arXiv subjects

Naoyuki Sakumichi

Publications and source records attributed to Naoyuki Sakumichi.

At least 19 recordsLinked to original sources

arXiv2026

Partitioning Law of Polymer Chains into Flexible Polymer Networks

The equilibrium partitioning of linear polymer chains into flexible polymer networks is governed by intricate entropic constraints arising from the configurational degrees of freedom of both chains and networks; however, a quantitative understanding remains elusive. Using model hydrogels with precisely defined network structures, we experimentally demonstrate a universal law governing the partitioning of linear polymers into flexible polymer networks. We establish a label-free contactless method to measure the partition ratio, based on the increase in the osmotic pressure induced by the partitioning of the external polymer chains. Moreover, we reveal a universal law in which the partition ratio is determined solely by $R_g / l_\mathrm{cycle}$, where $R_g$ is the gyration radius of the polymer chain and $l_\mathrm{cycle}\equiv ξ^{-1/3}$ is the characteristic mesh size of the network, defined by the cycle rank $ξ$, i.e., the number density of elastically effective cycles.

cond-mat.soft↗

arXiv2026

Universal Negative Energetic Elasticity in Polymer Chains: Crossovers among Random, Self-Avoiding, and Neighbor-Avoiding Walks

Negative energetic elasticity in gels challenges the conventional understanding of gel elasticity; despite extensive research, a concise explanation remains elusive. In this study, we use the weakly self-avoiding walk (the Domb-Joyce model; DJ model) and interacting self-avoiding walk (ISAW) to investigate the emergence of negative energetic elasticity in polymer chains. Using exact enumeration, we show that both the DJ model and ISAW exhibit negative energetic elasticity, which is caused by effective soft-repulsive interactions between polymer segments. Moreover, we find that a universal scaling law for the internal energy of both models, with a common exponent of $7/4$, holds consistently across both random-walk-self-avoiding-walk and self-avoiding-walk-neighbor-avoiding-walk crossovers. These findings suggest that negative energetic elasticity is a fundamental and universal property of polymer networks and chains.

cond-mat.soft↗

arXiv2025

Analytical Expression for Fracture Profile in Viscoelastic Crack Propagation

We derive an analytical expression for the strain field during steady-state crack propagation in viscoelastic solids described by the standard linear solid (Zener) model. This expression reveals three regions in the fracture profile and in the strain field ahead of the crack tip, each distinguished by power-law exponents that evolve with distance from the crack tip. These features explain the experimentally observed crack-tip sharpening in rubbers and gels as the crack-propagation velocity increases, often associated with catastrophic failure triggered by a velocity jump. Furthermore, we establish de Gennes' viscoelastic trumpet on a continuum-mechanical foundation, previously based only on a scaling argument.

cond-mat.soft↗

arXiv2024

Polymer Network Diffusion in Charged Gels

The swelling kinetics of charged polymer gels reflect the complex competition among elastic, mixing, and ionic contributions. Here, we used dynamic light scattering to investigate the collective diffusion coefficient of model gels, whose polymer network structure was controlled so that the three contributions were comparable. We demonstrate that the collective diffusion coefficient stems from the sum of elastic, mixing, and ionic contributions, without evident cross-correlations. The significant ionic contribution conforms to the Donnan equilibrium, which explains equilibrium electrical potential gradients in biological systems.

cond-mat.soft↗

arXiv2023

Phantom-Chain Simulations for the Effect of Node Functionality on the Fracture of Star-Polymer Networks

The influence of node functionality (f) on the fracture of polymer networks remains unclear. While many studies have focused on multi-functional nodes with f>4, recent research suggests that networks with f=3 exhibit superior fracture properties compared to those with f=4. To clarify this discrepancy, we conducted phantom chain simulations for star-polymer networks varying f between 3 and 8. Our simulations utilized equimolar binary mixtures of star branch prepolymers with a uniform arm length. We employed a Brownian dynamics scheme to equilibrate sols and induce gelation through end-linking reactions. We prevented the formation of odd-order loops owing to the binary reaction and second-order loops algorithmically. We stored network structures at various conversion ratios (ϕ_c) and minimized energy to reduce computation costs induced by structural relaxation. We subjected the networks to stretching until fracture to determine stress and strain at break and work for fracture, ε_b, σ_b, and W_b. These fracture characteristics are highly dependent on ϕ_c for networks with small f but relatively insensitive for those with large f. Thus, the networks with small f exhibit greater fracture properties than those with large f at high ϕ_c, whereas the opposite relationship occurs at low ϕ_c. We analyzed ε_b, σ_b, and W_b concerning the cycle rank ξ and the broken strand fraction ϕ_bb. We found ε_b, σ_b/ϕ_bb, and W_b/ϕ_bb monotonically decrease with increasing ξ, and the data for various f and ϕ_c superpose with each other to draw master curves. These results imply that the mechanical superiority of the networks with small f comes from their smaller ξ that gives higher ε_b, σ_b/ϕ_bb, and W_b/ϕ_bb than the networks with large f.

cond-mat.soft↗

arXiv2023

Solvent-Induced Negative Energetic Elasticity in a Lattice Polymer Chain

The negative internal energetic contribution to the elastic modulus (negative energetic elasticity) has been recently observed in polymer gels. This finding challenges the conventional notion that the elastic moduli of rubberlike materials are determined mainly by entropic elasticity. However, the microscopic origin of negative energetic elasticity has not yet been clarified. Here, we consider the $n$-step interacting self-avoiding walk on a cubic lattice as a model of a single polymer chain (a subchain of a network in a polymer gel) in a solvent. We theoretically demonstrate the emergence of negative energetic elasticity based on an exact enumeration up to $n=20$ and analytic expressions for arbitrary $n$ in special cases. Furthermore, we demonstrate that the negative energetic elasticity of this model originates from the attractive polymer--solvent interaction, which locally stiffens the chain and conversely softens the stiffness of the entire chain. This model qualitatively reproduces the temperature dependence of negative energetic elasticity observed in the polymer-gel experiments, indicating that the analysis of a single chain can explain the properties of negative energetic elasticity in polymer gels.

cond-mat.soft↗

arXiv2023

Universality of Osmotic Equation of State in Star Polymer Solutions

We experimentally measure the osmotic pressures of linear polymers and three-, four-, and eight-arm star polymers in a good solvent via membrane osmometry. These results reveal that the osmotic equations of state in the star polymer solutions are universally described by the same scaling function that describes linear polymer solutions. This universality is achieved by canceling increasing overlap concentrations and decreasing osmotic pressure, owing to the increased arm number. We further clarify the molar mass and arm number dependencies of the gyration radius and interpenetration factor, ensuring universality in star polymer solutions.

cond-mat.soft↗

arXiv2022

Semidilute Principle for Gels

Polymer gels such as jellies and soft contact lenses are soft solids consisting of three-dimensional polymer networks swollen with a large amount of solvent. For approximately 80 years, the swelling of polymer gels has been described using the Flory--Huggins mean-field theory. However, this theory is problematic when applied to polymer gels with large solvent contents owing to the significant fluctuations in polymer concentration. In this study, we experimentally demonstrate the superiority of the semidilute scaling law over the mean-field theory for predicting the swelling of polymer gels. Using the semidilute scaling law, we experimentally determine the universal critical exponent $ν$ of the self-avoiding walk via swelling experiments on polymer gels. The experimentally obtained value $ν\simeq 0.589$ is consistent with the previously reported value of $ν\simeq 0.588$, which was obtained by precise numerical calculations. Furthermore, we theoretically derive and experimentally demonstrate a scaling law that governs the equilibrium concentrations. This scaling law contradicts the predictions made by de Gennes' $c^{*}$ theorem. A major deficiency of the $c^*$ theorem is that the network elasticity, which depends on the as-prepared state, is neglected. These findings reveal that the semidilute scaling law is a fundamental principle for accurately predicting and controlling the equilibrium swelling of polymer gels.

cond-mat.soft↗

arXiv2022

Tri-branched gels: Rubbery materials with the lowest branching factor approach the ideal elastic limit

Unlike hard materials such as metals and ceramics, rubbery materials can endure large deformations due to the large conformational degree of freedom of the crosslinked three-dimensional polymer network. However, the effect of the branching factor of the network on the ultimate mechanical properties of rubbery materials has not yet been clarified. This study shows that tri-branching, which entails the lowest branching factor, results in a large elastic deformation near the theoretical upper bound. This ideal elastic limit is realized by reversible strain-induced crystallization, providing on-demand reinforcement. The findings indicate that the polymer chain is highly orientated along the stretching axis, whereat enhanced reversible strain-induced crystallization is observed in the tri-branched and not in the tetra-branched network. A mathematical theory of structural rigidity is used to explain the difference in the chain orientation. Although tetra-branched polymers have been preferred since the development of vulcanization, these findings highlighting the merits of tri-branching will prompt a paradigm shift in the development of rubbery materials.

cond-mat.mtrl-sci↗

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

Temperature Dependence of Polymer Network Diffusion

The swelling dynamics of polymer gels are characterized by the (collective) diffusion coefficient $D$ of the polymer network. Here, we measure the temperature dependence of $D$ of polymer gels with controlled homogeneous network structures using dynamic light scattering. An evaluation of the diffusion coefficient at the gelation point $D_{\mathrm{gel}}$ and the increase therein as the gelation proceeds $ΔD\equiv D-D_{\mathrm{gel}}$ indicates that $ΔD$ is a linear function of the absolute temperature with a significantly large negative constant term. This feature is formally identical to the recently discovered "negative energy elasticity" [Y. Yoshikawa et al., Phys. Rev. X 11, 011045 (2021) (arXiv:1912.13191)], demonstrating a nontrivial similarity between the statics and dynamics of polymer networks.

cond-mat.soft↗

arXiv2021

Linear elasticity of polymer gels in terms of negative energy elasticity

We recently found that the energy contribution to the linear elasticity of polymer gels in the as-prepared state can be a significant negative value; the shear modulus is not proportional to the absolute temperature [Y. Yoshikawa et al., Phys. Rev. X 11, 011045 (2021) (arXiv:1912.13191)]. Our finding challenges the conventional notion that the polymer-gel elasticity is mainly determined by the entropy contribution. Existing molecular models of classical rubber elasticity theories, including the affine, phantom, and junction affine network models, cannot be used to estimate the structural parameters of polymer gels. In this focus review, we summarize the experimental studies on the linear elasticity of polymer gels in the as-prepared state using tetra-arm poly(ethylene glycol) (PEG) hydrogels with a homogenous polymer network. We also provide a unified formula for the linear elasticity of polymer gels with various network topologies and densities. Using the unified formula, we reconcile the past experimental results that seemed to be inconsistent with each other. Finally, we mention that there are still fundamental unresolved problems involving the linear elasticity of polymer gels.

cond-mat.soft↗

arXiv2021

Negative energy elasticity in a rubberlike gel

Rubber elasticity is the archetype of the entropic force emerging from the second law of thermodynamics; numerous experimental and theoretical studies on natural and synthetic rubbers have shown that the elasticity originates mostly from entropy change with deformation. Similarly, in polymer gels containing a large amount of solvent, it has also been postulated that the shear modulus (the modulus of rigidity) $G$, which is a kind of modulus of elasticity, is approximately equivalent to the entropy contribution $G_S$, but this has yet to be verified experimentally. In this study, we measure the temperature dependence of the shear modulus $G$ in a rubberlike (hyperelastic) polymer gel whose polymer volume fraction is at most 0.1. As a result, we find that the energy contribution $G_E=G-G_S$ can be a significant negative value, reaching up to double the shear modulus $G$ (i.e., $\left|G_E\right| \simeq 2G$), although the shear modulus of stable materials is generally bound to be positive. We further argue that the energy contribution $G_E$ is governed by a vanishing temperature that is a universal function of the normalized polymer concentration, and $G_E$ vanishes when the solvent is removed. Our findings highlight the essential difference between rubber elasticity and gel elasticity (which were previously thought to be the same) and push the established field of gel elasticity into a new direction.

cond-mat.soft↗

arXiv2020

Universal equation of state describes osmotic pressure throughout gelation process

The equation of state of the osmotic pressure for linear-polymer solutions in good solvents is universally described by a scaling function. We experimentally measure the osmotic pressure of the gelation process via osmotic deswelling. We find that the same scaling function for linear-polymer solutions also describes the osmotic pressure throughout the gelation process involving both the sol and gel states. Furthermore, we reveal that the osmotic pressure of polymer gels is universally governed by the semidilute scaling law of linear-polymer solutions.

cond-mat.stat-mech↗

arXiv2019

Monopole Dominance of Confinement in SU(3) Lattice QCD

To check the dual superconductor picture for the quark-confinement mechanism, we evaluate monopole dominance as well as Abelian dominance of quark confinement for both quark-antiquark and three-quark systems in SU(3) quenched lattice QCD in the maximally Abelian (MA) gauge. First, we examine Abelian dominance for the static $Q\bar Q$ system in lattice QCD with various spacing $a$ at $β$=5.8-6.4 and various size $L^3$x$L_t$. For large physical-volume lattices with $La \ge$ 2fm, we find perfect Abelian dominance of the string tension for the $Q\bar Q$ systems: $σ_{Abel} \simeq σ$. Second, we accurately measure the static 3Q potential for more than 300 different patterns of 3Q systems with 1000-2000 gauge configurations using two large physical-volume lattices: ($β$,$L^3$x$L_t$)=(5.8,$16^3$x32) and (6.0,$20^3$x32). For all the distances, the static 3Q potential is found to be well described by the Y-Ansatz: two-body Coulomb term plus three-body Y-type linear term $σL_{min}$, where $L_{min}$ is the minimum flux-tube length connecting the three quarks. We find perfect Abelian dominance of the string tension also for the 3Q systems: $σ^{Abel}_{3Q}\simeq σ_{3Q} \simeq σ$. Finally, we accurately investigate monopole dominance in SU(3) lattice QCD at $β$=5.8 on $16^3$x32 with 2,000 gauge configurations. Abelian-projected QCD in the MA gauge has not only the color-electric current $j^μ$ but also the color-magnetic monopole current $k^μ$, which topologically appears. By the Hodge decomposition, the Abelian-projected QCD system can be divided into the monopole part ($k_μ\ne 0$, $j_μ=0$) and the photon part ($j_μ\ne 0$, $k_μ=0$). We find monopole dominance of the string tension for $Q\bar Q$ and 3Q systems: $σ_{Mo}\simeq 0.92σ$. While the photon part has almost no confining force, the monopole part almost keeps the confining force.

hep-lat↗

arXiv2017

Exactly solvable model for a velocity jump observed in crack propagation in viscoelastic solids

Needs to impart appropriate elasticity and high toughness to viscoelastic polymer materials are ubiquitous in industries such as concerning automobiles and medical devices. One of the major problems to overcome for toughening is catastrophic failure linked to a velocity jump, i.e., a sharp transition in the velocity of crack propagation occurred in a narrow range of the applied load. However, its physical origin has remained an enigma despite previous studies over 35 years. Here, we propose an exactly solvable model that exhibits the velocity jump incorporating linear viscoelasticity with a cutoff length for a continuum description. With the exact solution, we elucidate the physical origin of the velocity jump: it emerges from a dynamic glass transition in the vicinity of the propagating crack tip. We further quantify the velocity jump together with slow- and fast-velocity regimes of crack propagation, which would stimulate the development of tough polymer materials.

cond-mat.soft↗

arXiv2015

Perfect Abelian dominance of confinement in quark-antiquark potential in SU(3) lattice QCD

In the context of the dual superconductor picture for the confinement mechanism, we study maximally Abelian (MA) projection of quark confinement in SU(3) quenched lattice QCD with $32^4$ at $β$=6.4 (i.e., $a \simeq$ 0.058 fm). We investigate the static quark-antiquark potential $V(r)$, its Abelian part $V_{\rm Abel}(r)$ and its off-diagonal part $V_{\rm off}(r)$, respectively, from the on-axis lattice data. As a remarkable fact, we find almost perfect Abelian dominance for quark confinement, i.e., $σ_{\rm Abel} \simeq σ$ for the string tension, on the fine and large-volume lattice. We find also a nontrivial summation relation of $V(r) \simeq V_{\rm Abel}(r) + V_{\rm off}(r)$.

hep-lat↗

arXiv2015

The three-quark potential and perfect Abelian dominance in SU(3) lattice QCD

We study the static three-quark (3Q) potential for more than 300 different patterns of 3Q systems with high statistics, i.e., 1000-2000 gauge configurations, in SU(3) lattice QCD at the quenched level. For all the distances, the 3Q potential is found to be well described by the Y-ansatz, i.e., one-gluon-exchange (OGE) Coulomb plus Y-type linear potential. Also, we investigate Abelian projection of quark confinement in the context of the dual superconductor picture proposed by Yoichiro~Nambu~{\it et al.} in SU(3) lattice QCD. Remarkably, quark confinement forces in both Q$\bar{\rm Q}$ and 3Q systems can be described only with Abelian variables in the maximally Abelian gauge, i.e., $σ_{\rm Q \bar Q} \simeq σ_{\rm Q \bar Q}^{\rm Abel} \simeq σ_{\rm 3Q} \simeq σ_{\rm 3Q}^{\rm Abel}$, which we call ``perfect Abelian dominance'' of quark confinement.

hep-lat↗