Network chain segment

The uniaxial contribution to the stress-induced orientation (the second term in Equation 15.4) has been attributed mainly to orientational interactions between chain segments. When guest molecules are introduced in a rubber matrix, these interactions take place between network chain segments and guest molecules as well. This effect has been recognised earlier, and may be used to study indirectly the behaviour of the matrix. Two types of guest molecules have been used for this purpose. 

Figure 2.30 Idealized network structure of a crosslinked polymer. indicates a crosslink (junction) and —> signifies continuation of the network structure. Wavy, lines between crosslinks are active network chain segments. (Note that for a tetrafunctional crosslink, as shown here, the number of crosslinks is one-half the number of active network chain segments.)...

The presence of carbon-black filler usually does not affect the NMR data in contrast to functionalized silicate filler. This is attributed to rapid transverse relaxation of network chain segments near carbon-black filler particles caused by paramagnetic centers in the filler. Thus, for the technologically important... 

The first relationships between macroscopic sample deformation, chain extension, and entropy reduction were expressed by Guth and Mark (28) and by Kuhn (29,30) (see Section 5.3). Mark and Kuhn proposed the model of a random coil polymer chain (Figure 9.4) which forms an active network chain segment in the cross-linked polymer. When the sample was stretched, the chain had extended in proportion, now called an affine deformation. When the sample is relaxed, the chain has an average end-to-end distance, ro (Figure 9.4), which increases to r when the sample is stretched. (Obviously, if the sample is compressed or otherwise deformed, different chain dimensional changes will occur.)... 

Figure 9.4 A network chain segment (a) relaxed, with a random coii conformation, and (b)...

According to the statistical thermodynamic approach to be developed below, each conformation that a network chain segment may take is equally probable. The number of such conformations depends on the end-to-end distance, r, of the chain, reaching a rather sharp maximum at tq. The retractive force of an elastomer is developed by the thermal motions of the chains, statistically driven toward their most probable end-to-end distance, Tq. 

An Example of Rubber Elasticity Calculations Suppose that an elastomer of 0.1 cm x 0.1 cm x 10 cm is stretched to 25 cm length at 35°C, a stress of 2 X10 dynes/cm being required. What is the concentration of active network chain segments ... 

Effect on the number of network chain segments concentration, n. The quantity n decreases with volume ... 

The present experiment is based on the rapid swelling of elastomers by organic solvents. Application of the Flory-Rehner equation yields the number of active network chain segments per unit volume, a measure of the extent of vulcanization (C1,C2). 

Figure 10.7 (8) illustrates the stress relaxation of a poly(dimethyl siloxane) network, silicone rubber, in the presence of dry nitrogen. The reduced stress, o(t)/(T(0),is plotted,so that under the initial conditions its value is always unity. Since the theory of rubber elasticity holds (Chapter 9), what is really measured is the fractional decrease in effective network chain segments. The bond interchange reaction of equation (10.2) provides the chemical basis of the process. While the rate of the relaxation increases with temperature, the lines remain straight, suggesting that equation (10.2) can be treated as the sole reaction of importance. 

According to Lake and Thomas, this difference has been attributed to the polymeric nature of the molecular chains comprising the network many bonds must be stressed in order to break any one bond. As defined in Chapter 9, Me is the molecular weight of an active network chain segment bound on either side by cross-links. The equation predicts that lower cross-link densi-... 

A system exhibiting short-range orientational correlations among interacting species requires to modify the usual pair interaction parameters Xij (i = network chain segment, j = free chain segment or... 

Our approach to the problem of gelation proceeds through two stages First we consider the probability that AA and BB polymerize until all chain segments are capped by an Aj- monomer then we consider the probability that these are connected together to form a network. The actual molecular processes occur at random and not in this sequence, but mathematical analysis is feasible if we consider the process in stages. As long as the same sort of structure results from both the random and the subdivided processes, the analysis is valid. 

V and n are the number of network chains per unit volume and the number of the segments in a network chain, respectively... 

The 6-function makes sure that if two segments and 2 meet on the huge network chain they can form a permanent constraint R( i) = R( 2)- Hence, this process will produce a network junction of functionality/n = 4, usually realized as sulfur bridges in technical elastomers like, for example, tire treads. 

An example of a relevant optical property is the birefringence of a deformed polymer network [246]. This strain-induced birefringence can be used to characterize segmental orientation, both Gaussian and non-Gaussian elasticity, and to obtain new insights into the network chain orientation (see Chapter 8) necessary for strain-induced crystallization [4,16,85,247,248]. 

If we were to have an isolated polymer chain with a single nuclear spin attached to each segment (the marked chain) crosslinked into an unmarked network, the second moment of the NMR line of that spin species would carry information relating to the separation of chain segments, and to their relative orientation with respect to the field direction. If the network were to be subjected to a bulk deformation, these geometrical parameters would be altered, and hence we would expect a corresponding change in the value of the experimentally measured... 

The degree of cross-linking can be expressed in terms of cross-links per gram or per unit volume. If C is the moles of cross-links per unit volume, n the number of network chains per unit volume, d the density of cross-linked polymer, and Me the number-average molecular weight of the polymer segments between cross-links, then... 

Load Sharing of Filler Particles. Comparison of ultimate strength of a propellant and its unfilled binder matrix almost always shows that the propellant has up to several times the tensile strength of the matrix. This filler reinforcement is presently thought to stem from additional crosslinks formed between filler particles and the network chains of the binder matrix (5, 8, 9, 34). Effective network chains are defined as the chain segments between crosslinks. From the classical theory of elasticity, the strength and/or modulus of an elastomer is proportional to the number of effective network chains per unit volume, N, or... 

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