J. Phys. Chem. 1083, 87,4562-4563
4562
Transition Phenomena in Monolayers at the Air-Water Interface? Bhalachandra L. Tembe,z John E. MacCarthy,I and John J. Kozak' mparfment of Chemistry and Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556 (Received: August 3, 1983)
Models for intermolecular potentials are used within the framework of a perturbation theory for fluids to explore the factors which may determine or even dominate the thermodynamic behavior of monolayers at the air-water surface, both in pure phase regimes and in regimes where transition phenomena are observed experimentally. We find that one has to use (density)renormalized interparticle potential functions to achieve agreement with experimental data on the oleic and eladic acid systems. Systems of reduced dimensionality (d) have attracted considerable interest in recent years and several theoretical models have been proposed to understand the behavior of systems such as lipid monolayers' and monolayers of molecules adsorbed on solid surfaces.2 We have developed recently a method based on the use of complementary variational principles and perturbation theory: to obtain equations of state for classical fluids in d = 2 and d = 3. In d = 3 theoretical calculations based on models of intermolecular potentials agree well with the experimental pressure-density data of rare gases, even in the gas-liquid critical region. Similar calculations in d = 2 give good agreement with the experimental data for krypton adsorbed on graphite4 both in the low-density regime as well as in the region of two-dimensional melting. In this Letter we report a comparison of our calculations on fatty acid monolayers at the air-water interface with available experimental data on these system^.^ Lipid monolayers can exist in several states at the airwater interface. At high densities there is an ordered phase which is succeeded by a liquid extended phase at intermediate densities; and, at low densities there is the socalled gas phase. At high densities the molecules in the monolayer are aligned more or less perpendicular to the interface with the carboxyl head groups (-COOH) in contact with the interface. We represent the excluded volume interactions at these densities by a hard-core potential; the diameter of the hard cores (a) is taken to be the diameter of the head groups. We add a perturbation term ( Up(r))to this hard-core reference potential (UR(r)) which carries the reference system into the system of interest. One of the potentials used in our calculations is the square-well (square-shoulder) potential which is defined by
Us&) = Udr) + U,(r) where
lJR(r) =
m
for r
Up(r) = -6 = -c/kT for =0 f o r r > ya
55 A2), this effect and the fact that the fatty acid molecules begin to align parallel to the interface cause the surface pressure to drop very close to zero. If the reduction in the pressure were due to Coulombic forces alone, we see from Figure 2 that a density (area/molecule) for the fatty acids of -55 Azwould correspond roughly to an effective ion pair area of -160 (in d = 3 ) and -370 A2 (in d = 2). A comparison of curves b and c of Figure 2 for Coulombic systems in d = 3 and 2, respectively, illustrates that the screening of ionic interactions in d = 2 is much stronger than in d = 3. On the other hand, when the area/molecule of the fatty acids is decreased below 55 A2,repulsive forces begin to dominate. The concentrations of the ions in the interface also increase and this reduces the effect of ionic interactions-due to an increase in the screening. Thus, we see that the trend in curve a of Figure 2 is partially accounted for by the role played by ionic interactions at the interface. Although the calculations presented here are based on a very simple model, they indicate that when one is considering a system as structurally complex as a (quasi-) two-dimensional monolayer assembly (wherein the monolayer molecules are (approximately) parallel to the interface in the low-density regime and are aligned (more or less) perpendicular to the interface in the high-density regime), it is necessary to use density-dependent potentials. It will be the goal of our future research to determine whether such potentials can be identified and then used within the context of a microscopic theory to yield a better description of the thermodynamic behavior of monolayer assemblies at the air-water interface.
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Acknowledgment. The research described herein was supported in part by the Office of Basic Energy Sciences of the Department of Energy.
