Swelling of networks

The evaluation of the elastic free energy AFei rests on the assumption that the root-mean-square distance between the ends of the chain is distorted by the same factor a representing the linear expansion of the spatial distribution. As in the treatment of the swelling of network... 

In this Chapter we will consider the elasticity and swelling of networks which deviate from our definition of ideal networks only because of a certain number of network defects (see Chapter II, Section 2). We will designate by v the number of elastically effective network chains, which in an ideal network equals the number of chains because of the absence of defects. 

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). 

Swelling of network rubbers by solvent liquids represents an isotropic deformation. Stretching a swollen rubber network superimposes an anisotropic deformation. The two deformations may be combined as described below to obtain an estimate of the force (or modulus) required to deform a swollen rubber compared to that for unswollen rubber. The... 

Alfrey and Lloyd (10,11) have studied the swelling of networks prepared in solution in a variety of solvents. The swelling of these networks prepared at several dilutions differed from each other as well as from networks prepared in bulk. 

Because the elasticity of polymer networks is of an entropy form, the elasticity term can be written as AGg = —T ASg defining ASg as the change of entropy due to deformation including swelling of networks [3]. We will introduce the deformation ratio that is expressed as the ratio of the length before and after elongation as a = L/L where Lq and L are the... 

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... 

FIGURE 3.29 Schematic representation of the effect of cross-hnk density on the swelling of networks. Curve 1 represents the coexistence curve of an UCST polymer solution and curves 2, 3, and 4 are for gels with increasing cross-hnk density. 

Therefore, for At = 10 g/mol, = 3.56, that is, the individual polymer molecules occupy almost 4 times the volume in cyclohexane than they do in any theta solvent. It was mentioned in Section 2.5 that polymers in contact with solvents of like solubility parameter 5 should show the greatest solvation effects, that is, swelling of networks or enhancement of viscosity of solutions. Now we can identify this solvating ability with a, the expansion factor. 

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