Vanadium separation with activated carbon and iron/activated carbon nanocomposites in fixed bed column: experimental and modelling study

In this work, iron nanoparticles were impregnated onto a commercial activated carbon surface to produce a novel adsorbent called iron-activated carbon nanocomposite (I-AC). Commercial activated carbon (CAC) and I-AC were used for vanadium separation in a fixed-bed column. The effects of various operating parameters such as inlet vanadium ion concentration, adsorbent dose and volumetric flow rate on vanadium separation performance of CAC were investigated. The performance of both adsorbents was compared in three adsorption/desorption cycles. The experimental breakthrough curves of vanadium ions in the fixed-bed column were modeled using the film-pore-surface diffusion model (FPSDM). The four mass transfer parameters characterizing this model, namely the external mass-transfer coefficient (k _f ), pore and surface diffusion coefficients (D _p and D _s ), and axial dispersion coefficient (D _L ) were evaluated through the model. Modelling and experimental results showed that the I-AC nanocomposite has a better performance for vanadium separation in comparison to AC. Sensitivity analysis on the FPSDM showed that the pore and surface diffusion, external mass transfer and axial dispersion play a significant role in vanadium separation using the I-AC. On the other hand, surface diffusion resulted to be relatively less important when CAC was used.     

Prediction of power consumption in mechanically agitated gassed reactor in viscous batch

Transport characteristics such as volumetric mass transfer coefficients, k_La, power input, P, gas hold-up, γ, and mixing time, t_m, are the key parameters in the design of mechanically agitated gasliquid contactors. For their successful design, values of the key parameters can be estimated using empirical correlations. Power input in this case is very often used as the scale of energy dissipation for other characteristics. Our goal was to propose reliable power input correlations for viscous batch processes, which are widely used in industry. The measurements were carried out in a pilot-plant vessel and also results from a laboratory vessel were used to develop the correlations. Different types of impellers and their combinations were used, including radial, axial, and combined liquid flow impellers. The power input was measured in a multiple-impeller vessel at different impeller frequencies and several gas flow rates. Correlation equations describing the behavior of particular impellers were evaluated. In addition, separate correlations for the bottom and upper sections in the multiple-impeller vessel were presented. These correlations can be used for impeller power prediction in industrial scale vessels under a wide range of operational conditions.     

New linear driving force correlation spanning long and short cycle time pressure swing adsorption processes

A simple, semi-empirical, generalized expression was developed for the LDF mass transfer coefficient k as a function of the half cycle time θ _c that encompasses and transitions between the well-known regions governed by the long cycle time constant Glueckauf k and the short cycle time dependent k. This new expression can be used to estimate k = f(θ _c ) for any system, irrespective of the loading and irrespective of θ _c , no matter if k is in the cycle time dependent region or not. A three times wider transition region between the Glueckauf k and the cycle time dependent k was also established, with the Glueckauf LDF limit now valid for θ _c  > 0.3 and the short cycle time limit now valid for θ _c  < 0.01. When evaluating this region for several adsorbate-adsorbent systems, the minimum Glueckauf θ _c spanned three orders of magnitude from thousands of seconds to just a few seconds, indicating a cycle time dependent k is not necessarily limited to what is normally considered a short cycle time. For virtually any θ _c less than this minimum Glueckauf θ _c , this new first-of-its-kind expression can be used to readily provide an accurate value of k = f(θ _c ). Since the widely accepted half cycle time concept does not apply to the actual simulation of a multi-step, unequal step time, pressure swing adsorption process, the value of k = f(θ _c ) from this new expression can be based on either the shortest cycle step in the cycle or a different value of k = f(θ _c ) for each cycle step time in the cycle, with validity confirmed either by experiment or by process simulation using the exact solution to the pore diffusion equation.     

Random packing of monoatomic structures

The dependence of the first coordination number k _n on the packing factor k _y is obtained for four cubic structures: fcc, bcc, simple cubic, and diamond. The k _n (k _y ) dependence is described by a third-degree polynomial k _n = ?71.76782 + 467.78914 k _y ? 925.48451 k _y ² + 603.01146 k _y ³ with the confidence factor R _d = 1. The k _n (k _y ) function has an N loop with a maximum at k _n = 6.32; k _y = 0.454 and a minimum at k _n = 5.84; k _y = 0.573. The tangents intersect the k _n (k _y ) curve at extrema at k _y = 0.4 and k _y = 0.625. Around the N loop, i.e., at 5.84 ≤ k _n ≤ 6.32 and 0.4 ≤ k _y ≤ 0.625, two or three packing factors correspond to a certain value of the coordination number. Therefore, this range of the k _n and k _y values can be defined as a “random packing” region. Estimations presented here agree well with the results of calculations, both geometric and numerical. For monoatomic solids with the random packing parameters, the difference between the specific volumes of the solid and liquid phases is insignificant. The dilatancy effect is possible in the region where ?k _n / ?k _y ≤ 0.     

Experimental study of extraction fraction and mass transfer coefficient in a microchannel using butyl acetate/acetic acid/water chemical system

The droplet flow regime in microchannels can increase the mass transfer and chemical reactions considerably. In this work, the mass transfer of immiscible fluids of water as the solvent and butyl acetate containing 5 vol% of acetic acid as the feed is experimentally studied in a vertical flow inside a microchannel with the inner diameter of 8 mm. Effect of total flow velocity, Re number and volumetric flux ratio of two phases (Q_aq/Q_or) on the extraction fraction of acetic acid, mass transfer coefficient and droplet size were investigated. Based on the experiments, increasing the flux ratio can shift the flow regime from the plug to the droplet. Compared to the plug flow, the extraction fraction increased by 2–3 times in the droplet regime, depending on the total velocity, while the average diameter of the droplets decreased. Moreover, with the increase in the total velocity, the extraction fraction is reduced by 22%. However, in the case of the plug flow, the extraction fraction does not change appreciably with the increase in the total flow velocity. The mass transfer coefficient was found to increase monotonously with increasing Re number and an enhancement of 133% was achieved in the droplet flow regime.     

Von den Größen der chemischen Kinetik

An Hand der denkbar einfachsten chemischen Reaktion\(A\underset{2}{\overset{1}{\longleftrightarrow}}B\) wird gezeigt, daß die Geschwindigkeitskoeffizienten (Gk)k ₁ undk ₂ sowie ihr Quotient, also die Gleichgewichtskonstante (Glk)K=k ₁/k ₂,keine Eigene xistenz beistzen. Sie werden erst dann physikalischwinklich und sinnvoll, wenn sie mit ihrenStoffgrößen gepaart sind, ink ₁ A undk ₂ B und Geschwindigkeiten, inKA=B zum Gleichgewichte.     

Determination of the retention characteristics in thin-layer chromatography taking into account the actual position of the mobile phase front

To reveal the actual position of the mobile phase front, corresponding to the free volume of the layer in thin-layer chromatography, it is suggested to use a nonsorbable low-molecular-weight marker. The expressions for the capacity coefficient k′ equilibrium coefficient K _d , and corrected R _f values (R′_f) were obtained taking into account the correction of the position of the mobile phase front.     

Bestimmung der Dissoziationskonstanten der Formen H5 Y +, H4 Y und H3 Y − der ÄDTE

A critical examination of the methods used in evaluating the constantsk ₆, k₅, k₁ andk ₂ of EDTA shows that potentiometric titration is suitable for the determination of the constantsk ₁ andk ₂ only, but not fork ₆ andk ₅. On the other hand the dependence of the solubility of EDTA upon pH can be used to evaluatek ₁,k ₂ andk ₅, but notk ₆ for the applied experimental conditions (25°C; ionic strength 0,1 m).     

Heat transfer in a jacketed agitated vessel equipped with multistage impellers

In this work, heat transfer via the cylindrical part of the jacket in an agitated vessel has been investigated. Heat transfer coefficients were determined using the transient method based on measuring the temperature dependency of the liquid batch on time. A multistage impeller made of two impellers was used in a cylindrical vessel with dished bottom. The lower impeller was a curved blade turbine with the diameter of d = 100 mm and the upper impeller was either a pitched three-blade or pitched four-blade impeller with the diameter of d₁ = 67 mm. Three different impeller clearances in a multistage configuration, H₃/d₁ = 1, 1.5, and 2, were used in our measurements. The vessel was equipped with two baffles. Experimental results were evaluated using the Euler’s method and nonlinear regression procedure in the Matlab® software and they are summarized in form of Nusselt number correlations describing their dependency on the Reynolds number.     

Effect of solvent nature on the photoreduction kinetics of substituted benzoquinones

Effect of the solvent nature on the kinetics of photoreduction of substituted benzoquinones in the presence of hydrogen donors has been studied. It has been found that the effective photoreduction rate constant (k_H) for quinones decreases with an increase in solvent polarity. For the 3,6-di-tert-butylbenzoquinone–1,2-N,N-dimethylaniline pair, the dependence of ln k_H on the difference of the reciprocals of optical and static solvent permitivities (1/ε _∞–1/ε₀) is stepwise with a break point corresponding to CH₂Cl₂. A similar relationship lnk_H = f(1/ε _∞–1/ε₀) is observed for the p-chloranil–mesitylene pair. In the study of the photoreduction kinetics for a series of seven o-benzoquinones in the presence of p-derivatives of N,N-dimethylaniline in CH₂Cl₂, it has been found that the dependence of k_H on the free energy of electron transfer (ΔG_e) has a maximum for the 3,6-di-tert-butylquinone-1,2–N,N-dimethylaniline pair at ΔG_e = 0.11 eV.     

Method for calculating the sizes of nucleation centers upon homogeneous crystallization from a supercooled liquid

An alternative approach to calculating critical sizes l_k of nucleation centers and work A_k of their formation upon crystallization from a supercooled melt by analyzing the variation in the Gibbs energy during the phase transformation is considered. Unlike the classical variant, it is proposed that the transformation entropy be associated not with melting temperature T_L but with temperature T < T_L at which the nucleation of crystals occurs. New equations for l_k and A_k are derived. Based on the results from calculating these quantities for a series of compounds, it is shown that this approach is unbiased and it is possible to eliminate known conflicts in analyzing these parameters in the classical interpretation.     

Catalytic effects of cationic nanoparticle (CTABr/NaX/H<Subscript>2</Subscript>O,X = Cl,Br) for the piperidinolysis of phenyl salicylate ions

The expression of pseudo-second-order rate constants (k _X) for cationic nanoparticle (CN) [CTABr/NaX/H₂O, X = Br, Cl, CTABr = cetyltrimethylammonium bromide] catalyzed piperidinolysis-ionized phenyl salicylate (PSa^–), at constant [CTABr]_T, 0.1 M piperidine (Pip), and 35°C, were calculated from the relationship: k _obs = (k ₀ + k _X[NaX])/(1 + K ^X/S[NaX]), in which k ₀, k _X, and K ^X/S are constant kinetic parameters and k _obs represents the pseudo-first-order rate constant for Pip reaction with phenyl salicylate ion in the presence of CN. The source of the large catalytic effect of CN catalyst was shown to be due to the transfer of PSa^– from pseudo-phase of the CNs to the bulk aqueous phase through X^–/PSa^– ion exchange at the surface of the CNs.     

Effect of donor and acceptor properties of solvents on the kinetics of photoreduction of sterically hindered <Emphasis Type="Italic">о</Emphasis>-benzoquinones

Effect of the solvent nature on the kinetics of photoreduction of 3,6-di-tert-butyl-1,2-benzoquinone and its six derivatives in the presence of N,N-dimethylaniline and 4-(N,N-dimethylamino)benzaldehyde has been investigated. It has been found that for the о-quinone—amine pair, for which the free energy change of electron transfer is ΔG_e > +0.11 eV, the rate constant of о-quinone photoreduction k_H decreases proportionally to the increase in the acceptor number of the solvent. For the о-quinone—amine pair with ΔG_e < +0.11 eV, the k_H value decreases proportionally to the increase in the donor number of the solvent. It has been established that the enhancement of the electron-acceptor properties of the solvent leads to the emergence of kinetic isotope effect for the reactant pairs of 3,6-di-tert-butyl-1,2-benzoquinone and 4,5-dimethoxy-3,6-di-tert-butyl-1,2-benzoquinone with N,N-di-methylaniline (ΔG_e = +0.11 and +0.22 eV, respectively).     

The use of recurrent equations in chromatography

Recurrent equations A(x + k) = aA(x) + b were shown to be applicable to the approximation not only of virtually arbitrary properties of organic compounds (A) in homologous series (A = n _C, k = 1 or 2) but also of the dependences of chromatographic retention parameters on the number of carbon atoms in homologue molecules (A = t _R). The same equations described the temperature dependences of retention times of arbitrary compounds under isothermal separation conditions in gas chromatography (x = T, k = ΔT = const) and the dependences of retention times on the concentration of an organic solvent as an eluent component (x = C, k = ΔC = const) under isocratic separation conditions in high performance liquid chromatography.     

Kinetic model of copper electrodeposition in sulfate solution containing trisodium citrate complexing agent

Simultaneous solution of two kinetic models of electrodeposition of copper in sulfate solution is studied in this paper. Bulk concentration of species involved in the numerical solution was calculated using MATLAB software. COMSOL Multiphysics software was used for the numerical solution of copper electrodeposition. Numerical results were evaluated using experimental data obtained by linear sweep voltammetry technique. The experimental data was almost fitted using COMSOL optimization physic module. It was found that kinetic parameters of Cu²⁺ (k^1Cu), Cu¹⁺ (k_2Cu), and CuCitH (k_1CuCitH) and diffusion coefficient and charge transfer coefficient of Cu²⁺ (\({D_{C{u^{2 + }}}}\), α_Cu1), Cu¹⁺ (α_Cu2) and CuCitH (D_CuCitH, α_CuCitH) affect the fitting of the experimental data with the computed ones. The variables such as concentration profiles and optimum kinetic parameters that cannot be experimentally measured were achieved by analysis of the model. The parameters, that not affect the fitting, were recognized and kept constant when using the optimization.     

Bending moduli of dendritic polymer brushes in a good solvent

The effect of branching on the Helfrich mean k _C and Gaussian k _G bending moduli of polymer brushes consisting of dendrons grafted to both sides of a thin impermeable surface (membrane) is studied theoretically. The case of an athermal solvent is considered. The moduli are calculated from a change in the free energy of a brush upon cylindrical and spherical bending of the grafting surface, respectively. The grafting density σ, the total number of monomer units N, and the number of generations g in tethered dendrons are varied. Two variants of the self-consistent field method are applied: the analytical approach and the numerical Scheutjens-Fleer method. The first method is applied at small values of σ, when the density profile of monomer units of grafted chains is parabolic in shape. The second method is free of these restrictions. The universal ratio between moduli is found: k _G =?64/105k _C . Both methods predict that the values of moduli decrease with increasing g at constant N and σ. The scaling dependence N ³ remains valid for the moduli of dendritic brushes with different generation numbers g at all of the considered values of σ. The analytical approach also gives the universal scaling dependence k _C ～ k _G ～ σ^7/3; however, the numerical method predicts that the dependences of moduli on σ become stronger with increasing degree of branching of tethered dendrons.     

Dissolution kinetics of silver metal nanoparticles in their reaction with nitric acid in an reverse micelle solution of AOT

The dissolution of silver nanoparticles in their reaction with aqueous HNO₃ solubilized to an reverse micelle solution of sodium bis(2-ethylhexyl)sulfosuccinate in decane is studied spectrophotometrically. A physicochemical model is advanced for quantifying the process kinetics on th basis of the following autocatalytic scheme: Ag⁰ + H⁺ + NO ₃ ^? → Ag⁺ + products (k ₁), and Ag⁰ + Ag⁺ + NO ₃ ^? → 2Ag⁺ + products (k ₂). The effective rate constant k ₂ decreases with decreasing solubilization capacity V _S/V _O (where V _S is the volume of the solubilized dispersed aqueous phase and V _O is the volume of the micelle solution); the solubilization capacity determines the size of the micelle cavities in which the reaction between Ag⁰ and HNO₃ occurs: k ₂ = 74 (V _S/V _O) · 100% ≈ 3.8%), 41 (2.9), and 35 (2.0) L/(mol s). The effective constant k ₁ is determined with a high uncertainty; the effect of V _S/V _O on k ₁ has the opposite tendency.     

Substituent effects on the kinetics of acid-catalyzed hydrolysis of methyl cellulose

The kinetics of the hydrolysis of methyl cellulose (MC, DS 1.27 and 1.95) was studied by a two-step procedure, comprising partial hydrolysis in 1 M TFA in water and water/acetone at 120 °C for various time periods, labeling of generated reducing ends by reductive amination, complete depolymerization by methanolysis followed by trimethylsilylation, and gas chromatographic analysis of the two sets of partially O-methylated glucose derivatives. Rate constants of MCs were all in the order of 10^?4 s^?1. In aqueous TFA, overall rate of hydrolysis of the MC with lower DS was faster than of the MC with higher DS. When substituting half of the water by acetone, reaction was slowed down while selectivity regarding different O-methyl glucosyl residues increased. Compared to the parent glucosyl unit methylation at O-2 and at O-6 decreased rate of hydrolysis, while 3-O-methyl favored it especially in the early stage of the conversion of the macromolecules. Beside slight differences between the two MCs and reaction conditions, rate constants k _i (i = position of methyl) followed the order k ₃₆ ≈ k ₃ > k ₀ ≈ k ₂₃ > k ₆ > k ₂ ≥ k ₂₃₆ > k ₂₆. For the higher substituted MC2 an initial slow phase with more pronounced differences of k _i, followed by a faster less selective period was observed. Regioselectivity of hydrolysis with respect to methyl positions was expressed as standard deviation of k _i and was between 16 and 46% depending on MC and conditions. Findings are discussed with respect to electronic effects, solvent-effect, H-bonding pattern and solution state.     

How does the extent of substitution of methane with chlorine influence the mechanism and kinetics of the reactions between chloromethanes and atomic chlorine

A theoretical investigation of the reaction mechanism and kinetics of the reaction between chloromethanes CH_4–xCl_x (x = 1–3) and chlorine atoms was performed. The height of the reaction barrier was found to decrease with the degree of substitution of chloromethanes with atomic chlorine. A direct dynamics method was employed to study the kinetic nature of these hydrogen-abstraction reactions. The sequence of calculated reaction rate coefficients is: k(CH₃Cl + Cl) < k(CH₂Cl₂ + Cl) < k(CHCl₃ + Cl).