Steric layer thickness

Fig. 6.2. Schematic Fepresentation of the close approach of two sterically stabilized particles a=particle radius, 5=steric layer thickness and f(,=minimum distance of closest approach of the particle surfaces.

The second factor postulated to be responsible for coagulation is an increase in the van der Waals attraction between the stabilizing sheaths arising from the increased segmental concentration that accompanies any reduction in steric layer thickness. This seems likely to be a minor effect, however. 

Here d=centre-to-centre distance and R = 2 a + S), where a = particle radius and 5 = steric layer thickness. The pair potential V(d) was assumed to be... 

The simplest interpretation of the dramatic increase in the measured force when D Rg is that it is the elastic repulsion arising from the compression of the attached polystyrene chains by the close approach of the opposite plate. Since the first sign of steric interaction occurs at ca 3/J, this suggests that the steric layer thickness is 1 -SRg. Consequently, elastic compression of the chains would certainly be expected when D Rg. 

As the particle size shrinks below a micron, the steric layer thickness required to stabilize the particle also shrinks. For a 100 nm particle, stability will be achieved when Rg 50 nm while for 10 nm particle, the above estimates suggest steric layer ofthickness of 0.1-1 nm will be sufficient to keep particles out of a deep van der Waals minimum. Indeed if the particles are treated as being molecularly smooth and the minimum distance... 

For many applications such as catalysis and possible functional devices, SAMs are simply too thin, the organized structure not flexible enough or the sterical situation within the layer too confined in order to incorporate a desired function or respond to changes in the environment in a dynamic and reversible way. One approach to increase the layer thickness of well-ordered self-assembled stractures of up to 100 nm is the formation of SAM and LB multilayers by means of consecutive preparation steps (Fig. 9.1 (3)) [5, 108]. This strategy was successfully applied by several research groups, but requires the constant intervention of the experimenter to put one type of monomolecular layer on top of the other. The dynamic behavior of the layer is limited by the crystal-like organization of the system and the extreme confinement of all surface-bonded molecules. Hence, surface... 

In order to be able to include a steric contribution in the interparticle energy calculation, an estimate of the adsorbed layer thickness is required. This is very difficult to access experimentally probably the only technique which might be able to provide an estimate is small-angle neutron scattering which was beyond the scope of this work. As a result, a theoretical estimation of the thickness was made, based on a few key observations. This is described below. 

Using this data for the layer thickness, the total energy of interaction was calculated by summing the electrostatic and steric contributions, the latter of which was calculated according to the method of Ottewill. Total interaction energies at three values of interparticle separation are shown in Figure 11 as a function of polymer dose. 

Steric elution mode occurs when the particles are greater than 1 jm. Such large particles have negligible diffusion and they accumulate near the accumulation wall. The mean layer thickness is indeed directly proportional to D and inversely proportional to the field force F (see Equation 12.3). The condition is depicted in Figure 12.4b. The particles will reach the surface of the accumulation wall and stop. The particles of a given size will form a layer with the particle centers elevated by one radius above the wall the greater the particle dimension, the deeper the penetration into the center of the parabolic flow profile, and hence, larger particles will be displaced more rapidly by the channel flow than smaller ones. This behavior is exactly the inverse of the normal elution mode and it is referred to as inverted elution order. The above-described mechanism is, however, an oversimplified model since the particles most likely do not come into contact with the surface of the accumulation wall since, in proximity of the wall, other forces appear—of hydrodynamic nature, that is, related to the flow—which lift the particles and exert opposition to the particle s close approach to the wall. 

It is relevant to examine the role played by the relative sizes of the steric layer and that of the free polymer molecules. If the molecular weight of the adsorbed polymer is small compared to that of the free polymer, the thickness... 

In addition to the molecular weight of the free polymer, there axe other variables, such as the nature of the solvent, particle size, temperature, and thickness of adsorbed layer which have a major influence on the amount of polymer required to cause destabilization in mixtures of sterically stabilized dispersions and free polymer in solution. Using the second-order perturbation theory and a simple model for the pair potential, phase diagrams relat mg the compositions of the disordered (dilute) and ordered (concentrated) phases to the concentration of the free polymer in solution have been presented which can be used for dilute as well as concentrated dispersions. Qualitative arguments show that, if the adsorbed and free polymer are chemically different, it is advisable to have a solvent which is good for the adsorbed polymer but is poor for the free polymer, for increased stability of such dispersions. Larger particles, higher temperatures, thinner steric layers and better solvents for the free polymer are shown to lead to decreased stability, i.e. require smaller amounts of free polymer for the onset of phase separation. These trends are in accordance with the experimental observations. 

A reduction in poly electrolyte charge density to 10% results in further increase in adsorbed layer thickness. The steep steric repulsion is now... 

The most significant finding is that the plateau values at high electrolyte concentration are much larger than twice the adsorption layer thickness /iTOt > 2h (Table 3.6). This is rather unexpected since above Cw.cr, electrostatic repulsion is suppressed and steric interaction alone is expected to stabilise the film. If so, a total thickness close to the double brush thickness, i.e. /ijot 2h, would be expected. 

At film thickness larger than twice the adsorption layer thickness this type of force vanishes [248], Therefore, such a mechanism is operative only at Ijtot 2Iii = 21.2 nm, i.e. hw < 28.0 nm (Table 3.5). The solid line in Fig. 3.40 is the best fit of Eq. (3.87). The van der Waals component has no practical influence on the numerical procedure. The fitted value h = 11.1 nm is in good agreement with the value of 10.6 nm used in the three layers model. Thus, de Gennes theory [248] gives a satisfactory description of the steric interactions at film thickness where brush-to-brush contact is realised. 

Often in ceramic processing, where the surface potential is small or the double layer thickness is thin, the electrostatic repulsion is not sufficient to stabilize the colloidal suspension against coagulation. As a result another form of stabilization is needed—steric stabilization. Steric stabilization has been reviewed by two recent books, one by Napper [27] and the other by Sato and Rudi [26]. The following presentation draws heavily fiium both these books. 

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