Molecular weight between linkings

The value of E in the rubbery region was theoretically and experimentally studied and it was found to be proportional to the crosslinking density (g) or inverse to the molecular weight between linkings (Mc). Tobolsky 1,28>, used Eq. (9) to demonstrate the interrelationship ... 

A cross-linked polymer has a density of 0.94 g cm" at 25°C and a molecular weight between crosslinks of 28,000. The conformation of one bond in the middle of the molecule changes from trans to gauche, and the molecule opens up by 120°. In w-butane, the trans to gauche transformation requires about 3.3 kJ mol". Estimate a value for AH of stretching based on this model, and use the law of cosines to estimate the magnitude of the opening up that results. 

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 9. SANS measurements of R /Rt° and RL/R ° for stretched radiation cross-linked polystyrene. is determined by measurements in which the neutron is parallel (iso) and perpendicular (aniso) to the stretching direction. Mc is molecular weight between crosslinks. Theoretical curves 2 and 3 are drawn for tetrafunctional networks. Data from Ref. 21.

C. C. Han, H. Yu and their colleagues (23) have presented some new SANS data on end-linked trifunctional isoprene networks. These are shown in Figure 10. Those materials of low molecular weight between crosslinks exhibit greater chain deformation consistent with the thesis that the junction points are fixed. This is the reverse of that found by Beltzung et al. for siloxane networks. 

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...

The synthesis and phase behavior of the model polydiethylsiloxane networks have also been studied. The networks were made by hydrosilylation of well-defined vinyl and allyl telechelic siloxanes obtained by kinetically controlled polymerization of cyclic trisiloxane.314 The effects of molecular weight between the cross-linkings on segment orientation in polydiethylsiloxane elastomers were studied.315... 

Condensation in acid medium gives soluble, fusible phenolic resins, with an average molecular weight between 600 and 1,500, and a structure consisting essentially of phenol residues linked by methylene groups in the ortho- and para-positions they are called Novolaks. No further condensation occurs on heating... 

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]...

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