Elastically effective cross-link density

Figure 5. Elastically effective cross-link density versus bake temperature for a high...

Determination of cross-link density from compression experiments is perhaps the most effective means of determining cross-link density as long as samples of the appropriate geometry can be prepared. When a hydrogel is subjected to an external force, it undergoes elastic deformation which can be related to the effective cross-link density of the network [63,99], Here the measurements made to extract cross-link density from polymer deformation are briefly discussed. 

Efficiency of the cross-linking reaction can be defined as the ratio of effective cross-link density, px, to the theoretical cross-link density, p(. Theoretical cross-link density assumes that all of the cross-linker added to the formulation created elastically effective cross-links however, it cannot be defined for nonchemical methods. Thus the theoretical cross-link density, p is given as... 

The rate at which coals swell is dictated by the rate at which the solvent diffuses into the coal. This is controlled by solvent properties, the size of the coal particles, and the average molecular weight between the cross-links of the coal matrix (Olivares and Peppas, 1992). Coal is a glassy solid at room temperature, but transitions to a flexible state as it absorbs solvent and the flexible nature of the swollen coal suggested lower effective cross-link density, and suggested that the elasticity of the solvent swollen coal may be predominantly rubber-like. The transition from the glassy to rubbery state is generally very sharp (Olivares and Peppas, 1992). 

Measurement of the rubbery plateau modulus ( ) provides a direct means by which to assess cross-link density in polymer networks. Classical rubber elasticity theory (Treloar, 1975 Mark, 1982 Hill, 1997) relates the elastic modulus in the rubbery region to effective cross-link density (v ) as shown, for example, in the equation suggested by Hill (1997) ... 

Usually two methods of estimating the effective cross-linking density are used. The first is based on elasticity theory. It computes the concentration of the cross-links in the network from the value of the elastic modulus and the polymer density according to the equation ... 

For semi- and full IPNs made of poly(oxyethylene) and poly(acrylic acid), the effective cross-link densities were determined from the elastic modulus and were compared with values estimated assuming the additivity of crosslink densities of components [113]. Discrepancies between estimated and calculated values are observed. 

Fig. 3. Effect of cross-link density where A represents tear strength, fatigue life, and toughness B, elastic recovery and stiffness C, strength and D,...

FIGURE 17.11 The effect of ri (the number of statistical chain elements in a cord between cross-links) on the relation between stress and strain of a polymer gel in elongation. a0 is the force divided by the original cross-sectional area of a cylindrical test piece, v is twice the cross-link density, L is the length, and L0 the original length of the test piece. (After calculations by L. R. G. Treloar. The Physics of Rubber Elasticity. Clarendon, Oxford, 1975.)... 

Based on studies of an homologous, endlihked, epoxy/amine network series, the simple theory of rubber elasticity has proved effective for determining reasonable cross-link densities from equilibria modulus measurements in the rubbery state. 

A network of effective cross-links behaves as a normal elastic network for t T. We discussed the classical theory of high elasticity in Chapter 7. The Young s modulus of a network, as you remember, is of the order of ksT multiplied by the density of cross-links. (As usual, ks is Boltzmann s constant, and T is the temperature.)... 

The type and level of cure-site bearing comonomer, because it is used at low levels, has little influence on the oil swefling, heat resistance, and low-temperature flexihUity. Instead, it determines the cure behavior and cross-link density. Thus, it has effects on mechanical properties, elasticity, and permanent set. Older grades of ACM are being replaced because of their poor vulcanization characteristics. New grades, prepared with undisclosed commoners, are much more rapidly vulcanized and give excellent properties without postcure (e.g., in an oven, as required for earlier grades). 

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