Monolayers isotherm

Tphe force-area (tt-A), surface potential-area (AV-A), and surface vis-cosity-area (-q-A) characteristics of long-chain fatty acid monolayers at the air-water interface have been extensively investigated over acid and neutral aqueous solutions (17). Studies of fatty acid monolayer isotherms at high pH and the specific cation effect on the isotherms are less numerous. The difficulties inherent in working at high pH are ... 

Menzel1811 more recently described the properties and behavior of monolayers prepared from azobenzene-containing poly(L-glutamate)s possessing the structures XIX and XX (n= 2) shown in Scheme 11. These monolayers showed photomechanical effects opposite to those described above for azo-modified poly(L-lysine)s. In fact, they expanded when exposed to UV light (trans—>tis isomerization), and shrank when exposed to visible light (ds— trans isomerization). The expansion was found to be smaller than expected from comparison of the monolayer isotherms obtained from irradiated and nonirradiated solutions. This was attributed to the trans-cis photoconversion of the azo units, which occurs with lower yields in monolayers... 

To illustrate the interpretation of such sub-steps, the monolayer isotherms for the adsorption of Xe on FeCl2 (Larher, 1992) are shown in Figure 4.2. At temperatures below 99.57 K, there is a single vertical step, which corresponds to the transformation of 2-D gas to the solid phase. Very little further compression of the monolayer is possible before its completion at Point B. A smaller sub-step becomes apparent at temperatures above 99.57 K. As a result of the careful studies of Thorny and Duval and Larher, the consensus interpretation is that this small sub-step represents a first-order transition between the 2-D liquid and solid phases. It is evident that, in the case of the Xe/FeCl2 system, 99.57 K is the two-dimensional triple point. 

In principle, a /-plot can be used to assess the micropore capacity provided that the standard multilayer thickness curve has been determined on a non-porous reference material with a similar surface structure to that of the microporous sample. In our view, it is not safe to select a standard isotherm with the same BET C value (i.e. the procedure recommended by Brunauer (1970) and Lecloux and Pirard (1979)) since this does not allow for the fact that the sub-monolayer isotherm shape is dependent on both the surface chemistry and the micropore structure. 

Regarding with k-mer multilayer adsorption in two dimension, we propose an approximation to the adsorption isotherm based on the recently developed Occupation Balance approach (OB) [6]. In the simplest case of k=2, the monolayer isotherm for noninteracting dimers adsorbed on a square lattice can be written as. 

Muris et al. [31] used adsorption isotherms and calorimetric measurements, to study CH4 (and Kr) adsorbed on as-received carbon nanotubes produced by arc discharge, also from Montpellier. This study provided the first complete monolayer isotherm for any gas adsorbed on nanotube bundles. They found that for both CH4 and Kr there were two substeps present in the first-layer data. These two substeps indicate that in the first layer adsorption occurs on two... 

Figure 36. Monolayer isotherms of 109c on subphases of (top) pH 10, 20 °C middle) pH 7, 20 °C, CUSO4 bottom) pH 10,20 °C, Cu(CI04)2. Insets, corresponding Brewster angle micrographs (BAM) of the LE/LC coexistence phase.

Figiire 6. Effect of Ca and Mg ions on 7r-A and AV-A isotherms of nonadecylbenzene-sulfonate monolayer isotherms subsolutions contain 0.01 M NaCl(41)... 

Extensive investigation of the monolayer isotherm behavior at the n-heptane and isooctane/aqueous NaCl interfaces (8) has shown that d r(trans)dr and AA s for each film the heats of transition can be calculated from the two-dimensional Clapeyron equation (3). Based upon the variation observed in the heats calculated in a previous study these heats are not significantly different, even at 3°C. In contrast, however (see both isotherms of Figure 1 and data of Table I), the work of compression from high areas to the area at which phase separation begins depends... 

Very recently this technique was also applied for studies of monolayer isotherms of insoluble surfactants (Kwok et al. 1994) and the dynamic behaviour of insoluble monolayers. In Appendix 6C these investigations are discussed in more detail. 

The classification of the low concentration region of the sample isotherm into linear, concave, and convex isotherms has been discussed (Section 2-4). For adsorption of a compound from the gas phase, Brunauer et al. (30) have described the five basic isotherm types shown in Fig. 3-5. Type I isotherms occur when monolayer adsorption is distinctly favored over multilayer adsorption. After an initial rapid uptake of adsorbate by the adsorbent, the surface monolayer is completed and further adsorption does not occur. If additional layers begin to adsorb prior to completion of the first monolayer, isotherms of type II result. These are typical of physical adsorption. Type III isotherms are less common and occur in adsorption systems where the attraction between adsorbed molecules are strong and adsorbent-adsorbate interactions are either relatively weak or are independent of surface coverage (e.g., uniform surface graphites). As a result the total attraction of an adsorbed molecule... 

The easiest penetration experiments are those with a monolayer of an insoluble component spread on a subphase which contains a soluble component of the same homologous series. An example is the study by Fainerman et al. [115] of the penetration of the soluble dodecyl dimethyl phosphine oxide (C,2DMPO) into a monolayer of the insoluble eicosyl dimethyl phosphine oxide (CjqDMPO). The monolayer isotherm of C20DMPO at 20 °C shows a break... 

Juang and Liu [74,75] presented that the interfacial tensions between water/ -hexane and water/toluene in the synthesis of ether-ester compounds by PTC could be measured. These two-phase systems contained PT catalyst, an aqueous phase reactant, and/or alkali. The interfacial data could be well described by the Gibbs adsorption equation coupled with the Langmuir monolayer isotherm. 

As the first, Langmuir proposed description of adsorption on the energetically heterogeneous polycrystalline surface by means of a finite sum of monolayer isotherms. He assumed that the surface of such an adsorbent is composed of a finite number of crystal planes of the same energy falling to one active site. For adsorption on amorphous surfaces, addition can be replaced by integration. 

FIG. 2 The composite monolayer isotherms corresponding to the five types of excess isotherm and calculated by Eqs. (37) and (38). 

The overall isotherms for the loeal BET-type adsorption are represented by Eq. (25). These isotherms may be obtained trom equations generated by Langmuir local behavior [Eq. (15) or (16)] in the following way In the monolayer isotherms Xi ), one replaces the pressure p by the functions H h), and the parameters K andby C = K p and p = Pa/Ps> respectively, and then multiplies the redefined isotherm by the function giQi) [5]. 

The BET model has been generalized by using of various monolayer isotherms for heterogeneous surfaces Langmuir-Freundlich [94], Toth [95], generalized Freundheh (GF) [94], Dubinin-Radushkevich [67,95,96], and others [5]. These equations have been apphed to the interpretation of experimental data [5,6]. The above-discussed procedure has also extended to the adsorption with lateral interactions on randomly heterogeneous surfaces also [5]. 

The adsorption data suggest high affinity between the mineral and the alcohol molecules at low alcohol concentrations. It also indicates that monolayer adsorption takes place for ethanol, propanol, and butanol molecules, while a multilayer adsorption takes place for methanol. At the plateau section of the monolayer isotherms, the adsorption density decreases with increasing chain length of the alcohol. The low area available for each molecule indicates that the alcohols are more or less perpendicularly oriented on to the mineral siuface. As previously mentioned, the adsorption strength of alcohol molecules is normally correlated with the acidity of the siuface and through the donor-acceptor properties of the alcohol molecules. 

An estimate for the association constants of aliphatic alcohols can be derived from the literature, and Table 1 contains the monomer-tetramer equilibrium constants for various systems [31]. The high values of the equilibrium constants show that, even at the low alcohol concentration region used here, a large proportion of the alcohol molecules take part in the assoeiation process. An equilibrium constant of 220 calculated on the molal scale implies that, at alcohol concentrations as low as 0.1 molal, about 26% of the alcohol molecules will be H-bonded. This shows quite clearly that alcohol association should be taken into account. Therefore, all the monolayer isotherms were modified to take into account die self-association of the alcohol molecules in die hydrocarbon solution by suggesting that only the free alcohol monomers adsorb on to the clay surface. 

III. MONOLAYER ISOTHERM EQUATIONS APPLICABLE TO HETEROGENEOUS OXIDE SURFACES... 

In the frame of the uniform interpretation of gas/solid adsorption it is necessary to calculate the function /(pj.) of the BET equation for comparison with those of the monolayer isotherm equations. After application of Eqs (39) and (51) we have... 

In Section V.A it has been shown that a monolayer isotherm measured on a heterogeneous surface has always an increasing function y(p. ) which, in most cases, can be described by the Toth equation. It was also shown that in the case of multilayer adsorption the function ) always has a decreasing domain which may begin at a rel-... 

From the monolayer part of the isotherm, applying one of the consistent monolayer isotherm equations. 

FIG. 23 Component isotherms of ethane isoflierm measured on BPL-activated carbon at -60.5°C. The monolayer isotherm (O) is calculated from the T equation (116) the multilayer component ( ) is calculated from Eq. (143) when P P q (For parameters see Table 2.)... 

This statement is supported by data for oxygen and argon isotherms measured on the same silica gel. As can be seen in Figs 27 and 28 these isotherms have measurable - identifiable from the fiinetions i /(pj.) - monolayer domains, but there are not a sufficient number of data for a fitting procedure needed to calculate the parameters of a monolayer isotherm equation. 

From pure monolayer isotherms of Type I and from the monolayer domain of Type n isotherms the speeifie surfaee area ean be ealeulated from a mono-layer equation identified by the shape of the function T(pj.). 

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