Average molecular area, surface

According to Eyring (Moore and Eyring, 1938) and Joly (1956), Newtonian flow in a monolayer is the result of a cohesive attraction between surfactant molecules. For every molecule that flows from higher to lower surface pressure in a motion parallel to the canal walls, there is another molecule ready to fill the hole vacated by the first. The mechanism for this cohesive flow is presumably attractive van der Waals interactions between hydrocarbon chains. This model assumes that the average intermolecular separation in a surface-continuous monolayer does not exceed the cross-sectional area of the molecule as defined by the average molecular area A of the film at the surface pressure n in the pressurized compartment of the viscometer. 

The surface shear viscosity of a monolayer is a valuable tool in that it reflects the intermolecular associations within the film at a given thermodynamic state as defined by the surface pressure and average molecular area. These data may be Used in conjunction with II/A isotherms and thermodynamic analyses of equilibrium spreading to determine the phase of a monolayer at a given surface pressure. This has been demonstrated in the shear viscosities of long-chain fatty acids, esters, amides, and amines (Jarvis, 1965). In addition,... 

Determination of miscibility by additive properties such as average molecular area can give only qualitative interpretations of II/A data. For example, if the film components are ideally miscible, the average molecular area of the binary film at a fixed surface pressure will be the sum of each of the molecular areas of the individual components 1 and 2 in their pure films, and will follow equation (11), where N is the mole fraction. Unfortunately,... 

When spread from dilute hexane solution, acid-dependent enantiomeric discrimination was observed in the 11/A compression isotherms of the monolayer at 25°C (Fig. 12). It is interesting to note that at higher subphase acidities, both racemic and enantiomeric film systems become more highly expanded, and the surface pressures where enantiomeric discrimination commences occur at high (85-90 A2/molecule) average molecular areas. This may be taken as direct evidence of headgroup ionization effects. The surface... 

Figure 17 shows the 11/A isotherms of racemic and enantiomeric films of the methyl esters of 7V-stearoyl-serine, -alanine, -tryptophan, and -tyrosine on clean water at 25°C. Although there appears to be little difference between the racemic and enantiomeric forms of the alanine surfactants, the N-stearoyl-tyrosine, -serine, and -tryptophan surfactants show clear enantiomeric discrimination in their WjA curves. This chiral molecular recognition is first evidenced in the lift-off areas of the curves for the racemic versus enantiomeric forms of the films (Table 2). As discussed previously, the lift-off area is the average molecular area at which a surface pressure above 0.1 dyn cm -1 is first registered. The packing order differences in these films, and hence their stereochemical differentiation, are apparently maintained throughout the compression/expansion cycles. 

To resolve the problem of negative /3 values obtained with the Frumkin theory, the improved Szyszkowski-Langmuir models which consider surfactant orientational states and aggregation at the interface have been considered [17]. For one-surfactant system with two orientational states at the interface, we have two balances, i.e., Ft = Fi + F2 and Ftco = Ficoi + F2C02, which can be used in conjunction with Eq. 24 to derive two important equations for determining the total surface excess and averaged molecular area required in the calculation of surface tension, i.e.,... 

The average molecular area (A) at the surface may be calculated by the following equationi... 

Here v is taken in radial direction, i is the average distance between sites on the surface, in the Langmuir model related to the (average) molecular area o, is the number of sites per unit area and is the average residence time of molecules on the surface sites. It is typical that (5.8.3] does not contain the bulk viscosity. The equation has a molecular foundation. It is expected to apply when viscous forces in the bulk are not rate-determining, i.e. at high Ca. One would expect Blake s... 

The mixed films, CTAB (1) + egg-lecithin (2), were treated as two-dimensional mixtures of known composition. From the average molecular areas at a given surface pressure, we deduced the partial molecular areas di and a2 at the same pressure (2) using the classical Bakhuis-Rooseboom method. The pressure of the mixed films as a function of the partial molecular areas is shown in Figure 2. Also shown are the isotherms of the pure components 1 and 2 and of the 1/1 mixed real film. 

We have shown (Ref. 2, Figure 6) that at surface pressures from 18 to 26 dynes/cm the partial areas of the constituents are independent of the composition of the mixed films if the molar fraction of component 2 is 0.27-0.70. In this case the error for the partial molecular areas results from the error on experimental average molecular areas equal to 10%. However, an additional error must be considered above 26 dynes/cm resulting from the tangent slope to the curve (Ref. 2, Figure 2) which can be estimated as 10%. 

Pure fatty acids on acidic aqueous subphases give surface pressure-surface area isotherms wifh a distinct plateau and a sharp pressure rise when the mono-layer is formed (see Sec. 1.7). This behavior corresponds to domain formation at low pressure (<2 mN/m), change of packing within the domains at about 7 mN/m, and formation of a continuous monolayer at surface pressure of >20 mN/m. The average molecular area of fatty acids is about 22 A. X- ray diffraction of the monolayers has been used to characterize the various orientations of... 

Fig. 9 Experimental and ideal average molecular areas determined by the additivity rule for the DMPC/PEO-lipid(12,13) system at low (5mN/m) and high (30mN/m) surface pressures versus PEO-lipid molar fraction...

Fig. 3 Dependence of the surface pressure on the average molecular area of an 8CB film on the air-water interface, (a-e) indicate different arrangements of the molecules at the interface. A monolayer is formed in region b, whereas a trilayer is formed in region d. The isotherm is taken at 20 0.5 °C. In the inset the structure of 8CB is sketched...

Finally, it is perfectly possible to choose a standard state for the surface phase. De Boer [14] makes a plea for taking that value of such that the average distance apart of the molecules is the same as in the gas phase at STP. This is a hypothetical standard state in that for an ideal two-dimensional gas with this molecular separation would be 0.338 dyn/cm at 0°C. The standard molecular area is then 4.08 x 10 T. The main advantage of this choice is that it simplifies the relationship between translational entropies of the two- and the three-dimensional standard states. 

In which the ratio m/n is close to 3. The silane was produced by free radical copolymerization of vinyltriethoxysilane with N-vinylpyrrolidone. Its number-average molecular weight evaluated by vapour-phase osmometry was 3500. Porous silica microballs with a mean pore diameter of 225 A, a specific surface area (Ssp) of 130 m2/g and a pore volume of 0.8 cm3/g were modified by the silane dissolved in dry toluene. After washings and drying, 0.55% by weight of nitrogen and 4.65% of carbon remained on the microballs. Chromatographic tests carried out with a series of proteins have proved the size-exclusion mechanism of their separation. 

Assuming an average molecular weight of 1200 for the dispersant and a surface area of 25 m2/gm for the carbon black. 

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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