Statistical mechanical determination of nanocluster size distributions in the phase coexistence region of a first order phase transition from the isotherms of DMPC monolayers at the air–water interface

A statistical mechanical deconvolution procedure for the experimentally measured surface pressure–area isotherms has been presented to obtain the surface pressure dependence of the liquid expanded (LE) and liquid condensed (LC) nanocluster size distributions in the LE–LC phase coexistence region of the first order phase transition of Dimyristoyl phosphatidylcholine (DMPC) monolayers at the air–water interface. This study presents the application of the deconvolution formulation introduced originally by Freire and Biltonen for the experimentally measured specific heat to calculate the submicroscopic lipid cluster distribution function in the phase coexistence region [E. Freire, R. L. Biltonen, Biopolymers, 1978, 17, 481–496] and extends their formulation to surface pressure isotherms. The present procedure involves the extraction of the pressure partition function calculated from the isotherm and utilizes the general relation between molecular density fluctuations and macroscopic lateral compressibility. In this procedure the high-density LC phase boundary has been determined uniquely. The average nanoscopic cluster sizes obtained in this study have been compared with the results from previous experimental studies. The cause of the finite difference between the values of the LC phase boundary area obtained from the present deconvolution procedure and the conventional extrapolation method on the same isotherm has been discussed from the viewpoint of slow hierarchical growth from nanoscopic clusters to macroscopic domains in the coexistence region.