Tailored Media for Homogeneous Cellulose Chemistry: Ionic Liquid/Co-Solvent Mixtures

Co-solvents can minimize two of the major problems associated with the use of ionic liquids (ILs) as solvents for homogeneous derivatization of cellulose: high viscosity and limited miscibility with non-polar reagents or reaction products. Thus, the effects of 18 solvents and 3 binary solvent mixtures on cellulose solutions in three ILs were systematically studied with respect to the solution phase behavior. The applicable limits of these mixtures were evaluated and general guidelines for the use of co-solvents in cellulose chemistry could be advanced: Appropriate co-solvents should have EN T values (normalized empirical polarity) > 0.3, very low ``acidity`` (alpha < 0.5), and relatively high ""basicity`` (beta >= 0.4). Moreover, novel promising co-solvents and binary co-solvent mixtures were identified.

Coincidence theorems and its applications to equilibrium problems

Given two maps h : X x K -> R and g : X -> K such that, for all x is an element of X, h(x, g(x)) = 0, we consider the equilibrium problem of finding (x) over tilde is an element of X such that h((x) over tilde, g(x)) >= 0 for every x is an element of X. This question is related to a coincidence problem.