Chain link number, defined

The same relation is found for the end-linking of molecules of low functionality if = 3 or 4) and for the vulcanization of long molecular chains. The second-moment average number of cross-linking sites along the chain, f2, is defined as... 

Tropocollagen molecules are firmly linked together, particularly at their ends, by covalent networks of altered lysine side chains. The number of these links increases with age. Type IV collagens form networks with a defined mesh size. The size-selective filtering effect of the basal membranes in the renal glomeruli is based on this type of structure (see p. 322). 

The number of possible conformations n for each mobile molecular segment is reciprocal to the density of cross-links AT (defined for 100 C-C groups in the polymer chain). 

For a self-avoiding chain with N + 1 points (N links) on a square lattice or a simple cubic lattice, a contact can be defined as two points that are non-adjacent on the chain, and nearest neighbours on the lattice. Now let us consider the selfavoiding chains which have a given origin, N links, p contacts, and the same end-to-end vector r let ZN p r ) be the number of configurations of these chains. This number has been counted by W. Orr39 for N < 8 on the square lattice and for N < 6 on the simple cubic lattice. 

Pure number defining the two-body contact energy on a lattice Total number of closed chains of N links, drawn on a lattice, starting from the site at the origin... 

As discussed further in the following section, it can be shown that the statistical distribution of end-to-end distances for any real chain reduces to the Gaussian form if the number of rotatable links is sufficiently large. By suitably choosing n and / for the freely jointed random-link model, both rms and the fully extended length can be made equal to the corresponding values for the real chain. These values define the equivalent freely jointed random chain. For example, if it is assumed that in a real polyethylene chain (i) the bonds are fixed at the tetrahedral angle and (ii) there is free... 

The basis of this approach has been discussed by Edwards and many authors have used the formalism in a lot of different contexts, ue. spin glasses, " electron localization or glasses. For simplicity consider a purely entropic system. Suppose there is a constraint called y. This label defines a crosslink in the rubber problem by saying which monomer of which polymer chain is linked to another monomer of another chain. The number of configurations available when y applies is Q, giving the quenched entropy... 

We define the number of chain links as follows. If an initial active center is responsible for the formation of n active centers of the same type, the chain will have n Unks. For example. Figure 12.4 shows the example of a chain with three links. 

Two types of well defined branched polymers are acessible anionically star-shaped polymers and comb-like polymers87 88). Such macromolecules are used to investigate the effect of branching on the properties, 4n solution as well as in the the bulk. Starshaped macromolecules contain a known number of identical chains which are linked at one end to a central nodule. The size of the latter should be small with respect to the overall molecular dimensions. Comb-like polymers comprise a linear backbone of given length fitted with a known number of randomly distributed branches of well defined size. They are similar to graft copolymers, except that backbone and branches are of identical chemical nature and do not exhibit repulsions. 

If [TO4] groups are linked to form chains, multiplicity is the number of linked chains the observed multiplicities in this case are m = 2,3, 4, and 5. Analogously, multiplicity is defined as the number of mutually linked sheets. If several [TO4] groups are linked in a chain, periodicity (p) is the number of groups that defines the structural motive (i.e., after p groups, the chain is obtained by simple translation). Dimensionality of [TO4] groups is the degree of condensation of a crystal structure. The condensation of an infinite number of tetrahedra may lead to infinite unidimensional chains d = 1), bidimensional sheets d = 2), and tridimensional lattices d = 3). The dimensionality of an isolated [TO4] tetrahedron is zero d = 0). 

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