The interfacial and thermodynamic properties of nonionic surfactants and their mixtures are of both theoretical and practical interest. The nonionic surfactants used in this study are polyoxyethylene (10) alkyl ether [CnE10; m ) 10 and n ) 12, 16] and N-decanoyl-N-methylglucamine (MEGA-10). The critical micelle concentrations of pure surfactants and their mixtures were determined by surface tension measurements at different mixed ratios and temperatures. Interfacial parameters such as the maximum surface excess (Γmax) and the minimum area per molecule (Amin) at the air/water interface were also determined from surface tension data. Standard thermodynamic parameters of micellization and adsorption were also computed and discussed. Steady-state fluorescence studies were also carried out to determine the micellar aggregation number (Nagg) and the microenvironment/polarity in the mixed micelle from the I1/I3 ratio. The interaction parameters that measure the interaction between the surfactant molecules in the mixed micelle were computed by Rubingh's approach. 1 H NMR was also used to investigate the interaction between the surfactants.

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The interfacial and thermodynamic properties of SDBS/C 12 E 10 mixed system in aqueous solution in the presence of additives, i.e., poly(ethylene glycol) 400, sucrose, and urea have been investigated. The critical micelle concentrations (cmc) were determined by both surface tension and conductivity measurements. The maximum surface excess (Γ max ) and minimum area per molecule (A min ) were determined from surface tension data. The thermodynamic parameters of micellization and adsorption were computed and discussed. The enthalpyentropy compensation effect was observed in all the cosolvent systems. The partition coefficient of these hydrophilic additives between the micelle and the solvent was found to be zero. The transfer quantities, which are sensitive to the solvent structure, were also computed. The interaction parameters between the surfactant molecules both in the presence and absence of additives were evaluated by Rubingh's approach. Micellar aggregation number (N agg ) for the mixed system in the presence and absence of additives were determined by fluorescence measurements. 1 H NMR was also used to study the behavior of surfactants in mixed micelles.

We study the distribution of non-overlapping spacing ratios of higher-orders for complex interacting many-body quantum systems, with and without spin degree of freedom (in addition to the particle number). The Hamiltonian of such systems is well represented by embedded one-plus two-body random matrix ensembles (with and without spin degree of freedom) for fermionic as well as bosonic systems. We obtain a very good correspondence between the numerical results and a recently proposed generalized Wigner surmise like scaling relation. These results confirm that the proposed scaling relation is universal in understanding spacing ratios in complex many-body quantum systems. Using spin ensembles, we demonstrate that the higher order spacing ratio distributions can also reveal quantitative information about the underlying symmetry structure.

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We study the mechanism of thermalization in finite many-fermion systems with random k-body interactions in the presence of a mean-field. The system Hamiltonian H, for m fermions in N single particle states with k-body interactions, is modeled by mean field one-body h(1) and a random k-body interaction V(k) with strength λ. Following the recent application of q-Hermite polynomials to these ensembles, a complete analytical description of parameter q, which describes the change in the shape of state density from Gaussian for q = 1 to semi-circle for q = 0 and intermediate for 0 < q < 1 , and variance of the strength function are obtained in terms of model parameters. The latter gives the thermalization marker λ t defining the thermodynamic region. For λ ⩾ λ t , the smooth part of the strength functions is very well represented by conditional q-normal distribution (f CN ), which describes the transition in strength functions from Gaussian to semi-circle as the k-body interaction changes from k = 2 to m in H. In the thermodynamic region, ensemble averaged results for the first four moments of the strength functions and inverse participation ratio are found to be in good agreement with the corresponding smooth forms. For higher body rank of interaction k, the system thermalizes faster.

We analyze the structure of eigenstates in many-body bosonic systems by modeling the Hamiltonian of these complex systems using Bosonic Embedded Gaussian Orthogonal Ensembles (BEGOE) defined by a mean-field plus k-body random interactions. The quantities employed are the number of principal components (NPC), the localization length (lH) and the entropy production S(t). The numerical results are compared with the analytical formulas obtained using random matrices which are based on bivariate q-Hermite polynomials for local density of states F k (E|q) and the bivariate q-Hermite polynomial form for bivariate eigenvalue density ρ biv:q (E, E k ) that are valid in the strong interaction domain. We also compare transport efficiency in many-body bosonic systems using BEGOE in absence and presence of centrosymmetry. It is seen that the centrosymmetry enhances quantum efficiency.