Dendrimers and hyperbranched polymers represent a revolution in methodology for directed synthesis of monodisperse polymers with enormous possibility of novel architectures. They demonstrate ability to attain micelle-like structures with distinct internal and external character. Furthermore polyfunctional character of dendrimers allows varied response to environment and promise as selective sensors, carrier for drugs, encapsulation of toxic chemicals and metals. One of the key problems are the characterization of the structures. Theory and simulation can be essential to provide and predict structure and properties. Here, we present some recent advances in theory, modeling and simulation of dendritic polymers.

The photophysics of exciton localization and energy transfer are examined in two unique classes of phenylacetylene dendrimers. One set of supermolecules is observed to efficiently and rapidly funnel absorbed radiation toward the molecular locus, while a slight change in molecular structure creates an effective “anti-funnel”, greatly reducing the efficiency of energy trapping. Lifetime-based and steady state fluorescence studies are used to determine the rates of intramolecular energy transfer and to glean information on molecular geometry and intermolecular interactions in two solvents.

Several new azobenzene-containing dendritic molecules have been prepared and characterized. The photoresponsive characterization of these dendrimers illustrates the insensitivity of the photochromic behavior of the azobenzene with respect to the nature of the attached dendritic fragment.

The one- and two-exciton manifolds of conjugated dendrimers possessing fractal geometries are studied using the Frenkel exciton model. Two-photon spectra can be used to determine both the magnitude and the sign of short-range coupling among segments. Self-similarity and the high degree of symmetry make it possible to compute the one-exciton states and the optical response with reduced numerical effort that scales linearly rather than exponentially with the number of generations. The third-order optical response and exciton scattering matrix are expressed in compact forms using irreducible representation of optical excitations, totally avoiding the expensive explicit calculation of two-exciton eigenstates.

We report on the diffusion-limited A + B reaction in highly anisotropic spaces. In addition to the highly non-classical behavior of the density of reactants predicted for isotropic spaces, we observe a dimensional crossover in A + B → 0 reactions due to the geometrical compactness of the tubular 2- and 3-dimensional spaces (baguettelike structures). For slabs, we find the crossover time Tc. = Wα, which scales as , where a, b and β are given by the earlier and the late time inverse density scalings of ρ− 1 ˜-, ta and ρ−1 - tbWβ, respectively. We also obtain a critical width W, below which the chemical reaction progresses without traversing a 2- or 3-dimensional Ovchinnikov-Zeldovich reaction regime. We find that there exist different hierarchies of dimensionally forced crossovers, depending on the initial conditions and geometric restrictions. Kinetic phase diagrams are employed and exponents are given for the A + B elementary reactions in various euclidean geometries. Monte-Carlo simulations illustrate some of the kinetic hierarchies.

We apply weak-coupling perturbation theory and strong-coupling perturbation theory to the Holstein molecular crystal model in order to elucidate the effects of anisotropy on polaron properties in D dimensions. The ground state energy is considered as a primary criterion through which to study the effects of anisotropy on the self-trapping transition, with particular attention given to shifting of the self-trapping line and the adiabatic critical point. The effects of dimensionality and anisotropy on electron-phonon correlations and polaronic mass enhancement are studied, with particular attention given to the polaron radius and the characteristics of quasi-l-D and quasi-2-D structures. Perturbative results are confirmed by selected comparisons with variational calculations and quantum Monte Carlo data.

We present theoretical, computational (molecular dynamics), and experimental results describing the dynamical properties of a set of monodisperse, spherical particles confined to a two dimensional surface. An interaction model, which includes the interaction between the particles via collisions as well as the interaction with the substrate, shows that the properties of this granular system are influenced significantly by the latter. In particular, we analyze in detail the effects of slipping and rolling friction, which are usually overlooked. Theoretically, we explore the possibility of formulating a continuum, hydrodynamic-like theory applicable to this system. Further, we apply our model to the particular problem of a system of two kinds of particles with different frictional properties. Our experiments have found that friction-based segregation of particles moving on a horizontally shaken substrate can be achieved. Computational results give further insight into this novel segregation mechanism and confirm that careful and realistic modeling is needed in order to understand this effect.

We present a study of humidity effects on the maximum stability angle in granular media. We show that a granular medium of small glass beads exhibits aging properties: the first avalanche angle increases logarithmically with the resting time of the pile. This aging behavior is found to depend on the relative humidity of the surrounding atmosphere. A short interpretation of this effect, based on a model of activated capillary condensation, is proposed.