Concentration dependence of excluded volume effects

The concentration dependence of the excluded volume effects in polymer solutions is investigated. Through thermodynamic arguments for the interpenetration of polymer segments and the free energy change, we show that the disappearance of the excluded volume effects should occur at medium concentration. The result is in accord with the recent experimental observations.     

Solution of the excluded volume problem for biaxial particles

We report the solution of the excluded volume problem for a pair of biaxial hard molecules; namely, sphero-platelets. As an application of this result we study the isotropic to nematic liquid crystal transition for a fluid composed of these particles in the Onsager limit (length δ breadth or width). We show that the range of stability of the isotropic phase decreases with increasing particle biaxiality.     

Solution of the excluded volume problem for biaxial particles

Abstract

We report the solution of the excluded volume problem for a pair of biaxial hard molecules; namely, sphero-platelets. As an application of this result we study the isotropic to nematic liquid crystal transition for a fluid composed of these particles in the Onsager limit (length δ breadth or width). We show that the range of stability of the isotropic phase decreases with increasing particle biaxiality.     

Macroion adsorption: the crucial role of excluded volume and co-ions

The adsorption of charged colloids (macroions) onto an oppositely charged planar substrate is investigated theoretically. Taking properly into account the finite size of the macroions, unusual behaviors are reported. It is found that the role of the co-ions (the little salt-ions carrying the same sign of charge as that of the substrate) is crucial in understanding the mechanisms involved in the process of macroion adsorption. In particular, the co-ions can accumulate near the substrate's surface and lead to a counterintuitive surface charge amplification.     

Effect of excluded volume interactions on the interfacial properties of colloid-polymer mixtures

We report a numerical study of equilibrium phase diagrams and interfacial properties of bulk and confined colloid-polymer mixtures using grand canonical Monte Carlo simulations. Colloidal particles are treated as hard spheres, while the polymer chains are described as soft repulsive spheres. The polymer-polymer, colloid-polymer, and wall-polymer interactions are described by density-dependent potentials derived by Bolhuis and Louis [Macromolecules 35, 1860 (2002)]. We compared our results with those of the Asakura-Oosawa-Vrij model [J. Chem. Phys. 22, 1255 (1954); J. Polym Sci 33, 183 (1958); Pure Appl. Chem. 48, 471 (1976)] that treats the polymers as ideal particles. We find that the number of polymers needed to drive the demixing transition is larger for the interacting polymers, and that the gas-liquid interfacial tension is smaller. When the system is confined between two parallel hard plates, we find capillary condensation. Compared with the Asakura-Oosawa-Vrij model, we find that the excluded volume interactions between the polymers suppress the capillary condensation. In order to induce capillary condensation, smaller undersaturations and smaller plate separations are needed in comparison with ideal polymers.     

Algorithm for rapid calculation of excluded volume of large molecules

An algorithm is described for rapid calculation of excluded volume of large molecules. The excluded volume is defined based on coordinates of constituent atoms as the volume of overlapping spheres, each standing for a space around an atom inaccessible for a solvent molecule. A computer program based on the algorithm has been tested on a protein, ovomucoid. The accuracy of the numerical calculation is discussed.     

Effects of excluded volume interaction and dimensionality on diffusion-mediated reactions

The kinetic problem of a diffusion-mediated reaction, in which minority reactants are immobile and majority reactants are mobile, is known as the target problem. The standard theory of the target problem ignores the excluded volume interaction between the mobile reactants. Recently, a new theory of the target problem was proposed where the effect of excluded volume interaction was analytically investigated using a lattice model with prohibited double occupancy of the lattice sites. The results of that theory are approximate and need verification. In this work, we perform Monte Carlo simulations on lattices and use their results to assess the accuracy of the analytical theory. We also generalize our theory to the case of different dimensionality and perform calculations for lattices in one- and two-dimensional systems. The analytical results accurately reproduce the simulation results except in the dilute limit in one dimension. For any dimensions, the decay of the target survival probability is accelerated by the presence of excluded volume interaction.     

Kinetic effects of excluded volume and selective adsorption in macromolecule solutions

Kinetic effects of excluded volume and selective adsorption in macromolecule solutions have been studied for an arbitrary position of reacting groups along the chain. It has been shown that the reactivities of similar functional groups can depend upon their location along the chain and also upon the nature of the solvent.     

The optimized Rouse-Zimm theory of excluded volume effects on chain dynamics

Based on the optimized Rouse-Zimm (ORZ) approximation to the Kirkwood diffusion equation, we investigate the effects of excluded volume interactions on the single chain dynamics. By incorporating the nonuniformly expanded moments of interbead distances into the expressions for the diffusion and structure matrices appearing in the ORZ diffusion equation, we obtain the general relaxation spectrum for flexible chains that is valid over the range from theta; solvents to good solvents. The present theory involves four parameters: the Kuhn statistical length b(0), the bead number N, the excluded volume parameter z, and the hydrodynamic interaction parameter h(*). These model parameters are determined from structural data of polymers with the aid of the quasi-two-parameter theory. The set of relaxation times of ORZ normal modes calculated with these bead-and-spring model parameters enables the theoretical prediction of various frictional and dynamical properties of polymers within a unified framework. The present ORZ theory generalizes the Ptitsyn-Eizner-type approaches by incorporating the nonuniform chain expansion effect into the structure matrix as well as the diffusion matrix.     

Polymers in an external periodic field: the effect of the excluded volume interactions

By developing and making use of the "transfer operator" formalism, we calculate the number density and average Flory end-to-end distance of the polymers placed in an external periodic field. The considered mathematical problem is of immediate relevance for such realistic physical systems as the homopolymers immersed in the host structure of alternating layers that have different affinities for homopolymers (e.g., lamellar microphases of copolymers, ripple morphology of the mixed brush, and lipidwater systems). In contrast to the conventional ground state dominance approximation, the developed method makes it possible to calculate the characteristic size (Flory radius R(F)) of the polymers in the direction of applied external periodic field, with the effect of the excluded volume taken into account. The excluded volume interactions are shown to qualitatively change the behavior of R(F) as a function of the reduced field strength theta relative to the case of ideal Gaussian polymers. In particular, in the limit of strong fields theta>1 the average Flory radius R(F) is found to saturate to its minimal value, which is calculated as a function of the excluded volume parameter u. This finding is in distinct contrast to the result for the Flory radius R(F) in the case of ideal polymers where R(F) approaches zero as the interaction parameter theta increases.     

Response of the mean-square optical anistropy of chain molecules to the imposition of excluded volume

The influence of the chain expansion produced by excluded volume on the mean-square optical anisotropy has been studied in six types of polymers. The mean-square optical anistropy for a specified configuration is calculated using the valence optical scheme. Realistic rotational isomeric state models are used for the configurational statistics of the unperturbed chains. Excluded volume is introduced by hard sphere interactions. Results obtained with chains of 100, 200, 300, and 400 bonds permit extrapolation to the behavior expected for much longer chains. The mean-square optical anisotropy of polyethylene is insensitive to excluded volume. A similar conclusion was obtained several years ago in a study of chains confined to a tetrahedral lattice and weighted in a manner appropriate for the short-range interactions in polyethylene.² Different behavior is seen in poly(vinyl chloride), poly(vinyl bromide), polystyrene, poly(p-chlorostyrene), and poly(p-bromostyrene). The mean-square optical anisotropy of these five vinyl polymers is sensitive to the imposition of excluded volume if the stereochemical composition is exclusively racemic. Much smaller effects are seen in meso chains and in chains with Bernoullian statistics and an equal probability for meso and racemic dyads.     

Effect of the excluded volume on specific rate of combination reactions between polymer radicals

The specific rate k_D for reaction between polymer radicals is formulated when the potential of average force on the basis of the excluded volume affects the motion of the polymer radicals. This rate is given by \documentclass{article}\pagestyle{empty}\begin{document}$ k_D = Fk_S \left( {{\rm with}\ {F} = \sum\limits_{s = 0}^\infty {{{[ ‐ 2(\alpha ^2 ‐ 1)]} \mathord{\left/ {\vphantom {{[ ‐ 2(\alpha ^2 ‐ 1)]} {(s + 1)^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern‐\nulldelimiterspace} 2}} }}} \right. \kern‐\nulldelimiterspace} {(s + 1)^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern‐\nulldelimiterspace} 2}} }}} } \right) $\end{document} where k_S is specific rate of reaction between radical chain ends and α is the average expansion of the polymer arising from the long-range effects. The effect of the excluded volume reduces k_D. F depends on the degree of polymerization of the polymer radical when α ≠ 1. These results are discussed in terms of the experimental data for very low polymer concentrations.     

Incorporating the excluded solvent volume and surface charges for computing solvation free energy

Gauss's law or Poisson's equation is conventionally used to calculate solvation free energy. However, the near‐solute dielectric polarization from Gauss's law or Poisson's equation differs from that obtained from molecular dynamics (MD) simulations. To mimic the near‐solute dielectric polarization from MD simulations, the first‐shell water was treated as two layers of surface charges, the densities of which are proportional to the electric field at the solvent molecule that is modeled as a hard sphere. The intermediate water was treated as a bulk solvent. An equation describing the solvation free energy of ions using this solvent scheme was derived using the TIP3P water model. © 2013 Wiley Periodicals, Inc.     

Electrical double layer around a spherical colloid particle: the excluded volume effect

The influence of the excluded volume effect on both the spatial distribution of ionic species and the electrostatic potential distribution in the neighborhood of a suspended spherical particle is examined on the basis of a modified Poisson-Boltzmann equation, which takes into account the finite ion size by means of a Langmuir-type correction. We find that kappaa (kappa and a being the reciprocal Debye length and the particle radius, respectively) ceases to be a valid parameter for the characterization of the electrical double layer, and that it is necessary to use both parameters kappa and a to characterize adequately the system. We also find that the excluded volume effect considerably increases the surface potential (for a given value of the surface charge density) as compared to the case when ideal ion behavior is assumed. This suggests the use of the particle charge rather than the surface potential in order to characterize the system. Because of this, an approximate equation for the surface charge density of spherical colloid particles, valid for a wide range of system parameter values, is also reported.     

The importance of excluded solvent volume effects in computing hydration free energies

Continuum dielectric methods such as the Born equation have been widely used to compute the electrostatic component of the solvation free energy, DeltaG(solv)(elec), because they do not need to include solvent molecules explicitly and are thus far less costly compared to molecular simulations. All of these methods can be derived from Gauss Law of Maxwell's equations, which yields an analytical solution for the solvation free energy, DeltaG(Born), when the solute is spherical. However, in Maxwell's equations, the solvent is assumed to be a structureless continuum, whereas in reality, the near-solute solvent molecules are highly structured unlike far-solute bulk solvent. Since we have recently reformulated Gauss Law of Maxwell's equations to incorporate the near-solute solvent structure by considering excluded solvent volume effects, we have used it in this work to derive an analytical solution for the hydration free energy of an ion. In contrast to continuum solvent models, which assume that the normalized induced solvent electric dipole density P(n) is constant, P(n) mimics that observed from simulations. The analytical formula for the ionic hydration free energy shows that the Born radius, which has been used as an adjustable parameter to fit experimental hydration free energies, is no longer ill defined but is related to the radius and polarizability of the water molecule, the hydration number, and the first peak position of the solute-solvent radial distribution function. The resulting DeltaG(solv)(elec) values are shown to be close to the respective experimental numbers.     

Influence of excluded volume on the conformational property of tail-like chain on the simple cubic lattice

The influence of excluded volume on the conformational property of linear tail-like chain with one end attached to a flat surface is investigated by means of dynamic Monte Carlo method. Conformational properties such as mean-square end-to-end distance 〈R²〉, mean-square radius of gyration 〈S²〉 and mean asphericity parameter 〈A〉 are calculated for random walking (RW) and self-avoiding walking (SAW) tail-like chains on the simple cubic lattice. We find that the EV has nearly the same effect on 〈R²〉 as on 〈S²〉: (1) 〈R²〉_SAW/〈R²〉_RW≈〈S²〉_SAW/〈S²〉_RW∝n^0.204±0.05, where n is the chain length, and (2) the limiting value of 〈R²〉/〈S²〉≈7.7 for both chains. The distribution P(R) of the SAW tail-like chain can be expressed as a R⁴ correction of that of the RW one. We find that the value 〈A〉 of the SAW tail-like chain is bigger than that of the RW tail-like chain for all chain lengths, and the limiting values are 0.446±0.006 and 0.403±0.005 respectively.     

Application of the padé approximant method to excluded volume effects in polymer chains

Closed formulas for the expansion factor α and the h function appearing in the second virial coefficient are derived by the Padé approximant method, using the first two or three series coefficients. The equations for α agree well with experimental results for small z, the excluded volume parameter. The equation for h agrees well with data over the entire accessible range of z.     

Molecular silverware. I. General solutions to excluded volume constrained problems

General mathematical solutions to excluded volume constrained problems in computational chemistry are reported. The solutions have been used to create a new family of molecular modeling algorithms to facilitate the study of molecular interactions in condensed phases. The new algorithms, collectively known as Molecular Silverware, are for the most part interactive and designed for packing, solvating, and sampling molecules embedded in simple or complex topological environments. Multifolded, disconnected, or porous molecular structures are permitted. Molecular Silverware assists the preparation of Monte Carlo and molecular dynamics simulations at a small fraction of the total simulation time. Primary targets for applications include the study of molecular recognition mechanisms and the selective binding of DNA, RNA, peptides, saccharides and other biopolymers in solution as well as the prediction of phase separation behavior and physical properties of non-crystalline condensed phases such as bulk polymers, polymer blends, organic liquids, membranes, micelles, gels, crosslinked networks, glasses, and amorphous heterogeneous catalysts. As a result of this new approach to excluded volume constraints, the computer simulation of noncrystalline condensed phases is no longer hampered by the lack of a general and efficient method for the creation and configurational sampling of small and large molecular assemblies at high densities.