arXiv subjects

Takashi Uneyama

Publications and source records attributed to Takashi Uneyama.

At least 55 records · Page 3Linked to original sources

arXiv2022

Percolation induced gel-gel phase separation in a dilute polymer network

Cosmic large-scale structures, animal flocks, and living tissues are non-equilibrium organized systems created by dissipative processes. Despite the uniqueness, the realization of dissipative structures is still difficult. Herein, we report that a network formation process in a dilute system is a dissipative process, leading to percolation induced gel-gel phase separation (GGPS) in a prominent miscible polymer-water system. The dilute system, which forms a monophase structure at the percolation threshold, eventually separates into two gel phases in a longer time scale as the network formation progresses. The dilute hydrogel with GGPS exhibits an unexpected mesoscale co-continuous structure and induces adipose growth in subcutaneous. The formation mechanism of GGPS and a cosmic large-scale structure is analogous, in terms of attractive interactions in a diluted system driving phase separation. This unique phenomenon unveils the possibility of dissipative structures enabling advanced functionalities and will stimulate research fields related to dissipative structures.

cond-mat.soft↗

arXiv2021

Linear Viscoelasticity of Dumbbells Interacting via Gaussian Soft-Core Potential

In polymer melts, the interaction between segments are considered to be screened and the ideal Gaussian chain statistics is recovered. The experimental fact that linear viscoelasticity of unentangled polymers can be well described by the Rouse model is naively considered as due to this screening effect. Although various theoretical models are based on the screening effect and the screening effect is believed to be reasonable, the screening effect cannot be fully justified on a solid theoretical basis. In this work, we study the screening effect by utilizing a simple dumbbell type model. We perform simulations for dumbbell systems in which particles interact via the Gaussian soft-core potential. We show that, if the density of dumbbells is high, the Gaussian soft-core interaction is actually screened and the static structures are well described by the ideal model without Gaussian soft-core interaction. We also show that the relaxation moduli of interacting dumbbell systems approximately coincide to those of the non-interacting dumbbell systems. In the low density systems, we observe the deviations from the ideal non-interacting systems. For example, the relaxation moduli become relatively broad. However, the relaxation moduli of such systems can be decomposed into the relaxation modes by the Gaussian soft-core interaction and the bond. The bond relaxation mode can be successfully described by a single Maxwell relaxation with effective relaxation strength and time. Our results support a naive use of the Rouse model to analyze unentangled polymer melts.

cond-mat.soft↗

arXiv2021

Plateau Moduli of Several Single-Chain Slip-Link and Slip-Spring Models

We calculate the plateau moduli of several single-chain slip-link and slip-spring models for entangled polymers. In these models, the entanglement effects are phenomenologically modeled by introducing topological constraints such as slip-links and slip-springs. The average number of segments between two neighboring slip-links or slip-springs, $N_{0}$, is an input parameter in these models. To analyze experimental data, the characteristic number of segments in entangled polymers $N_{e}$ estimated from the plateau modulus is used instead. Both $N_{0}$ and $N_{e}$ characterize the topological constraints in entangled polymers, and naively $N_{0}$ is considered to be the same as $N_{e}$. However, earlier studies showed that $N_{0}$ and $N_{e}$ (or the plateau modulus) should be considered as independent parameters. In this work, we show that due to the fluctuations at the short time scale, $N_{e}$ deviates from $N_{0}$. This means that the relation between $N_{0}$ and the plateau modulus is not simple as naively expected. The plateau modulus (or $N_{e}$) depends on the subchain-scale details of the employed model, as well as the average number of segments $N_{0}$. This is due to the fact that the subchain-scale fluctuation mechanisms depend on the model rather strongly. We theoretically calculate the plateau moduli for several single-chain slip-link and slip-spring models. Our results explicitly show that the relation between $N_{0}$ and $N_{e}$ is model-dependent. We compare theoretical results with various simulation data in the literature, and show that our theoretical expressions reasonably explain the simulation results.

cond-mat.soft↗

arXiv2020

Multi-chain slip-spring simulations with various slip-spring densities

Although it has been established that the multi-chain slip-spring (MCSS) model can reproduce entangled polymer dynamics, the effects of model parameters have not been fully elucidated yet. In this study, we systematically investigated the effects of slip-spring density. For the diffusion and the linear viscoelasticity, the simulation results exhibited universality. Namely, the results from the simulations with various slip-spring densities can be superposed with each other by the conversion factors for the bead number per chain, unit of length, unit of time, and modulus. The diffusion and the viscoelasticity were in good agreement with the literature data for the standard bead-spring simulations, including the molecular weight dependence. The universality among the MCSS simulations with various slip-spring density also held under mild shear if the slip-spring density was not significantly high. The results imply that the level of coarse-graining for the MCSS model can be arbitrarily chosen as in the Rouse model.

cond-mat.soft↗

arXiv2020

Short time dynamics of tracer in ideal gas

A small tagged particle immersed in a fluid exhibits the Brownian motion and diffuses at the long-time scale. Meanwhile, at the short-time scale, the dynamics of the tagged particle cannot be simply described by the usual generalized Langevin equation with the Gaussian noise, since the number of collisions between the tagged particle and fluid particles is rather small. At such a time scale, we should explicitly consider individual collision events between the tagged particle and the surrounding fluid particles. In this study, we analyzed the short-time dynamics of the tagged particle in an ideal gas, where we do not have static nor hydrodynamic correlations between fluid particles. We performed event-driven hard sphere simulations and show that the short-time dynamics of the tagged particle is correlated even under such an idealized situation. Namely, the velocity autocorrelation function becomes negative when the tagged particle is relatively light and the fluid density is relatively high. This result can be attributed to the dynamical correlation between collision events. To investigate the physical mechanism, which causes the dynamical correlation, we analyzed the correlation between successive collision events. We found that the tagged particle can collide with the same ideal gas particle several times, and such collisions cause the strong dynamical correlation for the velocity.

cond-mat.stat-mech↗

arXiv2020

Coarse-Graining of Microscopic Dynamics into Mesoscopic Transient Potential Model

We show that a mesoscopic coarse-grained dynamics model which incorporates the transient potential can be formally derived from an underlying microscopic dynamics model. As a microscopic dynamics model, we employ the overdamped Langevin equation. By utilizing the path probability and the Onsager-Machlup type action, we calculate the path probability for the coarse-grained mesoscopic degrees of freedom. The action for the mesoscopic degrees of freedom can be simplified by incorporating the transient potential. Then the dynamic equation for the mesoscopic degrees of freedom can be simply described by the Langevin equation with the transient potential (LETP). As a simple and analytically tractable approximation, we introduce additional degrees of freedom which express the state of the transient potential. Then we approximately express the dynamics of the system as the the combination of the LETP and the dynamics model for the transient potential. The resulting dynamics model has the same dynamical structure as the responsive particle dynamics (RaPiD) type models [W. J. Briels, Soft Matter 5, 4401 (2009)] and the multi-chain slip-spring type models [T. Uneyama and Y. Masubuchi, J. Chem. Phys. 137, 154902 (2012)]. As a demonstration, we apply our coarse-graining method with the LETP to a single particle dynamics in a supercooled liquid, and compare the results of the LETP with the molecular dynamics simulations and other coarse-graining models.

cond-mat.stat-mech↗

arXiv2019

Dissipation in Langevin Equation and Construction of Mobility Tensor from Dissipative Heat Flow

The rheological behavior of a material is strongly related to the energy dissipation, and the understanding and modeling of dissipation is important from the view point of rheology. To study rheological properties with some mesoscopic and macroscopic dynamics models, the modeling of dynamic equation which appropriately incorporates the dissipation is important. Although there are several methods to construct mesoscopic and macroscopic dynamic equations, such as the Onsager's method, their validity is not fully clear. In this work, we theoretically analyze the dissipation in a mesoscopic Langevin equation in detail, from the view point of stochastic energetics. We show that the dissipative heat flow from the heat bath to the system plays an important role in the mesoscopic dynamics. The dissipative heat flow is unchanged under the variable transform, and thus it is a covariant quantity. We show that we can construct the Langevin equation and also perform a coarse-graining based on the dissipative heat flow. We can derive the mobility tensor from the dissipative heat flow, and construct the Langevin equation by combining it and the free energy. Our method can be applied to various systems, such as the dumbbell model and the diffusion type equation for the density field, to give the coarse-grained dynamic equations for them.

cond-mat.soft↗

arXiv2019

Brownian motion with alternately fluctuating diffusivity: Stretched-exponential and power-law relaxation

We investigate Brownian motion with diffusivity alternately fluctuating between fast and slow states. We assume that sojourn-time distributions of these two states are given by exponential or power-law distributions. We develop a theory of alternating renewal processes to study a relaxation function which is expressed with an integral of the diffusivity over time. This relaxation function can be related to a position correlation function if the particle is in a harmonic potential, and to the self-intermediate scattering function if the potential force is absent. It is theoretically shown that, at short times, the exponential relaxation or the stretched-exponential relaxation are observed depending on the power law index of the sojourn-time distributions. In contrast, at long times, a power law decay with an exponential cutoff is observed. The dependencies on the initial ensembles (i.e., equilibrium or non-equilibrium initial ensembles) are also elucidated. These theoretical results are consistent with numerical simulations.

cond-mat.stat-mech↗

arXiv2019

Effect of Inertia on Linear Viscoelasticity of Harmonic Dumbbell Model

The overdamped (inertialess) dumbbell model is widely utilized to study rheological properties of polymers or other soft matters. In most cases, the effect of inertia is merely neglected because the momentum relaxation is much faster than the bond relaxation. We theoretically analyze the effect of inertia on the linear viscoelasticity of the harmonic dumbbell model. We show that the momentum and bond relaxation modes are kinetically coupled and the inertia can affect the bond relaxation if the momentum relaxation is not sufficiently fast. We derive an overdamped Langevin equation for the dumbbell model, which incorporates the weak inertia effect. Our model predicts the bond relaxation dynamics with the weak inertia effect correctly. We discuss how the weak inertia affects the linear viscoelasticity of a simple harmonic dumbbell model and the Rouse model.

cond-mat.soft↗

arXiv2019

Relaxation Functions of Ornstein-Uhlenbeck Process with Fluctuating Diffusivity

We study a relaxation behavior of an Ornstein-Uhlenbeck (OU) process with a time-dependent and fluctuating diffusivity. In this process, the dynamics of a position vector is modeled by the Langevin equation with a linear restoring force and a fluctuating diffusivity (FD). This process can be interpreted as a simple model of the relaxational dynamics with internal degrees of freedom or in a heterogeneous environment. By utilizing the functional integral expression and the transfer matrix method, we show that the relaxation function can be expressed in terms of the eigenvalues and eigenfunctions of the transfer matrix, for general FD processes. We apply our general theory to two simple FD processes, where the FD is described by the Markovian two-state model or an OU type process. We show analytic expressions of the relaxation functions in these models, and their asymptotic forms. We also show that the relaxation behavior of the OU process with an FD is qualitatively different from those obtained from conventional models such as the generalized Langevin equation.

cond-mat.stat-mech↗

arXiv2018

A Transient Bond Model for Dynamic Constraints in Meso-Scale Coarse-Grained Systems

The dynamical properties of entangled polymers originate from the dynamic constraints due to the uncrossability between polymer chains. We propose a highly coarse-grained simulation model with transient bonds for such dynamically constrained systems. Based on the ideas of the responsive particle dynamics (RaPiD) model [P. Kindt and W. J. Briels, J. Chem. Phys. 127, 134901 (2007)] and the multi-chain slip-spring model [T. Uneyama and Y. Masubuchi, J. Chem. Phys. 137, 154902 (2012)], we construct the RaPiD type transient bond model as a coarse-grained slip-spring model. In our model, a polymer chain is expressed as a single particle, and particles are connected by transient bonds. The transient bonds modulate the dynamics of particles but they do not affect static properties in equilibrium. We show the relation between parameters for the entangled polymer systems and those for the transient bond model. By performing simulations based on the transient bond model, we show how model parameters affect the linear viscoelastic behavior and the diffusion behavior. We also show that the viscoelastic behavior of entangled polymer systems can be well reproduced by the transient bond model.

cond-mat.soft↗

arXiv2015

Fluctuation Analysis of Time-Averaged Mean-Square Displacement for Langevin Equation with Time-Dependent and Fluctuating Diffusivity

The mean-square displacement (MSD) is widely utilized to study the dynamical properties of stochastic processes. The time-averaged MSD (TAMSD) provides some information on the dynamics which cannot be extracted from the ensemble-averaged MSD. In particular, the relative standard deviation (RSD) of the TAMSD can be utilized to study the long time relaxation behavior. In this work, we consider a class of Langevin equations which are multiplicatively coupled to time-dependent and fluctuating diffusivities. Various interesting dynamics models such as entangled polymers and supercooled liquids can be interpreted as the Langevin equations with time-dependent and fluctuating diffusivities. We derive a general formula for the RSD of the TAMSD for the Langevin equation with the time-dependent and fluctuating diffusivity. We show that the RSD can be expressed in terms of the correlation function of the diffusivity. The RSD exhibits the crossover at the long time region. The crossover time is related to a weighted average relaxation time for the diffusivity. Thus the crossover time gives some information on the relaxation time of fluctuating diffusivity which cannot be extracted from the ensemble-averaged MSD. We discuss the universality and possible applications of the formula via some simple examples.

cond-mat.stat-mech↗

arXiv2014

Self-Consistent Field Model Simulations for Statistics of Amorphous Polymer Chains in Crystalline Lamellar Structures

We calculate statistical properties of amorphous polymer chains between crystalline lamellae by self-consistent field model simulations. In our model, an amorphous subchain is modelled as a polymer chain of which ends are grafted onto the crystal-amorphous interfaces. The crystal-amorphous interfaces are expressed as impenetrable surfaces. We incorporate the interaction between segments to satisfy the incompressible condition for the segment density field. The simulation results show that amorphous polymer chains feel thin potential layers, which are mainly repulsive, near the crystal-amorphous interfaces. The impenetrable and incompressible conditions affect the statistics of polymer chains and the chain statistics becomes qualitatively different from the ideal Gaussian chain statistics without any constraints. We show the effects of the system size and the graft density to statistical quantities. We also show that the tie subchain statistics obey rather simple statistics.

cond-mat.soft↗

arXiv2012

Multi-chain Slip-spring Model for Entangled Polymer Dynamics

It has been established that the entangled polymer dynamics can be reasonably described by single chain models such as tube and slip-link models. Although the entanglement effect is a result of the hard-core interaction between chains, linkage between the single chain models and the real multi-chain system has not been established yet. In this study, we propose a multi-chain slip-spring model where bead-spring chains are dispersed in space and connected by slip-springs inspired by the single chain slip-spring model [A. E. Likhtman, Macromolecules 38, 6128 (2005)]. In this model the entanglement effect is replaced by the slip-springs, not by the hard-core interaction between beads so that this model is located in the niche between conventional multi-chain simulations and single chain models. The set of state variables are the position of beads and the connectivity (indices) of the slip-springs between beads. The dynamics of the system is described by the time evolution equation and stochastic transition dynamics for these variables. We propose a simple model which is based on the well-defined total free-energy and the detailed balance condition. The free energy in our model contains a repulsive interaction between beads, which compensate the attractive interaction artificially generated by the slip-springs. The explicit expression of linear relaxation modulus is also derived by the linear response theory. We also propose a possible numerical scheme to perform simulations. Simulations reproduced expected bead number dependence in transitional regime between Rouse and entangled dynamics for the chain structure, the central bead diffusion, and the linear relaxation modulus.

cond-mat.soft↗

arXiv2012

Crossover Time in Relative Fluctuations Characterizes the Longest Relaxation Time of Entangled Polymers

In entangled polymer systems, there are several characteristic time scales, such as the entanglement time and the disengagement time. In molecular simulations, the longest relaxation time (the disengagement time) can be determined by the mean square displacement (MSD) of a segment or by the shear relaxation modulus. Here, we propose the relative fluctuation analysis method, which is originally developed for characterizing large fluctuations, to determine the longest relaxation time from the center of mass trajectories of polymer chains (the time-averaged MSDs). Applying the method to simulation data of entangled polymers (by the slip-spring model and the simple reptation model), we provide a clear evidence that the longest relaxation time is estimated as the crossover time in the relative fluctuations.

cond-mat.soft↗

arXiv2012

Concentration Dependence of Rheological Properties of Telechelic Associative Polymer Solutions

We consider concentration dependence of rheological properties of associative telechelic polymer solutions. Experimental results for model telechelic polymer solutions show rather strong concentration dependence of rheological properties. For solutions with relatively high concentrations, linear viscoelasticity deviates from the single Maxwell behavior. The concentration dependence of characteristic relaxation time and moduli is different in high and low concentration cases. These results suggest that there are two different concentration regimes. We expect that densely connected (well percolated) networks are formed in high-concentration solutions, whereas sparsely connected (weakly percolated) networks are formed in low-concentration solutions. We propose single chain type transient network models to explain experimental results. Our models incorporate the spatial correlation effect of micellar cores and average number of elastically active chains per micellar core (the network functionality). Our models can reproduce non-single Maxwellian relaxation and nonlinear rheological behavior such as the shear thickening and thinning. They are qualitatively consistent with experimental results. In our models, the linear rheological behavior is mainly attributable to the difference of network structures (functionalities). The nonlinear rheological behavior is attributable to the nonlinear flow rate dependence of the spatial correlation of micellar core positions.

cond-mat.soft↗

arXiv2011

Detailed Balance Condition and Effective Free Energy in the Primitive Chain Network Model

We consider statistical mechanical properties of the primitive chain network (PCN) model for entangled polymers from its dynamic equations. We show that the dynamic equation for the segment number of the PCN model does not reduce to the standard Langevin equation which satisfies the detailed balance condition. We propose heuristic modifications for the PCN dynamic equation for the segment number, to make it reduce to the standard Langevin equation. We analyse some equilibrium statistical properties of the modified PCN model, by using the effective free energy obtained from the modified PCN dynamic equations. The PCN effective free energy can be interpreted as the sum of the ideal Gaussian chain free energy and the repulsive interaction energy between slip-links. By using the single chain approximation, we calculate several distribution functions of the PCN model. The obtained distribution functions are qualitatively different from ones for the simple slip-link model without any direct interactions between slip-links.

cond-mat.soft↗

arXiv2011

Single Chain Slip-Spring Model for Fast Rheology Simulations of Entangled Polymers on GPU

We propose a single chain slip-spring model, which is based on the slip-spring model by Likhtman [A. E. Likhtman, Macromolecules, 38, 6128 (2005)], for fast rheology simulations of entangled polymers on a GPU. We modify the original slip-spring model slightly for efficient calculations on a GPU. Our model is designed to satisfy the detailed balance condition, which enables us to analyze its static or linear response properties easily. We theoretically analyze several statistical properties of the model, such as the linear response, which will be useful to analyze simulation data. We show that our model can reproduce several rheological properties such as the linear viscoelasticity or the viscosity growth qualitatively. We also show that the use of a GPU can improve the performance drastically.

cond-mat.soft↗