Chain segment concentration

Fig. 2.15 Relative ideal chain segment concentrations at a wall and at a sphere fen-q = 0.1, = 1, and 9 = 10 accOTding to (2.59). With increasing q the profile shifts closer to the surface...

Effect on the number of network chain segments concentration, n. The quantity n decreases with volume ... 

The attitude we adopt in this discussion is that only those chain segments in the middle of the chain possess sufficient regularity to crystallize. Hence we picture crystallization occurring from a mixture in which the concentration of crystallizable units is Xj and the concentration of solute or diluent is Xg. The effect of solute on the freezing (melting) point of a solvent is a well-known result T j, is lowered. Standard thermodynamic analysis yields the relationship... 

We assume that polymer molecules consist of a large number of chain segments of equal length, joined by flexible links. Each link then occupies one site on the lattice. The solution has to be sufficiently concentrated that the occupied lattice sites are distributed at random, rather than having them clustered together in a non-random way. 

Figure 9. The cable model for the structure of concentrated calcium pectate gels. Egg-box dimers link single-chains segments (top left) and are themselves ed together by larger aggregates of either egg-box or 3i helical chains (lower right)...

In the limit of very short chain segments, for example, at high concentration of diamagnetic dopants, the probability, I, of a collective reversal of all the spins of the segment scales as ... 

Figure 3. 0tot and i-ts components, 0ev and 0chain length, for p = 10- (hexagonal lattice, Xs = 1, X = 0.5). The inset gives a quantitative picture of the segment concentration profile in the adsorbed layer. (Reproduced with permission from Ref. 16. Copyright 1982, Academic Press (London).)... 

Figure 7. The distribution of chain segment density, at 8 = 0.75, in an interfacial region with M = 6. The various curves correspond to the same values of mean segment concentration as in Figure 5.

V, is the molar volume of polymer or solvent, as appropriate, and the concentration is in mass per unit volume. It can be seen from Equation (2.42) that the interaction term changes with the square of the polymer concentration but more importantly for our discussion is the implications of the value of x- When x = 0.5 we are left with the van t Hoff expression which describes the osmotic pressure of an ideal polymer solution. A sol vent/temperature condition that yields this result is known as the 0-condition. For example, the 0-temperature for poly(styrene) in cyclohexane is 311.5 K. At this temperature, the poly(styrene) molecule is at its closest to a random coil configuration because its conformation is unperturbed by specific solvent effects. If x is greater than 0.5 we have a poor solvent for our polymer and the coil will collapse. At x values less than 0.5 we have the polymer in a good solvent and the conformation will be expanded in order to pack as many solvent molecules around each chain segment as possible. A 0-condition is often used when determining the molecular weight of a polymer by measurement of the concentration dependence of viscosity, for example, but solution polymers are invariably used in better than 0-conditions. 

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