Fig 15 - uploaded by Hajime Tanaka
Content may be subject to copyright.
6 Schematic figure explaining the physical mechanism of V.P.S. in soft matter. Here, big dark grey particles represent slow components such as polymers, colloids, and proteins, whereas small lighter-shaded particles represent solvent molecules. After initiation of phase separation the small particles can relax very quickly to the lowest-energy configuration. However, once the big particles are connected to form a network structure with the help of hydrodynamic interactions, there is no simple way to relax to the final lowest-energy configuration (the image furthest to the right). The connectivity prevents big particles from lowering the contact energy by forming a more compact structure. In other words, the diffusion is prevented by the mechanical stress generated by the connectivity: stress-diffusion coupling. This coarsening mechanism can be active even in the absence of thermal noise (even at T = 0), since it is of a purely mechanical nature (Tanaka and Araki, 2007). This figure is reproduced from Fig. 1 of (Tanaka, 2009).
Source publication
In this article, we review the basic physics of viscoelastic phase separation including fracture phase separation. We show that with an increase in the ratio of the deformation rate of phase separation to the slowest mechanical relaxation rate the type of phase separation changes from fluid phase separation, to viscoelastic phase separation, to fra...
Similar publications
Mode-coupling instabilities are known to trigger self-excited vibrations in sliding contacts. Here, the conditions for mode-coupling (or "flutter") instability in the contact between a spherical oscillator and a moving viscoelastic substrate are studied. The work extends the classical 2-Degrees-Of-Freedom conveyor belt model and accounts for viscoe...
Atomic Force Microscopy (AFM) is no longer used as a nanotechnology tool responsible for topography imaging. However, it is widely used in different fields to measure various types of material properties, such as mechanical, electrical, magnetic, or chemical properties. One of the recently developed characterization techniques is known as loss tang...
A closed-form solution for the adhesive contact of soft spheres of linear elastic material is available since 1971 thanks to the work of Johnson, Kendall, and Roberts (JKR). A similar solution for viscoelastic spheres is still missing, though semi-analytical and numerical models are available today. In this note, we propose a closed-form analytical...
Citations
... 35 Due to the lack of a rigorous theoretical foundation for the constitutive relation of a polymer solution in an out-of-equilibrium state undergoing demixing, the bulk stress term was initially introduced relying on physical intuition. 24,27,44 Later, a more rigorous derivation of the constitutive equation has been made based on dumbbell models. 37,45−47 Nevertheless, the microscopic origin of the viscoelastic stress and the breakdown of self-similar coarsening in polymer VPS remain unclear at the fundamental level. ...
... The above results provide the microscopic origin for introducing the bulk stress in the constitutive equation of demixing polymer solutions. 24,27,35,44 These results support the argument 24,35,41 that the temporal change in the volume fraction even after forming a sharp interface between the two phases in polymer VPS is of mechanical origin rather than due to the composition dependence of the diffusion constant. 34 We note that although the structural relaxation time of the dense phase, τ α , is almost the same for colloid and polymer VPS at k B T/ε = 0.067 ( Figure S3a in the Supporting Information), the power-law coarsening of ∝ t 1/2 holds for the former ( Figure S3e in the Supporting Information) but not for the latter (Figure 2b). ...
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.
... The aspect of dynamic asymmetry was raised for mainly polymer/solvent systems by Tanaka [29,30]. However, the viscosities of 3MP and D 2 O are very similar [31] and so dynamic asymmetry can be safely neglected. ...
We observed criticality in the structure and dynamics of a three-dimensional (3D) and two-dimensional (2D) Ising system consisting of 3-methyl pyridine (3MP)/D2O without and with antagonistic salt. We could describe both dynamic criticalities by the Kawasaki crossover function. The dynamic critical exponent was z=0.063±0.020 and 0.005±0.019 for three and two dimensions, which confirms earlier observations in the 3D case and confirms expectations in the 2D case. The amplitudes of the critical dynamics are governed by the bare viscosities experimentally, and by the coefficient R theoretically [the latter is proportional to (4−d)−1 with the dimensionality d]. This finding is in accordance with the lubrication effect [N. Gov, A. G. Zilman, and S. Safran, Phys. Rev. E 70, 011104 (2004)], which is also connected to lamellar systems of the Brazovskii criticality [M. Gvaramia et al., Colloid Polym. Sci. 297, 1507 (2019)]. This lubrication effect is tightly connected to a laminar flow enforced by the domain structure, and it also holds for our 2D Ising system. The experimental techniques employed were small-angle neutron and x-rays scattering for the static criticality, and dynamic light scattering and neutron spin echo spectroscopy for the critical dynamics. Furthermore, the criticality of the viscosities was measured.
... 1(a) and 1(b)]. The viscoelastic length is the characteristic length scale above which dynamics are dominated by diffusion and below which dynamics are dominated by viscoelastic effects [41]. This length is a rheological length scale (many times the radius of gyration as shown in the Supplemental Material [16]) intrinsic to entangled polymers [42,43]. ...
... Here, the asymmetry is between the regions of polymer film and the regions occupied by holes. This stage of spinodal dewetting shows analogy to the viscoelastic phase separation [48] due to the dynamic asymmetry between holes and polymer film (which supports all the stress) [41,49]. ...
... Viscoelastic effects in polymers are kinetic effects; they cannot be included in the Hamiltonian, and dynamic equations are required to describe them. It is quite difficult to make any theoretical prediction, such as on the exact form of stress generated during viscoelastic dewetting, as there are no theories for the rheological behavior of a system in nonequilibrium states [41,49]. Here, the coherent x-ray speckle is used to probe this kinetic viscoelasticity during 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.
... Many interesting new phenomena such as phase inversion, transient formation of network-like structures and volume shrinking, arise due to the dynamic asymmetry of the mixture and the viscoelastic behaviour. The dynamic asymmetry [30] follows from the different time-scales of the polymer and the solvent. For such problems the term viscoelastic phase separation was coined by Tanaka [29] . ...
The 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 non-convex 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.
... Phase separation, coarsening, and dynamical arrest in interacting nonequilibrium systems arise in a variety of contexts in physics and biology. Examples include turbulent mixtures [1], driven granular materials [2], constrained systems at low temperatures [3,4], as well as soft matter and biological systems [5]. Hard-core particle systems that model several types of materials often display glassy dynamics and provide examples of unusually slow coarsening toward phase separation, however, they remain hard to characterize theoretically. ...
We study the early-time and coarsening dynamics in the light-heavy model, a system consisting of two species of particles (light and heavy) coupled to a fluctuating surface (described by tilt fields). The dynamics of particles and tilts are coupled through local update rules, and are known to lead to different ordered and disordered steady-state phases depending on the microscopic rates. We introduce a generalized balance mechanism in nonequilibrium systems, namely, bunchwise balance, in which incoming and outgoing transition currents are balanced between groups of configurations. This allows us to exactly determine the steady state in a subspace of the phase diagram of this model. We introduce the concept of irreducible sequences of interfaces and bends in this model. These sequences are nonlocal, and we show that they provide a coarsening length scale in the ordered phases at late times. Finally, we propose a local correlation function (S) that has a direct relation to the number of irreducible sequences, and is able to distinguish between several phases of this system through its coarsening properties. Starting from a totally disordered initial configuration, S displays an initial linear rise and a broad maximum. As the system evolves toward the ordered steady states, S further exhibits power-law decays at late times that encode coarsening properties of the approach to the ordered phases. Focusing on early-time dynamics, we posit coupled mean field evolution equations governing the particles and tilts, which at short times are well approximated by a set of linearized equations, which we solve analytically. Beyond a timescale set by an ultraviolet (lattice) cutoff and preceding the onset of coarsening, our linearized theory predicts the existence of an intermediate diffusive (power-law) stretch, which we also find in simulations of the ordered regime of the system.
... Phase separation, coarsening and dynamical arrest in interacting non-equilibrium systems arises in a variety of contexts in physics and biology. Examples include turbulent mixtures [1], driven granular materials [2], constrained systems at low temperatures [3,4], as well as soft matter and biological systems [5]. Hard core particle systems that model several types of materials often display glassy dynamics and provide examples of unusually slow coarsening towards phase separation, however, they remain hard to characterize theoretically. ...
We study the early time and coarsening dynamics in a system consisting of two species of particles ($light$ and $heavy$) coupled to a fluctuating surface (described by tilt fields). The dynamics of particles and tilts are coupled through local update rules, and lead to different ordered and disordered steady state phases depending on the microscopic rates. We introduce a generalised balance mechanism in non-equilibrium systems, namely $bunchwise~balance$, in which incoming and outgoing transition currents are balanced between groups of configurations. This allows us to exactly determine the steady state in a subspace of the phase diagram of this model. We introduce the concept of $irreducible~sequences$ of interfaces and bends in this model. These sequences are non-local, and we show that they provide a coarsening length scale in the ordered phases at late times. Finally, we propose a $local$ correlation function ($\mathcal{S}$) that has a direct relation to the number of irreducible sequences, and is able to distinguish between several phases of this system through its coarsening properties. Starting from a totally disordered initial configuration, $\mathcal{S}$ displays an initial linear rise and a broad maximum. As the system evolves towards the ordered steady states, $\mathcal{S}$ further exhibits power law decays at late times that encode coarsening properties of the approach to the ordered phases. Focusing on early time dynamics, we posit coupled mean-field evolution equations governing the particles and tilts, which at short times are well approximated by a set of linearized equations, which we solve analytically. Beyond a timescale set by an ultraviolet (lattice) cutoff and preceding the onset of coarsening, our linearized theory predicts the existence of an intermediate diffusive (power-law) stretch, which we also find in simulations of the ordered regime of the system.
... During VPS process, the slow phase cannot catch up with the deformation rate spontaneously generated by phase separation itself, and thus forms a network structure to store elastic energy created by the driving force of phase separation itself [14,15]. The most notable characteristics of VPS is that the transient network structure composed of the minor phase which usually has slower dynamics than that of major phase. ...
As an important regulation parameter, shearing process during bitumen modification can be easily adjusted. However, the effect of shearing time on the properties of modified bitumen and its original reason is still unclear. To explore this concern, bitumen/polyethylene (PE)/ethylene-vinyl acetate copolymer (EVA) blend (PMB) with fixed weight ratio of 100/5/5 was studied by imposing different shear time within 1–4 h under 180 °C. It was found longer shearing time could improve rutting resistance but deteriorate the ductility at low temperature. Due to the crystalline nature of PE/EVA and the immiscibility between these polymers and bitumen, the possible reason was firstly explored on terms of crystallinity and phase structure of PMBs. A shearing-heating system connected with optical microscopy was innovatively employed for in-situ phase structure observation. After excluding both effects of crystallization and phase separation on the different properties of PMBs, the relationship between thermal ageing and shearing was subsequently explored. An in-situ quiescent TGA measurement under 180 °C for 3 h revealed a continuous weight loss of PMBs. FTIR results suggested the thermal-oxidation behavior of EVA. Combined these two results, the thermal-oxidation process and hardening effect were the main reasons for different properties of PMBs with different shearing time.
The 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.
