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 thi s scientific motivation for studying surfactant monolayers, the technologic al use of monolayers for interfacial control and molecular assembly demands a clear understanding of monolayer structure. X-ray and neutron reflectivi ty have become prime techniques for determining this structure. We present x-ray reflectivity data for a representative surfactant monolayer system an d outline an objective procedure for obtaining the maximum amount of struct ural information possible. Our approach combines tight control of instrumen tal parameters, dynamically optimized Monte Carlo and simulated annealing t o probe the chi(2) hypersurface, and a set of statistical criteria for acce pting and rejecting fits. We justify our procedure through tests using simu lated 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 a dequately. A single good fit may yield structural parameters which are quit e misleading, yet physically plausible. Thus, one must never be satisfied w ith performing just a single fit. In cases for which multiple, statisticall y equivalent fits are obtained, the apparent ambiguity is substantially mit igated 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 extrem ely difficult to find. Our analysis procedures can be generalized to other monolayer or multilayer systems and are also applicable to neutron reflecti vity.