Location of spectroscopic probes in self-aggregating assemblies. I. The case for 5-doxylstearic acid methyl ester serving as a benchmark spectroscopic probe to study micelles.
A strategy to locate spectroscopic probes in micelles is presented which involves establishing a "benchmark" probe, i.e., one whose position is well-known and against which other probe positions may be established. Theoretically calculated values of the fraction of the micelle polar shell occupied by water, H(shell), are compared with experimental values measured with the spin probe 5-doxylstearic acid methyl ester (5DSE) for a series of sodium n-alkyl sulfate micelles as functions of both the aggregation numbers and the alkyl chain length. The theoretical values involve one adjustable parameter that may be taken to be the volume in the polar shell inaccessible to water, V(dry). Under the hypothesis that the thickness of the polar shell (5 Angstroms) remains constant as either the aggregation number or the chain length is varied, we find excellent agreement between the theoretical predictions and the experimental results, using the same value of V(dry) for chain lengths 8-12 and for aggregation numbers varying from approximately 38 to 130. We argue that these are compelling reasons that 5DSE follows the zero-order model (ZOM) of probe location. The ZOM applies to any probe that rapidly diffuses within the confines of the micelle polar shell and nowhere else. Thus, 5DSE can serve as a benchmark in the sodium alkyl sulfate micelles. As a further check, results are also presented for ammonium dodecyl sulfate micelles, where 5DSE is also found to follow the ZOM, i.e, no further adjustable parameters are needed to pass from the sodium alkyl sulfate micelles to ammonium dodecyl sulfate micelles. In contrast, results are also presented for a similar spin probe 16-doxylstearic acid methyl ester (16DSE) that is found not to adhere to the ZOM in any of the micelles. A simple first-order correction to the ZOM in which 16DSE is displaced slightly from the polar shell is shown to account for the results well. The necessary displacements, which range from about 0.7 Angstroms outside the polar shell to 1.3 Angstroms inside, are not correlated with either chain lengths or aggregation numbers; however, they correlate rather well with H(shell). Calibrations of 6-, 7-, 10-, and 12DSE spin probes are presented in the Appendix, making them available to measure microviscosities and effective water concentrations.