Isotherms high-affinity

Proteins often have the same high-affinity isotherms as do synthetic polymers and are also slow to equilibrate, due to many contacts with the surface. Proteins, however, have the additional complication that they can partially or completely unfold at the solid-liquid interface to expose their hydrophobic core units to a hydrophobic surface... 

The H-type (high affinity) isotherm is indicative of strong adsorbent-adsorbate interactions such as inner sphere complexes. 

As mentioned, nnlike small analyte molecnles, macromolecnles can be irreversibly retained on the packing snrface in the given elnent and at given temperature (Section 16.6). In the case of interactions that lead to the adsorption of solnte on the adsorbent surface (Sections 16.3.5 and 16.6) this sitnation is described by the high-affinity isotherms (Figure 16.2) up to a certain threshold concentration of given polymeric adsorbate, all its molecules are adsorbed and their concentration in... 

The adsorption of polymeric surfactants is more complex, since in this case the process is irreversible and produces a high-affinity isotherm with a steep rise in the adsorption value at low polymer concentrations (in this region most of the molecules are completely adsorbed). Subsequently, the adsorbed amount remains virtually constant, giving a plateau value that depends on the molecular weight, temperature and solvency of the medium for the chains (this topic was discussed in detail in Chapter 6). 

A plot of F versus C2 gives the adsorption isotherm. Two types of isotherms can be distinguished a Langmuir type for reversible adsorption of surfactants (Figure 18.17) and a high-affinity isotherm (Figure 18.18) for the irreversible... 

In both cases a plateau adsorption value F is reached at a given value of C2. In general, the value of F is reached at a lower C2 for polymeric surfactant adsorption when compared to small molecules. The high-affinity isotherm obtained with polymeric surfactants implies that the first added molecules are virtually... 

The amount of adsorption F can be determined in the same way as for surfactants, although in this case the adsorption process may take a long equilibrium time. Most polymers show a high-affinity isotherm, as is illustrated in Figure 19.5. 

The shape of the equilibrium isotherm (adsorbed amount F as a function of the concentration c in solution) yields information about the free energy of adsorption. For most flexible, highly solvated polymers high-affinity isotherms are obtained, i.e. isotherms in which the initial part coincides with the F-axis after which a levelling off takes place to a (pseudo-) plateau. 

When r = 1, 9 is very small and the adsorption increases linearly with the increase in 0 (Henry s type isotherm). On the other hand, when r = 10 the isotherm deviates from such a straight line and approaches a Langmuirian type with a near-plateau value at high 0 values. However, when r > 20, high affinity isotherms are obtained. In this case, the adsorption rises very steeply at low polymer concentrations and thereafter it reaches a pseudo-plateau region. The adsorption isotherms for chains with r = 100 and above are typical of those obtained experimentally for most polymers that are not too polydisperse (i.e. showing a steep rise followed by a nearly horizontal pseudo-plateau (which only increases by few percent per decade increase in 0. ... 

Considering the action of adsorbs in the polymer - adsorbent systems, the situation differs from that observed with low-molecular substances and can be depicted by the high affinity isotherms (see Figure 10). In the case of adsorption of low-molecular compounds, their concentration in the supernatant is only exceptionally zero. On the contrary, up to a certain threshold concentration, which is often called the saturation onset, actually all molecules of many polymeric adsorbates may be adsorbed so that their concentration in the supernatant is negligible. 

Figure 5.11. A sketch of a typical polymer adsorption isotherm for a polymer in a good solvent adsorbed onto a solid surface, showing the characteristics of a high-affinity isotherm.

FIGURE 14.3. Because of the nature of polymer adsorption, monolayer coverage is almost assured and high-affinity isotherms are the norm. 

As an illustration. Figure 14.5 shows the adsorption isotherms at 25°C for PVA (containing 12% acetate groups) on polystyrene latex [18]. The figure shows the high-affinity isotherms for the polymers and the increase in adsorption of the polymer with increase of the molecular weight. Similar isotherms are expected for the adsorption of the polymer on oil droplets. However, in the latter case it is not possible to obtain the full isotherm, since to produce the emulsion one requires a minimum amount of polymer. In addition, the surface area of the emulsion has to be determined at each point from the droplet size distribution. 

The adsorption of a polymer from solution onto a surface is usually described in terms of an adsorption isotherm. This relates the amount of polymer at the particle surface (mg/ m ) with the amount of polymer in solution (ppm or mg/L). In contrast with the Langmuir-type low-affinity isotherms displayed by small molecules, polymers tend to show high-affinity isotherms of the type shown in Figure 1. 

Adsorption Isotherms. Because of the strong tendency of polymer chains to adsorb at attractive surfaces, the surface gets saturated at very small bulk concentrations. Adsorption isotherms of this nature are known as high affinity isotherms. The adsorption isotherm of polymer chains adsorbing on solid substrates depends on the polymer molecular weight, solvent quality, and polymer-surface interactions. Figure 3 a illustrates the adsorption isotherms for polymer chains in a good solvent as a function of concentration. The surface excess... 

Most polymers (particularly those with high molecular weight) give a high-affinity isotherm (Figure 7.37). 

Fig. 7.37. Typical high-affinity isotherm for polymer adsorption.

The details of determining the adsorption isotherm of PVA on both latices has been described previously [19]. Both latices gave a high affinity isotherm with a saturation adsorption (plateau) value of 4.3 mgm , which is in close agreement with the value obtained before for the same PVA sample on a similar latex [21]. 

Severai methods can be appiied for assessment of dispersants (i) Adsorption isotherms This is by far the most common quantitative method for assessment and seiection of a dispersant. A good dispersant shouid give a high affinity isotherm as is iiiustrated in Fig. f.58. The adsorbed amount T is recorded as a function of the equiiibrium soiution concentration C2 ieft in soiution after adsorption, in generai, the vaiue of T( is reached at iower C2 for poiymeric surfactant adsorption when compared with smaii moiecuies. 

The high affinity isotherm obtained with poiymeric surfactants implies that the first added moiecuies are virtuaiiy compieteiy adsorbed and such a process is irreversible. The irreversibility of adsorption is checked by carrying out a desorption experiment. The suspension at the plateau value is centrifuged and the supernatant liquid is replaced by pure carrier medium. After redispersion, the suspension is centrifuged again and the concentration of the polymeric surfactant in the supernatant liquid is analytically determined. For lack of desorption, this concentration will be very small indicating that the polymer remains on the particle surface. 

At pH 10.6, the surface of the substrate is negatively charged and sodium ions are adsorbed as counterions in the inner Helmholtz plane (IHP) of the electrical double layer (e.d.L). Adsorption of HDP gives a high-affinity isotherm, which reaches the plateau at equilibrium concentrations consistent with the critical micelle concentration (CMC) of HDPCl, 0.9 mmol/dm [36]. The adsorbed amount is 0.7 mmol/g at saturation, and the surface area occupied by one molecule is about 0.2 nm. This means that the adsorbed amount is somewhat higher than would be expected for close-packed monolayer coverage (0.3 nmVmolecule). 

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