Two-Dimensional Anisotropy Measurements Showing Local Heterogeneity in a Polymer Melt

Nonlinear measurements of kinetics and generalized dynamical modes. I. Extracting the one-dimensional Green's function from a time series

Often, a single correlation function is used to measure the kinetics of a complex system. In contrast, a large set of k-vector modes and their correlation functions are commonly defined for motion in free space. This set can be transformed to the van Hove correlation function, which is the Green's function for molecular diffusion. Here, these ideas are generalized to other observables. A set of correlation functions of nonlinear functions of an observable is used to extract the corresponding Green's function. Although this paper focuses on nonlinear correlation functions of an equilibrium time series, the results are directly connected to other types of nonlinear kinetics, including perturbation-response experiments with strong fields. Generalized modes are defined as the orthogonal polynomials associated with the equilibrium distribution. A matrix of mode-correlation functions can be transformed to the complete, single-time-interval (1D) Green's function. Diagonalizing this matrix finds the eigendecays. To understand the advantages and limitation of this approach, Green's functions are calculated for a number of models of complex dynamics within a Gaussian probability distribution. Examples of non-diffusive motion, rate heterogeneity, and range heterogeneity are examined. General arguments are made that a full set of nonlinear 1D measurements is necessary to extract all the information available in a time series. However, when a process is neither dynamically Gaussian nor Markovian, they are not sufficient. In those cases, additional multidimensional measurements are needed.

Micelle Heterogeneity from the 2D Kinetics of Solute Rotation

The chemical and physical properties of microstructured materials vary with position. The photophysics of solute molecules can measure these local properties, but they often show multiple rates (rate dispersion), which complicates the interpretation. In the case of micelles, rate dispersion in a solute's anisotropy decay has been assigned to either local anisotropy or heterogeneity in the local viscosity. To resolve this conflict, the rotation of PM597 molecules in SDS micelles has been measured by polarized MUPPETS (multiple population-period transient spectroscopy). This 2D technique shows that heterogeneity is strong and that local anisotropy is minimal. The results suggest that on a subnanosecond time scale, the solute sees only one strong fluctuation of the micelle structure. The anisotropic, average structure emerges on longer time scales.