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.     

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.     

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.     

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.     

An analytical approximation for the orientation-dependent excluded volume of tangent hard sphere chains of arbitrary chain length and flexibility

Onsager-like theories are commonly used to describe the phase behavior of nematic (only orientationally ordered) liquid crystals. A key ingredient in such theories is the orientation-dependent excluded volume of two molecules. Although for hard convex molecular models this is generally known in analytical form, for more realistic molecular models that incorporate intramolecular flexibility, one has to rely on approximations or on computationally expensive Monte Carlo techniques. In this work, we provide a general correlation for the excluded volume of tangent hard-sphere chains of arbitrary chain length and flexibility. The flexibility is introduced by means of the rod-coil model. The resulting correlation is of simple analytical form and accurately covers a wide range of pure component excluded volume data obtained from Monte Carlo simulations of two-chain molecules. The extension to mixtures follows naturally by applying simple combining rules for the parameters involved. The results for mixtures are also in good agreement with data from Monte Carlo simulations. We have expressed the excluded volume as a second order power series in sin?(γ), where γ is the angle between the molecular axes. Such a representation is appealing since the solution of the Onsager Helmholtz energy functional usually involves an expansion of the excluded volume in Legendre coefficients. Both for pure components and mixtures, the correlation reduces to an exact expression in the limit of completely linear chains. The expression for mixtures, as derived in this work, is thereby an exact extension of the pure component result of Williamson and Jackson [Mol. Phys. 86, 819-836 (1995)].     

A modification of Koopmans' theorem by imposition of the virial theorem in molecules

Imposition of the virial theorem on Koopmans' theorem permits the introduction of some relaxation effect in the electronic cloud of atomic (less than 5%) or molecular (less than 1.3% for the systems studied) systems and a partitioning of the ionization energy. The method is applied in some diatomic hydrides. It is observed that the imposition of the virial theorem improves the ionization of the innermost molecular orbitals significantly, while the improvement is negligible for the outermost orbitals. The ionization energy is divided among three different terms that elucidate some aspects of the nature of the ionization process.     

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.     

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.     

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.     

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.     

Thermodynamics of polymeric fluids – effect of volume on the configurational entropy of chain molecules

Various conformation‐dependent properties of chain molecules have been successfully treated within the rotational isomeric state approximation. The conformation entropy is one of such properties which can be readily defined by the partition function, the sum of all possible configurations of the chain. Flexible polymers often exhibit crystallization and in some cases liquid‐crystallization as well. In these first‐order transitions, changes in the spatial arrangement of polymer chains are considered to be a major factor involved. In order to explicitly determine the conformational contribution to the melting entropy, the latent entropy observed under the isobaric condition must be corrected for the volume change. The entropy separation involves a hypothetical assumption that the volume of the isotropic fluid may be compressed to that of the solid state without affecting the configurational part of the entropy of molecules. Finally thermodynamic significance of the conformation entropy in these transitions is emphasized on the basis of the critical studies of the entropy‐volume relation of chain molecules in the liquid state.     

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.     

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.