A Note on Non-equilibrium Work Fluctuations and Equilibrium Free Energies

We consider in this paper, a few important issues in non-equilibrium work fluctuations and their relations to equilibrium free energies. First we show that Jarzynski identity can be viewed as a cumulant expansion of work. For a switching process which is nearly quasistatic the work distribution is sharply peaked and Gaussian. We show analytically that dissipation given by average work minus reversible work $W_R$, decreases when the process becomes more and more quasistatic. Eventually, in the quasistatic reversible limit, the dissipation vanishes. However estimate of $p$ - the probability of violation of the second law given by the integral of the tail of the work distribution from $-\infty$ to $W_R$, increases and takes a value of $0.5$ in the quasistatic limit. We show this analytically employing Gaussian integrals given by error functions and Callen-Welton theorem that relates fluctuations to dissipation in process that is nearly quasistatic. Then we carry out Monte Carlo simulation of non-equilibrium processes in a liquid crystal system in the presence of an electric field and present results on reversible work, dissipation, probability of violation of the second law and distribution of workComment: 15 pages, 4 figure

Liquid crystal films on curved surfaces: An entropic sampling study

The confining effect of a spherical substrate inducing anchoring (normal to the surface) of rod-like liquid crystal molecules contained in a thin film spread over it has been investigated with regard to possible changes in the nature of the isotropic-to-nematic phase transition as the sample is cooled. The focus of these Monte Carlo simulations is to study the competing effects of the homeotropic anchoring due to the surface inducing orientational ordering in the radial direction and the inherent uniaxial order promoted by the intermolecular interactions. By adopting entropic sampling procedure, we could investigate this transition with a high temperature precision, and we studied the effect of the surface anchoring strength on the phase diagram for a specifically chosen geometry. We find that there is a threshold anchoring strength of the surface below which uniaxial nematic phase results, and above which the isotropic fluid cools to a radially ordered nematic phase, besides of course expected changes in the phase transition temperature with the anchoring strength. In the vicinity of the threshold anchoring strength we observe a bistable region between these two structures, clearly brought out by the characteristics of the corresponding microstates constituting the entropic ensemble.Comment: 14 pages, 5 figure

NQR in herbicides. I: Investigation of NQR in 2,​4-​dichlorophenoxyacetic acid

NQR frequencies were measured for 2,​4-​dichlorophenoxyacetic acid over the temp. range from 77 K to room temp; the temp. dependence of the torsional frequencies in the mol. was detd. for the 2 lines, due to the 2 chem. inequiv. chlorines, on the basis of the theory of H. Bayer (1951) and by the method of R. J. C. Brown (1960)​. The temp. variation of the NQR frequency does not exhibit any discontinuity, suggesting that there is no phase transition taking place over the temp. range investigated. The variation of the torsional frequencies about the principal X and Y axes of the elec. field gradient with temp. is not linear over the entire temp. range

Temperature-​dependence of chlorine-​35 N.Q.R. in sodium chloroacetate

The NQR in sodium chloroacetate was investigated from 77 K to room temp. A single line was obsd. throughout this temp. range. Torsional frequencies of the mol. were calcd. in the above temp. range from Bayer's theory. The temp. coeff. of the torsional frequencies was calcd. by Brown's method

Temperature dependence of chlorine NQR in 2,​4-​dichlorophenoxyacetic acid

NQR in 2,​4-​dichlorophenoxyacetic acid is investigated in the range 77 K to room temp. Two lines are obsd. for the 2 chem. inequiv. sites of Cl. Torsional frequencies of the mol. are calcd. in the above temp. range on the basis of Bayer's theory

Proton NMR study of molecular dynamics in ammonium tribromo stannate (NH4SnBr3)

The proton second moment M2 and spin-lattice relaxation time T1 have been measured in ammonium tribromo stannate (NH4SnBr3) in the temperature range 77-300 K, to determine the ammonium dynamics. The continuous wave signal is strong and narrow at 77 and 300 K but has revealed an interesting intensity anomaly between 210 and 125 K. T1 shows a maximum (13 s) around 220 K. No minimum in the T1 vs 1000/T plot was observed down to 77 K. M2 and T1 results are interpreted in terms of NH+ 4 ion dynamics. The activation energy Ea for NH+ 4 ion reorientation is estimated to be 1.4 kcal mol-1. © 1993

Zeeman effect of chlorine nuclear quadrupole resonance and hydrogen bonding in 2,6-, 2,5- and 3,5-dichlorophenols

The Zeeman effect of chlorine nuclear quadrupole resonance in polycrystalline samples of 2,6-, 2,5 and 3,5-dichlorophenol has been investigated at room temperature in order to study the effect of hydrogen bonding on the electric field gradient asymmetry parameter η. While the two n.q.r. lines in 3,5-dichlorophenol gave an asymmetry parameter of ≈ 10%, those in 2,6- and 2,5-dichlorophenol gave different values of η for the two chlorines. The chlorine atom which is ortho to the OH group and involved in hydrogen bonding (i.e., corresponding to the low frequency line) gave an asymmetry parameter of 0.21 in 2,6-dichlorophenol and 0.17 in 2,5-dichlorophenol while the other chlorine (i.e., corresponding to the high frequency line) gave a lower value of 0.12 in 2,6-dichlorophenol and 0.11 in 2,5-dichlorophenol. These values of η are discussed in terms of hydrogen bonding and bond parameters

Effect of electric field on the rheological and dielectric properties of a liquid crystal exhibiting nematic-to-smectic-A phase transition

We report simultaneous measurements of shear viscosity (η) and dielectric constant (ε) of octyloxy cyanobiphenyl (8OCB) in the nematic (N) and smectic-A (SmA) phases as functions of temperature and electric field. With increasing electric field η increases in the N phase whereas it decreases in the SmA phase and saturates beyond a particular field in both the phases. The flow curves in the intermediate-field range show two Newtonian regimes in the N phase. The temperature-dependent behavior of η and ε at zero or at small electric field suggests the occurrence of several structures that results from precessional motion of the director along the neutral direction as reported in similar other system. We show that the precessional motions are gradually suppressed with increasing electric field and the effective viscosity resembles with the Miesowicz viscosity η 1 at high enough electric field. In the intermediate field range the temperature-dependent η exhibits anomalous behavior across the N-SmA phase transition which is attributed to the large contribution of Leslie coefficient α 1

Hybrid Nematic Films: A detailed Monte Carlo investigation, Mol. Cryst. Liq. Cryst., 500, 118-131 (2009)

Detailed Monte Carlo (MC) simulations of a nematic film with antagonistic boundary conditions corresponding to homeotropic and homogeneous planar anchoring at the two surfaces are presented. The simulations are based on the Lebwohl-Lasher lattice spin model with boundary conditions chosen to mimic the cell anchoring. The model was investigated using both a standard Metropolis and a reweighting Monte Carlo method recently implemented for continuous systems