On the power spectrum of undulations of simulated bilayers

The best finite Fourier Series for a smooth surface $h(x,y)$ closest to the positions of heads of amphiphiles in the least-square sense, agrees fully with the Fourier coefficients obtained by a direct summation over raw data points. Both metods produce structure factors $S(q)$ containing all necessary features: small-q divergence, a minimum, the raise to the ubiquitous nearest neighbor peak near $q=2\pi/$(coll.diameter) and further peaks. The Laurent series is also discussed.Comment: submitted as Letter+Suppl.Material to J.Chem.Phy

Extended Capillary Waves and the Negative Rigidity Coefficient in the d=2 SOS model

The solid-on-solid (SOS) model of an interface separating two phases is exactly soluble in two dimensions (d=2) when the interface becomes a one-dimensional string. The exact solution in terms of the transfer matrix is recalled and the density-density correlation function $H(z_1,z_2;\Delta x)$ together with its projections, is computed. It is demonstrated that the shape fluctuations follow the (extended) capillary-wave theory expression $S(q)=kT/(D+\gamma q^2 +\kappa q^4)$ for sufficiently small wave vectors $q$. We find $\kappa$ {\it negative}, $\kappa <0$ . At $q=2\pi$ there is a strong nearest-neighbor peak. Both these results confirm the earlier findings as established in simulations in d=3 and in continuous space, but now in an exactly soluble lattice model.Comment: file.tex plus 4 (four) figures in Postscrip

Metastable liquid lamellar structures in binary and ternary mixtures of Lennard-Jones fluids

We have carried out extensive equilibrium molecular dynamics (MD) simulations to investigate the Liquid-Vapor coexistence in partially miscible binary and ternary mixtures of Lennard-Jones (LJ) fluids. We have studied in detail the time evolution of the density profiles and the interfacial properties in a temperature region of the phase diagram where the condensed phase is demixed. The composition of the mixtures are fixed, 50% for the binary mixture and 33.33% for the ternary mixture. The results of the simulations clearly indicate that in the range of temperatures $78 < T < 102 ^{\rm o}$K, --in the scale of argon-- the system evolves towards a metastable alternated liquid-liquid lamellar state in coexistence with its vapor phase. These states can be achieved if the initial configuration is fully disordered, that is, when the particles of the fluids are randomly placed on the sites of an FCC crystal or the system is completely mixed. As temperature decreases these states become very well defined and more stables in time. We find that below $90 ^{\rm o}$K, the alternated liquid-liquid lamellar state remains alive for 80 ns, in the scale of argon, the longest simulation we have carried out. Nonetheless, we believe that in this temperature region these states will be alive for even much longer times.Comment: 18 Latex-RevTex pages including 12 encapsulated postscript figures. Figures with better resolution available upon request. Accepted for publication in Phys. Rev. E Dec. 1st issu

Molecular Dynamics Study of the Nematic-Isotropic Interface

We present large-scale molecular dynamics simulations of a nematic-isotropic interface in a system of repulsive ellipsoidal molecules, focusing in particular on the capillary wave fluctuations of the interfacial position. The interface anchors the nematic phase in a planar way, i.e., the director aligns parallel to the interface. Capillary waves in the direction parallel and perpendicular to the director are considered separately. We find that the spectrum is anisotropic, the amplitudes of capillary waves being larger in the direction perpendicular to the director. In the long wavelength limit, however, the spectrum becomes isotropic and compares well with the predictions of a simple capillary wave theory.Comment: to appear in Phys. Rev.

Elastic constants of nematic liquid crystals of uniaxial symmetry

We study in detail the influence of molecular interactions on the Frank elastic constants of uniaxial nematic liquid crystals composed of molecules of cylindrical symmetry. A brief summary of the status of theoretical development for the elastic constants of nematics is presented. Considering a pair potential having both repulsive and attractive parts numerical calculations are reported for three systems MBBA, PAA and 8OCB. For these systems the length-to-width ratio ${x_0}$ is estimated from the experimentally proposed structure of the molecules. The repulsive interaction is represented by a repulsion between hard ellipsoids of revolution (HER) and the attractive potential is represented by the quadrupole and dispersion interactions. From the numerical results we observe that in the density range of nematics the contribution of the quadrupole and dispersion interactions are small as compared to the repulsive HER interaction. The inclusion of attractive interaction reduces the values of elastic constants ratios. The temperature variation of elastic constants ratios are reported and compared with the experimental values. A reasonably good agreement between theory and experiment is observed