Viscoelastic Phase Separation Research Articles

Liquid DNA Coacervates form Porous Capsular Hydrogels via Viscoelastic Phase Separation on Microdroplet Interface

AbstractLiquid–liquid phase separation (LLPS) droplets of biopolymers are known as functional microdroplets in living cells and have recently been used to construct protocells and artificial cells. The formation of DNA coacervates (also referred to as DNA droplets) from branched DNA nanostructures and the control of their physical properties via DNA nanostructure design are demonstrated previously. For the construction of artificial cells or protocells, however, even though physical effects such as surface tension, wetting, and viscoelasticity are more important in a tiny (micrometer‐sized), confined environment than in a bulk solution environment, they have not been explored yet. This study shows that a tiny, confined environment using a water‐in‐oil (W/O) microdroplet interface modulates the phase separation dynamics of DNA coacervates, leading to micrometer‐sized porous capsular structures. The porous structures are produced via two types of viscoelastic phase separation (VPS) processes in DNA coacervates: i) simple VPS and ii) cluster‐cluster aggregation after VPS. Finally, it is shown that environmental chemical stimulation can manipulate porous capsular DNA hydrogels extracted from W/O microdroplets. These results provide an approach for designing and fabricating artificial cells or protocells with complex structures and physicochemical properties.

Coarsening dynamics of ternary polymer solutions with mobility and viscosity contrasts.

Using phase-field simulations, we investigate the bulk coarsening dynamics of ternary polymer solutions undergoing a glass transition for two models of phase separation: diffusion only and with hydrodynamics. The glass transition is incorporated in both models by imposing mobility and viscosity contrasts between the polymer-rich and polymer-poor phases of the evolving microstructure. For microstructures composed of polymer-poor clusters in a polymer-rich matrix, the mobility and viscosity contrasts significantly hinder coarsening, effectively leading to structural arrest. For microstructures composed of polymer-rich clusters in a polymer-poor matrix, the mobility and viscosity contrasts do not impede domain growth; rather, they change the transient concentration of the polymer-rich phase, altering the shape of the discrete domains. This effect introduces several complexities to the coarsening process, including percolation inversion of the polymer-rich and polymer-poor phases-a phenomenon normally attributed to viscoelastic phase separation.

Controlling the coarsening dynamics of ferrogranular networks by means of a vertical magnetic field.

We are exploring in experiments the aggregation process in a shaken granular mixture of glass and magnetized steel beads, filled in a horizontal vessel, after the shaking amplitude is suddenly decreased. Then the magnetized beads form a transient network that coarsens in time into compact clusters, resembling a viscoelastic phase separation [Tanaka, J. Phys.: Condens. Matter 12, R207 (2000)0953-898410.1088/0953-8984/12/15/201], where attached beads represent the slow phase. Here we investigate how a homogeneous magnetic field oriented in vertical direction impedes the emergence and growth of the networks. With increasing field amplitude this phase is replaced by a fluctuating arrangement of repelling, isolated steel beads. The experimental results are compared with those of computer simulations. Coarse-grained molecular dynamics confirms the impact of an applied magnetic field on the structural transitions and allows us to investigate long-time regimes and magnetic response not yet accessible in the experiment. It turns out that an applied magnetic field has different impacts, depending on it strength. It can be used either to slow down the dynamics of the structural transitions without changing the type of the resulting phases and only affecting the amount and sizes of clusters, or to fully impede the formation of network-like and compact aggregates of steel beads.

Methylcellulose as a non-bonding gelling agent for calcium chloride methanol fuel gels

Carbohydrate-based fuel gels find diverse applications across industries ranging from renewable energy and transportation to military and emergency preparedness. This study investigates the thermal properties, gel characteristics, combustion performance, micro-, and nano-scale structure of methylcellulose (MC) in methanol and the effect of calcium chloride (CaCl2) addition. The results show that MC exhibits viscoelastic phase separation due to the lower critical solution temperature, resulting in gelation at the 22 wt%. Thermogravimetric analysis reveals good thermal stability of MC in methanol, with a single decomposition stage. Adding CaCl2 modifies rheological behavior and enhances the thermal properties of the MC/methanol gel, with improved combustion and ignition performance due to the formation of CaCl2-methanolates. Small-angle X-ray scattering analysis indicates changes in nanoscale aggregates, correlation length, and fractal dimension with increasing CaCl2 content. This study provides valuable insights into the properties of MC-based fuel gels and their potential applications.

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.

Existence and weak-strong uniqueness for global weak solutions for the viscoelastic phase separation model in three space dimensions

The aim of this work is to prove the global-in-time existence of weak solutions for a viscoelastic phase separation model in three space dimensions. To this end, we apply the relative energy concept provided by [7]. We consider the case of regular polynomial-type potentials and positive mobilities, as well as the degenerate case with logarithmic potential and vanishing mobility.

Relative energy and weak–strong uniqueness of a two‐phase viscoelastic phase separation model

AbstractThe aim of this paper is to analyze a viscoelastic phase separation model. We derive a suitable notion of the relative energy taking into account the nonconvex nature of the energy law for the viscoelastic phase separation. This allows us to prove the weak–strong uniqueness principle. We will provide the estimates for the full model in two space dimensions. For a reduced model, we present the estimates in three space dimensions and derive conditional relative energy estimates.

Viscoelastic phase separation in biological cells

Biological phase separation forming membraneless organelles in cytoplasm and nucleus has attracted considerable attention. Liquid-like condensates are often created as spherical droplets. However, various condensates with network-like morphologies, including protein granules, localisation bodies, and centrosome assemblies, have recently been discovered in cells. Therefore, what controls the morphology of biological phase separation is a critical issue but remains elusive. Here, based on the knowledge of viscoelastic phase separation in soft matter physics, we propose that the difference in the molecular dynamics between the two phases controls the condensate morphology. Small and large mobility differences between the two phases should lead to droplet-like and network-like morphologies of the minority phase, respectively. We show that asymmetric partitioning of high-molecular-weight unstructured polymers (e.g., messenger RNA) between the two phases increases the dynamic asymmetry between the phases to form a network-like pattern of the slower phase, which may further be stabilised through inter-polymer binding.

Global existence of weak solutions to viscoelastic phase separation: part II. Degenerate case

The aim of this paper is to prove global in time existence of weak solutions for a viscoelastic phase separation. We consider the case with singular potentials and degenerate mobilities. Our model couples the diffusive interface model with the Peterlin–Navier–Stokes equations for viscoelastic fluids. To obtain the global in time existence of weak solutions we consider appropriate approximations by solutions of the viscoelastic phase separation with a regular potential and build on the corresponding energy and entropy estimates.

Global existence of weak solutions to viscoelastic phase separation part: I. Regular case

We prove the existence of weak solutions to a viscoelastic phase separation problem in two space dimensions. The mathematical model consists of a Cahn–Hilliard-type equation for two-phase flows and the Peterlin–Navier–Stokes equations for viscoelastic fluids. We focus on the case of a polynomial-like potential and suitably bounded coefficient functions. Using the Lagrange–Galerkin finite element method complex behavior of solution for spinodal decomposition including transient polymeric network structures is demonstrated.

Viscoelastic Phase Patterning in Artificial Protein Hydrogels

Viscoelastic forces can affect the dynamics of pattern formation during phase separation in polymeric materials. We programmed an artificial protein hydrogel to undergo viscoelastic phase separation above a critical temperature. Highly dynamic phase patterns that coarsened under the influence of viscoelastic stresses spontaneously emerged in these gels. Local oxidative crosslinking promoted by mild photobleaching could be used to initiate phase separation locally, enabling the creation of non-equilibrium patterns that evolved under the influence of surface tension and viscoelastic stresses to yield dynamic structures of controlled size and shape.

Kinetic viscoelasticity during early polymer-polymer spinodal dewetting

The dewetting kinetics of a supported polymer bilayer were measured in situ using coherent grazing-incidence x-ray scattering. X-ray photon correlation spectroscopy provides both the two-time correlation functions and the cross-correlation function which measures the average spatial shift of the speckles produced by the coherent x rays. The stress in the ultrathin top dewetting film can be directly observed due to the exquisite sensitivity to sample curvature changes provided by the x-ray speckle correlation functions. The hole-opening events in the film are found to be associated with significant changes to the stress. These results are interpreted through an analogy between viscoelastic spinodal dewetting and early-stage bulk viscoelastic phase separation. The frequency of hole-initiation events during dewetting decreases with time as a power law, and the power-law exponent can be linked to nonlinear viscoelastic effects, showing similarity in their stress relief dynamics to aftershock decays.

Density Functional Theory for Polymer Phase Separations Induced by Coupling of Chemical Reaction and Elastic Stress

AbstractA density functional theory is applied to phase separation dynamics influenced by crosslinking reactions in dense polymer solutions. The crosslinking reaction is modeled by a change from non‐crosslinked polymers comprising transient network (TN) to crosslinked polymers participating in the percolated permanent network (PN). Deformed TN polymers are considered to relax to the isotropic equilibrium state according to the Maxwellian linear viscoelastic constitutive equation, which is used in the modeling of viscoelastic phase separations. The PN is modeled by a linear elastic constitutive model. When TN polymers are taken into the PN by crosslinking reaction, the instantaneous deformation of the TN polymers are frozen, and such frozen deformations are accumulated as time goes on. A series of simulations is performed using this model, so that two specific features of the viscoelastic and reactive phase separation are obtained, i.e., 1) two‐stage phase separation process that leads to a domain structure with two different characteristic length scales, and 2) fixing the phase‐separated structure before reaching the macrophase separation.

Formation of Multi-Channel Collagen Gels Investigated Using Particle Tracking Microrheology.

Collagen is one of the most common materials used to form scaffolds for tissue engineering applications. The multi-channel collagen gel (MCCG) obtained by the dialysis of an acidic collagen solution in a neutral buffer solution has a unique structure, with many capillaries of diameters several tens to a few hundred micrometers, and could be a potential candidate as a biomimetic scaffold for three-dimensional tissue engineering. In the present study, the formation of MCCG was investigated by in situ rheological measurements based on a particle tracking method (particle tracking microrheology, PTM). PTM enabled us to measure changes in the rheological properties of collagen solutions under the continuous exchange of substances during dialysis. When an observation plane was set perpendicular to the direction of gel growth, we first observed convectional flow of the collagen solution, followed by phase separation and gelation. We showed that the structure of the MCCG originated from the transient structure formed during the initial stage of viscoelastic phase separation and was fixed by the subsequent gelation.

Systematic derivation of hydrodynamic equations for viscoelastic phase separation

We present a detailed derivation of a simple hydrodynamic two-fluid model, which aims at the description of the phase separation of non-entangled polymer solutions, where viscoelastic effects play a role. It is directly based upon the coarse-graining of a well-defined molecular model, such that all degrees of freedom have a clear and unambiguous molecular interpretation. The considerations are based upon a free-energy functional, and the dynamics is split into a conservative and a dissipative part, where the latter satisfies the Onsager relations and the second law of thermodynamics. The model is therefore fully consistent with both equilibrium and non-equilibrium thermodynamics. The derivation proceeds in two steps: firstly, we derive an extended model comprising two scalar and four vector fields, such that inertial dynamics of the macromolecules and of the relative motion of the two fluids is taken into account. In the second step, we eliminate these inertial contributions and, as a replacement, introduce phenomenological dissipative terms, which can be modeled easily by taking into account the principles of non-equilibrium thermodynamics. The final simplified model comprises the momentum conservation equation, which includes both interfacial and elastic stresses, a convection–diffusion equation where interfacial and elastic contributions occur as well, and a suitably convected relaxation equation for the end-to-end vector field. In contrast to the traditional two-scale description that is used to derive rheological equations of motion, we here treat the hydrodynamic and the macromolecular degrees of freedom on the same basis. Nevertheless, the resulting model is fairly similar, though not fully identical, to models that have been discussed previously. Notably, we find a rheological constitutive equation that differs from the standard Oldroyd-B model. Within the framework of kinetic theory, this difference may be traced back to a different underlying statistical-mechanical ensemble that is used for averaging the stress. To what extent the model is able to reproduce the full phenomenology of viscoelastic phase separation is presently an open question, which shall be investigated in the future.

Analysis of a viscoelastic phase separation model

A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological viscoelastic terms. By construction, the model is consistent with the second law of thermodynamics. We study well-posedness of the model in two space dimensions, i.e., existence of weak solutions, a weak-strong uniqueness principle, and stability with respect to perturbations, which are proven by means of relative energy estimates. Our numerical simulations based on the new viscoelastic phase separation model are in good agreement with physical experiments. Furthermore, a good qualitative agreement with mesoscopic simulations is observed.

Viscoelastic phase separation model for ternary polymer solutions.

When a polymer solution undergoes viscoelastic phase separation, the polymer-rich phase forms a network-like structure even if it is a minor phase. This unique feature is induced by polymer dynamics, which are constrained by the temporal entanglement of polymer chains. The fundamental mechanisms of viscoelastic phase separation have already been elucidated by theory and experiments over the past few decades; however, it is not yet well understood how viscoelastic phase separation occurs in multicomponent polymer solutions. Here, we construct a new viscoelastic phase separation model for ternary polymer solutions that consist of a polymer, solvent, and nonsolvent. Our simulation results reveal that a network-like structure is formed in the ternary bulk system through a phase separation mechanism similar to that observed in binary polymer solutions. A difference in dynamics is also found in that the solvent, whose affinity to the polymer is similar to that of the nonsolvent, moves freely between the polymer-rich and water-rich phases during phase separation. These findings are considered important for understanding the phase separation mechanism of ternary mixtures often used in the manufacture of polymeric separation membranes.

Effect of annealing method and chemical reaction on the structure and properties of polyethylene/polyethylene glycol modified bitumen

Polyethylene (PE) and polyethylene glycol (PEG) are employed to modify bitumen. The rheological stability is revealed by complex modulus (G*) variation with temperature, and it is found that the starting temperature and stable value of G* plateau can be regulated by different annealing treatments. The sample annealed under the temperature (100 °C) close to the crystallization temperature of PE has the best rheological stability. The reason for this effect is explored on terms of crystallization behavior of PE, whose crystallinity is related to the stiffness of PE-rich network induced by viscoelastic phase separation. When the PEG modifier is partially replaced by the same fraction of 4,4′-diphenylmethane diisocyanate (MDI), the complex modulus, thermal stability and solvent resistance of PE modified bitumen can be significantly improved, while the PE-rich network structure is refined. The main reason for these results is the chemical reaction between MDI and polar groups of PEGs and/or bitumen to form large-scale urethane/urea structure, which is revealed by Fourier transform infrared spectrometer.

Anisotropic viscoelastic phase separation in polydisperse hard rods leads to nonsticky gelation

Spinodal demixing into two phases having very different viscosities leads to viscoelastic networks-i.e., gels-usually as a result of attractive particle interactions. Here, however, we demonstrate demixing in a colloidal system of polydisperse, rod-like clay particles that is driven by particle repulsions instead. One of the phases is a nematic liquid crystal with a highly anisotropic viscosity, allowing flow along the director, but suppressing it in other directions. This phase coexists with a dilute isotropic phase. Real-space analysis and molecular-dynamics simulations both reveal a long-lived network structure that is locally anisotropic, yet macroscopically isotropic. We show that our system exhibits the characteristics of colloidal gelation, leading to nonsticky gels.

An overview of viscoelastic phase separation in epoxy based blends.

The viscoelastic effects during reaction induced phase separation play an important role in toughening epoxy-based blends. The large difference in molecular weight/glass transition temperature between the blend components before the curing reaction results in dynamic asymmetry, causing viscoelastic effects during phase separation accompanying the curing reaction. This review will focus on the key factors responsible for viscoelastic phase separation in epoxy-based blends and hybrid nanocomposites. Time-resolved characterization techniques such as rheometry, small angle laser light scattering, optical microscopy etc., are mainly used for monitoring the viscoelastic effects during phase separation. Incorporation of nanofillers in epoxy thermoplastic blends enhances the viscoelastic phase separation due to the increase in dynamic asymmetry. Different theoretical models are identified for the determination of processing parameters such as temperature, viscosity, phase domain size, and other parameters during the viscoelastic phase separation process. The effect of viscoelastic phase separation has a very strong influence on the domain parameters of the blends and thereby on the ultimate properties and applications.