A Hard Sphere Model for Bimolecular Recombination of Heavy Ions

We propose a hard sphere model of bimolecular recombination RM+ + X– → MX + R, where M+ is an alkali ion, X– is a halide ion, and R is a neutral rare gas or mercury atom. Calculations are carried out for M+ = Cs+, X– = Br–, R = Ar, Kr, Xe, Hg, for collision energies in the range from 1 to 10 eV, and for distributions of the RM+ complex internal energy corresponding to temperatures of 500, 1000, and 2000 K. The excitation functions and opacity functions of bimolecular recombination in the hard sphere approximation are found, and the classification of the collisions according to the sequences of pairwise encounters of the particles is considered. In more than half of all the cases, recombination occurs due to a single impact of the Br– ion with the R atom. For the recombination XeCs+ + Br–, the hard sphere model enables one to reproduce the most important characteristics of the collision energy dependence of the recombination probability obtained within the framework of quasiclassical trajectory calculations.

Method for investigating rarefied gas flow around a cylindrical surface at arbitrary Knudsen numbers

A moment method for solving the linearized kinetic Boltzmann equation for arbitrary Knudsen numbers is presented. The isothermal flow of a rarefied gas around a cylindrical surface (the limiting cylindrical Couette problem) is investigated. The moments of the collision integral are calculated for the hard sphere model. The moment of resistance force acting per unit length of the surface, the profile of the gas flow velocity in the transient regime, and the gas velocity on the surface are calculated.

Reaction Rate Theory-Based Mathematical Approximation For The Amount Of Time It Takes For Cellular Respiration To Occur

The venerable process of cellular respiration is essential for cells to produce energy from glucose molecules, in order to carry out cellular work. The process is responsible for producing molecules of ATP, a molecule which is thermodynamically coupled with other biochemical and biophysical processes in order to provide energy for such processes to occur. While the process of cellular respiration is essential to biology, one cycle of the process occurs only in a matter of milliseconds, and so, it would be impractical to measure the time it takes for the process to occur through conventional means. Therefore, using concepts from reaction rate theory, particularly Marcus Theory of electron transfer, Michaelis-Menten kinetics for enzymatic catalysis, and the hard-sphere model of collision theory, I formulate and propose a mathematical approximation for the amount of time it takes forcellular respiration to occur. Through this heuristic approach, quantitatively knowing the amount of time it takes for one cycle of cellular respiration to occur could potentially have future applications in biological research.

Convergence of coupling-parameter expansion-based solutions to Ornstein-Zernike equation in liquid state theory

The objective of this paper is to investigate the convergence of coupling-parameter expansion-based solutions to Ornstein-Zernike equation in liquid state theory. The analytically solved Baxter's adhesive hard sphere model is analyzed first using coupling-parameter expansion. It is found that the expansion provides accurate approximations to solutions - including the liquid-vapor phase diagram - in most parts of the phase plane. However, it fails to converge in the region where the model has only complex solutions. Similar analysis and results are, then, obtained using analytical solutions within the mean spherical approximation for the hard-core Yukawa potential. Next, convergence of the expansion is analyzed for the Lennard-Jonnes potential using an accurate density-dependent bridge function in the closure relation. Numerical results are presented which show convergence of correlation functions, compressibility versus density profiles, etc., in the single as well as two phase regions. Computed liquid-vapor phase diagrams, using two independent schemes employing the converged profiles, compare excellently with simulation data. Results obtained for the generalized Lennard-Jonnes potential, with varying repulsive exponent, also compare well with simulation data. All these results together establish the coupling-parameter expansion as a practical tool for studying single component fluid phases modeled via general pair-potentials.

Comparison of Huggins Coefficients and Osmotic Second Virial Coefficients of Buffered Solutions of Monoclonal Antibodies

The Huggins coefficient kH is a well-known metric for quantifying the increase in solution viscosity arising from intermolecular interactions in relatively dilute macromolecular solutions, and there has been much interest in this solution property in connection with developing improved antibody therapeutics. While numerous kH measurements have been reported for select monoclonal antibodies (mAbs) solutions, there has been limited study of kH in terms of the fundamental molecular interactions that determine this property. In this paper, we compare measurements of the osmotic second virial coefficient B22, a common metric of intermolecular and interparticle interaction strength, to measurements of kH for model antibody solutions. This comparison is motivated by the seminal work of Russel for hard sphere particles having a short-range “sticky” interparticle interaction, and we also compare our data with known results for uncharged flexible polymers having variable excluded volume interactions because proteins are polypeptide chains. Our observations indicate that neither the adhesive hard sphere model, a common colloidal model of globular proteins, nor the familiar uncharged flexible polymer model, an excellent model of intrinsically disordered proteins, describes the dependence of kH of these antibodies on B22. Clearly, an improved understanding of protein and ion solvation by water as well as dipole–dipole and charge–dipole effects is required to understand the significance of kH from the standpoint of fundamental protein–protein interactions. Despite shortcomings in our theoretical understanding of kH for antibody solutions, this quantity provides a useful practical measure of the strength of interprotein interactions at elevated protein concentrations that is of direct significance for the development of antibody formulations that minimize the solution viscosity.

Effective hard-sphere model of diffusion in aqueous polymer solutions

An effective hard-sphere model of the diffusion and cross-diffusion of salt in unentangled polymer solutions is developed. Given the viscosity, sedimentation coefficient and osmotic pressure of the polymer, the model predicts the diffusion and cross-diffusion coefficients as functions of the polymer concentration and molecular weight. The results are compared with experimental data on NaCl diffusion in aqueous polyethylene glycol solutions, showing good agreement at polymer molecular weights up to 400\,g/L. At higher molecular weights the model becomes less accurate, likely because of the effects of entanglement. The tracer Fickian diffusivity can be written in the form of a Stokes-Einstein equation containing the solution viscosity. For NaCl diffusion in polyethylene glycol solutions, the Stokes-Einstein equation breaks down as the polymer size increases. Using Batchelor's viscous correction factor to determine an effective viscosity experienced by the salt ions within the polymer matrix leads to much closer agreement with experiment.

Effective hard-sphere model of diffusion in aqueous polymer solutions

An effective hard-sphere model of the diffusion and cross-diffusion of salt in unentangled polymer solutions is developed. Given the viscosity, sedimentation coefficient and osmotic pressure of the polymer, the model predicts the diffusion and cross-diffusion coefficients as functions of the polymer concentration and molecular weight. The results are compared with experimental data on NaCl diffusion in aqueous polyethylene glycol solutions, showing good agreement at polymer molecular weights up to 400 g/L. At higher molecular weights the model becomes less accurate, likely because of the effects of entanglement. The tracer Fickian diffusivity can be written in the form of a Stokes-Einstein equation containing the solution viscosity. For NaCl diffusion in polyethylene glycol solutions, the Stokes-Einstein equation breaks down as the polymer size increases. Using Batchelor’s viscous correction factor to determine an effective viscosity experienced by the salt ions within the polymer matrix leads to much closer agreement with experiment.

Thermophysical Properties of 1-Octyl-3-Methylimidazolium Acetate with Organic Solvents

Ionic liquid (IL) usually possesses high viscosity. In this work, the selected organic solvents, namely, dimethyl sulfoxide, N,N-dimethylacetamide, and N,N-dimethylformamide, were used as the diluents to lower IL viscosity. The thermophysical properties of the densities and viscosities for the binary mixtures of IL (i.e., 1-octyl-3-methylimidazolium acetate) with solvents were studied at normal pressure in the temperature ranges of 303.15 K to 348.15 K. The effects of the organic solvents on lowering IL viscosity were quantitatively evaluated. The excess properties of the mixtures were calculated to analyze the interactions between IL and solvents. The hard-sphere model was employed to reproduce the viscosity behavior of the pure substances and binary mixtures.