半互穿海藻酸钠/聚丙烯酰胺凝胶吸附结晶紫动力学/热力学行为和吸/脱附机理

将含有大量—COO-的聚阴离子海藻酸钠(SA)引入聚丙烯酰胺(PAM)凝胶网络中,采用自由基溶液聚合法制备半互穿网络结构的SA/PAM水凝胶.采用扫描电子显微镜(SEM)、X射线光电子能谱(XPS)和傅里叶变换红外光谱(FTIR)分析了SA/PAM水凝胶吸附结晶紫(CV)前后的孔洞形态和化学组成变化,采用多种模型研究了SA/PAM水凝胶对CV分子的吸附动力学和热力学行为,并探讨了脱附效率,提出了吸脱附机理.研究结果表明,SA的引入降低了孔径尺寸,增加了孔洞数量;SA/PAM-10凝胶对CV分子吸附量最大,达到13.5838 mg/g,符合伪一级吸附动力学模型,吸附速率受膜扩散和粒子内扩散过程共同影响;等温吸附过程符合Temkin和D-R模型,属于微孔多层吸附;热力学分析结果表明,吸附过程由熵驱动引起,非化学诱导因素影响所致;采用HCl进行脱附,最大脱附率高达94.18%,加入Na OH可实现SA/PAM水凝胶的可逆吸附;较高的吸附量主要源于SA分子链上的COO-与CV分子的—C N+—存在的静电作用,低pH值时由于—COO-和—NH2质子化导致与CV分子的静电斥力增大,脱附率随之增加.     

Effect of Temperature on Interfacial Adsorption of Cr(VI) on Wollastonite

An extensive study on the effect of temperature on interfacial adsorption of Cr(VI) on wollastonite has been carried out. Adsorption on the wollastonite surface increased from 69.5 to 91.7% by increasing the temperature from 30 to 50 degrees C under optimum conditions. Kinetic modeling of the process of adsorption of Cr(VI) was done and various parameters were determined. The process follows a first-order kinetic equation and the rate of uptake was found to be 2.40x10(-2) min(-1) at 30 degrees C, 2.5 pH, 0.5x10(-4) M Cr(VI) concentration, and 0.01 M NaClO(4) ionic strength. Kinetic and equilibrium modeling of the process of adsorption was undertaken and the equilibrium parameters were determined. The process of adsorption follows pore diffusion and the value of the rate constant of pore diffusion was found to be 5.00x10(-3) mg g(-1) min(-1/2) at 30 degrees C and optimum conditions. The values of the coefficient of mass transfer, beta(L), were determined at different temperatures. Thermodynamic studies of the removal process were performed. The study suggests that the process is a typical example of endothermic adsorption. Copyright 2001 Academic Press.     

金的离子交换与吸附化学 II: 大孔交联聚甲基丙烯酸酯MET-802对AuCl4^-的吸附及解吸动力学

研究了大孔交联聚甲基丙烯酸酯树脂(相当于Amberlite-XAD-7)吸附和解吸AuCl4^-的动力学. 结果表明, 两种过程均由液膜扩散转向粒内扩散主控. HCl浓度对吸附AuCl4^-过程影响甚微, 研究了HCl-硫脲为解吸剂时的动力学, 表明液膜扩散常数R和粒内扩散常数B对树脂半径r0的关系服从Boyd方程.     

Adsorption kinetics of an organic dye by wet hybrid gel monoliths

Wet hybrid gel monoliths are prepared with bis(trimethoxysilylpropyl)amine (TSPA) or the mixture of TSPA with n-propyltriethoxysilane (PTES) or bis(trimethoxysilyl)hexane (TSH) or tetraethoxysilane (TEOS) as precursors. The adsorption kinetics of an organic dye (erioglaucine disodium salt, EDS) by the gel monoliths in aqueous solutions is studied comprehensively. The effects of temperature, pH, and ionic strength on the adsorption kinetics are investigated. Kinetic studies show that in general the kinetic data are well described by the pseudo second-order kinetic model. Initial adsorption rate increases with the increase in temperature, but decreases with the increase in solution pH and ionic strength. The adsorption activation energy is found to be 17–51 kJ mol⁻¹ under our experimental conditions. The internal diffusion of the dye into the hybrid gels appears to be the rate-limiting step of the overall adsorption process. The adsorption is promoted by hydrogen bonding, hydrophobic and electrostatic attractions in acidic or neutral solutions, suppressed by the electrostatic repulsion in basic solutions and by the ionic exchange competition of Cl⁻ with the dye anions in solutions with a high NaCl concentration. After adsorption for 165 h, all the gel monoliths present a linear shrinkage less than 10%.     

Adsorption studies of cationic starch onto quartz surface through an electrode-separated piezoelectric sensor

In the construction of an electrode-separated piezoelectric sensor (ESPS), the quartz surface is in direct contact with the liquid phase. The negatively charged quartz crystal surface can adsorb cationic starch. This adsorption process was in situ monitored from the frequency shift of the ESPS. It was shown that the adsorption of cationic starch onto the quartz surface is reversible with respect the dilution of the bulk phase. The adsorption behavior can be described by Langmuir model. The adsorption density and kinetics parameters were estimated from the frequency responses of the ESPS. The influence of pH and ionic strength on adsorption parameters was investigated. It was shown that the influence of pH on the adsorption rate was slight. With increasing ionic strength, the rate constants for adsorption and desorption increase, but the adsorption equilibrium constant and saturation adsorption density decrease. The adsorption equilibrium constant and adsorption density reach a maximum in buffer of pH 10.     

Adsorption and desorption kinetics of benzene derivatives on mesoporous carbons

Adsorption and desorption of benzoic and salicylic acids and phenol from a series of synthesized mesoporous carbons is measured and analyzed. Equilibrium adsorption isotherms are best described by the Langmuir–Freundlich isotherm. Intraparticle diffusion and McKay’s pore diffusion models, as well as mixed 1,2-order (MOE), integrated Langmuir kinetic equation (IKL), Langmuir–Freundlich kinetic equation and recently derived fractal-like MOE (f-MOE) and IKL models were compared and used to analyze adsorption kinetic data. New generalization of Langmuir kinetics (gIKL), MOE and f-MOE were used to describe desorption kinetics. Analysis of adsorption and desorption half-times shows simple relation to the size of carbon pores.     

The role of electrostatic interactions in protease surface diffusion and the consequence for interfacial biocatalysis

This study examines the influence of electrostatic interactions on enzyme surface diffusion and the contribution of diffusion to interfacial biocatalysis. Surface diffusion, adsorption, and reaction were investigated on an immobilized bovine serum albumin (BSA) multilayer substrate over a range of solution ionic strength values. Interfacial charge of the enzyme and substrate surface was maintained by performing the measurements at a fixed pH; therefore, electrostatic interactions were manipulated by changing the ionic strength. The interfacial processes were investigated using a combination of techniques: fluorescence recovery after photobleaching, surface plasmon resonance, and surface plasmon fluorescence spectroscopy. We used an enzyme charge ladder with a net charge ranging from -2 to +4 with respect to the parent to systematically probe the contribution of electrostatics in interfacial enzyme biocatalysis on a charged substrate. The correlation between reaction rate and adsorption was determined for each charge variant within the ladder, each of which displayed a maximum rate at an intermediate surface concentration. Both the maximum reaction rate and adsorption value at which this maximum rate occurs increased in magnitude for the more positive variants. In addition, the specific enzyme activity increased as the level of adsorption decreased, and for the lowest adsorption values, the specific enzyme activity was enhanced compared to the trend at higher surface concentrations. At a fixed level of adsorption, the specific enzyme activity increased with positive enzyme charge; however, this effect offers diminishing returns as the enzyme becomes more highly charged. We examined the effect of electrostatic interactions on surface diffusion. As the binding affinity was reduced by increasing the solution ionic strength, thus weakening electrostatic interaction, the rate of surface diffusion increased considerably. The enhancement in specific activity achieved at the lowest adsorption values is explained by the substantial rise in surface diffusion at high ionic strength due to decreased interactions with the surface. Overall, knowledge of the electrostatic interactions can be used to control surface parameters such as surface concentration and surface diffusion, which intimately correlate with surface biocatalysis. We propose that the maximum reaction rate results from a balance between adsorption and surface diffusion. The above finding suggests enzyme engineering and process design strategies for improving interfacial biocatalysis in industrial, pharmaceutical, and food applications.     

表面等离子体子共振技术实时研究蛋白质在修饰表面的静电吸附行为

研究蛋白质在固相表面的静电吸附特性,进而控制蛋白质在修饰表面的静电吸附尤为重要,表面等离子体子共振可以检测金属表面吸附物质厚度和折射率的变化^[1]。这种技术已在研究生物分子相互作用^[2]和考察自组装单层的形成^[3]及蛋白质在固体表面吸附行为^[9-11]等方面得到广泛的应用。对蛋白质在固体表面吸附行为的研究多为考察不同的蛋白质在不同的修饰表面的吸附行为。然而,对蛋白质在修饰表面静电吸附的本质影响因素的研究却少有报道^[4]。本文使用表面等离子体子共振技术实时研究了蛋白质在甲羧基化葡聚糖修饰表面的静电吸附与溶液pH值及离子强度的依赖关系。     

Insights into adsorption of uncharged macrocyclic complexes into a Nafion Film: Adsorption characteristics and analysis of tetraphenylporphyrine zinc(II)

Tetraphenylporphine zinc(II) (ZnTPP) was found to be adsorbed from its CH2Cl2 solution into a Nafion (Nf) film. The characteristics of the adsorption of ZnTPP into the Nf film were studied using a visible absorption spectroscopic technique. The initial rate (v0, mol cm(-2) s(-1)) for uptake of ZnTPP was saturated with increasing ZnTPP concentration (c0, M) in the solution. This kinetic profile was analyzed in terms of a Michaelis-Menten model considering preequilibrium of ZnTPP adsorption between the solution and the outer layer of the Nf film, followed by diffusion to an inner bulk region, giving a maximum diffusion reflux of v(max) = (2.2 +/- 0.2) x 10(-13) mol cm(-2) s(-1). This is different from the kinetics for the Nf/phthalocyanine zinc(II) (ZnPc) film, which gives a linear plot of v(0) vs c(0). This can be explained by the relatively slow diffusion of ZnTPP in the film compared to that of ZnPc because of steric factors: ZnTPP contains bulky tetraphenyl moieties attached perpendicular to a porphyrin ring, whereas ZnPc has higher planarity. The isotherm for the adsorption of ZnTPP into the Nf film was analyzed using a Langmuir isotherm equation, yielding an equilibrium constant of (3.6 +/- 1.1) x 10(6) M(-1) and a saturated amount of adsorbed ZnTPP of (1.8 +/- 0.1) x 10(-9) mol cm(-2), suggesting monolayer adsorption of ZnTPP on the hydrophobic polymer network interfacial with hydrophilic transport channels without significant intermolecular overlap. This is in contrast to the multilayer adsorption mode suggested for the ZnPc adsorption. The tetraphenyl moieties could prevent the stacking of ZnTPP for multilayer adsorption.     

Characterization of polyelectrolyte multilayers by the streaming potential method

Polyelectrolyte multilayer adsorption on mica was studied by the streaming potential method in the parallel-plate channel setup. The technique was calibrated by performing model measurements of streaming potential by using monodisperse latex particles. Two types of polyelectrolytes were used in our studies: poly(allylamine) hydrochloride (PAH), of a cationic type, and poly(sodium 4-styrenesulfonate) (PSS) of an anionic type, both having molecular weight of 70,000. The bulk characteristics of polymers were determined by measuring the specific density, diffusion coefficient for various ionic strengths, and zeta potential. These measurements as well as molecular dynamic simulations of chain shape and configurations suggested that the molecules assume an extended, wormlike shape in the bulk. Accordingly, the diffusion coefficient was interpreted in terms of a simple hydrodynamic model pertinent to flexible rods. These data allowed a proper interpretation of polyelectrolyte multilayer adsorption from NaCl solutions of various concentrations or from 10(-3) M Tris buffer. After completing a bilayer, periodic variations in the apparent zeta potential between positive and negative values were observed for multilayers terminated by PAH and PSS, respectively. These limiting zeta potential values correlated quite well with the zeta potential of the polymers in the bulk. The stability of polyelectrolyte films against prolonged washing (reaching 26 h) also was determined using the streaming potential method. It was demonstrated that the PSS layer was considerably more resistant to washing, compared to the PAH layer. It was concluded that the experimental data were consistent with the model postulating particle-like adsorption of polyelectrolytes with little chain interpenetration. It also was concluded that due to high sensitivity, the electrokinetic method applied can be effectively used for quantitative studies of polyelectrolyte adsorption, desorption, and reconformation.     

有机膨润土结构对吡虫啉吸附热力学和动力学的影响机理

为深入了解有机膨润土结构对农药吸附性能的影响机理,论文制备十六烷基三甲基氯化铵(HTMA)载量系列变化的有机膨润土,通过吸附热力学和动力学研究了新烟碱杀虫剂吡虫啉与改性有机膨润土的相互作用和影响农药分子在有机膨润土层间扩散的结构因素。结果显示,季铵盐改性削弱了膨润土片层与吡虫啉的静电结合,但是增强与吡虫啉的疏水相互作用。吡虫啉吸附动力学与有机膨润土层间结构密切相关,低载量(<0.8′CEC)的HTMA对膨润土层间距的影响很小,但是层间堆积密度的增加导致吡虫啉吸附速率常数急剧下降。HTMA载量的进一步增加导致其层间排列方式由单层平铺向双层平铺的转变,层间距急剧增加使得吡虫啉吸附速率常数略有增大。     

Sorption of basic dyes onto granulated pillared clays: thermodynamic and kinetic studies

Effect of the granulation process onto the thermodynamic and kinetic sorption parameters of two basic dyes (Basic Yellow 28-BY 28 and Basic Green 4-BG 4) was evaluated in the present work. The charge surface properties of the surfactant-modified aluminium-pillared clay (CTAB-Al-Mont-PILC) particles were not modified, and the isoelectric point remains constant after high shear wet granulation. The Gibbs free energy of both BY 28 and BG 4 sorption was negative and decreased with the granulation; the endothermic nature of the sorption process was confirmed by the positive values of ΔH°. Adsorption kinetics of the two dyes, studied at pH 6 and 150 mg L(-1), follow the pseudo-first order kinetic model with observed rate constants of 2.5-4.2×10(-2) min(-1). The intraparticle diffusion model, proposed by Weber and Morris, was applied, and the intraparticle plots revealed three distinct sections representing external mass transfer, intraparticle diffusion and adsorption/desorption equilibrium. Diffusion coefficients, calculated from the Boyd kinetic equation, increased with the granulation and the particle size. Pseudo-first order kinetic constants, intraparticle diffusion rate constants and diffusion coefficients were determined for two other initial concentrations (50 and 100 mg L(-1)) and include in a statistical study to evaluate the impact of granulation and initial concentration on the kinetic parameters. Kruskal-Wallis tests, Spearman's rank order correlation and factor analysis revealed a correlation between (i) the diffusion coefficients and granulation, and between (ii) the intraparticle diffusion rate constants and initial concentration.     

Solute distribution and stability in emulsion-based delivery systems: an EPR study

Adsorption and desorption of human serum albumin (HSA) from aqueous solutions on mica were studied using AFM and in situ streaming potential measurements. A quantitative interpretation of these experiments was achieved in terms of the theoretical model postulating a 3D adsorption of HSA molecules as discrete particles. These measurements, performed for various ionic strength, allowed one to determine the coverage of HSA as a function of the zeta potential of mica. This allowed one to determine the amount of irreversibly bound HSA as a function of the ionic strength. It was found that the coverage of irreversibly adsorbed HSA increased from 0.52 mg m(-2) for I=1.3×10(-3) M to 1.6 mg m(-2) for I=0.15M (pH=3.5). The significant role of ionic strength was attributed to the lateral electrostatic repulsion among adsorbed HSA molecules, positively charged at this pH value. This was quantitatively interpreted in terms of the effective hard particle concept previously used for colloid particles. The experimental results confirmed that monolayers of irreversibly bound HSA of a well-controlled coverage can be produced by adjusting the ionic strength of the suspension.     

Modeling of adsorption dynamics at air-liquid interfaces using statistical rate theory (SRT)

A large number of natural and technological processes involve mass transfer at interfaces. Interfacial properties, e.g., adsorption, play a key role in such applications as wetting, foaming, coating, and stabilizing of liquid films. The mechanistic understanding of surface adsorption often assumes molecular diffusion in the bulk liquid and subsequent adsorption at the interface. Diffusion is well described by Fick's law, while adsorption kinetics is less understood and is commonly described using Langmuir-type empirical equations. In this study, a general theoretical model for adsorption kinetics/dynamics at the air-liquid interface is developed; in particular, a new kinetic equation based on the statistical rate theory (SRT) is derived. Similar to many reported kinetic equations, the new kinetic equation also involves a number of parameters, but all these parameters are theoretically obtainable. In the present model, the adsorption dynamics is governed by three dimensionless numbers: psi (ratio of adsorption thickness to diffusion length), lambda (ratio of square of the adsorption thickness to the ratio of adsorption to desorption rate constant), and Nk (ratio of the adsorption rate constant to the product of diffusion coefficient and bulk concentration). Numerical simulations for surface adsorption using the proposed model are carried out and verified. The difference in surface adsorption between the general and the diffusion controlled model is estimated and presented graphically as contours of deviation. Three different regions of adsorption dynamics are identified: diffusion controlled (deviation less than 10%), mixed diffusion and transfer controlled (deviation in the range of 10-90%), and transfer controlled (deviation more than 90%). These three different modes predominantly depend on the value of Nk. The corresponding ranges of Nk for the studied values of psi (10(-2)相似文献   

Frontal analysis for characterizing the adsorption-desorption behavior of beta-lactoglobulin on immunoadsorbents

High-performance frontal affinity chromatography was employed to study the adsorption-desorption kinetics characterizing the retention of beta-lactoglobulin (beta-LG) onto polyclonal anti-beta-lactoglobulin (anti-beta-LG) chromatographic supports. The adsorption and desorption processes were studied by analyzing two different elution fronts separated by a relatively long rinsing step. The method consists in performing two successive frontal injections of the protein. In between, the column was rinsed with a given volume of mobile phase (buffer alone). During this rinsing stage, a partial desorption may occur and a novel amount of protein could be adsorbed in the second frontal injection step. The whole process (first adsorption, possible desorption, and second adsorption) was simulated by a numerical procedure, in which the column was divided into a large number of slices. A model based on bi-Langmuir type kinetics was used to describe the adsorption of the protein on the support. The model assumes a non-uniform adsorbent with two types of binding sites. At equilibrium the adsorption isotherm is of the bi-Langmuir type. A global adsorption effect was considered which includes the effective binding process and the mass transfer resistances due to the transport to the binding site. Therefore, the column capacity and the kinetic parameters of the model (apparent adsorption and desorption rate constants) were determined from the best fit of the first and second adsorption fronts to the experimental ones. The other parameters of the model are the saturation capacities for the adsorption on each type of sites. The equilibrium affinity constants were estimated in a single experiment from the ratio of the apparent adsorption and desorption rate constants. The high values found (around 10(8) M(-1)) reveal a strong interaction of beta-LG with the immunoadsorbent. Kinetic measurements were carried out at different flow rates. Both the apparent adsorption and desorption kinetics were faster at larger flow rates, indicating an important contribution of the mass transfer resistance in the stagnant fluid at the particle boundary. However, as expected, close values were found for the resulting equilibrium constants calculated from the ratio of the apparent adsorption and desorption rate constant determined at various flow rates.     

Adsorption of lysozyme on a hemodialysis sulfonated polyacrylonitrile membrane, with and without preadsorbed poly(ethyleneimine) on the external faces

We present the influence of pH, from pH 4 to 10, with a focus on the neutral range, on the adsorption of lysozyme (isoelectric point pI=11) on a sulphonated membrane and the same membrane pre-treated with poly(ethyleneimine) (PEI). We found a steep increase of the adsorbed amount above pH 6 in phosphate buffer. The adsorbed amount was about twice as low in Tris buffer, around the neutral pH. The difference between the two types of buffer is attributed to their different ionic composition. High interfacial concentration in phosphate buffer is especially linked to the phosphate divalent anions. In the presence of divalent sulphate anions, we measured the same level of interfacial concentration than with phosphate buffer. With the PEI pre-treated membrane, we observed, on the time scale of our experiments (15–20 h), similar adsorbed amounts than on the raw membrane, showing that the PEI layer does not constitute a true barrier to the penetration of lysozyme into the membrane core. However, its presence leads to a slower adsorption rate in a system where convection does not occur through the membrane.     

法拉第吸脱附偶联过程循环伏安行为的有限元分析

法拉第吸脱附偶联过程的电化学行为较为复杂,难以定量获得其表界面反应动力学信息. 本文通过COMSOL有限元软件对法拉第吸脱附偶联过程的循环伏安行为进行数值分析,研究了反应物或产物不同吸附条件下的循环伏安行为. 结果表明：当反应物或产物弱吸附时,可通过阴、阳极峰电流之差实现饱和吸附量的定量表征. 随着吸附平衡常数的增大,反应由弱吸附向强吸附过渡,峰电流由扩散峰与吸脱附峰相互重叠过渡到相互分离的吸脱附“前波”或“后波”特征. 该吸脱附特征峰的形状和位置与电势依赖的吸附平衡常数有关. 吸附平衡常数及其电势依赖程度越大,吸脱附峰偏离扩散峰越远,吸脱附峰越尖锐. 该模型为法拉第吸脱附偶联过程的循环伏安研究提供了一种定量研究方法,能够帮助研究者从复杂的吸脱附伏安行为中定量获得饱和吸附量和吸附平衡常数等信息,并对涉及吸脱附的电催化研究具有一定指导意义.     

Adsorption and desorption of colloidal particles on glass in a parallel plate flow chamber—Influence of ionic strength and shear rate

The adsorption and desorption rates of 736 nm diameter polystyrene particles on glass were studiedin situ using a parallel plate flow chamber and automated image analysis. Adsorption and desorption rates were measured simultaneously during deposition, enabling the determination of initial deposition rates, blocked areas per particle, desorption rate coefficients, and the number of adhering particles in the stationary state. Deposition experiments were done from suspensions with different potassium nitrate concentrations (1, 10 and 50 mM) and at varying shear rates (15 to 200 s^–1). The initial deposition rate, the desorption rate, the blocked area per particle and the number of adhering particles in the stationary state showed major variations with the shear rate and the ionic strength of the suspension. At low ionic strength, the number of adhering particles showed an oscillatory behavior in time, presumably due to a varying interaction between particle and collector surface. Blocked areas, determined from deposition kinetics, ranged 705 to 2374 cross-sections at low ionic strength, and from 10 to 564 at high ionic strength and corresponded well with those estimated from local pair distribution functions which were obtained from an analysis of the spatial arrangement of the adhering particles.     

硅酸镁锂的有机改性及对Cr(Ⅵ)的吸附特性

采用水热法合成了硅酸镁锂(Laponite), 然后利用十六烷基三甲基溴化铵(CTMAB)对其进行有机改性, 研究了改性后的有机硅酸镁锂(CTMABL)对Cr(Ⅵ)的吸附特性. 结果表明, 改性后样品的比表面积和孔容积变小而平均孔径增大. CTMABL样品的d₍₀₀₁₎值从改性前的1.23 nm增加到1.79 nm, 表明CTMAB进入Laponite层间. 随着溶液pH值的提高, CTMABL对Cr(Ⅵ)的吸附效率明显下降; pH<8.5时, CTMABL颗粒表面电势为正, 能够与Cr(Ⅵ)阴离子发生静电吸引从而提高吸附效率. 随着固液比增加, 对Cr(Ⅵ)的去除效率迅速上升, 当固液比达到4 g/L后去除效率趋于稳定. 离子强度对Cr(Ⅵ)吸附过程的影响不明显. CTMABL对Cr(Ⅵ)的吸附符合准二级动力学模型, 吸附传质速率受膜扩散和颗粒内扩散过程共同影响. 等温吸附过程符合Langmuir模型, 热力学分析结果表明吸附过程是一个自发的吸热反应. 综合分析认为表面配合作用是主要的吸附机制, 同时静电引力在吸附过程中起到了促进作用.     

Adsorption kinetics of proteins onto solid surfaces in the limit of the interfacial interaction control

We have developed an experimental set-up using radiolabelled proteins for the continuous measurement, as a function of time, of the excess concentration of superficial protein at a solid/liquid interface. The experimental conditions were designed in order to minimize the coupling of the interfacial interaction with bulk diffusion, and therefore to work within the limit of the interfacial interaction control. Chemical kinetics were assumed to follow a Langmuir equation. The absorption (K_a) and desorption (K_d) rate constants have been evaluated in the case of fibrinogen and albumin adsorption, onto glass beads and synthetic hydroxyapatite powder, respectively. In order to determine these parameters, a non-linear differential equation (obtained by combining the Langmuir rate equation and a mass-balance equation) was solved by the fourth-order Runge-Kutta method. The results obtained are consistent with the hypothesis of an adsorption rate controlled by the interfacial interaction.