The Power of Heterogeneity: Parameter Relationships from Distributions

Clear distinction between CAC and CMC revealed by high-resolution NMR diffusometry for a series of bis-imidazolium gemini surfactants in aqueous solutions

The aggregation behavior in the transition region was studied for a series of dicationic surfactants 3,3′-[α,ω-(dioxaalkane)]bis(1-dodecylimidazolium)dichlorides with varied spacer length from two to twelve carbon atoms. We employed Nuclear Magnetic Resonance diffusometry and Bayesian DOSY analysis to obtain the aggregate size distribution in the transition region. The critical concentrations CC were independently obtained from surface tension, electric conductivity, UV-Vis and NMR methods. The micelle aggregation numbers were estimated from the self-diffusion coefficients and were independently confirmed using steady-state fluorescence quenching. The morphology of the aggregates was characterized by small-angle scattering of synchrotron radiation and molecular dynamics simulations. The obtained CC values are identified as critical aggregation concentrations CAC. A broad transition region was observed, and stable micelles were obtained at much higher concentrations than CAC. The accurate CMC values could not be identified for the systems in the study. We indicated that the distribution of aggregate size becomes small and the system becomes homogeneous at much larger concentrations than CAC (typically 15–20 mM). The existence of a slow exchange between two environments, an aggregate and aqueous environment, was confirmed by ¹H NMR and 2D HSQC NMR spectroscopy.

The aggregation behavior in the transition region was studied for a series of dicationic surfactants 3,3′-[α,ω-(dioxaalkane)]bis(1-dodecylimidazolium)dichlorides with varied spacer length from two to twelve carbon atoms.

Obtaining T1-T2 distribution functions from 1-dimensional T1 and T2 measurements: The pseudo 2-D relaxation model

We present the pseudo 2-D relaxation model (P2DRM), a method to estimate multidimensional probability distributions of material parameters from independent 1-D measurements. We illustrate its use on 1-D T1 and T2 relaxation measurements of saturated rock and evaluate it on both simulated and experimental T1-T2 correlation measurement data sets. Results were in excellent agreement with the actual, known 2-D distribution in the case of the simulated data set. In both the simulated and experimental case, the functional relationships between T1 and T2 were in good agreement with the T1-T2 correlation maps from the 2-D inverse Laplace transform of the full 2-D data sets. When a 1-D CPMG experiment is combined with a rapid T1 measurement, the P2DRM provides a double-shot method for obtaining a T1-T2 relationship, with significantly decreased experimental time in comparison to the full T1-T2 correlation measurement.