Crosslink connectivity

Figure 5.15 illustrates the two general types of crosslink. In Fig. 5.15 a), a short crosslink connects adjacent chains to form a four-armed star , the arms of which are normally unequal in length. In Fig. 5.15 b), a longer crosslink connects two adjacent molecules. When... 

The next breakthrough came with the discovery of how to make almost linear polymers with just a few crosslinked connections between molecules. These materials will not flow after crosslinking, and they become elastomers. A final type is the heavily crosslinked polymers such as epoxy and urea-formaldehyde, which are processed as monomers and then crosslinked at a suitable time and rate to make paints, adhesives, and very hard and durable plastic materials. 

For a given crosslink connected with (p chains, F is given by... 

The description of a network structure is based on such parameters as chemical crosslink density and functionality, average chain length between crosslinks and length distribution of these chains, concentration of elastically active chains and structural defects like unreacted ends and elastically inactive cycles. However, many properties of a network depend not only on the above-mentioned characteristics but also on the order of the chemical crosslink connection — the network topology. So, the complete description of a network structure should include all these parameters. It is difficult to measure many of these characteristics experimentally and we must have an appropriate theory which could describe all these structural parameters on the basis of a physical model of network formation. At present, there are only two types of theoretical approaches which can describe the growth of network structures up to late post-gel stages of cure. One is based on tree-like models as developed by Dusek7 I0-26,1 The other uses computer-simulation of network structure on a lattice this model was developed by Topolkaraev, Berlin, Oshmyan 9,3l) (a review of the theoretical models may be found in Ref.7) and in this volume by Dusek). Both approaches are statistical and correlate well with experiments 6,7 9 10 13,26,31). They differ mainly mathematically. However, each of them emphasizes some different details of a network structure. 

These theories are based on the classical theories of rubber elasticity of macromolecular solids, wherein permanent chemical crosslinks connect segments of molecules, forcing them to move together. This central idea can be applied to polymeric liquids. However in this case, the interactions between molecules are assumed to be localized at junctions and are supposed to be temporary. Whatever their nature, physical or topological, these crosslinks are continually created and destroyed but, at any time, they ensure sufficient connectivity between the molecules to give rise to a certain level of cooperative motion. 

Colloidal dispersion gel (CDG) is made of low concentrations of polymer and crosslinkers. Crosslinkers are the metals, such as aluminum citrate and chromium, referred to as aggregates. Polymer concentrations range from 100 to 1200 mg/L, normally 400 to 800 mg/L. The ratio of polymer to crosslinkers is 30 to 60. Sometimes, this type of gel is called a low-concentration crosslinked polymer. In such concentration range, there is not enough polymer to form a continuous network, so a conventional bulk-type gel cannot form. Instead, a solution of separate gel bundles forms, in which a mixture of predominantly intramolecular and minimal intermolecular crosslinks connect relatively small... 

Equation (6-83) assumes that the network is a perfect one in that all chains in the network are effective in giving rise to the elastic stress. Ideally each crosslink connects four network chains, while each such chain is terminated by two crosslinks. However, as illustrated in Figure 6-2, a number of network imperfections are possible. Each linear polymer chain with molecular weight M, even if all crosslinks are "normal," must give rise to two terminal chains that are incapable of supporting stress. Thus the number of effective chains must not include the imperfections due to chain ends. On incorporating this correction, the shear modulus can be written as 18... 

The most important molecular parameter characteristic of a polymer network is the concentration of the elastic chains or that of the crosslinks connecting the macromolecules. An active junction is joined by at least three paths to the polymer network and an active chain is defined as one terminated by active junctions at both ends. There are several ways to express the extent of crosslinking (1) the concentration of the elastically active chains, r ei/Po, where v is the number of chains connecting two elastically active junctions and To is the volume of the dry network, (2) the molecular weight of the polymer chains between the junctions... 

A network of crosslinks connecting chains is represented by the number of configurations, counted by the integral... 

Increasing reeling speed can produce stronger but less extensible fibers (Figure 6.7). As the crosslinks connecting protein chains in silk fibrils (see Figure 6.2), P-crystaUites play important roles in determining mechanical properties of silk. The size and orientation of the crystallites as well as the... 

---