Steric adsorbed layer thickness

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. 

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

State (g) represents the case of weak and reversible flocculation. This occurs when the secondary minimum in the energy distance curve is deep enough to cause flocculation. This situation can occur at moderate electrolyte concentrations, in particular with larger particles the same occurs with sterically and electrosterically stabihsed suspensions. It also occurs when the adsorbed layer thickness is not very large, particularly with large particles. The minimum depth required to cause... 

Adsorbed layer thickness 5 The steric interaction starts at h = 28 as the chains begin to overlap and increases as the square of the distance. Here, the important point is not the size of the steric potential but rather the distance h at which it begins. 

For sterically stabilised dispersions, the resulting energy-distance curve often shows a shallow minimum at particle-particle separation distance h comparable to twice the adsorbed layer thickness 5. For a given material, the depth of this minimum depends upon the particle size R, and adsorbed layer thickness S consequently, decreases with increase in S/R, as illustrated in Figure 11.4. 

The effective volume fraction increases with a relative increase of the dispersant layer thickness. Even at 10% volume fraction, a maximum packing (< = 0.67) is soon reached, with an adsorbed layer thickness that is comparable to the particle radius. In this case, overlap of the steric layers wiU result in significant increases in viscosity. Such considerations may help to explain why solids loading can be severely Hmited, especially with small particles. In practice, soUds loading curves can be used to characterize the system, and take the form of those illustrated in Figure 11.6... 

Figure 12.9), which shows a shallow minimum, G (weak attraction) at h 28 that is, at h 20 nm for the present W/O emulsion based on PHS-PEO-PHS block copolymer. When h < 25, Gj is increased very rapidly with further decreases in h. The depth of the minimum, G , will depend on the adsorbed layer thickness. In the present W/O emulsion, based on a PHS layer thickness of about 10 nm, G j is very small (fraction of kT). This shows that, with the present sterically stabilised W/O emulsion, there is only a very weak attraction at a relatively long distance of... 

Steric Stabilisation and the Role of the Adsorbed Layer Thickness 281... 

The last criterion for effective steric stabilization is to have a sufficiently thick or grafted polymer layer to screen the van der Waals attraction. An adsorbed layer thickness in the region of 5-10 nm is usually sufficient in most cases, particularly when the dispersion particle size is not too high (a few pm). With graft copolymers, a molecular weight of the side chains of the order of... 

In nature as well as in technology, polymeric emulsifiers and stabiUzers play a major role in the preparation and stabiUzation of emulsions. Natural materials such as proteins, starches, gums, cellulosics, and their modifications, as well as synthetic materials such as polyvinyl alcohol, polyacryhc add, and polyvinylpyrrolidone, have several characteristics that make them extremely useful in emulsion technology. By the proper choice of chemical composition, such materials can be made to adsorb strongly at the interface between the continuous and dispersed phases. By their presence, they can reduce interfacial tension and/or form a barrier (electrostatic and/or steric) between drops. In addition, their solvation properties serve to increase the effective adsorbed layer thickness, increase interfacial viscosity, and introduce other factors that tend to favor the stabilization of the system. 

Plots of G and G, versus h are illustrated in Figure 14.8. This figure shows that G increases very rapidly with decrease of h as soon as h becomes smaller than 2S (and % < 0.5). G, also increases very rapidly with decrease of h on further overlap. Combination of G , G, and G (the van der Waals attraction) results in the total Gj--h curve shown in Figure 14.8. This curve shows a minimum (G J ath — 25, but when h < 25, Gj- increases very rapidly with further decrease in h. The depth of the minimum, G , , depends on the adsorbed layer thickness. With increase of 5, G , decreases and at sufficiently high values of 5 (of the order of 5-10 nm), it reaches small values (fraction of kT units). This shows that with sterically stabilized dispersions, there is only weak attraction at relatively long distances of separation, which in most cases is overcome by the Brownian diffusion. Thus, one can say that the net interaction is repulsive, and this ensures the long-term stability of the dispersion. 

The above trend is also observed if G, G, and G" are plotted versus This is illustrated in Figure 16 for the above emulsions at a frequency of 2 Hz. At ( ) < 0.56, G" > G, whereas at c ) > 0.56, G > G". This reflects the increase in steric interaction with increase in ( ). At c ) < 0.56, the droplet-droplet separation is probably larger than twice the adsorbed layer thickness and hence the adsorbed layer are not forced to overlap or compress. In this case, the repulsive interaction between the adsorbed layers is relatively weak and the emulsion shows a predominantly viscous response. However, when > 0.56, the droplet-droplet separation may become smaller than twice the adsorbed layer thickness and the chains are forced to interpenetrate and/or compress. This leads to strong steric repulsion and the emulsion shows predominantly elastic response. The higher the ( ) value, the smaller the distance between the droplets and the stronger the steric interaction. This explains the rapid increase in G as ( ) increases above 0.56 and the progressively larger value of G relative to G". 

The effect of droplet size and its distribution on the adsorbed layer thickness may be inferred from a comparison of the results obtained with the o/w emulsions with those recently obtained using polystyrene latex dispersions containing grafted PEO chains of (molecular weight 2000) (49). As discussed earlier, the viscoelastic behavior of the system (which reflects the steric interaction) is determined by the ratio of the adsorbed layer thickness to the particle radius (8/R). The larger this ratio, the lower the volume fraction at which the system changes from predominantly viscous to predominantly elastic response. With relatively polydisperse systems, ( )cr shifts to higher values when compared to monodisperse systems with the same mean size. 

Unlike the Gj-h curve predicted by the DLVO theory (which shows two minima and one energy maximum), the Gj-h for systems that are sterically stabilised show only one minimum, G iin, followed by a sharp increase in Gt with decreasing h (when h, 23). The depth of the minimum depends on the Hamaker constant A, the particle radius R and adsorbed layer thickness 3 G iin increases with increasing... 

The inherently high colloid stability of nano-emulsions can be well understood from a consideration of their steric stabilisation (when using nonionic surfactants and/or polymers) and how this is affected by the ratio of the adsorbed layer thickness to droplet radius, as will be discussed below. 

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