Networks bimodal

For chains having fewer than 50 bonds, such as the short chains in a bimodal network, for example, the distribution departs markedly from the Gaussian limit. 

Most bimodal networks synthesized to date have been prepared from PDMS [88], One reason for this choice is the fact that the polymer is readily available with either hydroxyl or vinyl end groups, and the reactions these groups participate in are relatively free of complicating side reactions. These ideas can obviously be extended to higher modalities (trimodal, etc., eventually approaching an extremely broad, effectively-unimodal distribution) [102-104],... 

Figure 7 Typical dependence of nominal stress against elongation for two unimodal networks having either all short chains or all long chains, and a bimodal network having some of both.

Equi-biaxial extension results have been obtained by inflating sheets of unimodal and bimodal networks of PDMS [114,115]. Upturns in the modulus were found to occur at high biaxial extensions, as expected. Also of interest, however, are pronounced maxima preceding the upturns. Such dependences represent a challenging feature to be explained by molecular theories addressed to bimodal elastomeric networks in general. 

Some viscoelasticity results have been reported for bimodal PDMS [120], using a Rheovibron (an instrument for measuring the dynamic tensile moduli of polymers). Also, measurements have been made on permanent set for PDMS networks in compressive cyclic deformations [121]. There appeared to be less permanent set or "creep" in the case of the bimodal elastomers. This is consistent in a general way with some early results for polyurethane elastomers [122], Specifically, cyclic elongation measurements on unimodal and bimodal networks indicated that the bimodal ones survived many more cycles before the occurrence of fatigue failure. The number of cycles to failure was found to be approximately an order of magnitude higher for the bimodal networks, at the same modulus at 10% deformation [5] ... 

Birefringence measurements have been shown to be very sensitive to bimodality, and have therefore also been used to characterize non-Gaussian effects resulting from it in PDMS bimodal elastomers [5,123]. The freezing points of solvents absorbed into bimodal networks are also of interest since solvent molecules constrained to small volumes form only relatively small crystallites upon crystallization, and therefore exhibit lower crystallization temperatures [124—126]. Some differential scanning calorimetry (DSC) measurements on... 

Figure 1. Sketch of a portion of a bimodal network. The very short polymer chains are represented by heavy lines and the relatively long chains by thinner lines.

Swelling. Work in progress (52) indicates that the upturns in [f ] for PDMS bimodal networks are not decreased by swelling, which would have diminished any strain-induced crystallization (36,37). 

Strain-induced crystallization would presumably further improve the ultimate properties of a bimodal network. It would therefore obviously be of considerable importance to study the effect of chain length distribution on the ultimate properties of bimodal networks prepared from chains having melting points well above the very low value characteristic of PDMS. Studies of this type are being carried out on bimodal networks of polyethylene oxide) (55), poly(caprolactone) (55), and polyisobutylene (56). 

Kilian 103) has used the van der Waals approach for treating the thermoelastic results on bimodal networks. He came to a conclusion that thermoelasticity of bimodal networks could satisfactorily be described adopting the thermomechanical autonomy of the rubbery matrix and the rigid short segments. The decrease of fu/f was supposed to be related to the dependence of the total thermal expansion coefficient on extension of the rigid short segment component. He has also emphasized that calorimetric energy balance measurements are necessary for a direct proof of the proposed hypothesis. 

An additional bonus exists if the chains in the bimodal network readily undergo strain-induced crystallization.92,274,278,282 It has been observed that the extent to which the bimodal networks are superior to their unimodal counterparts is larger at lower temperatures. This indicates that the bimodal character of the chain length distribution facilitates strain-induced crystallization. Apparently the short chains increase the orientation of the long chains, and this facilitates the crystallization process. 

Figure 4.11 Sketch of a bimodal network. Reproduced by permission of Huthig and Wepf Verlag.

Some recent computational studies,287 however, indicate that it is possible to do simulations to identify those molecular weights and compositions that should maximize further improvements in mechanical properties. Results to date283 suggest that a trimodal network prepared by incorporating small numbers of very long chains into a bimodal network of long and short chains could have significantly improved ultimate properties. 

The ability of sulfur to form chains is also important in the sulfur vulcanization of diene elastomers such as natural rubber. In this case, strings of sulfur atoms of varying length form the cross-links that tie one chain to another. In this sense, they can be thought of as the short chains of a short chain-long chain bimodal network, as was described in Chapter 4. 

Bulky crosslinks or side-groups in the network chains, e.g., dendritic wedges [73], may also influence molecular mobility and viscoelastic properties of polymer networks. For example, UV curing of difunctional acrylates results in the formation of zip-like network junctions, which may be regarded as extreme cases of bimodal networks [52], Results obtained with the NMR T2 relaxation method agree well with those of mechanical tests... 

One of the most interesting types of model networks is the bimodal network (Figure 8), which consists of very short chains intimately end linked with the much longer chains that are representative of elastomeric materials (38-40, 44). In Figure 8 (44), the short chains are drawn arbitrarily thicker... 

Figure 8. Bimodal network. (Reproduced with permission from reference 44. Copyright 1979 Hiithig and WepfVerlag.)...

Non-Gaussian EflFects and Intermolecular Correlations in Bimodal Networks of Poly(dimethylsiloxane)... 

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