Modeling the Effects of Interfacial Characteristics on Gas Permeation Behavior of Nanotube–Mixed Matrix Membranes

Abstract

Theoretical approaches that accurately predict the gas permeation behavior of nanotube-containing mixed matrix membranes (nanotube-MMMs) are scarce. This is mainly due to ignoring the effects of nanotube/matrix interfacial characteristics in the existing theories. In this paper, based on the analogy of thermal conduction in polymer composites containing nanotubes, we develop a model to describe gas permeation through nanotube-MMMs. Two new parameters, "interfacial thickness" (a) and "interfacial permeation resistance" (R), are introduced to account for the role of nanotube/matrix interfacial interactions in the proposed model. The obtained values of a, independent of the nature of the permeate gas, increased by increasing both the nanotubes aspect ratio and polymer-nanotube interfacial strength. An excellent correlation between the values of a and polymer-nanotube interaction parameters, χ, helped to accurately reproduce the existing experimental data from the literature without the need to resort to any adjustable parameter. The data includes 10 sets of CO/CH permeation, 12 sets of CO/N permeation, 3 sets of CO/O permeation, and 2 sets of CO/H permeation through different nanotube-MMMs. Moreover, the average absolute relative errors between the experimental data and the predicted values of the proposed model are very small (less than 5%) in comparison with those of the existing models in the literature. To the best of our knowledge, this is the first study where such a systematic comparison between model predictions and such extensive experimental data is presented. Finally, the new way of assessing gas permeation data presented in the current work would be a simple alternative to complex approaches that are usually utilized to estimate interfacial thickness in polymer composites.

Modeling Permeation through Mixed-Matrix Membranes: A Review

“…A number of permeation models have been proposed for MMMs [68,69,72,76,82,87,133], based on Equations (15) and (16), as listed in Table 1, with the most popular models considering platelet or cubic filler particles [72,130,133] and few newly developed models considering tubular particles [69,76,82]. The simplest RMA models idealize the MMM as a two-phase laminated composite comprising multiple sheets of polymer and selective material alternated in series or in parallel to the flow direction [70,134], as depicted in Figure 2a,b, respectively.…”

“…While these simulation studies considered Finally, while RMA is much less popular for describing permeation in MMMs. With the introduction of nano-flake [181][182][183] and nanotube [184][185][186] based MMMs, models such as those of Cussler [51] and KJN [48] have become more popular as reference to compare with experimental [76,114,187] or simulation-based permeation data [171,172]. Amongst these works, Wang et al [171,172] performed simulations of 3D MMMs comprising ideal platelet and tubular particles, and compared simulation predictions to the Cussler and KJN models (cf.…”

“…Thus, applicability of early RMA/EMA models [62][63][64]66] and later adaptations [65,68,73,74] is often limited to narrow MMM operating conditions (Henry's law region) and ideal polymer-particle morphologies. Furthermore, although experimental studies on MMMs have shown that deviations from Henry's law are common under usual operating pressures (1-4 bar) [15,36,46,75], isotherm nonlinearity is incorporated into the permeation models through the Darken or free volume theories while assuming a uniform field based on the mean permeant concentration [71,[76][77][78][79], an assumption that needs to be relaxed for further progress.Over the last decade, increased efforts have been devoted to advance permeation models to integrate effects of filler morphology (e.g., particle size, shape, and agglomeration) [65,80,81] and defects at the particle-polymer interface in the form of a rigidified polymeric [76][77][78][79][82][83][84], and void [69,77,79,85] or pore-blocked [84] regions. However, while considering such non-idealities, these models share the uniform field assumption inherent to the EMA and RMA [69,76,77,86,87].…”

“…Thus, applicability of early RMA/EMA models [62][63][64]66] and later adaptations [65,68,73,74] is often limited to narrow MMM operating conditions (Henry's law region) and ideal polymer-particle morphologies. Furthermore, although experimental studies on MMMs have shown that deviations from Henry's law are common under usual operating pressures (1-4 bar) [15,36,46,75], isotherm nonlinearity is incorporated into the permeation models through the Darken or free volume theories while assuming a uniform field based on the mean permeant concentration [71,[76][77][78][79], an assumption that needs to be relaxed for further progress.…”

“…Over the last decade, increased efforts have been devoted to advance permeation models to integrate effects of filler morphology (e.g., particle size, shape, and agglomeration) [65,80,81] and defects at the particle-polymer interface in the form of a rigidified polymeric [76][77][78][79][82][83][84], and void [69,77,79,85] or pore-blocked [84] regions. However, while considering such non-idealities, these models share the uniform field assumption inherent to the EMA and RMA [69,76,77,86,87]. Thus, effects of the filler morphology together with isotherm nonlinearity are often embedded in a single empirical morphology-related parameter, such as in the Pal [65], Lewis-Nielsen [73], and Higuchi [88] models.…”