Thermodynamic properties and phase equilibria of charged hard sphere chain model for polyelectrolyte solutions

Two Methods Based on Integral Equation Approaches in Analyzing Polyelectrolyte Solutions: Macrophase Separation

To understand the phase behaviors of polyelectrolyte solutions, we provide two analytical methods to formulate a molecular equation of state for a system of fully charged polyanions (PAs) and polycations (PCs) in a monomeric neutral component, based on integral equation theories. The mixture is treated in a primitive and restricted manner. The first method utilizes Blum's approach to charged hard spheres, incorporating the chain connectivity contribution by charged spheres via Stell's cavity function method. The second method employs Wertheim's multi-density Ornstein-Zernike treatment of charged hard spheres with Baxter's adhesive potential. The pressures derived from these methods are compared to available molecular dynamics simulations data for a solution of PAs and monomeric counterions as a limiting case. Two-phase equilibrium for the system is calculated using both methods to evaluate the relative strength of phase segregation that leads to complex coacervation. Additionally, the scaling exponents for a selected solution near its critical point are examined.

Enabling High-Capacitance Supercapacitors by Polyelectrolyte Brushes

Polyelectrolyte brushes (PEBs) hold excellent potential for designing high-capacitance electrical double-layer capacitors (EDLCs), a crucial component of supercapacitors. Both experiments and computational simulations have shown their energy-storage advantage. However, the effect of PEBs on the energy storage of EDLCs is not yet fully understood. Herein, we systematically study the energy-storage effects of polyanionic (PA) and polycationic (PC) brushes using polymer density functional theory (DFT). First, the application of polymer DFT in polyelectrolyte-grafted EDLCs is successfully validated using molecular dynamics simulations. With the help of polymer DFT, an interfacial adhesion microstructure of the PA/PC brushes is observed. Most importantly, the results show that polyelectrolyte-grafted EDLCs achieve a significant increase in capacitance at low salt concentrations and surface voltages, offering an excellent energy-storage advantage over traditional EDLCs. However, this advantage is considerably diminished at high salt concentrations or surface voltages, showing unusual salt- and voltage-dependent behaviors of energy-storage capacity. Nonetheless, the PC-grafted EDLCs maintain their outstanding energy-storage performance, even at relatively high salt concentrations and surface voltages. These findings deepen our comprehension of PEBs at the molecular level and provide insights for the molecular design of high-capacitance supercapacitors.

Phase Behavior of Ion-Containing Polymers in Polar Solvents: Predictions from a Liquid-State Theory with Local Short-Range Interactions

The thermodynamic phase behavior of charged polymers is a crucial property underlying their role in biology and various industrial applications. A complete understanding of the phase behaviors of such polymer solutions remains challenging due to the multi-component nature of the system and the delicate interplay among various factors, including the translational entropy of each component, excluded volume interactions, chain connectivity, electrostatic interactions, and other specific interactions. In this work, the phase behavior of partially charged ion-containing polymers in polar solvents is studied by further developing a liquid-state (LS) theory with local shortrange interactions. This work is based on the LS theory developed for fully-charged polyelectrolyte solutions. Specific interactions between charged groups of the polymer and counterions, between neutral segments of the polymer, and between charged segments of the polymer are incorporated into the LS theory by an extra Helmholtz free energy from the perturbed-chain statistical associating fluid theory (PC-SAFT). The influence of the sequence structure of the partially charged polymer is modeled by the number of connections between bonded segments. The effects of chain length, charge fraction, counterion valency, and specific short-range interactions are explored. A computational App for salt-free polymer solutions is developed and presented, which allows easy computation of the binodal curve and critical point by specifying values for the relevant model parameters.

Nonelectrostatic Adsorption of Polyelectrolytes and Mediated Interactions between Solid Surfaces

Polymer-mediated interaction between two solid surfaces is directly connected to the properties of the adsorbed polymer layers. Nonelectrostatic interactions with a surface can significantly impact the adsorption of polyelectrolytes to charged surfaces. We use a classical density functional theory to study the effect of various polyelectrolyte solution properties on the adsorption and interaction between two like-charged surfaces. Our results show that nonelectrostatic interactions not only enhance polyelectrolyte adsorption but can also result in qualitatively different salt effects with respect to the adsorbed amount. In particular, we observe decreasing, increasing, and a previously unreported nonmonotonic behavior in the adsorbed amount of polymer with added salt under the conditions studied, although the nonmonotonic regime only occurs for a narrow range in the parameter space. With sufficient nonelectrostatic adsorption, the adsorbed polymer layers produce a long-range repulsive barrier that is strong enough to overcome dispersive interactions that cause surfaces to attract. Concurrently, a short-range bridging attraction is observed when the two polyelectrolyte layers span both the surfaces. Both the repulsive barrier and bridging attraction depend on the charge density of the polymer backbone and the bulk salt concentration but not on the chain length in the semidilute regime studied.

Pressure Effects on Self-Assembly in Mixtures Containing Zwitterionic Amphiphiles

To understand the responses of self-assembly in mixtures containing zwitterionic amphiphilic chains to high pressure, we introduce a self-consistent field theory in combination with a molecular equation-of-state model for them in a primitive way. The free energy density for those in the bulk state is first formulated. Its locally equilibrated excess part is then incorporated into Edwards Hamiltonian along with the electrostatic energy contributions to elicit the saddle point approximation to the partition function with proper self-consistent field equations. It is shown that charge-charge correlations enhance self-assembling tendency for the amphiphiles with the opposite charges on one component side, as the medium dielectric constant ε_r decreases. Those with the opposite charges at the two chain ends respond in a more complicated way to ε_r. Densification by applied pressure strengthens the self-assembly for both at a moderate ε_r, similar to typical phospholipids, but pressure effects are strongly dependent on the position of charges along the chains at a lower ε_r. It is argued that the manipulation of the dielectric environment and disparity in component dispersion interactions can yield useful materials exhibiting various types of baroresponsivity or thermoresponsivity with re-entrant self-assembly.

Screening lengths and osmotic compressibility of flexible polyelectrolytes in excess salt solutions

We report results of small angle neutron scattering measurements made on sodium polystyrene sulfonate in aqueous salt solutions. The correlation length (ξ) and osmotic compressibility are measured as a function of polymer (c) and added salt (cS) concentrations, and the results are compared with scaling predictions and the random-phase approximation (RPA). In Dobrynin et al.'s scaling model the osmotic pressure consists of a counter-ion contribution and a polymer contribution. The polymer contribution is found to be two orders of magnitude smaller than expected from the scaling model, in agreement with earlier observations made on neutral polymers in good solvent condition. RPA allows the determination of single-chain dimensions in semidilute solutions at high polymer and added salt concentrations, but fails for cS≤ 2 M. The χ parameter can be modelled as the sum of an intrinsic contribution (χ0) and an electrostatic term: χ∼χ0 + K'/√cS, where χ0 > 0.5 is consistent with the hydrophobic nature of the backbone of NaPSS. The dependence of χelec∼ 1/√cS disagrees with the random-phase approximation (χelec∼ 1/cs), but agrees with the light scattering results in dilute solution and Dobrynin et al.'s scaling treatment of electrostatic excluded volume.

Near-Critical Phase Behavior in Polyelectrolyte Solutions: Effect of Charge Fluctuations

The critical behaviors in polyelectrolyte (PE) solutions are studied by a renormalized Gaussian fluctuation theory. PEs are fully charged linear wormlike chains. The electrostatic interactions are considered in a continuum solvent while ignoring other interactions. The effects of temperature on the criticality are explored in a salt-free polyanion solution, and the effects of salt are explored in a symmetric mixed solution of polycation and polyanion. An unphysical phase coexistence (UPPC), in which a metastable dense phase coexists with an unstable dilute phase, always exists in the phase diagram. In the near-critical region, the UPPC could interfere with the real phase coexistence. The classical critical point is replaced by a "critical line", giving a flat top for the phase diagram. These behaviors are due to the effect of charge fluctuation in the near-critical region. Our results explain why the mean field approach overestimates the critical salt density by about 10% to experimental data in the study of coacervation between oppositely charged PEs.

Recent progress in the science of complex coacervation

Complex coacervation is an associative, liquid-liquid phase separation that can occur in solutions of oppositely-charged macromolecular species, such as proteins, polymers, and colloids. This process results in a coacervate phase, which is a dense mix of the oppositely-charged components, and a supernatant phase, which is primarily devoid of these same species. First observed almost a century ago, coacervates have since found relevance in a wide range of applications; they are used in personal care and food products, cutting edge biotechnology, and as a motif for materials design and self-assembly. There has recently been a renaissance in our understanding of this important class of material phenomena, bringing the science of coacervation to the forefront of polymer and colloid science, biophysics, and industrial materials design. In this review, we describe the emergence of a number of these new research directions, specifically in the context of polymer-polymer complex coacervates, which are inspired by a number of key physical and chemical insights and driven by a diverse range of experimental, theoretical, and computational approaches.

Wettability of ultra-small pores of carbon electrodes by size-asymmetric ionic fluids

Recently, we studied the phase behavior of ionic fluids under confinement using the classical density functional theory within the framework of the restricted primitive model. The theoretical results indicate that narrowing the pore size may lead to a drastic reduction in the electric double layer capacitance, while increasing the surface electrical potential would improve the ionic accessibility of micropores. In this work, we extend the theoretical investigation to systems containing size-asymmetric electrolytes that may exhibit a vapor-liquid like phase transition in the bulk phase. The effects of pore size and surface electric potential on the phase diagram and microscopic structures of the confined electrolytes were studied over a broad range of parameters. We found that decreasing the pore size or increasing the surface potential could destabilize the liquid phase in micropores, and capillary evaporation could occur regardless of the size asymmetry between cations and anions. Compared to that in a symmetric ionic system, the vapor-liquid phase separation is more likely to take place as the size asymmetry becomes more pronounced. The phase transition would alter the "accessibility" of ions to micropores and lead to coexisting micropores with different surface charge densities as identified by Monte Carlo simulation.

A unified analytical theory of heteropolymers for sequence-specific phase behaviors of polyelectrolytes and polyampholytes

The physical chemistry of liquid-liquid phase separation (LLPS) of polymer solutions bears directly on the assembly of biologically functional dropletlike bodies from proteins and nucleic acids. These biomolecular condensates include certain extracellular materials and intracellular compartments that are characterized as "membraneless organelles." Analytical theories are a valuable, computationally efficient tool for addressing general principles. LLPS of neutral homopolymers is quite well described by theory, but it has been a challenge to develop general theories for the LLPS of heteropolymers involving charge-charge interactions. Here, we present a theory that combines a random-phase-approximation treatment of polymer density fluctuations and an account of intrachain conformational heterogeneity based on renormalized Kuhn lengths to provide predictions of LLPS properties as a function of pH, salt, and charge patterning along the chain sequence. Advancing beyond more limited analytical approaches, our LLPS theory is applicable to a wide variety of charged sequences ranging from highly charged polyelectrolytes to neutral or nearly neutral polyampholytes. This theory should be useful in high-throughput screening of protein and other sequences for their LLPS propensities and can serve as a basis for more comprehensive theories that incorporate nonelectrostatic interactions. Experimental ramifications of our theory are discussed.

Does capillary evaporation limit the accessibility of nonaqueous electrolytes to the ultrasmall pores of carbon electrodes?

Porous carbons have been widely utilized as electrode materials for capacitive energy storage. Whereas the importance of pore size and geometry on the device performance has been well recognized, little guidance is available for identification of carbon materials with ideal porous structures. In this work, we study the phase behavior of ionic fluids in slit pores using the classical density functional theory. Within the framework of the restricted primitive model for nonaqueous electrolytes, we demonstrate that the accessibility of micropores depends not only on the ionic diameters (or desolvation) but also on their wetting behavior intrinsically related to the vapor-liquid or liquid-liquid phase separation of the bulk ionic systems. Narrowing the pore size from several tens of nanometers to subnanometers may lead to a drastic reduction in the capacitance due to capillary evaporation. The wettability of micropores deteriorates as the pore size is reduced but can be noticeably improved by raising the surface electrical potential. The theoretical results provide fresh insights into the properties of confined ionic systems beyond electric double layer models commonly employed for rational design/selection of electrolytes and electrode materials.

Density functional theory for charged fluids

An improved density functional theory (DFT) for an inhomogeneous charged system (including electrolyte and/or polyelectrolyte) is proposed based on fundamental measure theory, thermodynamic perturbation theory and mean-spherical approximation. Our DFT combines the existing treatment of hard-sphere contributions using fundamental measure theory (FMT) with a new treatment of the electrostatic correlations for the non-bonded ions and chain connectivity that are approximated by employing a first-order Taylor expansion, with the reference fluid density determined using the technique from Gillespie et al. [D. Gillespie et al., J. Phys.: Condens. Matter, 2002, 14, 12129]. We show that the first-order Taylor expansion for the non-bonded electrostatic correlations yields numerically comparable results to the more involved second-order expansion. Furthermore, we find that the existing treatment of the chain connectivity correlation predicts a spurious layer-by-layer phase at moderately large Bjerrum lengths, which is avoided in our new treatment. These simplifications and improvements should significantly facilitate the implementation and reduce the computational cost.

Electrostatic correlations and the polyelectrolyte self energy

We address the effects of chain connectivity on electrostaticfluctuations in polyelectrolyte solutions using a field-theoretic, renormalizedGaussian fluctuation (RGF) theory. As in simple electrolyte solutions [Z.-G. Wang,Phys. Rev. E 81, 021501 (2010)], the RGF provides a unified theory forelectrostatic fluctuations, accounting for both dielectric and charge correlationeffects in terms of the self-energy. Unlike simple ions, the polyelectrolyte self energydepends intimately on the chain conformation, and our theory naturally provides aself-consistent determination of the response of intramolecular chain structure topolyelectrolyte and salt concentrations. The effects of the chain-conformation on theself-energy and thermodynamics are especially pronounced for flexiblepolyelectrolytes at low polymer and salt concentrations, where application of thewrong chain structure can lead to a drastic misestimation of the electrostaticcorrelations. By capturing the expected scaling behavior of chain size from dilute tosemi-dilute regimes, our theory provides improved estimates of the self energy at lowpolymer concentrations and correctly predicts the eventual N-independenceof the critical temperature and concentration of salt-free solutions of flexiblepolyelectrolytes. We show that the self energy can be interpreted in terms of aninfinite-dilution energy μ_m,0^el and a finite concentrationcorrelation correction μ^corr which tends to cancel out the formerwith increasing concentration.

A theoretical study on the morphological phase diagram of supported lipid bilayers

A morphological phase diagram is constructed using classical density function theory (CDFT).

The Role of Correlation and Solvation in Ion Interactions with B-DNA

The ionic atmospheres around nucleic acids play important roles in biological function. Large-scale explicit solvent simulations coupled to experimental assays such as anomalous small-angle x-ray scattering can provide important insights into the structure and energetics of such atmospheres but are time- and resource intensive. In this article, we use classical density functional theory to explore the balance among ion-DNA, ion-water, and ion-ion interactions in ionic atmospheres of RbCl, SrCl2, and CoHexCl3 (cobalt hexamine chloride) around a B-form DNA molecule. The accuracy of the classical density functional theory calculations was assessed by comparison between simulated and experimental anomalous small-angle x-ray scattering curves, demonstrating that an accurate model should take into account ion-ion correlation and ion hydration forces, DNA topology, and the discrete distribution of charges on the DNA backbone. As expected, these calculations revealed significant differences among monovalent, divalent, and trivalent cation distributions around DNA. Approximately half of the DNA-bound Rb(+) ions penetrate into the minor groove of the DNA and half adsorb on the DNA backbone. The fraction of cations in the minor groove decreases for the larger Sr(2+) ions and becomes zero for CoHex(3+) ions, which all adsorb on the DNA backbone. The distribution of CoHex(3+) ions is mainly determined by Coulomb and steric interactions, while ion-correlation forces play a central role in the monovalent Rb(+) distribution and a combination of ion-correlation and hydration forces affect the Sr(2+) distribution around DNA. This does not imply that correlations in CoHex solutions are weaker or stronger than for other ions. Steric inaccessibility of the grooves to large CoHex ions leads to their binding at the DNA surface. In this binding mode, first-order electrostatic interactions (Coulomb) dominate the overall binding energy as evidenced by low sensitivity of ionic distribution to the presence or absence of second-order electrostatic correlation interactions.

A Thermodynamic Model for Genome Packaging in Hepatitis B Virus

Understanding the fundamentals of genome packaging in viral capsids is important for finding effective antiviral strategies and for utilizing benign viral particles for gene therapy. While the structure of encapsidated genomic materials has been routinely characterized with experimental techniques such as cryo-electron microscopy and x-ray diffraction, much less is known about the molecular driving forces underlying genome assembly in an intracellular environment and its in vivo interactions with the capsid proteins. Here we study the thermodynamic basis of the pregenomic RNA encapsidation in human Hepatitis B virus in vivo using a coarse-grained molecular model that captures the essential components of nonspecific intermolecular interactions. The thermodynamic model is used to examine how the electrostatic interaction between the packaged RNA and the highly charged C-terminal domains (CTD) of capsid proteins regulate the nucleocapsid formation. The theoretical model predicts optimal RNA content in Hepatitis B virus nucleocapsids with different CTD lengths in good agreement with mutagenesis measurements, confirming the predominant role of electrostatic interactions and molecular excluded-volume effects in genome packaging. We find that the amount of encapsidated RNA is not linearly correlated with the net charge of CTD tails as suggested by earlier theoretical studies. Our thermodynamic analysis of the nucleocapsid structure and stability indicates that ∼10% of the CTD residues are free from complexation with RNA, resulting in partially exposed CTD tails. The thermodynamic model also predicts the free energy of complex formation between macromolecules, which corroborates experimental results for the impact of CTD truncation on the nucleocapsid stability.

Electric double layer capacitance of restricted primitive model for an ionic fluid in slit-like nanopores: A density functional approach

We apply recently developed version of a density functional theory [Z. Wang, L. Liu, and I. Neretnieks, J. Phys.: Condens. Matter 23, 175002 (2011)] to study adsorption of a restricted primitive model for an ionic fluid in slit-like pores in the absence of interactions induced by electrostatic images. At present this approach is one of the most accurate theories for such model electric double layers. The dependencies of the differential double layer capacitance on the pore width, on the electrostatic potential at the wall, bulk fluid density, and temperature are obtained. We show that the differential capacitance can oscillate as a function of the pore width dependent on the values of the above parameters. The number of oscillations and their magnitude decrease for high values of the electrostatic potential. For very narrow pores, close to the ion diameter, the differential capacitance tends to a minimum. The dependence of differential capacitance on temperature exhibits maximum at different values of bulk fluid density and applied electrostatic potential.

Crowding effect on DNA melting: a molecular thermodynamic model with explicit solvent

A molecular thermodynamic model is developed to examine crowding effect on DNA melting. Each pair of nucleotides in double-stranded DNA and each nucleotide in single-stranded DNA are represented by two types of charged Lennard-Jones segments, respectively. Water molecules are mimicked explicitly as spherical particles, embedded in a dielectric continuum. Crowders with varying concentration, size, interaction strength, and chain length are considered. For DNA with a sequence of A(20), the melting temperature is predicted to increase by 1 K in the presence of Ficoll70 and by 7.5 K in the presence of Ficoll70-polyvinyl pyrrolidone360 mixture. The predictions agree well with experimental data. Furthermore, the melting temperature is found to increase with increasing crowder size, but reduce with increasing interaction strength and crowder length. The predicted changes of Gibbs energy, entropy and enthalpy are consistent with experimentally measured values. The study reveals that DNA melting in a crowded environment is influenced by both entropic and enthalpic effects.

Density functional theory for encapsidated polyelectrolytes: a comparison with Monte Carlo simulation

Genome packaging inside viral capsids is strongly influenced by the molecular size and the backbone structure of RNA∕DNA chains and their electrostatic affinity with the capsid proteins. Coarse-grained models are able to capture the generic features of non-specific interactions and provide a useful testing ground for theoretical developments. In this work, we use the classical density functional theory (DFT) within the framework of an extended primitive model for electrolyte solutions to investigate the self-organization of flexible and semi-flexible linear polyelectrolytes in spherical capsids that are permeable to small ions but not polymer segments. We compare the DFT predictions with Monte Carlo (MC) simulation for the density distributions of polymer segments and small ions at different backbone flexibilities and several solution conditions. In general, the agreement between DFT and MC is near quantitative except when the simulation results are noticeably influenced by the boundary effects. The numerical efficiency of the DFT calculations makes it promising as a useful tool for quantification of the structural and thermodynamic properties of viral nucleocapsids in vivo and at conditions pertinent to experiments.

Surfactant two-dimensional self-assembly under confinement

Confinement-induced structural rearrangements in supported self-assembled surfactant layers in aqueous salt solutions are investigated using classical density functional theory. The systematic study of the influence of the nature of electrolyte revealed that 2:1 electrolyte stabilizes the hemicylindrical configuration of ionic surfactant layers, while a confinement-induced transition to a tilted monolayer configuration was found in symmetric 1:1 and 2:2 electrolytes. On the basis of this study, we formulate a general model for the energetics of structural rearrangements in supported surfactant layers. This model provides a basis for directed self-assembly of surfactant templates with desired structure and stability for scalable synthesis of nanocomposite functional materials, templated crystal growth, and biomolecule adsorption.

Molecular thermodynamic model for DNA melting in ionic and crowded solutions

A molecular thermodynamic model is developed to predict DNA melting in ionic and crowded solutions. Each pair of nucleotides in the double-stranded DNA and each nucleotide in the single-stranded DNA are respectively represented by two types of charged Lennard-Jones spheres. The predicted melting curves and melting temperatures T(m) of the model capture the general feature of DNA melting and match fairly well with the available simulation and experimental results. It is found that the melting curve is steeper and T(m) is higher for DNA with a longer chain. With increasing the fraction of the complementary cytosine-guanine (CG) base pairs, T(m) increases almost linearly as a consequence of the stronger hydrogen bonding of the CG base pair than that of adenine-thymine (AT) base pair. At a greater ionic concentration, T(m) is higher due to the shielding effect of counterions on DNA strands. It is observed that T(m) increases in the presence of crowder because the crowder molecules occupy a substantial amount of system volume and suppress the entropy increase for DNA melting. At a given concentration, a larger crowder exhibits a greater suppression for DNA melting and hence a higher T(m). At the same packing fraction, however, a smaller crowder leads to a higher T(m).

Osmotic pressure and packaging structure of caged DNA

We present a theoretical model for aqueous solutions of double-stranded (ds) DNA with explicit consideration of electrostatic interactions, excluded-volume effects, van der Waals attractions, and salt ions. With reasonable parameters estimated from the DNA structure and experimental data for electrolytes, we are able to reproduce the DNA osmotic pressure in the bulk in good agreement with experiment. The predicted DNA osmotic pressure in lambda-bacteriophages is found to coincide with that of the PEG8000 solution that inhibits DNA ejection as reported in recent experiments. Based on the radial distributions of DNA segments and of counterions at different degrees of packaging, we find that in the presence of Mg(2+), DNA forms a multilayer structure near the inner surface of a fully loaded bacteriophage, but at low packing density the DNA segments are depleted from the surface owing to the local condensation of DNA induced by the divalent counterions. By contrast, the multilayer DNA structure is less distinctive in the presence of Na(+) despite the increase of the DNA density at contact, and the depletion near the capsid surface is not found at low packing density.

Density functional theory for planar electric double layers: closing the gap between simple and polyelectrolytes

We report a nonlocal density functional theory (NLDFT) for polyelectrolyte solutions within the primitive model; i.e., the solvent is represented by a continuous dielectric medium, and the small ions and polyions by single and tangentially connected charged hard spheres, respectively. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for hard-sphere repulsion, an extended first-order thermodynamic perturbation theory for chain connectivity, and a quadratic functional Taylor expansion for electrostatic correlations. With the direct and cavity correlation functions of the corresponding monomeric systems as inputs, the NLDFT predicts the segment-level microscopic structures and adsorption isotherms of polyelectrolytes at oppositely charged surfaces in good agreement with molecular simulations. In particular, it faithfully reproduces the layering structures of polyions, charge inversion, and overcharging that cannot be captured by alternative methods including the polyelectrolyte Poisson-Boltzmann equation and an earlier version of DFT. The NLDFT has also been used to investigate the influences of the small ion valence, polyion chain length, and size disparity between polyion segments and counterions on the microscopic structure, mean electrostatic potential, and overcharging in planar electric double layers containing polyelectrolytes.

Simple density functional approach to adsorption of biomolecules on solid surfaces

A simple density functional approach for modeling the adsorption of biomolecules is considered. The model comprises a three-component mixture consisting of spherical and differently charged ions and chain molecules. Spherical ions can form associative bonds with selected segments of a chain. To enable the formation of bonds between chain segments and spherical ions, the statistical associating fluid theory is applied. The present theory is used to study the structure of adsorbed layers, the excess adsorption isotherms, and the capacitance of the double layer.

Theoretical aspects and computer simulations of flexible charged oligomers in salt-free solutions

The structural and thermodynamic properties of a model solution containing flexible charged oligomers and an equivalent number of counterions were studied by means of the canonical Monte Carlo simulation and integral equation theory. The oligomers were represented as freely jointed chains of charged hard spheres. In accordance with the primitive model of electrolyte solutions, the counterions were modeled as charged hard spheres and the solvent as a dielectric continuum. Simulations were performed for a set of model parameters, independently varying the chain length and concentration of the oligomers. Structural properties in the form of pair distribution functions were calculated as functions of model parameters. In addition, thermodynamic properties such as the excess energy of solution and the excess chemical potential of counterions were obtained. These properties were correlated with the conformational averages of oligomers as reflected in the end-to-end distances and radii of gyration obtained from the simulations. The relation with the experimental data for heats of dilution and for the activity coefficient is discussed. Finally, theories based on Wertheim's integral equation approach (product reactant Ornstein-Zernike approach) [J. Stat. Phys. 42, 477 (1986)] in the so-called polymer mean spherical and polymer hypernetted chain approximations were tested against the new and existing computer simulations. For the values of parameters examined in this study, the integral equation theory yields semiquantitative agreement with computer simulations.