Low-affinity isotherms

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. 

With an S-type isotherm, the slope initially increases with adsorptive concentrations, but eventually decreases and becomes zero as vacant adsorbent sites are filled. This type of isotherm indicates that at low concentrations the surface has a low affinity for the adsorbate which increases at high concentrations. 

Type B is very common. It is concave with respect to the abscissa. Most surfaces are heterogeneous. There are adsorption sites, which have a high affinity, and regions, which have a low affinity. The high affinity sites are occupied first, which accounts for the steep increase at low pressure. Another reason is sometimes a lateral repulsion between adsorbed molecules. This type of adsorption isotherm is described by the Freundlich1 adsorption isotherm equation [366] ... 

TRAP recruitment requires Hgand-induced changes in receptors that allow simultaneous interactions of each TRAP trimer with three receptor intracellular domains. This observation implicates that monomeric TRAF-receptor interactions are of low affinity so that the interactions do not occur in the absence of receptor activation. A number of quantitative biophysical characterizations with isothermal titration calorimetry (ITC) and surface plasma resonance (SPR) have provided solid support to this view (Table III). 

In fig. 1.26 the effect of sample pretreatment is illustrated. The original sample is "Cab-0-Sir, a pyrogenic silica. It has a fairly low affinity for water. The isotherm type is between II and III (fig. 1.13). No hysteresis is observed. Stronger outgasslng (fig. (b)), further reduces the affinity for water the curve is now definitely of type II but also shows considerable hysteresis which was attributed to incomplete hydroxylation. In case (c) the surface is made hydro-phobic by methylatlon. The water adsorption isotherm (not shown) remains of type II but as Nj adsorption is not determined by hydrophilic groups, the corresponding Isotherm is of type III. Again, it is hysteresis-free. By application of the theories outlined before, information can be extracted from these isotherms in terms of available areas and enthalpies of adsorption. The authors extended this work with infrared studies. 

The isotherm for aspirin would be classified as Type III, indicating a low affinity for water followed by multilayer sorption. These four isotherms cover a broad range of moisture interaction with solids of pharmaceutical interest. 

On the value of c Can low affinity systems be studied by isothermal titration calorimetry J. Am. Chem. 

Thus, the equations of isotherms (30) and (31) can be used to determine the isoelectric points of proteins by the dependence of their sorption on pH. This approach is realized in Refs. [41,42]. However, it should be noted that this determination is only possible for a low affinity of protein molecules to surface sites. As Figs. 12 and 13 show, for a high affinity (a low Ka) a significant sorption is observed also at pH>pI for cation exchangers and at pH[Pg.721]

Not always do the adsorption isotherms reported for polymers belong to the high affinity type. Low affinity adsorption isotherms are obtained when the molecular weight of the polymer is not too high, or for polyelectrolytes at unfavorable electrostatic conditions. Negligibly low and even negative adsorption of polymers has been also reported. 

Uptake increases with pH, low affinity" sorption isotherms at constant pH. 

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). 

Sorption isotherms are C-type (linear or constant partitioning) or S-type, and low-affinity sorption (isotherms with shallow slopes) is typical. 

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