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Alessio Zaccone

Publications and source records attributed to Alessio Zaccone.

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

Delayed Arm Retraction Controls the Nonlinear Oscillatory Response of Long-Chain-Branched Polymer Melts

Long-chain branching profoundly modifies the nonlinear oscillatory response of entangled polymer melts by introducing arm-retraction pathways absent in linear polymers. We present a molecular tube theory that explains the characteristic maximum of the Nonlinearity Index (NLI) observed experimentally in long-chain-branched polymers. The theory extends the recently developed nonlinear tube-orientation description of linear polymers by incorporating branch-point force transmission and delayed arm retraction. The backbone initially develops nonlinear orientation as in the corresponding linear polymer, whereas long-arm retraction subsequently relaxes the stored branch-point tension and progressively erases backbone orientational memory. This competition produces a characteristic NLI maximum followed by a post-peak decay. The theory predicts two distinct nonlinear regimes corresponding to sparse and dense long-chain branching and introduces an architecture parameter governing the height and width of the nonlinear peak. The resulting framework provides a molecular interpretation of nonlinear Fourier rheology and directly links the nonlinear harmonic response to polymer architecture.

cond-mat.soft↗
arXiv2026

Electrical transport in ultra-thin films: from Fuchs-Sondheimer to quantum-confinement

Ultra-thin films are fundamental components of modern nanoelectronics, where reducing thickness to the few-nanometer scale leads to a dramatic increase in electrical resistivity. For decades, this behavior has been interpreted in terms of classical size effects, primarily surface scattering within the Fuchs--Sondheimer theory and grain-boundary scattering in the Mayadas--Shatzkes model. While these approaches successfully describe transport when the film thickness is comparable to the electronic mean free path, growing experimental evidence indicates that they become insufficient under extreme confinement. This review discusses the crossover from classical scattering to a quantum-confinement regime in which the electronic states available for transport are fundamentally restructured by finite size. We review the recently proposed reciprocal-space confinement theory, which predicts an exponential increase of resistivity with decreasing thickness at the nanoscale, and discuss how it can be combined with classical surface-scattering models to provide a unified description of ultra-thin metallic and semiconducting films. Finally, we summarize recent experimental evidence supporting this picture and discuss its implications for future nanoelectronic devices, nanoscale interconnects, and quantum transport under extreme spatial confinement.

cond-mat.mes-hall↗
arXiv2026

Thermal rectification due to phonon confinement in nanoparticles

We demonstrate that thermal rectification can arise at the contact between two spherical nanoparticles of identical material but different size due to the geometric confinement of phonons. This confinement suppresses long-wavelength phonons differently in differently sized particles and creates a size-dependent gap in the phonon density of states. This gives rise to direction-dependent heat transport even in perfectly homogeneous materials. We develop an analytical model based on phonon confinement and phonon ray-tracing in the Casimir regime and derive expressions for heat fluxes and rectification efficiency as functions of particle sizes and temperatures. The model predicts measurable rectification efficiencies for nanoparticles with radii of a few tens of nanometers, reaching fraction of percent at room temperature and much larger values at low temperatures. The proposed mechanism provides a straightforward and scalable route to thermal rectification in granular nanomaterials without requiring material heterogeneity or strong nonlinearities.

cond-mat.mes-hall↗
arXiv2026

Thermal Rectification from Size-Dependent Phonon Confinement in Nanoparticle Assemblies

Thermal insulation remains an important technological challenge across the vast number of applications, from living quarters to quantum technology. Here, we exploit the size-dependent modification of the phonon density of states arising from phonon confinement in nanoparticles to fabricate a simple phonon rectifier. The smaller of the two connected nanoparticles imposes stronger phonon confinement leading to rectifying phonon transport. This concept is extended to the macroscale by constructing two overlapping layers of differently sized nanoparticles, thereby realizing a macroscopic phonon diode. Following the localized heat deposition by laser light, the temperature profiles across a phonon-diode were measured by infrared imaging. Although the rectifying strength is moderate, the abundance of optimization possibilities makes this method promising for ultra-low volume thermal insulation at both the nano- and macroscale

cond-mat.mtrl-sci↗
arXiv2026

The Physics of Topological Defects in Glasses

Topological defects play a central role in the mechanical behavior of crystalline materials, yet their relevance to amorphous solids has only recently begun to emerge. Over the last few years, theoretical, computational, and experimental studies have revealed the presence of well-defined topological invariants in vibrational eigenmodes, non-affine displacement fields, and deformation-induced vector fields of glasses. These defects have been shown to correlate strongly with soft spots, localized plastic rearrangements, yielding, and shear-band formation, suggesting a new perspective on the microscopic origins of plasticity in disordered materials. In this review, we provide a comprehensive overview of recent developments in the rapidly growing field of topological defects in glasses. We discuss the underlying theoretical concepts, including Burgers vectors, non-affine plasticity, vibrational modes, and topological invariants, and review recent numerical and experimental advances. Finally, we assess the current achievements, limitations, and open questions, and discuss future directions toward a unified topological description of plasticity and mechanical failure in amorphous solids.

cond-mat.dis-nn↗
arXiv2026

Constraint-Limited Tube Orientation of Entangled Polymers in Oscillatory Shear Deformation

We develop a molecularly motivated description of the nonlinear index (NLI) in oscillatory shear deformation of entangled polymers. The central assumption is that the shear component of the tube-orientation tensor cannot grow without bound. Convective constraint release (CCR), chain stretch, and tube dilation progressively reduce the number and lifetime of orientational constraints, but the maximum shear alignment of a tube segment is geometrically limited by $S_{xy}\leq 1/2$. This motivates a constraint-limited orientation closure in which the NLI first grows approximately with strain amplitude and then approaches the limiting value $\mathrm{NLI}_{\max}=3$ asymptotically rather than through an artificial cutoff. The same framework yields a molecular expression for the characteristic half-saturation strain $\gamma_s$, defined by $\mathrm{NLI}(\gamma_s)=3/2$, in terms of the entanglement number, oscillation frequency, and a critical number of remaining orientational constraints. We further derive architecture-dependent expressions for the nonlinear onset strain $\gamma_c$ for linear, sparsely long-chain-branched, and more regularly branched polymers. The resulting framework provides a compact bridge between Fourier harmonic analysis, CCR-based tube dynamics, and the progressive loss of orientational memory in highly deformed entangled polymer liquids.

cond-mat.soft↗
arXiv2026

Theory of distribution skewness effect on polydisperse random close packing

We investigate the random close packing density, $\phi_\textrm{RCP}$, of polydisperse hard sphere systems using a theoretical framework based on the equilibrium model of crowding. We derive a closed-form solution for $\phi_\textrm{RCP}$ in terms of the moments of the diameter distribution, enabling an analytical exploration of the effects of polydispersity ($\delta$) and skewness ($S$) on packing density. For a binary mixture, it is possible to explore a broader range of dependence of $\phi_\textrm{RCP}$ on $\delta$ for a given $S$ or on $S$ for a given $\delta$. We show that the dependencies of $\phi_\textrm{RCP}$ on skewness for a variety of continuous distributions collapse onto a theoretical master curve obtained for the binary mixture case. By correcting the theory so that it obeys known exact limiting behaviours for extreme size asymmetry, our analytical predictions not only agree with previously obtained numerical results, but also predict previously unexplored regions of the $\phi_\textrm{RCP}$ parameter space.

cond-mat.soft↗
arXiv2026

Local Structural Signatures of Shear Bands in Metallic Glasses via Electron Nanodiffraction

Structural changes in a glass due to deformation are subtle and difficult to quantify using conventional imaging and diffraction techniques. Additionally, transmission electron microscopy (TEM) sample preparation using energetic ions often causes structural modifications that are challenging to detect in disordered materials. By preparing inverted cross-sectional transmission electron microscopy lamellae of shear bands formed during bending, and employing cryogenic ion polishing to minimize preparation artefacts, we preserve the intrinsic atomic structure. Using sensitive, new parameters derived from electron nano-diffraction, we directly probe the local nano-scale structure in the plastic zone beneath surface shear steps in metallic glasses. Mapping of local centrosymmetry and strain reveals nanoscale, stripe-like regions oriented at 45 degree to the applied strain where strain has localized. These regions exhibit a high density of local atomic structures that have transformed to configurations with reduced centrosymmetry and increased magnitudes of shear and normal strain. Our results demonstrate that plastic deformation in metallic glasses arises from coordinated nanoscale structural transformations, providing direct experimental insight into a long-standing problem.

cond-mat.mtrl-sci↗
arXiv2026

Microscopic Nonaffine Deformation Theory of LAOS in Polymers

We develop a molecularly motivated framework connecting large-amplitude oscillatory shear (LAOS) nonlinearities in entangled polymers to frequency-dependent nonaffine relaxation in disordered solids. The central idea is that the first harmonic in LAOS measures the residual phase-locked elastic response, whereas the higher harmonics encode the Fourier signature of strain-dependent nonaffine relaxation. The finite-amplitude modulus is interpreted as a local tangent stiffness of the evolving microstructure, in the spirit of elastoplastic and incremental nonaffine models. For entangled polymers, the analogue of the decreasing coordination number in cage-breaking theories of glass mechanics is identified not with the tube-orientation tensor itself, but with the fraction of surviving tube constraints. This distinction leads naturally to a crossover description controlled by a characteristic strain amplitude $\gamma_c$, rather than by universal fixed power-law exponents. The fitted value $N_{\max}\simeq1.72$ indicates that the present experimental data approach a strong but not fully saturated nonlinear state, remaining below the ideal limiting value predicted for complete constraint collapse. Finally, a constraint-counting argument combining an eight-chain affine network representation with the central-force nonaffine isostatic threshold gives a limiting estimate $|\mathrm{NLI}|_{\max}=3$. The results support the interpretation of the NLI as a Fourier-resolved dynamic nonaffinity parameter and establish a bridge between tube-based polymer dynamics, LAOS harmonic analysis, elastoplastic rheology, and microscopic nonaffine lattice dynamics.

cond-mat.soft↗
arXiv2026

Ginzburg-Landau Theory for Confined Thin-Film Superconductors

We develop a Ginzburg-Landau theory for superconducting thin films under quantum confinement. Starting from the Ginzburg-Landau theory and the recently developed confinement theory of metallic thin films, explicit analytical expressions are derived for the coherence length, penetration depth, electronic mean free path, and Ginzburg-Landau parameter in confined geometries. The central result is that quantum confinement directly renormalizes the intrinsic superconducting coherence length through confinement-induced modifications of the electronic density of states and Fermi energy. This effect is absent in conventional thin-film transport theories based solely on surface scattering. As a consequence, confinement simultaneously suppresses the coherence length and enhances the penetration depth, thereby driving superconductors toward stronger type-II behavior over a broad thickness range. The interplay between quantum confinement and disorder can also produce reentrant type-I/type-II crossovers. The theory predicts a crossover regime in which confinement-induced renormalization of superconducting length scales and transport scattering become strongly intertwined. Comparison with recent penetration-depth measurements in Al thin films shows that the observed enhancement of the penetration depth originates from the interplay between confinement-induced renormalization of the coherence length and suppression of the effective mean free path by surface and disorder scattering. The results establish a direct connection between quantum confinement and superconducting electrodynamics in confined metallic films.

cond-mat.supr-con↗
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

Prediction of new superconducting bilayers heterostructures using quantum confinement and proximity effects

A central challenge in nanoscale superconductivity is to understand and exploit the combined action of quantum confinement and proximity effects in experimentally realistic metallic heterostructures. We theoretically investigate superconducting bilayer heterostructures in which these two effects coexist. Using a generalized Eliashberg framework that incorporates both quantum confinement and proximity coupling, we show that their interplay can substantially enhance the superconducting critical temperature. In particular, the theory predicts superconductivity in selected bilayers whose constituent materials are nonsuperconducting or only weakly superconducting in the bulk. These results identify quantum-confined bilayers as a promising route to engineering emergent superconductivity in metallic heterostructures.

cond-mat.supr-con↗
arXiv2026

Universal inverse-cube thickness scaling of projectile penetration energy in ultrathin films

Ultrathin films of widely different materials exhibit a dramatic enhancement of projectile penetration resistance under high--velocity impact. Despite extensive simulations and experiments, a unifying physical explanation has remained elusive. Here we show that the thickness dependence of the specific penetration energy obeys a universal law, $E_p^*(h)=E_{p,\infty}^*+B h^{-3}$, independent of chemical composition and degree of disorder. The inverse--cube scaling is traced back to a finite--size correction to the effective shear modulus arising from the suppression of long--wavelength nonaffine deformation modes in confined solids. The scaling quantitatively describes impact data for multilayer graphene, graphene oxide, and polymer thin films, revealing a common elastic origin for nanoscale impact resistance.

cond-mat.mtrl-sci↗
arXiv2026

Modeling the Slow Arrhenius Process (SAP) in Polymers

Amorphous glass-forming polymers exhibit multiple relaxation processes, including the structural {\alpha}-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 {\alpha}-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 {\alpha}-relaxation and the SAP within a unified framework. We propose that the SAP represents the high-temperature limit of an {\alpha}-like process in a coarse-grained fluid of dynamically correlated clusters. With renormalized interaction energies and coordination parameters, the same model quantitatively reproduces both {\alpha} 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↗
arXiv2026

Hidden universality in dislocation-loops mediated three-dimensional crystal melting

Understanding why and how crystalline solids melt remains a central problem in condensed-matter physics. Dislocation loops are fundamental topological excitations that control the thermodynamic stability of crystals, yet their role in setting universal aspects of melting has remained unclear. Here we show, within dislocation-mediated melting theory, that the free-energy condition for loop proliferation leads to a universal ratio between the energy of a minimal dislocation loop and the thermal energy at melting. For minimal dislocation loops that begin to proliferate at the onset of melting, this ratio takes the purely geometric value $\mathcal{E}_* = E_{\rm loop}/(k_B T_m) \approx 25.1$, independent of elastic moduli and chemistry-dependent details. This result provides a microscopic explanation for recent empirical findings by Lunkenheimer \emph{et al.}, who identified a closely related universal energy scale $\approx 24.6$ from viscosity data. The same framework also rationalizes the empirical $2/3$ rule relating the glass-transition and melting temperatures.

cond-mat.mtrl-sci↗