Theories based on free-volume concepts have been developed to characterize the self and mutual-diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer-solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free-volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free-volume based approaches used to evaluate solvent self-diffusion coefficients in glassy polymer-solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free-volume methodology has been found to be consistent with molecular dynamics simulations.
INTRODUCTIONThe diffusion of small molecules in polymers is of considerable practical importance and has been studied extensively. Diffusion theories based on the free-volume concept have been used extensively to correlate and predict solvent self-diffusion coefficients in rubbery polymersolvent systems.1-6 These methods provide accurate predictions over a wide range of temperatures and concentrations above the glass transition temperature of the pure polymer. As polymer solutions are cooled over practical time scales, the rate of cooling exceeds the rate of relaxation of the polymer, and a nonequilibrium state referred to as the glassy state results. This phenomenon causes volume to be trapped in the polymer in excess of that expected at equilibrium. Free-volume theory presumes that this extra volume is available to facilitate mass transport in the glassy state. Based on this concept, the original free-volume theory was adapted to describe the diffusion of a trace amount of a solvent in a glassy polymer, 7,8 and it was further extended to describe self-diffusion below the mixture glass transition temperature at finite concentrations of the solvent.
Ofloxacin with Refresh Plus and ofloxacin alone had a more positive effect on epithelial healing than ciprofloxacin. The ciprofloxacin eyes were significantly more prone to impaired or delayed wound healing and to the development of corneal haze.
The chemical industry contributes to 6% of global anthropogenic greenhouse gas (GHG) emissions. A handful of chemical processes (ammonia, nitric acid, methanol, olefins, aromatics, and chlor-alkali) account for 65% of those emissions. Decarbonization of the chemical industry will depend on addressing the intermittency of renewable electricity possibly via low-carbon hydrogen production using water electrolysis. A low-carbon power grid, which could happen in the next decade, would enable the chemical industry to reduce its GHG emissions by at least 35 percent. The remaining heat-based and direct emissions could be addressed by direct use of low-carbon electricity for heat or by generating hydrogen that can be used as a fuel and reducing agent coupled with CO2 capture and utilization efforts. Herein, we discuss how materials innovations could enable the transition to a lower carbon future when based on first-principles and economic realities.
Graphical Abstract
The capillary-column inverse gas chromatography method was used to measure the diffusion and partition coefficients of ethylbenzene, styrene, and acrylonitrile in polybutadiene (PBD) at infinite dilution of the solvents. Experiments were performed over a temperature range of 50-125°C. At temperatures well above the glass-transition temperature of PBD, the diffusivities were correlated using an Arrhenius expression. The Arrhenius parameters in turn were intercorrelated and shown to be a function of the occupied volume, thus providing a method for predicting the diffusion of other solvents in the same polymer. Further, the activation energy was predicted using the Duda-Vrentas free-volume approach. The activation energy thus obtained was compared with the activation energy of the Arrhenius approach. The weight-fraction activity coefficient data were compared to the predictions of the group contribution, lattice-fluid equation-of-state, and the UNIquac Functional-group Activity Coefficient (UNIFAC) free-volume models.
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