Diffusing uphill with James Clerk Maxwell and Josef Stefan

Diffusiophoresis of a Nonionic Micelle in Salt Gradients; Roles of Preferential Hydration and Salt-Induced Surfactant Aggregation

Diffusiophoresis is the migration of a colloidal particle in water driven by concentration gradients of cosolutes such as salts. We have experimentally characterized the diffusiophoresis of tyloxapol micelles in the presence of MgSO4, a strong salting-out agent. Specifically, we determined the multicomponent-diffusion coefficients using Rayleigh interferometry, cloud points, and dynamic-light-scattering diffusion coefficients on the ternary tyloxapol-MgSO4-water system at 25 °C. Our experimental results show that micelle diffusiophoresis occurs from a high to a low salt concentration (positive diffusiophoresis). Moreover, our data were used to characterize the effect of salt concentration on micelle size and salt osmotic diffusion, which occurs from a high to a low surfactant concentration. Although micelle diffusiophoresis can be attributed to the preferential hydration of the polyethylene glycol surface groups, salting-out salts also promote an increase in the size of micellar aggregates, ultimately leading to phase separation at high salt concentration. This complicates diffusiophoresis description, as it is not clear how salt-induced surfactant aggregation contributes to micelle diffusiophoresis. We, therefore, developed a two-state aggregation model that successfully describes the observed effect of salt concentration on the size of tyloxapol micelles, in the case of MgSO4 and the previously reported case of Na2SO4. Our model was then used to theoretically evaluate the contribution of salt-induced aggregation to diffusiophoresis. Our analysis indicates that salt-induced aggregation promotes micelle diffusiophoresis from a low to a high salt concentration (negative diffusiophoresis). However, we also determined that this mechanism marginally contributes to overall diffusiophoresis, implying that preferential hydration is the main mechanism causing micelle diffusiophoresis. Our results suggest that sulfate salts may be exploited to induce the diffusiophoresis of PEG-functionalized particles such as micelles, with potential applications to microfluidics, enhanced oil recovery, and controlled-release technologies.

Toward Bottom-Up Understanding of Transport in Concentrated Battery Electrolytes

Bottom-up understanding of transport describes how molecular changes alter species concentrations and electrolyte voltage drops in operating batteries. Such an understanding is essential to predictively design electrolytes for desired transport behavior. We herein advocate building a structure-property-performance relationship as a systematic approach to accurate bottom-up understanding. To ensure generalization across salt concentrations as well as different electrolyte types and cell configurations, the property-performance relation must be described using Newman's concentrated solution theory. It uses Stefan-Maxwell diffusivity, ij , to describe the role of molecular motions at the continuum scale. The key challenge is to connect ij to the structure. We discuss existing methods for making such a connection, their peculiarities, and future directions to advance our understanding of electrolyte transport.

Bootstrapping time correlation functions of molecular dynamics

Molecular dynamics is often considered as a numerical experiment. The error bars on the results are therefore mandatory, but sometimes difficult to determine and computationally demanding. As a low-cost approach, we describe the application of the bootstrap (BS) method to the quantification of uncertainties pertaining to the time correlation functions. We chose the autocorrelation functions of velocity and interdiffusion current for a binary ionic mixture as a test bed, and we assessed the merit of the Darken approximation relating both of them. The intrinsic errors related to phase space sampling is investigated comparing the BS method with the reference method of replica. We also study how the BS method can assist in addressing the finite-size effects.

Droplet Formation and Growth Mechanisms in Reaction-Induced Spontaneous Emulsification of 3-(Trimethoxysilyl) Propyl Methacrylate

Spontaneous emulsification of 3-(trimethoxysilyl) propyl methacrylate (TPM) can produce complex and active colloids, nanoparticles, or monodisperse Pickering emulsions. Despite the applicability of TPM in particle synthesis, the nucleation and growth mechanisms of TPM emulsions are still poorly understood. We investigate droplet formation and growth of TPM in aqueous solutions under quiescent conditions. Our results show that in the absence of stirring the mechanisms of diffusion and stranding likely drive the spontaneous emulsification of TPM through the formation of co-soluble species during hydrolysis. In addition, turbidity and dynamic light scattering experiments show that the pH modulates the growth mechanism. At pH 10.1, the droplets grow via Ostwald ripening, while at pH 11.5, the droplets grow via monomer addition. Adding surfactants [Tween, sodium dodecyl sulfate (SDS), or cetyltrimethylammonium bromide] leads to <100 nm droplets that are kinetically stable. The growth of Tween droplets occurs through addition of TPM species while the number density of droplets is kept constant. In addition, in the presence of the ionic surfactant SDS, electrostatic repulsion between the solubilized TPM species and SDS leads to a significant increase in the number density of droplets as well as additional nucleation events. Finally, imaging of the solubilization of TPM in capillaries shows that in the absence of a surfactant, TPM hydrolysis is likely the rate-limiting step for emulsification, whereas the presence of silica particles in the aqueous phase likely acts as a catalyst of TPM hydrolysis. Our experiments highlight the importance of diffusion and solubilization of TPM species in the aqueous phase in the nucleation and growth of droplets.

Application of microimaging to diffusion studies in nanoporous materials

Microimaging on the basis of, respectively, interference microscopy and IR microscopy permit the observation of the distribution of guest molecules in nanoporous solids and their variation with time. Thus attainable knowledge of both concentration gradients and diffusion fluxes provides direct access to the underlying diffusion phenomena. This includes, in particular, the measurement of transport diffusion under transient, i. e. under non-equilibrium conditions, and of self- or tracer diffusion on considering the rate of tracer exchange. Correlating the difference in guest concentration close to the external surface to its equilibrium value with the influx into the nanoporous solid, microimaging does as well allow the direct determination of surface resistances. Examples illustrating the variety of information thus attainable include the comparison of mass transfer under equilibrium and non-equilibrium conditions, single- and multicomponent diffusion and chemical reactions. They, finally, introduce into the potentials of microimaging for an in-depth study of mass transfer in mixed-matrix membranes. This tutorial review may serve as first introduction into the topic. Further references are linked for the interested reader.

Diffusion in nanopores: inspecting the grounds

This paper provides a general overview of the phenomenon of guest diffusion in nanoporous materials. It introduces the different types of diffusion measurement that can be performed under both equilibrium and non-equilibrium conditions in either single- or multicomponent systems. In the technological application of nanoporous materials for mass separation and catalytic conversion diffusion often has a significant impact on the overall rate of the process and is quite commonly rate controlling. Diffusion enhancement is therefore often a major goal in the manufacture of catalysts and adsorbents.

Metrics for Evaluation and Screening of Metal-Organic Frameworks for Applications in Mixture Separations

For mixture separations, metal-organic frameworks (MOFs) are of practical interest. Such separations are carried out in fixed bed adsorption devices that are commonly operated in a transient mode, utilizing the pressure swing adsorption (PSA) technology, consisting of adsorption and desorption cycles. The primary objective of this article is to provide an assessment of the variety of metrics that are appropriate for screening and ranking MOFs for use in fixed bed adsorbers. By detailed analysis of several mixture separations of industrial significance, it is demonstrated that besides the adsorption selectivity, the performance of a specific MOF in PSA separation technologies is also dictated by a number of factors that include uptake capacities, intracrystalline diffusion influences, and regenerability. Low uptake capacities often reduce the efficacy of separations of MOFs with high selectivities. A combined selectivity-capacity metric, Δq, termed as the separation potential and calculable from ideal adsorbed solution theory, quantifies the maximum productivity of a component that can be recovered in either the adsorption or desorption cycle of transient fixed bed operations. As a result of intracrystalline diffusion limitations, the transient breakthroughs have distended characteristics, leading to diminished productivities in a number of cases. This article also highlights the possibility of harnessing intracrystalline diffusion limitations to reverse the adsorption selectivity; this strategy is useful for selective capture of nitrogen from natural gas.

A New Method for the Measurement of the Diffusion Coefficient of Adsorbed Vapors in Thin Zeolite Films, Based on Magnetoelastic Sensors

In the current work an experimental method is used in order to calculate the diffusivity D (diffusion coefficient) of various vapors in thin zeolite films. The method is based on adsorption data from magnetoelastic sensors on top of which a zeolite layer was synthesized, and the diffusivity is extracted by fitting the data to Fick’s laws of diffusion. In particular, the method is demonstrated for two volatile organic compound (VOC) vapors on two different zeolites, the p-Xylene adsorption in Faujasite type zeolite with D=1.89×10−13 m2/s at 120 °C and the propene adsorption in Linde Type A type zeolite with D=5.9×10−14 m2/s at 80 °C, two diffusion coefficients which are extracted experimentally for first time. Our results are within the order of magnitude of other VOC/zeolite values reported in literature.

Highlighting Thermodynamic Coupling Effects in the Immersion Precipitation Process for Formation of Polymeric Membranes

In the immersion precipitation process for membrane formation, a polymer casting film is placed in contact with a nonsolvent in a coagulation bath; an essential feature of the membrane formation process is the foray into the metastable region of the ternary phase diagram for the nonsolvent/solvent/polymer system. The primary objective of this article is to trace the origins of such forays. The Maxwell-Stefan diffusion formulation is combined with the Flory-Huggins description of phase equilibrium thermodynamics to set up a model for describing the transient equilibration trajectory that is followed in the polymer casting film. Four different systems are analyzed: water/acetone/CA, water/DMF/PVDF, water/NMP/PSF, and water/NMP/PEI (CA = cellulose acetate; PVDF = poly(vinylidene fluoride); PSF = polysulfone; PEI = polyetherimide, DMF = dimethyl formamide; NMP = N-methyl-2-pyrrolidone). The analysis shows that diffusional forays are mainly engendered due to thermodynamic coupling effects; such effects are quantified by the set of thermodynamic factors , where a _i , the activity of species i, is dependent on the volume fractions, ϕ _i and ϕ _j , of both nonsolvent (i) and solvent (j). In regions close to phase transitions, the off-diagonal elements Γ _ij (i ≠ j) are often negative and may attain large magnitudes in relation to the diagonal elements Γ _ii . Strong thermodynamic coupling effects cause the transient equilibration trajectories to be strongly curvilinear, causing ingress into the metastable region. If thermodynamic coupling effects are ignored, no such ingress occurs. It is also shown that analogous diffusional forays may lead to emulsion formation in partially miscible liquid mixtures.

Thermodynamically Consistent Methodology for Estimation of Diffusivities of Mixtures of Guest Molecules in Microporous Materials

The Maxwell-Stefan (M-S) formulation, that is grounded in the theory of irreversible thermodynamics, is widely used for describing mixture diffusion in microporous crystalline materials such as zeolites and metal-organic frameworks (MOFs). Binary mixture diffusion is characterized by a set of three M-S diffusivities: Đ ₁, Đ ₂, and Đ ₁₂. The M-S diffusivities Đ ₁ and Đ ₂ characterize interactions of guest molecules with pore walls. The exchange coefficient Đ ₁₂ quantifies correlation effects that result in slowing-down of the more mobile species due to correlated molecular jumps with tardier partners. The primary objective of this article is to develop a methodology for estimating Đ ₁, Đ ₂, and Đ ₁₂ using input data for the constituent unary systems. The dependence of the unary diffusivities Đ ₁ and Đ ₂ on the pore occupancy, θ, is quantified using the quasi-chemical theory that accounts for repulsive, or attractive, forces experienced by a guest molecule with the nearest neighbors. For binary mixtures, the same occupancy dependence of Đ ₁ and Đ ₂ is assumed to hold; in this case, the occupancy, θ, is calculated using the ideal adsorbed solution theory. The exchange coefficient Đ ₁₂ is estimated from the data on unary self-diffusivities. The developed estimation methodology is validated using a large data set of M-S diffusivities determined from molecular dynamics simulations for a wide variety of binary mixtures (H₂/CO₂, Ne/CO₂, CH₄/CO₂, CO₂/N₂, H₂/CH₄, H₂/Ar, CH₄/Ar, Ne/Ar, CH₄/C₂H₆, CH₄/C₃H₈, and C₂H₆/C₃H₈) in zeolites (MFI, BEA, ISV, FAU, NaY, NaX, LTA, CHA, and DDR) and MOFs (IRMOF-1, CuBTC, and MgMOF-74).

Highlighting the Influence of Thermodynamic Coupling on Kinetic Separations with Microporous Crystalline Materials

The main focus of this article is on mixture separations that are driven by differences in intracrystalline diffusivities of guest molecules in microporous crystalline adsorbent materials. Such "kinetic" separations serve to over-ride, and reverse, the selectivities dictated by mixture adsorption equilibrium. The Maxwell-Stefan formulation for the description of intracrystalline fluxes shows that the flux of each species is coupled with that of the partner species. For n-component mixtures, the coupling is quantified by a n × n dimensional matrix of thermodynamic correction factors with elements Γ _ij ; these elements can be determined from the model used to describe the mixture adsorption equilibrium. If the thermodynamic coupling effects are essentially ignored, i.e., the Γ _ij is assumed to be equal to δ _ij , the Kronecker delta, the Maxwell-Stefan formulation degenerates to yield uncoupled flux relations. The significance of thermodynamic coupling is highlighted by detailed analysis of separations of five different mixtures: N₂/CH₄, CO₂/C₂H₆, O₂/N₂, C₃H₆/C₃H₈, and hexane isomers. In all cases, the productivity of the purified raffinate, containing the tardier species, is found to be significantly larger than that anticipated if the simplification Γ _ij = δ _ij is assumed. The reason for the strong influence of Γ _ij on transient breakthroughs is traceable to the phenomenon of uphill intracrystalline diffusion of more mobile species. The major conclusion to emerge from this study is that modeling of kinetic separations needs to properly account for the thermodynamic coupling effects.