The Porous Phase Barrier and Crystallization

Abstract

A porous body can be used as a phase barrier, or to safely store or transmit a metastable fluid phase (B) under certain definable conditions even when a stable phase (A) outside the porous body is in intimate contact with the metastable phase inside the body. The condition to be met can be expressed by

R < 2σV _A [(S _B -S _A ) cos θ _A δT]

where R is effective (“cylindrical”) radius of the pores; δT is degrees of supercooling (or superheating); σ is specific surface free energy of the phase boundary; θ _A is the contact anglen of Phase A with the material of the porous body; V and S are partial molal volume and entropy of the indicated phases, respectively. Phase B, the “metastable” phase by conventional test, is found to be the stable phase so long as it remains confined within sufficiently small pores. If the “metastable” phase (B) is a supercooled liquid, strongly adsorbed by the porous material (θ _A > 90°), Phase A can be crystalline, as demonstrated by the natural process of frost heaving of soil. This implies new methods of managing crystallization processes, including one whereby saline water is purified by an “ice sandwich” that sustains reverse osmosis and another whereby components of a binary eutectic mixture may be completely separated.     

Zur unverträglichkeit von polymergemischen. 1. Lichtstreuungsmessungen am system polystyrol/polymethylmethacrylat/benzol

A polystyrene (PS) with M?_w = 9,7 · 10⁴ was investigated by means of light scattering in the isorefractive polymer/solvens-mixture polymethylmethacrylate (PMMA)/benzene. It was found, that the second osmotic virial coefficient A₂ of PS was strongly dependent on the average viscosimetric molecular weight M?_v and on the concentration of PMMA, but scarcely on the temperature in the range of 20°C to 60°C. The θ-Point, where A₂ is zero, was independent of the temperature within experimental error. By defining the PMMA concentration at the θ-Point as c_θ, and by reducing the measured PMMA concentration c to c/c_θ, an unequivocal relation was obtained between A₂ and c/c_θ, which is independent of molecular weight and molecular weight distribution of PMMA. PS shows a high second virial coefficient in dimer and trimer MMA as well as in non-hydrogenated and hydrogenated MMA. The investigated PS constitutes a θ-System in PMMA of a degree of polymerisation of P?_w, ～ 17without the use of benzene.     

Interactions of CO and NO with the perovskite-type oxide larho3

Some aspects of the interactions of CO and NO with LaRhO₃ have been studied. The reduction of this oxide with CO occurs where the contracting sphere model is of perovskite structure stable up to a concentration of anion vacancies of ca. 2e^? per molecule. By reduction of LaRhO₃ at 817 K, rhodium was obtained, highly dispersed on a matrix of La₂O_3. After a reduction-oxidation cycle at 871 K the particle size of the perovskite decreased drastically. The activation energy of the reduction (67 kJ mol^?1) was significantly lower than that of other LaMO₃ oxides of group-VIII metals. Coverages of CO(θ_CO) and NO(θ_NO) at room temperature were lower than 3%, θ_NO being substantially higher than θ_CO. The reversibly adsorbed fractions of CO and NO underwent a remarkable decrease after preadsorbing NO and CO, respectively. This competitive adsorption is assumed to be associated with the adsorption of CO and NO on metallic sites. NO preadsorption inhibited the total adsorption of CO more severely than the reverse, indicating that NO is bound more strongly than CO to the LaRhO₃ surface.     

Effects of concentration dependence of surface diffusivity on the transport and adsorption of gases in a solid sphere with bidisperse pores

A model for transport and adsorption of gases in a biporous solid sphere was presented assuming a linear adsorption isotherm and linear concentration dependence of surface diffusivity. When put into dimensionless form this model is characterized by four dimensionless parameters. To help assessing the error involved in using constant effective diffusivities, numerical results were presented for the uptake of pure gases into a biporous solid sphere with concentration dependent diffusivity and compared with those for effective diffusivity model. The error in transient uptake was found to be as large as ten percent.     

An Effective Moisture Diffusivity Model Deduced from Experiment and Numerical Solution of Mass Transfer Equations for a Shrinkable Drying Slab of Microalgae Spirulina

From experimental data, Spirulina effective moisture diffusivity was analytically estimated by considering two diffusion regions and the product shrinkage. Then, the moisture diffusivity was deduced from the numerical solutions of mass transfer equations by minimizing the difference between experimental and simulated drying curves and by taking into account the slab thickness variation. The range of moisture diffusivity used for simulations was estimated from minimal and maximal values of experimental effective diffusivities and calculation started with the mean value of experimental effective diffusivities. Identified effective diffusivities ranged from 1.79 × 10^?10 to 6.73 × 10^?10 m²/s. These diffusivities increased strongly with drying temperature and decreased slightly with moisture content. A suitable model correlating effective diffusivity, temperature, and moisture content was then established. Effective diffusivities given by this model were very close to experimental ones with a relative difference ranging from 0.5 to 24%.     

Dimensionless Analysis of D-Optimal Designs for 1-Dimensional Sorption Kinetic Experiments

D-optimal designs are developed for adsorption kinetics experiments for three 1-dimensional sample geometries: the infinite slab, the infinite cylinder, and the sphere. The well-known solutions to Fick’s second law with constant diffusivity, homogeneous initial concentration, and a convective boundary condition were used as the adsorption kinetic models. Prior to solving for the D-optimal designs, it is shown that the designs can be cast in terms of two dimensionless groups, the Biot number and the Fourier modulus. Finally, the D-optimal designs for the three geometries are presented and compared.     

Theoretical and Experimental Estimation of Binary Gas Diffusivities in a Nonisothermal Stefan Diffusion Column

Binary gas diffusivities D_AB are essential to analyze chemical engineering transport processes. One of Josef Stefan's memorable moving-front problems involved a column with liquid A at the bottom and a gas mixture of A and B on top. This system has been used by several groups to determine D_AB's under assumed isothermal conditions. A device for such purposes is Armfield's CERa apparatus; however, its operation is not isothermal. This study's hypothesis is that the nonisothermality of the gas relative to the liquid affects the D_AB estimates. A mass and energy transport model was developed to describe events in the gas once the evaporation-diffusion of A begins. The model included D_AB as a key parameter and different phase temperatures (liquid hotter than gas). A numerical algorithm solved for the instantaneous mole fraction of A, temperature, and interfacial position. The model predicted the transient and spatial transport phenomena of four gas pairs (A = common solvent; B = bone-dry air). The simulations gave lower D_AB's in nonisothermal versus isothermal columns, the errors being proportional to the temperature difference between the phases. Six binary gas experiments were carried out in a nonisothermal CERa at two room temperatures. The experimental D_AB's underestimated the isothermal diffusivities with errors of 23–52%, while the parallel simulations followed this trend but with smaller errors (4.1–6.3%). D_AB underestimation due to column nonisothermality is novel in the gas diffusivity literature. Improvements to the theoretical and experimental techniques presented should result in better D_AB estimates.     

Application of the Vrentas–Duda free-volume theory of diffusion below the glass-transition temperature: Application to hypromellose acetate succinate–solvent systems

The Vrentas–Duda free-volume theory for diffusion characterizes the diffusivity of a solvent in a polymer in terms of the concentration and size of the solvent, the temperature, and the glass transition temperature (T_g) of the individual components. The effective T_g of the polymer, however, is a function of the concentration of the solvent. This article introduces a modification that corrects for this change in the glass-transition temperature, thus providing more accurate diffusivities. The model has been verified by comparison with experimental diffusivities of water, acetone, methanol, and tetrahydrofuran in hypromellose acetate succinate (HPMCAS). HPMCAS is widely used in the production of pharmaceutical formulations. One common application is the formation of amorphous solid dispersions with poorly soluble active pharmaceutical ingredients (APIs) for dissolution and solubility enhancement. Frequently, the APIs and HPMCAS are put into solution and spray dried at an outlet temperature below the normal glass-transition temperature. The modified free-volume theory is able to directly predict or correlate with only one adjustable parameter the diffusivities as a function of the concentration and temperature. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47351.     

Magnetic resonance imaging to measure concentration profiles of solutes diffusing in stagnant beds of cellulosic fibers

The evolution of the concentration profiles of an adsorbing solute diffusing in a stagnant bed of cellulosic fibers is measured using magnetic resonance imaging. Effective diffusivities are calculated by matching concentration profiles with a numerical model of one‐dimensional Fickian diffusion. The measured values of the effective diffusion coefficients are interpreted using a model that accounts for the porosity, tortuosity, and adsorption equilibrium constant. The effective diffusivities in fiber beds are significantly lower than the bulk diffusivity of the solute and highly dependent on fiber type. The diffusivity is lower for the fiber type that exhibited stronger adsorption properties. The influence of concentration, adsorption, and other fiber characteristics on diffusion rates and rates of reaction is discussed. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Experimental study of vapor permeation of C5C7 alkane through PDMS membrane

Vapor permeation through dense membrane is regarded as an effectively way to separate volatile organic compounds (VOC) from industrial gas stream. This study proposes a new method to get the solubility and diffusivity of pure VOC vapor in dense membrane. C₅H₁₂, C₆H₁₄ and C₇H₁₆ were selected as sample VOC components to conduct newly developed sorption experiment with polydimethylsiloxane (PDMS) membrane. For each considered VOC component, its solubility was obtained from measured sorption equilibrium concentration in PDMS membrane, and its diffusivity was determined by fitting diffusion equation to the measured transient concentration of VOC component. The permeation behavior of VOCs in PDMS membrane was analyzed in terms of their solubility, diffusivity and permeability. Furthermore, the obtained solubility of these VOC components was utilized to get the vapor–membrane interaction parameters in UNIQUAC model. This opens an effective way to obtain the activity coefficient of VOC components for predicting their permeation performance in PDMS membrane.     

Dual mode roll-up effect in multicomponent non-isothermal adsorption processes with multilayered bed packing

Roll-up is a common phenomenon occurring in multicomponent adsorption processes when the concentrations of some components at the outlet of the adsorber exceed their inlet levels. Previous investigations attributed the roll-up effect typically to the displacement of one component by another because of the difference in adsorption affinities or diffusivities. In this work, we report the existence of a peculiar type of roll-up caused by thermal effect solely in our multicomponent non-isothermal breakthrough experiments where the light component CO₂ was swept off by a pure thermal wave developed from water vapour adsorption. Even though, the formation of a pure thermal wave is well known, it does not lead to the above roll-up without a multilayered bed packing. To our surprise, a secondary roll-up of CO₂ caused by H₂O displacement was also observed, since the front of the water concentration wave ran behind its thermal wave in our case. The parameters affecting the formation of this special dual mode roll-up were investigated and summarised. This work will give guidance to the design of multilayered cyclic adsorption processes, e.g. determination of layering ratios and duration of the feed step.     

Carboxybetaine,sulfobetaine, and cationic block copolymer coatings: A comparison of the surface properties and antibiofouling behavior

Two different zwitterionic block copolymers (BCs) and a cationic BC were synthesized from the same BC precursor, which consisted of a polystyrene (PS) block and a poly[N‐(3‐dimethylamino‐1‐propyl)acrylamide] block. The zwitterionic BCs contained the dimethylammonioacetate (carboxybetaine) and dimethylammoniopropyl sulfonate (sulfobetaine) groups. Thin films cast from these polymers were investigated for surface wettability, surface charge, and protein adsorption. Surface‐energy parameters calculated with advancing contact angle (θ_a) and receding contact angle (θ_r) of different probe liquids showed that it was θ_r and not θ_a that was representative of the polar/ionic groups in the near‐surface regions of the coatings. Electrophoretic mobility was used to characterize the influence of pH on the net surface charge. In aqueous dispersions, the carboxybetaine polymer showed an ampholyte behavior with an isoelectric point of 6, whereas the sulfobetaine polymer was found to be anionic at all pH values between 2 and 10. Protein adsorption on the carboxybetaine BC was relatively independent of the net charges on the protein or the polymer, but the negatively charged sulfobetaine polymer showed a higher adsorption of positively charged protein molecules. Regardless of the net protein charge, both zwitterionic coatings adsorbed less protein compared to the PS and poly(2,3,4,5,6‐pentafluorostyrene) controls. The sulfobetaine and cationic BCs adsorbed higher amounts of oppositely charged protein molecules than like‐charged protein molecules. However, the adsorption of oppositely charged protein was much higher on the cationic surface than on the sulfobetaine surface. The zwitterionic BCs, particularly the carboxybetaine polymer, from this article are expected to function as stable, low‐fouling surface modifiers in different biological environments. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Multicomponent mass transfer in films and rigid drops: The influence of concentration-variable diffusivity

The typical approach to multicomponent mass transfer calculations assumes that the multicomponent diffusivities are constant. The errors which result because of this assumption have been accepted because of the complexity of the calculations resulting when diffusivity as a function of concentration is included. The influence of this assumption, previously not demonstrated, has now been determined for two physical situations—a stagnant film and a rigid drop (a solid sphere, or liquid drop in which there is no internal circulation). Multicomponent diffusivities, concentration profiles, and mass fluxes have been computed to compare results for constant, and for concentration-variable, diffusivity. Results include the cases of flux operating against the concentration gradient and non-zero flux of components with no imposed gradient. The technique used to estimate mass transfer rates in multicomponent mixtures considers the effects of multicomponent interactions (friction) among molecules and also the thermodynamic correction to these interactions based on the Maxwell-Stefan (MS) formulation. A program written in Mathcad was used to carry out the calculations. The coupled differential equations which represent solute balances were solved numerically applying a central finite difference scheme and the Crank-Nicholson method. The resulting system of equations in matrix form were solved with a program also generated with Mathcad. Results show that concentration-variable diffusivity may give significantly different (as much as 80%) component mass transfer flux values, when determined for high fluxes and large imposed concentration differences. However, even in this regime, it may be possible to formulate suitable constant ‘average’ diffusivities to produce results which are much closer to those predicted with concentration-dependent diffusivities.     

Absolute surface coverage of tungsten-alumina catalysts

Absolute surface coverages (θ) of a series of tungsten-alumina catalysts prepared by the equilibrium adsorption method were determined by ion scattering spectroscopy (ISS) and low-temperature CO adsorption. The θ_CO values for the W catalysts were very similar to those obtained with the ISS method, for a given W loading. A linear increase in W coverage with increasing W loading, reaching ~55% coverage for the 13.1% W solid, was observed. The calculated W cross-sections (22.0- 24.5Ų/W) were in agreement with other reports in the literature. Due to the inherent limitations of each method, the combined use of ISS and low-temperature CO adsorption is recommended for estimating absolute surface coverages in tungsten-alumina catalysts.     

Modelling of catalytic reactors containing core–shell pellets with various morphologies for series reactions

Modelling of series reactions was performed for core–shell catalysts. Mathematical solutions of concentrations inside the pellets were derived from reaction–diffusion equations considering inert-core thickness (ξ_c) for first-order kinetics. Transient behaviours of catalytic reactors containing core–shell pellets were predicted, assuming pseudo-steady state approximation. In a batch reactor, the removal rate of reactants increased with increasing Thiele modulus and decreasing ξ_c in the order of sphere > cylinder > slab. The transient concentration of the intermediate product was maximum and affected by the distribution coefficient, diffusivity ratio, particle shape, and ξ_c. In a continuously stirred tank reactor, the concentration was affected by feed rate and catalyst loading, and conversion could be enhanced by a cascade connection. In a fixed-bed reactor, the concentration increased with increasing ξ_c due to an insufficient catalyst volume. Péclet number and particle shape also affected the concentration, implying that axial dispersion and interfacial area are important design parameters.     

The Moisture Migration Behavior of Plasticized Starch Biopolymer

Using plasticized starch pellets as a precursor for making thermoformed products is a commercially viable and profitable idea. However, drying of plasticized starch is quite complex in nature, partly due to the synergistic interactions between starch and plasticizers in the presence of water. The migration of water from starch pellets plasticized by two components, glycerol and xylitol, at three different temperatures was investigated in the present work. Evidence for synergistic interaction between plasticizers and water within starch is shown by the reduced effective moisture diffusivities and moisture migration fluxes at different overall plasticizer concentrations. In addition, the effective moisture diffusivities showed stronger dependence on moisture concentration and the plasticizer molecular weight even though the moisture flux was comparable. The drying process was characterized by two effective diffusion coefficients (D ₁, D ₂) and, interestingly, the coefficients were an order of significance apart. The Peleg model was investigated for predicting the drying behavior and it is shown that the Peleg constants k ₁ and k ₂ increase with temperature. k ₂, Which is related to material structure and morphology, showed comparable modification by addition of plasticizers, indicating that plasticizers were able to modify the fundamental structure, and xylitol showed greater average k ₂ values than glycerol. Further, because k ₁ is related with moisture diffusivity, the effect of temperature on diffusivity was interpreted using the Arrhenius relationship. The activation energy values confirm that plasticizers can lock in water within the new structure. Overall, the larger structure of xylitol showed better stability in controlling moisture diffusivities and migration fluxes. These findings can provide better insights in designing and controlling the vapor barrier properties of starch-based packaging materials.     

Selective transport of CO2, CH4, and N2 in coals: insights from modeling of experimental gas adsorption data

Selective adsorption and transport of gases in coal are important for natural gas recovery and carbon sequestration in depleted coal seams for environmental remediation. Gases are stored in coal mainly in the adsorbed state. In this study, the interaction energies of adsorbates (CO₂, CH₄, and N₂) and micropores with various widths are investigated using a slit-shape pore model. The experimental adsorption rate data of the three gases conducted on the same coal sample are numerically simulated using a bidisperse model and apparent diffusivities of each adsorbate in the macropore and micropore are determined. The results indicate that the relative adsorbate molecule size and pore structure play an important role in selective gas adsorption and diffusion in micropores. Generally, the microporous coals diffusion is activated and the apparent micropore diffusivities of gases in coal decrease strongly with increase in gas kinetic diameters. Apparent micropore diffusivity of CO₂ is generally one or two order of magnitude higher than those of CH₄ and N₂ because their kinetic diameters have the relation: CO₂ (0.33 nm)<N₂ (0.36 nm)<CH₄ (0.38 nm). In contrast to theoretical values, apparent macropore diffusivity of CO₂ is also larger than those of CH₄ and N₂, suggesting that coal has an interconnected pore network but highly constricted by ultra micropores with width <∼0.6 nm. It is also found that the apparent diffusivity strongly decreases with an increase in gas pressure, which may be attributed to coal matrix swelling caused by gas adsorption. Therefore, rigorous modeling of gas recovery and production requires consideration of specific interaction of gas and coal matrix.     

Equilibrium of benzidine inclusion adsorption on cyclodextrin copolymer

Insoluble β‐cyclodextrin (β‐CD) copolymer was prepared by reacting β‐CD with hexamethylene diisocyanate, and its inclusion adsorption behavior was investigated. The physical and chemical properties of CD copolymer were characterized by SEM, FTIR, DSC, TGA, XRD, and BET N₂ adsorption. The effects that shaking time and temperature exerted on the inclusion adsorption of benzidine on CD copolymer have been studied at relative low initial benzidine concentration. The procedure of the inclusion adsorption could be described by the Freundlich equation, and the thermodynamic constants ΔH^θ, ΔS^θ and ΔG^θ were obtained simultaneously. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Radial gas dispersion in a column packed with screen cylinders

Gaseous eddy diffusivity measurements were made by a point injection technique in a 6.5-in. column packed with open-end screen cylinders varying in size from 3/8-in. to 1 1/2-in. diameter, and made from wire cloth varying from 4 to 28 mesh/in. Oxygen was used as the tracer gas. Only packings made from 4 to 10 mesh/in. produced concentration profiles which were symmetric. The latter data show that turbulent diffusivity increases linearly with gas flow rate, but decreases with decreasing mesh opening and wire diameter. A correlation is presented for turbulent diffusivities as a function of the Reynolds number, d_muρ/m?, and the ratio d_w/d_m.     

Contribution of interferometry and mechanical parameters in evaluating molecular orientation for drawn polyester

Mechanical and structural parameters related to the optical properties of polyester (PET) (woollen type) fibres drawn at room temperature have been investigated. The changes in the strain were evaluated to obtain the molecular orientation factors 〈P₂(cos θ)〉 and 〈P₄(cos θ)〉. From the optical orientation, the values of f₂(θ), f₄(θ) and f₆(θ) orientation parameters were calculated. The structure and properties of oriented PET have been studied in the light of the rubber elasticity theory. The dielectric constant, magnetic susceptibility, number N′ of chains between crosslinks per unit volume, optical configuration parameter and the segment anisotropy, were among the calculated parameters. The results of the extension were used to calculate the shrinkage factor. Relationships between the calculated parameters and the draw ratios, together with micro-interferograms, are given for illustration. The present study throws light on how the applied stress changes the molecular orientation factors and the structural parameters. © 1999 Society of Chemical Industry