Adsorbed amounts

FIG. 11 Adsorbed amount as a function of bulk concentration for a non-interacting (empty symbols) and adsorbing (full symbols) wall. Diamonds and triangles correspond to a system with semi-rigid chains, circles and squares for flexible chains [28]. 

If n = 1, the adsorbed amount would be proportional to the pressure in adsorption phenomena n > 1. 

Experimentally, the adsorbed amount is usually expressed as T i.e. mass polymer/area of surface. This is usually obtained from a mass balance technique, after analysing the equilibrium solution, r a 0ex> but an exact correlation is difficult to establish. 

FIG. 8 Dependence of the adsorbed amount of C12E4 on the applied potential. Concentration of C12E4 in nitrobenzene is 50 (curve 1), 20 (curve 2), 10 (curve 3), and 5 (curve 4)mmoldm (From Ref. 47, reproduced by permission. The Chemical Society of Japan.) 

The deviations are all on the same side, viz., the actual adsorbed amount is too great. Further investigation will probably show what is the cause of this phenomenon. 

When a component of interest is considerably surface active, its adsorbed amount is high even when its bulk concentration is low. The second terms on the right-hand side of Eqs. (4)-(6) are then small and the relative surface excesses are simply taken as the surface excesses, which, in turn, may be seen as the surface concentration. For example, dilaur-oylphosphatidylcholine forms a saturated monolayer in the liquid-expanded state at the nitrobenzene-water interface when its concentration in nitrobenzene is 10 moldm [30]. Then the experimentally obtained value, 1.76 x 10 °molcm, can be considered to be the surface concentration. 

Table 1 gives details of the adsorbed amounts for the six polymer fractions obtained at an equilibrium concentration of 2000 ppm. Based on the full adsorption isotherm 02) these values correspond 

A very similar effect of the surface concentration on the conformation of adsorbed macromolecules was observed by Cohen Stuart et al. [25] who studied the diffusion of the polystyrene latex particles in aqueous solutions of PEO by photon-correlation spectroscopy. The thickness of the hydrodynamic layer 8 (nm) calculated from the loss of the particle diffusivity was low at low coverage but showed a steep increase as the adsorbed amount exceeded a certain threshold. Concretely, 8 increased from 40 to 170 nm when the surface concentration of PEO rose from 1.0 to 1.5 mg/m2. This character of the dependence is consistent with the calculations made by the authors [25] according to the theory developed by Scheutjens and Fleer [10,12] which predicts a similar variation of the hydrodynamic layer thickness of adsorbed polymer with coverage. The dominant contribution to this thickness comes from long tails which extend far into the solution. 

Polymers typically exhibit a high-affinity adsorption isotherm as shown in Fig. XI-5 here the adsorbed amount increases very rapidly with bulk concentration and then becomes practically independent of concentration. 

In its broad sense, an adsorption isotherm is an experimental or theoretical functional relationship between the adsorbed amount of a component and its amount in the bulk phase adjacent to the interface. Usually, the adsorption isotherm of a component i has the form 

An adsorption-desorption transition is illustrated schematically in Figure 1, where we plot a displacement isotherm, i.e. the adsorbed amount of a polymer as a function of the composition of a mixture of solvent and displacer. At the left in Figure 1, where the concentration of displacer is low, the polymer surface excess is positive. As we increase the proportion of displacer in the mixture, we observe a decrease in the adsorbed amount. At a certain composition the adsorbed amount of polymer becomes zero. The concentration at which the polymer surface excess just vanishes will be denoted as the critical displacer concentration cr. Beyond 4>cr, the surface excess of the polymer is negative (and very small if the polymer concentration is low). 

The first term predominates at low values of the flow rate F (and thereby at low pumping speeds S), and with high ratios of the system volume V to the initially adsorbed amount. Then, the pressure-time dependence is essentially the same as in a closed system, i.e. it has a monotonously increasing S-shape. The least distortion through the second term clearly occurs in the vicinity of the maximum desorption rate where P passes through an inflection point so that dP/dt has its maximum. 

Alternatively, data points can be collected in the decreasing pressure mode . This procedure is usually applied for the quantification of activated adsorption processes (Reuel and Bartholomew, 1984), such as the adsorption of H2. After the pretreatment of the sample (usually after reduction or reaction, and evacuation for a certain period to remove all the adsorbed surface species) the temperature is lowered to the temperature of measurement. First, a known amount of adsorbate gas is added to the reactor. Subsequently, the pressure in the catalyst compartment is lowered stepwise by expansion of the gas into the repeatedly evacuated reference volume. The adsorbed amount of gas can be calculated for each step. From this procedure, the monolayer capacity of the catalyst can be evaluated. 

To improve accuracy, usually data are collected at various pressures, followed by the extrapolation of the adsorbed amount of gas to zero pressure. In commercial equipment this is often done in the so-called increasing pressure mode by the stepwise injection of small amounts of gas. Note that these methods can only be used easily for non-activated adsorption (Reuel and Bartholomew, 1984), e.g. for CO chemisorption. 

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