonstrate the sensitivity of PGL-1 to temperature changes.

Differences in mechanical properties lead to anomalous phase separation in a model cell co-culture.

During the morphogenesis of tissues and tumors, cells often interact with neighbors with different mechanical properties, but the understanding of its role is lacking. We use active Brownian dynamics simulations to study a model co-culture consisting of two types of cells with the same size and self-propulsion speed, but different mechanical stiffness and cell-cell adhesion. As time evolves, the system phase separates out into clusters with distinct morphologies and transport properties for the two cell types. The density structure factors and the growth of cell clusters deviate from behavior characteristic of the phase separation in binary fluids. Our results capture emergent structure and motility previously observed in co-culture experiments and provide mechanistic insights into intercellular phase separation during development and disease.

Modeling the interplay between solvent evaporation and phase separation dynamics during membrane

Herein, the numerical simulation of polymeric membrane formation is investigated when a coupling between phase separation and solvent evaporation occurs. A binary polymer/solvent system is considered and simulations were performed in 2D geometries, first in a horizontal 2D plan, then in a vertical cross-section plan. The phase separation was simulated using Cahn-Hilliard equations and the Flory-Huggins theory was used to describe the thermodynamics of the binary system. The solvent evaporation was coupled to the phase separation using a continuous mass flux at the upper interface of the system, whose magnitude is controlled by a mass transfer driving force. The simulated patterns were analyzed using Minkowski descriptors and Fourier analysis. The results exhibit a strong influence of solvent evaporation in the vicinity of the upper interface, leading to the formation of a dense skin, whose kinetics in concentration and thickness was shown to depend on the initial polymer concentration and the mass transfer coefficient. Beneath the dense layer, the system tends to relax to minimize its free energy so that the phase separation in the bulk solution was found homogeneous and weakly affected by the solvent evaporation.

Electrochemical Kinetics of Graphite Degradation in Lithium-Ion Batteries

Growth of the solid electrolyte interphase (SEI) is a major driver of capacity fade in LIBs. Despite its importance, the fundamental mechanisms remain unclear, primarily because of the complicated reaction pathways involved [1–3]. SEI growth can be both electrochemical and chemical in nature [4,5], and thus, it is a strong function of the potential and degree of lithiation of the electrode. We model the early-stage and long-term growth of SEI by accurately capturing the potential dependence of its formation kinetics as well as long term rate limiting steps. Battery degradation involves a complex interplay of multiple phenomena, most of which are unknown. Our model captures some of the essential trends that we see while cycling hundreds of commercial cells [6]. This is done using the Multiphase Porous Electrode Theory (MPET) framework [7] on graphite (phase separating) and carbon black (non phase separating) particles.Lithium plating is another key degradation phenomenon that has been elusive, and it becomes important while trying to fast-charge batteries, i.e., 0% - 80% state-of-charge in 30 mins. We show that lithium plating is a key function of electrode morphology, phase-separation dynamics and potential. Phase-separation in graphite is modeled in the electrode using the Cahn-Hilliard Reaction framework described by Bazant [8]. We understand the electrochemistry of the onset of lithium plating with in-situ measurements connected to real time cell potential in a phase-separating electrode [9].Results indicate that the peak SEI-forming currents are higher for higher driving currents and that SEI only grows during electrode lithiation, i.e. the battery only degrades while being charged. Additionally we capture a transition in the time-dependence of capacity fade from a steep initial drop to a more gradual ‘square-root-of-time’ trend by modeling the SEI as a bilayer with different rate-limiting steps for each type of SEI. We also find that onset of lithium plating is correctly captured only when phase separation in active material is accounted for. Further, the onset of plating is delayed on electrodes with a thick SEI layer – understanding SEI/plating coupling is integral to predicting fast charging manufacturing protocols for LIBs. This work holds promise for the predictive design of procedures [10] for manufacture and formation of LIBs. [1] Cohen, Y. S.; Cohen, Y.; Aurbach, D. Micromorphological Studies of Lithium Electrodes in Alkyl Carbonate Solutions Using in Situ Atomic Force Microscopy. J. Phys. Chem. B 2000, 104, 12282–12291. https://doi.org/10.1021/jp002526b.[2] Horstmann, B.; Single, F.; Latz, A. Review on Multi-Scale Models of Solid-Electrolyte Interphase Formation, Current Opinion in Electrochemistry 13, 62-69 2019.[3] Nie, M.; Abraham, D. P.; Seo, D. M.; Chen, Y.; Bose, A.; Lucht, B. L. Role of Solution Structure in Solid Electrolyte Interphase Formation on Graphite with LiPF6 in Propylene Carbonate. J. Phys. Chem. C 2013, 117 (48), 25381–25389, https://doi.org/10.1021/jp409765w.[4] Das, S.; Attia, P. M.; Chueh, W. C.; Bazant, M. Z. Electrochemical Kinetics of SEI Growth on Carbon Black: Part II. Modeling. J. Electrochem. Soc. 2019, 166 (4), E107– E118. https://doi.org/10.1149/2.0241904jes.[5] Attia, P. M.; Das, S.; Harris, S. J.; Bazant, M. Z.; Chueh, W. C. Electrochemical Kinetics of SEI Growth on Carbon Black: Part I. Experiments. J. Electrochem. Soc. 2019, 166 (4), E97–E106. https://doi.org/10.1149/2.0231904jes.[6] Severson, K. A., Attia, P. M., Jin, N., Perkins, N., Jiang, B., Yang, Z., ... & Bazant, M. Z. (2019). Data-driven prediction of battery cycle life before capacity degradation. Nature Energy, 4(5), 383-391.[7] Smith, R. B.; Bazant, M. Z. Multiphase Porous Electrode Theory, J. Electrochem. Soc. 2017, 164 (11). https://doi.org/10.1149/2.0171711jes.[8] Bazant, M. Z., Theory of chemical kinetics and charge transfer based on nonequilibrium thermodynamics, Accounts of Chemical Research, 46(5), 1144–1160. https://doi.org/10.1021/ar300145c[9] T. Gao, Y. Han, S. Das, T. Zhou, D. Fraggedakis, N. Nadkarni, C. N. Yeh, W. Chueh, J. Li, M.Z. Bazant, Interplay of lithium intercalation and plating on graphite using in-situ optical measurements, submitted.[10] Huang, W.; Attia, P. M.; Wang, H.; Renfrew, S. E.; Jin, N.; Das, S.; Zhang, Z.; Boyle, D. T.; Li, Y.; Bazant, M. Z.; McCloskey, B. D.; Chueh, W. C. and Cui, Y.; Nano Letters 2019 19 (8), 5140-5148. DOI: 10.1021/acs.nanolett.9b01515

Induced interactions and quench dynamics of bosonic impurities immersed in a Fermi sea

We unravel the ground state properties and the non-equilibrium quantum dynamics of two bosonic impurities immersed in an one-dimensional fermionic environment by applying a quench of the impurity-medium interaction strength. In the ground state, the impurities and the Fermi sea are phase-separated for strong impurity-medium repulsions while they experience a localization tendency around the trap center for large attractions. We demonstrate the presence of attractive induced interactions mediated by the host for impurity-medium couplings of either sign and analyze the competition between induced and direct interactions. Following a quench to repulsive interactions triggers a breathing motion in both components, with an interaction dependent frequency and amplitude for the impurities, and a dynamical phase-separation between the impurities and their surrounding for strong repulsions. For attractive post-quench couplings a beating pattern owing its existence to the dominant role of induced interactions takes place with both components showing a localization trend around the trap center. In both quench scenarios, attractive induced correlations are manifested between non-interacting impurities and are found to dominate the direct ones only for quenches to attractive couplings.

Topology and control of self-assembled domain patterns in low-dimensional ferroelectrics

Whilst often discussed as non-trivial phases of low-dimensional ferroelectrics, modulated polar phases such as the dipolar maze and the nano-bubble state have been appraised as essentially distinct. Here we emphasize their topological nature and show that these self-patterned polar states, but also additional mesophases such as the disconnected labyrinthine phase and the mixed bimeron-skyrmion phase, can be fathomed in their plurality through the unifying canvas of phase separation kinetics. Under compressive strain, varying the control parameter, i.e., the external electric field, conditions the nonequilibrium self-assembly of domains, and bridges nucleation and spinodal decomposition via the sequential onset of topological transitions. The evolutive topology of these polar textures is driven by the (re)combination of the elementary topological defects, merons and antimerons, into a plethora of composite topological defects such as the fourfold junctions, the bimeron and the target skyrmion. Moreover, we demonstrate that these manipulable defects are stable at room temperature and feature enhanced functionalities, appealing for devising future topological-based nanoelectronics.

Motility-Induced Microphase and Macrophase Separation in a Two-Dimensional Active Brownian Particle System.

As a result of nonequilibrium forces, purely repulsive self-propelled particles undergo macrophase separation between a dense and a dilute phase. We present a thorough study of the ordering kinetics of such motility-induced phase separation (MIPS) in active Brownian particles in two dimensions, and we show that it is generically accompanied by microphase separation. The growth of the dense phase follows a law akin to the one of liquid-gas phase separation. However, it is made of a mosaic of hexatic microdomains whose size does not coarsen indefinitely, leaving behind a network of extended topological defects from which microscopic dilute bubbles arise. The characteristic length of these finite-size structures increases with activity, independently of the choice of initial conditions.

Kinetics of field-induced phase separation of a magnetic colloid under rotating magnetic fields.

This paper is focused on the experimental and theoretical study of the phase separation of a magnetic nanoparticle suspension under rotating magnetic fields in a frequency range, 5 Hz ≤ ν ≤ 25 Hz, relevant for several biomedical applications. The phase separation is manifested through the appearance of needle-like dense particle aggregates synchronously rotating with the field. Their size progressively increases with time due to the absorption of individual nanoparticles (aggregate growth) and coalescence with neighboring aggregates. The aggregate growth is enhanced by the convection of nanoparticles toward rotating aggregates. The maximal aggregate length, Lmax ∝ ν-2, is limited by fragmentation arising as a result of their collisions. Experimentally, the aggregate growth and coalescence occur at a similar timescale, ∼1 min, weakly dependent on the field frequency. The proposed theoretical model provides a semi-quantitative agreement with the experiments on the average aggregate size, aggregation timescale, and size distribution function without any adjustable parameter.

A new method of preparing high-performance high-entropy alloys through high-gravity combustion synthesis

A new method of high-gravity combustion synthesis (HGCS) followed by post-treatment (PT) is reported for preparing high-performance high-entropy alloys (HEAs), Cr0.9FeNi2.5V0.2Al0.5 alloy, whereby cheap thermite powder is used as the raw material. In this process, the HEA melt and the ceramic melt are rapidly formed by a strong exothermic combustion synthesis reaction and completely separated under a high-gravity field. Then, the master alloy is obtained after cooling. Subsequently, the master alloy is sequentially subjected to conventional vacuum arc melting (VAM), homogenization treatment, cold rolling, and annealing treatment to realize a tensile strength, yield strength, and elongation of 1250 MPa, 1075 MPa, and 2.9%, respectively. The present method is increasingly attractive due to its low cost of raw materials and the intermediate product obtained without high-temperature heating. Based on the calculation of phase separation kinetics in the high-temperature melt, it is expected that the final alloys with high performance can be prepared directly across master alloys with higher high-gravity coefficients.

Modification of Polysulfone Ultrafiltration Membranes via Addition of Anionic Polyelectrolyte Based on Acrylamide and Sodium Acrylate to the Coagulation Bath to Improve Antifouling Performance in Water Treatment.

Surface modification of polysulfone ultrafiltration membranes was performed via addition of an anionic polymer flocculant based on acrylamide and sodium acrylate (PASA) to the coagulation bath upon membrane preparation by non-solvent induced phase separation (NIPS). The effect of PASA concentration in the coagulant at different coagulation bath temperatures on membrane formation time, membrane structure, surface roughness, hydrophilic-hydrophobic balance of the skin layer, surface charge, as well as separation and antifouling performance was studied. Scanning electron microscopy (SEM), atomic force microscopy (AFM), Fourier transform infrared (FTIR) spectroscopy, contact angle and zeta potential measurements were utilized for membrane characterization. Membrane barrier and antifouling properties were evaluated in ultrafiltration of model solutions containing human serum albumin and humic acids as well as with real surface water. PASA addition was found to affect the kinetics of phase separation leading to delayed demixing mechanism of phase separation due to the substantial increase of coagulant viscosity, which is proved by a large increase of membrane formation time. Denser and thicker skin layer is formed and formation of macrovoids in membrane matrix is suppressed. FTIR analysis confirms the immobilization of PASA macromolecules into the membrane skin layer, which yields improvement of hydrophilicity and change of zeta potential. Modified membrane demonstrated better separation and antifouling performance in the ultrafiltration of humic acid solution and surface water compared to the reference membrane.

Capillary thinning of elastic and viscoelastic threads: From elastocapillarity to phase separation

The formation and destabilisation of viscoelastic filaments are of importance in many industrial and biological processes. Filament instabilities have been observed for viscoelastic fluids but recently also for soft elastic solids. In this work, we address the central question how to connect the dynamical behavior of viscoelastic liquids to that of soft elastic solids. We take advantage of a biopolymer material whose viscoelastic properties can be tuned over a very large range by its pH, and study the destabilization and ensuing instabilities in uniaxial extensional deformation. In agreement with very recent theory, we find that the interface shapes dictated by the instabilities converge to an identical similarity solution for low-viscosity viscoelastic fluids and highly elastic gels. We thereby bridge the gap between very fluid and strongly elastic materials. In addition, we provide direct evidence that at late times an additional filament instability occurs due to a dynamical phase separation.

The Effects of Inhomogeneous Elasticity and Dislocation on Thermodynamics and the Kinetics of the Spinodal Decomposition of a Fe-Cr System: A Phase-Field Study

The effects of inhomogeneous elasticity and dislocation on the microstructure evolution of α′ precipitate in a Fe-Cr system was investigated using a Computer Coupling of Phase Diagrams and Thermochemistry (CALPHAD)-type free energy incorporated phase-field method. In order to simulate the precipitation behavior by phase-field modeling in consideration of inhomogeneous elasticity, a Multiphysics Object-Oriented Simulation Environment (MOOSE) framework was used, which makes it easy to use powerful numerical means such as parallel computing and finite element method (FEM) solver. The effect of inhomogeneous elasticity due to the compositional inhomogeneity or the presence of dislocations affects the thermodynamic properties of the system was investigated, such as the lowest Cr concentration at which spinodal decomposition occurs. The effect of inhomogeneous elasticity on phase separation kinetics is also studied. Finally, we analyzed how inhomogeneous elasticity caused by compositional fluctuation or dislocation affects microstructure characteristics such as ratio between maximum precipitate size with respect to the average on early stage and later stage, respectively.

Surface-directed spinodal decomposition on morphologically patterned substrates.

This paper is the second in a two-part exposition on surface-directed spinodal decomposition (SDSD), i.e., the interplay of kinetics of wetting and phase separation at a surface which is wetted by one of the components of a binary mixture. In our first paper [P. Das, P. K. Jaiswal, and S. Puri, Phys. Rev. E 102, 012803 (2020)2470-004510.1103/PhysRevE.102.012803], we studied SDSD on chemically heterogeneous and physically flat substrates. In this paper, we study SDSD on a chemically homogeneous but morphologically patterned substrate. Such substrates arise in a vast variety of technological applications. Our goal is to provide a theoretical understanding of SDSD in this context. We present detailed numerical results for domain growth both inside and above the grooves in the substrate. The morphological evolution can be understood in terms of the interference of SDSD waves originating from the different surfaces comprising the substrate.

The Roles Played by DMF in the Structure Formation of Epoxy-Based Porous Monolith

Epoxy-based porous monoliths are prepared by chemically induced phase separation. The roles played by N,N-dimethylformamide (DMF) in both curing and phase separation kinetics are studied in detail. It is found that the addition of DMF not only changes the speed of phase separation, but the way. Meanwhile, the occurrence of secondary phase separation is partly inhibited, which is in favor of the formation of skeletal network structure. In addition, the schematic pseudo phase diagrams were deduced, which are of great significance to understand the roles played by DMF for the targeted control of materials structure. The results show that by the addition of DMF, the phase diagram moves to the lower right, which means more porogen is needed to obtain skeletal network structure. The spinodal line moves toward the binodal line and the internal space of spinodal line is enlarged. Therefore, it becomes more available to obtain skeletal network structure.

Effect of Halloysite Nanotubes on the Rheological and Phase Separation Behaviors in a Poly(ethylene oxide)/Ionic Liquid Mixture

AbstractA series ternary composites of poly(ethylene oxide)/ionic liquid 30/70 (P30) with uniformly dispersed halloysite nanotubes (HNTs) are investigated in the homogeneous and two‐phase regions. For P30/HNTs composites, a relatively lower percolation threshold about 3 wt% of HNTs loading is observed in the single‐phase region of P30. Beyond the percolation threshold, the steady shear flow exhibits two shear‐thinning regions due to the coupled relaxation of HNTs network and polymer entanglement. In the two‐phase region of P30, the mobility of ionic liquids (ILs) can be impeded accounting for the filler network forming. Not only the phase recovery during cyclic heating–cooling treatment near the phase boundary is accelerated, but also the phase separation kinetics is significantly retarded owing to HNTs dispersed in the PEO‐rich phase impeding the escaping of ILs from PEO phase. The lower storage modulus G′ for P30/HNTs‐4wt% compared to P30/HNTs‐3wt% in a two‐phase region is connected with the competition between the filler contribution and additional elasticity induced by phase separation.

A non-uniform time-stepping convex splitting scheme for the time-fractional Cahn–Hilliard equation

In this paper, a non-uniform time-stepping convex-splitting numerical algorithm for solving the widely used time-fractional Cahn–Hilliard equation is introduced. The proposed numerical scheme employs the L1+ formula for discretizing the time-fractional derivative and a second-order convex-splitting technique to deal with the non-linear term semi-implicitly. Then the pseudospectral method is utilized for spatial discretization. As a result, the fully discrete scheme has several advantages: second-order accurate in time, spectrally accurate in space, uniquely solvable, mass preserving, and unconditionally energy stable. Rigorous proofs are given, along with several numerical results to verify the theoretical results, and to show the accuracy and effectiveness of the proposed scheme. Also, some interesting phase separation dynamics of the time-fractional Cahn–Hilliard equation has been investigated.