Amphiphile concentration

Lattice models have been studied in mean field approximation, by transfer matrix methods and Monte Carlo simulations. Much interest has focused on the occurrence of a microemulsion. Its location in the phase diagram between the oil-rich and the water-rich phases, its structure and its wetting properties have been explored [76]. Lattice models reproduce the reduction of the surface tension upon adsorption of the amphiphiles and the progression of phase equilibria upon increasmg the amphiphile concentration. Spatially periodic (lamellar) phases are also describable by lattice models. Flowever, the structure of the lattice can interfere with the properties of the periodic structures. 

In Figure 1, the pairs (or triad) of phases that form ia the various multiphase regions of the diagram are illustrated by the corresponding test-tube samples. Except ia rare cases, the densities of oleic phases are less than the densities of conjugate microemulsions and the densities of microemulsions are less than the densities of conjugate aqueous phases. Thus, for samples whose compositions He within the oleic phase-microemulsion biaodal, the upper phase (ie, layer) is an oleic phase and the lower layer is a microemulsion. For compositions within the aqueous phase-microemulsion biaodal, the upper layer is a microemulsion and the lower layer is an aqueous phase. When a sample forms two layers, but the amphiphile concentration is too low for formation of a middle phase, neither layer is a microemulsion. Instead the upper layer is an oleic phase ("oil") and the lower layer is an aqueous phase ("water"). 

However, often the identities (aqueous, oleic, or microemulsion) of the layers can be deduced rehably by systematic changes of composition or temperature. Thus, without knowing the actual compositions for some amphiphile and oil of poiats T, Af, and B ia Figure 1, an experimentaUst might prepare a series of samples of constant amphiphile concentration and different oil—water ratios, then find that these samples formed the series (a) 1 phase, (b) 2 phases, (c) 3 phases, (d) 2 phases, (e) 1 phase as the oil—water ratio iacreased. As illustrated by Figure 1, it is likely that this sequence of samples constituted (a) a "water-continuous" microemulsion (of normal micelles with solubilized oil), (b) an upper-phase microemulsion ia equiUbrium with an excess aqueous phase, ( ) a middle-phase microemulsion with conjugate top and bottom phases, (d) a lower-phase microemulsion ia equiUbrium with excess oleic phase, and (e) an oA-continuous microemulsion (perhaps containing iaverted micelles with water cores). 

Here the functions g(0) and /(0) are defined in a suitable way to produce the desired phase behavior (see Chapter 14). The amphiphile concentration does not appear expHcitly in this model, but it influences the form of g(0)— in particular, its sign. Other models work with two order parameters, one for the difference between oil and water density and one for the amphiphile density. In addition, a vector order-parameter field sometimes accounts for the orientional degrees of freedom of the amphiphiles [1]. 

In Figure 4 the results from the three different groups are in excellent agreement for butanol concentrations of 90 wt% and greater, although the data from the Russian group scatter somewhat more around our results than do the values interpolated from Westmeier s data.(14.16). At lower amphiphile concentrations the isoperibolic calorimeter measurements are in noticeably better agreement with the data of ref. 16 than with the Russian work (14-16). However, almost all results fall within the 95% confidence interval (dashed lines) for our results. 

A generic progression of phases, going from low to high amphiphile concentration, is... 

Fig. 2.16. 13C NMR chemical shift of carbon 4 (numbering starting from the polar head) in nonylam-monium bromide as a function of the inverse amphiphile concentration. A positive shift is downfield. Solid line calculated with an aggregation number of 33. (After Ref.51))...

The phase separation model is particularly useful for describing the amount of micellized amphiphile and how molecular properties vary with amphiphile concentration. The average of a quantity Q (which can be a diffusion coefficient, a NMR chemical shift, a NMR relaxation time etc.) is determined by the fractions micellized,... 

In reality several aggregation numbers of the micelles occur, but from the simple equilibrium in (3.2) one can make a number of relevant conclusions. The larger the value of n, the more cooperative is the association and the more one approaches phase separation behavior. This is illustrated in Fig. 3.1 which shows plots, for two values of n, of the fraction of the amphiphile that enters the micelle as a function of the total amphiphile concentrations. A comparison with the experimental data in Figs. 

Fig. 3.1. The relative amount of amphiphile fm that is incorporated into the micellar aggregate at an infinitesimal increase in the total concentration S as a function of total amphiphile concentration, fm = 1 -, calculated from the mass action law model (Eq. 3.2) with n = 10...

When a semipolar, e.g., an alcohol, or a nonpolar, e.g., an alkane, substance is added to a micellar system the additives are solubilized in the micelles. The presence of a solubilized molecule in the micelle reduces the activity of the amphiphile in the aggregate. It is thus a natural consequence that the CMC (with respect to amphiphile concentration) is lowered. A strict thermodynamic analysis4,181 18 2) gives, in analogy with Henry s law ... 

If one considers solely the consecutive equilibria, the concentration of monomer can only increase with increasing total amphiphile concentration even above the CMC. (Apart from the trivial decrease in the monomer concentration calculated on the total volume which may arise when the micelles occupy a substantial volume fraction). However, if one realizes that micelles are not only composed of amphiphile, the result may be different. Thus counterion binding helps to stabilize the micelles and for ionic surfactants it can be predicted that the monomer activity may decrease with increasing surfactant concentration above the CMC. Good evidence for a decreasing monomer concentration above the CMC has been provided in the kinetic investigations of Aniansson et al.104), and recently Cutler et al.46) demonstrated, from amphiphile specific electrode studies, that the activity of dodecylsulfate ions decreases quite appreciably above the CMC for sodium dodecylsulfate solutions (Fig. 2.14). 

The catalytic effect for reactions involving an ionic reactant usually shows a strong dependence on the total amphiphile concentration. The maximal effective rate constant is attained at concentrations just over the CMC. Romsted284 showed that this occurs due to the competition between the ion binding of the reactive ions (OH- in the example above) and the counterions of the amphiphile. Recently, Diekman and Frahm285 286 showed that it is possible to rationalize the kinetic data by describing the ion distribution through a solution of the Poisson-Boltzman equation. (See Fig. 5.1). 

For ionic amphiphiles the first formed aggregates are closely spherical. At higher amphiphile concentrations there is a tendency for the formation of rod-shaped micelles168. Also the addition of salt favours the rod-shape aggregates33. It has been suggested that disc-shaped micelles also occur160 but experimental evidence in favor of this view has only been obtained for mixed micelles of lecithin and sodium cho-late179. ... 

The analysis of the first effect can be made by comparing a spherical and an infinite rod-shaped aggregate with the same radius, surface charge density and amphiphile concentration. The infinite rod really corresponds to the condition in thenor-... 

Fig. 6.3. The calculated reduced surface potential = e(ri)/kT versus the logarithm of the amphiphile concentration C (M) with no salt added for a spherical, cylindrical and planar aggregate. The surface charge density has been chosen as fixed at a8 = 0.228 Cm- 2. The radii of the sphere and the cylinder are 1.8 nm...

Fig. 6.4. The calculated reduced surface potential 4> = e(r()/kT versus the inverse radius for a sphere and a cylinder. Amphiphile concentration 45 mM and surface charge density <7S = 0.228 Cm-2...

From this description a well-defined critical concentration emerges as that total amphiphile concentration corresponding to a transition from the monotonic decreasing size distribution function to a size distribution function exhibiting two extrema. This critical concentration corresponds to a surfactant solution with no appreciable amount... 

The total amphiphile concentration at this value of = cr>t gives the critical concentration Ctrit. 

Figure 2. variation in the aggregate size dstrbution function with nonaggregated amphiphile concentration for 8 = 3 A, a = 8 X 104 cal AVmol, he 8. 

Jahn and Strey [40] investigated systems with varying water-to-oil ratios at constant amphiphile concentration. The TEM images support the notion of a bicontinu-... 

Physically, the amphiphile concentration C3D =Crex p[fiiD/kT) is the one at which the reference 3D lamellar phase neither grows nor dissolves. 

Equations (3.123), (3.124) and (3.128) show that both r and W increase sharply with the amphiphile concentration C in a relatively narrow range. For this reason, a critical amphiphile concentration Cc for bilayer rupturing in less than tc seconds can be defined by the condition T(Cc) = Tc. Using Eq. (3.124) leads to [402,403]... 

Similarly, a threshold amphiphile concentration C, for bilayer observation can be introduced by the definition W(C,) = 1/2 which, in view of Eq. (3.128), yields... 

Eq. (3.132) shows that ta increases with increasing C, the physical reason for this being the lowering of the density n, (and hence of the overall area Sh) of the holes in the bilayer at higher C values. When the total amphiphile concentration in the solution exceeds CMC, the concentration C of the monomer amphiphile remains virtually constant and to from Eq. 

One of the most important theoretical predictions is the existence of truly (i.e. infinitely) stable bilayers for C > Ce provided Ce < CMC. By fitting theoretical to experimental rfC) dependences it is possible to determine the equilibrium amphiphile concentration Ce and thus to judge whether in a given C range a bilayer, and in some cases, the corresponding disperse system, can be infinitely stable. BLMs, for example, are known to live for months and years. Thermodynamically, there is no difference between foam bilayers and BLMs so that the long lifetime of BLMs is apparently due to their existence in contact with amphiphile solutions of concentrations C either slightly bellow or above Cr. 

The systematic study of foam bilayers from phospholipids [28,38-40] reveals that they do not rupture spontaneously at any concentration allowing their formation. That is why in the case of phospholipid foam bilayer the dependence of their mean lifetime on the bulk amphiphile concentration cannot be measured in contrast to foam bilayer from common surfactants [41,42], This infinite stability of phospholipid foam bilayers is the cause for the steep W(d) and W(C) dependences. In the case of AF foam bilayers this high stability was confirmed by a very sensitive method [19,43] consisting of a-particle irradiation of foam bilayers. As discussed in Sections 2.1.6 and 3.4.2.2, the a-particle irradiation substantially shortens the mean lifetime of foam bilayers. The experiments showed that at all temperatures and dilutions studied (even at d,), the foam bilayers from AF did not rupture even at the highest intensity of irradiation applied, 700 (iCi. 

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