Study of the mass transfer kinetics in a monolithic column

The purpose of this work is to investigate the mass transfer kinetics of butylbenzoate on a monolithic RPLC column, with methanol-water (65:35, v/v) as the mobile phase. We used the perturbation method, measuring the height equivalent to a theoretical plate (HETP) of the peaks obtained as the response to small pulses of solute injected on a concentration plateau. The equilibrium isotherm of butylbenzoate was previously determined by frontal analysis. It is well accounted for by a liquid-solid extended multilayer BET isotherm model. The equilibrium data derived from the pulse method are in excellent agreement with those of frontal analysis in the accessible concentration range of 0 to 8 g/dm3. Plots of the HETP of small pulses. injected on eight different plateau concentrations, were acquired in a wide range of mobile phase flow velocities. The axial dispersion and the mass transfer kinetic coefficients were derived from these data. The validity of these measurements is discussed. The mass kinetics of butylbenzoate depends strongly on the plateau concentration. Processes involving adsorptive interactions between the solute and the stationary phase, e.g. surface diffusion and adsorption-desorption kinetics, combine in series to the external mass transfer kinetics and to effective pore diffusivity.     

萘在介孔分子筛MCM-41与SBA-15上的吸附特性研究

对低浓度气相萘在两种常见介孔分子筛MCM-41和SBA-15上的吸附特性进行研究。得到了萘在两种吸附剂上的吸附等温线和不同初始浓度下的穿透曲线,并分别与吸附等温线模型(Langmuir、Freundlich、D-R)和恒定浓度波动力学模型进行了拟合。结果表明, Langmuir模型能很好描述低浓度气相萘的吸附等温线(R²均在99%以上);具有微孔结构的SBA-15对萘的吸附能力要优于仅具备介孔结构的MCM-41。动力学模型在初始浓度较低时能较好地预测萘在吸附剂上的穿透曲线,且在SBA-15上的相关系数高于MCM-41;萘在2.76 mol/L时具有较大介孔的SBA-15的总传质系数K_a更高,表明萘在SBA-15上的总传质阻力更低,更能较快达到传质平衡。     

Theoretical study of the accuracy of the pulse method,frontal analysis,and frontal analysis by characteristic points for the determination of single component adsorption isotherms

The adsorption isotherms of selected compounds are our main source of information on the mechanisms of adsorption processes. Thus, the selection of the methods used to determine adsorption isotherm data and to evaluate the errors made is critical. Three chromatographic methods were evaluated, frontal analysis (FA), frontal analysis by characteristic point (FACP), and the pulse or perturbation method (PM), and their accuracies were compared. Using the equilibrium-dispersive (ED) model of chromatography, breakthrough curves of single components were generated corresponding to three different adsorption isotherm models: the Langmuir, the bi-Langmuir, and the Moreau isotherms. For each breakthrough curve, the best conventional procedures of each method (FA, FACP, PM) were used to calculate the corresponding data point, using typical values of the parameters of each isotherm model, for four different values of the column efficiency (N=500$N=500$, 1000, 2000, and 10,000). Then, the data points were fitted to each isotherm model and the corresponding isotherm parameters were compared to those of the initial isotherm model. When isotherm data are derived with a chromatographic method, they may suffer from two types of errors: (1) the errors made in deriving the experimental data points from the chromatographic records; (2) the errors made in selecting an incorrect isotherm model and fitting to it the experimental data. Both errors decrease significantly with increasing column efficiency with FA and FACP, but not with PM.     

硅胶基质固定相离子对反相液相色谱法测定强离解化合物的正辛醇/水分配系数

反相液相色谱(RPLC)是测定正辛醇/水分配系数(log P)的有效方法,但由于缺少同类型模型化合物,RPLC在测定强离解化合物的log P时遇到挑战。该文在硅胶基质C18色谱柱上,采用离子抑制反相液相色谱(IS-RPLC)和离子对反相液相色谱(IP-RPLC)分别对中性化合物、酚酸、羧酸、磺酸及部分两性化合物的保留行为进行了系统研究。在IS-RPLC模式下,利用中性化合物、弱离解的酚酸和苯羧酸作为模型化合物,建立了表观正辛醇/水分配系数(log D)与纯水相保留因子对数值(log k_w)的定量结构-保留行为关系(QSRR)模型,测定了19种离解化合物的log D值,作为后续IP-RPLC的模型化合物及验证化合物。在IP-RPLC模式下,将中性、弱离解和强离解化合物作为混合模型组,以溶质静电荷n_e、氢键酸碱性参数A和B为桥梁,建立了线性良好的log D-log k_w-IP模型,采用3种不同类型的离解化合物进行了外部验证实验,预测值误差低于10%,证实了模型的可靠性。在此基础上,预测了8种强离解化合物的log D_7.0值(pH 7.0条件下的log D值)。研究表明,利用结构相关参数沟通不同类型的模型化合物,是实现IP-RPLC测定强离解化合物log D值的一种行之有效的方法。与聚乙烯醇基质色谱柱相比,通用型的硅胶基质色谱柱上尽管存在着更多的次级作用,但可以为强离解化合物log D的测定提供更灵活的选择。     

活性炭纤维填充床脱除水中酚类化合物及填充床的再生初探

研究了活性炭纤维填充床脱除水中酚类化合物及其填充床的再生方法。结果表明当平衡浓度变化范围为0到0.8kg/m^3时,吸附等温线符合Langmuir型;用乙醇或热的NaOH稀溶液可再生被酚饱和的活性炭纤维填充床,再生效率达90％以上,建立了考虑轴向弥散、纤维内扩散和外膜传质阻力的填充床数学模型,模型由正交配置方法离散,Gear方法求解以预测穿透曲线。模型预测值与实验数据吻合较好,结果确认轴向弥散是影响活性炭纤维填充床穿透曲线的主要因素。     

计时电量法求NiCl2(bpy)3在DMF中的扩散系数和速率常数

讨论了NiCl₂(bpy)₃(bpy：2,2-联吡啶)在DMF中的电化学行为. 控制电位使电极过程处于扩散控制下, 采用计时电量法求得了29 ℃时NiCl₂(bpy)₃在DMF中的扩散系数为5.99×10^－6 cm²•s^-1, 不同温度下的扩散系数随温度升高而增大. 选择合适的电极电位, 使电极过程处于扩散和电化学混合控制下, 采用计时电量法求得了不同电极电位下的反应速率常数k_f, 以及不同温度下的标准速率常数k⁰, 求得了表观活化能为14.4 kJ•mol^-1.     

Effect of temperature on the equilibrium and kinetics of galactose,glucose, and lactose adsorption on a cation exchanger

Galacto-oligosaccharides are typically produced by an enzymatic reaction when the post-reaction mixture contains considerable amounts of lactose and glucose and a smaller amount of galactose. In order to develop a process of chromatographic removal of saccharide impurities, adsorption equilibria and kinetics of these di- and monosaccharides were investigated for Diaion UBK 530, an industrialgrade strong cation-exchanger in the Na⁺ form. Frontal chromatographic experiments were carried out in the temperature range of 30–70°C and a broad interval of saccharide concentrations up to 350 g L^?1. Breakthrough curves were described using the equilibrium-dispersive model with the linear adsorption isotherm. Both the distribution and the axial dispersion coefficient values depended on the saccharide molecule type and size. No significant effect of temperature or concentration on the distribution coefficient was observed. The apparent dispersion coefficients of all saccharides exhibited some decrease with the temperature, which was caused by the decrease of the intraparticle mass transfer resistance. An analysis showed that both the intraparticle mass transfer and the axial dispersion had a significant influence on the front dispersion.     

Competitive effect of glucose–fructose adsorption in a fixed‐bed chromatographic column

A continuous separation system such as a simulated moving‐bed process requires adsorption data with precise equilibrium and kinetic model parameters of a single chromatographic column. The adsorption of glucose and fructose in a fixed‐bed chromatographic column was investigated to determine the competition effect of each component resulting from their initial molar ratios. The model parameters including bed porosity and axial dispersion coefficient were determined using the moment analysis method. The equilibrium isotherm parameters were estimated by conducting experiments at various molar ratios and initial sugar concentrations. The parameters obtained were then used for the simulation of dynamic breakthrough curves of glucose and fructose. The equilibrium isotherms revealed that the linear adsorption pattern provided good prediction for each molar ratio using the Henry equation. In addition, the modified Langmuir model was proposed to account for the competitive adsorption, due to the cooperative competition effect whereby glucose was promoted to the active sites by fructose to a greater degree than vice versa. A good agreement between the experimental and numerical data of the adsorption time profiles was also observed.     

Sorption of phenols from water in column systems using surfactant-modified montmorillonite

The sorption of phenol, m-nitrophenol (m-NP), and o-cresol from water onto montmorillonite modified with cetyltrimethylammonium bromide (CTAB) in a column was studied. The sorption isotherms were fitted by the Langmuir equation. Column experiments were performed at 25 degrees C to determine the breakthrough curves at different flow rates, feed sorbate concentrations, and bed lengths. It was shown that the proposed constant-pattern wave approach with the Langmuir model could well describe the breakthrough curves. The time required when the effluent concentration reached half of the feed concentration (t(1/2)) decreased with increasing feed flow rate, but the mass transfer coefficient (KLa) increased. In addition, an increase in feed sorbate concentration led to a decrease of both values of t(1/2) and KLa. The effect of axial dispersion on breakthrough dynamics in these sorption systems was finally discussed.     

宏观均相多孔电极电化学阻抗谱基础

电化学阻抗谱可用于诊断多孔电极内电荷转移反应,即界面电荷集聚和电荷传导,以及反应物质输运。本文采用复相量方法,在同态假设条件下,重新推演多孔电极阻抗谱模型,厘清传统多孔电极阻抗谱模型中的模糊性表述。(1) 定义多孔电极表征输入参数,包括电极基体电子电导率σ₁ 、电解质离子电导率σ₂、界面电荷传递电导率g_ct、单位面积界面电容C、固相扩散系数D、速度常数k、电极厚度d、特征孔深L_p 和单位体积表面积S_c;(2) 解析阻抗谱特征输出参数,包括场扩散常数K,特征频率ω₀、ω₁、ω₂、ω₃和 ω_max,它们分别相关于界面传导反应、有限场扩散、氧化还原反应、孔内扩散和最小特征孔尺寸,以及分别对应于从传导到扩散和从扩散到饱和的转折频率f_k1 和f_k2;(3) 当参数X和Z同时变化时(X = σ₁和Z = d,S_c,L_p,C,g_ct,D,k),通过阻抗谱特征参数的演变规律,分析了电荷转移反应中X和Ζ参数耦合竞争;(4)为深入分析电荷转移反应中参数X和Z的耦合竞争,引入了分叉频率f_XZ和f_ZX 。f_XZ和f_ZX所处位置可以用于表征参数X和Z影响电荷转移反应的深度和广度。当分叉频率f_XZ和f_ZX不存在时,表明电荷转移反应中参数X和Z在全频率范围内存在耦合竞争。总之,借助于特征频率和分叉频率,本文一方面研究了动力学参数和微观结构参数对多孔电极中电荷转移反应的影响,另一方面分析谱图的变化及其背后的阻抗谱特征演化规律。本文研究结果可为阻抗谱的系统仿真和辨识提供理论基础,可为多孔电极内电荷转移反应的竞争分析提供技术支撑,还可为电化学储能系统的优化设计提供诊断工具。     

Kinetic Study of the Mass Transfer of Bovine Serum Albumin on Cibacron Blue Cellulose Membranes by Using the Multi-Plate and Transport Models

The mass transfer kinetics of bovine serum albumin on Cibacron blue F3GA cellulose affinity membranes has been investigated. It was found that the multi-plate (MP) and transport models successfully described experimental breakthrough curves obtained by single-step frontal analysis. The correlation between the two models was used to estimate the rate coefficients of mass transfer from experimental data. The flow rate was found to have little effect on the performance of affinity membrane separations. The improvement of the performance by increasing the thickness of the membranes was limited. The transport model was simplified by approximating the very sharp Langmuir isotherm determined by a rectangular isotherm and an analytical solution obtained although this was found to be unsuited to describe the experimental data.     

Batch and continuous fixed-bed column biosorption of thorium(IV) from aqueous solutions: equilibrium and dynamic modeling

Biosorption of thorium(IV) from aqueous solution by Cystoseira indica alga was investigated in batch and fixed-bed column experiments. In the batch study the effects of pH and initial concentration were investigated. The optimum pH for Th(IV) biosorption was found to be 3.5. The experimental isotherms obtained at different pH conditions were analyzed using three two-parameter models and three three-parameter models. Among the two-parameter models the Langmuir model and among the three-parameter models the Redlich–Peterson model vividly described the equilibrium data. The results showed that C. indica alga is a homogeneous biosorbent and Th(IV) biosorption is a favorable and physical process. The maximum biosorption capacity from the Langmuir model was 151.3, 195.7 and 120.6 mg/g at pH 2.5, 3.5 and 4.5, respectively. The continuous isotherm obtained from the column data was modeled by the Langmuir model and the maximum biosorption capacity was 283.8 mg/g. The experimental data were fitted by the use of an analytical and a numerical model, namely Clark and mass transfer models. The results showed that the mass transfer model adequately described the experimental data. Sensitivity analysis revealed that the value of k _in has more effect than the axial dispersion coefficient (D _z) on the shape of breakthrough curve.     

Biosorption of Chromium(III) by Biomass of Seaweed Sargassum sp. in a Fixed-Bed Column

This work aimed at modeling chromium biosorption using the biomass of seaweed Sargassum sp. in a fixed-bed column. The mathematical model used was obtained from the mass balance of the component in the liquid phase and in the biosorbent material. The effects of both axial dispersion in the column and the resistance to mass transfer in the solid were considered for the solution of the partial differential equations of the model, using the Galerkin method on finite elements. To represent the equilibrium data of the batch system the Langmuir isotherm were used. The chromium ion adsorption capacity of the seaweed Sargassum sp., at a temperature of 30°C and pH 3.5, was 2.61 mmol/g. The model performance was evaluated from experimental data obtained at 30°C for flow rates of 2, 6 and 8 mL/min. The parameters of the model, mass transfer and axial dispersion coefficients, were adjusted from these experimental data. The model proved adequate to describe chromium biosorption dynamics in fixed-bed columns.     

Investigation of enzymatic hydrolysis of lipid-like substrates in monolayers

The parameters of enzymatic hydrolysis of novel lipid-like substrates assembled in monolayers at water–air interface were estimated by a simple method. The method is based on measurement of the initial velocity of the reaction registered by the decrease of the monolayer area (caused by the enzymatic hydrolysis) at surface pressure of 10 mN/m in a single–compartment trough. Hydrolysis of trilaurin and three 1,3-dilaurylpseudoglycerides acylated by phenylalanine, leucine and valine was characterized by catalytic constants k_cat and apparent Michael's constants K_m(app) (using lipase from Pseudomonas fluorescens as catalyst). It was found that k_cat of the synthetic pseudoglycerides (7–13 per s) are higher than k_cat of trilaurin (4 per s) that can be explained by the presence of positively charged primary aminogroups in the substrates. K_m(app) values were found to be similar for all the substrates studied (ca. 2×10⁻⁶ M). The proposed method allows estimation of the kinetic constants in traditional dimensions.     

A novel thermodynamic state recursion method for description of nonideal nonlinear chromatographic process of frontal analysis

A novel thermodynamic state recursion (TSR) method, which is based on nonequilibrium thermodynamic path described by the Lagrangian-Eulerian representation, is presented to simulate the whole chromatographic process of frontal analysis using the spatial distribution of solute bands in time series like as a series of images. TSR differs from the current numerical methods using the partial differential equations in Eulerian representation. The novel method is used to simulate the nonideal, nonlinear hydrophobic interaction chromatography (HIC) processes of lysozyme and myoglobin under the discrete complex boundary conditions. The results show that the simulated breakthrough curves agree well with the experimental ones. The apparent diffusion coefficient and the Langmuir isotherm parameters of the two proteins in HIC are obtained by the state recursion inverse method. Due to its the time domain and Markov characteristics, TSR is applicable to the design and online control of the nonlinear multicolumn chromatographic systems.     

Two trends of sample dispersion variation with carrier flow rate in a single flow-injection manifold

Two trends of sample dispersion variation with carrier flow rate in a single flow-injection manifold are completely revealed for the first time and an inflection point in the dispersion coefficient (D) vs. flow rate (q) curve is discovered. With the increase of the flow rate, the value of D increases before the inflection point but decreases after the inflection point. The value of the carrier flow rate at the inflection point (q_m) is independent of the sample injection volume, the tube length, the tube coil radius and the tube inner diameter. It is only affected by the substance diffusion coefficient (D_m) of the analysis. The value of q_m decreases as D_m increases. Therefore, the value of D_m for a sample can be estimated according to the D_m vs. q_m curve.     

Elimination of non-uniform, extra-device flow effects in membrane adsorbers

Commercial use of membrane adsorbers in the biotechnology industry is increasing. Here the system time lag created by membrane adsorber peripherals and the membrane adsorber flow distribution headers has been modeled using an anion exchange membrane and bovine serum albumin (BSA). The system time lag was modeled as a zero order and first order time lag. The zero and first order time lags have been removed from the breakthrough curve. The method used does not involve fitting a mathematical expression to the breakthrough curve. Further no assumptions are made regarding the shape of the breakthrough curve in the absence of the time lag. The method has been used to calculate the Langmuir isotherm parameters.The membrane capacity was found to be twice as large as the capacity determined after removal of the time lag. The Langmuir constant was five times as large for the system without accounting for the time lag. Errors in fitting isotherm parameters can significantly impact frontal analysis and membrane adsorber scale-up. The Langmuir isotherm calculated under dynamic conditions with the system time lag removed, was in agreement with the static adsorption isotherm.     

Chromium adsorption in olive stone activated carbon

In this work, Cr(III) adsorption on activated carbon obtained from olive stones in an upflow fixed-bed column at 30^∘C was studied. The flow rate influence on the breakthrough curves at a feed concentration of 0.87 meq/L was investigated in an attempt to minimize the diffusional resistances. Breakthrough curves for a flow range of 2–8 mL/min were obtained at 10.5 cm bed height and inlet diameter of 0.9 cm. The mass transfer parameters indicated that the bed minimal resistance was attained at 2 mL/min. Therefore, the data equilibrium was carried out until the bed was saturated at 2 mL/min. The dynamic system generated a favorable isotherm with a maximum chromium uptake of 0.45 meq/g. A column sorption mathematical model was created considering the axial dispersion in the column and the intraparticle diffusion rate-controlling steps. The isotherm was successfully modeled by the Langmuir equation and the mathematical model described the experimental dynamic data adequately for feed concentrations from 0.26 to 3.29 meq/L.     

Influence of the particle porosity on chromatographic band profiles

The mass transfer kinetics of butyl benzoate, eluted on a monolithic RPLC column with methanol-water (65:35, v/v) as the mobile phase was investigated, using the perturbation method to acquire isotherm data and the mobile phase velocity dependence of the height equivalent to a theoretical plate of perturbation peaks to acquire kinetics data. The equilibrium isotherm of butyl benzoate is accounted for by the liquid-solid extended multilayer BET isotherm model. The total porosity of the column varies much with the butyl benzoate concentration, influencing strongly the parameters of its mass transfer kinetics and the profiles of the breakthrough curves. Using all these parameters, the general rate model of chromatography predicts band profiles and Van Deemter curves that are in excellent agreement with experimental results provided the influence of concentration on the porosity is properly taken into account. This agreement confirms the validity of the models selected for the isotherm and for the mass transfer kinetics.     

Kinetic analysis of coupled transport of thiocyanate ions through liquid membranes at different temperatures

Non-steady-state kinetics of coupled transport of thiocyanate ions through liquid membrane (trichloromethane), containing hexadecyl trimethyl ammonium chloride as a carrier, was examined at different temperatures. The kinetics of thiocyanate transport could be analyzed in the formalism of two, consecutive, irreversible first order reactions. The influence of temperature on the kinetic parameters (k_1d, k_2m, R_m^max, t_max, J_d^max, J_a^max) have been also investigated. The membrane entrance rate, k_1d, and the membrane exit rates, k_2m and k_2a, increase with temperature. For maximum membrane entrance and exit fluxes, J_d^max and J_a^max, the activation energies were found from the slopes of the two linear relationships: 7:75 and 8.30 kcal/mol, respectively. The values of the found activation energy indicate that the process is controlled by species difussion.