Swelling of Network Structures

A three-dimensional network polymer such as vulcanized rubber, although incapable of dispersing completely, may nevertheless absorb a large quantity of a suitable liquid with which it is placed in contact. 

A close analogy exists between swelling equilibrium and osmotic equilibrium. The elastic reaction of the network structure may be interpreted as a pressure acting on the solution, or swollen gel. In the equilibrium state this pressure is sufficient to increase the chemical potential of the solvent in the solution so that it equals that of the excess solvent surrounding the swollen gel. Thus the network structure performs the multiple role of solute, osmotic membrane, and pressure-generating device. 

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Statistical mechanics of swelling of network structures. J. Chem. Phys. 18, 108 (1950). 

Of significant interest is the swelling of network structures either by ordinary solvents or by solvents in the near-critical or supercritical state. The development in this case is based on the assumption that the partition function of our system may be factored into three contributions the two factors aheady considered (one due to physical and the other due to hydrogen bonding interactions) and... 

In the 1940s, Flory and Rehner (Flory and Rehner 1943a, b Flory 1953) were the first to formulate the theory of swelling of network structures . Here the change of ambient conditions can be represented by a change of the Gibb s free energy AF (see also Chap. 3). 

The modern theory of real networks now permits a more accurate determination of network structures through use of equations (84),(87), and (95) (187-204). Stress-strain measurements can he analyzed as shown in Figure 17. The phantom modulus thus determined leads to v and Me through equations (75) and (76) (189). Swelling equilibrium data are similarly analyzed through equation (94), with the parameter k given hy equation (87) (189). 

Figure 4. Effect of network structural parameters on swelling equilibria of...

As stated above, swelling of a network in a well-characterized solvent is a convenient means of obtaining information on the structure of networks, or conversely, of characterizing the polymer-solvent interactions when the network structure is known. In recent years, much emphasis has been placed on swelling of networks... 

Because thermosetting plastics have an irregular form they are amorphous and because of the network structure are invariably rigid. They do not dissolve without decomposition but may swell in appropriate solvents, the amount of swelling decreasing with increased cross-link density. 

Queslel, J. P. and Mark,J.E. Swelling Equilibrium Studies of Elastomeric Network Structures. Vol. 71, pp. 229—248. 

Polymers of dienes such as butadiene frequently contain a substantial portion of gel which will not dissolve in a good solvent, though it may swell to a volume 20 to 100 or more times that of the polymer itself. This gel, which may comprise up to 90 percent or more of the polymer, consists of a space-network structure formed as a result of a very few cross-linkages provided by occasional (perhaps 1 in 1000 or less) diene units both double bonds of which have entered into the polymerization (see Chap. VI). 

If the polymer is hard, insoluble, and infusible without decomposition, and if it refuses to swell greatly in any solvent, it may be assumed either that it is highly crystalline, with a melting point above its decomposition temperature, or that it possesses a closely interconnected network structure (e.g., as in a highly reacted glyceryl phthalate or a phenol-formaldehyde polymer). Differentiation between these possibilities is feasible on the basis of X-ray diffraction. 

After the formation of the network structure has been completed, let the sample be subjected to any type of homogeneous strain (including swelling, to be treated in Chap. XIII) which may be described as an alteration of its dimensions X, Y, and Z by factors and az,... 

It has been shown in Chapter XI that the force of retraction in a stretched network structure depends also on the degree of cross-linking. It is possible therefore to eliminate the structure parameter ve/Vo) by combining the elasticity and the swelling equations, and thus to arrive at a relationship between the equilibrium swelling ratio and the force of retraction at an extension a (not to be confused with the swelling factor as). In this manner we obtain from Eq. (XI-44) and Eq. (39)... 

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