Network chain length

Data on crack initiation were also presented by Le May and Kelley [105] but not further analysed. The authors were concerned that influences other than the network chain length could complicate or obscure simple relations. They suspected... 

With regard to elastomers of controlled structure, those having unusual distributions of network chain lengths have been of particular interest [88,89]. The most novel elastomer of this type consists of a binary combination of unusually short network chains (molecular weights of a few hundred) and the much longer chains typically associated with elastomeric behavior (molecular weights of ten or twenty thousand). Such a network is sketched in Figure 6. 

Figure 6 A network having a bimodal distribution of network chain lengths. The short chains are arbitrarily shown by heavier lines than the long chains, and the dots represent the crosslinks, typically resulting from the end linking of functionally terminated chains. 

IR dichroism has also been particularly helpful in this regard. Of predominant interest is the orientation factor S=( 1/2)(3—1) (see Chapter 8), which can be obtained experimentally from the ratio of absorbances of a chosen peak parallel and perpendicular to the direction in which an elastomer is stretched [5,249]. One representation of such results is the effect of network chain length on the reduced orientation factor [S]=S/(72—2 1), where X is the elongation. A comparison is made among typical theoretical results in which the affine model assumes the chain dimensions to change linearly with the imposed macroscopic strain, and the phantom model allows for junction fluctuations that make the relationship nonlinear. The experimental results were found to be close to the phantom relationship. Combined techniques, such as Fourier-transform infrared (FTIR) spectroscopy combined with rheometry (see Chapter 8), are also of increasing interest [250]. 

J.E. Mark, Improved elastomers through control of network chain-length distributions. In P.N. Prasad, J.E. Mark, S.H. Kandil and Z.H. Kafafi (Eds.), Science and Technology of Polymers and Advanced Materials, Plenum, New York, 1998, p. 85. 

This suggests that network chain length distribution had negligible effect on the equilibrium tensile behavior for the range of investigated in this study = 1.1-2.5). 

Mark, J. E. Improved Elastomers Through Control of Network Chain-Length Distribution. In Science and Technology of Polymers and Advanced Materials Emerging Technologies and Business Opportunities, Prasad, P. N., Ed. Plenum New York, 1998 pp 85-98. 

The accumulation of structural information regarding a network is not an easy task. Direct measurements through optical techniques are often open to various interpretations. Also, their resolving power with respect to factors, important in elasticity, (as, for example, network chain length distribution) is often insufficient. It is, therefore, necessary to obtain structural information through studies of the network formation processes (Chapter II). 

The cyclic fragment at m/z = 459 probably reflects the network chain length of the crosslinked polymer. 

H and 2H NMR have been used in styrene-butadiene rubber (SBR) with and without carbon-black fillers to estimate the values of some network parameters, namely the average network chain length N. The values obtained from both approaches were checked to make sure that they were consistent with each other and with the results of other methods [71, 72, 73]. To this purpose, a series of samples with various filler contents and/or crosslink densities were swollen with deuterated benzene. The slopes P=A/ X2-X 1) obtained on deuterated benzene in uniaxially stretched samples were measured. The slopes increase significantly with the filler content, which suggests that filler particles act as effective junction points [72, 73]. 

Thus, the level of sophistication which one may consider for the application of rubber-like elasticity theory to epoxy networks may depend on the application. For highly crosslinked systems (M < 1,000), a quantitative dependence of the rubbery modulus on network chain length has recently been demonstrated , but the relevance of higher order refinements in elasticity theory is questionable. Less densely crosslinked epoxies, however, are potentially suitable for testing modern elasticity theories because they form via near quantitative stepwise reactions. Detailed investigations of such networks have been reported by Dusek and coworkers in recent studies ... 

The shear modulus of a rubber is inversely proportional to the average network chain length according to the Gaussian theory of rubber elasticity [19]. Therefore, examination of the storage modulus above the Tg provides the evidence for network hydrolytic resistance. Figure 12.13 shows that the storage modulus (Eg)... 

Characterizing cross-linked networks according to molar mass is unrealistic in regard to their infinite size. Such cross-linked networks are classified according to the network chain length, kind of cross-link, and cross-link density. Here a cross-link point is defined as a group from which more than two network chains extend. A network chain corresponds to that portion of the chain which joins two cross-link points together. 

Three-dimensional cross-linked networks are, according to definition, considered to be infinite in size. It is therefore pointless to consider their molecular weights. Such cross-link networks are classified according to the network chain lengths, branch type, and branch density. 

MX is the number-average network chain length. With very extensive cross-linking this formula cannot be used, because in such a case the number of free ends is too high. 

Madkour, T. Mark, J. E., Some Evidence on Pore Sizes in Poly(dimethylsiloxane) Elastomers Having Unimodal, Bimodal, or Trimodal Distributions of Network Chain Lengths. Polym. Bull. 1993, 31, 615-621. 

Multimodal networks represent a method to determine the effect of network chain-length distribution - on rubberlike elasticity. Chain-length distribution has not received much attention even though manipulation of the chain-length distribution can give large improvements in mechanical properties. There are two primary reasons for this... 

There are a number of reasons for developing techniques for controlling network chain-length distributions one is to check the weakest-link theory for elastomer rupture, which states that the shortest chains are the culprits in causing rupture. Due to their limited extensibility, short chains supposedly break at relatively small deformations and then act as rupture nuclei. 

The distribution of network chain lengths in a bimodal elastomer can be much different from the usual unimodal distribution obtained in less-controlled methods of cross linking. Figure 7.15 shows a schematic... 

Network chain-length distributions in which is the number of chains in an infinitesi-... 

Some Rheovibron viscoelasticity results have been reported for bimodal PDMS networks. Measurements are first carried out on uni-modal networks consisting of the chains used in combination in the bimodal networks. One of the important observations was the dependence of crystallinity on the network chain-length distribution. 

The network chain-length distributions shown in figure 7.15, with the addition of the extremely broad pseudo-unimodal distribution obtainable by combining a number of samples of the same polymer made in different polymerizations. 

Sun, C.-C. Mark, J. E., The Effect of Network Chain Length Distribution, Specifically Bimodality, on Strain-Induced Crystallization. J. Polym. Sci., Polym. Phys. Ed. 1987,25, 2073-2083. 

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