Isotherm amphiphilic

One can further elaborate a model to have a concrete form of /(ft), depending on which aspect of the adsorption one wants to describe more precisely, e.g., a more rigorous treatment of intermolecular interactions between adsorbed species, the activity instead of the concentration of adsorbates, the competitive adsorption of multiple species, or the difference in the size of the molecule between the solvent and the adsorbate. An extension that may be particularly pertinent to liquid interfaces has been made by Markin and Volkov, who allowed for the replacement of solvent molecules and adsorbate molecules based on the surface solution model [33,34]. Their isotherm, the amphiphilic isotherm takes the form... 

This is the final expression for the isotherm that we will call the amphiphilic isotherm [23]. It is straightforward to derive classical adsorption isotherms from the amphiphilic isotherm (65). 

Therefore, the amphiphilic isotherm (65) could be considered as a generalization of the Frumkin isotherm, taking into account the replacement of some solvent molecules with larger molecules of surfactant. Of course, the amphiphilic isotherm includes all the features of the Frumkin isotherm and displays some additional ones. To elucidate them, it will be convenient to change the variable to the relative concentration y = X /x ( = 0.5), where X (0.5) is the concentration corresponding to the surface coverage 6 = 0.5 ... 

This equation gives the coverage fraction 6> as a function of relative concentration y, while a and p are the parameters of this isotherm, the first being the attraction constant and the second, the size of surfactant. These parameters play an important role because their effect on the shape of amphiphilic isotherm is very strong. 

Amphiphilic isotherm (65) analysis can be used for the determination of the interfacial structure. An amphiphilic molecule, which consists of two moieties with opposing properties such as a hydrophilic polar head and a hydrophobic hydrocarbon tad, should be used as an analytical tool located at the interface. Pheophytin a is a well-known surfactant molecule that contain a hydrophobic chain (phytol) and a hydrophilic head group. The value of p, less than 1.0, indicates that adsorbed molecules of n-octane are parallel to the interface between octane and water [23] (Fig. 11). Substitution of one adsorbed octane molecule requires about 4 to 5 adsorbed pheophytin... 

Surface Micelles. The possibility of forming clusters of molecules or micelles in monolayer films was first proposed by Langmuir [59]. The matter of surface micelles and the issue of equilibration has been the subject of considerable discussion [191,201,205-209]. Nevertheless, many ir-a isotherms exhibit nonhorizontal lines unexplained by equations of state or phase models. To address this, Israelachvili [210] developed a model for ir-u curves where the amphiphiles form surface micelles of N chains. The isotherm... 

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. 

Traditional amphiphiles contain a hydrophilic head group and the hydrophobic hydrocarbon chain(s). The molecules are spread at molecular areas greater (-2-10 times) than that to which they will be compressed. The record of surface pressure (II) versus molecular area (A) at constant temperature as the barrier is moved forward to compress the monolayer is known as an isotherm, which is analogous to P-V isotherms for bulk substances. H-A isotherm data provide information on the molecular packing, the monolayer stability as de-... 

FIG. 19 H-A isotherms of amphiphilic hexa-azacrown (noted as 3 in the figure) and 1 1 mixtures with C60 andC70 (top) and for 1 1, 1 2, and 1 3 mixtures of C60 and the amphiphilic hexa-azacrown (bottom). (Reproduced from Ref. 254 with permission of the author. Copyright 1991 Wiley-VCH.)... 

Figure 17 shows the chemical structures of anionic amphiphile sodium-1,2-bis (tetradecylcarbonyl)ethane-l-sulfonate (2Cj4SNa)[34] and poly(ethyleneimine)(PEI). A benzene/ethanol (9 1)(WV) solution of anionic amphiphile was spread on the pure water surface or the PEI-water solution (lxlO5 unit M in monomer unit, pH=3.2) surface at a subphase temperature, Tsp of 293 K. At this pH, ca. 70 % of nitrogen atom in PEI molecule was protonated[35]. Surface pressure-area(ji-A) isotherms were measured with a microprocessor controlled film balance system. 

Fig. 20. re-A isotherm for the 2Ci4SNa amphiphile spread on cationic polymer(PEI) solution subphase, and the bright field images and ED patterns of the monolayers at 0, 10, and 30 mN-m-. ... 

From comparison of the ji-A isotherms obtained under the various conditions, it can be summarized that the 1 1 ion complexation of the anionic amphiphiles with the cationic surfactant can be used to form their stable monolayers. Especially, when the amphiphile is so soluble as S7COOH, the ion complexation with a... 

Fig.3. Surface pressure-area isotherms of azobenzene-linked amphiphiles 1 ...

It is found that, even a monolayer of lipid (on water), when compressed can undergo various states. In the following text, the various states of monomolecular films will be described as measured from the surface pressure, n, versus area, A, isotherms, in the case of simple amphiphile molecules. On the other hand, the Il-A isotherms of biopolymers will be described separately since these have a different nature. 

Liquid Condensed Films (Lco) As the area per molecule (or the distance between molecules) is further decreased, a transition to a so-called liquid condensed (Lco) state is observed. These states have also been called solid expanded films (Adam, 1941 Gaines, 1966 Birdi, 1989, 1999 Adamson and Gast, 1997). The n versus A isotherms of n-pentadecylic acid (amphiphile with a single alkyl chain) have been studied, as a function of temperature (Birdi, 1989). 

The measurements of n versus A isotherms generally exhibit, when compressed, a sharp break in the isotherms that has been connected to the collapse of the mono-layer under given experimental conditions. The monolayer of some lipids, such as cholesterol, is found to exhibit an unusual isotherm (Figure 4.7). The magnitude of FI increases very little as compression takes place. In fact, the collapse state or point is the most useful molecular information from such studies. It has been found that this is the only method that can provide information about the structure and orientation of amphiphile molecules at the surface of water (Birdi, 1989). 

The II-A isotherms suggest an orientation that aligns the long axis of the polymer rod in the plane of the interface with the EO chains of the hydrophilic dendrons extended into the water layer and the hydrophobic dendrons pointed upward from the surface. The stability of the dendronized polymers likely arises from the balance between the polar and nonpolar regions exposed at the surface of the polymeric cylinder (Bo et al. 1999 Schluter and Rabe 2000). Ariga and colleagues (2004) constmcted a series of spider web dendritic amphiphiles that project hydrophilic Lys-Lys-Glu tripeptides and hydrophobic chains at each generational level (Fig. 11.42). 

This arrangement projects hydrophobic and hydrophilic surfaces above and below the plane of the dendron in a display that mimics the two-dimensional structure of lipid clusters. Accordingly, the amphiphile can efficiently spread out along the surface like a spider web. The II-A isotherms revealed that these molecules form stable monolayers with collapse pressures in the range of 40-60 mN/m. The addition... 

I1M isotherms of amphiphile monolayers on aqueous subphase have been used to determine occupied molecular areas (Am[,i) and other (implied) structural properties. The area of the monolayer can be monitored during film transfer to obtain information on film structure. An example is seen in Figure 3.5.12 (10) for a DDAB mono-layer, sustained at a surface pressure of 20 mN m on a K2PtCl4 subphase. A uniform transfer is demonstrated over 10 dip cycles (average transfer of 1.03), and a Y-type film is evident from the same transfer for both up and down portions of... 

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