A model complex-forming nonionic polymer-anionic surfactant system in aqueous solution has been studied at different surfactant concentrations. Using pulsed-field-gradient diffusion NMR spectroscopy, we obtain the self-diffusion coefficients of poly͑ethylene glycol͒ ͑PEO͒ and sodium dodecyl sulfate ͑SDS͒ simultaneously and as a function of SDS concentration. In addition, we obtain NMR relaxation rates and chemical shifts as a function of SDS concentration. Within the context of a simple model, our experimental results yield the onset of aggregation of SDS on PEO chains ͑CAC= 3.5 mM͒, a crossover concentration ͑C 2 =60 mM͒ which signals a sharp change in relaxation behavior, as well as an increase in free surfactant concentration and a critical concentration ͑C m = 145 mM͒ which signals a distinct change in diffusion behavior and a crossover to a solution containing free micelles. C m also marks the concentration above which obstruction effects are definitely important. In addition, we obtain the concentration of SDS in monomeric form and in the form of free micelles, as well as the average number of SDS molecules in a PEO-SDS aggregate ͑N Aggr ͒. Taken together, our results suggests continuous changes in the aggregation phenomenon over much of the concentration but with three distinct concentrations that signal changes in the nature of the aggregates.

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Protein aggregation is an important biophysical phenomenon, and it is technically challenging to quantify. Scattering studies in concentrated protein solutions are not in complete agreement over the existence of an equilibrium cluster phase. We use pulsed-field-gradient NMR spectroscopy to characterize diffusion in the long-time limit in concentrated lysozyme solutions and find strong evidence for the existence of an equilibrium phase that consists of both lysozyme monomers and clusters (aggregates). They indicate too that there is rapid exchange between monomer and aggregate on the NMR time scale, and that macroscopic measurables (e.g., the relaxation rate and the observed diffusion coefficient) reflect a weighted average of the two fractions. Our results are quantitatively compared, with no fit parameters, to simple theories of macromolecular crowding.

Pulsed-field-gradient nuclear magnetic resonance (PFG-NMR) is used to obtain the true hydrodynamic size of complexes of peptides with sodium dodecyl sulfate SDS micelles. The peptide used in this study is a 19-residue antimicrobial peptide, GAD-2. Two smaller dipeptides, alanine-glycine (Ala-Gly) and tyrosine-leucine (Tyr-Leu), are used for comparison. We use PFG-NMR to simultaneously measure diffusion coefficients of both peptide and surfactant. These two inputs, as a function of SDS concentration, are then fit to a simple two species model that neglects hydrodynamic interactions between complexes. From this we obtain the fraction of free SDS, and the hydrodynamic size of complexes in a GAD-2-SDS system as a function of SDS concentration. These results are compared to those for smaller dipeptides and for peptide-free solutions. At low SDS concentrations ([SDS] ≤ 25 mM), the results self-consistently point to a GAD-2-SDS complex of fixed hydrodynamic size R = (5.5 ± 0.3) nm. At intermediate SDS concentrations (25 mM < [SDS] < 60 mM), the apparent size of a GAD-2-SDS complex shows almost a factor of two increase without a significant change in surfactant-to-peptide ratio within a complex, most likely implying an increase in the number of peptides in a complex. For peptide-free solutions, the self-diffusion coefficients of SDS with and without buffer are significantly different at low SDS concentrations but merge above [SDS] = 60 mM. We find that in order to obtain unambiguous information about the hydrodynamic size of a peptide-surfactant complex from diffusion measurements, experiments must be carried out at or below [SDS] = 25 mM.

We use complementary experiments-proton NMR diffusometry and relaxometry, deuterium NMR lineshapes, and rheometry-to construct a comprehensive picture of the microscopic structure of a mixed-surfactant wormlike micellar system composed of a zwitterionic surfactant and an anionic surfactant in brine. In this system, at some surfactant concentrations, the time for micellar breaking and recombination s b is not small compared with the micellar reptation time s R , weakening the condition to obtain a stress relaxation function with just one relaxation time at long times. From NMR relaxometry, we determine the overlap concentration. Deuterium NMR spectral lineshapes indicate the presence of a wide angular distribution in the orientational order. NMR diffusometry and rheology probe different timescales and yield complementary information indicating polymer-like behaviour at the corresponding lengthscales. Via NMR, surfactant diffusion coefficients are seen to decrease with increasing diffusion time, consistent with restricted diffusion within a reptating micelle. At the same time, comparison of measurements with protonated and deuterated surfactants strongly suggests that the measured short and long time diffusion coefficients correspond to intra-micellar and micellar diffusion, respectively. Fitting the diffusion results to a simple model, the average end-to-end micellar distance is estimated to be in the 1 mm range and only weakly dependent on concentration. The water diffusion measurements, on the other hand, imply a high degree of water structuring at the micellar surface. We also find that the wormlike micelles obeyed simple polymer-like scaling behaviors, with a crossover from Zimm-like (diffusion) to Rouse-like (rheology) exponents.