Network unimodal

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] ... 

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. 

If a unimodal pore network of arbitrary size is considered then, if the spatial distribution of pore sizes is non-random, the desorption percolation transition would be apparently smeared out (in addition to any finite size effect). It is possible that particular pores occupied by liquid-like phase might gain access to the vapour phase before would be expected to be the case for a purely random system because the actual layout of the pores might provide a convenient access route that would not have existed at that bond occupation level in a random system. The simulations of the nitrogen sorption... 

Figure 1. Theoretical curves of stress against strain for unimodal PDMS networks consisting of chains with 20 and 40 skeletal bonds, respectively.

This article describes models for linear chains of homopolymers and for unimodal, unfilled polymer networks. 

FIGURE 5.3. First three tiers of a unimodal, symmetrically grown, tetrafunctionai network (< = 4) with tree-like topology. 

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. 

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... 

But what happens in the case of bimodal networks having such overwhelming numbers of short chains that they cannot be ignored There is a synergistic effect leading to mechanical properties that are better than those obtainable from the usual unimodal distribution. The following sections describe these results in detail. 

If the network consists entirely of short chains, then the material is brittle (which means that the maximum extensibility is very small). If the network consists of long chains, the ultimate strength is very low. As a result, neither unimodal material has a large area under its stress-strain curve and, thus, neither is a tough elastomer. 

Schematic stress-strain isotherms in elongation for a unimodal elastomer in the Mooney-Rivlin representation of modulus against reciprocal elongation. The isotherms are represented as the dependence of the reduced stress ([f ] = f /(a - on reciprocal elongation. (f = f/A, f = elastic force, A = undeformed area, a = elongation). The top three are for a crystallizable network curve A for a relatively low temperature, B for an increased temperature, and C for the introduction of a swelling diluent. Isotherm D is for an unswollen unimodal network that is inherently noncrystallizable.

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. 

Wang, S. Mark, J. E., Unimodal and Bimodal Networks of Poly(dimeth)dsiloxane) in Shear. J. Polym. Sci., Polym. Phys. Ed. 1992,30,801-807. 

Wen, J. Mark, J. E., Torsion Studies of Thermoelasticity and Stress-Strain Isotherms of Unimodal, Bimodal, and Filled Networks of Polyfdimethylsiloxane). Polym. J. 1994,26,151-157. 

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