Free energy of desorption

Using umbrella sampling, Tieleman and Marrink [18] determined a PMF for transferring a DPPC lipid from water to the center of a DPPC bilayer (Figure 3B). The DPPC PMF has a deep minimum at its equilibrium position and a steep slope in free energy as it moved into bulk water. The free energy of desorption (AGdesorb) was 80 kj/mol, and is directly related to its excess chemical potential in the bilayer compared to water. 

The activation free energy of desorption may be computed from the rate of desorption as determined experimentally from the change in the surface potential with time. The theory of absolute rates has been applied to desorption by Eley (120) and Higuchi et cd. (107) to obtain energies and entropies of activation as a function of coverage. The rate of desorption is given by,... 

This study presents an experimental approach for measuring the cohesive energies in condensed lipid monolayers which avoids the difficulty of measuring extremely low values of tt. The approach depends on evaluating the free energy of desorption (or adsorption) of condensed films and comparing this value with the free energy of desorption of the film in the ideal-gas state. 

For this study, compounds were selected which formed condensed films when spread as a monolayer on water, yet whose solubility in water was sufficiently high to allow measurements of the rate of film desorption from the surface to the bulk solution. For these compounds the free energies of desorption may be obtained from monolayer desorption studies (6). 

For an adsorbed film in equilibrium with a solution of surface-active molecules, the standard free energy of desorption may be written as... 

Thus, the rate constant for desorption can be expressed as a function of the standard free energy of desorption, A, and the change in free energy of the monolayer resulting from interactions within the film, , when the film is compressed. It is noteworthy that Equation 6 is similar to one developed by Davies (6). 

The free energy of desorption for a —CH2— group, (W0 — Wc), was obtained by comparing, at the same pH and film area, the desorption rate constants for two films differing only in the length of the hydrocarbon chain. From Equation 11, assuming D/c8 and Wc are constant for Am = 2, when m is large, it follows that... 

To evaluate the free energy of cohesion in the hydrocarbon region of the monolayer, Wc, it is necessary only to obtain the value of W0, the free energy of desorption of the hydrocarbon in the absence of interac-... 

Measurement of the free energies of monolayer desorption from the rates of desorption depends on whether equilibrium exists between the monolayer and a thin region of solution immediately beneath the film. The relation which tests this condition (Equation 8) must correctly predict the dependence of the rate constant for desorption, k8, on 7r. For the sulfate, phosphonate, and carboxyl films in this study Equation 8 is obeyed within the range of experimental error (2 to 5%). Therefore, it is reasonable to assume that the necessary equilibrium condition does exist. The cohesive forces in the monolayer follow directly from the evaluation of the free energies of desorption. 

Implicit in the determination of Wr, the cohesive energy in the hydrocarbon region of the long-chain monolayer, is the assumption that W0, the free energy of desorption for one —CH2— group, obtained with relatively short hydrocarbon chains, is independent of the length of the hydrocarbon moiety. The validity of this assumption can be checked for sulfate films where W(. may be obtained from desorption studies as... 

Assuming that the work of adhesion between a saturated hydrocarbon and a second phase Is equal to the free energy of desorption per mole of CHj groups, Dorris and Gray (5 ) proposed the equation for the estimation of the London component of the surface free energy of the adsorbent ... 

Several theories relating molecular properties to perceived odor quality have been advanced. Examples include the work of Wright (16,] ) who links odor quality to molecular vibrations in the far-infrared, and of Amoore (18) who links odor quality to molecular shape, size, and electronic nature and who introduced the concept of primary class. Beets (19) has discussed odor quality relative to molecular shape as represented by oriented profiles, chirality, and functional groups. In a recently published book (20) he has expanded these discussions. Theimer and coworkers (, , 23) have discussed the Importance of the molecular cross-sectional areas, free energies of desorption, and chirality in relation to odor. A discussion of musk odor quality and molecular structure has been presented by Teranishi (24). Laffort and coworkers ( ) have related odor quality to four molecular properties derived from gas chromatographic retention indices measured on four stationary phases. 

Several probes are used to obtain the relationship between RTlnVN and ay. From this relationship the reference retention volume,, is calculated and used to calculate the acid-base interaction s contribution to the free energy of desorption ... 

Figure 10.1.7 shows the correlation between the number of carbon atoms in n-aUcanes and the net retention volume of solvent using IGC measurements. Such a correlation must be established to calculate the acid-base interaction s contribution to the free energy of desorption, AGab, as pointed out in discussion of equations [10.1.5] and [10.1.6]. Figure 10.1.8 shows that the Flory interaction parameter (measured by IGC) increases as the temperature increases. 

All other polar probes exhibit higher net retention volumes, En. and the difference between their net retention volume and that of the n-alkanes for the same value of the dispersive component of surface energy leads to the value of the free energy of desorption, AGjp, corresponding to the specific acid-base interaction, expressed as ... 

The strength of the solid/liquid interactions determines the average retention time of a probe. Retention time data for each probe is converted into net retention volumes, Fn- The free energy of desorption is given by... 

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