Water sorption by the calcium chloride/silica gel composite: The accelerating effect of the salt solution present in the pores

The kinetics of isothermal water sorption by the CaCl₂/silica gel composite initiated by a small stepwise pressure rise over the sample has been investigated at a constant underlying plate temperature of 35°C. The initial portion of the kinetic curves is consistent with Fick’s diffusion model: the amount of sorbed water increases in proportion to the square root of the sorption time. This makes it possible to determine the effective diffusivity of water (D _eff). At small amounts of sorbed water (w < 0.19 g/g), D _eff changes slightly. The diffusivity of water in the composite pores (D) calculated for the same conditions is close to the Knudsen diffusivity of water vapor in mesopores. The D _eff value grows with an increasing water content of the composite; that is, sorbed water accelerates water transport in the pores. This is likely due to the appearance of an extra diffusion channel, namely, diffusion through the aqueous solution of the salt, whose formation begins on the silica gel surface at w > 0.1 g/g. The contribution from this channel increases markedly when the amount of adsorbed water is above 0.25 g/g. This can be explained by the formation of the “connected” phase of the solution in the pores.     

Kinetics of water sorption on a CaCl2-in-silica-gel-pores sorbent: The effects of the pellet size and temperature

Kinetics of water vapor sorption on the CaCl₂-in-KSK-pores composite (SWS-1L) have been studied at T = 33–69°C and vapor pressures of 8–70 mbar for pellet sizes of 2R _pel = 0.355–0.425, 0.71–0.85, and 1.2–1.4 mm. Sorption has been measured under isothermal conditions on a thermobalance by abruptly raising the vapor pressure in the measurement cell by a small value and then maintaining the new pressure. In the initial portion of the kinetic curves, the amount of sorbed water (Δm) increases in proportion to the sorption time (t) to the power 1/2. From the slope of the Δm versus t ^1/2 curve, it is possible to derive the sorption rate constant k _D = D _eff/R ² _pel and the effective diffusivity D _eff. The latter is independent of R _pel for 2R _pel ≥ 0.71 mm. The rate of water sorption on smaller (0.355-to 0.425-mm) pellets grows less rapidly, apparently because of the effect of the heat of sorption. The effective diffusivity is determined by the local slope of the water vapor sorption isotherm for SWS-1L. Applying an appropriate correction enables one to calculate the effective diffusivity for water vapor in the sorbent pores, which appears to be D _e = (0.35 ± 0.17) × 10^?6 m²/s. This value is approximately 10 times smaller than the Knudsen water diffusion coefficient calculated for a single cylindrical pore with a size equal to the average pore size of the composite. Two possible causes of this discrepancy are discussed, specifically, an increase in the pore tortuosity because of the presence of the salt and the interaction between water and the salt.     

Diffusion in glassy polymers: A model using a homogenization method and the effective medium theory

Glassy polymers are considered as inhomogeneous with regions in which the gas sorption follows Henry's law and others where it follows Langmuir's law. It is assumed that the linear dimensions of these regions are small compared with the macroscopic length of interest but large compared with the mean free path of the penetrant gas molecules. Applying an homogenization method it is shown that the average flux is directly proportional to the concentration gradient in the polymer. This relationship can be expressed in terms of an effective diffusion coefficient D_eff, which depends on the details of the microstructure. D_eff is evaluated in the framework of the effective medium theory and compared with experimental data for diffusion of five vapors in ethylcellulose.     

The sorption of quercetin by high-basicity anion exchangers

The sorption of quercetin on anionites with various porosities in the OH⁻ and Cl⁻ forms was studied under static conditions. The equilibrium (distribution coefficients K _p) and kinetic (effective diffusion coefficients D _eff) parameters of quercetin sorption on AV-17-2P and AV-17-6M anionites in the Cl⁻ and OH⁻ forms were calculated. The mechanism of quercetin interactions with the anion exchangers was studied by electron microscopy and IR spectroscopy. Original Russian Text ? N.A. Udalova, S.I. Karpov, V.F. Selemenev, I.A. Sharmar, 2009, published in Zhurnal Fizicheskoi Khimii, 2009, Vol. 83, No. 6, pp. 1143–1149.     

Specific Features of Lincomycin and Gentamicin Sorption from Aqueous Solutions of Their Salts and Bases by Monocarboxyl Cellulose

Sorption of antibiotics lincomycin and gentamicin from aqueous solutions of their salts and bases by the samples of monocarboxyl cellulose with different content of carboxyl groups was studied. The nature of sorption interactions and factors affecting this process was disclosed. Electrostatic interactions were shown to play a determining role in the mechanism of the antibiotic binding with monocarboxyl cellulose. Single-charged lincomycin was found to be sorbed by monocarboxyl cellulose via stoichiometric binding characterized by the 1 : 1 sorbent-to-sorbate ratio. Multicharged gentamicin was also sorbed from solutions of its sulfate and base due to electrostatic interactions; however, several protonated amino groups of gentamicin molecule are involved in binding, thus resulting in the cross-linking of monocarboxyl cellulose macromolecules.     

Sorption and diffusion of gases in a polyimide

Sorption and diffusion of gases (CO₂, N₂, and He) in a polyimide (PI2080) film were measured by using an apparatus which gives the sorption rate curves from the initial state to the equilibrium state. Nonlinear isotherms observed for CO₂ sorption were interpreted successfully in terms of the dual-mode model for sorption in glassy polymers. Linear isotherms observed for N₂ and He seemed to obey Henry's law. Two diffusion coefficients (D_I and D_E) were obtained using the short-time method and the long-time method for a Fickian diffusion model, together with the equilibrium solubility (C_e) from each experiment. The initial sorption rate curves agreed with the calculated curves using D_I, however near sorption equilibrium the curves are in accord with the calculated curves using D_E. These observations suggest that some relaxation process is superimposed on the diffusion process. The non-Fickian transport data were correlated successfully with a model that combines time-dependent diffusion and the Fickian model.     

Effect of microheterogeneities on the diffusion of gases through glassy polymers

The diffusion of gases through glassy polymers is studied and the effective diffusion coefficient D^eff is represented as the result of the superposition of two fundamental mechanisms, namely slipping and hopping. D^eff is calculated by a two-point correlation method. Comparisons are made with experimental data of Meares for diffusion coefficients of Kr, O₂, He, and A in poly(vinyl acetate) in the glassy state. Good fits are obtained and yield significant parameters.     

A Local D4h Symmetric Dysprosium(III) Single-Molecule Magnet with an Energy Barrier Exceeding 2000 K**

Three six-coordinate Dy^III single-molecule magnets (SMMs) [Dy(O^tBu)₂(L)₄]⁺ with local D_4h symmetry are obtained by optimizing the equatorial ligands. One of the compounds with L=4-phenylpyridine shows an energy barrier (U_eff) of 2075(11) K, which is the third largest U_eff, and the first U_eff>2000 K for SMMs with axial-type symmetry so far. Ab initio analysis indicates that the exceptional uniaxial magnetic anisotropy is deeply related to the axially compressed octahedral geometry. This work provides a new insight into the local D_4h symmetry for high-performance SMMs.     

Identification of unknown diffusion coefficient in pure diffusive linear model of chronoamperometry. I. The theory

Coefficient identification problem for diffusion equation u _t (x, t) = (D(x)u _x (x, t)) _x arising in chronoamperometry is studied. The adjoint problem approach is developed for the case when the output measured data is given in the form of left/right flux. Analytical formulas for determination of the values D(0), D(L) at the endpoints x = 0; L, of the unknown coefficient D(x), via the solution v(x, t) of the constant coefficient equation v _t (x, t) = D v _xx (x, t) is obtained. The integral identity relating solutions of the forward and corresponding adjoint problems is derived. This integral identity permits one to prove the monotonicity and invertibility of input-output map, as well as formulate the gradient of the cost functional via the solutions of the direct and adjoint problems.     

An application of an homogenization method to a model of diffusion in glassy polymers

The sorption of gases in polymers below their glass-transition temperature T_g is known in many cases to be described by the “dual sorption” theory, according to which the gas is held in accordance with both the Langmuir and Henry's laws. Based on this theory, expressions for the “effective diffusion coefficient” in the glassy polymers have been obtained by investigators in the past, notably by Paul and Koros.² The present analysis regards the glassy polymers as inhomogeneous with regions on which the gas sorption follows the Langmuir law. Assuming that the linear dimensions of these regions, which are often referred to as “microvoids” (although they are not space filled by vacuum), are small compared to the macroscopic length of interest but large compared to the mean free path of the penetrant gas molecules, we derive a rigorous relation between the average flux and the concentration gradient in the polymer and show that this relation can be expressed in terms of an “effective diffusion coefficient” D_eff which depends on the details of the microstructure, i.e., the size, shape and spatial distribution of the “microvoids.” This expression for D_eff is shown to reduce to that of Paul and Koros² in two situations: (1) when the “voids” consist of slabs running parallel to the concentration gradient, and (2) when the “voids” are spherical and the temperature of the polymer is not too different from T_g. The results of the present study lead to an alternative procedure for interpreting the experimental data on sorption and permeation which may have some advantages over the procedure currently employed. Finally, the analysis presented here is also applicable to polymers containing adsorptive fillers.     

Cationic grafting of olefins from PVC: The effect of reaction conditions

The cationic grafting of isobutylene, styrene, α-methylstyrene, and β-pinene from a poly(vinyl chloride) (PVC) backbone was investigated. Grafting-from was induced by Et₂AlCl in 1,2-dichloroethane and methylene dichloride solutions from 20 to −70 °C. The effects of temperature and proton trap [2,6-di-tert-butylpyridine (DtBP)] on grafting-from efficiency (G_eff), extent of grafting, branch length (molecular weight), and number of branches per PVC molecule were determined. Reducing the temperature invariably increased the G_eff and the molecular weight of polyisobutylene, polystyrene, poly(α-methylstyrene), and poly(β-pinene) branches attached to PVC. The magnitude of the effects was different with the various olefins and depended on the reaction conditions. The effect of DtBP was examined in the 5 × 10⁻⁴–4 × 10⁻³ mol/L range. By increasing the DtBP concentration the G_eff increased; however, the number-average molecular weight of the grafted branches decreased. The lengths of the grafted branches can be controlled, and G_eff's close to 100% were obtained. The fact that the proton trap reduced the molecular weights of grafted branches suggests that besides proton scavenging, DtBP may also abstract protons from the growing carbenium ion site. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1675–1680, 2001     

Diffusion with discontinuous swelling. V. Type II diffusion into sheets and spheres

Type II diffusion into uniform spheres (radius R) and sheets (thickness 2l) is calculated under the assumption that the glass-gel boundary proceeds at a constant velocity v from the surface towards the interior of the sample, that the diffusion coefficient D_g in the glass is constant and that the diffusion coefficient D_r of the rubbery gel is so much higher than vR or vl that practically no sorbate gradient is needed for the transport through the gel of the sorbate. The diffusion process is completed when this boundary reaches the center of the sample. The concentration profile of the sorbate in the glassy matrix in front of the boundary varies with time and velocity v. It does not, however, influence the boundary propagation velocity. Hence the often observed increase of the rate of the weight gain just at the end of the diffusion process is not considered at all. The relative weight gain of the sample W(t)/W_∞ as a function of time is the only quantity usually measured. From the ordinate intercept A and the initial slope B of the plot of W(t)/t^1/2W_∞ vs. t^1/2, one can calculate the characteristic transport properties, i.e., the diffusion coefficient D_g of the glass and the velocity v of the glass–gel boundary.     

A Film-Pore-Surface Diffusion Model for the Adsorption of Acid Dyes on Activated Carbon

The sorption of acid dyes from aqueous effluents onto activated carbon has been studied. The effects of initial dye concentration and activated carbon mass on the rate of Acid Blue 80, Acid Red 114 and Acid Yellow 117 removal have been investigated. A three-resistance mass transport model based on film, pore and surface diffusion control has been applied to model the concentration decay curves. The model incorporates an effective diffusion coefficient D _eff, which is dependant on the equilibrium solid phase concentration or fractional surface coverage. The results of the film-pore-surface diffusion model are compared with the data obtained from the basic film-pore diffusion model. It has been found that the film-pore-surface diffusion model provides a major improvement over the data correlated by the film-pore diffusion model. Also, the relationship between surface diffusion and fractional surface coverage has been investigated for the adsorption of acid dyes on activated carbon.     

Sorption and diffusion of organic vapors in amorphous Teflon AF2400

Vapor sorption in amorphous Teflon AF2400 of various organic solutes was studied in a wide range of activity at 25 °C by means of the gravimetric technique. The sorption isotherms of hexane, toluene, and chloroform were shown to be concave to the pressure axis and are consistent with the dual mode sorption model (DMS). The parameters of the DMS model k_D and b reveal a linear correlation with squared critical temperature of solutes T. The third model parameter, the Langmuir sorption capacity C′_H decreases when the size of solutes (critical volume) increases. Sorption isotherms of methanol and ethanol were shown to be convex to the pressure axis and are consistent with cluster formation in this strongly hydrophobic polymer. Concentration‐dependent diffusion coefficients D were determined using a linear implicit difference scheme in analysis of sorption kinetics. It was shown that D values increase exponentially with concentration for all the solutes, except alcohols for which exponential reduction of D(C) was observed. The partitioning of the thermodynamic and mobility contributions in D indicated that the reduction of D values of alcohols is consistent with clustering phenomena in AF2400. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 832–844, 2006     

A Film-Pore-Surface Diffusion Model for the Adsorption of Acid Dyes on Activated Carbon

The sorption of acid dyes from aqueous effluents onto activated carbon has been studied. The effects of initial dye concentration and activated carbon mass on the rate of Acid Blue 80, Acid Red 114 and Acid Yellow 117 removal have been investigated. A three-resistance mass transport model based on film, pore and surface diffusion control has been applied to model the concentration decay curves. The model incorporates an effective diffusion coefficient D _eff, which is dependant on the equilibrium solid phase concentration or fractional surface coverage. The results of the film-pore-surface diffusion model are compared with the data obtained from the basic film-pore diffusion model. It has been found that the film-pore-surface diffusion model provides a major improvement over the data correlated by the film-pore diffusion model. Also, the relationship between surface diffusion and fractional surface coverage has been investigated for the adsorption of acid dyes on activated carbon.     

Toluene diffusion in butyl rubber

The sorption isotherm and the polymer mass-fixed diffusion coefficients, D, for toluene in butyl rubber have been measured by the incremental sorption method to concentrations of 130%, corresponding to a solvent volume fraction of 0.578. The increase in D with concentration is strongly exponential to a concentration of 30% and then begins to level out. Since the nature of the dimensional change occurring in vapor sorption was not known, the values of D were converted to solvent self-diffusion coefficients, D₁, assuming both swelling in the thickness direction (1D) and isotropically (3D). The free volume (FV) theory of Fujita was fitted to the resulting D₁ with the zero concentration diffusion coefficient and the self-diffusion coefficient of toluene as limiting values leaving only a single arbitrary parameter. In this form the FV theory was able to describe the trend of the experimental D₁ for the 1D and 3D cases equally well. Values of D were back-calculated from the FV relations for the 1D and 3D cases for comparison with the experimental results and with the diffusion coefficient determined by immersion in toluene. These comparisons favor the assumption that swelling is isotropic. It appears that the simple free volume relation is capable of providing a satisfactory representation of the experimental data with only a single fitting parameter, although there are moderate quantitative discrepancies. © 1994 John Wiley & Sons, Inc.     

On the diffusion of gases in partially crystalline polymers

The diffusion of gases through partially crystalline polymers is studied. The effective diffusion coefficient D^eff is obtained as the result of the averaged superposition of two fundamental mechanisms, namely, diffusion through the crystallites is considered to be zero, and diffusion through the rubbery fraction of the polymer obeys a Fujita-like free-volume theory. The predicted D^eff is compared with experimental data of Kreituss and Frisch. The behavior of the diffusion coefficient in terms of concentration and crystalline fraction is satisfactorily explained through the model.     

A Branched Pore Model Analysis for the Adsorption of Acid Dyes on Activated Carbon

A new branched-pore adsorption model has been developed using an external mass transfer coefficient, K _f, an effective diffusivity, D _eff, a lumped micropore diffusion rate parameter, K _b, and the fraction of macropores, f, to describe sorption kinetic data from initial adsorbent-adsorbate contact to the long-term adsorption phase. This model has been applied to an environmental pollution problem—the removal of two dyes, Acid Blue 80 (AB80) and Acid Red 114 (AR114), by sorption on activated carbon. A computer program has been used to generate theoretical concentration-time curves and the four mass transfer kinetic parameters adjusted so that the model achieves a close fit to the experimental data. The best fit values of the parameters have been determined for different initial dye concentrations and carbon masses. Since the model is specifically applicable to fixed constant values of these four parameters, a further and key application of this project is to see if single constant values of these parameters can be used to describe all the experimental concentration-time decay curves for one dye-carbon system.The error analysis and best fit approach to modeling the decay curves for both dye systems show that the correlation between experimental and theoretical data is good for the fixed values of the four fitted parameters. A significantly better fit of the model predictions is obtained when K _f, K _b and f are maintained constant but D _eff is varied. This indicates that the surface diffusivity may vary as a function of surface coverage.     

The transient response of electrodes coated with membrane-type polymer films under conditions of diffusion and migration of the redox ions

Membrane transport processes involving diffusion and migration of the electroactive species A and product B are analysed. The transport equations (Nernst-Planck equation) are solved by digital simulation techniques with boundary conditions appropriate for the system electrode/membrane-type polymer coating. A large potential step leads to a zero surface concentration of A at time t = 0. Time-dependent concentration gradients of A and B, and field strengths are derived. The current transients are shown to follow Cottrell's law; however, the observed “effective” diffusion coefficients, D_eff, differ from D_A.     

Gas transport properties of annealed polyimide films

Sorption and permeation of CO₂ in various annealed polyimide (PI) films were investigated. Dual-mode sorption and partial immobilization models were used to analyze the data. Sorption of CO₂ in PI film quenched from above the glass transition temperature (T_g) is greater than in film as received. In fact, sorption is decreased over the entire pressure range by cooling the film slowly. These changes in sorption of CO₂ can be attributed to a change in the Langmuir sorption capacity C′_H by annealing, since the other dual-mode sorption parameters, k_D and b, are almost independent of annealing. The value of C′_H is increased by quenching, and decreased by slow cooling from above T_g. The two diffusion coefficients D_D and D_H according to the Henry and Langmuir modes, respectively, for CO₂ also depend markedly on annealing. Diffusion coefficients of quenched PI films are increased and those of film cooled slowly are decreased compared with values for PI film as received. The change in D_H is larger than that in D_D. The permeability coefficient of quenched PI films at 100 cmH_g is about 1.7 times that of PI film as received. The film structure formed by quenching can enhance permselectivity.