Surfactant parameters

The surfactant number or surfactant parameter [28, 29 and 30], N is defined as a dimensionless group ... 

In the structure with all the surfactant molecules located at monolayers, the volume fraction of surfactant should be proportional to the average surface area times the width of the monolayer divided by the volume, i.e., Ps (X Sa/V. The proportionality constant is called the surfactant parameter [34]. This is true for a single surface with no intersections. In our mesoscopic description the volume is measured in units of the volume occupied by the surfactant molecule, and the area is measured in units of the area occupied by the amphiphile. In other words, in our model the area of the monolayer is the dimensionless quantity equal to the number of amphiphiles residing on the monolayer. Hence, it should be identified with the area rescaled by the surfactant parameter of the corresponding structure. 

A detailed justification of the surfactant parameter approach is still the subject of theoretical investigations, and we will return to several issues below. We mention that the surfactant parameter approach is consistent with the fluid mosaic model of Singer and Nicolson. It tells us that the self-assembly of amphiphiles is driven by the strong segregation of water and hydrocarbon chains, and that packing effects dominate the self-assembly process. 

All of the above considerations have sometimes led to a too rigid picture of the membrane structure. Of course, the mentioned types of fluctuations (protrusions, fluctuations in area per molecule, chain interdigitations) do exist and will turn out to be important. Without these, the membrane would lack any mechanism to, for example, adjust to the environmental conditions or to accommodate additives. Here we come to the central theme of this review. In order to come to predictive models for permeation in, and transport through bilayers, it is necessary to go beyond the surfactant parameter approach and the fluid mosaic model. 

The absolute value of the characteristic parameter of the surfactant a can be estimated from a single experiment by using Eq. 4 for HLD = 0 if all other variables values are known. For instance in the example of Fig. 2 scan oil ACN = 6 for hexane, 3 vol% 2-butanol/(A) = - 0.16, temperature 25 °C, and since the three-phase behavior is exhibited for the test tube with aqueous phase salinity S = 2.2% NaCl, then the surfactant parameter value is ct = 0.32. 

Surfactants not only aggregate to spherical micelles but also form cylinders, bilayers, inverted micelles, etc. [524], The type of aggregate structure formed depends on different factors. An important factor is the so-called surfactant parameter, also referred to as the packing ratio [533] ... 

The most problematic quantity in the definition of the surfactant parameter is the head group area. For ionic surfactants a a depends on both the electrolyte and the surfactant concentration. In this case the surfactant parameter is only of limited usefulness for a quantitative... 

Example 12.2. The head group area of SDS in water (no additional background salt) is 0.62 nm2. This leads to a surfactant parameter of... 

Bilayers are preferentially formed for Ns = 0.5...1. Lipids that form bilayers cannot pack into micellar or cylindrical structures because of their small head group area and because their alkyl chains are too bulky to fit into a micelle. For bilayer-forming lipids this requires that for the same head group area a a, and chain length Lc, the alkyl chains must have twice the volume. For this reason lipids with two alkyl chains are likely to form bilayers. Examples are double-chained phospholipids such as phophatidyl choline or phophatidyl ethanolamine. Lipids with surfactant parameters slightly below 1 tend to form flexible bilayers or vesicles. Lipids with Ns = 1 form real planar bilayers. At high lipid concentration this leads to a so-called lamellar phase. A lamellar phase consist of stacks of roughly parallel planar bilayers. In some cases more complex, bicontinuous structures are also formed. As indicated by the name, bicontinuous structures consist of two continuous phases. 

Co is called the spontaneous curvature. The spontaneous curvature is a more general parameter than the surfactant parameter Ns, defined by Eq. (12.4). It makes it easier to discuss the phase behavior of microemulsions because we get away from the simple geometric picture. 

In water, surfactants form spontaneously defined aggregates such as spherical micelles, cylinders, or bilayers, once the concentration has exceeded the CMC. Which aggregate is formed is largely determined by the surfactant parameter. 

N JVagg Ni Ns n nc P Po Aggregation number of surfactant micelles Number of molecules of a certain species i (dimensionless or mol) Surfactant parameter Refractive index, integer number Number of carbon atoms in an alkyl chain Pressure (Pa), probability Equilibrium vapor pressure of a vapor in contact with a liquid having a planar surface (Pa)... 

When both oil (o) and water (w) are present, o/w microemulsions will be formed when v/a0lc < 1 w/o microemulsions when v/ac c>U and lamellar phases when v/a0lc 1 (Israelachvili etal., 1980 Mitchell and Ninham, 1981). The v/a ratio depends on the surfactant chemical structure (lc and v) and on surface repulsions between headgroups (aD), (Mitchell and Ninham, 1981). When repulsions increase, the surfactant parameter (v/aGlc) increases and micelles get smaller. As a consequence, size and CMC are related surfactants with low CMC aggregate into large molecules, while the higher the CMC, the smaller the micelles. 

The correlation between the volume or stability of the foam and the hydrophile-lipophile balance (HLB) of surfactants or their mixtures is used to generalise the experimental results derived about the stabilising ability of complex foaming compositions or homologues surfactant series. HLB is an important surfactant parameter, characterising the relative... 

Figure 4.2 View of the curvature of aggregates formed by surfactant molecules of various siufactant parameters, v/al. (Left ) If the surfactant parameter is less than one, the interface between the polar and hydrophobic regions curves towards the chain region, and the average molecular shape is tapered towards the hydrophobic end of the molecule. (Middle ) If the surfactant parameter is exactly equal to one, the interface exhibits no preferential curr atiue, and the molecules are on average cylindrical. (Right) If the surfactant parameter exceeds one, the interface curves towards the polar regions, and the molecule tapers towards the head-group.

These examples allow us to describe tiie structure of surfactant aggregates in terms of the value of the surfactant parameter. Indeed, this is the case for simple closed surfaces, where the interior contains the hydrophobic fraction (v/al[Pg.145]

Setting v(l) equal to the chain volume, v, I to the chain length and (0) to the head-group area, a, leads to a simple general expression for the surfactant parameter in terms of the curvatures of the interface between hydrophilic and hydrophobic regions, scaled by the characteristic distance, 1 ... 

Consider, for example a spherical micelle. By our convention, if the interface encloses hydrophobic regions, the mean curvature is negative. Consequently, the surfactant parameter for a spherical micelle of radius R is given by ... 

Equation (4.3) shows that the magnitude of the surfactant parameter fixes only the fimction of the interfadal curvatures, (1 + HZ + KZ2/3), rather than the curvatures of the interface themselves. In other words, the interfacial geometry - the structure of the surfactant aggregate - is not fixed by the surfactant parameter alone. Both the mean and Gaussian cur atures can be varied cooperatively without altering the value of the surfactant parameter. Nevertheless, the surfactant parameter does furnish a local constraint upon the curvatures of the interface. 

We have seen that the local constraint on the surface curvatures, set by the surfactant parameter, can be treated within the context of differential geometry, which deals with the intrinsic geometry of the surface. In contrast, the global constraint, set by the composition of the mixture, is dependent upon the extrinsic properties of the surface, which need not be related to its intrinsic characteristics. (For example, the surface to volume ratio of a set of parallel planes can assume any value by suitably tuning the spacing bebveen the planes. Similarly, the ratio of surface area to external volume i.e. the volume of space outside each sphere closer to that sphere than any other) of a lattice of spheres depends upon the separation between the spheres.)... 

The curvature of the bilayer, characterised by at the mid-surface, is set by the block shape. In terms of the surfactant parameter, the approximate form (valid if v/al is close to unity [7]) is ... 

Figure 4.6 Schematic views of bilayer configurations as the value of the surfactant parameter, v/al, varies for a double-chain surfactant or lipid. The stippled regions denote polar regions (water plus head-groups). (Left ) v/al > 1, cross-section fiirough a pore of a saddle-shaped bilayer, whose mid-surface is a minimal surface (centre ) v/al = 1, a planar bilayer (right ) v/al < 1, a "blistered" bilayer, containing a vacuous region. In the last case, a reversed bilayer (Fig. 4.7) is favoured over the bilayer configuration iUustrated.

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