arXiv subjects

Alan R. Denton

Publications and source records attributed to Alan R. Denton.

At least 19 recordsLinked to original sources

arXiv2023

Osmotic Pressure and Swelling Behavior of Ionic Microcapsules

Ionic microcapsules are hollow shells of hydrogel, typically 10-1000 nm in radius, composed of cross-linked polymer networks that become charged and swollen in a good solvent. The ability of microcapsules to swell/deswell in response to changes in external stimuli (e.g., temperature, pH, ionic strength) suits them to applications, such as drug delivery, biosensing, and catalysis. Equilibrium swelling behavior of ionic microcapsules is determined by a balance of electrostatic and elastic forces. The electrostatic component of the osmotic pressure of a microcapsule -- the difference in pressure between the inside and outside of the particle -- plays a vital role in determining swelling behavior. Within the spherical cell model, we derive exact expressions for the radial pressure profile and for the electrostatic and gel components of the osmotic pressure of a microcapsule, which we compute via Poisson-Boltzmann theory and molecular dynamics simulation. For the gel component, we use the Flory-Rehner theory of polymer networks. By combining the electrostatic and gel components of the osmotic pressure, we compute the equilibrium size of ionic microcapsules as a function of particle concentration, shell thickness, and valence. We predict concentration-driven deswelling at relatively low concentrations at which steric interactions between particles are weak, and demonstrate that this response can be attributed to crowding-induced redistribution of counterions. Our approach may help to guide the design and applications of smart, stimuli-responsive colloidal particles.

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arXiv2023

Osmotic Swelling Behavior of Surface-Charged Ionic Microgels

In recent years, ionic microgels have garnered much attention due to their unique properties, especially their stimulus-sensitive swelling behavior. The tunable response of these soft, permeable, compressible, charged colloidal particles is increasingly attractive for applications in medicine and biotechnologies, such as controlled drug delivery, tissue engineering, and biosensing. The ability to model and predict variation of the osmotic pressure of a single microgel with respect to changes in particle properties and environmental conditions proves vital to such applications. In this work, we apply both nonlinear Poisson-Boltzmann theory and molecular dynamics simulation to ionic microgels (macroions) in the cell model to compute density profiles of microions (counterions, coions), single-microgel osmotic pressure, and equilibrium swelling ratios of spherical microgels whose fixed charge is confined to the macroion surface. The basis of our approach is an exact theorem that relates the electrostatic component of the osmotic pressure to the microion density profiles. Close agreement between theory and simulation serves as a consistency check to validate our approach. We predict that surface-charged microgels progressively deswell with increasing microgel concentration, starting well below close packing, and with increasing salt concentration, in qualitative agreement with experiments. Comparison with previous results for microgels with fixed charge uniformly distributed over their volume demonstrates that surface-charged microgels deswell more rapidly than volume-charged microgels. We conclude that swelling behavior of ionic microgels in solution is sensitive to the distribution of fixed charge within the polymer-network gel and strongly depends on bulk concentrations of both microgels and salt ions.

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arXiv2023

Effective interactions, structure, and pressure in charge-stabilized colloidal suspensions: Critical assessment of charge renormalization methods

Charge-stabilized colloidal suspensions display a rich variety of microstructural and thermodynamic properties, which are determined by electro-steric interactions between all ionic species. The large size asymmetry between molecular-scale microions and colloidal macroions allows the microion degrees of freedom to be integrated out, leading to an effective one-component model of microion-dressed colloidal quasi-particles. For highly-charged colloids with strong macroion-microion correlations, nonlinear effects can be incorporated into effective interactions by means of charge renormalization methods. Here, we compare and partially extend several practical mean-field methods of calculating renormalized colloidal interaction parameters, including effective charges and screening constants, as functions of concentration and ionic strength. Within the one-component description, we compute structural and thermodynamic properties from the effective interactions and assess the accuracy of the different methods by comparing predictions with elaborate primitive-model simulations [P. Linse, J. Chem. Phys. 113, 4359 (2000)]. We also compare various prescriptions for the osmotic pressure of suspensions in Donnan equilibrium with a salt ion reservoir, and analyze instances where the macroion effective charge becomes larger than the bare one. The methods assessed include single-center cell, jellium, and multi-center mean-field theories. The strengths and weaknesses of the various methods are critically assessed, with the aim of guiding optimal and accurate implementations.

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arXiv2021

Influence of Solvent Quality on Depletion Potentials in Colloid-Polymer Mixtures

As first explained by the classic Asakura-Oosawa (AO) model, effective attractive forces between colloidal particles induced by depletion of nonadsorbing polymers can drive demixing of colloid-polymer mixtures into colloid-rich and colloid-poor phases, with practical relevance for purification of water, stability of foods and pharmaceuticals, and macromolecular crowding in biological cells. By idealizing polymer coils as effective penetrable spheres, the AO model qualitatively captures the influence of polymer depletion on thermodynamic phase behavior of colloidal suspensions. In previous work, we extended the AO model to incorporate aspherical polymer conformations and showed that fluctuating shapes of random-walk coils can significantly modify depletion potentials [W. K. Lim and A. R. Denton, Soft Matter 12, 2247 (2016); J. Chem. Phys. 144, 024904 (2016)]. We further demonstrated that the shapes of polymers in crowded environments depend sensitively on solvent quality [W. J. Davis and A. R. Denton, J. Chem. Phys. 149, 124901 (2018)]. Here we apply Monte Carlo simulation to analyze the influence of solvent quality on depletion potentials in mixtures of hard sphere colloids and nonadsorbing polymer coils, modeled as ellipsoids whose principal radii fluctuate according to random-walk statistics. We consider both self-avoiding and non-self-avoiding random walks, corresponding to polymers in good and theta solvents, respectively. Our simulation results demonstrate that depletion of polymers of equal molecular weight induces much stronger attraction between colloids in good solvents than in theta solvents and confirm that depletion interactions are significantly influenced by aspherical polymer conformations.

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arXiv2019

Modeling deswelling, thermodynamics, structure, and dynamics in ionic microgel suspensions

Ionic microgel particles in a good solvent swell to an equilibrium size determined by a balance of electrostatic and elastic forces. When crowded, ionic microgels deswell owing to a redistribution of microions inside and outside the particles. The concentration-dependent deswelling affects the interactions between the microgels, and consequently the suspension properties. We present a comprehensive theoretical study of crowding effects on thermodynamic, structural, and dynamic properties of weakly cross-linked ionic microgels in a good solvent. The microgels are modeled as microion- and solvent-permeable colloidal spheres with fixed charge uniformly distributed over the polymer gel backbone, whose elastic and solvent-interaction free energies are described using Flory-Rehner theory. Two mean-field methods for calculating the crowding-dependent microgel radius are investigated, and combined with calculations of the net microgel charge characterizing the electrostatic part of an effective microgel pair potential, with charge renormalization accounted for. Using this effective pair potential, thermodynamic and static suspension properties are calculated including the osmotic pressure and microgel pair distribution function. The latter is used in our calculations of dynamic suspension properties, where we account for hydrodynamic interactions. Results for diffusion and rheological properties are presented over ranges of microgel concentration and charge. We show that deswelling mildly enhances self- and collective diffusion and the osmotic pressure, lowers the suspension viscosity, and significantly shifts the suspension crystallization point to higher concentrations. The paper presents a bottom-up approach to efficiently computing suspension properties of crowded ionic microgels using single-particle characteristics.

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arXiv2019

Osmotic Pressure of Permeable Ionic Microgels: Poisson-Boltzmann Theory and Exact Statistical Mechanical Relations in the Cell Model

Ionic microgels are soft colloidal particles, composed of crosslinked polymer networks, that ionize and swell when dispersed in a good solvent. Swelling of these permeable, compressible particles involves a balance of electrostatic, elastic, and mixing contributions to the single-particle osmotic pressure. The electrostatic contribution depends on the distributions of mobile counterions and coions and of fixed charge on the polymers. Within the cell model, we employ two complementary methods to derive the electrostatic osmotic pressure of ionic microgels. In Poisson-Boltzmann (PB) theory, we minimize a free energy functional with respect to the electrostatic potential to obtain the bulk pressure. From the pressure tensor, we extract the electrostatic and gel contributions to the total pressure. In a statistical mechanical approach, we vary the free energy with respect to microgel size to obtain exact relations for the microgel electrostatic osmotic pressure. We present results for planar, cylindrical, and spherical geometries. For models of membranes and microgels with fixed charge uniformly distributed over their surface or volume, we derive analogues of the contact value theorem for charged colloids. We validate these relations by solving the PB equation and computing ion densities and osmotic pressures. When implemented within PB theory, the two methods yield identical electrostatic osmotic pressures for surface-charged microgels. For volume-charged microgels, the exact electrostatic osmotic pressure equals the average of the corresponding PB profile over the gel volume. We demonstrate that swelling of ionic microgels depends on variation of the electrostatic pressure inside the particle and discuss implications for interpreting experiments.

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arXiv2018

Influence of Solvent Quality on Conformations of Crowded Polymers

The structure and function of polymers in confined environments, e.g., biopolymers in the cytoplasm of a cell, are strongly affected by macromolecular crowding. To explore the influence of solvent quality on conformations of crowded polymers, we model polymers as penetrable ellipsoids, whose shape fluctuations are governed by the statistics of self-avoiding walks, appropriate for a polymer in a good solvent. Within this coarse-grained model, we perform Monte Carlo simulations of mixtures of polymers and hard-nanosphere crowders, including trial changes in polymer size and shape. Penetration of polymers by crowders is incorporated via a free energy cost predicted by polymer field theory. To analyze the impact of crowding on polymer conformations in different solvents, we compute average polymer shape distributions, radius of gyration, volume, and asphericity over ranges of polymer-to-crowder size ratio and crowder volume fraction. The simulation results are accurately predicted by a free-volume theory of polymer crowding. Comparison of results for polymers in good and theta solvents indicates that excluded-volume interactions between polymer segments significantly affect crowding, especially in the limit of crowders much smaller than polymers. Our approach may help to motivate future experimental studies of polymers in crowded environments, with possible relevance for drug delivery and gene therapy.

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arXiv2018

Concentration-Dependent Swelling and Structure of Ionic Microgels: Simulation and Theory of a Coarse-Grained Model

We study swelling and structural properties of ionic microgel suspensions within a comprehensive coarse-grained model that combines the polymeric and colloidal natures of microgels as permeable, compressible, charged spheres governed by effective interparticle interactions. The model synthesizes the Flory-Rehner theory of cross-linked polymer gels, the Hertz continuum theory of effective elastic interactions, and a theory of density-dependent effective electrostatic interactions. Implementing the model using Monte Carlo simulation and thermodynamic perturbation theory, we compute equilibrium particle size distributions, swelling ratios, volume fractions, net valences, radial distribution functions, and static structure factors as functions of concentration. Trial Monte Carlo moves comprising particle displacements and size variations are accepted or rejected based on the total change in elastic and electrostatic energies. The theory combines first-order thermodynamic perturbation and variational free energy approximations. For illustrative system parameters, theory and simulation agree closely at concentrations ranging from dilute to beyond particle overlap. With increasing concentration, as microgels deswell, we predict a decrease in the net valence and an unusual saturation of pair correlations. Comparison with experimental data for deionized, aqueous suspensions of PNIPAM particles demonstrates the capacity of the coarse-grained model to predict and interpret measured swelling behavior.

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arXiv2018

Structure and Stability of Charged Colloid-Nanoparticle Mixtures

Physical properties of colloidal materials can be modified by addition of nanoparticles. Within a model of like-charged mixtures of particles governed by effective electrostatic interactions, we explore the influence of charged nanoparticles on the structure and thermodynamic phase stability of charge-stabilized colloidal suspensions. Focusing on salt-free mixtures of particles of high size and charge asymmetry, interacting via repulsive Yukawa effective pair potentials, we perform molecular dynamics simulations and compute radial distribution functions and static structure factors. Analysis of these structural properties indicates that increasing the charge and concentration of nanoparticles progressively weakens correlations between charged colloids. We show that addition of charged nanoparticles to a suspension of like-charged colloids can induce a colloidal crystal to melt and can facilitate aggregation of a fluid suspension due to attractive van der Waals interactions. We attribute the destabilizing influence of charged nanoparticles to enhanced screening of electrostatic interactions, which weakens repulsion between charged colloids. This interpretation is consistent with recent predictions of an effective interaction theory of charged colloid-nanoparticle mixtures.

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arXiv2017

Effective Electrostatic Interactions in Colloid-Nanoparticle Mixtures

Interparticle interactions and bulk properties of colloidal suspensions can be substantially modified by addition of nanoparticles. Extreme asymmetries in size and charge between colloidal particles and nanoparticles present severe computational challenges to molecular-scale modeling of such complex systems. We present a statistical mechanical theory of effective electrostatic interactions that can greatly ease large-scale modeling of charged colloid-nanoparticle mixtures. By applying a sequential coarse-graining procedure, we show that a multicomponent mixture of charged colloids, nanoparticles, counterions, and coions can be mapped first onto a binary mixture of colloids and nanoparticles and then onto a one-component model of colloids alone. In a linear-response approximation, the one-component model is governed by a single effective pair potential and a one-body volume energy, whose parameters depend nontrivially on nano particle size, charge, and concentration. To test the theory, we perform molecular dynamics simulations of the two-component and one-component models and compute structural properties. For moderate electrostatic couplings, colloid-colloid radial distribution functions and static structure factors agree closely between the two models, validating the sequential coarse-graining approach. Nanoparticles of sufficient charge and concentration enhance screening of electrostatic interactions, weakening correlations between charged colloids and destabilizing suspensions, consistent with experiments.

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arXiv2016

Swelling, Structure, and Phase Stability of Compressible Microgels

Microgels are soft colloidal particles that, when dispersed in a solvent, swell and deswell in response to changes in environmental conditions, such as temperature, concentration, and $p$H. Using Monte Carlo simulation, we model bulk suspensions of microgels that interact via Hertzian elastic interparticle forces and can expand or contract via trial moves that allow particles to change size in accordance with the Flory-Rehner free energy of cross-linked polymer gels. We monitor the influence of particle compressibility, size fluctuations, and concentration on bulk structural and thermal properties by computing particle swelling ratios, radial distribution functions, static structure factors, osmotic pressures, and freezing densities. For microgels in the nanoscale size range, particle compressibility and associated size fluctuations suppress crystallization, shifting the freezing transition to a higher density than for the hard-sphere fluid. As densities increase beyond close packing, microgels progressively deswell, while their intrinsic size distribution grows increasingly polydisperse.

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arXiv2016

Counterion-Induced Swelling of Ionic Microgels

Ionic microgel particles, when dispersed in a solvent, swell to equilibrium sizes that are governed by a balance between electrostatic and elastic forces. Tuning of particle size by varying external stimuli, such as $p$H, salt concentration, and temperature, has relevance for drug delivery, microfluidics, and filtration. To model swelling of ionic microgels, we derive a statistical mechanical theorem, which proves exact within the cell model, for the electrostatic contribution to the osmotic pressure inside a permeable colloidal macroion. Applying the theorem, we demonstrate how the distribution of counterions within an ionic microgel determines the internal osmotic pressure. By combining the electrostatic pressure, which we compute via both Poisson-Boltzmann theory and molecular dynamics simulation, with the elastic pressure, modeled via the Flory-Rehner theory of swollen polymer networks, we show how deswelling of ionic microgels with increasing concentration of particles can result from a redistribution of counterions that reduces electrostatic pressure. A linearized approximation for the electrostatic pressure, which proves remarkably accurate, provides physical insight and greatly eases numerical calculations for practical applications. Comparing with experiments, we explain why soft particles in deionized suspensions deswell upon increasing concentration and why this effect may be suppressed at higher ionic strength. The failure of the uniform ideal-gas approximation to adequately account for counterion-induced deswelling below close packing of microgels is attributed to neglect of spatial variation of the counterion density profile and the electrostatic pressure of incompletely neutralized macroions.

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arXiv2015

Influence of Polymer Shape on Depletion Potentials and Crowding in Colloid-Polymer Mixtures

Depletion-induced interactions between colloids in colloid-polymer mixtures depend in range and strength on size, shape, and concentration of depletants. Crowding by colloids in turn affects shapes of polymer coils, such as biopolymers in biological cells. By simulating hard-sphere colloids and random-walk polymers, modeled as fluctuating ellipsoids, we compute depletion-induced potentials and polymer shape distributions. Comparing results with exact density-functional theory calculations, molecular simulations, and experiments, we show that polymer shape fluctuations play an important role in depletion and crowding phenomena.

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arXiv2015

Depletion-Induced Forces and Crowding in Polymer-Nanoparticle Mixtures: Role of Polymer Shape Fluctuations and Penetrability

Depletion forces and macromolecular crowding govern the structure and function of biopolymers in biological cells and the properties of polymer nanocomposite materials. To isolate and analyze the influence of polymer shape fluctuations and penetrability on depletion-induced interactions and crowding by nanoparticles, we model polymers as effective penetrable ellipsoids, whose shapes fluctuate according to the probability distributions of the eigenvalues of the gyration tensor of an ideal random walk. Within this model, we apply Monte Carlo simulation methods to compute the depletion-induced potential of mean force between hard nanospheres and crowding-induced shape distributions of polymers in the protein limit, in which polymer coils can be easily penetrated by smaller nanospheres. By comparing depletion potentials from simulations of ellipsoidal and spherical polymer models with predictions of polymer field theory and free-volume theory, we show that polymer depletion-induced interactions and crowding depend sensitively on polymer shapes and penetrability, with important implications for bulk thermodynamic phase behavior.

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arXiv2015

Ion Density Deviations in Semipermeable Ionic Microcapsules

By implementing the nonlinear Poisson-Boltzmann theory in a cell model, we theoretically investigate the influence of polyelectrolye gel permeability on ion densities and pH deviations inside the cavities of ionic microcapsules. Our calculations show that variations in permeability of a charged capsule shell cause a redistribution of ion densities within the capsule, which ultimately affects the pH deviation and Donnan potential induced by the electric field of the shell. We find that semipermeable capsules can induce larger pH deviations inside their cavities that can permeable capsules. Furthermore, with increasing capsule charge, the influence of permeability on pH deviations progressively increases. Our theory, while providing a self-consistent method for modeling the influence of permeability on fundamental properties of ionic microgels, makes predictions of practical significance for the design of microcapsules loaded with fluorescent dyes, which can serve as biosensors for diagnostic purposes.

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arXiv2015

Structure and Osmotic Pressure of Ionic Microgel Dispersions

We investigate structural and thermodynamic properties of aqueous dispersions of ionic microgels -- soft colloidal gel particles that exhibit unusual phase behavior. Starting from a coarse-grained model of microgel macroions as charged spheres that are permeable to microions, we perform simulations and theoretical calculations using two complementary implementations of Poisson-Boltzmann (PB) theory. Within a one-component model, based on a linear-screening approximation for effective electrostatic pair interactions, we perform molecular dynamics simulations to compute macroion-macroion radial distribution functions, static structure factors, and macroion contributions to the osmotic pressure. For the same model, using a variational approximation for the free energy, we compute both macroion and microion contributions to the osmotic pressure. Within a spherical cell model, which neglects macroion correlations, we solve the nonlinear PB equation to compute microion distributions and osmotic pressures. By comparing the one-component and cell model implementations of PB theory, we demonstrate that the linear-screening approximation is valid for moderately charged microgels. By further comparing cell model predictions with simulation data for osmotic pressure, we chart the cell model's limits in predicting osmotic pressures of salty dispersions.

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arXiv2014

Ion Density Deviations in Polyelectrolyte Microcapsules: Influence on Biosensors

Polyelectrolyte microcapsules loaded with fluorescent dyes have been proposed as biosensors to monitor local pH and ionic strength for diagnostic purposes. In the case of charged microcapsules, however, the local electric field can cause deviations of ion densities inside the cavities, potentially resulting in misdiagnosis of some diseases. Using nonlinear Poisson-Boltzmann theory, we systematically investigate these deviations induced by charged microcapsules. Our results show that the microcapsule charge density, as well as the capsule and salt concentrations, contribute to deviations of local ion concentrations and pH. Our findings are relevant for applications of polyelectrolyte microcapsules with encapsulated ion-sensitive dyes as biosensors.

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arXiv2014

Polymer Crowding and Shape Distributions in Polymer-Nanoparticle Mixtures

Macromolecular crowding can influence polymer shapes, which is important for understanding the thermodynamic stability of polymer solutions and the structure and function of biopolymers (proteins, RNA, DNA) under confinement. We explore the influence of nanoparticle crowding on polymer shapes via Monte Carlo simulations and free-volume theory of a coarse-grained model of polymer-nanoparticle mixtures. Exploiting the geometry of random walks, we model polymer coils as effective penetrable ellipsoids, whose shapes fluctuate according to the probability distributions of the eigenvalues of the gyration tensor. Accounting for the entropic cost of a nanoparticle penetrating a larger polymer coil, we compute the crowding-induced shift in the shape distributions, radius of gyration, and asphericity of ideal polymers in a theta solvent. With increased nanoparticle crowding, we find that polymers become more compact (smaller, more spherical), in agreement with predictions of free-volume theory. Our approach can be easily extended to nonideal polymers in good solvents and used to model conformations of biopolymers in crowded environments.

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