Using x-ray reflectivity to determine the structure of surfactant monolayers.

Interactions among the multiple degrees of freedom of surfactant molecules cause fascinating richness in the structure of their monolayers. Beyond this scientific motivation for studying surfactant monolayers, the technological use of monolayers for interfacial control and molecular assembly demands a clear understanding of monolayer structure. X-ray and neutron reflectivity have become prime techniques for determining this structure. We present x-ray reflectivity data for a representative surfactant monolayer system and outline an objective procedure for obtaining the maximum amount of structural information possible. Our approach combines tight control of instrumental parameters, dynamically optimized Monte Carlo and simulated annealing to probe the chi(2) hypersurface, and a set of statistical criteria for accepting and rejecting fits. We justify our procedure through tests using simulated data. Results indicate that an ensemble of fits must be performed for each set of reflectivity data in order to survey the chi(2) hypersurface adequately. A single good fit may yield structural parameters which are quite misleading, yet physically plausible. Thus, one must never be satisfied with performing just a single fit. In cases for which multiple, statistically equivalent fits are obtained, the apparent ambiguity is substantially mitigated by averaging the parameters over the ensemble of good fits. We also introduce a method of dealing with cases for which a good fit may be extremely difficult to find. Our analysis procedures can be generalized to other monolayer or multilayer systems and are also applicable to neutron reflectivity.