By D East, G C Margerison
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Additional info for An Introduction to Polymer Chemistry
If we rewrite eqn. 4) so that the difference between the property of the solution and that of the pure solvent appears on the left-hand side, we obtain the following exprès- 54 AN INTRODUCTION TO POLYMER CHEMISTRY sions for the four coUigative properties, Αρλ, ATf, ATb and n. 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.
These ideas present no special difficulty if we are dealing with a polymer containing molecules all of the same molecular weight. The critical solution temperature is a function of the molecular weight just like any of the other physical properties. However, most polymers contain molecules with a range of molecular weights, a fact which we shall discuss in some detail in Chapter 2. Consequently discussions of limited solubility behaviour must be conducted in the terms used for multicomponent systems; since, in general, the lower molecular weight species are the more soluble, it follows that, where limited miscibility exists in a polymer-solvent system, there is an enrichment in low molecular weight species in the solventrich phase and a corresponding enhancement in the concentration of high molecular weight species in the gel phase.
Flexible linear molecules in more concentrated solution The previous picture of a solution of a polymer is only useful for very dilute solutions (usually less than 1 % by weight of polymer—see Chapter 2). Because of the large dimensions of polymer molecules with high molecular weights, increasing the concentration of polymer from these low values quickly results in entanglement of the polymer chains. That is, the INTRODUCTION 21 solution changes from that shown in Fig. 9 to that shown in Fig. 10 on adding more polymer.