Biblioteca Digital

Quantitative description of the thermodynamic consequences of macromolecular crowding (excluded volume nonideality) is an important component of analyses of the thermodynamics and kinetics of noncovalent interactions of biopolymers in vivo and in concentrated polymer solutions in vitro. By analyzing previously published thermodynamic data, we have investigated extensively the comparative applicability of two forms of scaled particle theory (SPT). In both forms, macromolecules are treated as hard spheres, but MSPT, introduced by Ross and Minton, treats the solvent as a structureless continuum, whereas bulk water molecules are included explicitly as hard spheres in BSPT, an approach developed by Berg. Here we use both MSPT and BSPT to calculate the excluded volume component of the macromolecular activity coefficient of hemoglobin (Hb) at concentrations up to 509 mg/ml by fitting osmotic pressure data for Hb and sedimentation equilibrium data for Hb and sickle-cell Hb (HbS). Both forms of SPT also are used here to analyze the effects of other globular proteins (BSA and Hb) on the solubility of HbS. In applying MSPT and BSPT to analyze macromolecular crowding, the extent of hydration delta Hb (in gH2O/gprotein) is introduced as an adjustable parameter to specify the effective (hard sphere) radius of hydrated Hb. In our nonlinear least-squares fittings based on BSPT...

Like the hard sphere expansion (HSE) theory, the hard convex body expansion (HCBE) theory separates any residual thermodynamic property into a contribution from molecular repulsion, which is calculated directly from a hard convex body (HCB) equation of state, and other contributions from molecular attraction, which are obtained by the corresponding states principle (CSP) using pure reference fluids. The HSE theory yields good agreement with the experimental thermodynamic data for light hydrocarbon mixture systems. However, there is a limit to molecular size and shape difference in mixtures where the intermolecular repulsion can be represented by hard sphere mixture. A HCB equation of state developed by Naumann and Leland (1984) is applicable to pure components and their mixtures. The HCB equation of state for a pure component is characterized by two dimensionless geometrical parameters, $\alpha$ and $\tau\sp{-1},$ which are combinations of three molecular dimensions of a convex body--volume(V), surface area(S), and mean radius(R). Two dimensionless geometrical parameters are determined directly from Pitzer's acentric factor. The molecular volume is evaluated by equating the HCB equation of state to the optimal repulsion evaluated by the expansion method. The surface area and the mean radius are obtained from known dimensionless geometrical parameters and molecular volume. Four kinds of convex bodies are considered in this work. These are prolate spherocylinders...

The many-body expansion Vint = ∑i rHS, with rHS being the hard-sphere radius at the start of the repulsive wall of t

Several properties of trapped hard sphere bosons are evaluated using variational Monte Carlo techniques. A trial wave function composed of a renormalized single particle Gaussian and a hard sphere Jastrow function for pair correlations is used to study the sensitivity of condensate and non-condensate properties to the hard sphere radius and the number of particles. Special attention is given to diagonalizing the one body density matrix and obtaining the corresponding single particle natural orbitals and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single particle orbital with highest occupation. The effect of interaction on other quantities such as the ground state energy, the mean radial displacement, and the momentum distribution are calculated as well. Results are compared with Mean Field theory in the dilute limit.; Comment: 11 pages, 10 figures, latex, revtex4b

Simple closed analytical expression for approximate direct correlation function (DCF) for multi--Yukawa hard--core system of particles is presented. The obtained DCF is a solution of the Ornstein--Zernike equation with multi--Yukawa closure valid in the linear approximation in the potential. This approximation includes linear corrections to the hard-- sphere DCF inside the core radius.; Comment: 5 pages

We consider many-body effects on particle scattering in one, two and three dimensional Bose gases. We show that at zero temperature these effects can be modelled by the simpler two-body T-matrix evaluated off the energy shell. This is important in 1D and 2D because the two-body T-matrix vanishes at zero energy and so mean-field effects on particle energies must be taken into account to obtain a self-consistent treatment of low energy collisions. Using the off-shell two-body T-matrix we obtain the energy and density dependence of the effective interaction in 1D and 2D and the appropriate Gross-Pitaevskii equations for these dimensions. We present numerical solutions of the Gross-Pitaevskii equation for a 2D condensate of hard-sphere bosons in a trap. We find that the interaction strength is much greater in 2D than for a 3D gas with the same hard-sphere radius. The Thomas-Fermi regime is therefore approached at lower condensate populations and the energy required to create vortices is lowered compared to the 3D case.; Comment: 22 pages, 6 figures

The properties of a hard-sphere fluid in contact with hard spherical and cylindrical walls are studied. Rosenfeld's density functional theory (DFT) is applied to determine the density profile and surface tension $\gamma$ for wide ranges of radii of the curved walls and densities of the hard-sphere fluid. Particular attention is paid to investigate the curvature dependence and the possible existence of a contribution to $\gamma$ that is proportional to the logarithm of the radius of curvature. Moreover, by treating the curved wall as a second component at infinite dilution we provide an analytical expression for the surface tension of a hard-sphere fluid close to arbitrary hard convex walls. The agreement between the analytical expression and DFT is good. Our results show no signs for the existence of a logarithmic term in the curvature dependence of $\gamma$.; Comment: 15 pages, 6 figures

The surface tension of compliant materials such as gels provides resistance to deformation in addition to and sometimes surpassing that due to elasticity. This article studies how surface tension changes the contact mechanics of a small hard sphere indenting a soft elastic substrate. Previous studies have examined the special case where the external load is zero, so contact is driven by adhesion alone. Here, we tackle the much more complicated problem where, in addition to adhesion, deformation is driven by an indentation force. We present an exact solution based on small strain theory. The relation between indentation force (displacement) and contact radius is found to depend on a single dimensionless parameter: $\omega=\sigma(\mu R)^{-2/3}(9\pi W_{\textrm{ad}}/4)^{-1/3}$, where $\sigma$ and $\mu$ are the surface tension and shear modulus of the substrate, $R$ is the sphere radius, and $W_{\textrm{ad}}$ is the interfacial work of adhesion. Our theory reduces to the Johnson-Kendall-Roberts theory and Young-Dupr\'e equation in the limits of small and large $\omega$ respectively, and compares well with existing experimental data. Our results show that, although surface tension can significantly affect the indentation force, the magnitude of the pull-off load in the partial wetting liquid-like limit is reduced only by 1/3 compared with the JKR limit...

We study a birthday inequality in random geometric graphs: the probability of the empty graph is upper bounded by the product of the probabilities that each edge is absent. We show the birthday inequality holds at low densities, but does not hold in general. We give three different applications of the birthday inequality in statistical physics and combinatorics: we prove lower bounds on the free energy of the hard sphere model and upper bounds on the number of independent sets and matchings of a given size in d-regular graphs. The birthday inequality is implied by a repulsion inequality: the expected volume of the union of spheres of radius r around n randomly placed centers increases if we condition on the event that the centers are at pairwise distance greater than r. Surprisingly we show that the repulsion inequality is not true in general, and in particular that it fails in 24-dimensional Euclidean space: conditioning on the pairwise repulsion of centers of 24-dimensional spheres can decrease the expected volume of their union.

We analyze the phase diagram of a model of hard spheres of chemical radius one, which is defined over a generalized Bethe lattice containing short loops. We find a liquid, two different crystalline, a glassy and an unusual crystalline glassy phase. Special attention is also paid to the close-packing limit in the glassy phase. All analytical results are cross-checked by numerical Monte-Carlo simulations.; Comment: 24 pages, revised version

Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is explicitly found. This allows the derivation of the equation of state for the fluid taking both the virial and the compressibility routes. An analysis of the virial coefficients and the determination of the radius of convergence of the virial series are carried out. Molecular dynamics simulations of the same system are also performed and a comparison between the simulation results for the compressibility factor and theoretical expressions for the same quantity is presented.; Comment: 12 pages, 4 figures; v3: Equation (A.19) corrected (see http://dx.doi.org/10.1063/1.2390712)

We find an improved estimate of the radius of analyticity of the pressure of the hard-sphere gas in $d$ dimensions. The estimates are determined by the volume of multidimensional regions that can be numerically computed. For $d=2$, for instance, our estimate is about 40% larger than the classical one.; Comment: 4 pages, to appear in Journal of Statistical Physics

We study the Asakura-Oosawa model in the "protein limit", where the penetrable sphere radius $R_{AO}$ is much greater than the hard sphere radius $R_c$. The phase behaviour and structure calculated with a full many-body treatment show important qualitative differences when compared to a description based on pair potentials alone. The overall effect of the many-body interactions is repulsive.; Comment: 9 pages and 11 figures, submitted to J. Phys.: Condensed Matter, special issue "Effective many-body interactions and correlations in soft matter"

Using molecular-dynamics simulation, we have calculated the interfacial free energy, \gamma, between a hard-sphere fluid and hard spherical and cylindrical colloidal particles, as functions of the particle radius R and the fluid packing fraction \eta= \rho\sigma^3/6, where \rho and \sigma are the number density and hard-sphere diameter, respectively. These results verify that Hadwiger's theorem from integral geometry, which predicts that \gamma for a fluid at a surface, with certain restrictions, should be a linear combination of the average mean and Gaussian surface curvatures, is valid within the precision of the calculation for spherical and cylindrical surfaces up to \eta about 0.42. In addition, earlier results for \gamma for this system [Bryk, et al., Phys. Rev. E, 68, 031602 (2003)] using a geometrically-based classical Density Functional Theory are in excellent agreement with the current simulation results for packing fractions in the range where Hadwiger's theorem is valid. However, above \eta about 0.42, \gamma(R) shows significant deviations from the Hadwiger form indicating limitations to its use for high-density hard-sphere fluids. Using the results of this study together with Hadwiger's theorem allows one, in principle...

We derive an exact, analytic expression for the fourth virial coefficient of a system of polydisperse spheres under the constraint that the smallest sphere has a radius smaller than a given function of the radii of the three remaining particles.; Comment: 10 pages RevTex with EPS figures

The minimal vertex-cover (or maximal independent-set) problem is studied on random graphs of finite connectivity. Analytical results are obtained by a mapping to a lattice gas of hard spheres of (chemical) radius one, and they are found to be in excellent agreement with numerical simulations. We give a detailed description of the replica-symmetric phase, including the size and the entropy of the minimal vertex covers, and the structure of the unfrozen component which is found to percolate at connectivity $c\simeq 1.43$. The replica-symmetric solution breaks down at $c=e\simeq 2.72$. We give a simple one-step replica symmetry broken solution, and discuss the problems in interpretation and generalization of this solution.; Comment: 32 pages, 9 eps figures, to app. in PRE (01 May 2001)

Using the first seven known virial coefficients and forcing it to possess two branch-point singularities, a new equation of state for the hard-sphere fluid is proposed. This equation of state predicts accurate values of the higher virial coefficients, a radius of convergence smaller than the close-packing value, and it is as accurate as the rescaled virial expansion and better than the Pad\'e [3/3] equations of state. Consequences regarding the convergence properties of the virial series and the use of similar equations of state for hard-core fluids in $d$ dimensions are also pointed out.; Comment: 6 pages, 4 tables, 3 figures; v2: enlarged version, extension to other dimensionalities; v3: typos in references corrected

We report on the crystallization kinetics in an entropically attractive colloidal system using a combination of time resolved scattering methods and microscopy. Hard sphere particles are polystyrene microgels swollen in a good solvent (radius a=380nm, starting volume fraction 0.534) with the short ranged attractions induced by the presence of short polymer chains (radius of gyration rg = 3nm, starting volume fraction 0.0224). After crystallization, stacking faulted face centred cubic crystals coexist with about 5% of melt remaining in the grain boundaries. From the Bragg scattering signal we infer the amount of crystalline material, the average crystallite size and the number density of crystals as a function of time. This allows to discriminate an early stage of conversion, followed by an extended coarsening stage. The small angle scattering (SALS) appears only long after completed conversion and exhibits Furukawa scaling for all times. Additional microscopic experiments reveal that the grain boundaries have a reduced Bragg scattering power but possess an increased refractive index. Fits of the Furukawa function indicate that the dimensionality of the scatterers decreases from 2.25 at short times to 1.65 at late times and the characteristic length scale is slightly larger than the average crystallite size. Together this suggests the SALS signal is due scattering from a foam like grain boundary network as a whole.; Comment: 33 pages...

A point process is R-dependent, if it behaves independently beyond the minimum distance R. This work investigates uniform positive lower bounds on the avoidance functions of R-dependent simple point processes with a common intensity. Intensities with such bounds are described by the existence of Shearer's point process, the unique R-dependent and R-hard-core point process with a given intensity. This work presents several extensions of the Lov\'asz Local Lemma, a sufficient condition on the intensity and R to guarantee the existence of Shearer's point process and exponential lower bounds. Shearer's point process shares combinatorial structure with the hard-sphere model with radius R, the unique R-hard-core Markov point process. Bounds from the Lov\'asz Local Lemma convert into lower bounds on the radius of convergence of a high-temperature cluster expansion of the hard-sphere model. This recovers a classic result of Ruelle on the uniqueness of the Gibbs measure of the hard-sphere model via an inductive approach \`a la Dobrushin.

This work is concerned with the theoretical estimation of the low-shear viscosity of concentrated suspensions of charged-stabilized latex particles. Calculations are based on the assumption that particles interacting through purely repulsive potentials behave as equivalent hard-spheres (HS), and suspension viscosity may be analyzed in the framework of HS systems. In order to predict numerically the HS radius, the pair potential due to double-layer interaction, as a function of particle concentration, was investigated by using Poisson-Boltzmann theory and the cell model. Calculations explain appropriately experimental data for a wide range of particle sizes, volume fractions and salt concentrations. The problem concerning the effective surface charge of latex particles is also discussed.