On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state.

Transverse Density Fluctuations around the Ground State Distribution of Counterions near One Charged Plate: Stochastic Density Functional View

We consider the Dean–Kawasaki (DK) equation of overdamped Brownian particles that forms the basis of the stochastic density functional theory. Recently, the linearized DK equation has successfully reproduced the full Onsager theory of symmetric electrolyte conductivity. In this paper, the linear DK equation is applied to investigate density fluctuations around the ground state distribution of strongly coupled counterions near a charged plate, focusing especially on the transverse dynamics along the plate surface. Consequently, we find a crossover scale above which the transverse density dynamics appears frozen and below which diffusive behavior of counterions can be observed on the charged plate. The linear DK equation provides a characteristic length of the dynamical crossover that is similar to the Wigner–Seitz radius used in equilibrium theory for the 2D one-component plasma, which is our main result. Incidentally, general representations of longitudinal dynamics vertical to the plate further suggest the existence of advective and electrical reverse-flows; these effects remain to be quantitatively investigated.

Modified method of conductometric data analysis to calculate the conductivity of surfactant ions

Methodology for simple analytical refinement of the equivalent electrical conductivities of surfactant ions and counterions was proposed in the framework of the Debye – Hückel – Onsager theory as applied to surfactant dispersions at various concentrations. The developed methodology is based on the use of the mathematical form for the concentration dependencies of the specific conductivity in the premicellar region and makes it possible to calculate the equivalent conductivities of surfactant ions both under infinite dilution conditions and near the CMC. One of the advantages of the described method is the possibility of calculating the ion conductivities in the presence of a minimum number of experimental points (formally, a straight line can be constructed and its tangent of the angle of inclination can be determined even by two points corresponding to region 0.2 CMC — 0.8 CMC). Using the values of the equivalent conductivities of surfactant ions and counterions calculated for the required concentrations, allows to determine the parameters of the solution more accurately, including the contribution of micelles to the total conductivity of the solution.

Modified method of conductometric data analysis to calculate the degree of ionization and conductivity of micelles

Methods for calculation of specific conductance of ions and micelles and the degree of micelle ionization using conductometric data in various approximations of the Debye – Hückel – Onsager theory were considered. The analysis of the existing calculation methods was carried out to identify their drawbacks and to suggest ways of their elimination. The calculation method of the micellar parameters on the basis of conductometric data using micellar size was modified, and a new formula for determining the degree of micelle ionization was obtained. All calculations using the modified method were performed in the first and the second approximations, and the newly obtained values of the micellar parameters are in greater agreement with the results of other studies. Based on the calculations performed, it was shown that the contribution of micelles to the total conductivity of micellar solution cannot be neglected, since at high concentrations the contribution of micelles exceeds the contribution of counterions and can exceed 50%.

Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory

Due to failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as DSMC to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. Here, evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with applicability in the rarefied gas regime, are derived. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients, that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier-Stokes-Fourier (NSF) solutions for two one-dimensional steady-state problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement to DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to NSF solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed.

Frequency Variation of the AC Order Parameter Susceptibility of the Metamagnetic Ising Model

The extensive investigation of the absorptive and reactive parts of the AC order parameter susceptibility spectra of iron group dihalides, which is obtained on the basis of Onsager theory of irreversible processes, revealed the fact that the diagonal phenomenological rate coefficients γs and γm have an important impact on the nature of the order parameter relaxation process. The number of the relaxation peaks appearing in the double logarithmic plots of χs′′ versus field frequency ω and the number of plateau regions in χs′ spectrum depends on the values of γs and γm. Only for γs≫γm does the relaxation evolve from a simple Debye exponential at high temperatures to a two-step process at lower temperatures in which there exist two long relaxation times characterizing the relaxation of staggered magnetization. In parallel with these characteristics of the order parameter relaxation, Cole-Cole plots (χs′′-χs′) are shown to consist of two arcs in the metamagnetic phase and of a semicircle in the paramagnetic phase.