Structure, dependence chain concentrations

These transient polymeric chains resulting from dipole-dipole interactions are responsible for the increase in solvent viscosity which is asymptotic above a certain concentration. The structure dependence of both solubility and viscosity in triorganotin compounds is known (1,2,3). For example, trimethyl and tripropyltin fluorides are insoluble in most organic solvents while the bulky trineophyltin fluoride (4) dissolves in many solvents but does not increase their viscosity. 

Figure 3. Dependence of the structure factors A, Ae, and As on the stoichiometric network chain concentrations.

The Eyring analysis does not explicity take chain structures into account, so its molecular picture is not obviously applicable to polymer systems. It also does not appear to predict normal stress differences in shear flow. Consequently, the mechanism of shear-rate dependence and the physical interpretation of the characteristic time t0 are unclear, as are their relationships to molecular structure and to cooperative configurational relaxation as reflected by the linear viscoelastic behavior. At the present time it is uncertain whether the agreement with experiment is simply fortuitous, or whether it signifies some kind of underlying unity in the shear rate dependence of concentrated systems of identical particles, regardless of their structure and the mechanism of interaction. 

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. 

In general, borates are structurally complex, since the boron atoms can be in 3 and/or 4 coordination and oligomer, ring, and chain polymers are all found (Christ and Clark, 1977 Wells, 1975). We shall not attempt to describe fully the complexity of these structures but will concentrate on the fundamental polyhedral units. The molecular geometric and electronic structures of these materials can be studied using many of the site-specific spectroscopies previously discussed. The bulk properties of the materials also change, of course, depending upon the molecular structure. 

So far, all theoretical models are based on surfactant solutions with a distribution of surfactant molecules as monomers. One of the specific properties of surfactants is that they form aggregates once a certain concentration, the critical micelle concentration CMC, is reached. The shape and size of such aggregates are different and depend on the structure and chain length of the molecules. At higher concentrations, far beyond the CMC, the phase behaviour is often complex giving rise to novel physical properties (Hoffmann 1990). 

---