Observation of two diffusive relaxation modes in microemulsions by dynamic light scattering

Water-in-oil microemulsions stabilized by AOT and dispersed in n-alkane oils with a constant molar water-to-surfactant ratio were studied by dynamic light scattering. A dilution series (in the range of volume fraction of water plus surfactant, phi approximately 0.02-0.52) was used, which allowed us to extract information about droplet sizes, diffusion coefficients, interactions, and polydispersity from experimental data. We report the observation of two diffusive relaxation modes in a concentrated microemulsion (0.20 < phi < 0.5) due to density (collective diffusion) and concentration or polydispersity (self-diffusion) fluctuations. Below this concentration it was difficult to resolve two exponentials unambiguously, and in this case one apparent relaxation mode was observed. It was found that for a given composition self-diffusion is more pronounced in apparent relaxation mode for a shorter chain length alkane. The concentration dependence of these diffusion coefficients reflects the effect of hard sphere and the supplementary attractive interactions. It was observed that the attractive part becomes more pronounced in the case of a large alkane chain oil at a given temperature. This explains the shift of the region of microemulsion stability to lower temperatures for higher chain length alkanes. Increase in hydrodynamic radius, Rh, obtained from the diffusion coefficient extrapolated to infinite dilution was observed with increase of alkane chain length. The polydispersity in microemulsion systems is dynamic in origin. Results indicate that the time scale for local polydispersity fluctuations is at least 3 orders of magnitude longer than the estimated time between droplet collisions.     

Study of Molecular Interactions in Binary Mixtures of Aniline with Carboxylic Acids at 293.15 K, 303.15 K and 313.15 K

Ultrasonic velocity, density, refractive index and viscosity of binary mixtures of aniline with acetic acid (AA) and propionic acid (PA) have been measured at 293.15, 303.15 and 313.15 K over the entire composition range. Further, the specific heat ratio, heat capacity, effective Debye temperature and pseudo-Gruensisen parameter and non-linearity parameter have been evaluated using ultrasonic absorption data. The deviation in isentropic compressibility, excess molar volume, excess intermolecular free length, deviation in molar refraction, deviation in viscosity, relaxation time, enthalpy, entropy and Gibbs energy of activation have been calculated from the experimental data and fitted with the Redlich-Kister polynomial equation. A comparative study has also been made between experimental and theoretically calculated values of densities using the HBT and Rackett density models. Mixing rules for the prediction of refractive index, e.g. Lorentz-Lorenz (L-L), Eykmen (Eyk), Weiner (W), Heller (H), Gladstone-Dale (G-D), Arago-Biot (A-B) and Newton (N) have been applied to these binary mixtures.     

Effect of polymer and ion concentration on mechanical and drug release behavior of gellan hydrogels using factorial design

Developing optimized hydrogel products requires an in-depth understanding of the mechanisms that drive hydrogel tunability. Here, we performed a full 4 × 4 factorial design study investigating the impact of gellan, a naturally derived polysaccharide (1%, 2%, 3%, or 4% w/v) and CaCl₂ concentration (1, 3, 7, or 10 mM) on the viscoelastic, swelling, and drug release behavior of gellan hydrogels containing a model drug, vancomycin. These concentrations were chosen to specifically provide insight into gellan hydrogel behavior for formulations utilizing polymer and salt concentrations expanding beyond those commonly reported by previous studies exploring gellan. With increasing gellan and CaCl₂ concentration, the hydrogel storage moduli (0.1–100 kPa) followed a power-law relationship and on average these hydrogels had higher liquid absorption capability and greater total drug release over 6 days. We suggest that the effects of gellan and CaCl₂ concentration and their interactions on hydrogel properties can be explained by various phenomena that lead to increased swelling and increased resistance to network expansion.     

Homotopy analysis method with a non-homogeneous term in the auxiliary linear operator

We demonstrate the efficiency of a modification of the normal homotopy analysis method (HAM) proposed by Liao [2] by including a non-homogeneous term in the auxiliary linear operator (this can be considered as a special case of “further generalization” of HAM given by Liao in [2]). We then apply the modified method to a few examples. It is observed that including a non-homogeneous term gives faster convergence in comparison to normal HAM. We also prove a convergence theorem, which shows that our technique yields the convergent solution.     

Approximate controllability of retarded semilinear stochastic system with non local conditions

This paper deals with the approximate controllability of retarded semilinear stochastic system with nonlocal conditions in Hilbert Spaces under the assumption that the corresponding linear system is approximately controllable. The control function for this system is suitably constructed by using the infinite dimensional controllability operator. With this control function, the sufficient conditions for the approximate controllability of the proposed problem in Hilbert Space are established. The results are obtained by using Banach fixed point theorem. Finally, two examples are provided to illustrate the application of the obtained results.