Reorientation isotherm

Let us consider an example where the reorientation isotherm can be successfully applied to experimental data. In Fig. 2.9 the surface pressure isotherm of (N-16-alkyl-N,N-dimethylammonio)-acetic acid bromide [13,25] is presented. 

The slope of the dependence b on nc calculated for the Frumkin isotherm is also lower than that calculated for the reorientation isotherm. The increment of adsorption free energy, calculated from the b values for the reorientation model, = -2.78 kJ/mol, is almost equal to the... 

Calculations for adsorption layers described by a reorientation isotherm have been also performed, however, analytical solutions cannot be given [159], Based on the reorientation model given by Eqs. (2.84) to (2.88) the exchange of matter function was calculated and compared with experimental data. It was shown that the particularities of the adsorption model has a significant influence on the resulting dilational elasticities. Hence one can conclude that dilational elasticity experiments are much more sensitive to processes of adsorbed molecules. 

The Tritons have been described in the last paragraph by a diffusion controlled kineties based on a Langmuir isotherm. As it was shown in the preceding Chapter 3, oxethylated surfactants can be usually better described by a reorientation isotherm [226]. This is however only true for high quality samples such as define compounds of the type C EO , while for technical products like the Tritons an isotherm more complicated than the Langmuir isotherm does not make sense. An analysis of dynamic surface and interfacial tensions for CioEOg solutions had been performed in [227]. 

Let us first look into the dynamic surface tensions for CjoEOg at the water/air interface, as it was measured by Chang et al. [228] using the pendent bubble method. The experimental data given in Fig. 4.29 are compared with calculations for two models, based on the Langmuir and the reorientation isotherm (two-state model). 

As mentioned above reorientation processes in the adsorption layer can mimic adsorption processes faster than expected from diffusion. For modelling the adsorption process with molecular reorientation the Ward and Tordai equation (37) as the most general relationship between the dynamic adsorption F(t) and the subsurface concentration c(0,t) can be used. As additional relationship the reorientation isotherm Eqs. (18) to (20) are included into the model. 

When we use the reorientation isotherm as obtained on the basis of the above described algorithm (surface tension values at times corresponding to the adsorption times), we get the picture shown in Fig. 32. The experimental points are well described at all shown concentrations, up to a certain time moment, where the experimental data deviate from the theoretical curve, obviously due to an impurity component. This effect depends on the surfactant sample and was not observed by Lee et al. (2003). Note, however, that these authors did not measure the surface tensions for times larger than 1 hour so that the deviation was maybe not remarkable enough to be detected. 

The monolayer resulting when amphiphilic molecules are introduced to the water—air interface was traditionally called a two-dimensional gas owing to what were the expected large distances between the molecules. However, it has become quite clear that amphiphiles self-organize at the air—water interface even at relatively low surface pressures (7—10). For example, x-ray diffraction data from a monolayer of heneicosanoic acid spread on a 0.5-mM CaCl2 solution at zero pressure (11) showed that once the barrier starts moving and compresses the molecules, the surface pressure, 7T, increases and the area per molecule, M, decreases. The surface pressure, ie, the force per unit length of the barrier (in N/m) is the difference between CJq, the surface tension of pure water, and O, that of the water covered with a monolayer. Where the total number of molecules and the total area that the monolayer occupies is known, the area per molecules can be calculated and a 7T-M isotherm constmcted. This isotherm (Fig. 2), which describes surface pressure as a function of the area per molecule (3,4), is rich in information on stabiUty of the monolayer at the water—air interface, the reorientation of molecules in the two-dimensional system, phase transitions, and conformational transformations. 

The surface potential as function of particle area (AV A isotherm) is another indicator of the quality of the monolayer structure. The surface potential at the air-water interface changes as the film-forming molecules reorient themselves during the compression process. For a closely packed monolayer, the surface potential is directly proportional to the surface dipole moment (/r ) by [13] ... 

Fig. 13a,b. a Surface pressure - film area isotherms of (1) dendrimer 1, (2) dendrimer 2, and (3) hyperbranched polymer with OH end groups [74]. b Schematic interpretation of the phase transitions from a dense monolayer (I) via a reoriented monolayer (II) to a thick liquid film (III)... 

Consider the isothermal transformation of a disordered (amorphous) solid to an ordered (crystalline) solid. Obviously, there must be enough thermal energy to allow individual atoms to move around and reorient themselves, but assuming this is possible, it is generally found that at constant temperature, the amount of amorphous material transformed to crystalline material, dx (on a volume basis) per unit time, dt, is given by... 

Class 3 yields isotherms with no transformation points. The polymers spread slowly and do not produce appreciable surface pressures on short contact with the water substrate. This class includes larger aliphatic pendant groups, as well as aromatic groups. These polymers do not orient themselves on the water substrate. The molecular-interaction forces of this class with the water surface are lower than those of class 2. The bulkiness of the groups further reduces interaction and impedes reorientation. 

The shape of a zeolite sorption uptake isotherm, a quantitation of the amount of a given sorbate taken up as a function of its partial pressure in the gas phase in equilibiitun with the zeolite sorbent, depends both on the zeolite sorbate interaction and on the sorbate - sorbate interactions. Simulation of such isotherms for one or more sorbates is accomplished by the Grand Canonical Monte Carlo method. Additional to the molecular reorientation and movement attempts is a particle creation or annihilation, the probability of which scales with the partial pressure [100,101]. This procedure thus simulates the eqmlibrium between the sorbed phase in the zeolite and an infinite gas / vapor bath. Reasonable reproduction of uptake isotherms for simple gases has been achieved for a small number of systems (e.g. [100,101]), and the molecular simulations have, for example, explained at a molecular level the discontinuity observed in the Ar - VPI-5 isotherm. 

The generalised adsorption isotherms, Eqs. (50), can be used to generate simpler isotherms applicable to real systems. Here, for simplicity we examine the following adsorption processes at monolayers of constant thickness a) the single adsorption of a neutral or ionic adsorbate which possess a constant orientation at the monolayer, (b) the reorientation from a flat position to a normal one of a neutral adsorbate, and c) the co-adsorption of two adsorbates. 

It was shown in the detailed investigation of Graham and Phillips [34,36,43] that the F-Cb isotherm for /3-casein at air/water interface revealed a well-defined plateau over the wide concentration range. However, at Cb> 10 2 wt % the film thickness and F increase further (without any significant changes in 0) due to the presence of reversibly adsorbed molecules. This reversibility can be connected with either formation of second and subsequent layers [36] or molecular reorientation of adsorbed /3-cascin molecules [26]. The adsorption isotherms for lysozyme and bovine serum albumin (BSA) do not... 

A drop of a dilute solution (1%) of an amphiphile in a solvent is typically placed on the water surface. The solvent evaporates, leaving behind a monolayer of molecules, which can be described as a two-dimensional gas, due to the large separation between the molecules (figure C2.4.3). The movable barrier pushes the molecules at the surface closer together, while pressure and area per molecule are recorded. The pressure-area isotherm yields information about the stability of monolayers at the water surface, a possible reorientation of the molecules in the two-dimensional system, phase transitions and changes in the conformation. While being pushed together, the layer at... 

Let us consider now the dependence of the shape of surface pressure isotherms on the parameters of the reorientation model. The dependence of surface pressure on the maximum area C0 is illustrated in Fig. 2.5. Here Eqs. (2.84)-(2.88) are employed with (02 = const and a = 0. All calculated curves are normalised in such a way that for the concentration 1 O " mol/1, the surface pressure is 30 mN/m. One can see in Fig. 2.5 that with the increase of (Oj the inflection of the isotherm becomes more pronounced, however, for the ratio a)i/( 2 = 4 the calculated curve almost coincides with the one calculated from the von Szyszkowski-Langmuir equation (2.41) which assumes only one adsorption state with (Oo = < = const. 

The above analysis of the viscoelastic behaviour for adsorption layers of a reorientable surfactant leads to important conclusions. It is seen that the most important prerequisite for a realistic prediction of the elastic properties is the adequacy of the theoretical model used to describe the equilibrium adsorption of the surfactant. For example, when we use the von Szyszkowski-Langmuir equation instead of the reorientation model to describe the interfacial tension isotherm, this rather minor difference drastically affects the elasticity modulus of the surface layer. The elasticity modulus, therefore, can be regarded to as a much more sensitive parameter to find the correct equation of state and adsorption isotherm, rather than the surface or interfacial tension. Therefore the study of viscoelastic properties can give much more insight into the nature of subtle phenomena, like reorientation, aggregation etc. 

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