X-ray diffraction of Langmuir-Blodgett films: Establishing a new method for the calculation of electron density distributions from a single set of intensity data

Abstract

A new method for direct determination of the signs of X-ray diffraction reflections from Langmuir-Blodgett (LB) films has been established. It is based on the ability to separate the Q 0 function, the convolution square of the unknown structure ϱ 0, from the generalized Patterson function ( Q function) of the bilayer stack and on the existence of a unique convolution square root. The only restrictions are the existence of a centre of symmetry and that the system is bounded in space even in molecular dimensions. Both conditions are ideally fulfilled in LB films and the electron density distribution ϱ 0 normal to the membrane plane can be directly calculated. The FORTRAN program used has an execution time of about 1 min. This method thus seems to have great advantages (much less time needed and more reliable results) over the widely used swelling technique. The resulting electron density distributions of different LB films yield information about orientation, conformation and localization of molecular subunits and membrane components.