Use of Wheeler–Jonas equation to explain xenon dynamic adsorption breakthrough curve on granular activated carbon

The Wheeler–Jonas equation (WJ equation) is widely used to predict breakthrough of volatile organic compounds on granular activated carbon (GAC) and the most important criteria is to calculate the overall adsorption rate constant (k _v ) and amount adsorbed based on breakthrough curve. The operational factors, including temperatures, concentrations and flow rates, for packed bed, can affect the values of k _v more or less and to what degree has not yet been systematically investigated. What’s more, the relation between the dynamic adsorption coefficient (k _d) or Henry constant, which is used for the design of packed bed, and WJ equation is not clear. In order to solve these problems, we performed xenon dynamic adsorption on GAC adsorber experiments under different values of xenon concentrations, flow rates and temperatures, obtained the breakthrough curves for elution times versus xenon concentrations, and then employed WJ equation to explain breakthrough curves. The experimental results indicate that the WJ equation can fit the breakthrough curve very well and k _d be integrated into the WJ equation. The values of k _v are proportional to the values of flow rates and k _d, but independent of that of temperatures and xenon concentrations.     

Effect of Ionic Surfactants on the Adsorption of Quercus infectoria Natural Dye on Cotton Fiber: A Kinetic Study

The adsorption kinetics of Quercus infectoria natural dye on cotton in the absence and presence of the cationic (cetyl trimethyl ammonium bromide; CTAB) and anionic (sodium lauryl sulfate; NaLS) surfactants has been investigated at three temperatures, namely, 40°C, 50°C, and 60°C. On increasing the surfactant content in the surfactant-dye mixture, the initial rate of adsorption (h _i) and the adsorption capacity at equilibrium (q _e) were found to increase while pseudo-second-order rate constant (k ₂) was found to decrease. The retarding effect of surfactant on k ₂ was in order of CTAB > NaLS. The activation parameters for adsorption process have been evaluated in each case, and the mechanism of adsorption process has been discussed.     

Adsorption of carbon dioxide on microporous carbon adsorbent PAU-10

Carbon dioxide adsorption on the microporous carbon adsorbent PAU-10 within the 177.8—423 K temperature and 0.1—5.13·10⁶ Pa pressure intervals was studied. The isosteres of absolute adsorption are well approximated by straight lines, which do not change their slope on going to temperatures higher than the critical temperature of CO₂. An increase in the differential molar isosteric heat of adsorption (q _st) at 0 < a < 1 mmol g^–1 is explained by the influence of the endothermic effect of adsorption expansion of the adsorbent. In the region of high pressures and nonideal gas phase, q _st is temperature-dependent.     

An analytical method of micropore filling of a supercritical gas

The supercritical gas adsorbed in the micropore having a strong molecular field was presumed to transform into the quasi-vapor to be filled in the micropore (quasi-vaporization adsorption mechanism). The Dubinin-Radushkevitch (DR) equation for micropore filling of vapor was extended to the quasi-vaporized supercritical gas using the quasi-saturated vapor pressureP _{0 q} and the inherent micropore volumeW _L . The reason why the concepts ofP _0q andW _L were introduced was explained with the molecule-pore interaction potential theory which is based on the Lennard-Jones interaction. The extended DR equation was named the supercritical DR equation. TheW _L was evaluated by the Langmuir plot of the adsorption isotherm for a supercritical gas and both ofP _0q andW _L provided the single reduced adsorption isotherms of supercritical NO, N₂, and CH₄ on activated carbon fibers and high surface area carbons were analyzed by the supercritical DR plots. The wide applicability of the reduced adsorption isotherm to these adsorption data was explicity shown. The two phase model of the organized and confined fluids was proposed in order to improve the quasi-vaporization adsorption mechanism.     

Influence of heating rate on kinetic quantities of solid phase thermal decomposition

Thermogravimetric analyses of thermal decomposition (pyrolysis, thermal dissociation and combustion) of 9 different samples were carried out in dynamic conditions at different heating rates. The kinetic parameters (E, A and k_m) of thermal decomposition were determined and interrelations between the parameters and heating rate q were analyzed. There were also relations between Arrhenius and Eyring equations analyzed for thermal decomposition of solid phase. It was concluded that Eyring theory is an element, which interconnects used thermokinetic equations containing Arrhenius law and suggests considering kinetic quantities in way relative to 3 kinetic constants (E, A and k_m). Analysis of quantities other than km (i.e. E, A, Δ⁺H, Δ⁺S) in relation to heating rate is an incomplete method and does not lead to unambiguous conclusions. It was ascertained that in ideal case, assuming constant values of kinetic parameters (E and A) towards heating rate and satisfying both Kissinger equations, reaction rate constant k_m should take on values intermediate between constants (k_m)₁ and (k_m)₂ determined from these equations. Whereas behavior of parameters E and A towards q were not subjected to any rule, then plotting relation k_m vs. q in the background of (k_m)₁ and (k_m)₂ made possible classification of differences between thermal decomposition processes taking place in oxidizing and oxygen-free atmosphere.     

Adsorption of Pesticides onto Granular Activated Carbon: Determination of Surface Diffusivities Using Simple Batch Experiments

The Homogeneous Surface Diffusion Model (HSDM) has been successfully used to predict the adsorption kinetics for several chemicals inside batch adsorber vessels. In addition to the adsorption equilibrium, this model is based on external mass transfer and surface diffusion. This paper presents the determination of the surface diffusion coefficient (D _s) using a differential column batch reactor (DCBR). The adsorption kinetics for three pesticides onto granular activated carbon have been established experimentally. Their corresponding three diffusion coefficients were determined by fitting the computer simulations to the experimental concentration-time data. The results show that this original apparatus increases by an order of magnitude the range of reachable diffusion coefficient compared to perfectly mixed contactors. Moreover the computed D _s values are more accurate because of the better assessment of the external mass transfer coefficient (k _f) for fixed beds.     

Octadecyltrichlorosilane adsorption kinetics on Si(100)/SiO2 surface: contact angle,AFM, FTIR and XPS analysis

Octadecyltrichlorosilane (OTS) adsorption kinetics on Si(100)/SiO₂ surface has been studied as a function of concentration by sequential and nonsequential dipping techniques. The contact angle technique is used to evaluate growth kinetics and thermal stability and to determine critical surface tension of the OTS layer. Atomic force microscopy (AFM), Fourier transform infrared (FTIR) spectroscopy and X‐ray photoelectron spectroscopy (XPS) are used to confirm OTS adsorption. Langmuir isotherms are employed to analyze the kinetics data to obtain adsorption and desorption rate constants (k_a & k_d) as well as Gibbs free energy, (ΔG_ads). These parameters, k_a, k_d and ΔG_ads(y) are found to depend exponentially (y = y₀ + A.exp(?x/t)) on the OTS concentration (x). The OTS layers are found to be thermally stable up to a temperature of 230 °C and the critical surface tension obtained from the Zisman plot is found to be ～19.8 dynes/cm. OTS monolayer coverage obtained by AFM measurement agrees quite closely with that obtained from contact angle measurements. FTIR and XPS results confirm OTS adsorption. Copyright © 2006 John Wiley & Sons, Ltd.     

Adsorption of Gases, Vapors and Liquids by Microporous Adsorbents

Adsorption of Xe, Kr, Ar, N₂, O₂, H₂ CH₄, CO₂, He, and freons by PAU-10 and ACC microporous carbon adsorbents as well as by A and X zeolites was investigated over a wide range of pressures (0.1 Pa – 20 MPa) and temperatures (77, 120–600 K). The amount of gases, vapors and liquids adsorbed by microporous adsorbents increases steadily with increasing pressure and does not change dramatically if phase transitions occur in the adsorptive. Isosteres of adsorption constructed as a curve of ln P against f(1/T)_a retain a linear form over a wide range of pressures and temperatures. The slope of isosteres does not vary on going through the critical temperature of the gaseous phase. At high pressures, due to non-ideality of the gaseous phase and non-inert behavior of the adsorbent the differential molar heat of adsorption is dependent on temperature. At high fillings of micropores the differential molar isosteric heat capacities of adsorption systems show maxima that indicate the occurrence of structural rearrangements in the adsorbate.     

On the Nitroxide Quasi‐Equilibrium in the Alkoxyamine‐Mediated Radical Polymerization of Styrene

Summary: The range of validity of two popular versions of the nitroxide quasi‐equilibrium (NQE) approximation used in the theory of kinetics of alkoxyamine mediated styrene polymerization, are systematically tested by simulation comparing the approximate and exact solutions of the equations describing the system. The validity of the different versions of the NQE approximation is analyzed in terms of the relative magnitude of (dN/dt)/(dP/dt). The approximation with a rigorous NQE, k_c[P][N] = k_d[P N], where P, N and P N are living, nitroxide radicals and dormant species respectively, with kinetic constants k_c and k_d, is found valid only for small values of the equilibrium constant K (10⁻¹¹–10⁻¹² mol · L⁻¹) and its validity is found to depend strongly of the value of K. On the other hand, the relaxed NQE approximation of Fischer and Fukuda, k_c[P][N] = k_d[P N]₀ was found to be remarkably good up to values of K around 10⁻⁸ mol · L⁻¹. This upper bound is numerically found to be 2–3 orders of magnitude smaller than the theoretical one given by Fischer. The relaxed NQE is a better one due to the fact that it never completely neglects dN/dt. It is found that the difference between these approximations lies essentially in the number of significant figures taken for the approximation; still this subtle difference results in dramatic changes in the predicted course of the reaction. Some results confirm previous findings, but a deeper understanding of the physico‐chemical phenomena and their mathematical representation and another viewpoint of the theory is offered. Additionally, experiments and simulations indicate that polymerization rate data alone are not reliable to estimate the value of K, as recently suggested.

Validity of the rigorous nitroxide quasi‐equilibrium assumption as a function of the nitroxide equilibrium constant.     

A study of dimethylferrocene diffusion and electrode kinetics using microelectrode voltammetry in poly(ethylene glycol) solvent

The heterogeneous electron transfer rate constant (k _s) of dimethylferrocene (DMFc) was estimated using cyclic voltammetric peak potential separations taken typically in a mixed diffusion geometry regime in a polyelectrolyte, and the diffusion coefficient (D) of DMFc was obtained using a steady-state voltammogram. The heterogeneous electron transfer rate constant and diffusion coefficient are both smaller by about 100-fold in the polymeric solvent than in the monomeric solvent. The results are in agreement with the difference of longitudinal dielectric relaxation time (τ_L) in the two kinds of solvents, poly(ethylene glycol) (PEG) and CH₃CN, indicating that k _s varies inversely with τ_L; k _s is proportional to D of DMFc. Both D and k _s of DMFc in PEG containing different supporting electrolytes and at different temperatures have been estimated. These results show that D and k _s of DMFc increase with increasing temperature in the polyelectrolyte, whereas they vary only slightly with changing the supporting electrolyte. Received: 5 February 1998 / Accepted: 23 July 1998     

Computer simulation of brownian motion of a polyelectrolyte molecule (charged bead-spring model)

A Langevin equation of motion for a charged bead-spring statistical chain is written in difference form and the relaxation and equilibrium behavior of the chain is studied by computer simulation. Results are presented for the behavior of end-to-end length h, principal axes of the polymer ellipsoid L₁, L₂, L₃, and chain contour length c in terms of their averages, root mean square values, root mean square fluctuations, orientations, and relaxation strengths and times. The simulation was made with various sets of parameters, bead number N, charge on the bead q, and radius of ion atmosphere around the bead k^?1. It is found that 〈h²〉^1/2 and 〈L₁²〉^1/2 increase more strongly with increasing q and decreasing κ than 〈L₂²〉^1/2, 〈L₃²〉^1/2, and 〈c₁²〉^1/2, indicating that the chain is expanded in three dimensions and at the same time is extended along the end-to-end direction. The relaxation time τ_rot of rotation of the end-to-end vector, which is proportional to N² at q = 0, increases with increasing q and tends to be proportional to N³ for an extended chain, while the relaxation time τ_conf of the magnitude of h is almost independent of q and is always proportional to N². It is concluded that the extended chain possesses a well-defined end-to-end axis and the chain rotates as a whole with a relaxation time τ_rot which is much longer than τ_conf. The complex viscosity of the chain is calculated from the Fourier transform of the time–correlation function of momentum flux and is found to have a frequency spectrum similar to that observed for aqueous solutions of poly(acrylic acid). The dominant mode appearing in the low-frequency range is evidenced to arise from the rotation of the extended chain.     

Surface Modification of Bituminous Coal and Its Effects on Methane Adsorption

This paper studied the role of O‐containing groups over the coal surface in methane adsorption. The coal was modified with H₂SO₄, (NH₄)₂S₂O₈ or H₂SO₄/(NH₄)₂S₂O₈), respectively, to introduce O‐containing functional groups, and characterized by proximate analysis, ultimate analysis, Boehm titration, X‐ray photoelectron spectroscopy (XPS) and nitrogen adsorption. The results of ultimate analysis, Boehm titration and XPS indicate that there were increases in terms of both the content of oxygen and the quantities of O‐containing groups over the modified coals surface, especially for the carboxyl. Nitrogen adsorption shows that the modified coals possessed higher surface area and pore volume than that of 0‐XQ. The methane adsorption data were measured at 298 K at pressures up to 4.0 MPa by the volumetric method and fitted well by Langmuir model. Experimental results implied that O‐containing groups and pore structure affected methane adsorption. The adsorption capacities decreased as increasing quantities of O‐containing groups.     

Determination of chain stiffness and polydispersity from static light-scattering

Chain stiffness is often difficult to distinguish from molecular polydisperity. Both effects cause a downturn of the angular dependence at large q² (q = (4π/λ)sin θ/2) in a Zimm plot. A quick estimation of polydisperity becomes possible from a bending rod (BR) plot in which lim (c → 0) qRθ/Kc is plotted against q(〈S²〉_z)^1/2 = u. Flexible and semiflexible chains show a maximum whose position is shifted from u_max = 1.41 for monodisperse chains towards larger values as polydispersity is increased, while simultaneously, the maximum height is lowered. Stiff chains display a constant plateau at large q, its value is πM_L where M_L is the linear mass density. Using Koyama's theory, the number of Kuhn segments can be determined from the ratio of the maximum height to the plateau height, if the polydispersity index z = (M_w/M_n ? 1)^?1 is known. Thus, if the weight-average molecular weight M_w, is known, the contour length L_w, the number of Kuhn segments (N_k)_w, the Kuhn segment length l_k and the polydispersity of the stiff chains can be determined. The influence of excluded volume is shown to have no effect on this set of data. The reliability of this set can be cross-checked with the mean-square radius of gyration 〈s²〉_z which can be calculated from the Benoit-Doty equation for polydisperse chains. Rigid and slightly bending rods exhibit no maximum in the BR plot, and the effect of polydispersity can no longer be distinguished from a slight flexibility if only static scattering techniques are applied.     

X-ray investigation of the nematic and reentrant nematic phases of N-[(4-n-octyloxybenzoyloxy)-salicilidene]-4′-cyanoaniline

We have performed an X-ray scattering study of the nematic-smectic A and reentrant nematic-smectic A phase transitions in N-[(4-n-octyloxybenzoyloxy)-salicilidene]-4′-cyanoaniline (OOBOSCA). A diffractometer with a linear position sensitive detector was used. The results show that the smectic phase in OOBOSCA is of the A_d type with an interlayer spacing incommensurate with the molecular length L; d ∽ 1·2L. In the reentrant nematic phase two types of fluctuation modes were found. One of them corresponds to the monolayer wavevector q ₁ ∽ 2π/L, and the other is due to the partial bilayer fluctuations with the wavevector q ₂ ∽ 0·8q ₁. The temperature dependences of the interlayer spacing, X-ray scattering intensity and longitudinal correlation length for both types of layering in the reentrant nematic phase are presented. The change of the fluctuation regime from S_Ad, to S_Cd type with decreasing temperature in the reentrant nematic phase of OOBOSCA was found. The results are discussed on the basis of models with competing order parameters. The influence of alkyl chain flexibility on the stability of a partial bilayer smectic phase is also considered.     

Investigations by electrochemical quartz crystal impedance system-electrodeposition of silver and polyaniline

An electrochemical quartz crystal impedance system (EQCIS) which allows rapid and simultaneous measurements of admittance spectra of piezoelectric quartz crystal resonance during electrochemical processes was developed by combining an HP 4395A Network/Spectrum/Impedance analyzer with an EG & G M283 potentiostat. Non-linear least square regression analyses of simultaneously acquired conductance and susceptance data were discussed in detail, giving that R_m, C_s, 1/C_m (or L_m) and of as estimation parameters is the best choice among various fitting routines. Equivalent electrical circuit parameters of quartz crystal resonance during electrodeposition of silver and polyaniline and electrochemical processes of the deposits were obtained and discussed according to changes in electrode mass, electrode surface roughness and film conductivity etc. The significant changes of motional resistance R_m and static capacitance C, observed in the silver case was believed to result mainly from changes in electrode surface roughness and the linear relationship between them was well explained by the following equation, C_s = C_q+ C_e = ε_qA_q/ h_q + ε_ek²R_m/[h_e(ωρ_Lη_L]1/2.     

Scattering function for wormlike chains with finite thickness

The particle scattering function P(k) is approximately evaluated for the Kratky–Porod wormlike chain with a circular cross section to examine the effect of chain diameter d on the scattering curve of k²P(k) versus k, the magnitude of the scattering vector, for stiff chains and also the applicability of the cross‐section plot of ln[kP(k)] versus k² to them. In the evaluation, series expansions from the rod and coil limits up to the fifth‐order and third‐order deviations, respectively, are combined together. The major results or conclusions derived are as follows. First, the conventional equation, P(k) = P₀(k) exp(?k²d²/16), for straight cylinders overestimates k²P(k) at relatively large values of k, whereas its alternative, P(k) = P₀(k)[2J₁(kd/2)/(kd/2)]², is a good approximation to exact P(k) unless contour length L is shorter than 10d. Here, P₀(k) denotes the scattering function for the chain contour, and J₁(x) is the Bessel function of the first order. Second, as d is increased for a fixed value of L (relative to the Kuhn segment length), the k²P(k)–k curve lowers with a pronounced maximum, and the peak position shifts to a lower scattering angle. Third, if the chain is somewhat flexible, the cross‐section plot has an approximately linear region, with a slope fairly close to ?d²/16 expected from the aforementioned conventional equation. This plot for rods appreciably bends down, and thus the experimental observation of an approximately linear relation (over a wide k range) implies that, in contrast to the prevailing notion, the polymer examined is not completely rigid but instead is somewhat flexible. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1398–1407, 2004     

Chiral imidazole metalloenzyme models: Synthesis and enantioselective hydrolysis for α-amino acid esters

Chiral imidazole hydrolytic metalloenzyme models with characteristics of chiral centers directly link to imidazole N-atoms and varieties in both alkyl chain length and number of alkyl chains, have been synthesised and investigated for enantioselective hydrolysis of Boc-α-amino acid esters. The result indicates that both hydrolysis rates and enantioselectivities are increased with increases in the alkyl chain length and the number of the alkyl chains in the lipophilic chiral imidazole-type surfactants in many cases. The lipophilic chiral imidazole 4d ((S)-1-hexadecoxy-2-(1-imidazolyl)-propane), which has one long alkyl chain, shows higher hydrolysis rate and enantioselectivity (k_D = 132.5 × 10⁻⁵, k_D/k_L = 5.38), 5d ((S)-1,5-dihexadecoxy-2-(1-imidazolyl)-pentane), which has two long alkyl chains, shows the highest hydrolysis rate and enantioselectivity (k_D = 201.5 × 10⁻⁵, k_D/k_L = 11.72). Additionally, the effects of the metals, the additives, the solvents and the substrates on the hydrolysis rates and enantioselectivities are examined.     

Autoxidation of poly-4-methylpentene-1. I. The role of diffusion in autoxidation kinetics

An apparatus is described for the measurement of oxygen uptake into a polymer sample at constant oxygen pressures in the range 20–1000 mm Hg. Measurements of the rate of oxygen uptake into poly-4-methylpentene-1 show that the rate is accurately first-order in oxygen pressure over the range 50–800 mm pressure for temperatures ranging from 122 to 154°C and film thickness in the range 0.001–0.025 cm. A theoretical treatment of the kinetics of a reaction in which oxygen diffuses into both faces of a thin film, in which it is consumed by a first-order reaction shows that the oxidation rate ρ per unit area of film surface is given by ρ = ρ_∞ tanh ßL/2 where ρ_∞ is the limiting oxidation rate for a thick film, L is the film thickness, and ß = (k/D)^1/2, k being the oxidation rate constant and D the diffusion constant. Values of D and the activation energy for diffusion calculated from autoxidation data are in good agreement with values determined directly.     

Adsorption of N719 Dye on Anatase TiO2 Nanoparticles and Nanosheets with Exposed (001) Facets: Equilibrium,Kinetic, and Thermodynamic Studies

Anatase TiO₂ nanosheets (TiO₂ NS) with dominant (001) facets and TiO₂ nanoparticles (TiO₂ NP) with dominant (101) facets are fabricated by hydrothermal hydrolysis of Ti(OC₄H₉)₄ in the presence and absence of hydrogen fluoride (HF), respectively. Adsorption of N719 onto the as‐prepared samples from ethanol solutions is investigated and discussed. The adsorption kinetic data are modeled using the pseudo‐first‐order, pseudo‐second‐order, and intraparticle diffusion kinetics equations, and indicate that the pseudo‐second‐order kinetic equation and intraparticle diffusion model can better describe the adsorption kinetics. Furthermore, adsorption equilibrium data of N719 on the as‐prepared samples are analyzed by Langmuir and Freundlich models; this suggests that the Langmuir model provides a better correlation of the experimental data. The adsorption capacities (q_max) of N719 on TiO₂ NS at various temperatures, determined using the Langmuir equation, are 65.2 (30 °C), 68.2 (40 °C), and 76.6 (50 °C) mg g⁻¹, which are smaller than those on TiO₂ NP, 92.4 (30 °C), 100.0 (40 °C), and 108.2 (50 °C) mg g⁻¹, respectively. The larger adsorption capacities of N719 for TiO₂ NP versus NS are attributed to its higher specific surface areas. However, the specific adsorption capacities (q_max/S_BET) at various temperatures are 1.5 (30 °C), 1.6 (40 °C), and 1.7 (50 °C) mg m⁻² for TiO₂ NS, which are otherwise higher than those for NP, 0.9 (30 °C), 1.0 (40 °C), and 1.1 (50 °C) mg m⁻², respectively. The larger specific adsorption capacities of N719 for TiO₂ NS versus NP are because the (001) surface is more reactive for dissociative adsorption of reactant molecules compared with (101) facets. Notably, the q_max and q_max/S_BET for both TiO₂ samples increase with increasing temperature, suggesting that adsorption of N719 on the TiO₂ surface is an endothermic process, which is further confirmed by the calculated thermodynamic parameters including free energy, enthalpy, and entropy of adsorption process. The present work will provide a new understanding on the adsorption process and mechanism of N719 molecules onto TiO₂ NS and NP, and this should be of great importance for enhancing the performance of dye‐sensitized solar cells.     

Fixed bed adsorption of CO2/H2 mixtures on activated carbon: experiments and modeling

We present breakthrough experiments in a fixed bed adsorber packed with commercial activated carbon involving feed mixtures of carbon dioxide and hydrogen of different compositions. The experiments are carried out at four different temperatures (25?°C, 45?°C, 65?°C and 100?°C) and seven different pressures (1?bar, 5?bar, 10?bar, 15?bar, 20?bar, 25?bar and 35?bar). The interpretation of the experimental data is done by describing the adsorption process with a detailed one-dimensional model consisting of mass and heat balances and several constitutive equations, such as an adsorption isotherm and an equation of state. The dynamic model parameters, i.e. mass and heat transfer, are fitted to one single experiment (reference experiment) and the model is then further validated by predicting the remaining experiments. Furthermore, the choice of the isotherm model is discussed. The assessment of the model accuracy is carried out by comparing simulation results and experimental data, and by discussing key features and critical aspects of the model. This study is valuable per se and a necessary step toward the design, development and optimization of a pressure swing adsorption process for the separation of CO₂ and H₂ for example in the context of a pre-combustion CO₂ capture process, such as the integrated gasification combined cycle technology.