By D East, G C Margerison
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4Pi = 4 3 · N+K'2N2+K^N*+ ... •"0 RTÌV9 AT, = ' x · N+K"2N*+K"3N3+ ... 5) 3 •N+K^"N +K'a"N +.. =^-N+K^"N2+K^"N3+. In each case, the appropriate value of Κλ has been written out explicitly, the symbols having the following meanings: Vl is the molar volume of the solvent at the various temperatures at which the values Δρΐ9 ATf, and ΔTb are measured; N0 is the Avogadro number ; Δρχ is the difference between the partial pressure of the solvent vapour above the solution and the vapour pressure of the pure solvent p\ at the same temperature ; ATf is the difference between the freezing point of the solution and that of the pure solvent Tf, whose latent heat of fusion is Lp ATb is the difference between the boiling point of the solution and that of the pure solvent Tb, whose latent heat of vaporization is Lv; π is the osmotic pressure of the solution at a temperature T.
The most important is the conception that a complex reaction such as polymerization is made up of a series of elementary reactions in which only one, two or three molecules take part. If we represent the possible elementary reactions symbolically as follows Case 1 Case 2 Case 3 A -► products A + B -> products A + B + C -*■ products INTRODUCTION then all theories of -d[A] dt -d[A] dt -d[A] dt 35 reaction rates suggest that = &i[A] for case 1 = ^2[A][B] for case 2 = k3[A][B][C] for case 3 where kl9 k2 and kz are constants termed the unimolecular, bimolecular and termolecular rate constants.
Although these quantities are truly equilibrium properties —the distribution of configurations being constant in time— they are characteristic of the polymer-solvent system and the temperature and not just of the polymer alone because of the interaction between the polymer and the solvent. Thus the same polymer dissolved in two different types of solvent at the same temperature can have quite different values of the root mean square end-to-end distance. This problem will be discussed in Chapter 2.