arXiv subjects

Valeriy V. Ginzburg

Publications and source records attributed to Valeriy V. Ginzburg.

At least 19 recordsLinked to original sources

arXiv2026

The Trachenko-Zaccone equation: nonlinear relaxation from glasses to complex systems

The Trachenko-Zaccone equation provides a compact nonlinear dynamical framework for describing non-Debye relaxation in disordered condensed matter. Originally developed to rationalize stretched- and compressed-exponential relaxation in liquids and glasses from the dynamics of interacting local relaxation events, the same equation has subsequently appeared in broader contexts, including polymer relaxation and nonlinear models of global population dynamics. This review retraces the conceptual development of the equation, with particular emphasis on its physical origin in Kostya Trachenko's feed-forward interaction mechanism, its mathematical structure, and its possible generalizations. We also include personal recollections of the work with Kostya Trachenko at Queen Mary University of London in August 2019, during which the equation emerged in essentially its present form. After reviewing applications to stress relaxation, glassy materials, polymer relaxation and population dynamics, we discuss future directions including time-dependent feedback parameters, coupled order parameters, heterogeneous and spatially resolved formulations, flux terms, network versions and stochastic extensions. The central theme of the review is that the Trachenko-Zaccone equation should be viewed not only as a model of glassy relaxation, but as a general nonlinear feedback equation with potential applications across complex systems.

cond-mat.dis-nn↗

arXiv2026

Modeling the Fatigue Behavior of Amorphous Polymers

Prediction of material durability is both very important and very difficult. In many cases, material durability is measured by subjecting a sample to repeating oscillatory cycles (in shear or tension-compression) until it fails in either ductile or brittle fashion. Typically, the stress amplitude is denoted S, and the number of cycles N, so the resulting dependence is known as the SN-curve. For many materials, SN curve has been shown to obey the empirical Basquin's law, N = AS^(-m), where the prefactor A was a function of the temperature, load frequency, and sample history, and the power law m was a real number, usually between 3 and 12. Here, we derive the Basquin's law using a linearized version of the Long's plasticity model and demonstrate that within this framework, m = 3. We also derive the expression for the prefactor A. Finally, we show that our theory successfully describes experimental data for three amorphous polymers, PS, PMMA, and PVC.

cond-mat.mtrl-sci↗

arXiv2026

Microscopic constitutive theory of stress overshoot, yielding, and strain hardening in amorphous materials

We develop a microscopic constitutive theory for the nonlinear deformation of metallic and polymer glasses based on nonaffine elasticity coupled to irreversible many-body relaxation. The theory predicts the full stress--strain response, from linear elasticity through stress overshoot and yielding to steady plastic flow. We show that stress overshoot originates from the competition between a nonaffine elastic instability induced by strain-driven loss of mechanical connectivity at the atomic/molecular level, and viscous dissipation associated with structural relaxation. For polymer glasses, finite chain extensibility naturally accounts for strain hardening at large deformation. The stretched-exponential relaxation exponent is obtained independently from stress or modulus relaxation measurements and provides the primary dynamical input to the theory. Using a small set of physically meaningful parameters, the model quantitatively reproduces experimental stress--strain curves for metallic glasses, polycarbonate, PMMA, and epoxy resins over a broad range of strain rates. These results establish a unified microscopic framework linking relaxation dynamics, yielding, plastic flow, and strain hardening in amorphous solids.

cond-mat.soft↗

arXiv2026

Predicting the Brittle-to-Ductile Transition in Amorphous Polymers

Brittle-ductile transition (BDT) is an important characteristic of amorphous (and semicrystalline) polymers. For a given strain rate, at temperatures above BDT, the polymers exhibit strain softening followed by yield and strain hardening, while at temperatures below BDT, the same materials exhibit brittle failure at relatively low strains. Surprisingly, today there is no simple model describing BDT as a function of polymer chemistry, sample history, deformation type, and strain rate. Experimental data suggest that BDT is often, though not always, associated with the beta-transition. We formulate a simple scalar model to describe the visco-elasto-plastic shear stress-strain curves as functions of temperature and strain rate. We also show that within this model, there is always an upper bound on the strain rate where the material can have a uniform viscoplastic flow; this upper bound is taken to represent the BDT. We stipulate that this upper bound is inversely proportional to the Johari-Goldstein beta-relaxation time. Using our "general" Sanchez-Lacombe "two-state, two-(time)scale" (SL-TS2) model, we compute the BDT for three polymers (polystyrene, poly(methylmethacrylate), and poly(vinylchloride)) and found a good agreement with experimental data.

cond-mat.soft↗

arXiv2026

Modeling the Slow Arrhenius Process (SAP) in Polymers

Amorphous glass-forming polymers exhibit multiple relaxation processes, including the structural α-relaxation associated with the glass transition and faster secondary relaxations that typically follow Arrhenius behavior. Recently, a distinct slow Arrhenius process (SAP) has been observed at frequencies well below the α-process. Although Arrhenian in its temperature dependence, the SAP involves much longer relaxation times and its microscopic origin remains unclear. Here, we extend the two-state, two-timescale (TS2) theory to describe both the α-relaxation and the SAP within a unified framework. We propose that the SAP represents the high-temperature limit of an α-like process in a coarse-grained fluid of dynamically correlated clusters. With renormalized interaction energies and coordination parameters, the same model quantitatively reproduces both α and SAP data across multiple polymers without additional adjustable parameters and explains the observed Meyer-Neldel compensation behavior. The theory further predicts that the SAP should deviate from Arrhenius behavior at sufficiently low temperatures, transitioning to Vogel-Fulcher-Tammann-Hesse-like dynamics, thereby offering a physically transparent interpretation of cluster-scale relaxation in glass-forming polymers.

cond-mat.soft↗

arXiv2025

Dual Cross-Linked Hydrogels: Linear Rheology and Fractional Calculus Modeling

Hydrogels are increasingly recognized as a versatile platform for applications spanning from tissue engineering to soft robotics or flexible electronics. Recent efforts have focused on enhancing and tailoring their mechanical performance to meet application-specific demands. However, the intricate viscoelastic response of hydrogels remains challenging to capture using conventional phenomenological models. In this study, we prepared a series of tough dual crosslinked hydrogels -- poly(methacrylamide-co-acrylic acid)-Fe3+ and systematically tuned their mechanical properties by leveraging the salting-out effect. The viscoelastic behavior of the hydrogels was characterized under shear deformations, and a four-parameter Fractional Maxwell Model (FMM) was constructed to quantitatively describe oscillatory shear, creep, and stress relaxation responses. The influence of salt concentration on each FMM parameter was analyzed and correlated with bulk mechanical performance. This framework provides a first step toward capturing the complex viscoelastic nature of the advanced hydrogels and lays the foundation for developing more comprehensive nonlinear constitutive models.

cond-mat.soft↗

arXiv2025

General Two-Parameter Model of Alpha-Relaxation in Glasses

In the vicinity of the glass transition, the characteristic relaxation time (e.g., the alpha-relaxation time in dielectric spectroscopy) of a glass-former exhibits a strongly super-Arrhenius temperature dependence, as compared to the classical Arrhenius behavior at high temperatures. A comprehensive description of both regions thus requires five parameters. Here, we demonstrate that many glass-formers exhibit a universal scaling, with only two material-specific parameters setting the timescale and the temperature scale; the other three being universal constants. Furthermore, we show that the master curve can be described by the recently developed two-state, two-(time) scale (TS2) theory (Soft Matter 2020, 16, 810) and regress the universal TS2 parameters. We also show the connection between the TS2 model and the Hall-Wolynes elastic relaxation theory.

cond-mat.dis-nn↗

arXiv2025

Universality of Dynamic and Thermodynamic Behavior of Polymers near their Glass Transition

Describing the dynamics and thermodynamics of amorphous materials near the glass transition is a major challenge in soft-matter physics and polymer engineering. Here, we show that the dependence of the dielectric alpha-relaxation time on temperature can be captured by a universal equation with only two independent parameters, Tg and fragility, m. This is similar in spirit to the ideas of van Krevelen and Bicerano, and can be related to the Boyer-Spencer and Simha-Boyer rules for the volumetric thermal expansion via a modified free-volume approach such as Sanchez-Lacombe "Two-state, two-(time)scale" (SL-TS2) theory. The model is compared to experimental data for nine amorphous polymers with varying values of Tg and m, and a good qualitative and quantitative agreement is found. We also derive the relationship between the experimental and computational (high-cooling-rate) Tg, and compare our model prediction for the Tg-shift between the two with the simulation results of Afzal et al., finding a good qualitative and semi-quantitative agreement. The results could serve as a guidance for future simulation studies.

cond-mat.soft↗

arXiv2025

New Insights into the Dependence of Glass Transition Temperature and Dynamic Fragility on Molecular Weight in Oligomers and Polymers

In an earlier preprint (V. V. Ginzburg, O. V. Gendelman, R. Casalini, and A. Zaccone, arxiv:2409.17291), we demonstrated that the dynamic (relaxation time) and volume equations of state for many amorphous polymers are near-universal -- each material is characterized by two governing parameters -- the glass transition temperature, T_{g}, and the elementary relaxation time, /tau_{el}. The dynamic fragility, m, is uniquely related to /tau_{el}. The earlier analysis was based on the data for high polymers (degree of polymerization, N > 200, and molecular weight, Mw > 20,000 g/mol). Here, we investigate the dependence of T_{g} and /tau_{el} on N (or, equivalently, on the molecular weight, M). We consider the dielectric spectroscopy data for homologous series of four polymers: polystyrene (PS), poly-(2-vinylpyridine) (P2VP), poly(dimethylsiloxane) (PDMS), and polybutadiene (PB). It is shown that the relaxation time curves for various oligomers can be successfully collapsed onto the same master curve as the high polymers. The glass transition temperature and the dynamic fragility are found to be linear functions of 1/M, in agreement with the Fox-Flory equation. The scaling results are interpreted based on the SL-TS2 theory, ensuring that the model description is consistent with the Boyer rules for the coefficients of thermal expansion above and below T_{g}, as well as the thermodynamical scaling for the pressure dependence of the relaxation time.

cond-mat.soft↗

arXiv2024

Modeling the Dielectric Relaxation in Semicrystalline Polymers -- Understanding the Role of the Interphase between the Amorphous and Crystalline Domains

Semicrystalline polymers (SCP) represent important class of materials used in many applications from packaging to transportation to electronics to pharmaceuticals. Understanding the structure and dynamics of the crystalline and amorphous fractions within SCP is an important challenge for both experimentalists and theoreticians. Recently, Cheng et al. (S. Cheng et al., J. Chem. Phys. 160, 114904 (2024)) utilized Broadband Dielectric Spectroscopy (BDS) to explore the relaxation time profiles within the amorphous region of a semi-crystalline poly(L-lactic acid) (PLLA) with ordered alternative stacking of crystalline/amorphous phases. Here, we build on those initial results and model the relaxation time distribution using the combination of the Doolittle free volume theory (FVT) and the compressible Self-Consistent Field Theory (cSCFT). We show that the new modeling framework successfully captures the temperature and position dependence of the local relaxation time of the semicrystalline PLLA above the glass transition temperature of the amorphous region. Finally, we derive a new empirical equation for the relaxation time profiles in amorphous regions of SCPs.

cond-mat.soft↗

arXiv2024

Stochastic Generalized-Order Constitutive Modeling of Viscoelastic Spectra of Polyurea-Graphene Nanocomposites

Polyurea (PUa) elastomers are extensively used in a wide range of applications spanning from biomedical to defense fields due to their enabling mechanical properties. These materials can be further reinforced through the incorporation of nanoparticles to form nanocomposites. This study focuses on an IPDI-based PUa matrix with exfoliated graphene nanoplatelet (xGnP) fillers. We propose a generalized constitutive model by integrating one Fractional Maxwell Model (FMM) and one Fractional Maxwell Gel (FMG) branch in a parallel configuration via introducing a new dimensionless number to bridge between these branches physically and mathematically. Through systematic local-to-global sensitivity analyses, we investigate the behavior of these nanocomposites to facilitate simulation, design, and performance prediction. Consistently, the constructed models share the same most/least influential model parameters. $α_1$ and $E_{c_1}$, the power exponent and the characteristic modulus of the first branch, are found to be the most influential model parameters, while $τ_{c_2}$ and $τ_{c_1}$, the characteristic time-scales of each branch, are recognized as the least influential model parameters. The proposed PU nanocomposite constitutive laws can now make an impact to the design and optimization of coating and shock-absorbing coatings in a range of applications.

math.NA↗

arXiv2023

Unified physical framework for stretched-exponential, compressed-exponential, and logarithmic relaxation phenomena in glassy polymers

We develop a simple yet comprehensive nonlinear model to describe relaxation phenomena in amorphous glass-formers near the glass transition temperature. The model is based on the two-state, two-(time)scale (TS2) framework, and describes the isothermal relaxation of specific volume, enthalpy, or shear stress via a simple first-order nonlinear differential equation (the Trachenko-Zaccone [TZ] equation) for local cooperative events. These nonlinear dynamics of cooperatively rearranging regions (CRR) naturally arise from the TS2 framework. We demonstrate that the solutions of the TZ equation comprehensively encompass the Debye exponential relaxation, the Kohlrausch-Williams-Watts (KWW) stretched and compressed relaxations, and the Guiu-Pratt logarithmic relaxation. Furthermore, for the case of stress relaxation modeling, our model recovers, as one of its limits, the Eyring law for plastic flow, where the Eyring activation volume is related to thermodynamic parameters of the material. Using the example of polystyrene (PS), we demonstrate how our model successfully describes the Kovacs "asymmetry of approach" specific volume and enthalpy experiments, as well as the stress relaxation. Other potential applications of the model, including the dielectric relaxation, are also discussed. The presented approach disentangles the physical origins of different relaxation laws within a single general framework based on the underlying physics.

cond-mat.soft↗

arXiv2023

Polyurea-Graphene Nanocomposites -- the Influence of Hard-Segment Content and Nanoparticle Loading on Mechanical Properties

Polyurethane and polyurea-based adhesives are widely used in various applications, from automotive to electronics to medical. The adhesive performance depends strongly on its composition, and developing the formulation-structure-property relationship is crucial to making better products. Here, we investigate the dependence of the linear viscoelastic properties of polyurea nanocomposites, with IPDI-based polyurea (PUa) matrix and exfoliated graphene nanoplatelet (xGnP) fillers, on the hard segment weight fraction (HSWF) and the xGnP loading. We characterize the material using scanning electron microscopy (SEM) and dynamical mechanical analysis (DMA). It is found that changing HSWF leads to a significant variation in the stiffness of the material, from about 10 MPa for the 20% HSWF to about 100 MPa for the 30% HSWF to about 250 MPa for the 40% HSWF polymer (as measured by the tensile storage modulus at room temperature). The effect of the xGNP loading is significantly more limited and is generally within experimental error, except for the 20% HSWF material where the xGNP addition leads to about 80% increase in stiffness. To correctly interpret the DMA results, we developed a new physics-based rheological model for the description of the storage and loss moduli. The model is based on the fractional calculus approach and successfully describes the material rheology in a broad range of temperatures (-70°C to +70°C) and frequencies (0.1 to 100 s-1), using only six physically meaningful fitting parameters for each material. The results provide guidance for the development of nanocomposite PUa-based materials.

cond-mat.mtrl-sci↗

arXiv2022

Combined Description of Pressure-Volume-Temperature and Dielectric Relaxation of Several Polymeric and Low-Molecular-Weight Organic Glass-Formers using 'SL-TS2' Mean-Field Approach

We apply our recently-developed mean-field 'SL-TS2' (two-state Sanchez-Lacombe) model to simultaneously describe dielectric alpha-relaxation time and pressure-volume-temperature (PVT) data in four polymers (polystyrene, poly(methylmethacrylate), poly(vinyl acetate) and poly(cyclohexane methyl acrylate)) and four organic molecular glass formers (ortho-terphenyl, glycerol, PCB-62, and PDE). Previously, it has been shown that for all eight materials, the Casalini-Roland thermodynamical scaling, /tau_{/alpha} = f(TV_{sp}^{/gamma}) (where T is temperature and V_{sp} is specific volume), (Casalini, R.; Roland, C. M. Phys. Rev. Lett. 2014, 113 (8), 85701), is satisfied. It has also been previously shown that the same scaling emerges naturally (for sufficiently low pressures) within the 'SL-TS2' framework (Ginzburg, V. V. Soft Matter 2021, 17, 9094). Here, we fit the ambient pressure curves for the relaxation time and the specific volume as functions of temperature for the eight materials and observe a good agreement between theory and experiment. We then use the Casalini-Roland scaling to convert those results into 'master curves', thus enabling predictions of relaxation times and specific volumes at elevated pressures. The proposed approach can be used to describe other glass-forming materials, both low-molecular-weight and polymeric.

cond-mat.soft↗

arXiv2022

Modeling the Dynamics of the Coronavirus SARS-CoV-2 Pandemic using Modified SIR Model with the 'Damped-Oscillator' Dynamics of the Effective Reproduction Number

The COVID-19 pandemic has been a great catastrophe that upended human lives and caused millions of deaths all over the world. The rapid spread of the virus, with its early-stage exponential growth and subsequent 'waves', caught many medical professionals and decision-makers unprepared. Even though epidemiological models have been known for almost a century (since the 'Spanish Influenza' pandemic of 1918-20), the real-life spread of the SARS-CoV-2 virus often confounded the modelers. While the general framework of epidemiological models like SEIR (susceptible-exposed-infected-recovered) or SIR (susceptible-exposed-infected) was not in question, the behavior of model parameters turned out to be unpredictable and complicated. In particular, while the 'basic' reproduction number, R0, can be considered a constant (for the original SARS-CoV-2 virus, prior to the emergence of variants, R0 is between 2.5 and 3.0), the 'effective' reproduction number, R(t), was a complex function of time, influenced by human behavior in response to the pandemic (e.g., masking, lockdowns, transition to remote work, etc.) To better understand these phenomena, we model the first year of the pandemic (between February 2020 and February 2021) for a number of localities (fifty US states, as well as several countries) using a simple SIR model. We show that the evolution of the pandemic can be described quite successfully by assuming that R(t) behaves in a 'viscoelastic' manner, as a sum of two or three 'damped oscillators' with different natural frequencies and damping coefficients. These oscillators likely correspond to different sub-populations having different reactions to proposed mitigation measures. The proposed approach can offer future data modelers new ways to fit the reproduction number evolution with time (as compared to the purely data-driven approaches most prevalent today).

q-bio.PE↗

arXiv1999

Simulation of Hard Particles in a Phase-Separating Binary Mixture

We simulate the motion of spherical particles in a phase-separating binary mixture. By combining cell dynamical equations with Langevin dynamics for particles, we show that the addition of hard particles significantly changes both the speed and the morphology of the phase separation. At the late stage of the spinodal decomposition process, particles significantly slow down the domain growth, in qualitative agreement with earlier experimental data.

cond-mat.stat-mech↗

arXiv1996

Self-Consistent Model of Annihilation-Diffusion Reaction with Long-Range Interactions

We introduce coarse-grained hydrodynamic equations of motion for diffusion-annihilation system with a power-law long-range interaction. By taking into account fluctuations of the conserved order parameter - charge density - we derive an analytically solvable approximation for the nonconserved order parameter - total particle density. Asymptotic solutions are obtained for the case of random Gaussian initial conditions and for system dimensionality $d \geq 2$. Large-t, intermediate-t and small-t asymptotics were calculated and compared with existing scaling theories, exact results and simulation data.

cond-mat↗

arXiv1996

Scaling Model of Annihilation-Diffusion Kinetics for Charged Particles with Long-Range Interactions

We propose the general scaling model for the diffusio n-annihilation reaction $A_{+} + A_{-} \longrightarrow \emptyset$ with long-range power-law i nteractions. The presented scaling arguments lead to the finding of three different regimes, dep ending on the space dimensionality d and the long-range force power e xponent n. The obtained kinetic phase diagram agrees well with existing simulation data and approximate theoretical results.

cond-mat↗