Titel

Institute of Experimental Physics / Computational Physics Group

Lamellar Phases in Hard Particle Mixtures

Franz Vesely, Alexander Borodin
franz.vesely@univie.ac.at

Mixtures of parallel linear particles and spheres tend to demix upon compression. The linear species usually concentrates in regular layers, thus forming a smectic phase. With increasing concentration of spheres this "smectic demixing" transition occurs at ever lower packing densities. For the specific case of hard spherocylinders and spheres Koda et al. have explained the layering effect in terms of a second virial approximation to the free energy. We extend this approach from spherocylinders to other linear particles, namely fused spheres, ellipsoids, and sphero-ellipsoids. Monte Carlo simulation is used to check the predictions of this theory.

Possible applications of the lamellar demixing effect range from liquid crystal technology to the creation of periodic structures in dispersions of nanotubes.

Packing density at smectic demixing as a function of the relative concentration of spheres, for linear particles with length $L=6$; the three top curves pertain to spheroellipsoids with $c=4$, $6$, and $10$, respectively; the two lower curves are for fused spheres with $n=9$ (bottom) and $n=11$; the fourth curve from above gives the results for the reference spherocylinder-sphere mixture. Snapshot of a fused spheres/spheres mixture at the lamellar transition. The number fraction of spheres is 0.4; the packing density is eta=0.463

A Study of Gay-Berne Pure and Mixed Substances Using NPT-Monte-Carlo

Dorian Bridi dorianbridi@gmx.net

The goal of this study is to better understand the behaviour of mixtures consisting of spheroid molecules of two different lengths. The potential that currently best depicts naturally occurring liquid crystals such as n-pentylbenzenthio-4-n-decyloxybenzoate is the Gay-Berne potential which adapts well to the anisotropic character of the molecules while preserving the hard core and soft tail credentials of the Lennard-Jones potential. The study shows that phase diagrams of different hypothetical substances with varying characteristics can be predicted including the transitions into the nematic and smectic phases as well as the so-called “smectic demixing” phenomenon found mixtures. Liquid crystals have interesting optical properties and are used in LCD displays which explains their importance.

The smectic demixing effect has recently become a field of intensive study. Earlier simulations by Renato Lukac (U of Vienna, dissertation 2000) had two possible shortcomings: (a) they were done in the NVT ensemble, while the isobaric (NPT) ensemble may be more appropriate to studying phase transitions; and (b) the parametrization of the Gay-Berne particles was such that even in the spherical limit the attractive interaction would remain anisotropic. There was a slight risk that the latter feature would have introduced artefacts. Therefore a new set of simulations was started in which the macroscopic conditions are isobaric-isothermal, and the an attractive potential is used that approaches a simple Lennard-Jones interaction when the aspect ratio equals 1.

Preliminary results indicate that the results of Renato Lukac hold good, with only minor quantitative modifications.

Diffusion Constant of Lennard-Jones Dumbbell Fluids

Franz Vesely
franz.vesely@univie.ac.at

The transport coefficients of simple dumbbell molecules will depend on the bond length. Following a suggestion by Manfred Zeidler (Aachen) we have calculated the diffusion constant of dumbbells for bond lengths ranging from 0.22 to 0.73 (in LJ units). This refers to real molecules such as O₂ (0.22) or Cl₂ (0.73). Intriguingly, our exploratory simulations indicated that the suitably reduced diffusion constant remains more or less constant, decreasing only from 0.112 to 0.104.

A possible problem with such a study is that "equivalent" thermodynamical states are hard to define. In our investigation we used the critical densities and temperatures given by Tokumasu et al. (J. Chem Phys. 118 (2003) 3677). The counterintuitive results we found, as well as data provided by Johann Fischer (BoKu Vienna) indicate that the states we studied may not be exactly equivalent. More extensive simulations and a new set of critical data will be used to clear up the situation.

Snapshot of a Lennard-Jones dumbbell sample with bond length 0.73, roughly related to Cl₂. Velocity autocorrelation function of various dumbbell fluids at equivalent thermodynamic states. The area under each curve yields the value of the diffusion constant.

More on High Performance Scientific Computing at Vienna University

Lamellar Phases in Hard Particle Mixtures Franz Vesely, Alexander Borodin franz.vesely@univie.ac.at Mixtures of parallel linear particles and spheres tend to demix upon compression. The linear species usually concentrates in regular layers, thus forming a smectic phase. With increasing concentration of spheres this "smectic demixing" transition occurs at ever lower packing densities. For the specific case of hard spherocylinders and spheres Koda et al. have explained the layering effect in terms of a second virial approximation to the free energy. We extend this approach from spherocylinders to other linear particles, namely fused spheres, ellipsoids, and sphero-ellipsoids. Monte Carlo simulation is used to check the predictions of this theory. Possible applications of the lamellar demixing effect range from liquid crystal technology to the creation of periodic structures in dispersions of nanotubes.

Packing density at smectic demixing as a function of the relative concentration of spheres, for linear particles with length $L=6$; the three top curves pertain to spheroellipsoids with $c=4$, $6$, and $10$, respectively; the two lower curves are for fused spheres with $n=9$ (bottom) and $n=11$; the fourth curve from above gives the results for the reference spherocylinder-sphere mixture.	Snapshot of a fused spheres/spheres mixture at the lamellar transition. The number fraction of spheres is 0.4; the packing density is eta=0.463
A Study of Gay-Berne Pure and Mixed Substances Using NPT-Monte-Carlo Dorian Bridi dorianbridi@gmx.net The goal of this study is to better understand the behaviour of mixtures consisting of spheroid molecules of two different lengths. The potential that currently best depicts naturally occurring liquid crystals such as n-pentylbenzenthio-4-n-decyloxybenzoate is the Gay-Berne potential which adapts well to the anisotropic character of the molecules while preserving the hard core and soft tail credentials of the Lennard-Jones potential. The study shows that phase diagrams of different hypothetical substances with varying characteristics can be predicted including the transitions into the nematic and smectic phases as well as the so-called “smectic demixing” phenomenon found mixtures. Liquid crystals have interesting optical properties and are used in LCD displays which explains their importance. The smectic demixing effect has recently become a field of intensive study. Earlier simulations by Renato Lukac (U of Vienna, dissertation 2000) had two possible shortcomings: (a) they were done in the NVT ensemble, while the isobaric (NPT) ensemble may be more appropriate to studying phase transitions; and (b) the parametrization of the Gay-Berne particles was such that even in the spherical limit the attractive interaction would remain anisotropic. There was a slight risk that the latter feature would have introduced artefacts. Therefore a new set of simulations was started in which the macroscopic conditions are isobaric-isothermal, and the an attractive potential is used that approaches a simple Lennard-Jones interaction when the aspect ratio equals 1. Preliminary results indicate that the results of Renato Lukac hold good, with only minor quantitative modifications.

Diffusion Constant of Lennard-Jones Dumbbell Fluids Franz Vesely franz.vesely@univie.ac.at The transport coefficients of simple dumbbell molecules will depend on the bond length. Following a suggestion by Manfred Zeidler (Aachen) we have calculated the diffusion constant of dumbbells for bond lengths ranging from 0.22 to 0.73 (in LJ units). This refers to real molecules such as O₂ (0.22) or Cl₂ (0.73). Intriguingly, our exploratory simulations indicated that the suitably reduced diffusion constant remains more or less constant, decreasing only from 0.112 to 0.104. A possible problem with such a study is that "equivalent" thermodynamical states are hard to define. In our investigation we used the critical densities and temperatures given by Tokumasu et al. (J. Chem Phys. 118 (2003) 3677). The counterintuitive results we found, as well as data provided by Johann Fischer (BoKu Vienna) indicate that the states we studied may not be exactly equivalent. More extensive simulations and a new set of critical data will be used to clear up the situation.

Snapshot of a Lennard-Jones dumbbell sample with bond length 0.73, roughly related to Cl₂.	Velocity autocorrelation function of various dumbbell fluids at equivalent thermodynamic states. The area under each curve yields the value of the diffusion constant.