Cross-link molecular weight between

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). 

For the affine network model, the molecular weight between cross-links MC/af is obtained as... 

Figure 7. SANS measurements of R versus A. of swollen polystyrene networks. Mc is the molecular weight between cross-links. Key A, DVB/LE — 3 , DVB/ LE = 6 O, DVB/LE = 10. Data from Ref. 19.

Figure 1. Molecular weight between cross-links obtained from swelling data as a function of DCP...

Figure 6. PIP after Saunders, 1956. Stress optical coefficient as a function of molecular weight between cross-links (3, 52). PBD is polybutadiene. PIP is polyisoprene.

Figure 11. Variation of molecular weight between cross-links as a function of molecular weight...

Gluck-Uirsch, J., Kokini, J. L. (1997). Determination of the molecular weight between cross-links of waxy maize starches using the theory of rubber elasticity. J. RheoL, 41, 129-139. 

Fig. 5. Relation between the average molecular weight between cross-links, Mc, and the volume fraction of gelatinized collagen (gelatin), v2. The swelling agent is 0.19 mol/1 citric acid - phosphate buffer solution, pH 7.4 at 80 °C. Experimental data obtained after cross-linking with various aldehydes solid circles, formaldehyde open circles, glutaraldehyde squares, glyoxal. The curve is predicted by Eq. (2) with X = 0.52 0.04 [38]...

Number average molecular weight between cross-links. 

According to this method, the sample is calibrated by calculating the volume fraction of the polymer, v%, from the weight changes, or the dimensions of the sample, after immersion in a liquid for which ft is known (this is the case for many polymer-solvent systems). From V2 and /z, one obtains Met the average molecular weight between cross-links, according to the relation ... 

Model networks of known structure can be prepared by end-linking functionally-terminated polymer chains [3, 4, 157]. Because of the nature of this network formation process, the molecular weight of the starting chains becomes the critically important molecular weight between cross-links, Mc. Control of Mc and its... 

A final analogous situation occurs in the in-situ silica generation of silica particles within a polymer network. At least in some cases, the particles are constrained in size by the network strands, in that the maximum particle size observed decreases with decrease in the molecular weight between cross-links (increase in extent of cross-linking) [262, 263]. 

FIG. 6.5 Glass transition temperature, Tg, of styrene-divinylbenzene copolymers as a function of the reciprocal value of the molecular weight between cross-links, 1/Mcri (constructed from results presented by Bicerano, 2002). 

The shear modulus of the rubber network is related to the molecular weight between cross-link points or M. The lower the molecular weight of chains between cross-links (network chains), the higher the cross-link density and the higher the modulus. This is shown in the following expression ... 

Equation (4-46) predicts that the stress-strain properties of an elastomer that behaves like an entropy spring will depend only on the temperature, the density of the material, and the average molecular weight between cross-links. In terms of nominal strain this equation is approximately... 

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