First network modulus

The result is important for the discussion in Part 3. Multiplication of the v-values by RT gives the corresponding moduli. The effective modulus of the first network after removal of first network crosslinks, Gie, has been calculated for a first network modulus, G-j, of 0.75 MPa. In Figure 1, G. e is plotted against the modulus of the second network before removal of the first network cross-links, G2. It can be seen that the memory effect increases with increasing modulus or degree of cross-linking of the second network. Gx and G2 max are related to the experiment to be discussed in Part 3. 

Figure 1. Effective first network modulus, Gle, after complete removal of first network cross-links plotted against second network modulus, Gi. Calculated from the composite network theory of Flory (19J for G, — 0.75 MPa.

Figure 2. The principle of the two-network method for cross-linking in a state of simple extension. First network with modulus Gy is entirely due to chain entangling. Second network with modulus Gx is formed by cross-linking in the strained state. Both Gy and Gx can be calculated from the two-network theory.

Sequential IPN. The preceding analysis does not apply to the case of a sequential IPN. The formation of this system originates with the synthesis of the network (1). Then, network (1) is swollen with monomer (2) which is subsequently polymerized in situ to form a second network. Due to perturbed chain dimensions, the modulus of the first network is higher than the corresponding modulus in the unswollen state by a factor equal to v [ ] ... 

Sperling and coworkers supported the viewpoint of Thiele and Cohen. Furthermore, they came out with the su estion [228] that the behavior of IPNs is largely governed by the first network and found the corroboration of this idea in the results of the following experiments. A set of 0.22 X 2.2 Millar IPNs was synthesized in such a manner that the volume fractions of both networks were varied from 75 25 to 25 75, and for aU the IPNs, Youngs modulus, measured in the experiment, was compared with the modulus, E, calculated according to Eq. [2.2] (see ref [229]) as follows ... 

In all cases, the modulus showed a minimum when plotted vs. mixture composition which was most pronounced for the normal IPN. With the normal IPN, the plot resembled a superposition of the linear plots obtained with the pre-swollen networks. The hypothesis was advanced that the first network is topologically close to a pre-swollen network and that the second one may have a constrained structure but is at least partially similar to a pre-swollen network. 

The net effect is that tackifiers raise the 7g of the blend, but because they are very low molecular weight, their only contribution to the modulus is to dilute the elastic network, thereby reducing the modulus. It is worth noting that if the rheological modifier had a 7g less than the elastomer (as for example, an added compatible oil), the blend would be plasticized, i.e. while the modulus would be reduced due to network dilution, the T also would be reduced and a PSA would not result. This general effect of tackification of an elastomer is shown in the modulus-temperature plot in Fig. 4, after the manner of Class and Chu. Chu [10] points out that the first step in formulating a PSA would be to use Eqs. 1 and 2 to formulate to a 7g/modulus window that approximates the desired PSA characteristics. Windows of 7g/modulus for a variety of PSA applications have been put forward by Carper [35]. 

As pointed out in the first part of this work, tetrafunctionally crosslinked PDMS also shows some dependence of the energy part of the modulus on network density and on the measuring method, but the effects observed there, are much smaller than the great variation of /a with branching density in case of networks... 

Number-average molecular weights are Mn = 660 and 18,500 g/ mol, respectively (15,). Measurements were carried out on the unswollen networks, in elongation at 25°C. Data plotted as suggested by Mooney-Rivlin representation of reduced stress or modulus (Eq. 2). Short extensions of the linear portions of the isotherms locate the values of a at which upturn in [/ ] first becomes discernible. Linear portions of the isotherms were located by least-squares analysis. Each curve is labelled with mol percent of short chains in network structure. Vertical dotted lines indicate rupture points. Key O, results obtained using a series of increasing values of elongation 0, results obtained out of sequence to test for reversibility. 

The paper first considers the factors affecting intramolecular reaction, the importance of intramolecular reaction in non-linear random polymerisations, and the effects of intramolecular reaction on the gel point. The correlation of gel points through approximate theories of gelation is discussed, and reference is made to the determination of effective functionalities from gel-point data. Results are then presented showing that a close correlation exists between the amount of pre-gel intramolecular reaction that has occurred and the shear modulus of the network formed at complete reaction. Similarly, the Tg of a network is shown to be related to amount of pre-gel intramolecular reaction. In addition, materials formed from bulk reaction systems are compared to illustrate the inherent influences of molar masses, functionalities and chain structures of reactants on network properties. Finally, the non-Gaussian behaviour of networks in compression is discussed. 

The moduli and Tg s of the networks formed from the bulk reactions of the five systems of Figure 9 are shown in Table IV(29). The first five columns define the systems, the next two give the experimental values of G(at 298K) and Tg, and the last three give the values of pr,c, Mc, and G/G°. The last quantity is the reduction in rubbery shear modulus on the basis of that expected for the perfect network(G°). G/G° is in fact equal to M /Mc. 

Even though the governing phenomena of coupled reaction and mass transfer in porous media are principally known since the days of Thiele (1) and Frank-Kamenetskii (2), they are still not frequently used in the modeling of complex organic systems, involving sequences of parallel and consecutive reactions. Simple ad hoc methods, such as evaluation of Thiele modulus and Biot number for first-order reactions are not sufficient for such a network comprising slow and rapid steps with non-linear reaction kinetics. 

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