Continuous-model description of layer fluctuations in finite smectic systems

GLOBAL PROPERTIES OF BIOMIMETIC MEMBRANES: PERSPECTIVES ON MOLECULAR FEATURES

Global properties of biological model membranes such as, e.g., structure or elasticity, are known to be closely related to their local features. If a membrane active compound interacts with the membrane assembly, the membrane will primarily be affected on the local, molecular level. The local perturbation may than, through some coupling, translate into a global adjustment of the membrane. In order to address this coupling x-ray and neutron diffraction data analysis techniques have been developed that allow accurate monitoring of changes in global properties. This offers new perspectives on molecular membrane features that in combination with complementary techniques, such as differential scanning calorimetry, spectroscopy or dynamic scattering lead to a better understanding of biomimetic membranes. The present article reviews these aspects giving application examples for single- and multicomponent membranes, respectively.

Structure and interaction potentials in solid-supported lipid membranes studied by X-ray reflectivity at varied osmotic pressure

Highly oriented solid-supported lipid membranes in stacks of controlled number N approximately 16 (oligo-membranes) have been prepared by spin-coating using the uncharged lipid model system 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). The samples have been immersed in aqueous polymer solutions for control of osmotic pressure and have been studied by X-ray reflectivity. The bilayer structure and fluctuations have been determined by modelling the data over the full q-range. Thermal fluctuations are described using the continuous smectic Hamiltonian with the appropriate boundary conditions at the substrate and at the free surface of the stack. The resulting fluctuation amplitudes and the pressure-distance relation are discussed in view of the inter-bilayer potential.

Full q-space analysis of x-ray scattering of multilamellar membranes at liquid-solid interfaces

A method for analyzing the x-ray scattering of a stack of phospholipid membranes at the solid-liquid interface in excess water is presented. It is argued that bilayers near the substrate fluctuate less significantly than the ones away from it and, therefore, make a larger contribution to the specular reflection at the low index Bragg peaks. But the diffuse scattering due to thermal fluctuations corrupts the Bragg peaks at high angles so that the specular contribution is not clearly observable. In the midst the specular reflection and the diffuse scattering cannot be separated easily and must be analyzed simultaneously. The height-difference correlation function derived from a modified Caillé theory enables one to simulate the longitudinal and the transverse scans in the same theoretical framework to yield more reliable structural parameters. The theoretical apparatus is successfully applied to the experimental data on DOPC membranes.

Smectic layer displacement fluctuations in solid substrate supported smectic-A films

In this paper we present results of calculations of static and dynamic characteristics of smectic layer displacement fluctuations in solid substrate supported smectic-A films with due regard for asymmetric profiles of the bending elastic constant K and the smectic layer compressibility B. We also take into account difference in properties of boundary surfaces of the film, namely, the surface tension of the free surface is taken to be finite whereas that of a film-substrate interface is assumed to be infinitely large. Profiles of the smectic layer displacement fluctuations and correlations between them are calculated for films formed of liquid crystalline compounds with the bulk smectic-A to nematic phase transition. The calculations are performed at temperatures much lower than that of the bulk phase transition and at maximum temperatures of existence of films of given thickness. The time dependent displacement-displacement correlation functions for thermal smectic layer displacement fluctuations and time dependent intensity-intensity correlation functions for diffuse x-ray scattering from the films are also calculated. It is shown that unlike free-standing smectic-A films, an effect of the temperature on dynamics of smectic layer displacement fluctuations in solid substrate supported smectic-A films can be observed in experiments on coherent x-ray dynamic scattering from not very thick films (N approximately 20) and at significantly smaller wave vector transfer component in the film plane.

Solid-supported lipid multilayers: structure factor and fluctuations

We present a theoretical description of the thermal fluctuations in a solid-supported stack of lipid bilayers, for the case of vanishing surface tension gamma = 0 and in the framework of continuous smectic elasticity. The model is successfully used to model the reflectivity profile of a thin (16 bilayers) DMPC sample under applied osmotic pressure and the diffuse scattering from a thick (800 bilayers) stack. We compare our model to previously existing theories.

Disjoining pressure in free-standing smectic-A films and its effect on their reflectivity

The results of calculations of a disjoining pressure and smectic layer spacings in free-standing smectic-A films (FSSAF's) heated above the temperature of disappearance of the smectic order in bulk liquid crystal samples are presented. An effect of the disjoining pressure on the optical reflectivity of FSSAF's having a different number of the smectic layers is investigated. The results of calculations are in agreement with results of experimental optical-reflectivity investigations of FSSAF's.

Dynamics of free-standing smectic-A films

The eigenvibrations and time-dependent layer displacement-layer displacement correlation functions are analyzed in a free-standing thin smectic-A films with the help of a discrete layer model. The film motions are described using the Chebyshev polynomials of second kind, U(n)(x). The eigenfrequencies problem is essentially simplified within the framework of this approach since the numerical solution of the high degree algebraic characteristic equation is replaced by the analytical solution of a rather simple trigonometrical equation. The dependences of eigenmodes on wave number q(perpendicular) were analyzed. For small q(perpendicular) one mode is a low frequency acoustic wave and other modes are high frequency optical oscillations. As the wave number q(perpendicular) increases all modes successively turn into relaxation when starting with the acoustic mode. The rather simple expression for susceptibility matrix and for spectral densities of layer displacement correlation functions were obtained using the Chebyshev polynomials. It was shown that the frequency dependences of spectral densities are sensitive to wave number q(perpendicular). For small q(perpendicular) the spectral densities of displacement-displacement correlation functions have a sharp peak and for large q(perpendicular) they turn into a contours of Lorentzian type.

Surface oscillations of smectic-A liquid crystals

A theoretical description of free surface motion is presented for a semi-infinite unbounded smectic-A (Sm-A) liquid crystal. The characteristic equation is analyzed in a wide range of frequencies and wave numbers. It is shown that at low frequencies the surface eigenmotion is a wave of the second sound type. The wave velocity is twice that of the maximum second sound velocity in the bulk phase. This Rayleigh mode may be excited and detected as surface transverse waves. At high frequencies the surface eigenmotion is a damping viscous mode. The spectral intensities of the surface displacement fluctuations are presented in rather simple form for separate areas of wave numbers and frequencies. These results may be used to describe light scattering experiments. It is shown that the surface tension is negligible when describing Sm-A surface eigenmotions, in contrast to ordinary liquids. At the same time the surface tension is sufficient for surface displacement fluctuations at low frequencies.

Thermal fluctuations and x-ray scattering from free-standing smectic-A films

The present paper is devoted to theoretical investigation of thermal fluctuations and correlations between them in free-standing smectic-A films (FSSAF's) formed of liquid crystal compounds with bulk smectic-A-isotropic (SmA-I) and SmA-nematic (SmA-N) phase transitions, as well as small angle x-ray scattering from these FSSAF's. The study took into account the dependence of the bending elastic constant K and the smectic layer compressibility B on the distance from the boundary free surfaces of the films. The results of calculation are compared with those obtained in the framework of the Holyst model [Phys. Rev. Lett. 65, 2153 (1990); Phys. Rev. A. 44, 3692 (1991)] for spatially uniform FSSAF's. It has been found that, well below the temperature at which the smectic order in the bulk liquid crystal disappears, taking into account the profiles of the elastic moduli K and B does not produce noticeable differences from this model. However, at maximum temperatures of existence of FSSAF's, our results are considerably different from the predictions of the Holyst model. The results obtained are applied to calculation of specular and diffuse x-ray reflectivities of FSSAF's in the whole temperature interval of their existence. Displacement of the molecular centers within the film layers along those normal to them and the deviation of the local orientational order in FSSAF's from the ideal are also taken into account. The results of calculation are in agreement with experiments on the small angle x-ray scattering from FSSAF's.

Layer dynamics of freely standing smectic-A films

The dynamics of freely standing thermotropic smectic-A films are studied in the isothermal, incompressible limit via a continuous hydrodynamic description. The role of permeation in the films, the structure of the hydrodynamic normal modes, and the form of the autocorrelation functions for the smectic layer and order-parameter fluctuations are discussed. We find two characteristic lengths l(d)=sqrt[alphad/B] and l(c)=sqrt[eta(2)(3)d/8rhoalpha] associated with the dynamic behavior of the system, where alpha is the surface tension, d is the film thickness, B is the elastic constant for layer compression, eta(3) is the layer sliding viscosity, and rho is the density of the liquid crystal. The crossover from filmlike to bulklike behavior is controlled by l(d) alone; the crossover from overdamped to underdamped dynamics when the in-plane length scale is large compared to l(d) is controlled by l(c) alone.