As will be clear from the contributions in this book, computer simulations techniques actually generate configurations of the system, i.e. We shall discuss the calculation of observables in liquid crystals in fairly general terms, but adopting a rather special point of view, that of computer simulations. 1 if we can assume that the molecules have cylindrical symmetry. We assume the molecules to be classical, rigid particles with centre of mass at position r and orientation П‰ given for instance by a set of three Euler angles (О±, ОІ, Оі), or only two angles (О±, ОІ) as illustrated in fig. Typically we shall consider that volume V and temperature T are fixed together with N (canonical conditions), but we shall also refer to the case where pressure P is fixed together with T (isobaric conditions). Single particle properties We consider a system of N molecules at certain specified thermodynamic conditions. We also briefly describe the calculation of dynamic properties from molecular dynamics simulations using Linear Response theory. In this Chapter we introduce the description of single and pair particle static properties of liquid crystals, and discuss their calculation from computer simulations. The theoretical description of the problem is highly involved, but a qualitative picture can be obtained from considering the fluid velocity-velocity correlation within the point-particle approximation for the particles. When a colloidal particle is set in motion either by an external force or by a thermal fluctuation, it perturbs the surrounding fluid which propagates the perturbation to neighbouring particles, thus modifying their state of motion. 1 Introduction Hydrodynamic interactions play a crucial role in suspensions of colloidal particles. We show that hydrodynamic interactions develop in a sonic time scale, not in a vorticity time scale. This allows to discuss the time scales involved in the propagation of hydrodynamic interactions and its relevance on the dynamics of suspended colloidal particles. We present explicit expressions in real space and time for the equilibrium correlation functions of the density and velocity fields in a compressible fluid. Also, numerical results for the motor domains of ncd and kinesin, small arbitrarily shaped proteins with known x-ray structures, show reasonable agreement with the experimental data obtained from transient electric birefringence experiments. This approach has been tested for ellipsoidal particles and a good agreement with theoretical results has been obtained. The average dielectric constant of the mixture is calculated using the finite element method. Since the particles of interest are small compared to the wavelength of light, a quasi-static approximation for the refractive index is used, i.e., that it is equal to the square root of the dielectric constant of the suspension. The form birefringence of the solution is calculated as the difference in its refractive index when all the particles of refractive index n 2 are either parallel to or normal to the direction of the polarization of light. Macromolecules are treated as arbitrarily shaped particles suspended in a solvent of refraction index n 1. In view.ДЄBSTRACT An approach based on the finite element method (FEM) is employed to calculate the optical properties of macromolecules, specifically form birefringence. Further, reference will usually be made to these sources, where the original studies are cited. As many comprehensive discussions of the theoretical basis for the methods of interest are available, the limited space here is devoted to some of the more practical aspects of the several scattering methods to be discussed. berry & cotts 1 9/23/97 INTRODUCTION The use of light scattering methods to characterize polymers or colloidal particles in dilute solutions (dispersions) is discussed in the following. The theoretical foundations are summarized to give the expressions most often utilized, central issues in the calibration and use of light scattering photometers are considered, and several examples are discussed, including the use of light scattering as a detector in connection with size exclusion chromatograpy. Static and dynamic light scattering methods for use in the characterization of dilute solutions of polymers or suspensions of dispersed particles are presented.

Dynamic light scattering size exclusion