Extracting Two Parameters From a P2 Orientation Distribution
Curtis Meuse, Joseph B. Hubbard
Individual molecules are seldom identical. This poses a problem for optical spectroscopy. For instance, if molecular property distributions are not characterized, differences in the distribution of molecular properties between sample and standards are interpreted as error in the number of molecules or molecular concentration measured. Using polarized internal reflection infrared spectroscopy and self-assembled monolayers and bilayers supported on gold layers and published orientation models we observed average molecular orientations similar to previous monolayer studies, however, surface concentrations determined from s and p polarized spectra differed by 20%. We propose to form a P2 orientation order parameter that depends not only on an average orientation angle, but also on the average deviation from that average, ie., the width of the orientation distribution. We compare these two parameters, obtained from the analysis of internal reflection optical measurements on self assembled alkanethiol monolayers tethered to gold surfaces, with those derived from a molecular dynamics simulation of the same system. Using our model we determine that the alkane chains have an average tilt of 30 and a width of 7 around the average. These values then are similar to the mean of 29 and a width of 5 in the molecular dynamics simulation. The values are almost certainly even closer since the simulation was run for a hypothetical surface density and the half width width at half height of 5 does not include the foot of greater angular distribution easily visible on the left side of the 0.215 nm2 plot in the right hand part of the figure. Finally, we compare measurements of our new parameters between samples or sample substructures with different degrees of order to support the idea that sample heterogeneity is being measured.