Adsorbed amounts

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. 

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]. 

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. 

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. 

The adsorption of gases on solid surfaces proceeds to such an extent that approximately 10 7 gr. is present per cm.2 in the equilibrium state. This is of the same order of magnitude as the strength of the limiting capillary layer of a liquid ( 184), hence it is not improbable, as suggested by Faraday (9) (1884), that the adsorbed gas is sometimes present in the liquid state. The adsorbed amount increases with the pressure and diminishes with rise of temperature. The first effect does not follow a law of simple proportionality, as in the case of the absorption of gases by liquids, rather the adsorbed amount does not increase so rapidly, and the equation ... 

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

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. 

Table 2. Equilibrium constant of adsorption (K) and adsorbed amount at saturation (Vo) for NOx at 673 K on ln/H-ZSM-5 and lr/ln/H-ZSM-5.

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. 

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. 

The appreciation of the importance of adsorption phenomena at liquid interfaces is probably as old as human history, since it is easily recognized in many facets of everyday life. It is not surprising that liquid interfaces have been a favorite subject of scientific interest since as early as the eighteenth century [3,4], From an experimental point of view, one obvious virtue of the liquid interfaces for studying adsorption phenomena is that we can use surface tension or interfacial tension for thermodynamic analysis of the surface properties. The interfacial tension is related to the adsorbed amount of surface active substances through the Gibbs adsorption equation. 

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. 

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... 

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.)... 

Gopa et al. [23] reported about open Zeolite/water systems for the storage of solar heat. In their work they were presenting stability tests, methods for the definition of the adsorption enthalpy in dependence on the adsorbed amount of water and the possible heating power during the discharging process. 

One important restriction of the applicability of all the above-mentioned conclusions should be always kept in mind—that only the properties of strongly bound particles were studied. Always when the second gas was introduced, it reacted with the chemisorbed layer of the first one, the gas phase being pumped off beforehand. This need not be a serious restriction with the hydrogen layer at 78°K and the oxygen layers both at 78° and 300°K, where only a few percent are desorbed during evacuation. However, in the case of hydrogen at room temperature, as much as approximately 25% of the adsorbed amount can be desorbed by mere pumping off the gas phase (19). 

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. 

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). 

HPC exhibited a notable increase in adsorption with increasing NaCl concentration. Entrapment in the interlayer of recovered sodium montmorillonite did not vary with salinity the extent of entrapment was greater with the 4 M.S. HE and HP celluloses than either of the 2.0 M.S. polymers. Mixed ethers of HEC (2 M.S.) containing an anionic (carboxymethyl) or cationic (3-0-2-hydroxypropyltrimethylaramonium chloride) group at 0.4 M.S. levels did not adsorb from fresh water. Adsorption of these polar mixed ethers increased with increasing electrolyte until electrostatic and solvation effects were negated in 0.54N NaCl solutions and the adsorbed amounts typical of a 2 M.S. HEC were observed. Interlayer entrapments comparable to the equivalent M.S. HEC were observed at lower (0.18N) electrolyte concentrations. 

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... 

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