Determination of Hansen Solubility Parameters for the Solid Surface of Cellulose Acetate Butyrate by Inverse Gas Chromatography

The specific retention volumes, , for adsorption of 21 solute probes on the solid surface of cellulose acetate butyrate (CAB) were determined in the temperature range 343.15 to 403.15 K by inverse gas chromatography (IGC). The weight fraction activity coefficients, , and Flory–Huggins interaction parameters, , were evaluated using . Both and values decreased with increase of temperature in all the solutes. Further, the values increased with increase of chain length in n-alkanes, but in the case of alcohols the trend was reversed. values were less than 0.5 in polar solutes and greater than 0.5 in 1-alkanes and alcohols. The Hansen solubility parameters (HSP) were calculated by relating with the cohesive energy of adsorption of the solutes on the surface of CAB. The adsorption model proposed by Snyder and Karger was used to determine the HSP for the CAB. The dispersive, , polar, , and hydrogen bonding components of HSP decreased with increase of temperature and the relative error associated with these parameters increased with increase of temperature. The characterization of the solid surface of CAB in terms of the three solubility parameter components was analyzed and is discussed.     

Hansen Solubility Parameters in the Analysis of Solvent–Solvent Interactions by Inverse Gas Chromatography

The Flory–Huggins interaction parameters, for a solute with pure nonvolatile solvents and with binary mixtures of nonvolatile solvents were evaluated using Inverse Gas Chromatography (IGC) data at 403.15 K. The five solvents used have similar structure and nearly the same molar volume and their mixtures form regular solutions. The values were used to evaluate the Hansen solubility parameters (HSP) for the pure solvents and mixed solvent systems. The HSP are plotted as a function of composition of the polar solvent. The dispersion component, , and the polar component, , exhibited negative deviation whereas the hydrogen bonding component, , showed positive deviation in the four mixtures. However, the total solubility parameter was found to be almost linear with composition in the four binary systems. Further the total solubility parameter, , was used to calculate the molar excess heat of vaporization for the solvents (C78 + POH, C78 + PCN, C78 + TTF, and C78 + TMO) that was found to be negative for C78 (19,24-dioctadecyldotetracontane) + POH(18,23-dioctadecylhentetracontan-1-ol) and C78 + PCN(1-cyano-18,23-dioctadecylhentetracontane) systems and positive for C78 + TTF [19,24-bis(18,18,18-trifluorooctadecyl)-1,1,1,42,42,42-hexafluorodotetracontane), and C78 + TMO(17,22-bis-(16-methoxyhexadecyl)-1,38-dimethoxyoctatriacontane] and the other systems.     

Dual-Mode Sorption of Inorganic Acids in Polybenzimidazole (PBI) Membrane

The sorption behaviors of sulfuric, perchloric, and phosphoric acids in polybenzimidazole membranes have been investigated. The results of sorption isotherms are consistent with the general form of a dual-mode sorption isotherm. The dual-mode sorption parameters were found using a least-squares program by fitting experimental data to a dual-mode equation. Results indicate a correlation between permeant properties like acidity, size, and the affinity constant in Langmuir-mode sorption species. Moreover, the results show that the size of the permeants has the dominant effect on Henry's constant. The obtained results for , site saturation constant, in Langmuir-mode sorption in the case of perchloric and phosphoric acids, reveals that the two acid molecules interact with two N?H basic groups in the polybenzimidazole repeat units. But in the case of sulfuric acid, it is shown that sulfuric acid neutralizes some of the basic groups in the polymer by its strong second hydrogen and the obtained value for was 1.25.     

Thermal Oxidation and Structural Changes of Degraded Polyethylene in an Oxygen Atmosphere

High-temperature bulk thermolysis of high density polyethylene was performed to obtain degraded polyethylene, which was then left in an oxygen atmosphere for oxidation reaction at 160°C at different oxidation times, yielding a series of polyethylene degradation–oxidation products. Using infrared spectroscopy, chemical titration, gel chromatography, and differential scanning calorimetry, the structural changes of the polyethylene degradation–oxidation products were investigated. Hydroxyl, carboxyl, ester, and other functional groups were introduced into the molecular chains of oxidation products, and the number of carboxyl groups sharply increased with increasing oxidation time. The breaking of molecular chains as well as combination reactions, such as esterfication, during the oxidation process lead to decrease of number-average molecular weight () and increase of both weight-average molecular weight () and molecular weight distribution, and an initial increase and leveling off of the carboxyl number per molecular chain. It is noteworthy that oxidation occurred primarily near weak bonds, mainly terminal vinyl unsaturations. Thus, compared with degraded polyethylene, the oxidation products showed little changes in the melting and crystallization behaviors; even when the oxidation time was up to 4 hr, the drop in the melting and crystallization temperature was less than 3°C. These results might lay a foundation for exploring tailored low molecular weight polymers to be used just as they are or after chemical modifications of olefinic functions.     

Hansen Solubility Parameters for the Solid Surface of Cellulose Acetate Propionate by Inverse Gas Chromatography

The specific retention volumes, V ⁰ _g , for adsorption of 21 solute probes on the solid surface of cellulose acetate propionate (CAP) were determined in the temperature range 343.15–403.15 K by inverse gas chromatography. In the temperature range studied the retention diagrams drawn between vs. 1/T were found to be linear for all the solutes. Hansen solubility parameters (HSPs) were calculated by relating with the cohesive energy of adsorption of the solutes on the surface of CAP following the Snyder and Karger adsorption model. The three components of HSP decreased linearly with increase of temperature. The HSP of CAP were compared with the corresponding values determined on cellulose acetate butyrate (CAB) and discussed in the light of the chemical nature of the two solid surfaces. Enthalpies of adsorption were found to be more negative for CAP than for CAB.     

Interrelations of discrete Painlevé equations through limiting procedures

We study the discrete Painlevé equations associated to the affine Weyl group which can be obtained by the implementation of a special limits of -associated equations. This study is motivated by the existence of two -associated discrete both having a double ternary dependence in their coefficients and which have not been related before. We show here that two equations correspond to two different limits of a -associated discrete Painlevé equation. Applying the same limiting procedures to other -associated equations we obtained several -related equations most of which have not been previously derived.