Spatial segment density

Fig. 1. Spatial segment density distribution of a flexible polymer coil in a good solvent from a dilute to a concentrated solution (schematic).

This is reasonable since the polymer coil dimension in a 0-solvent is significantly smaller than that in a good solvent. The value of < in dilute solution is higher in the 0-solvent than that in DCE, which also reflects a higher spatial segment density of the coil in a 0-... 

With reference to an actual polymer molecule we should, of course, speak of the potential at a point within the molecule, since the potential will decrease radially from its center in the manner dictated by the spatial distribution of the fixed charges (which like the segment density, may often be approximated by a Gaussian distribution) and that of the counter-ions. For the purpose of the present qualitative discussion, however, we refer merely to the potential finside the molecule. 

The flexible helix modeled here is best described by the entire array of conformations it can assume. A comprehensive picture of this array is provided by the three-dimensional spatial probability density function Wn(r) of all possible end-to-end vectors (25, 35). This function is equal to the probability per unit volume in space that the flexible chain terminates at vector position relative to the chain origin 0,as reference. An approximate picture of this distribution function is provided by the three flexible single-stranded B-DNA chains of 128 residues in Figure 5(a). The conformations of these molecules are chosen at random by Monte Carlo methods (35, 36) from the conformations accessible to the duplex model. The three molecules are drawn in a common coordinate system defined by the initial virtual bond of each strand. For clarity, the sugar and base moieties are omitted and the segments are represented by the virtual bonds connecting successive phosphorus atoms. 

Spatial fluid density variations are frequently inherited from the filling history of the reservoir. The initial fluids expelled from a source rock are relatively dense liquids. As a source rock becomes more thermally mature, it expels progressively lighter fluids and eventually gases. When such fluids fill a reservoir, and fill and spill from compartment to compartment within a reservoir, each part of the reservoir can end up with different proportions of fluids of different maturity and density. Field observations show that the segment of the reservoir closest to the source kitchen has often received the latest, lowest density charge. Those areas farthest away from the source kitchen may contain earlier denser fluids that have filled and spilled to their current location. 

ABSTRACT. Excimer fluorescence is developed as a quantitative probe of isolated chain statistics and intermolecular segment density for miscible and immiscible blends of polystyrene (PS) with poly(vinyl methyl ether) (PVME). Rotational isomeric state calculations combined with a one-dimensional random walk model are used to explain the dependence of the excimer to monomer intensity ratio on PS molecular weight for 5% PS/PVME blends. A model for a three-dimensional random walk on a spatially periodic lattice is presented to explain the fluorescence of miscible PS/PVME blends at high concentrations. Finally, a simple two-phase morphological model is employed to analyze the early stages of phase separation kinetics. 

The treatment of polymer bmshes as outlined above rests on the mean-field assumption, that is, the interactions between segments of the polymer chain are described by a constant background potential. While the mean-field approach was shown to be suitable to rationalize experimental observations on the dependence of H on N for dense polymer bmshes, it fails to predict more detailed information about the internal stmcture of the bmsh, such as the segment density 4>(z) (where z denotes the spatial coordinate normal to the interface direction) that is relevant to understand properties of polymer bmshes such as chain interpenetration or interactions between the bmsh and its environment. These limitations have motivated research in more accurate analytical and simulation (often self-consistent field-based) techniques to describe the interactions and density profile within polymer bmshes. 

The rate of water vapor diffusion per unit leaf area, Jw> equals the difference in water vapor concentration multiplied by the conductance across which Acm occurs (// = g/Ac - Eq. 8.2). In the steady state (Chapter 3, Section 3.2B), when the flux density of water vapor and the conductance of each component are constant with time, this relation holds both for the overall pathway and for any individual segment of it. Because some water evaporates from the cell walls of mesophyll cells along the pathway within the leaf, is actually not spatially constant in the intercellular airspaces. For simplicity, however, we generally assume that Jm, is unchanging from the mesophyll cell walls out to the turbulent air outside a leaf. When water vapor moves out only across the lower epidermis of the leaf and when cuticular transpiration is negligible, we obtain the following relations in the... 

---