Statistic thermodynamic analysis of fructans – Part 2: Chain configuration parameters of non-branched and branched fructans – Branching structure and molar mass distribution of branched fructans

Applying statistical thermodynamic models for chain configurations in combination with linkage analysis, molar mass distribution and small angle X-ray scattering data allow the unambiguous structural elucidation of branched fructans. The radius of gyration of fructans can be accurately predicted by applying a random flight model with bond angle restrictions. The structural factor g has been calculated and correlated with experimental data only allowing a comb shaped structure for branched fructans. A formula for calculating the molar mass distribution of comb shaped branched fructans is proposed. Amalgamation of experimental and theoretical data prove a regular comb shape structure for the branched fructans of U. maritima, L. bulbiferum and A. tequilana.

CONFORMATION AND CONFINEMENT ENERGY OF INTERACTING END-GRAFTED MOLECULES

The conformation and confinement energy of flexible molecules grafted on a surface are considered in the framework of classical "random flight" model. Interactions among molecules are included in the analysis and closed form solutions are presented for two limiting cases where the core interaction is either very strong or very weak. The case of stiff molecules is also considered via a different approach where their thermally-induced bending deformations, as well as interactions, have been taken into account. We will demonstrate that, under seemingly identical conditions, the behavior of stiff molecules is quite different from that of flexible ones. Predictions obtained here agree with various experimental observations on the grafting density of single- and double-stranded DNAs on a gold surface.

A random-flight evaluation of the constants of relative dispersion in idealized turbulence

In the idealized problem of homogeneous isotropic stationary inertial-range turbulence the rate of relative dispersion of an ensemble of tracer pairs can be characterized by a constant C0. In order to compute this constant with random-flight equations, however, it is necessary first to know the values of two other constants, C1 and C2, that occur in the two-particle velocity-component relations of Lagrangian tracers (Faller 1992).C1 and C2 are found by an elaborate trial and error procedure in a new two-tracer random-flight model of dispersion that matches input and output values of these two variates. The constant C0 is then computed using the Lagrangian relations and is found to be significantly smaller than when the Eulerian Kármán/Howarth correlations are used.The probability density distribution of tracer separations has a kurtosis slightly larger than that of a comparable Gaussian distribution. At small spacings the frequency of tracer spacings is six to ten times larger than would be expected from a Gaussian distribution. The distribution function for the speed of separation of the Lagrangian tracers has a negative skewness similar to that found for two-point Eulerian velocities.