Average molecular weight between crosslinks

Mc number average molecular weight between crosslinks... 

Fig. 42. Comparison of the experimental and calculated Hartmann-Hahn mismatch sideband patterns for polybutadienes with the average molecular weight between crosslinks M = 6810 (A), Mc = 2730 (B) and Mc = 1020 (adapted from Ref. 250>)...

The number of repeating units between crosslinks, N, a parameter appearing in equation (1), can be simply defined as the jratio of the number average molecular weight between crosslinks, Mc, to the average molecular weight of the clusters, Mq. 

Calculate the variation in entropy corresponding to a polydimethylsiloxane network of mass 6.89 g, with an average molecular weight between crosslinks Me = 8.3 X 10, subjected to a reversible uniaxial extension at 25°C until the length is double its initial length. 

For a crossllnked rubber sample, one simple parameter which can be used to roughly characterize the material is the crosslink density (v) or the average molecular weight between crosslinks (Mg a 1/v). It should be clear that this single parameter cannot completely represent a network in general. Nevertheless, it is well known that the viscoelastic behavior of a polymer network will vary with crosslink density as schematically depicted in Figure 1 for the creep behavior of a polymer at two crosslink densities < Vq. Here the kinetic theory of rubber elasticity... 

The average molecular weight between crosslinking points can be estimated, based on Ideal rubber elasticity theory In which... 

Usually, crosslink density is expressed in terms of the average molecular weight between crosslinks, M. There are several experimental techniques available for measurement of crosslink density, such as DMA, equilibrium swelling, NMR spectroscopy, and dielectric measurements, among other methods. Reviews on these experimental techniques are available in the literature (e.g.. Ref. [42]). Some aspects about three of the most important techniques are briefly highlighted here. 

Swelling experiments and stress-strain measurements are widely used to estimate the crosslinking density in liquid-crystalline networks [101,106-108], For ideal rubbers with tetrafunctional crosslinks, these techniques allow the evaluation of the number average molecular weight between crosslinks [104, 105]. 

Figure 8.9. Effect of diootyl sebaoate concentration in PVC composition on the average molecular weight between crosslinks. [Data from Wang Y Simonsen J Neto C P Rocha J Rials T G Hart E, J. Appl. Polym. Sci., 62, No.3, 17th Oct. 1996, p.501-8.

The number of chains per unit volume can be related to the density p and the average molecular weight between crosslinks M ... 

Crosslinked polymers can be characterised conveniently by defining their crosslink density as branch points per unit volume or average molecular weight between crosslinks. This parameter in conjunction with the molecular nature of the polymer defines whether the material will behave as an elastomer or as a rigid material, which shows either ductile or brittle failure behaviour. Fillers can be used to modify properties further across the whole range of polymer behaviour. Because inorganic fillers are, compared to most polymers, much stiffer and less extensible materials, their incorporation into a polymer will usually produce a composite material of reduced strain to failure and increased stiffness relative to the polymer, i.e., the composite will be less elastomeric or less ductile. Nevertheless, large quantities of fillers are used in polymers that already have low strains to failure and show brittle failure behaviour. This chapter will confine itself to a discussion of the use of fillers in ductile and brittle crosslinked polymers. 

Table 1 lists the swelling data for different bimodal PDMS networks swollen to equilibrium in benzene and in toluene at 25 C. x is the mole percent of short chains and M, represents the average molecular weight between crosslinks. 

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