Phase Separation Model Research Articles

Mesoscale Modeling of Phase Separation Controlled by Hydrosilylation in Polyhydromethylsiloxane (PHMS)-Containing Blends.

Controlling morphology of polysiloxane blends crosslinked by the hydrosilylation reaction followed by pyrolysis constitutes a robust strategy to fabricate polymer-derived ceramics (PDCs) for a number of applications, from water purification to hydrogen storage. Herein, we introduce a dissipative particle dynamics (DPD) approach that captures the phase separation in binary and ternary polymer blends undergoing hydrosilylation. Linear polyhydromethylsiloxane (PHMS) chains are chosen as preceramic precursors and linear vinyl-terminated polydimethylsiloxane (v-PDMS) chains constitute the reactive sacrificial component. Hydrosilylation of carbon–carbon unsaturated double bonds results in the formation of carbon–silicon bonds and is widely utilized in the synthesis of organosilicons. We characterize the dynamics of binary PHMS/v-PDMS blends undergoing hydrosilylation and ternary blends in which a fraction of the reactive sacrificial component (v-PDMS) is replaced with the non-reactive sacrificial component (methyl-terminated PDMS (m-PDMS), polyacrylonitrile (PAN), or poly(methyl methacrylate) (PMMA)). Our results clearly demonstrate that the morphology of the sacrificial domains in the nanostructured polymer network formed can be tailored by tunning the composition, chemical nature, and the degree of polymerization of the sacrificial component. We also show that the addition of a non-reactive sacrificial component introduces facile means to control the self-assembly and morphology of these nanostructured materials by varying the fraction, degree of polymerization, or the chemical nature of this component.

Analytical Solution to the Flory-Huggins Model.

A self-consistent analytical solution for binodal concentrations of the two-component Flory–Huggins phase separation model is derived. We show that this form extends the validity of the Ginzburg–Landau expansion away from the critical point to cover the whole phase space. Furthermore, this analytical solution reveals an exponential scaling law of the dilute phase binodal concentration as a function of the interaction strength and chain length. We demonstrate explicitly the power of this approach by fitting experimental protein liquid–liquid phase separation boundaries to determine the effective chain length and solute–solvent interaction energies. Moreover, we demonstrate that this strategy allows us to resolve differences in interaction energy contributions of individual amino acids. This analytical framework can serve as a new way to decode the protein sequence grammar for liquid–liquid phase separation.

DbEmbryo multi-omics database for analyses of synergistic regulation in early mammalian embryo development.

During early mammalian embryo development, different epigenetic marks undergo reprogramming and play crucial roles in the mediation of gene expression. Currently, several databases provide multi-omics information on early embryos. However, how interconnected epigenetic markers function together to coordinate the expression of the genetic code in a spatiotemporal manner remains difficult to analyze, markedly limiting scientific and clinical research. Here, we present dbEmbryo, an integrated and interactive multi-omics database for human and mouse early embryos. dbEmbryo integrates data on gene expression, DNA methylation, histone modifications, chromatin accessibility, and higher-order chromatin structure profiles for human and mouse early embryos. It incorporates customized analysis tools, such as “multi-omics visualization,” “Gene&Peak annotation,” “ZGA gene cluster,” “cis-regulation,” “synergistic regulation,” “promoter signal enrichment,” and “3D genome.” Users can retrieve gene expression and epigenetic profile patterns to analyze synergistic changes across different early embryo developmental stages. We showed the uniqueness of dbEmbryo among extant databases containing data on early embryo development and provided an overview. Using dbEmbryo, we obtained a phase-separated model of transcriptional control during early embryo development. dbEmbryo offers web-based analytical tools and a comprehensive resource for biologists and clinicians to decipher molecular regulatory mechanisms of human and mouse early embryo development.

Versatile Sequential Casting Processing for Highly Efficient and Stable Binary Organic Photovoltaics.

Forming an ideal bulk heterojunction (BHJ) morphology is a critical issue governing the photon to electron process in organic solar cells (OSCs). Complementary to the widely-used blend casting (BC) method for BHJ construction, sequential casting (SC) can also enable similar or even better morphology and device performance for OSCs. Here, BC and SC methods on three representative donor:acceptor (D:A) blends are utilized, that is, PM6:PC71 BM, PM6:IT-4F and PM6:L8-BO. Higher power conversion efficiencies (PCEs) in all cases by taking advantage of beneficial morphology from SC processing are achieved, and a champion PCE of 18.86% (certified as 18.44%) based on the PM6:L8-BO blend is reached, representing the record value among binary OSCs. The observations on phase separation and vertical distribution inspire the proposal of the swelling-intercalation phase-separation model to interpret the morphology evolution during SC processing. Further, the vertical phase segregation is found to deliver an improvement of device performance via affecting the charge transport and collection processes, as evidenced by the D:A-ratio-dependent photovoltaic properties. Besides, OSCs based on SC processing show advantages on device photostability and upscale fabrication. This work demonstrates the versatility and efficacy of the SC method for BHJ-based OSCs.

MS3 of Ti2AlN powder at 700 °C with controllable morphology and its formation mechanism analyzed by DFT-TST-SD

Ti2AlN powder with ∼97 wt% purity has been synthesized at 700 °C (far below all the previously reported temperatures) via molten salt shielded synthesis (MS3) in the air. The effects of sintering temperature, holding time, and salt content on its purity and particle size are investigated. The reaction mechanism from reactants to products is disclosed through density functional and transition state theories (DFT and TST). The regulation mechanism in morphology is illustrated by the spinodal decomposition (SD) and phase separation model. When the holding time or salt content improves, the purity increases. Ti2AlN powder synthesized at 700 °C for 2 h with a salt content of 80 wt% exhibits a purity of 97.7 wt%, an average particle size of 13.8 μm, and a uniform layer structure. Ti2AlN is reacted via Ti + Al + TiN→Ti2AlN, which occurs when the free energy of Ti–Al–TiN exceeds that of Ti2AlN by the energy barrier of 4.08 eV, and it is a necessary condition for achieving the result that the synthesis is completed at the critical temperature of 700 °C. Grain growth and the surface tension of molten salt regulate the morphology. The above mechanism has been revealed for the first time in this field to date.

Influence of alcohols on the lower consolute behavior and thermodynamic approach of Triton X-114 aqueous two-phase systems

The addition of foreign material to surfactants shows the change in temperature at which the clouding process occurs. This work evaluates the impact of n-alcohols on Cloud Point (CP) of nonionic surfactant Triton X-114 at variable concentrations. It was found that the CP of pure Triton X-114 shows concentration-dependent variation. The presence of lower alcohols improves CP value whereas the addition of higher alcohols brings down CP with variation as concentration increases. These effects can be clarified in view of the site of the impact of molecular design of added substances on the stability of micelle organization. The foaming ability and foam stability data are also used to discuss the stability of micellar accumulation. Considering CP as a threshold temperature of the solubility, the thermodynamic parameters of the clouding process ΔG0cl, ΔH0cl, and ΔS0cl, have been assessed, using the “Phase Separation Model”. The outcomes of the work demonstrate that the clouding phenomenon of Triton X-114 is an exothermic and non-spontaneous process.

Automated matching of two-time X-ray photon correlation maps from phase-separating proteins with Cahn-Hilliard-type simulations using auto-encoder networks.

Machine learning methods are used for an automated classification of experimental two-time X-ray photon correlation maps from an arrested liquid-liquid phase separation of a protein solution. The correlation maps are matched with correlation maps generated with Cahn-Hilliard-type simulations of liquid-liquid phase separations according to two simulation parameters and in the last step interpreted in the framework of the simulation. The matching routine employs an auto-encoder network and a differential evolution based algorithm. The method presented here is a first step towards handling large amounts of dynamic data measured at high-brilliance synchrotron and X-ray free-electron laser sources, facilitating fast comparison with phase field models of phase separation.

A phase separation model for binary fluids with hereditary viscosity

We consider a diffuse interface model for an incompressible binary viscoelastic fluid flow. The model consists of the Navier–Stokes–Voigt equations where the instantaneous kinematic viscosity has been replaced by a memory term incorporating hereditary effects coupled with the Cahn–Hilliard equation with Flory–Huggins potential. The resulting system is subject to no‐slip condition for the (volume averaged) fluid velocity and to no‐flux boundary conditions for the order parameter and the chemical potential . We first establish the well‐posedness of the initial and boundary value problem. Then, taking advantage of an Ekman‐type damping, we obtain a dissipative estimate. Thus, we can define a dissipative dynamical system on a suitable phase space. Also, we show that any weak solution is such that regularizes in finite time, and in dimension two, it stays uniformly away from pure phases; that is, the instantaneous strict separation property holds. Finally, we prove the existence of the global attractor, and exploiting the strict separation property, we demonstrate that an exponential attractor exists in dimension two.

Mathematical Modeling of Phase Separation and Branching Process of the Film Structure during Binary Thin Film Deposition

In this study, we applied a mathematical model to explore the mechanism and factors leading to phase separation and the formation of branching structures with nanocolumns extending from larger clusters formed on the substrate of a grown film. The mathematical model simulated the growth of a thin film over time by using partial differential equations, including the processes of adsorption, phase separation, and diffusion due to the curvature of the thin film surface. The modeling results revealed the possible mechanism that could lead to the formation of the described branching structures. That mechanism can be divided into two main steps. The first step is the growth of a relatively large cluster (of a component that makes up the branching phase) on the substrate during the initial growth stages. The second step is the division process of that large cluster into smaller clusters in the later growth stages. The model parameters influencing the growth conditions that lead to the formation mechanism of the branching structures were determined, and their influences on the phase structure were analyzed.

Nanoscale Structure and Dynamics of Model Membrane Lipid Raft Systems, Studied by Neutron Scattering Methods

Quasi-elastic neutron scattering (QENS) and small angle neutron scattering (SANS), in combination with isotopic contrast variation, have been used to determine the structure and dynamics of three-component lipid membranes, in the form of vesicles, comprising an unsaturated [palmitoyl-oleoyl-phosphatidylcholine (POPC) or dioleoyl-phosphatidylcholine (DOPC)], a saturated phospholipid (dipalmitoyl-phosphatidylcholine (DPPC)), and cholesterol, as a function temperature and composition. SANS studies showed vesicle membranes composed of a 1:1:1 molar ratio of DPPC:DOPC:cholesterol and a 2:2:1 molar ratio of DPPC:POPC:cholesterol phase separated, forming lipid rafts of ∼18 and ∼7 nm diameter respectively, when decreasing temperature from 308 to 297 K. Phase separation was reversible upon increasing temperature. The larger rafts observed in systems containing DOPC are attributed to the greater mis-match in lipid alkyl chains between DOPC and DPPC, than for POPC and DPPC. QENS studies, over the temperature range 283–323K, showed that the resulting data were best modelled by two Lorentzian functions: a narrow component, describing the “in-plane” lipid diffusion, and a broader component, describing the lipid alkyl chain segmental relaxation. The overall “in-plane” diffusion was found to show a significant reduction upon increasing temperature due to the vesicle membranes transitioning from one containing rafts to one where the component lipids are homogeneously mixed. The use of different isotopic combinations allowed the measured overall reduction of in-plane diffusion to be understood in terms of an increase in diffusion of the saturated DPPC lipid and a corresponding decrease in diffusion of the unsaturated DOPC/POPC lipid. As the rafts are considered to be composed principally of saturated lipid and cholesterol, the breakdown of rafts decreases the exposure of the DPPC to cholesterol whilst increasing the exposure of cholesterol to unsaturated lipid. These results show the sensitivity of lipid diffusion to local cholesterol concentration, and the importance of considering the local, rather that the global composition of a membrane when understanding the diffusion processes of lipids within the membrane. The novel combination of SANS and QENS allows a non-intrusive approach to characterize the structure and dynamics occurring in phase-separated model membranes which are designed to mimic the lateral heterogeneity of lipids seen in cellular membranes–a heterogeneity that can have pathological consequences.

Challenges and Opportunities for Bayesian Statistics in Proteomics.

Proteomics is a data-rich science with complex experimental designs and an intricate measurement process. To obtain insights from the large data sets produced, statistical methods, including machine learning, are routinely applied. For a quantity of interest, many of these approaches only produce a point estimate, such as a mean, leaving little room for more nuanced interpretations. By contrast, Bayesian statistics allows quantification of uncertainty through the use of probability distributions. These probability distributions enable scientists to ask complex questions of their proteomics data. Bayesian statistics also offers a modular framework for data analysis by making dependencies between data and parameters explicit. Hence, specifying complex hierarchies of parameter dependencies is straightforward in the Bayesian framework. This allows us to use a statistical methodology which equals, rather than neglects, the sophistication of experimental design and instrumentation present in proteomics. Here, we review Bayesian methods applied to proteomics, demonstrating their potential power, alongside the challenges posed by adopting this new statistical framework. To illustrate our review, we give a walk-through of the development of a Bayesian model for dynamic organic orthogonal phase-separation (OOPS) data.

Phase separation on cell surface facilitates bFGF signal transduction with heparan sulphate

Liquid-liquid phase separation (LLPS) plays important roles in various cellular processes, facilitating membrane-less organelles construction, chromatin condensation, signal transduction on inner membrane and many other processes. Current perception is that LLPS relies on weak multivalent interactions and crowded environments intracellularly. In this study, we demonstrate that heparan sulfate can serve as a platform to induce the phase separation of basic fibroblast growth factor on cell surface. The phase separation model provides an alternative mechanism how bFGF is enriched to its receptors, therefore triggering the signaling transduction. The research provides insights on the mechanism how growth factors can be recruited to cell surface by heparan sulfate and execute their functions, extending people’s view on phase separation from intracellular to extracellular proteins at cellular level.

Observation and Manipulation of a Phase Separated State in a Charge Density Wave Material.

The 1T polytype of TaS2 has been studied extensively as a strongly correlated system. As 1T-TaS2 is thinned toward the 2D limit, its phase diagram shows significant deviations from that of the bulk material. Optoelectronic maps of ultrathin 1T-TaS2 have indicated the presence of nonequilibrium charge density wave phases within the hysteresis region of the nearly commensurate (NC) to commensurate (C) transition. We perform scanning tunneling microscopy on exfoliated ultrathin flakes of 1T-TaS2 within the NC-C hysteresis window, finding evidence that the observed nonequilibrium phases consist of intertwined, irregularly shaped NC-like and C-like domains. After applying lateral electrical signals to the sample, we image changes in the geometric arrangement of the different regions. We use a phase separation model to explore the relationship between electronic inhomogeneity present in ultrathin 1T-TaS2 and its bulk resistivity. These results demonstrate the role of phase competition morphologies in determining the properties of 2D materials.

Molecular insights into the effect of alkanediols on FUS liquid-liquid phase separation

FUS (Fused in Sarcoma) is a multifunctional RNA-binding protein that has been extensively investigated as a minimal model of biomolecular liquid-liquid phase separation (LLPS). Aqueous solutions of alkanediols are popular disruptors of many phase-separated condensates in vivo and in test tubes including those of FUS. However, little is known about how non-covalent interactions with biorelevant diols alter the physicochemical environment of condensates. Here, we use a combination of microscopy, nuclear magnetic resonance (NMR) spectroscopy, and biochemical assays to evaluate the effect of alkyl chain diols of different lengths and configurations (1,4-butanediol, 1,5-pentanediol, isomers of hexanediol) on FUS SYGQ-rich and RGG-rich domain structure, interactions, and phase separation.

Physics-driven coarse-grained model for biomolecular phase separation with near-quantitative accuracy

In recent years, various physics- and data-driven sequence-dependent protein coarse-grained models have been developed to study biomolecular liquid—liquid phase separation (LLPS) and elucidate the dominant physicochemical driving forces. Here, we present Mpipi, a multiscale coarse-grained model that describes almost quantitatively the change in protein critical temperatures as a function of amino-acid sequence. The model is parameterised from both atomistic simulations and bioinformatics data and accounts for the dominant role of π–π and hybrid cation–π/π–π interactions and the much stronger attractive contacts established by arginines than lysines.

The origin of fast‐charging lithium iron phosphate for batteries

AbstractSince the report of electrochemical activity of LiFePO4 from Goodenough's group in 1997, it has attracted considerable attention as cathode material of choice for lithium‐ion batteries. It shows excellent performance such as the high‐rate capability, long cyclability, and improved safety. Furthermore, the raw materials cost of LiFePO4 are lower and abundant compared with conventional Li‐ion battery oxides compounds. The lithium extraction from LiFePO4 operates as biphase mechanism accompanied by a relatively large volume change of ∼6.8%, even though, nanosized LiFePO4 shows exceptionally high‐rate capability during cycling. In the aim to explain this remarkable feature, recent reports using cutting‐edge techniques, such as in situ high‐resolution synchrotron X‐ray diffraction, explained that the origin of the observed high‐rate performance in nanosized LiFePO4 is the absence of phase separation during battery operation at high current densities. In this review, the importance of understanding lithium insertion mechanisms towards explaining the significantly fast‐charging performance of LiFePO4 electrode is highlighted. In particular, phase separation mechanisms, are unclear and deserve considerable attention. Several proposed models for Li diffusion and phase separation in LiFePO4 are summarized. In addition, the crystallographic aspects, defect structures of LiFePO4 are also reviewed. Finally, the status of development of other olivine‐type LiMPO4 (M = Co, Mn, and Ni) are summarized.

Theoretical modelling of liquid-liquid phase separation: from particle-based to field-based simulation.

Liquid-liquid phase separation (LLPS) has proved to be ubiquitous in living cells, forming membraneless organelles (MLOs) and dynamic condensations essential in physiological processes. However, some underlying mechanisms remain challenging to unravel experimentally, making theoretical modeling an indispensable aspect. Here we present a protocol for understanding LLPS from fundamental physics to detailed modeling procedures. The protocol involves a comprehensive physical picture on selecting suitable theoretical approaches, as well as how and what to interpret and resolve from the results. On the particle-based level, we elaborate on coarse-grained simulation procedures from building up models, identifying crucial interactions to running simulations to obtain phase diagrams and other concerned properties. We also outline field-based theories which give the system's density profile to determine phase diagrams and provide dynamic properties by studying the time evolution of density field, enabling us to characterize LLPS systems with larger time and length scales and to further include other nonequilibrium factors such as chemical reactions.

Controlling liquid–liquid phase separation of G-quadruplex-forming RNAs in a sequence-specific manner

We constructed a minimum liquid-liquid phase separation model system to form liquid droplets using only G-quadruplex-forming oligonucleotides and R- and G-rich oligopeptides. We found that the G-quadruplex structure is an essential component for RNA to form droplets with the peptide. Based on this model system and our findings, droplet redissolution via structure transition from a G-quadruplex to a duplex was achieved in a sequence-specific manner.

Vacuum residue coking process simulation using molecular-level kinetic model coupled with vapor-liquid phase separation

In this work, a molecular-level kinetic model was built to simulate the vacuum residue (VR) coking process in a semi-batch laboratory-scale reaction kettle. A series of reaction rules for heavy oil coking were summarized and formulated based on the free radical reaction mechanism. Then, a large-scale molecular-level reaction network was automatically generated by applying the reaction rules on the vacuum residue molecules. In order to accurately describe the physical change of each molecule in the reactor, we coupled the molecular-level kinetic model with a vapor–liquid phase separation model. The vapor–liquid phase separation model adopted the Peng-Robinson equation of state to calculate vapor–liquid equilibrium. A separation efficiency coefficient was introduced to represent the mass transfer during the phase separation. We used six sets of experimental data under various reaction conditions to regress the model parameters. The tuned model showed that there was an excellent agreement between the calculated values and experimental data. Moreover, we investigated the effect of reaction temperature and reaction time on the product yields. After a comprehensive evaluation of the reaction temperature and reaction time, the optimal reaction condition for the vacuum residue coking was also obtained.

Phase separation of RNA-binding protein promotes polymerase binding and transcription.

An RNA-involved phase-separation model has been proposed for transcription control. However, the molecular links that connect RNA to the transcription machinery remain missing. Here we find that RNA-binding proteins (RBPs) constitute half of the chromatin proteome in embryonic stem cells (ESCs), some being colocalized with RNA polymerase (Pol) II at promoters and enhancers. Biochemical analyses of representative RBPs show that the paraspeckle protein PSPC1 inhibits the RNA-induced premature release of Pol II, and makes use of RNA as multivalent molecules to enhance the formation of transcription condensates and subsequent phosphorylation and release of Pol II. This synergistic interplay enhances polymerase engagement and activity via the RNA-binding and phase-separation activities of PSPC1. In ESCs, auxin-induced acute degradation of PSPC1 leads to genome-wide defects in Pol II binding and nascent transcription. We propose that promoter-associated RNAs and their binding proteins synergize the phase separation of polymerase condensates to promote active transcription.