Cross-linked network parameter

Blends of elastomers are routinely used to improve processability of unvulcanized rubbers and mechanical properties of vulcanizates like automobile tires. Thus, cis-1,4-polybutdiene improves the wear resistance of natural rubber or SBR tire treads. Such blends consist of micron-sized domains. Blending is facilitated if the elastomers have similar solubility parameters and viscosities. If the vulcanizing formulation cures all components at about the same rate the cross-linked networks will be interpenetrated. Many phenolic-based adhesives are blends with other polymers. The phenolic resins grow in molecular weight and cross-link, and may react with the other polymers if these have the appropriate functionalities. As a result, the cured adhesive is likely to contain interpenetrating networks. 

The viscosity method for soluble polymers and the swelling method for cross-linked network polymers yield quite unambiguous values for polymer solubility parameters, so long as one is confined to a series of structurally similar solvents. For example, the data in Figure 6-1 apply to aliphatic hydrocarbons as well as to long-chain esters and ketones. Cycloaliphatic hydrocarbons and short-chain esters such as ethyl acetate deviate significantly from the curves shown. 

If the Flory-Huggins interaction parameter is known from other methods, the effective number of cross-linked network chains can be calculated from the observed volume fraction of polymer in the gel. 

Owing to their cross-linked network, thermosetting resigns are principally known to be less susceptible to corrosion than some thermoplastic materials. Nonetheless, as shown by Bornbaum (2010), a prediction of long-term stability of polymers in fuel cell operation is hardly possible. Thus, the immersion or accelerated lifetime test should be applied on every novel material which has not been operated successfully in a fuel cell over a several thousand hours. These tests may save considerable amounts of time and can be performed before a fuel cell is set up. Nevertheless and finally, only a long-term test in fuel cells at various parameters and different conditions can provide ultimate certainty as to whether a newly developed composite is suitable or not. 

In the case of perfect networks, combination of equations (47), (107), (112) and (113) yields equation (124). Thus, k depends on the inverse square-root of the phantom modulus and is independent of swelling. The factor is Avogadro s number, which appears in equation (124) since n in equation (112) is the number of junctions and not the number of moles of junctions. In the case of randomly cross-linked networks, use of equation (61) yields equation (125). In the case of networks formed by random cross-linking of star polymers, equation (63) is used instead of equation (61) to derive the expression for k. The other parameter C is the result of the relationship between k and network inhomogeneities and its magnitude is estimated by experiment. 

The additional term on the right-hand side of the above equation compared to Equation 2.17 is negligible for small values of V2 or for cross-links of high functionality. Equations 2.17 and 2.18 can be represented in the form of nomographs for ease of determination of an unknown parameter given that the other parameters in the equation are known. Figure 2.4 represents such a nomograph based on Equation 2.18 for tetrafunctionally cross-linked networks (f= 4). 

We shall see in Chapter 7 how to obtain the values of the interaction parameter % given theoretically in Equation 2.13 from the measurements of viscosity of dilute polymer solutions. If the polymer comprises a cross-linked network, solution cannot occur, but individual parts of the polymer chains, that is, polymer segments, can solvate to give a swollen gel. Once again, it is expected that the maximum swelling will take place when the value of 82 matches 8j of the solvent and the interaction parameter % is at its minimum. 

Model Networks. Constmction of model networks allows development of quantitative stmcture property relationships and provide the abiUty to test the accuracy of the theories of mbber elasticity (251—254). By definition, model networks have controlled molecular weight between cross-links, controlled cross-link functionahty, and controlled molecular weight distribution of cross-linked chains. Sihcones cross-linked by either condensation or addition reactions are ideally suited for these studies because all of the above parameters can be controlled. A typical condensation-cure model network consists of an a, CO-polydimethylsiloxanediol, tetraethoxysilane (or alkyltrimethoxysilane), and a tin-cure catalyst (255). A typical addition-cure model is composed of a, ffl-vinylpolydimethylsiloxane, tetrakis(dimethylsiloxy)silane, and a platinum-cure catalyst (256—258). 

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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