Interpenetrational-plus-compressional domain

Fig. 10.1. Schematic representation of the three domains of close approach for sterically stabilized flat plates (a) the noninterpenetrational domain (d>2 , ) (b) the interpenetrational domain (Ls

The interpenetrational-plus-compressional domain (dless than the span of the stabilizing moieties, the moieties on one surface are compressed by the opposing impenetrable surface. Interpenetration of the segments attached to one surface with the segments of the opposing compressed chains can still occur. This zone may therefore be termed the interpenetrational-plus-compressional domain (see Fig. 10.1c). 

Flory in his now classic theory of the intramolecular expansion factor a. Despite the expenditure of considerable effort, Flory s theory, or at least the Stockmayer (1960) modified version of it, has scarcely been improved upon in later years if comparison with experiment forms the judgemental basis (Yamakawa, 1971). In any event, the high segment densities often generated in the interpenetrational-plus-compressional domain are difficult to comprehend using the Flory-Huggins theory, especially if the interaction parameter is assumed to be concentration independent. 

The interpenetrational-plus-compressional domain is also important in heterostericdly stabilized dispersions where the different stabilizing sheaths are composed of compatible polymers. Elastic repulsion can give rise to heterosteric stabilization. 

B. The interpenetrational-plus-compressional domain. For dsteric layers are compressed and fid fiao- The simplifying relationships in this domain are iifid dx=Hfid steric interaction must be independent of which of the plates we designate I and II. Accordin y, we find in this domain, denoted by the subscript /+ C... 

In the interpenetrational-plus-compressional domain, the mixing free energy calculated as described above must be supplemented by the elastic free energy. Meier (1967) expressed this by the Boltzmann entropy relationship... 

One disadvantage of the approach of Fischer (1958) and Ottewill and Walker (1968) is that, as noted above, the formulae proposed by these authors are only valid for the mixing of constant segment density steric layers in the interpenetrational domain. Once the interpenetrational-plus-compressional domain is entered, no allowance is made for the elastic contribution to the free energy. The elastic interactions can become important, even paramount, when the minimum distance of separation between the surfaces of the particles (Hq) is less than the barrier layer thickness. An additional defect of the Fischer approach is apparent in this domain the overlap volume is decreased below that given by equation (12.8) because part of it is occupied by the cores of the particles. Both the Fischer and the Ottewill and Walker theories disregard this decrease in volume. Implicit in their formulae is the notion that the solid cores become equivalent to the steric barriers. This is, of course, quite unphysical. 

The corresponding expression for the interpenetrational-plus-compressional domain will be omitted because in that domain the chains would be expected to adopt a more symmetrical Gaussian-type distribution. 

In the interpenetrational-plus-compressional domain, the Gaussian distribution yields... 

In the interpenetrational-plus-compressional domain, for which the Fischer approach is incorrect, Smitham et al. (1975) showed that... 

The elastic repulsion. Once the interpenetrational-plus-compressional domain is entered, not only must the mixing contribution to the steric repulsion be considered but so too must the elastic contribution. As the second particle approaches closer than the span of the stabilizing chains, the chains are compressed and so must lose configurational entropy. This is the origin of the elastic repulsion. The elastic repulsion is relatively insensitive to the solvency of the dispersion medium, being influenced by its nature only insofar as the solvency affects the chain conformation. 

Comparison of theory with experiment. It will be shown in Section 13.3.2.1 that the flat plate potentials can be used to calculate the osmotic disjoining pressures in concentrated monodisperse sterically stabilized dispersions. Evans and Napper (1977) have compared the theoretical predictions using the above equations with those measured by Homola and Robertson (1976) for polystyrene latex particles stabilized by poly(oxyethylene) of molecular weight ca 2 000 in aqueous dispersion media. The elastic repulsion in the interpenetrational-plus-compressional domain was estimated from the following expression for the constant segment density model... 

The interpenetrational-plus-compressional domain. In the interpenetrational-plus-compressional domain, defined by hexcess free energy of mixing is given by... 

Qualitative predictions of the theory Provided that L3 is not excessively small, the interpenetrational domain will determine the flocculation behaviour in heterosterically stabilized systems, just as it does in homosteric stabilization. In the limit of small L3, the interpenetrational-plus-compressional domain may well become important in predicting incipient instability. The elaboration of the general principles that govern heterosteric stabilization is then quite different. 

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