arXiv subjects

David Andelman

Publications and source records attributed to David Andelman.

At least 19 recordsLinked to original sources

arXiv2026

Phase transitions and microphases in elastomers. II. Anisotropy-driven morphologies

In swollen elastomers, elasticity can arrest macroscopic demixing between the polymer network and the solvent, producing stable domains of finite size. While previous theories have focused on isotropically swollen elastomers, anisotropy strongly influences the phase behavior of many related systems, such as gels and crosslinked polymer blends. Building on the approach developed in Part I of this two-part paper, we investigate the effects of two experimentally induced sources of anisotropy: uniaxial swelling and stiffness gradients. We show that uniaxial swelling can lead to the formation of stable lamellar microphases and modify phase behavior, while stiffness gradients can cause spatial variations in the characteristic microphase size.

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arXiv2026

Non-uniform swelling of polyelectrolyte hydrogels: effects of charge regulation

We investigate the impact of charge regulation (CR) on the non-uniform swelling behavior of polyelectrolyte hydrogels. The Poisson-Boltzmann theory with electro-elastic coupling between the local polymer density and elastic deformation is considered. We investigate the spatial distributions of the elastic displacement and polymer density under different salt concentrations and compare charge-regulated gels with fixed-charge (non-CR) gels of the same net charge. Our results show that the CR induces spatially varying charge fractions, which strengthen the electro-elastic response and lead to stronger non-uniform swelling compared with non-CR gels. These findings provide a theoretical basis for understanding and controlling non-uniform swelling in responsive polyelectrolyte hydrogels.

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arXiv2026

Phase transitions and microphases in elastomers. I. Emergence of stable domains

Elasticity often plays a key role in regulating phase separation in physical systems. Recent experiments have shown that elastic effects can be used to control microphase separation in swollen elastomers. Here, microphase separation arises from a mismatch between the characteristic length scales of elastic and thermodynamic interactions. In this first part of a two-part paper, we show that microphase formation in elastomers can be explained using conventional theories of elasticity through a nonlocal thermodynamic-elastic coupling arising from volume conservation. Our theory reproduces the observed dependence of phase transition temperature and domain size on elastomer stiffness in isotropically swollen elastomers. In the companion paper, we investigate the effects of anisotropic swelling and inhomogeneous elastic moduli.

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arXiv2026

Lateral hydrodynamics in supported membranes: The Evans-Sackmann model and its extensions

We review the theoretical development and modern applications of the Evans-Sackmann hydrodynamic model for lateral transport in supported fluid membranes. We first cover the original formulation, emphasizing the linear momentum decay term that captures membrane-substrate coupling mediated by a thin lubricating fluid layer. This coupling term enables quantitative interpretation of tracer diffusion measurements in supported bilayers. Building on this foundation, we survey theoretical extensions that relax standard boundary conditions at the inclusion perimeter, where inclusions refer to embedded objects such as proteins, lipid domains, or tracer particles within the membrane. We discuss the drag of a disk and a liquid domain, as well as the dynamics of membrane phase separation. We further highlight how the supported-membrane mobility tensor serves as a unifying tool for systematic treatments of correlated diffusion, polymer dynamics, phase separation kinetics, and many-body interactions in quasi-two-dimensional environments. Finally, we discuss recent extensions to active and chiral membranes, where odd viscosity provides a transverse hydrodynamic response and offers a possible route for detecting chirality in two-dimensional fluids.

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arXiv2026

Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics

The Onsager principle provides a variational route to the phenomenological equations of dissipative dynamics through the minimization of the Rayleighian. We develop a covariant formulation of the Onsager principle for active and inertial systems, ensuring geometric consistency under coordinate transformations. To further incorporate thermal fluctuations, we formulate the Onsager-Machlup principle for active and inertial systems by considering the Onsager-Machlup functional and the corresponding path probability for stochastic trajectories. Requiring that the path probability obeys the detailed fluctuation theorem, we show that the extended Onsager-Machlup theory is consistent with stochastic thermodynamics. The extended OP and OMP offer a unified and useful variational framework for deriving the dynamical equations of active and inertial systems.

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arXiv2026

The effects of ionic valency and size asymmetry on counterion adsorption

We study the effect of asymmetry in solvent and ionic size on the equilibrium properties of multivalent ionic solutions near a charged surface. For a single ionic species in solution, we derive a generalized Grahame equation at the charged surface. For general size ratio between the ions and the solvent, we obtain analytical results for the concentration profiles as a function of the distance from the surface. For weak surface charge and small ion-to-solvent size ratio, the profile follows the classical Poisson-Boltzmann equation in dilute solution conditions. However, for high surface charge and large ionic size, the concentration profile saturates near the surface, leading to distinctive dependencies of the solution properties on the surface charge density and size asymmetry. Furthermore, the crossover between dilute and saturated regimes depends on the surface charge and ionic size asymmetry. We suggest that a solution containing multiple ionic species of different valencies and sizes stratifies close to the surface in the saturation regime. This leads to the formation of layers that are ordered according to the ions' valency-to-size ratio.

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arXiv2026

Collapse of a single polymer chain: Effects of chain stiffness and attraction range

Chain-like macromolecules in solution, whether biological or synthetic, transform from an extended conformation to a compact one when temperature or other system parameters change. This collapse transition is relevant in various phenomena, including DNA condensation, protein folding, and the behavior of polymers in solution. We investigate the interplay of chain stiffness and range of attraction between monomers in the collapse of a single polymer chain. We use Monte Carlo simulations based on the pruned-enriched Rosenbluth method. We demonstrate that the competition between the persistence length, l_p, and the range of attraction, r_c, determines whether the chain's collapse behavior resembles that of flexible chains or stiff ones. When l_p is larger than r_c, the chain collapses sharply with decreasing temperature, whereas if l_p is smaller than r_c, it contracts gradually. Notably, in the regime of small l_p and large r_c, this rounding into a gradual compaction persists upon increasing the chain length and may remain in place in the limit of infinite chain length. Furthermore, for small r_c, the transition temperature (theta-temperature) increases with l_p, whereas for large r_c the theta-temperature decreases with l_p. Thus, stiffness promotes collapse for small r_c but suppresses it for large r_c. Our findings are in agreement with recent experiments on the contraction of single-stranded RNA as compared to double-stranded DNA, and provide valuable insights for understanding polymer collapse and the essential polymer parameters affecting it.

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arXiv2024

Theory of Microphase Separation in Elastomers

Inspired by recent experiments, we present a phase-field model of microphase separation in an elastomer swollen with a solvent. The imbalance between the molecular scale of demixing and the mesoscopic scale beyond which elasticity operates produces effective long-range interactions, forming stable finite-sized domains. Our predictions concerning the dependence of the domain size and transition temperature on the stiffness of the elastomer are in good agreement with the experiments. Analytical phase diagrams, aided by numerical findings, capture the richness of the microphase morphologies, paving the way to create stable, patterned elastomers for various applications.

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arXiv2024

Diffusive dynamics of charge regulated macro-ion solutions

Onsager's variational principle is generalized to address the diffusive dynamics of an electrolyte solution composed of charge-regulated macro-ions and counterions. The free energy entering the Rayleighian corresponds to the Poisson-Boltzmann theory augmented by the charge-regulation mechanism. The dynamical equations obtained by minimizing the Rayleighian include the classical Poisson-Nernst-Planck equations, the Debye-Falkenhagen equation, and their modifications in the presence of charge regulation. By analyzing the steady state, we show that the charge regulation has an important impact on the non-equilibrium macro-ion spatial distribution and their effective charge, deviating significantly from their equilibrium values. Our model, based on Onsager's variational principle offers a unified approach to the diffusive dynamics of electrolytes containing components that undergo various charge association/dissociation processes.

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arXiv2024

Frequency-Dependent Conductivity of Concentrated Electrolytes: A Stochastic Density Functional Theory

The response of ionic solutions to time-varying electric fields, quantified by a frequency-dependent conductivity, is essential in many electrochemical applications. Yet, it constitutes a challenging problem due to the combined effect of Coulombic interactions, hydrodynamics, and thermal fluctuations. Here, we study the frequency-dependent conductivity of ionic solutions using a stochastic density functional theory. In the limit of small concentrations, we recover the classical Debye and Falkenhagen (DF) result, predicting an increase in conductivity with field frequency. At higher concentrations, we use a modified Coulomb interaction potential that accounts for the hard-core repulsion between the ions, which was recently employed in the zero-frequency case. Consequently, we extend the DF result to concentrated electrolytes. We discuss experimental and numerical studies and the complexity of observing the DF effect in such setups.

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arXiv2024

Design and Fabrication of Nano-Particles with Customized Properties using Self-Assembly of Block-Copolymers

Functional nanoparticles (NPs) have gained significant attention as a promising application in various fields, including sensor, smart coating, drug delivery, and more. Here, we propose a novel mechanism assisted by machine-learning workflow to accurately predict phase diagram of NPs, which elegantly achieves tunability of shapes and internal structures of NPs using self-assembly of block-copolymers (BCP). Unlike most of previous studies, we obtain onion-like and mesoporous NPs in neutral environment and hamburger-like NPs in selective environment. Such novel phenomenon is obtained only by tailoring the topology of a miktoarm star BCP chain architecture without the need for any further treatment. Moreover, we demonstrate that the BCP chain architecture can be used as a new strategy for tuning the lamellar asymmetry of NPs. We show that the asymmetry between A and B lamellae in striped ellipsoidal and onion-like particles increases as the volume fraction of the A-block increases, beyond the level reached by linear BCPs. In addition, we find an extended region of onion-like structure in the phase diagram of A-selective environment, as well as the emergence of an inverse onion-like structure in the B-selective one. Our findings provide a valuable insight into the design and fabrication of nanoscale materials with customized properties, opening up new possibilities for advanced applications in sensing, materials science, and beyond.

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arXiv2023

Charge Regulation of Polyelectrolyte Gels: Swelling Transition

We study the effects of charge-regulated acid/base equilibrium on the swelling of polyelectrolyte gels, by considering a combination of the Poisson-Boltzmann theory and a two-site charge-regulation model based on the Langmuir adsorption isotherm. By exploring the volume change as a function of salt concentration for both nano-gels and micro-gels, we identify conditions where the gel volume exhibits a discontinuous swelling transition. This transition is driven exclusively by the charge-regulation mechanism and is characterized by a closed-loop phase diagram. Our predictions can be tested experimentally for polypeptide gels.

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arXiv2022

The Process-Directed Self-Assembly of Block Copolymer Particles

The kinetic paths of structural evolution and formation of block copolymer (BCP) particles are explored using dynamic self-consistent field theory (DSCFT). It is shown that the process-directed self-assembly of BCP immersed in a poor solvent leads to the formation of striped ellipsoids, onion-like particles and double-spiral lamellar particles. The theory predicts a reversible path of shape transition between onion-like particles and striped ellipsoidal ones by regulating the temperature (related to the Flory-Huggins parameter between the two components of BCP, \chi_{AB}) and the selectivity of solvent toward one of the two BCP components. Furthermore, a kinetic path of shape transition from onion-like particles to double-spiral lamellar particles, and then back to onion-like particles is demonstrated. By investigating the inner-structural evolution of a BCP particle, it is identified that changing the intermediate bi-continuous structure into a layered one is crucial for the formation of striped ellipsoidal particles. Another interesting finding is that the formation of onion-like particles is characterized by a two-stage microphase separation. The first is induced by the solvent preference, and the second is controlled by the thermodynamics. The findings lead to an effective way of tailoring nanostructure of BCP particles for various industrial applications.

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arXiv2022

Pair dynamics of active force dipoles in an odd-viscous fluid

We discuss the lateral dynamics of two active force dipoles, which interact with each other via hydrodynamic interactions in a thin fluid layer that is active and chiral. The fluid layer is modeled as a two-dimensional (2D) compressible fluid with an odd viscosity, while the force dipole (representing an active protein or enzyme) induces a dipolar flow. Taking into account the momentum decay in the 2D fluid, we obtain analytically the mobility tensor that depends on the odd viscosity and includes nonreciprocal hydrodynamic interactions. We find that the particle pair shows spiral behavior due to the transverse flow induced by the odd viscosity. When the magnitude of the odd viscosity is large as compared with the shear viscosity, two types of oscillatory behaviors are seen. One of them can be understood as arising from closed orbits in dynamical systems, and its circular trajectories are determined by the ratio between the magnitude of the odd viscosity and the force dipole. In addition, the phase diagrams of the particle dipolar angles are obtained numerically. Our findings reveal that the nonreciprocal response leads to complex dynamics of active particles embedded in an active fluid with odd viscosity.

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arXiv2022

The Chain Flexibility Effects on the Self-assembly of Diblock Copolymer in Thin Film

We investigate the effects of chain flexibility on the self-assembly behavior of symmetric diblock copolymers (BCPs) when they are confined as a thin film between two surfaces. Employing worm-like chain (WLC) self-consistent field theory, we study the relative stability of parallel (L$_{\parallel}$) and perpendicular (L$_{\perp}$) orientations of BCP lamellar phases, ranging in chain flexibility from flexible Gaussian chains to semi-flexible and rigid chains. For flat and neutral bounding surfaces (no surface preference for one of the two BCP components), the stability of the L$_{\perp}$ lamellae increases with chain rigidity. When the top surface is flat and the bottom substrate is corrugated, increasing the surface roughness enhances the stability of the L$_{\perp}$ lamellae for flexible Gaussian chains. However, an opposite behavior is observed for rigid chains, where the L$_{\perp}$ stability decreases as the substrate roughness increases. We further show that as the substrate roughness increases, the critical value of the substrate preference, $u^{*}$, corresponding to an L$_{\perp}$-to-L$_{\parallel}$ transition, decreases for rigid chains, while it increases for flexible Gaussian chains. Our results highlight the physical mechanism of tailoring the orientation of lamellar phases in thin-film setups. This is of importance, in particular, for short (semi-flexible or rigid) chains that are in high demand in emerging nanolithography and other industrial applications.

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arXiv2022

Conductance of concentrated electrolytes: multivalency and the Wien effect

The electric conductivity of ionic solutions is well understood at low ionic concentrations of up to a few millimolar but becomes difficult to unravel at higher concentrations that are still common in nature and technological applications. A model for the conductivity at high concentrations was recently put forth for monovalent electrolytes at low electric fields. The model relies on applying a stochastic density-functional theory and using a modified electrostatic pair-potential that suppresses unphysical, short-range electrostatic interactions. Here, we extend the theory to multivalent ions as well as to high electric fields where a deviation from Ohm's law known as the Wien effect occurs. Our results are in good agreement with experiments and recent simulations.

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arXiv2021

Conductivity of Concentrated Electrolytes

The conductivity of ionic solutions is arguably their most important trait, being widely used in electrochemical, biochemical, and environmental applications. The Debye-H\"uckel-Onsager theory successfully predicts the conductivity at very low ionic concentrations of up to a few millimolars, but there is no well-established theory applicable at higher concentrations. We study the conductivity of ionic solutions using a stochastic density functional theory, paired with a modified Coulomb interaction that accounts for the hard-core repulsion between the ions. The modified potential suppresses unphysical, short-range electrostatic interactions, which are present in the Debye-H\"uckel-Onsager theory. Our results for the conductivity show very good agreement with experimental data up to 3 molars, without any fit parameters. We provide a compact expression for the conductivity, accompanied by a simple analytical approximation.

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arXiv2021

Hydrodynamic lift of a two-dimensional liquid domain with odd viscosity

We discuss hydrodynamic forces acting on a two-dimensional liquid domain that moves laterally within a supported fluid membrane in the presence of odd viscosity. Since active rotating proteins can accumulate inside the domain, we focus on the difference in odd viscosity between the inside and outside of the domain. Taking into account the momentum leakage from a two-dimensional incompressible fluid to the underlying substrate, we analytically obtain the fluid flow induced by the lateral domain motion, and calculate the drag and lift forces acting on the moving liquid domain. In contrast to the passive case without odd viscosity, the lateral lift arises in the active case only when the in/out odd viscosities are different. The in/out contrast in the odd viscosity leads to nonreciprocal hydrodynamic responses of an active liquid domain.

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