Molecular weight between branching points

The correlation of average molecular weight between branch points wdth the swelling of a urethane elastomer is shown in Figure 19. As the chain length between cross links increases, or cross linking decreases, swelling is increased, since the solvent molecule can penetrate more readily the three-dimensional polymer. 

Crosslinked polyurethanes are not soluble and of course swell, the degree of swelling decreases with the increase in crosslink density. For example, for a flexible polyurethane foam in the presence of acetone, the degree of swelling is around 116% at a molecular weight between branch points (Mc) of 1650 and becomes 90% at a Mc of 1070 and 83% at a Mc of 690 [2]. 

We have seen in Section 4, that a measurement of the critical current Jc> performed at two diameters (D < D and D > D ) should allow for the determination of two unknowns the molecular weight (proportional to X) and the distance between branch points. 

For crosslinked polymers (in this category they are the majority of polyurethanes, for example flexible, semiflexible and rigid PU foams, etc.), which have a MW that is practically infinite [12], the molecular weight between the branching points (Mc) is considered. The value of Mc depends strongly on the oligo-polyol structure. 

Molecular weight between the branching points Molecular weight distribution... 

In conclusion, graft copolymers of various chemical natures and grafting densities are accessible via various polymerization methods by grafting onto methods. However, until recently the control of the spacing between branch points combined with backbones of well-controlled molecular weight was rather difficult to achieve. 

As the properties of hyperbranched polymers are influenced by the nature of the backbone and the chain end functional groups, the degree of branching, the chain length between branching points, and the molecular weight and distribution, it is often useful to modify existing polymers to obtain versatihty in the above parameters and thus the properties required. 

Starch from a variety of crops such as com, wheat, rice and a potato is a source of biodegradable plastics, which are readily available at low cost when compared with most synthetic plastics (Ma, Chang, Yu, 2008a). Starch is comprised of amylose, a linear polymer with molecular weight between 103 and 106 and amylopectin, a branched polymer with a-(l-6)-linked branch points (Fig. 1.2a-b) (Dufresne Vignon, 1998). 

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. 

Here, A is a numerical prefactor having units of (Pa s mol)/g and is specific to molecular composition and temperature, Mb is the molecular weight (MW) between branch points, M is the critical MW for entanglements, Mw is the weight... 

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