Ellipsometric Chain Length Dependence of Fatty Acid Langmuir Monolayers. A Heads-and-Tails Model

Langmuir monolayers of even n-fatty acids with increasing number N of carbon atoms in the hydrocarbon chain (N = 11−23) were investigated on 1 × 10-2 M HCl aqueous subsolutions by means of Brewster angle ellipsometry. Isotherms, relating the coefficient of ellipticity Δρ to the area per molecule F, were continuously recorded and interpreted on the basis of literature phase diagrams and in situ X-ray reflectivity and diffraction investigations. Δρ/N dependencies for the liquid-expanded (LE), super-liquid or solid (LS/S), and condensed-solid (CS) monolayer phases were extracted from the isotherms at constant areas per molecule:  FLE = 28 ± 1 A2, FLS/S = 19.2 ± 0.3 A2, FCS = 18.5 ± 0.3 A2. They show Δρ-discontinuities at the LE−LS and S−CS transitions but no change at the LS−S transition. The experimental Δρ/N data for the solid condensed monolayer were compared with calculated Δρ/N dependencies using the “one-layer” ellipsometric model with bulk isotropic or theoretical anisotropic n/N data. A very good agreement of dΔρexp/dN with the slope of the calculated “isotropic” dependence, and a significant difference from the “anisotropic” slope was observed. The calculated “isotropic” Δρ/N dependence was shifted to higher Δρ-values probably due to a different hydration state of the carboxyl groups in the bulk solid phase and Langmuir monolayer. The “one-layer” model was also used in the alternative calculation of the isotropic refractive indices of the LE, LS−S, and CS phases from our Δρ/N data. The obtained n/N dependencies were compared with bulk n/N data for n-fatty acids and n-alkanes which differ only by a terminal COOH group. No agreement was found between bulk and monolayer values. A similarity of the trends was observed for the RCOOH system; both the bulk and monolayer n/N dependencies show discontinuities at the liquid−solid, as well as the LE−LS, phase transition. In contrast, the n/N dependence of the bulk n-alkanes is smooth for N between 5 and 30. Such a behavior shows that the headgroups contribute specifically to the optical characteristics of Langmuir monolayers. A simple “heads-and-tails” model based on the Lorentz−Lorentz relationship was proposed to relate the ellipsometric signal of the monolayer to the polarizability and thickness of the headgroup and hydrocarbon chain regions and to the optical anisotropy of the latter. Application of this model to our Δρ/N data under some physical restrictions shows that the anisotropy of the methyl group in closely packed vertical chains is below 3.3% of the isotropic value. The ellipsometric dimension of the monolayer headgroups obtained implies that they have hydration shells approximately one water molecule thick. The model explains the observation reported in the literature10 that Cd2+ and Pb2+ dissolved in the water substrate shift the ellipsometric chain length dependence to higher Δρ-values without affecting its slope. This effect seems to be due to the increased polarizability and decreased thickness (partial dehydration) of the headgroup region resulting from Cd2+ and Pb2+ binding to the carboxyl groups.