Interaction segmental

It has been outlined by several authors that the single macromolecule may be irreversibly bound because of the large number of weakly interacting segments. The first papers on the construction of polymer-coated silica adsorbents involved the physical adsorption of water-soluble polymers. Polyethylene oxides [28, 29] and poly-/V-vinylpyrrolidone [30] are examples of the stationary phases of this type. 

Another concept has been developed on a refined model based on two-step redox systems typical for organic compounds [94]. This concept treats a polymer chain with the degree of polymerization n as X weakly interacting segments containing k monomeric units, each of which can be charged up to a diionic state in two redox steps with different potentials (1 < k n, X k = n). 

Note that these random walks can have any number of intersections, but only the interaction of the pair rjA = rJ2 is taken into account. This situation is represented schematically by the Feynman diagram5 of Fig, 4,2b. The chain is drawn as a straight line, and the two interacting segments are connected by a broken line. This graphic representation generalizes to all orders of the cluster expansion. 

We next carry through the r-integrations associated with two interacting segments. The relevant labeled substructure of a diagram is shown in Fig. 1.6. It yields... 

In terms of our previous discussion, the result for the memory function raj(s) has to retain traces from, generally speaking, two consequent steps the transition from the microscopic picture of interacting segments to a picture of a system of interacting coarse-grained chains (equation (3.1) or (3.2)) and transition from one of these systems to the single-chain equation (3.3). 

EFFECTIVE HAMILTONIANS FOR THE LATTICES FORMED BY WEAKLY INTERACTED SEGMENTS... 

Fig.4. Electron hops in the system of two weakly interacted segments with three electrons...

In the case of the anisotropic rectangular lattice formed by two weakly interacted segments (>3=0), there arise effective exchange integrals J(k,l) subject to the condition [23]... 

Therefore, the ferromagnetic state energy of the rectangular lattice formed by weakly interacting segments with equal filling should be equal to zero in the second PT order in t2. 

Assume that the rectangular lattice consists of two weakly interacting segments, one of them having a nonzero value of a. This lattice may be considered as a simple correlated electron model for stacked donor-acceptor crystals. For a t2 one can use the cyclic spin permutation technique within... 

The opposite choice of sign for fl is made by other authors [for example, Grimley (117)1. The present choice makes the numerical value of /3 positive in almost all experimentally studied polymer solutions. It should also be remarked that Eq. (14), although written for a central potential w(r), is easily generalized to the case that w also depends on the relative orientations of the interacting segments [see, for example, Zimm (277)]. 

A complete quantitative description of the thermodynamics of polymer-polymer solutions also might need to include the effects of polymer tacticity. As demonstrated recently by Schurer et al. (50), changing the stereo configuration of poly (methyl methacrylate) from isotactic to syn-diotactic causes it to become miscible with PVC. These results suggest the importance of the spatial articulation of interacting segments in the polymer. 

Based on NMR studies, which play a prominent role in clarifying the mechanisms of interaction, monomeric units (or interacting segments) can be divided into three groups ... 

K. P. Hinshaw, R. B. Altman, and J. F. Brinkley. 1995. Shape-based models for interactive segmentation of medical images. In SPIE Medical Imaging 1995 Image Processing. San Diego Academic Press, pp. 771-780. 

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