Thermodynamic Study Of The Micellization Of Zwitterionic Surfactants And Their Interaction With Polymers In Water By Isothermal Titration Calorimetry.

The micellization of a homologous series of zwitterionic surfactants, a group of sulfobetaines, was studied using isothermal titration calorimetry (ITC) in the temperature range from 15 to 65 °C. The increase in both temperature and the alkyl chain length leads to more negative values of ΔGmic(0) , favoring the micellization. The entropic term (ΔSmic(0)) is predominant at lower temperatures, and above ca. 55-65 °C, the enthalpic term (ΔHmic(0)) becomes prevalent, figuring a jointly driven process as the temperature increases. The interaction of these sulfobetaines with different polymers was also studied by ITC. Among the polymers studied, only two induced the formation of micellar aggregates at lower surfactant concentration: poly(acrylic acid), PAA, probably due to the formation of hydrogen bonds between the carboxylic group of the polymer and the sulfonate group of the surfactant, and poly(sodium 4-styrenesulfonate), PSS, probably due to the incorporation of the hydrophobic styrene group into the micelles. The prevalence of the hydrophobic and not the electrostatic contributions to the interaction between sulfobetaine and PSS was confirmed by an increased interaction enthalpy in the presence of electrolytes (NaCl) and by the observation of a significant temperature dependence, the latter consistent with the proposed removal of hydrophobic groups from water.

The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.