scholarly journals A Simple Free Energy for the Isotropic-Nematic Phase Transition of Rods

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Remco Tuinier
Keyword(s):  
Free Energy ◽  
Nematic Phase ◽  
Analytical Form ◽  
Orientation Distribution ◽  
Scaled Particle Theory ◽  
Particle Theory ◽  
Aspect Ratios ◽  
Wide Range ◽  
Hard Rods ◽  
Simple Analytical Form

A free energy expression is proposed that describes the isotropic-nematic binodal concentrations of hard rods. A simple analytical form for this free energy was yet only available using a Gaussian trial function for the orientation distribution function (ODF), leading, however, to a significant deviation of the predicted binodals. The new free energy proposed here is based upon a rationalized correction to the orientational and packing entropies when using the Gaussian ODF. In combination with Parsons-Lee theory or scaled particle theory, it enables describing the isotropic-nematic phase coexistence concentrations of rods accurately using the simple Gaussian ODF for a wide range of aspect ratios.

scholarly journals Use of scaled-particle theory in the assessment of the Ph4As+/Ph4B− assumption for single ions

1979 ◽  
Vol 57 (1) ◽  
pp. 71-76 ◽  
Author(s):  
Michael H. Abraham ◽  
Asadollah Nasehzadeh
Keyword(s):  
Free Energy ◽  
Recent Work ◽  
Scaled Particle Theory ◽  
Cavity Formation ◽  
Energy Term ◽  
Free Energies ◽  
Particle Theory ◽  
Novel Method ◽  
Energy Of Interaction ◽  
Solvent Molecules

A novel method for the assessment of the Ph4As+/Ph4B− assumption for free energies of transfer of single ions has recently been suggested by Treiner, and used by him to deduce that the assumption is not valid for transfers between water, propylene carbonate, sulpholane, dimethylsulphoxide, N-methyl-2-pyrrolidone, and perhaps also dimethylformamide. The basis of the method is the estimation of the free energy of cavity formation by scaled-particle theory, together with the hypothesis that the free energy of interaction of Ph4As+ (or Ph4B−) with solvent molecules is the same in all solvents, ΔGt0(int) = 0. It is shown in the present paper that (a) whether or not the Ph4As+/Ph4B− assumption applies to transfer to a given solvent depends on which other solvent is taken as the reference solvent in Treiner's method, (b) the calculation of the cavity free energy term by scaled-particle theory and by the theory of Sinanoglu – Reisse – Moura Ramos (SRMR) yields values so different that the method cannot be considered reliable, (c) the calculation of cavity enthalpies and entropies for Ph4As+ or Ph4B− by scaled-particle theory yields results that are chemically not reasonable, (d) the hypothesis that ΔGt0(int) = 0 conflicts with SRMR theory, and (e) the conclusions reached by Treiner are not in accord with recent work that in general supports the Ph4As+/Ph4B− assumption for solvents that are rejected by Treiner.

Thermodynamics of transfer of Ph4C; scaled-particle theory and the Ph4As+/Ph4B− assumption for single ions

1979 ◽  
Vol 57 (15) ◽  
pp. 2004-2009 ◽  
Author(s):  
Michael H. Abraham ◽  
Asadollah Nasehzadeh
Keyword(s):  
Free Energy ◽  
Total Free Energy ◽  
Scaled Particle Theory ◽  
Free Energies ◽  
Particle Theory ◽  
Free Energy Of Transfer ◽  
Enthalpy And Entropy ◽  
Interaction Term ◽  
Energy Of Transfer ◽  
Entropy Of Transfer

Free energies of transfer of Ph4C from acetonitrile to 20 other solvents have been calculated from literature data. The contribution of the cavity term to the total free energy has been obtained from scaled-particle theory and Sinanoglu–Reisse–Moura Ramos theory. It is shown that there is little connection between the cavity term and the total free energy of transfer, and that there must be, in general, a large interaction term. If the latter is important for transfer of Ph4C, we argue that it must also be important for transfer of the ions Ph4As+ and Ph4B−. Previous suggestions that the interaction term is zero for transfer of these two ions are thus seen to be unreasonable. We also show, for six solvents, that the interaction term for Ph4C is very large in terms of enthalpy and entropy, and that scaled-particle theory seems not to apply to transfers of Ph4C between pure organic solvents.The free energy, enthalpy, and entropy of transfer of Ph4As+ = Ph4B− have been calculated by dividing the total transfer values into neutral and electrostatic contributions; reasonable agreement is obtained between calculated and observed values.

Propagation of electromagnetic waves in inhomogeneous plasmas

1994 ◽  
Vol 52 (3) ◽  
pp. 443-456 ◽  
Author(s):  
E. Busatti ◽  
A. Ciucci ◽  
M. De Rosa ◽  
V. Palleschi ◽  
S. Rastelli ◽  
...  
Keyword(s):  
Electromagnetic Waves ◽  
Inhomogeneous Plasma ◽  
Analytical Form ◽  
Reflection And Transmission Coefficients ◽  
Physical Parameters ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Simple Analytical Form

The reflection and transmission coefficients for an electromagnetic beam propagating in an inhomogeneous plasma are calculated analytically using the Magnus approximation in different physical configurations. The theoretical predictions for such coefficients are expressed in simple analytical form, and are compared with the exact results obtained by numerical solution of the wave propagation equations, using the Berreman 4 × 4 matrix method. It is shown that the theoretical approach is able to reproduce the correct results for reflection and transmission coefficients over a wide range of physical parameters. The accuracy of the theoretical analysis, at different orders of approximation, is also discussed.

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