Overcoming performance and convergence issues of discrete transform based modeling of crosslinking classical and reversible deactivated radical polymerizations

Population balances of polymer species in terms 'of discrete transforms with respect to counts of groups lead to tractable first order partial differential equations when ali rate constants are independent of chain length and loop formation is negligible [l]. Average molecular weights in the absence ofgelation are long known to be readily found through integration of an initial value problem. The extension to size distribution prediction is also feasible, but its performance is often lower to the one provided by methods based upon real chain length domain [2]. Moreover, the absence ofagood starting procedure and a higher numerical sensitivity hás decisively impaired its application to non-linear reversibly deactivated polymerizations, namely NMRP [3].

Impact of the cation symmetry on the mutual solubilities between water and imidazolium-based ionic liquids

Aiming at the evaluation of the impact of the ionic liquids (ILs) cation symmetry on their phase behaviour, in this work, novel mutual solubilities with water of the symmetric series of [C(n)C(n)im][NTf2] (with n=1-5) were determined and compared with their isomeric forms of the asymmetric [C(n)C(1)im][NTf2] group. While the solubility of isomeric ILs in water was found to be similar, the solubility of water in ILs follows the same trend up to a maximum cation alkyl side chain length. For n >= 4 in [C(n)C(n)im][NTf2] the solubility of water in the asymmetric ILs is slightly higher than that observed in the symmetric counterparts. The thermodynamic properties of solution and solvation derived from the experimental solubility data of ILs in water at infinite dilution, namely the Gibbs energy, enthalpy and entropy were used to evaluate the cation symmetry effect on the ILs solvation. It is shown that the solubility of ILs in water is entropically driven and highly influenced by the cation size. Accordingly, it was found that the ILs solubility in water of both symmetric and asymmetric series depends on their molecular volume. Based on these findings, a linear correlation between the logarithm of the solubility of ILs in water and their molar volume is here proposed for the [NTf2]-based ILs at a fixed temperature.

Densities, viscosities and derived thermophysical properties of water-saturated imidazolium-based ionic liquids

In order to evaluate the impact of the alkyl side chain length and symmetry of the cation on the thermophysical properties of water-saturated ionic liquids (ILs), densities and viscosities as a function of temperature were measured at atmospheric pressure and in the (298.15 to 363.15) K temperature range, for systems containing two series of bis(trifluoromethylsulfonyl)imide-based compounds: the symmetric [C n C n im][NTf2] (with n = 1-8 and 10) and asymmetric [C n C1im][NTf2] (with n = 2-5, 7, 9 and 11) ILs. For water-saturated ILs, the density decreases with the increase of the alkyl side chain length while the viscosity increases with the size of the aliphatic tails. The saturation water solubility in each IL was further estimated with a reasonable agreement based on the densities of water-saturated ILs, further confirming that for the ILs investigated the volumetric mixing properties of ILs and water follow a near ideal behaviour. The water-saturated symmetric ILs generally present lower densities and viscosities than their asymmetric counterparts. From the experimental data, the isobaric thermal expansion coefficient and energy barrier were also estimated. A close correlation between the difference in the energy barrier values between the water-saturated and pure ILs and the water content in each IL was found, supporting that the decrease in the viscosity of ILs in presence of water is directly related with the decrease of the energy barrier.