We studied the dependence of the dynamic properties on the generation G of a star-burst dendrimer model. The Rouse approximation for the mobility matrix was used for simplicity. We categorized all normal-mode displacements and considered various time-dependent correlation functions and the intrinsic viscosity. We determined three different time scales corresponding to (1) the diffusion of the center of mass through a distance equal to the dendrimer size, (2) the relaxation of the position of the center of mass relative to the central core monomer, and (3) the rotational and internal elastic motions of the molecule. These relaxation times depend differently on the generation G for large G:  the first time is approximately τD = 6G2 G ζ/k, the second time is approximately τs = 5.8ζ/k, and the third time is approximately τr = τe = 2 G +1ζ/k, where ζ is the friction coefficient for a single monomer and k = 3k B T/a 2 with k B being the Boltzmann constant, T the temperature, and a the average distance between the monomers. A linear dependence of the intrinsic viscosity on the generation was also found. These findings form the basis for further generalization of the theory to include hydrodynamic and excluded-volume interactions in order to model the actual systems more realistically.

The effect of anisotropic repulsive interactions on the isotropic-nematic phase transition of semiflexible polymers is studied by using the Onsager-type excluded-volume interaction. Exact, numerical solutions are obtained for the properties of the phase transition as functions of the flexibility of the polymers. The nematic ordering of different segments of the semiflexible polymers in the nematic state is also discussed.

Monte Carlo simulations were performed on star-burst dendrimer molecules having various numbers of spacer bonds P and various numbers of generations g. Each molecule is modeled by connecting freely-rotating rigid bonds in a star-burst architecture and by attaching to each end of the bond a hardsphere bead of diameter d. Dependence of the mean square end-center distance and the mean square monomer-center distance on P, g, and d were each found to follow a power-law scaling behavior in P for fixed g and small d. The results show that the scaling exponent ν for star-burst dendrimers has the same value as that of linear polymers. For different generations g, the asymptotic regime in which the scaling behavior is valid was found to be quite different. In the scaling regime, our results show that the size of dendrimers follows the scaling law (Pg) 1-ν N 2ν-1 , where N is the total number of monomers in a star-burst molecule. We also discuss physical properties in the high-concentration regime, where the scaling law is no longer valid.

The interfacial profile of the isotropic-nematic interface of a rigid-rod system is solved numerically based on a generalized Onsager model. For long rigid rods, the surface tension has the lowest value at a m. /2 tilt angle between the nematic director and the normal to the interface. The density and order parameter are found to have different interfacial widths and interfacial positions. We find a dip in the density profile near the isotropic phase when the nematic director is almost parallel to the interfacial normal. The surface tension obtained here is 50% lower than the best variational calculation.PACS number(s): 64.70.Md, 82.65. Dp, 68.10.Cr In 1949, Onsager considered a system of rigid rodlike molecules interacting with each other through steric, excluded-volume interactions [1]; he demonstrated that at sufFiciently high density, the system exhibits a firstorder, disorder (isotropic) to orientation-ordered (nematic) phase transition. Subsequent models and numerical simulations have confirmed Onsager's picture, which is now commonly regarded as the main mechanism for the formation of the nematic ordering in liquid crystals [2].The interfacial properties between the isotropic and nematic phases, however, have received less attention until recently [3 -8]. In particular, the role played by anisotropic steric excluded-volume interactions in determining the interfacial properties is still unsatisfactorily explained.Because of difficulties in solving this interfacial problem analytically, the existing theories propose either an artificially imposed interface profile (sharp or smooth) [4,5(a),6], or a square-gradient expansion [5(b)] which cannot be used to account for the e8'ect of a nontrivial tilt angle between the nematic director and interfacial normal [5(a}]. These theories have arrived at different answers regarding the possibilities of the existence of a nontrivial tilt angle. While Holyst and Poniewierski [4]claim that a tilt angle of m /3 between the director and interfacial normal exists as a result of the excluded-volume interactions of hard rods with a large aspect ratio L/d, other authors found that the excluded-volume interaction favors a m. /2 tilt angle for large aspect ratio [5,6]. An open question is whether or not these discrepancies are caused by the approximations mentioned above. In this paper we report a numerical solution of the generalized Onsager model for the isotropic-nematic interface of long rigid rods that avoids the pitfalls of these approximations. We conclude that, for long rigid rods, the surface tension has the lowest value at a n/2 tilt a. ngle.Based on a second-viral-coefficient approximation for a spacially inhomogeneous system, we can express the free energy of molecules with anisotropic shapes as [1] F = f d rd Qp(r, Q)l 4nmp(r, Q) + , ' f d rd r'-dQdQ'w(r, r', Q, Q')p(r', Q')p(r, Q) .Here the number density per unit solid angle, p(r, Q), is a function of the position r and solid angle Q. For steric interactions the function w is assumed to have value 1 when two rods...

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