摘要:

Date 1962 1962 1963 1963 1964 1964 1965 1965 1966 I966 1967 1967 1968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 1974 1975 1975 1976 1977 1977 1977 1978 I978 1979 1979 1980 1980 1981 1981 1982 1982 1983 1983 FARADAY DISCUSSIONS OF THE CHEMICAL SOCIETY Subject Inelastic Collisions of Atoms and Simple Molecules High Resolution Nulcear Magnetic Resonance The Structure of Electronically Excited Species in the Gas Phase Fundamental Processes in Radiation Chemistry Chemical Reactions in the Atmosphere Dislocations in Solids The Kinetics of Proton Transfer Processes Intermolecular Forces The Role of the Adsorbed State in Heterogeneous Catalysis Colloid Stability in Aqueous and Non-aqueous Media The Structure and Properties of Liquids Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Bonding in Metallo-organic Compounds Motions in Molecular Crystals Polymer Solutions The Vitreous State Electrical Conduction in Organic Solids Surface Chemistry of Oxides Reactions of Small Molecules in Excited States The Photoelectron Spectroscopy of Molecules Molecular Beam Scattering Intermediates in Electrochemical Reactions Gels and Gelling Processes Photo-eff ects in Adsorbed Species Physical Adsorption in Condensed Phases Electron Spectroscopy of Solids and Surfaces Precipitation Potential Energy Surfaces Radiation Effects in Liquids and Solids Ion-Ion and Ion-Solvent Interactions Colloid Stability Structure and Motion in Molecular Liquids Kinetics of State Selected Species Organization of Macromolecules in the Condensed Phase Phase Transitions in Molecular Solids Photoelectrochemistry High Resolution Spectroscopy Selectivity in Heterogeneous Catalysis Van der Waals Molecules Electron and Proton Transfer Intramolecular Kinetics Concentrated Colloidal Dispersions Oxidation 317 Volume 33* 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65* 66 67 68 69 70 71 72 73 74 75 76 * Not available; for current information on prices, etc., of available volumes, please contact the Marketing Oficer, Royal Society of Chemistry, Burlington House, London WI V OBN stating whether or not you are a member of the Society.Date 1962 1962 1963 1963 1964 1964 1965 1965 1966 I966 1967 1967 1968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 1974 1975 1975 1976 1977 1977 1977 1978 I978 1979 1979 1980 1980 1981 1981 1982 1982 1983 1983 FARADAY DISCUSSIONS OF THE CHEMICAL SOCIETY Subject Inelastic Collisions of Atoms and Simple Molecules High Resolution Nulcear Magnetic Resonance The Structure of Electronically Excited Species in the Gas Phase Fundamental Processes in Radiation Chemistry Chemical Reactions in the Atmosphere Dislocations in Solids The Kinetics of Proton Transfer Processes Intermolecular Forces The Role of the Adsorbed State in Heterogeneous Catalysis Colloid Stability in Aqueous and Non-aqueous Media The Structure and Properties of Liquids Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Bonding in Metallo-organic Compounds Motions in Molecular Crystals Polymer Solutions The Vitreous State Electrical Conduction in Organic Solids Surface Chemistry of Oxides Reactions of Small Molecules in Excited States The Photoelectron Spectroscopy of Molecules Molecular Beam Scattering Intermediates in Electrochemical Reactions Gels and Gelling Processes Photo-eff ects in Adsorbed Species Physical Adsorption in Condensed Phases Electron Spectroscopy of Solids and Surfaces Precipitation Potential Energy Surfaces Radiation Effects in Liquids and Solids Ion-Ion and Ion-Solvent Interactions Colloid Stability Structure and Motion in Molecular Liquids Kinetics of State Selected Species Organization of Macromolecules in the Condensed Phase Phase Transitions in Molecular Solids Photoelectrochemistry High Resolution Spectroscopy Selectivity in Heterogeneous Catalysis Van der Waals Molecules Electron and Proton Transfer Intramolecular Kinetics Concentrated Colloidal Dispersions Oxidation 317 Volume 33* 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65* 66 67 68 69 70 71 72 73 74 75 76 * Not available; for current information on prices, etc., of available volumes, please contact the Marketing Oficer, Royal Society of Chemistry, Burlington House, London WI V OBN stating whether or not you are a member of the Society.

ISSN:0301-7249    

DOI:10.1039/DC98477FX001

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 7- 16 Mass Transfer and Reactions at Interfaces BY PATRICK MEARES Chemistry Department, The University, Aberdeen AB9 2UE, Scotland Received 1 1 th April, 1984 HOMOGENEOUS DIFFUSIVE FLOW The teaching of the principles of mass transfer in physical chemistry courses commonly starts from either the interdiffusion of a pair of miscible liquids in a binary system or the diffusion of a single solute down its concentration gradient in a solvent. The treatment follows Fick's law with a constant diffusion coefficient and reveals that the choice of reference frame for the mass fluxes is ,not trivial, and that when the choice is made correctly the binary system is characterized by a single interdiff usion coefficient. Allowance for concentration dependence of the diffusion coefficient can be made with some increase in the mathematical complexity of the treatment.When more than two components have to be considered the complexity of the mathematical treatment increases substantially and, more seriously perhaps, so does the number of diffusion coefficients needed to describe the system. Fick's law can be generalized to d cj n - l -ji = D,- j = i dx where j i is the flux of i relative to the volume-average velocity. Thus a system of n components is described by ( n - 1)2 diffusion coefficients. If component n is treated as the solvent, ( n - 1 ) coefficients are of the form Djj and resemble in nature and size the diffusion coefficient of j in the solvent n as would be measured in, say, a diaphragm cell.The remainder are cross-coefficients Dii ( i # j ) which express the fact that a flux of i can be generated by a concentration gradient of j even in the absence of a gradient of i and that a concentration gradient of i can be generated by a flux of j . Multicomponent diffusion fluxes are frequently represented by using the notation of irreversible thermodynamics in the form (For simplicity, the difference between the centre-of-mass velocity and the volume- average velocity has been ignored.) Since the Onsager reciprocal relations L.. IJ = L.. I1 (3) apply and reduce the number of independent L, coefficients to in( n - 1 ), it is evident that, although D, # Dji, relations must exist which reduce the number of independent diffusion coefficients to in( n - 1). These relations cannot be used without a detailed knowledgeaof the way in which each chemical potential varies with each of the 78 MASS TRANSFER AND REACTIONS AT INTERFACES concentrations.In general this information is not available and would be as tedious to obtain experimentally as it would be to measure all of the ( n - 1)2 diffusion coefficients. Multicomponent diffusion will not be further developed here and reference may be made for more information to two excellent texts.’72 It must be remembered, however, that the cross-coefficients D,, although usually (except in macromolecular systems) smaller than the straight Djj coefficients, are frequently significant and can lead to unknown or unexpected phen~mena.~ MASS FLOW WITH REACTION Faced with so many experimental, theoretical and interpretive problems in the study of multicomponent diffusion in systems without phase boundaries, the physical chemist might be tempted to look for a simpler background against which to study reaction mechanisms.Such problems, however, cannot be evaded in many of the most important operations of the chemical industry. Furthermore, the objective of many industrial processes is to bring about a separation and consequently at least two phases are involved and molecular transport takes place between them. Thus it has come about that most of the work on mass transfer up to and across interfaces, with and without chemical reaction, has been carried out by chemical engineers and is frequently expressed in a terminology not wholly familiar to physical chemists.Despite the complexity of the molecular processes involved, it is essential to characterize the mass-transfer behaviour of any experimental system in an unam- biguous, although empirical, way if the kinetics and mechanism of concurrent chemical reactions are to be inferred from their effects on the rates of the processes taking place in the system. When a substance i is being transported across an interface and then consumed by a first-order reaction with rate constant k,, the rate of change of concentration of i in a volume element distant x from the surface may be written4 Here udci/i)y allows for convection with velocity u parallel to the interface and the third term on the right-hand side deals with the consumption of i by reaction. By solving eqn (4) with and without the reaction term one may obtain an expression for the mass-transfer coefficient of i with, kM, and without, k&, reaction.Provided the surface concentration and hydrodynamic conditions are kept constant, a reaction factor # is defined by # = k M / k ” , . Since d, is a function of the velocity constant k,, it is the experimental quantity upon which information about the reaction depends. The solution of the continuity eqn (4) can be carried out only when the mass transfer in the non-reacting system has been correctly modelled. Most of this introductory paper is devoted to an elementary discussion of this problem. The difficulty of characterizing the mass-flow conditions is emphasized by the wide variety of experimental arrangements that have been used by the authors whose work is included in this Discussion.Stirred and unstirred systems have been used to study gas/liquid, liquid/liquid and solid/liquid interfaces, and the interfaces themselves are sometimes planar and sometimes spherical. Many more complexP. MEARES 9 0 Fig. 1. Concentration profile at a solid/liquid interface in the presence of a stagnant liquid film of thickness 8. arrangements and surface geometries are to be found in industrial mass-transfer plants. THE STAGNANT-FILM MODEL Three models are in common use to describe mass transfer at interfaces. They are the stagnant-film model, the penetration model and the turbulent-boundary-layer modeL4 The stagnant-film model is probably the best known and was introduced by Nernst at the beginning of this century.It is assumed that the resistance to mass transfer up to a phase boundary in a liquid or a gas lies wholly within a thin layer adjacent to the surface and that all regions of the phase further from the surface than the thickness of this layer can be regarded as well stirred and of uniform composition. The fluid in immediate contact with a stationary surface is at rest and a pair of fluids in contact at an interface are at rest there relative to one another. Thus it is appropriate to model the resistant boundary layer as a stagnant film and to assign to it a thickness 6 (fig. 1). Transport across this film takes place by diffusion only and can usually be regarded as confined to the direction normal to the surface. Fluxes can be expressed by using Fick’s law and ignoring effects due to cross-coefficients D,.The flux j i relative to the volume-average velocity given by Fick’s equation must be corrected to find the flux Ji relative to the fixed surface. Thus n J i = j i + c i C J i q i= 1 where < is the partial molar volume of i.10 I I I MASS TRANSFER AND REACTIONS AT INTERFACES I I 1 1 - Fig. 2. Concentration profile at a liquid/liquid interface with stagnant films of thicknesses 6, and 6* and distribution coefficient K . The stagnant-film model is easy to visualize and set down but it can only be used quantitatively in the absolute sense in a few special cases. There are two difficulties ; the stagnant-layer thickness cannot be measured independently and, except at some fluid/solid interfaces, the concentrations at the surface will not be known.Where two fluid phases are in contact, only the bulk concentrations are known and it is necessary to elaborate the model to include two stagnant films, one on each side of the interface (fig. 2). Then one may assume also that there is no resistance to transfer at the interface itself, i.e. that the fluids in contact there are at partition equilibrium. This assumption is discussed more fully later. The total resistance to mass transfer is then given by the sum of the two stagnant-film resistances, which act in series. The values of S for the two films have to be estimated from measurements of mass-transfer coefficients of suitable substances under the same hydrodynamic conditions as will be used in the kinetic studies.Alternatively, the hydrodynamic conditions may be varied in a systematic way that permits extrapolation to S ---* 0, i.e. to conditions of perfect mixing in each phase. Finally, in order to estimate the resistance to mass transfer from the two sets of bulk concentrations and stagnant-film thicknesses, the equilibrium distribution or partition coefficients K of the materials in contact across the phase boundary must be known. This equilibrium might follow the linear law of Henry at a gas/liquid interface or for the partition of a solute between two solvents, but in a case where liquid ion-exchangers or ionophores are involved a quadratic or higher-order ion-exchange equilibrium isotherm is needed. The stagnant-film model has been particularly useful in work on membrane transport and in the study of electrode kinetics.In membrane science the membrane phase can be regarded as a stagnant phase and transport within it treated as due to molecular-diffusion processes, perhaps coupled with chemical reactions. TheP. MEARES 11 transport equations in the membrane are derived in terms of the surface concentra- tions. It does not affect the use of the model that these equations are frequently far more complex than Fickian diffusion equations. Usually it can be arranged that either the hydrodynamic conditions, and hence the values of 8, are the same at both membrane/solution interfaces or the solutions can be chosen so that the resistance to mass transfer is negligible at one side relative to the other. Then only one value of S is important.The stagnant film can be assigned an effective thickness by studying the transport of a suitable passively transported solute, and the assumption of equilibrium at the membrane faces is usually justified. The use of Fick's law and a characteristic value of S leads to a linear increase of flux with diffusion coefficient. However, there is no distinct plane at which the bulk changes from being well stirred to stagnant. The effectiveness of the stirring declines gradually as the surface is approached. The greater the value of D the greater will be the distance from the wall at which the diffusion flux becomes comparable with the convective eddy flux. A monotonous increase of S with D1j3 is expected but in view of the relatively small range spanned by the diffusion coefficients of a series of solutes in a single solvent, this variation of 6 is a less serious problem than many others met in multicomponent transport systems.PRECISELY KNOWN HYDRODYNAMICS Where the phase at one side of the interface is effectively solid it may be possible to extrapolate mass-transfer data obtained under various conditions so as to estimate the flux that would be obtained under perfect stirring conditions, ie. zero film thickne~s.~ Such extrapolation procedures are essentially empirical. However, when one phase takes the form of a disc, such as a metal electrode, which is rotated within a liquid then it is found6 that the stagnant-layer thickness has the same value over the whole surface of the disc. Further, if the rate of rotation is restricted to the regime of laminar motion in the fluid, the mass-transfer coefficient can be related to the rate of rotation and other measurable parameters of the system.An unam- biguous way of extrapolating out the liquid-phase mass-transfer resistance is then indicated by the theory. An important advance has been made by extending the rotating-disc technique from metal electrodes and catalysts and from rate-of-dissolution studies to the rotating diffusion cell,7 which has been used by several authors contributing to this Discussion. Exact treatments of mass transfer across a phase boundary have been carried out also for several practical cases involving laminar flow over plates, spheres and cylinders given stationary concentrations at the interfa~e.~ They represent a refine- ment of the stagnant-film model in these special cases. They are of particular value for studies on rates of absorption of gases by fluids.' THE PENETRATION MODEL The penetration model differs fundamentally from the stagnant-film theory.Whereas the latter is directed towards steady-state mass transfer, the former deals with transient conditions. If the fluid at the interface is constantly replaced by fresh fluid from the bulk in a time comparable to that required to establish a steady concentration gradient across the stagnant film, it is found that the rate of mass transfer of a substance into the fluid should vary with the square root of its diffusion12 MASS TRANSFER AND REACTIONS AT INTERFACES coefficient in the fluid.' The model can be used only in combination with various empirical quantities, especially the characteristic length of time during which an element of fluid remains in contact with the interface.This model is not developed more fully here because it does not appear to be appropriate in the papers which are to follow except perhaps in the studies of liquid membranes.' The liquid in contact with the moving emulsion droplets is subject to continual renewal, and permeation into each volume element of the fluid occurs only during the short period required for a droplet to pass through it. THE TURBULENT-BOUNDARY-LAYER MODEL When the velocity and its gradient in shearing flow near to an interface are large enough for the momentum forces to exceed the viscous forces the flow ceases to be laminar and becomes irregular and turbulent.Macroscopic volume elements of the liquid then 'diffuse' through the mass rather in the way that single molecules diffuse in steady conditions. The transporting effect of this irregular motion is referred to as eddy diffusion; it is normally far more effective than molecular diffusion in equalizing concentrations throughout the fluid. The theory of turbulent flow close to interfaces" is highly complex and yet relatively primitive in terms of the level of understanding achieved. One may imagine that close to a stationary interface turbulence is damped and that mass transfer across the interface will generate steep concentration gradients in a thin layer, the turbulent boundary layer, between the surface and the fully turbulent regions in the bulk, This thin layer consists of the stationary film at the interface across which transfer is by molecular diffusion and an intermediate layer in which eddy diffusion and molecular diffusion both play a role.An empirical quantity, the eddy diffusivity E, is thencissigned to take care of the turbulent contribution to the flux, giving In the nature of eddy flow it seems likely that E, which is a function of the hydrodynamic conditions, has about the same value for all components. It is unlikely that one would choose to disentangle the kinetic characteristics of a chemical reaction under the deliberate complication of turbulent conditions. None of the experimental contributions to this Discussion have done this but, as will be described, turbulence may arise at the interface for reasons other than the use of agitation at high Reynolds numbers.SURFACE RESISTANCE AND ADSORBED MONOLAYERS The foregoing discussion has been based on the assumption that the compositions and hence properties in each of the two phases would, at equilibrium, be uniform up to the interface and that during the non-equilibrium state of mass transfer between the phases there is no relative motion of the phases actually at the interfacial layer of molecules apart from the steady mass-transfer flux normal to the interface. The layers of molecules on either side of the interface are assumed to be in thermodynamic equilibrium with only a small energy of activation required for molecular exchanges between them, i.e.there is no barrier to mass flow in the interface itself. Clearly these assumptions are a great oversimplification. The properties of the system, such as density, concentration, dielectric constant etc. change abruptly at the interface. The molecules there are subjected to strong force fields which affect their properties, cause orientation and give rise to well understood phenomena suchP. MEARES 13 as interfacial electric-potential differences, adsorption and interfacial tension. When, as in the cases of interest here, one at least of the phases contains several components, their mole fractions will change as the surface is approached even at equilibrium. This surface activity normally leads to an accumulation near the surface of solutes which lower the surface tension.TJie thermodynamic interconnection of surface concentrations and surface pressure or surface tension y is made through the Gibbs isotherm in terms of the surface excess Ti: ri = -ay/api. (8) When the surface excess is large, i.e. for highly surface-active solutes, it is believed that the interfacial layer may consist almost wholly of a monomolecular film of the adsorbed solute. To the extent that the diffusion coefficients of the solutes are concentration- dependent, their values in the interfacial layer may differ, as a result of the surface excess concentrations, from those in the bulk. Far more importantly, a close-packed monolayer actually forming the interface may represent a substantial barrier to mass transfer. Thus in the case of the stagnant-film model, the total resistance R will be given by R = R , + R2 + R, where R1 and R2 are the two stagnant-film resistances and R, the surface resistance.In the absence of powerfully surface-active substances R, is usually negligible compared with R1 and R2 even under conditions of good stirring, but the effect of surfactants can be very marked for gas and vapour transfer at gas/liquid interfaces." Perhaps the most widely known is the effect of a monolayer of cetyl alcohol in retarding evaporation from reservoirs. The surface resistance to solute transfer at a liquid/liquid interface is usually negligible compared with that due to the stagnant films adjacent to the interface but surfactants may have a marked effect on another interfacial influence on mass transfer yet to be discussed.(9) SPONTANEOUS INTERFACIAL TURBULENCE It has been recognized for more than a century that, when a solute diffuses across an oil/ water interface, the interface may become unstable, turbulent motion may develop spontaneously and an emulsion may form of one phase dispersed in the other. Such phenomena are commonly grouped together as Marangoni effects. 4310-13 There is a fascinating and substantial literature on this subject and only a few simple principles can be mentioned here. The true Marangoni effects are driven by fluctuations in the interfacial tension. They should be distinguished from convection driven by an unstable density distribu- tion which can arise, for example, as a result of a substance transferring upwards across a phase boundary if the liquid left behind at the interface is then more dense than the bulk liquid lying below.Spontaneous density convection can also arise in multicomponent systems where a flow of one component generates a concentration gradient of another and, in the process, inverts the gravitationally stable density profi~e.~ The Marangoni effect can arise at a gas/liquid or liquid/liquid interface; tur- bulent effects develop at plane and at spherical interfaces. Fig. 3 and 4 show how such effects can arise at a plane interface where the transported substance lowers the interfacial tension. A local downward fluctuation in the interfacial tension due14 MASS TRANSFER AND REACTIONS AT INTERFACES gas or o i l ether or other material dissolved in water o-c surface-active Fig.3. Diagrammatic representation of surface-active material spreading from a a locally high concentration in the surface and dragging some of the underlying water with it. This brings up more surfactant to the surface and amplifies the disturbance (from Davies and Rideal)." Fig. 4. Diagrammatic representation of interfacial turbulence creating a surface ripple (from Ellis and B i d d ~ l p h ) . ~ ~ ( a ) A spot of very low surface tension is formed. ( b ) The spot spreads violently, forming an annulus and exposing the bulk liquid. ( c ) A large ripple is formed as the central motion reverses. to a local concentration fluctuation leads to an outward movement of the surface from the site of the fluctuation which drags up from the bulk still more of the surface active substance.Thus instead of dying away the disturbance is amplified. The balance of forces is such that, at the surface, a line across which the interfacial tension changes produces a ripple as it spreads outwards. The mutual interferences of many such ripples may produce a regular cellular pattern on a plane surface (plate l).'* In the case of a drop of one phase dispersed in another, violent kicking of the drop may appear.I4-l6 The precise theory of such effects is complex and incomplete although major advances have been made in recent years through the interest now manifest in dissipative structure^.'^ The importance of spontaneous turbulence in the study of interfacial reactions is that such turbulence greatly increases the rate of mass transfer across the interface.In practical terms, such an effect would be extremely beneficial in a process such as liquid extraction but on the other hand the unsuspected existence of interfacialPlate 1. Water desorhing from a 10 mm deep pool composed of equal volumes of water a n d 1,4-dioxane (from Berg et [To face page 14P. MEARES 15 turbulence in the kinetic study of a reaction could lead to erroneous conclusions. It is essential therefore to have a reliable set of criteria to enable the likelihood of interfacial instability to be predicted. The author was highly conscious of this problem while reading the preprinted papers for this Discussion. It is helpful that several of the main recent contributors to the theory of Marangoni effects are contributing also to the Discussion and may throw light on their relevance to some of the experimental situations described in the other papers.The first major theoretical analysis of the Marangoni effect" showed that instabil- ity for the transfer of a component that lowers the surface tension is likely to occur when transfer is out of the phase of higher viscosity or lower diffusion coefficient, i.e. for a gas/liquid interface desorption is liable to be unstable but adsorption is not. The absorption of carbon dioxide, however, which raises the surface tension of an aqueous solution, can give rise to instability especially when it is absorbed into a solution of mon~ethanolamine,~~ and the same is true for the absorption of ammonia by acetic acid solutions.20 It is frequently found that the presence of the interface of highly surface-active solutes reduces the spreading tendency of the surface fluctuations of the concentra- tion of the transferable solute.The adsorbed film of surfactants also introduces a surface elasticity and viscosity which damp the fluctuations and so preserves stability. Important new studies of the stability riter ria^'-^^ have served to extend and largely confirm the results of Sternling and Scriven." Especially pertinent here is the extension from purely diffusional and hydrodynamic effects of earlier work to include chemical reactions at interfaces.22 CONCLUSION In order to study the kinetics and mechanism of interfacial reactions it is essential to be able to disentangle the influences of reaction steps and mass transfer on the rate of the overall processes that can be observed in an experiment.The more precise is the knowledge of the mass-transfer restraints in the system the more fundamental are the conclusions that can be drawn regarding the chemical reactions. For this reason it is preferable to construct experimental systems with very well defined hydrodynamic situations as in rotating-disc or well developed laminar-flow systems. Alternatively, the use of carefully controlled conditions which can be characterized by studying the fluxes of inert substances in terms of the stagnant-film model or the penetration model is acceptable. It is not too serious that these model theories do not apply exactly to the experimental circumstances because much of the error cancels when one divides kM by k& in order to find the reaction factor 6.It is important, however, that substances occurring in the reacting system that were absent from the characterizing system do not induce interfacial instability and turbulence, which would greatly increase the rate of mass transfer across the interface and frustrate the attempt to derive the contribution of the reaction to the observed phenomena. D. D. Fitts, Non-equilibrium Thermodynamics (McGraw-Hill, New York, 1962). E. L. Cussler, Multicomponent DiNusion (Elsevier, Amsterdam, 1976). R. P. Wendt, J. Phys. Chem., 1962, 66, 1940. T. K. Sherwood, R. L. Pigford and C. R. Wilke, Mass Transfer (McGraw-Hill, New York 1975), chap. 5 and 8. H. D. Spriggs and N. N. Li, in MembraneSeparation Processes, ed.P. Meares (Elsevier, Amsterdam, 1976), chap. 2. ' B. G. Levich, Physico-chemical Hydrodynamics (Prentice-Hall, Englewood Cliffs, N.J., 1962).16 MASS TRANSFER AND REACTIONS AT INTERFACES W. J. Albery, A. M. Couper, J. Hadgraft and C. Ryan, J. Chem. SOC., Faraday Trans. 1, 1974,70, 1124. * P. V. Danckwerts, Gus-Liquid Reactions (McGraw-Hill, New York, 1970), chap. 5. D. J. Wasan, Z. M. Gu and N. N. Li, Faraday Discuss. Chem. SOC., 1984, 77, 67. l o J. T. Davies, Turbulence Phenomena (Academic Press, New York, 1972), chap. 9. I ' J. T. Davies and E. K. Rideal, Interfacial Phenomena (Academic Press, New York, 1961), chap. l 2 J. C. Berg, in Recen( Developments in Separation Science, ed. N . N . Li (C.R.C. Press, Cleveland, l 3 B. G. Levich and V. S. Krylov, Annu. Rev. Fluid Mech., 1969, 1, 293. l4 J. T. Davies and D. A. Haydon, Roc. 2nd Znt. Congr. Surface Activity (Butterworths, London, l 5 M. V. Ostrovsky and R. M. Ostrovsky, J. Colloid Interface Sci., 1983, 93, 392. I6 T. S. Slbrensen, J. Chem. Soc., Faraduy Trans. 2, 1980, 76, 1170. 7. Ohio, 1972), vol. 11, pp. 1-31. 1957), voi. I, pp. 417-425. P. Glansdorff and I. Prigogine, 7hermodynumic Theory of Structure, Stability and Fluctuations (Wiley-Interscience, London, 197 1 ). 17 '* C. V. Sternling and L. E. Scriven, AIChE J., 1959, 5, 514. I 9 P. V. Danckwerts and A. T. da Silva, Chem. Eng. Sci., 1967, 22, 1613. 2o A. J. M. A. Oyekan and H. Sawistowski, Chem. Eng. Sci., 1971, 26, 1772. 21 M. Hennenberg, P. M. Bisch, M. Vignes-Adler and A. Sanfeld, J. Colloid Interface Sci., 1979, 69, 22 W. Dalle Vedove and A. Sanfeld, J. Colloid Interface Sci., 1981, 84, 318; 328. 23 J. Reichenbach and H. Linde, J. Colioid Interface Sci., 1981, 84, 433. 24 S. R. M. Ellis and M. Biddulph, Chem. Eng. Sci., 1966, 21, 1107. 25 J. C. Berg, M. Boudart and A. Acrivos, J. Fluid Mech., 1966, 24, 721. 128; 1980, 74, 495.

ISSN:0301-7249    

DOI:10.1039/DC9847700007

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 17-31 Amines as Rate Promoters for Carbon Dioxide Hydrolysis BY D. W. SAVAGE* AND G. SARTORI Corporate Research, Exxon Research and Engineering Co., Annandale, New Jersey 0880 1, U.S.A. AND G. ASTARITA Chemical Engineering Department, University of Delaware, Newark, Delaware 1971 1, U.S.A. Received 17th January, 1984 Amines act as homogeneous catalysts for the carbon dioxide hydrolysis reaction, so that they are very effective rate promoters for carbon dioxide absorption in carbonate solutions. Experimental data show that the rate-promotion effect is a very conspicuous one, to the point where the catalysed reaction can be regarded as essentially instantaneous in comparison with diffusion phenomena. Possible mechanisms of this effect are discussed.The rate-enhancement effect is in addition to the effect that amines have on the capacity of carbonate solutions. The relationship between the rate and capacity effects is discussed. In the hot carbonate process for C02 removal from gases, the chemical sink for carbon dioxide is the bicarbonate ion; C 0 2 is chemically consumed by the following overall reaction: CO, + C0,2- + H,O - 2HC03-. (1) The chemistry of the process in the case where potassium (or sodium) carbonate is the only reactive species originally present in the liquid phase is well understood. The slow step of the overall sequence resulting in reaction ( I ) is CO, hydrolysis: and the kinetic constant of reaction (2) has been determined] for ionic strengths up to the highest ones used in industrial operation and for temperatures up to 110 "C.The vapour-liquid equilibrium (VLE) behaviour has also been satisfactorily modeled; a correlation is available for the physical solubility of CO, in concentrated carbonate solutions, and the mass-transfer rates can be predicted accurately from the available physicochemical information2 The hot carbonate process has many attractive features, but the rate of mass transfer is comparatively low, owing to the small value of the hydroxide ion concentration in reaction (2). Therefore, rate promoters have been in common industrial use for a long time. The industrially important rate promoters fall into two categories: inorganic (usually weak acids) and organic (amines, usually amino- alcohols). Rate promoters, in addition to their effect on the mass transfer rates, may also influence the VLE behaviour of the system.This paper is concerned mainly with the analysis of the rate-promotion effect of amines, and in particular of a new class of sterically hindered amines. The chemistry of hindered amines has been discussed recently by Sartori and Savage3. 1718 CARBON DIOXIDE HYDROLYSIS Rate promotion has been discussed in the literature, and two different mechan- isms have been considered. In the first mechanism the promoter acts as a homogeneous catalyst for reaction (2); this is the commonly accepted mechanism in the case of arsenious acid.- In the other mechanism the reaction steps are separated by diffusion steps; this has been called the 'shuttle me~hanism'~ and has been proposed to explain the low-temperature behaviour of amines as rate pro- moters.'" A paper has recently been published" where rate promotion is discussed in gene\ral terms; the two mechanisms have been shown to be only quantitatively but not qualitatively different.In this paper, the rate-promotion effect of hindered amines is discussed following the lines of the general argument developed in." We have performed mass-transfer rate and VLE experiments with a variety of amine promoters. We report results for two amines; diethanolamine (DEA), an amine in common commercial use as a rate promoter, and a sterica!ly hindered diamine (HDA). A hindered amine is defined structurally as a primary amine in which the amino group is attached to a tertiary carbon atom, or a secondary amine in which the amino group is attached to a secondary or tertiary carbon atom.Some examples of sterically hindered amines have been given.3 Hindered amines are characterized by a low tendency to form carbamates owing to the bulkiness of the substituent attached to the amino group. HDA contains a sterically hindered secondary amino group and an unhindered primary amino group. The latter serves mainly to increase the solubility of the diamine in the hot potassium carbonate solution. Before discussing the mass-transfer rate experiments a discussion will be given of the thermodynamic (VLE) behaviour of amine-promoted carbonate solutions in the presence of COz. The thermodynamic model is needed to calculate the driving forces for mass transfer and in the interpretation of the chemical kinetics.THERMODYNAMICS The thermodynamic analysis given here is based on a general methodology for developing the VLE behaviour of gas-treating systems described in ref. (4). Consider an aqueous solution originally made up of rn mol dm-3 of K2C03, and Rrn mol dm-3 of an amine rate promoter, RNH (for reasons that will become apparent later, we exclude from consideration the case where the amine is tertiary). As C02 is absorbed, the composition of the solution will change; let there be yrn mol dmW3 of chemically combined CO, in the solution (the original solution corresponding to y = 0). From a thermodynamic viewpoint we are interested in the prediction of the composition of the liquid phase, and of the corresponding equilibrium vapour pressure of C02, as functions of the degree of chemical saturation y .It should be borne in mind that, while in the case of an unpromoted solution ( R = 0) the value of y is restricted to the range 0-1 (except at very high C02 partial pressures where physical solubility of C 0 2 is significant), for a solution promoted by an alkaline species such as an amine the upper bound to the value of y becomes 1 +R, since the amine itself provides an additional chemical sink for C02 through its ability to transform into the protonated form RNH;. In addition to its free (RNH) and protonated (RNH2+) forms, the amine may also be present in the carbamate ion form, RNCOO-. We neglect the possibility that a significant amount of alkylate may form through reaction of alcoholic func- tional groups of the amine, since the range of pH values of interest is too low.Also, we will not consider in detail the additional complications arising in the case of polyamines.D. W. SAVAGE, G. SARTORI AND G. ASTARITA 19 Should the amine be entirely in the form of free amine, the concentrations of the relevant non-volatile components in the liquid phase would be given by [co32-] = rn( 1 - y ) [HC03-] = 2rny [RNH] = Rm [RNH2+] = [RNCOO-]=O. (6) However, the amine can become converted to its protonated and carbamate forms by the occurrence of the following reactions: HC03- + RNH -+ C032- + RNH2+ HC03- + RNH -+ RNCOO- + H20. (7) (8) Let f be the fraction of the amine converted (so that 1 -f is the fraction present as free amine). Thus [RNH] = Rm( 1 -f) (9) [HC03-] = m(2y - Rf) (10) O s f s m i n (1,2y/R).(1 1) [RNCOO-] = rnRg (12) Let g be the fraction of amine converted to the carbamate form. Thus [cO3*-] = rn[ 1 - y + R ( f - g)] o s g q [RNH2+] = Rrn(f- g) Eqn (9)-(15) give all the relevant concentrations in terms of the two parameters f and g. The value of the latter is in turn determined by the equilibrium condition for reactions (7) and (8). In particular, let A be the equilibrium constant for reaction (7), i.e. the ratio of the second dissociaton constant of carbonic acid to the protonation constant of the amine. As the alkalinity of the amine increases, so does the value of A ; a value of unity corresponds to an amine with pK, = 10.3 at room temperature. The equilibrium constant A is concentration-based and therefore in principle its value will depend on the composition of the liquid phase.There is precedent in the literature for using a lumped parameter such as ionic strength as a measure of the composition. However, the ionic strength of a carbonate solution does not change very significantly as y changes, and therefore it is reasonable to regard A as independent of y, although it will depend on rn. The equilibrium condition for reaction (7) thus becomes Let B be the product of the equilibrium constant of reaction (8) times the molarity rn. The value of B is the appropriate dimensionless measure of the stability of the carbamate:20 100 CARBON DIOXIDE HYDROLYSIS 10 P 1 0.1 0.01 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Y Fig. 1. Dimensionless CO, equilibrium partial pressure, p, plotted against CO, loading in solution, y (in mol C02 per mol initial K2C03).( a ) Unpromoted; ( b ) promoted (A = 1, B = 1, R = 0.3). The system of eqn (16) and (17) for the two unknowns f and g is equivalent to a fourth-order polynomial equation and thus possesses four roots. However, only one of the roots will be such that f and g are real and satisfy the constraints (1 1) and (1 5). Once f and g have been calculated, the concentratipns of the non-volatile components are known. If K is the equilibrium constant for reaction (1) and H is the Henry's-law constant for the physical solubility of CO,, the equilibrium partial pressure p* is given by H [HCO3-I2 K [C0,2-] p * = - Substitution of eqn (10) and (13) into (18) gives the dimensionless equilibrium partial pressure p as p*K (2y-Rf12 p=Hm= 1 - y + R ( f - g ) ' Limiting degenerate cases of course arise when either A or B is much larger or much smaller than unity.Results of the calculation are- therefore presented with respect to a base case where A = 1, B = 1 and R = 0.3. The base case corresponds to an amine with a room temperature pK, of 10.3, and a moderately stable carbamate. Fig. 1 shows the beneficial effect of promoter addition on the capacity of the solution (capacity may be considered to be the swing in C02 loading corresponding to a change in CO, partial pressure e.g. p=O.l-100). The effect is of particular importance if the partial pressure of CO, in the raw gas corresponds to a value of p > ca. 1 .o.D. W. SAVAGE, G.SARTORI AND G. ASTARITA 100 10 P 1 0.1 0.01 21 Y Fig. 2. As fig. 1. A= 1 , R=0.3. ( 1 ) B = 100, (2) B = 3 , (3) B = 1, (4) B=0.3. Fig. 2 shows the effect of the carbamate stability constant, B, on the VLE behaviour. As the carbamate stability decreases, the capacity of the solution increases. However, from this viewpoint, at values of B < ca. 0.3 the capacity increase becomes negligible; the curve for B = 0 being almost indistinguishable from that corresponding to B = 0.3. Conversely, there is a very significant loss of capacity as B is increased above the value of unity; the curve for B = 100 (an amine with a very stable carbamate) actually results in a capacity less than that of an unpromoted solution. Fig. 3 shows the effect of carbamate stability on the fraction of free amine.As will be discussed later, the effective rate promoter is considered to be the free amine, and therefore it is important to know what fraction of the total promoter is present in the rate-eff ective form. Again, as the carbamate stability constant decreases, the fraction of unconverted amine increases. With B values of 0.3 or less, a substantial fraction of amine is unconverted even at y values approaching the upper bound of 1 +R. Fig. 4 shows the effect of amine alkalinity on capacity. The effect is not very marked. However, if the value of A becomes less than ca. 0.3, the capacity decreases significantly. As the amine alkalinity decreases, more and more amine is present in the form of free amine. Therefore, from a purely thermodynamic viewpoint it would appear that an amine slightly less alkaline than the carbonate, and with a B value of 0.3 or less, is possibly the best organic rate promoter in terms of capacity enhancement and amount of free amine.The thermodynamic model discussed above does not strictly apply to a diamine, HNRR‘NH. For a diamine the following converted terms are possible: singly protonated (+H,NRR’NH, NHRR’NH;), doubly protonated (+H,NRR’NH;), singly carbamated (-OOCNRR’NH, HNRR’NCOO-), doubly carbamated ( --O C C N RR’ N C 0 0 -) and sel f -n eu t ral izi ng , ( - 0 C C N RR’ N H ;, ’ H , N RR’ NC 0 0 - ) .22 CARBON DIOXIDE HYDROLYSIS I I 1 I 1 I ' I 1 0.8 0.6 f 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1.0 1 . 2 1.4 Y Fig. 3. Fraction of amine converted,f; plotted against COz loading in solution, y.A = 1 , R = 0.3. 100 10 0.1 0.01 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Y Fig. 4. As fig. 1. B = 1, R=0.3. (1) A=0.3, (2) A = 1, (3) A = 3 , (4) A+m. However, consider a diamine where the two nitrogen atoms are separated by a comparatively short and hence rather stiff organic backbone, such as the HDA used in this work. The two amphoteric forms would require severe bending of this backbone, and therefore their formation can be neglected. The doubly protonated form and the doubly carbamated form are likely to be present at concentrationsD. W. SAVAGE, G. SARTQRI A N D G. ASTARITA 23 1000 100 1 0 .l 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Y Fig. 5. As fig. 1 . The solid curve is theoretical for A = 1, R = 0.3 and B = 0.3. The data points are for hindered amine (HDA), R =0.3.well below those of the singly protonated and singly carbamated forms, owing to the proximity of the two nitrogen atoms. The equilibrium equations between the two singly protonated forms, and between the two singly carbamated forms, are linear, so that either form is simply proportional to the sum of the two: [+H2NRR’NH]x [+H,NRR’NH] +[HNRR’NHl] and therefore the equations given above hold for the sum of the concentrations of the two protonated and the two carbamated forms. Of course, the possibility of double protonation results in the fact that the upper bound to y is 1 +2R rather than 1 + R ; the plot of log p* against y will have a high-pressure branch going from y = 1 + R to y = 1 +2R. This, however, occurs at unrealistically high values of p* for any realistically assumed value of the equilibrium constant for the formation of the doubly protonated form. The considerations above imply that the model is a reasonable approximation, and this is borne out by comparison with experimental VLE data.Fig. 5 shows data for a K2C03 solution containing 0.3 mol of HDA per mol of K2C03; the curve is calculated from the model. Fig. 6 is a similar plot for a DEA-promoted solution. The cyclic capacity of the HDA-promoted solution is significantly larger than that of the DEA-promoted solution provided the partial pressure of C02 in the feed gas is high enough for the high-pressure branch of the plot of p against loading to be utilized. RATE EXPERIMENTS The experimental determination of rates of absorption (and desorption) of C 0 2 into (or from) aqueous solutions of K2C03 containing the amine promoters has24 CARBON DIOXIDE HYDROLYSIS 1000 t 1 1 I I I 0 / 0.1 1 I I I I 1 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Y Fig. 6.As fig. 1. The solid curve is theoretical for B = 1.5. The data points are for DEA, R = 0.6. been carried out on a one-sphere absorber. The experimental technique has been described elsewhere.’ The data were reduced to an apparent mass-transfer coefficient kL defined as N H kL=- pi -p* where N is the mass transfer flux, H is the Henry’s-law constant for CO, in the solution, pi is the gas-liquid interface partial pressure of C 0 2 and p* is the equili- brium vapour pressure of CO, corresponding to the bulk liquid composition. The value of N was measured in the rate experiment.The value of H was assumed to be the same as in an unpromoted solution; the latter had been determined independently., The value of pi was the difference between the total pressure of the gas and the vapour pressure of water over the solution; the latter had been measured independently in VLE experiments. Finally, the value of p* was obtained from smooth curves drawn through the VLE data (see fig. 5 and 6). Fig. 7 is a typical rate plot obtained from one of the runs with DEA as the rate promoter. From the smooth curves drawn through the data in plots such as in fig. 7, the values of a promotion factor Ep have been derived. Ep is defined as follows: Ep = (kL)promoted/(kL)unpromoted. (21) The value of (kL)unpromoted was known from previous experiments carried out with K,CO, solutions,’ With ‘conventional’ amines such as DEA, the rate-promotion factor is approximately independent of fractional saturation (see fig.8). The values of E, are rather large; in fact they are at least as large as values reported in the literature,839 in spite of the fact that the latter were obtained under conditions where (kL)unpromoted is essentially equal to the value k t one would observe in the absence of any chemical reaction. In other words, although at high temperature evenD. W. SAVAGE, G. SARTORI AND G. ASTARITA 25 80 60 20 10 0.2 0.3 0.4 0.5 0.6 0.7 Y Fig. 7. Mass-transfer coefficient, kL (cm min-') plotted against C02 loading in solution, y, for a one-sphere absorber at 90 "C. 10 8 6 2 0.2 0.3 0.4 0.5 0.6 1' Fig. 8.Absorption promotion factor, E,, plotted against COz loading in solution, y, for a one-sphere absorber at 90 "C. unpromoted carbonate solutions show very significant rate enhancement over physical absorption, the addition of amines still has a large promotion effect. Our desorption rate data are much less extensive than the absorption data. The desorption runs indicate that gas-phase resistance is controlling; indeed the desorp- tion rates for both DEA- and HDA-promoted solutions superimpose in a plot of rate against equilibrium vapour pressure of CO,. Therefore the only conclusion which can be drawn from the desorption data is that the rate-promotion effect of26 CARBON DIOXIDE HYDROLYSIS 10 0 k , c -1 Y Fig. 9. As fig. 7. Flow rate (cm3 min-') as follows: H, 60; A, 60/130; 0, 130; 0, unpromoted.amines is strong enough to make the gas-phase resistance mass-transfer controlling. This conclusion is supported by the experimental result that desorption rates obser- ved in parallel experiments on a continuously stirred tank reactor (CSTR) are higher than those on the sphere unit. The CSTR, which contains a propeller in the vapour space, has of course better gas-phase mass-transfer properties. An estimate of the gas-phase mass-transfer coefficient for desorption runs allows estimation of an upper bound fur a reliable estimate of E , at ca. 3. Therefore one can only conclude that rate promotion in desorption is large enough to make E,> 3. Absorption data from three runs for HDA-promoted solutions are shown in fig. 9. Taking the data as a set, all data points fall within *30% of the mean line.The differences from run to run are believed to be real, reflecting minor variations in solution composition, flow rate and amine manufacturer. It is important to notice that the values of E, corresponding to the HDA data in fig. 9 are of the order of 8, as compared to 4-5 for the DEA data in fig. 7. The actual measured rates show an even larger .difference between HDA and DEA promoters. Owing to the difference in VLE behaviour, at any given value of y the value of p - p * is larger for HDA-promoted than for DEA-promoted solutions. In the interpretation of absorption-rate data, such as that reported in fig. 7 and 9, it is useful to first consider whether the observed behaviour is consistent with the instantaneous-reaction (I-model) or fast-reaction (F-model) regimes of mass transfer.For the exact definitions and analysis of I-models and F-models, see ref. (4). Available absorption-rate data strongly support an I-type model, at least for the more efficient hindered amine promoter. The evidence is as follows. (i) Absorption rates are much less than proportional to the physical driving force, pi - p * . Fig. 10130 vl E 120 B -e 2 110 -2 0" 7 100 --a \ 0 Y c) 0 90 D. W. SAVAGE, G. SARTORI AND G. ASTARITA 27 I I I 200 250 300 350 t/min Fig. 10. Total COz absorbed (dm3) plotted as a function of time, t, for a one-sphere absorber. ( a ) Slope = 0.17 dm' min-', (b) slope = 0.14 dm3 min-'. At the point shown by the arrow the pressure was increased from 50 to 105 kpag.is a plot for a run where the driving force was increased abruptly by a factor of ca. 2; the corresponding increase of the rate of absorption is only ca. 20%. (ii) Rates of absorption on the one-sphere absorber seem to be strongly influenced by the value of the liquid flow rate, as an I-model would predict. (iii) Values of kL are much larger for promoted than for unpromoted solutions. Since the latter are well correlated by an F-model,, it is likely that an I-model prevails in systems containing highly efficient rate promoters. INTERPRETATION OF DATA The discussion below follows an approach to the interpretation of rate-promotion behaviour presented in ref. (10). We recall that, given any promoter, Prom, a sequence of chemical reactions is presumed to take place which can be written as (22) CO,+Prom --+ Int Int+R+Prom --+ S (23) where Int is some intermediate, R is the non-volatile reactant and S is the chemical sink for CO,.The thermodynamic analysis presented in the first part of this work shows that, over a rather wide range of y values, the main reaction taking place during absorption is essentially the transformation of the carbonate ion to the bicarbonate ion. Therefore, R can be identified with C03,- and S with HC03-. It is quite likely that Prom is the free (unconverted) amine, although for the case of a diamine such as HDA forms in which one of the nitrogen atoms is converted could conceivably act as promoters. What the intermediate, Int, may be is open to speculation. There are two mechanisms of rate promotion which have been considered in the literature: the shuttle mechanism (SM) and homogeneous catalysis (HC).In the SM-model, reactions (22) and (23) are separated by diffusion steps, with reaction (22) taking place within the concentration boundary layer and reaction (23) in the bulk of the liquid. In the HC-model, both reactions (22) and (23) take place in the concentration boundary layer.28 CARBON DIOXIDE HYDROLYSIS An absolute upper limit for a SM rate promotion can be calculated on the basis of the following two hypotheses: (i) Reaction (22) proceeds in the I-regime and is essentially irreversible. (ii) All the amine in the solution is present in the form of ‘promoter’ (presumably free amine). Both hypotheses are very approximate, and both lead to a gross overestimate of E,.Reaction (22) is unlikely to be almost irreversible, since its reverse is required to take place in the bulk of the liquid. Furthermore, as little as 20% of the total amine may be present in the ‘promoter’ (free amine) form, as shown by the thermodynamic analysis given earlier. In view of these considerations, actual values of E, are expected to be significantly less than the value Ep,max obtained from the above two assumptions. The analysis of the SM in the literature’ refers to the case where there is no rate enhancement in the unpromoted solution, and therefore cannot be applied directly to the case at hand. The relevant differential equations for the film-theory model, taking into account the unpromoted rate enhancement, are, however, easy to integrate.The result is where C, is the promoter concentration, D is the diffusivity, k is the kinetic constant for direct hydrolysis of C02 via reaction with the hydroxide ion and K’ is the equilibrium constant for the following reaction: H20 +C032- HCO, +OH- (25) and [CO,*-] and [HC032-] are bulk-liquid values. The value of the product kK is well known.’ for DEA-promoted solution based on the hypothesis that C, equals the total amine concentration. Observed values are much too large; it appears that in the solutions considered there is not enough free amine to allow for the observed rate promotion via an SM. An even stronger argument for rejecting the SM hypothesis is the fact that quite significant rate promotion is observed also in desorption.The discussion in ref. (10) clearly shows that a SM cannot be active in both absorption and desorption. We conclude therefore that, at high temperatures, the rate promotion of amines takes place through a homogeneous catalysis (HC) mechanism. The analysis based on the HC hypothesis is straightforward. Since the experimental data suggest an I-model, and the HC hypothesis implies that the overall reaction takes place in the interface region, the I-model equations apply directly. This is, of course, an absolute upper bound: all resistance due to chemical kinetics has been eliminated, and absorption proceeds at a rate governed simply by the diffusion of reaction products from the interface to the bulk of the liquid. The upper bound for the rate of absorption is based on the HC mechanism: Fig.1 1 is a plot of EP/ where y* is the value of y corresponding to equilibrium with pi and yo is the bulk-liquid value of y . Fig. 12 is a plot of N/(Nmax)Hc for absorption into DEA- and HDA-promoted solutions. The ratio N/(Nrn,x)Hc is less than unity for both promoters, and as a first-order approximation appears to be independent of fractional saturation. It should be borne in mind that (Nmax)HC was calculated by assuming that all diffusivities are equal; a correction for unequal diffusivities would result in a valueD. W. SAVAGE, G. SARTORI AND G. ASTARITA 29 1 0.8 g. 0.6 Qn 0.4 a 2 0.2 Y Fig. 11. Normalized promotion factor, Ep/Ep,max, plotted against C02 loading in solution, y. 0.2 0.4 0.6 Fig. 12. Normalized absorption rate, N / [ NmaxlHC, plotted against COz loading in solution, y.(---) DEA data, 90 "C. Shaded area: HDA data, 90 "C. (Note: 70 and 90 "C data almost coincide.) v of (Nmax)HC ca. 20% lower than the one shown. This seems to indicate that the HDA-promoted data are, within experimental accuracy, in agreement with the I-model predictions: the rate-promotion effect is so large that the CO, hydrolysis is practically instantaneous at the conditions of the experiments. Supporting evidence for an I-model based on HC is obtained by considering the fact that temperature seems to have no effect on the value of N/(NmaJHC. Once the chemical-kinetic resistance has been eliminated, any further increase in the magnitude of the kinetic constants does not result in additional rate increases.The fact that our data are well correlated by an I-model implies, unfortunately, that no actual values of kinetic constants can be extracted from them; however, a30 CARBON DIOXIDE HYDROLYSIS lower bound can be estimated. An I-model is justified if the following condition is ~atisfied:~ For the conditions of our experiments, this results in a lower bound estimate for the apparent pseudo-first-order kinetic constant of 1 O6 s-', an extremely (incredibly) large value. It is important to point out that, when a rate promoter is active enough to make the rate of CO, hydrolysis essentially instantaneous as compared with diffusional phenomena (i. e. when an I-model applies), the mass-transfer rates actually observed will be determined uniquely by the equilibrium behaviour of the system.In fact, given a value of the partial-pressure driving force for absorption, pi - p * , the rate of mass transfer is proportional to the corresponding liquid-phase driving force y f -yo [see eqn (25)], where y f is related to pi by the equilibrium condition, and so is yo to p * . Consideration of fig. 2 shows that, as the capacity of a solution is increased, so is the value of y: -yo corresponding to any given pi - p * . Therefore, for any two promoters which both yield an essentially instantaneous hydrolysis reaction, the one exhibiting the larger capacity will also exhibit larger rates. POSSIBLE CHEMICAL MECHANISM Since actual values of apparent kinetic constants for the catalysed rate of hydrolysis could not be extracted from our data, any attempt to interpret the underlying chemical mechanism is very difficult. The literature on reactions between C 0 2 and amines is abundant, and a recent paper gives a good review.'' However, most of the information available is concerned with systems where the amine acts as a reagent, rather than as a catalyst for CO, hydrolysis.The only analogue of the system considered in this work is the case of the reaction of C 0 2 with tertiary amines. In fact, even if the tertiary amine acts as a reagent, it does so simply by providing the basicity required to neutralize the HC0,- ion, which is the actual chemical sink for COz. (Since a tertiary amine cannot form a carbarnate, it could in a sense be regarded as being infinitely hindered.) However, there are several indications in the literature11-13 that the rate of C 0 2 hydrolysis in tertiary amine solutions is significantly larger than one would calculate from the known value of the kinetic constant for direct hydrolysis: CO2 +OH- + HCO,-.Furthermore, the rate appears to be proportional to the concentration of free amine and not to the concentration of hydroxide ions. This seems to indicate that tertiary amines act as homogeneous catalysts for reaction (28), via a mechanism of the type given by reactions (22) and (23), with P being the unconverted amine. Blauwhoff et a2." and Donaldson and Van Nguyen" hypothesize that the intermediate I may be a hydrated form of the amine; Y u ' ~ hypothesizes that it may be a zwitterion-type of weakly bonded amine-CO, intermediate.Drawing from the analogy with tertiary amines, the fact that HDA, with B == 0.3 and hence a high concentration of free amine (see fig. 3), is a good rate promoter makes sense. However, it is not clear why HDA should be a more effective catalyst by several orders of magnitude than the tertiary amines. We acknowledge the contributions of A. L. Bisio, J. N. Begasse, R. E. Noone and W. C. Yu to this work.D. W. SAVAGE, G . SARTORI AND G. ASTARTTA NOMENCLATURE DEA = diethanolamine HDA = hindered diamine rn = original K2C03 concentration in mol dmW3 R = original molar ratio of amine to K2C03 y = concentration of chemically combined C 0 2 in mol dm-3 f = fraction of amine converted g = fraction of amine converted to carbamate A = equilibrium constant for reaction (7) B = equilibrium constant of reaction (8) X rn K = equilibrium constant for reaction (1) H = Henry's-law constant for C02 p" = equilibrium partial pressure of C 0 2 p = p * K / H m N = mass-transfer flux pi = partial pressure of C02 at interface k; = value of kL in the absence of chemical reaction K' = equilibrium constant for reaction (24) y* = value of y corresponding to equilibrium with p , y o =bulk liquid value of y kL = N H / ( PI -P*> E p = (kL)prumoted/(kL)unpromoted 31 ' D. W. Savage, G. Astarita and S. V. Joshi, Chem. Eng. Sci., 1980, 35, 1513. S. V. Joshi, G. Astarita and D. W. Savage, Chem. Eng. Progr., Symp. Ser., 1981, 77, 63. G. Sartori and D. W. Savage, Ind. Eng. Chem., Fundam., 1983, 22, 239. G. Astarita, D. W. Savage and A. L. Bisio, Gas Treating with Chemical Solvents (J. Wiley, New York, 1983). D. Roberts and P. V. Danckwerts, Chem. Eng. Sci., 1962, 17, 961. G. Astarita, G. Marrucci and F. Gioia, 111 Europ. Symp. Chem. React. Eng., 1964, supplement to Chem. Eng. Sci., 1965. G. Astarita, D. W. Savage, Adu. Transport Proc., 1983, 3, 340. A. L. Shrier, P. V. Danckwerts, Znd. Eng. Chem., Fundam., 1969, 8, 415. F. Leder, Chem. Eng. Sci., 26, 1381. l o G. Astarita, D. W. Savage, J. M. Longo, Chem. Eng. Sci., 1981, 36, 581. " P. M. M. Blauwhoff, G. F. Versteeg and W. P. M. Van Swaaij, Chem. Eng. Sci., 1983, 18, 1411. l 3 W. C. Yu, Ph.D. Thesis (University of Delaware, 1984). T. L. Donaldson and V. N. Van Nguyen, Ind. Eng. Chern., Fundam., 1980, 19, 260.

ISSN:0301-7249    

DOI:10.1039/DC9847700017

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 33-46 Kinetics of Carbon Dioxide Transfer across the Air/ Water Interface BY WILLIAM A. HOUSE* AND JOHN R. HOWARD Chemistry Laboratory, Freshwater Biological Association, East Stoke, Wareham, Dorset BH20 6BB AND GEOFFREY SKIRROW Department of Inorganic, Physical and Industrial Chemistry, University of Liverpool, Donnan Laboratories, Grove Street, Liverpool L69 3 BX Received 29 th November, 1983 The transport rate of COz into aqueous solution may be augmented by a chemically enhanced flux caused by the hydration of COz. The importance of hydration reactions in controlling C 0 2 transport depends upon the solution composition and temperature as well as the hydrodynamic conditions at the air/water interface. The transfer has been examined under conditions approaching laminar flow at low Reynolds number.Factors considered to be important in determining the transport rate under these conditions include temperature, pH, alkalinity, solution flow rate and the gas-phase composition. The transfer rate is expressed in the form [c021= K,A([C02],-[C02],) d t where A is the surface area, V is the solution volume and C[C02] is the total inorganic carbon concentration. The subscripts s and b refer to the surface and bulk solution concentra- tions, respectively, and KL is the gas transfer velocity. The C02 concentration at the solution surface is determined by assuming equilibrium between the gas-phase C 0 2 and the solution. In the absence of chemical enhancement, the transfer velocity is independent of the pH and solution alkalinity and depends only on the temperature and hydrodynamic conditions at the interface.However, at high pH values the hydration reactions between OH- and C 0 2 cause deviations from the physical transfer model and K , may be predicted from the solution of a second-order non-linear differential equation subject to appropriate boundary conditions and electroneutrality at all points within the diffusion layer. A numerical model is presented which permits KL to be calculated for various degrees of chemical enhancement. Experimental results for a range of bicarbonate concentrations [(2-40) X mol dmP3] and C 0 2 gas-phase compositions are given. The effects of temperature (20-35 "C) and flow rate (100-500 cm3 min-') have also been investigated.The carbonate alkalinity ([HCO; J + 2[C:O;-]) has a pronounced effect on K , at high pH. The results are interpreted using the numerical model and compared with calculations based on the assumption of instantaneous hydration equilibrium. The effect of carbonic anhydrase on catalysing the hydration reactions is also briefly discussed. When disequilibrium exists between a gas phase and a solution, then net gas transfer between the two phases will occur. For C02 transport, physical dissolution is accompanied by hydration and ionisation reactions,' i.e. 3334 c02 TRANSFER k , k-2 C02+OH- HCO, K , H,COf HCO, +H+ [ref. (2)] K , HCO, COi- +H+ [ref. (3)] (IV) where KI and K2 are the dissociation constants of carbonic acid and H,CO$= C 0 2 +H,CO,. Reactions (111) and (IV) are instantaneous but the hydration reactions (I) and (11) are relatively slow and, in certain conditions, may limit the mass-transport rate of C 0 2 into solution.For example, at 25 "C k , = 0.026 s-I, i.e. tl12 = 26.7 s. The purposes of this work are to ascertain the factors controlling interfacial CO, transport and to develop a model to describe the transfer between gas mixtures and KHC03 + K2C03 solutions having carbonate alkalinities, a , (= [HCOJ +2[COi-]), similar to those of natural freshwaters. Although the major ion components in hard waters are calcium and bicarbonate, the susceptibility of pure solutions of Ca(HC03)2 to heterogeneous nucleation and precipitation of calcite at high pH prevents their use over a wide pH range. The addition of inorganic phosphate (ca.20 pmol dm--') may confer some metastability on these solutions, but even so it is difficult to attain and maintain the pH values characteristic of biologically productive freshwater canals4 and therefore of interest in this work. Air/water CO, exchange is important in a number of geochemical and biological problems. The potential climatological and other consequences of an increasing concentration of atmospheric C 0 2 has stimulated discussion on transfer routes and rates.'.* Much of this has centred around transport to the sea, since this is likely to be a major CO, sink. Because of their much smaller areal extent, freshwater systems will make only a trivial contribution to atmospheric C 0 2 buffering, and interest in transfer to them arises instead from its biological implications for par- ticular local systems.Additionally, many freshwater systems show not only composi- tions and alkalinities which differ considerably from those of the open sea, but also wide diurnal and seasonal pH ranges, matched only in the marine environment by localised waters such as rock pools. For these reasons, knowledge of the factors which control interphase CO, transport for a range of chemical and physical environments is needed. This investigation concentrates on CO, transfer from the gas phase to bicarbonate solutions showing approximately laminar flow. This model system should give information about the importance of reactions (I) and (11) in controlling the transfer and enable predictions to be made of gas transfer in our field system, the Leeds to Liverpool The complicating effects of turbulence in the solution phase were minimised by using a channel with dimensions such that the gas/liquid surface area was sufficient to permit measurable transfer over several hours but yet ensure laminar flow conditions for moderate (ca.1 cm s-I) flow rates. EXPERIMENTAL APPARATUS The trough (fig. I ) was constructed from 15 mm thick Perspex and was provided with a gas-tight removable lid. The solution was recirculated (via inlet and exit ports B and D) by means of an impeller pump (Gorman-Rupp) and the volume flow rate measured with aW. A. HOUSE, J. R. HOWARD A N D G. SKIRROW 35 E L , l L I Fig. 1. Recirculating trough used in the C 0 2 transfer experiments. Key: (A) gas inlet, (B) solution inlet, (C) gas outlet, (D) solution outlet, (E) aperture for electrode and platinum resistance thermometer, (F) baffle, (G) floats and (H) platform.Platon flowmeter (0-800 cm3 min-I). This rate was adjusted to within f 10 cm3 min-' using a Variac (MC401) to control the pump driver voltage. Baffle F and the entrance well ensured even distribution of the entering solution over the trough width. The gas mixture (see below) was vented via ports A and C at ca. 1 dm3 min An aluminium-sheet air thermostat provided temperature control to k0.2 "C. The trough was mounted on a platform ca. 6 cm above the base of the thermostat cabinet and air was circulated underneath the platform via two 75 W heaters and a cooling coil. This arrangement produced a uniform temperature within the cabinet.Air and solution temperatures were measured using two four-wire platinum resistance thermometers [conforming to BS 1904 grade I1 (DIN 43760)l in conjunction with a Kelvin double bridge. CO, + N, gas mixtures were prepared by mixing the individual pure-gas components using a volumetric mixing apparatus designed to allow flexibility in the selection and control of the composition. Fine-control pressure regulators provided a constant pressure source for each gas and a needle valve controlled the nitrogen flow rate from its source at 1 dm3 min-'. A Platon Flostat type MN controlled the C 0 2 flow in the range 1-60 cm3 min-' and automati- cally compensated for upstream pressure variations. Gas flow rates were measured using conventional 'plumb-bob' float flowmeters which were calibrated using bubble meters.Low COz flows ( ( 6 cm3 min-') were determined from the pressure difference developed across a 8 cm length of 0.2 mm i.d. stainless-steel tube using a dibutyl phthalate manometer. The C 0 2 and N2 streams were mixed in a bead-packed vessel and the resulting mixture brought to the experimental temperature and saturated with water before entering the trough. Gas-chromato- graphic checks of the gas composition agreed with those expected from the measured flow rates to within 4% over the C 0 2 partial-pressure range 0.003-0.02 atm." MATERIALS A N D PROCEDURE Solutions were prepared using A.R. grade potassium carbonate and potassium chloride with singly distilled water. Carbonic anhydrase was obtained from bovine erythrocyte (Sigma Chemical Co.).Carbonate alkalinities of the solutions used (0.002-0.04 mol dmP3) were periodically checked to within 0.1 % by Gran titration7 with standard HCI. The solution (300crn3) was introduced into the trough, the pH electrode and platinum resistance thermometer probe inserted into the solution via aperture E and through an opening in float G (see fig. 1) and the liquid circulation commenced. The pH was continuously monitored using a Radiometer PHM64 instrument and a combination electrode (GK232 1 C). This approach had obvious advantages over sampling methods, although care was needed in electrode calibration. Performance checks before and after each experiment were essen- tial. The solution was monitored for at least 30 min before initiating the gas flow.The digital * 1 atm= 101 325 Pa.36 coz TRANSFER Table 1. Characteristic parameters for laminar flow flow rate at 25” C/cm3 min-’ C/cm s-’ Re h,/cm h,/cm 113 0.41 83 2.1 38 329 1.19 240 6.0 110 545 1.98 400 10.0 184 output from the meter was input at 1 or 2 min intervals to a microcomputer and stored until the termination of the run. Subsequently they were used to calculate solution compositions and gas transfer velocities for particular pH values. HYDRODYNAMIC CONSIDERATIONS Preliminary experiments enabled the hydrodynamics of the liquid flow to be characterised, and on the basis of these adjustments were made to the baffle F, floats G and platform H (see fig. 1). For laminar flow in a rectangular tube ( i e . beneath the first float), the Reynold’s number, Re, is8 4R6 R e = - V where R is the hydrodynamic radius ( i e .the cross-sectional area divided by the wetted perimeter), 0 is the mean velocity of the flow and Y is the kinematic viscosity. Laminar flow is expected when Re < 2000. Calculated values for the final design (fig. 1) using 300 cm3 of solution and flow rates in the range 113-545 cm3 min-’ (table 1) fall below this limit. A flow rate of 329 cm3 min-’ was adopted for most experiments. The ‘entrance’ length, h, over which the parabolic profile is developed (Levich’) is given by h.rO.1 r R e (2) where r is the half-width of the profile. For a rectangular cross-sectioned tube, parabolic profiles develop in both the vertical and horizontal planes leading to ‘entrance’ lengths h, and hf, respectively (table 1).The length of the float G on the inlet side (10 cm) ensured proper development of the vertical profile before gas exchange occurred. The floats also prevented exchange in the ‘mixing wells’ immediately after the baffle F and near the exit port D. Table 1 shows that h,>> h,, thus indicating that plug flow across the trough may be assumed at moderate flow rates. The profiles were also examined by photographing the pattern which developed following injection of a dye at port D. Well developed parabolic profiles were observed in the vertical plane. THEORETICAL For given solution conditions, the flux ( J ) across the interface will be proportional to the surface area ( A ) and the difference in the CO, partial pressures of the gas and liquid phases (pco2 and Pco2, respectively).The CO, concentrations in the uppermost surface layer (in equilibrium with pco,) and in the bulk solution are given, respectively, by [C02], = apco, and [CO,] = aPco2, where a is the solubility coefficient, and for a solution of volume V (3)W. A. HOUSE, J. R. HOWARD AND G. SKIRROW 37 where 1 [CO,] is the sum of the inorganic carbon species and K L is the mass transfer velocity. A similar, equivalent, equation can be deduced from Fick's first law on the assumption that as CO, passes through the boundary layer it behaves as an unreactive gas (KL is then independent of the solution pH). In fact, because of the hydration processes KL will not be constant but is expected to increase with increasing pH.Even so, eqn (3) can be used to obtain experimental values for KL, i.e. Kypt'. The results can be interpreted according to the severity of the hydration augmentation of the exchange rate. Three exchange possibilities can be envisaged: (i) no hydration reaction during boundary-layer passage, (ii) hydration equilibrium attained at all points within the layer (chemical-equilibrium model) and (iii) partial hydration during boundary-layer passage (finite-reaction model). These are examined below, where (i) is shown to be a special case of (ii). C H EM IC AL- EQU I LI B RI U M MODEL (C EM) If hydration equilibrium is reached at all points within the boundary layer, then the theoretical maximum flux of CO, across the interface is attained and may be calculated [see e.g.ref. (lo)]. In the following, the boundary layer is assumed to extend from the surface (x = 0) to x = aeR where [CO,] = [CO,],. Sefi is the effective thickness of the diffusion boundary layer. From Fick's law at steady state we have d2ci dC[C02] EDi-= - j dX2 dt (4) where i refers to each of the CO,, HCO, and C0:- species. The total flux JT (defined as positive when the solution phase is gaining inorganic carbon) is given by From the charge-balance equation for a bicarbonate/carbonate solution when the pH is not too extreme, i.e. [H'] and [OH-] are small in comparison with [HCOJ and [COZ-1, it follows that d[M"] d[HCOJ+2 d[CO:-] dx dx dx ( 6 ) Z-- - where M'+ is the balancing metal ion of charge z. If it is assumed that -- -0 d[M'+] dx then d[HCO,] - 2d[CO:-] dx dx ' _ - The further assumption that DHCO; = Dco:- leads to JHCO; = -2Jco:-.Thus from eqn (5) and (8) the total flux is JT= JCOz + i J H C O ; (7) (9)38 or C02 TRANSFER Integration of eqn (10) between the surface and the limit when [CO,] = [co2]b at x = Seff produces Under conditions such that chemical reactions contribute insignificantly to the total flux, eqn (1 1) reduces to Comparison of eqn (3) and (12) shows the transfer velocity to be defined by (13) K exptl - L - DCOJSeff. The concentration gradients of COz, H+, HCO, and C0:- may be computed from the chemical-equilibrium model by determining JT using eqn (1 1) and by integration of eqn (10) from the surface to some point within the film. The chemical augmentation of the flux may be quantified by defining a relative flux augmentation parameter, JR: l o JR = (JT - JCO,)/ JC02- (14) FINITE-REACTION MODEL (FRM) The possibility that the hydration reaction (11) may be rate-limiting is now considered. Combination of Fick’s second law with the rates of reactions (I) and (11) when steady-state flux conditions are attained at all points within the layer yields a non-linear differential equation: D C 0 2 7 d2[C~21-[C02](k,+k,[OH-])-[HCO;](k-,[H’]- - L2).Use in eqn (15) of the reduced form: T’ = x/ Seff gives zp= Dco d2[Co21 [CO,](kl + k,[OH-I) -[HCO;](k-,[H+] + kP2). & dTt2 It is necessary to solve eqn (16) with the following initial conditions: is fulfilled.W. A. HOUSE, J. R. HOWARD AND G. SKIRROW 39 Eqn (16) incorporates [HCOJTt. This may be evaluated by integration of eqn (10) between the surface and position T" and making [HCOJTt the subject: The values of [OH-] and [H+] in eqn (16) are determined numerically from the charge-balance condition within the boundary layer given the values of [CO2IT+ and [HCOJ,t.Thus the method of solution requires a choice of ijetf and an initial value of [HCOJ,. A numerical solution of eqn (16) is then sought for the chosen value of [HCOJ,. If the solution does not meet the boundary condition [eqn (IS)], then [HCOJ, is adjusted in an iterative manner until this condition is met. In practice, it is convenient to define a reduced parameter p =[HCOJ,/[K'] in applying the iterative adjustment. The relative flux augmentation parameter [eqn (14)] and transfer velocity may then be calculated as for the chemical-equilibrium model.Two distinct numerical methods were used to solve the differential equation. Both are available in the Numerical Algorithms Group (NAG) library. Most of the computations were performed using the variable-step Adams method.' ' Some results were also checked using the variable-order, variable-step Gear method." The K , value was found to be independent of the tolerance parameter used in the NAG routine. This parameter controls the error in the integration and in the determination of the position where [CO,]-,t = [CO2Ib. The relationship between the tolerance parameter and accuracy in the solution, i.e. in T', cannot be guaranteed. For this reason, various tolerance parameters were used to estimate the accuracy of the final KL.In all the calculations, p was adjusted iteratively to a relative accuracy of 10- '. RESULTS AND DISCUSSION In this analysis the thermodynamic constants KI and K 2 , the Henry's law solubility coefficient of C 0 2 and K , were taken from ref. (2), (3), (1 2) and (13), respectively. The rate constants and diffusion coefficients are given in table 2. STANDARD-CO NDITION EX PER1 M ENTS The reproducibility and calculation procedures were tested under predefined experimental conditions. Solution alkalinity and flow velocity were chosen to he similar to those of the freshwater system being studied (carbonate alkalinity, 0.004 mol dm-3; linear flow rate, ca. 1 cm s-'). For convenience, the temperature was chosen as 25 "C and the gas-phase partial pressure of C02 controlled at 0.008 f 0.0005 atm.These conditions caused the solution to absorb C02. The microcomputer stored the pH values at 1 min intervals. These were subsequently used in a 7-point quadratic smoothing routine to generate dpH/dt at 0.1 pH intervals in the pH range 10-7.6. Values of d 1 [CO,]/dt were then calculated from the relationship in which d C [CO,]/dpH is the CO, buffer capacity of the bicarbonate so1ution.16 The apparent equilibrium constants were calculated using the Davies equation17 for the activity coefficients. For the KHC03 + K2C03 solutions used, no correction for ion-pairing was needed. The experimental transfer velocity, Krptl, for each pH was computed using eqn (3).40 co2 TRANSFER Table2. Constants used in the data analysis k2 Dcoz k , / s - ' /dm3 mol-' s-' / m2 s-' T/"C [ref.(14)] [ref. (14)] [ref. (15)] 20 0.0 173 5900 1.785 25 0.0257 8500" 2.043 30 0.0373 12 400 2.320 35 0.05 I3 17 387 2.614 a Ref. (1). 1.6 1.2 o a - I 0.4 1 .o 0.6 0.6 0.4 Fig. 2. (a) Results from experiments in standard conditions (alkalinity 0.004 mol dm-3, 25 "C, flow rate 329 cm3 min-', pco2 = 0.008 f 0.0005 atm). 0, Mean of 4 experiments with standard deviations shown; (---) predicted by CEM; (-) predicted by FRM. (b) Alkalinity 0.002 mol dm-3 but otherwise standard conditions. a, Mean of 2 experiments ; (- - -) predicted by CEM; (-) predicted by FRM.V . A. HOUSE, J. R. HOWARD AND G. SKIKROW P 41 Fig. 3. ( a ) Alkalinity dependence of KYp" at 25 "C, flow rate 329 cm3 min-', pcoz = 0.008~0.0005atm. x, 0.002; U, 0.004; A, 0.01; 0, 0.02; 0, 0.04moldm-3.Solid lines are predicted from FRM. ( b ) Alkalinity dependence of K , predicted by CEM at 25 "C. W, 0.004; A, 0.01 ; 0, 0.02; 0, 0.04 mol dm-3. The mean results from four experiments are shown in fig. 2(a) together with the standard deviations. Transfer velocities decreased smoothly with descending pH and reached a plateau at pH < 8.2. The standard experiment was repeated at regular intervals to check the equipment performance. EFFECTS OF ALKALINITY AND IONIC STRENGTH The dependence of Kypt' on the solution alkalinity at 25 "C was investigated for the alkalinity range 0.002-0.04 mol dmP3 using K,CO, solutions and a gas-phase partial pressure of COz of 0.008+0.0005 atm. All the experiments were performed with a flow rate of 329 cm3 min-'.The results are shown in fig. 3(a). It was expected42 CO2 TRANSFER that the hydration reactions and the effects of chemical augmentation by HCO, and CO:-- ions would be less important at the lower alkalinities. For alkalinities below 0.00 1 rnol dm-3 the slowness of transfer made measurements impractical. The results summarised in fig. 2(b) are the mean of two experiments for an alkalinity of 0.002 mol dmP3 and were analysed using both the CEM and FRM. A program for use with the CEM minimised the quantity (where n is the number of data points) by systematically adjusting Seff. The agreement between the experimental and the CEM K L values obtained with the optimum SeE (Sefi=413 p m ; y=O.O12) is shown in fig. 2(b). This value of Seff was used in the FRM calculations.Fig. 2(b) shows that the transfer velocities are in good agreement with both models for pH < 9.4, but in the higher pH region (where the two model predictions diverge) the FRM gives better agreement. At pH 9.4 the predicted relative flux augmentation is 0.94 (FRM) and 0.97 (CEM). In view of the agreement between the two models at an alkalinity of 0.002 mol dm-3, the effective diffusion-layer thickness was fixed at 413 pm. This was considered to be a satisfactory compromise between using the more complex FRM to perform the optimisation and using a set of less reliable data for the transfer into 0.001 mol dmP3 alkalinity solution, where better agreement with the CEM at higher pH is expected. data for the higher alkalinity, 0.004 mol dmP3, and the comparisons are shown in fig.2(a). Flux-augmentation predictions based on the two models are also given. For this alkalinity JR(CEM) has risen to 1.99 at pH 9.4, and in general the difference between the two transfer-velocity predictions increases with increasing alkalinity. The particularly large increases in the transfer velocity with increasing alkalinity predicted by the CEM should be noted [see fig. 3(b)]. For example, at the alkalinity 0.04 mol dm-3 and pH 9.5, the CEM predicts a transfer velocity of 14.3 x m s-' compared with Kyptl of 2.69 x m s-I. The corresponding FRM prediction is 2.50 x loP5 m s-'. Fig. 3(a) summarises the overall agreement between the calculated (FRM) and experimental results for the alkalinity range examined. The effects of ionic strength are less dramatic.Transfer velocities were measured using 0.004 mol dm-3 alkalinity solutions with concentrations of KCl in the range 0.01-0.1 mol dmP3. An increase in KL of 0.15 x lo-' m s-' for the highest ionic strength solution at high pH values decreased to an undetectable amount below pH 8.1. This result was found to be in good agreement with the theoretical predic- tions from the CEM. Interpretations based on both models have been compared with observed EFFECT OF THE GAS-PHASE COMPOSITION The applied C02 partial pressure was expected to have a large effect on KFptl particularly in the high pH region, where chemical augmentation fluxes are sig- nificant. The lowest partial pressure that could be used was determined by the slowness of the transfer reaction.All the experiments were performed at 25 "C and 0.004 mol dmP3 alkalinity with partial pressures in the range of 0.03-0.0004 atm. values obtained with pcoz close to 0.008 atm are shown in fig. 4(a), together with the KL (FRM) predictions. As pco2 decreases, the rate-limiting effect of the hydration reaction increases, as shown by the changes in JR in table 3. K exptlW. A. HOUSE, J. R. HOWARD AND G. SKIRROW 43 3.2 2 .4 1 .6 7 0.8 E 4: m Lc, I \ h 0 0 Y .- - z 2.0 2 c" 2 U 1.6 1.2 0.8 O L I 7.6 8.0 8.4 8.8 9.2 96 10.0 PH Fig. 4. ( a ) pco2 dependence of KYpt' at 25 "C, flow rate 329 cm3 min-', alkalinity 0.004 mol dmP3. @, 0.0179; 0, 0.008; 0, 0.0027 atm. Solid lines are predicted by FRM. ( b ) Effect of temperature on KYpt' for alkalinity 0.004 mol dm-3, flow rate 329 cm3 min-', pco2 = 0.008 f 0.0005 atm.X , 20; 0 , 2 5 ; @, 30; 0,35" C. Solid lines are predicted from FRM. Tabte3. Comparison of results from the theoretical models with the experimental data to illustrate the effect of varying pCo2(carbonate alkalinity = 0.004 mol dm-3, 25 "C) chemical-equilibrium finite-reaction- model rate model Kexptl L PH PCO2 KL/ m s-' J R K J loP5 m s-' JR 10-5 rn s-l 9.8 0.0179 1.4 1.7 1.25 1.5 1.12 9.8 0.008 2.3 3.8 1.80 2.6 1.60 9.8 0.0027 6.2 11.6 2.53 4.1 2.43 8.2 0.0179 0.53 0.07 0.53 0.07 0.5 1 8.2 0.008 0.58 0.16 0.57 0.15 0.55 8.2 0.0027 0.70 0.42 0.64 0.29 0.6344 co, TRANSFER 0.2 I- Fig. 5. Flow-rate dependence of KYPt' under otherwise standard experimental conditions. 0, 113; -0-, 221; 0, 329; 0, 545 cm3 min-'.EFFECT OF TEMPERATURE Duplicate measurements of the transfer velocity at temperatures in the range 20-35 "C for 0.004 mol dmP3 alkalinity solutions and pco2 = 0.008 f 0.0005 atm are shown in fig. 4(b). The constants used at the selected temperatures are given in table 2. The value of Seff = 413 p m was retained throughout the temperature range. Observed KTpt' data and KL (FRM) predictions agree reasonably at 20, 25 and 35 "C. Agreement at 30 "C is less satisfactory and may reflect inadequacy in the selection of constants. These results support the assumption that Seff is not sensitive to small changes in temperature. EFFECT OF FLOW RATE The use of volume flow rates in the range 113-545 cm3 min-' (but otherwise standard conditions) showed a five-fold increase in flow to have a small but distinct effect on KPpt' (see fig.5). Below pH 9 this amounted to a difference of ca. 0.28 x loP5 m s-' in KFpt'. Interpretation in the pH range 7.80-8.60 using the CEM showed JR to be <0.4 for all the flow rates and good agreement between the CEM arid FRM was obtained. Using the CEM, the optimum values of Seff (for the pH range 7.8-8.6) were found to be 612,467,427 and 352 p m for flow rates of 113,221, 329 and 545 cm3 min-', respectively; the minimum values of y [eqn (20)] were 0.024, 0.007,0.006 and 0.009, respectively. The value of at 329 cm3 min-' is in agreementW. A. HOUSE, J. R. HOWARD AND G . SKIRROW 45 PH Fig. 6. Effect of carbonic anhydrase on the transfer velocity at two alkalinities (otherwise standard conditions): (a) alkalinity 0.01 mol dm-3, ( b ) alkalinity 0.002 mol dm-3.0, No carbonic anhydrase; a, with carbonic anhydrase (1 mg dm-3); (-) CEM predictions. with 413 pm, the value derived using the entire data between pH 9.70 and 7.80. For the flow-rate range examined, the empirical relationship 6,* = 445 (1 / U)0-34 with 6 in cms-' was noted. CATALYTIC EFFECT OF CARBONIC ANHYDRASE The enzyme carbonic anhydrase (which occurs in many marine and freshwater organiSms where it probably has important C02 exchange/respiratory functions) has been reported18 to catalyse the hydration reactions. Experiments were made at 25 "C for solution alkalinities of 0.002, 0.004 and 0.01 mol dmP3. The concentration of carbonic anhydrase was arbitrarily adjusted to 1 mg dm-3 to allow comparisons with the work of Berger and Libby on seawater." The results are shown in fig.6.46 coz TRANSFER The enzyme has a considerable catalytic effect at higher pH values. Transfer velocities increased but failed to attain the CEM predictions. The 20-fold increases reported by Berger and Libby were not found. In the lowest alkalinity solution, no catalytic effect could be discerned over the pH range 9.5-7.5. This lends further support to our conclusion that the COz transfer in these conditions is adequately described by the CEM. CONCLUSION The transfer of CO, into bicarbonate solutions has been investigated in a systematic manner under near-laminar-flow conditions. The transfer velocity is a complex function of the solution alkalinity, ionic strength, pH, temperature, gas- phase composition and flow rate.The finite-reaction-rate model has been used to successfully predict the transfer velocity in different solution conditions. At low pH the chemical-equilibrium model is adequate and has a number of advantages over the finite-reaction-rate model. The calculationS become far simpler and may be performed on a microcomputer. In addition, this model is particularly useful in investigating the effects of flow rate under conditions where the hydration reactions of C 0 2 are not markedly influencing the transfer rate. This enables the evaluation of for subsequent application in solution conditions where the hydration reactions become important. We are pleased to acknowledge the advice given by Dr R. G. Compton concerning the hydrodynamics and apparatus design and Mr G. I. Williams for developing the electronics associated with the apparatus. This work is part of a project supported by the Natural Environment Research Council. We thank N.E.R.C. for an award to J.R.H. and the Freshwater Biological Association for financial support to J.R.H. D. 31. Kern, J. Chem. Educ., 1960. 37, 13. ' H. S. Harned and R. Davis Jr, J. Am. Chem. SOC., 1943, 65, 2030. ' H. S. Harned and S. R. Scholes. J. Am. G e m . Soc., 1941, 63, 1706. ' W. S. Broecker, T. Takahashi. H. J. Simpson and T. H. Peng, Science, 1979, 206, 409. ' T. hi. L. Wigley, P. D. Jones and P. 31. Kelly, Narure (London), 1980, 283, 17. ' G. Gran, Analysr (London), 1952, 77, 661. J. R. Howard, G. Skirrow and W. A. House, Freshwater Bid., accepted for publication. R. Y. Giles, Schaum's Outline of Theory and Problems of Fluid Mechanics and Hydraulics (McGraw- Hill, New York, 1962). ' V. G. Levich. Physicochenrical Hydrodynamics (Prentice-Hall, Englewood Cliffs. N.J., 1962). p. 112. J. A. Quinn and N. C. Otto, 1. Geophys. Res., 1971, 76, 1539. G. Hall and J. M. Watt, Modern Numerical ibfethods for Ordinary Diferenrial Equations (Clarendon Press, Oxford, 1976). 10 I' R. F. Weiss. Marine Chem.. 1974, 2. 203. l 3 A. K. Covington, hl. A. Ferra and R. A. Robinson, J . Chem. SOC., Faraday Trans. I , 1977,73, 1721. I' A. Akperman and J . L. Gainer, J. Chem. Eng. Data, 1972, 17. 372. B. R. M'. Pinsent, L. Pearson and F. J. W. Roughton, Trans. Faraday Soc., 1956, 52, 1512. J. Saednia, PIi. D. Thesis (University of Liverpool, 1980). C. N.. Davies. J. Chem. Soc.. 1938. 2093. R. Berper and W. R. Libb}, Scietice. 1969, 164, 1395. I4 Ih 17

ISSN:0301-7249    

DOI:10.1039/DC9847700033

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. C . Tondre (University of Nancy, France) said: I have two questions that I would like to address to Prof. Astarita, one concerning the thermodynamic aspects of the work presented and a second related to the kinetic aspects. Concerning the first point it seems that the stability constant of the carbamate [eqn (8) and (17)) is an adjustable parameter in his treatment. One could probably obtain a good estimate of this parameter (at least for DEA) by the use of the product of the equilibrium constants of the individual reactions into which eqn (8) can be split: H2C03 S CO,+H,O (1) HCO,+H+ H2C03 (2) CO, + RNH + RNCOO- + H'. (3) The equilibrium constants for reactions (1) and (2) are well known, and in the case of DEA the equilibrium constant for reaction (3) has been obtained from stopped- flow experiments' and confirmed by 13C n.m.r.measurements.2 Has Prof. Astarita tried to measure the stability constant of HDA by such techniques? I come now to the kinetic part of my question: the authors seem to admit that the main contribution to C 0 2 absorption is not carbamate formation but rather the base-catalysed hydration reaction, and they mention a lower-bound estimate for the kinetic constant of 1 O6 s-'. Whereas the contribution of base-catalysed hydration reactions is probably significant for tertiary a m i r ~ e s , ~ - ~ the values obtained for the second-order rate constants are quite low (of the order of 3 to 5 dm3 mol-' s-') and for primary or secondary amines such a contribution is expected to be negligible compared with carbamate formation and pure hydration reactions.1,6 Carbamate formation has been suggested7 possibly to take place in two steps: (i) formation of a zwitterion by the attack of CO, on the nitrogen atom and (ii) a proton-removal step from the zwitterion, which can be base-catalysed. Could the influence of the amine on this last step be an explanation for the base-catalysis observed? Could the carbamate itself not be a sink for C02? Is it a question of pH? ' D. Barth, C. Tondre and J. J. Delpuech, Int. J. Chem. Kinet., 1983, 15, 1147. ' D. Barth, P. Rubini and J. J. Delpuech, Noun. J. Chim., 1983, 7 , 563. T. L. Donaldson and Y. N. Nguyen, Ind. Eng. Chem., Fundam., 1980, 19, 260. D. Barth, C. Tondre, G. Lappai and J. J. Delpuech, J. Phys. Chem., 1981,85, 3660. P.M. Blauwhoff, G. F. Versteeg and W. P. Van Swaaij, Chem. Eng. Sci., 1983, 38, 141 1. D. E. Penny and T. J. Ritter, J. Chem. SOC. Faraday Trans. 1, 1983, 79, 2103. P. V. Danckwerts, Chem. Eng. Sci., 1979, 34, 443. Dr. W. A. House (Freshwater Biological Association, Dorset) said: The chemical promoters have two effects: they catalyse the C02 hydration reaction and increase the capacity of the carbonate solutions for C02. Does Prof. Astarita know if the catalytic effect is maintained at low concentrations (1 mmol dmP3 or even 1 pmol drnp3) of promoter? Prof. H. Linde (Academy of Sciences of the G.D.R., Berlin) (communicated): In connection with the papers of Prof. Astarita and Dr. House I would like to consider the following problems. The promotion effect is strong enough in comparison with 4748 GENERAL DISCUSS I 0 N the hydration reaction to make the rate of adsorption and desorption controlled by mass transfer, i.e. strongly influenced by the value of the liquid flow rate.Is it possible that differences in the flow rate of the interface itself caused by interfacial dynamic effects have an additional and different influence on the transfer rate? Usually interfacial dynamic surface renewal depends strongly on its amplification by Marangoni instability due to driving forces and the resulting direction of mass- and/or heat-transfer and/or chemical reaction, as well as on damping of surface renewal by adsorption layers by the mechanism of Gibbs-Marangoni elasticity. For very clean water surfaces the amplification of surface renewal by Marangoni instability functioning as an intensification effect is possible. For water surfaces contaminated with even small amounts of surface-active agents or with absorption layers, additional damping effects of the forced surface renewal have to be taken into consideration under conditions of slow forced convec- tion (see Dr.House’s paper). If the flow velocity and surface dimensions are small enough, as in the experiment reported in fig. 1 of the paper, at least a part of the water surface is expected to be stagnant because of unfavourable contamination by adsorption layers. For extended water surfaces with very slow forced convection only, this stagnant layer, stemming from natural and man-made contamination is to be expected and causes the damping effect. Accordingly, stronger forced convection and extended surfaces are at the condi- tions required to break the adsorption layer and to reproduce the adsorption rate appropriate to the level of surface renewal.Prof. G. Astarita (University of Naples, Italy) said: There is one general point which needs to be clarified with regard to several of the questions which were asked. In our experiments the concentration of amine was never >30% of that of carbonate, and was often significantly less than that; therefore, the capacity of the solution is essentially due to the carbonate, and the main effect of the amine is to act as a rate promoter and not as a reactant. We have done some experiments with lower amine concentrations, although none at concentrations so low as to have no effect on capacity, and certainly nothing as low as 1 mmol dm-3.We have some indication that the catalytic effect would not be observable at extremely low amine concentra- tions. There are several reasons for our interpretation of the data in terms of homogeneous catalysis, rather than a shuttle mechanism, and these are discussed in the paper. The most relevant is that the shuttle mechanism, even with simplifying assumptions leading to a gross overestimate of the rate promotion, cannot account for the magnitude of the observed rates. As for the question of bifunctionality, we have also performed experiments with hindered monoamines, which exhibit very similar results. The amine used in the industrial process, for which results have been presented, has a second amino group added mainly to increase its solubility in concentrated carbonate solutions. It is true that, in the thermodynamic modelling, the value of B is treated as an adjustable parameter.However, the best fit with the data is obtained with B = 0.3, which is in good agreement with an independent estimate based on n.m.r. data. It is also true that carbamate stability data for ‘conventional’ amines do exist in the literature. However, the essentially novel feature of hindered amines is the very fact that they form carbamates which are remarkably less stable than those of conventional amines. As stated in the paper, the data are such that actual values of kinetic constants cannot be extracted from them, and therefore any discussion of the underlyingGENERAL DISCUSSION 49 'CI I 50.5- f 0 , 4 r.+ .- L1 2 ;=" 0.3 2 + 0.2 chemical mechanism is highly speculative. It is also possible that with hindered amines zwitterion formation is the first step; however, the following steps should lead to the formation of the bicarbonate, which is the chemical sink for carbon dioxide. The value of H represents the ratio (at equilibrium) of the partial pressure to the concentration of physically dissolved carbon dioxide; therefore in no way is it related to the capacity of the solution. We have assumed it to be the same as in unpromoted solution, and we believe this to be a reasonable assumption. Further- more, the results of the analysis are very insensitive to the value assumed for H, since instantaneous reaction conditions are approached.In reply to Prof. Linde's communicated remark I note that our experiments were conducted on a one-sphere liquid-gas device. The gas-liquid interface appeared by visual inspection as very smooth and regular, and therefore gross interfacial instabilities can be ruled out. Of course we have no way to ascertain that no microscopic instabilities did occur. However, the data are in reasonable agreement with those one would calculate for instantaneous reaction conditions on the assump- tion that no such instabilities are present, and therefore if they are present their effect must be no larger than the experimental inaccuracy. To answer Dr. House, I would merely say that we have no direct experimental evidence on the catalytic effect at very low amine concentrations.0 . o o o o o o o . 0 0 0 O 8 0 - a m i o;o&& a 0 . . .. OO*O .. 0 O ~ r W a. - 0 . I I I I 1 I I I I I I Dr. W. A. House (Freshwater Biological Association, Dorset) (communicated): In response to Prof. Linde's communicated comment, I emphasise that, as shown in fig. 5 of our paper, the effect of flow rates in the range 0.41-1.98cms-' was measured. As expected, the flow rate does affect the film model in a reduction in Seff, the diffusion boundary layer thickness. We have not analysed our results using a surface renewal-model because of the defined hydrodynamics in our experimental arrangement. Well developed parabolic profiles were observed in the vertical plane of the trough and plug flow in the horizontal plane.A slide of the parabolic profile was shown to participants at the Discussion. There is no evidence for Marangoni instabilities caused by adsorption of surface- active agents in our experiments. Presumably such effects would have been detected E 0 . 6 1 0 050 GENERAL DISCUSSION in the photographs of the dye flowing in the trough. Experiments were also per- formed using clean Ca( HC03)2 solutions and were compzred with results of transfer experiments using natural water from a canal and a chalk stream. The results have not been published, but are shown in fig. 1 of this Discussion. The results obtained from the two systems are in close agreement. The freshwater samples would be expected to contain surface-active agents and any additional resistance they caused would have reflected in changes in KL.However, we have made no systematic study of the effect of surface-active agents or insoluble monolayers under our experimental conditions. Dr. M. Spiro (Imperial College, London) (Communicated): In their theoretical treatment of the chemical-equilibrium model (CEM), House et al. included the assumption that the trace diffusion coefficients D of HCO, and C0:- are equal. This can be tested by making use of the Nernst relation' for any ion i DP = (RT/F2)(AY/zT) where R is the gas constant, T the absolute temperature, F the Faraday constant and zi the charge number of the ion. The values of the limiting molar conductance, A:, are known for both ions in aqueous solution at 25"C, being 45.42 and 138.5' S cm2 mol-' for HCO, and CO:-, respectively.Hence DO(HC0;) = 1.209 x D"(CO:-) = 0,922 x a difference of 31%. Both values will be smaller at finite ionic strengths.' theory of the CEM. Let us therefore write m2 s--' and m2 s-' Fortunately the assumption of equal diffusion coefficients is not essential to the D(HC0,) = [D(CO:-). According to Stokes' law, the [ value of 1.3 1 will not vary much with temperature. Then Fick's first law, together with eqn (7) of the paper, leads to the following revised equations: J(HC0,) = -2tD(CO:-) (8') JT = J ( C02) + 1 -- J ( HCO,) = J ( C02) + 0.62J( HCO,). ( 2 2 (9') The change from 0.5 to 0.62 in eqn (9) will affect the bicarbonate terms in subsequent equations such as (1 1) and (19). The optimum value derived from the data in fig. 2(b) of the paper should therefore be increased accordingly.' R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworths, London, 2nd edn, 1959), pp. 317 and 463. G. F. Cassford and A. D. Pethybridge, unpublished work. Dr. W. A. House (Freshwater Biological Association, Dorset) (communicated): Our assumption given after eqn (7), D(HCO,)=D(CO:-), was based on the rigid-sphere model in which the tracer diffusion coefficients are inversely propor- tional to the square root of the molecular weights. I agree with Dr. Spiro's comment that this restriction in the theory could have been avoided by using the Nernst relationship for D"(HC0,) and D"(CO:-) although there is uncertainty about theGENERAL DISCUSSION 51 effects of ionic strength on the diffusion coefficients.As Dr. Spiro shows, the effect of the assumption is to alter the magnitude of the chemical augmentation term in eqn (9). The non-augmented flux, J ( C02), remains unaltered. Repeat calculations with the revised diffusion coefficients for D(HC0,) and D(COf-) at an alkalinity of 0.002 mol dm-3 and otherwise standard conditions, show that the effect on KL is <0.1 x lo-' m s-' below pH 8. The additional augmentation flux will thus have a small effect on the evaluation of 6,ff determined for the various flow rates (see fig. 5 of our paper) and over the pH range 7.80-8.60. The general question of the choice of appropriate diffusion coefficients is difficult because of the range of experimental values reported in the literature at any temperature. A major source of error in estimating Sefi concerns D(C02).Differen- ces of up to 20% are obtained between the best theoretical predictions of D(C02) and experimental values in the temperature range 6.5-65 OC.' It is also worth noting that reliable experimental values of the limiting molar conductance of CO5- are not available for temperatures other than 25 "C and until recently2 were not available for HCOT. They can, however, be estimated using the Walden rule and the limiting molar conductances at 25 "C. I A. Akgerman and J. L. Gainer, J. Chem. Eng. Data, 1972, 17, 372. G. E. Cassford, Ph.D. Thesis (University of Reading, 1983), p. 130. Mr. V. K. Cheng (Monash University, Australia) (communicated): Perhaps I was confused by the drawing in fig. 1 of Dr. House's paper. Could he clarify why the platform H is considerably smaller in size than that of the trough.Surely the intrusion made by the platform in the water trough will induce turbulent flow at the edge of the platform. If the water level above the platform is not sufficiently high, the movement of the gas/water interface may be turbulent as well. Was there any competition between the maintenance of constant temperature and laminar fluid flow when the size of the platform was varied? The F.R.M. model assumes the coupling of the slow rate-determining steps (I and 11) at the interface and the mass transfer of products through the interfacial diffusion layer. Reaction I1 would suggest that the rate of hydration increases with pH. As a result, at lower pH the rate-determining characteristic of steps I and I1 and the deviation between the fitting of data with the F.R.M.and C.E.M. would be expected to be more marked. How do the accumulation of products from the various elementary steps and the mass-transfer characteristics, such as the concentration gradient of the reactants and products, relate to each other by the numerical models and by intuitive expectations? Dr. W. A. House (Freshwater Biological Association, Dorset) (communicated): The main reason for introducing platform H was to ensure mixing and thus even distribution of the solution in the 'well region' upon entering the trough from tube B. The platform H is smaller than the trough to produce the depression at the entrance. The position of the baffle F was found to be critical in ensuring that plug flow developed across the trough. No experiments were done with different sizes of platform. The 'well region' also provided a convenient section in the mixed solution for the temperature probe and pH electrode. With the flow rates used in these experiments, namely 2.0 > C/cm s-l> 0.4, the dye profile was photographed and found to be parabolic in the vertical plane. At higher flow rates some turbulence caused by the baffle and platform did develop, and so the hydrodynamic conditions were unsuitable for gas-transfer experiments.52 GENERAL DISCUSS I 0 N The hydration reactions occur at the air/water interface and as C02 passes through the diffusion boundary layer. Thus concentration gradients in COz, HCO,, COi- and H+ occur across the boundary layer. At the lower pH values (typically pH <8), the chemical augmentation flux is a small contribution to JT. The rate of the hydration reaction (11) depends on both [OH-] and [CO,] and the dehydration reaction upon [HCOJ [see eqn (16) of our paper]. Consequently the reaction moves to chemical equilibrium within the film with decreasing pH. As the pH decreases from 10 to 8 [CO,] and [HCO,] in the solution increase. For a fixed gas-phase composition the concentration gradients of HCO, and C0:- across the boundary layer decrease, leading to a large reduction in the second term in eqn (11).

ISSN:0301-7249    

DOI:10.1039/DC9847700047

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chern. SOC., 1984, 77, 53-65 Kinetics and Mechanism of Interfacial Reactions in the Solvent Extraction of Copper BY W. JOHN ALBERY,* RIAZ A. CHOUDHERY AND PETER R. FISK? Department of Chemistry, Imperial College, London SW7 2AY Received 13 th December, 1983 The rotating-diffusion-cell technique for studying reactions at liquid/liquid interfaces has been applied to the study of the kinetics and mechanism of the extraction of Cu2+, using an oxime ligand. The technique has been extended by using a ring electrode in the ring-disc configuration to measure the flux of Cu2+ when it is stripped from the organic phase into strong acid. Both extraction and stripping reactions have been studied at various acid concentrations. In the extraction direction the rate of reaction is first order in Cu2+ and first order in oxime at low concentrations of both reactants; at higher concentrations a limiting rate is observed.In the stripping direction a zero-order reaction is observed. This behaviour is interpreted in terms of an interfacial reaction in which the rate-limiting step is the attachment of the first oxime to Cu2+. The study of the kinetics of systems reacting at the interface between two liquids requires first an interface of defined area, and secondly control of the mass transfer bringing the reactants to the interface and taking the products away. Without control of the area and the mass transfer the measurement of rate constants and the deduction of mechanism is fraught with difficulty. We have therefore developed the rotating- diffusion-cell method14 for the study of such systems.In this method the liquid/liquid interface is established by surface tension on the pores of a Millipore filter. This defines both the location and the area of the interface. The filter disc is then rotated. The hydrodynamics of a rotating disc are known, and the transport of material to and from the disc surface has been calculated by Levich.’ The apparatus is illustrated in fig. 1. The use of a baffle ensures that one obtains the correct hydrodynamics and transport on both sides of the disc.’ The rate of reaction can be followed by analysing the composition of the solution in the outer or in the inner compartment. We have shown that a particularly sensitive method is the use of a pH-stat to titrate acidic or basic products of the reaction, thereby providing a continuous record of the rate of reaction and its variation with rotation speed.14 In this paper we describe a further development of the technique, in which the filter-paper disc is surrounded by a ring electrode to provide a second method, by which one can obtain a continuous measurement of the flux of the chemical species leaving the disc surface.The ring-disc electrode is a well established technique in electrochemistry.‘ Both the pH-stat and the ring-disc methods have been applied to a study of the kinetics and mechanism of the solvent extraction of copper using the oxime ligand ‘Acorga P50’. Over half a million tonnes of copper are produced by this method per annum. The reaction scheme is as follows: Cu:: + 2HL,, C U L ~ , ~ ~ ~ + 2H& t Present address: Ciba-Geigy Industrial Chemicals, Manchester.5354 where HL is SOLVENT EXTRACTION OF COPPER PULLEY PERSPEX CYLINDER BAFFLE TREATED FILTER UNTREATED FILTER GOLD ARC SILVER PAINTED CONTACT Fig. 1. The rotating diffusion cell. The lower diagram shows the ring-disc arrangement on the lower side of the filter paper. In our studies the organic phase is n-heptane. In the extraction direction, where the copper is being transferred into the organic phase, the reaction is followed by the pH-stat titrating the H+ as it is released. We have studied this reaction over a range of pH from 2 to 4. The stripping reaction in the opposite direction takes place when the pH is less than 1. It is therefore impossible to use the pH stat method. Instead the ring-disc technique is used to monitor Cu2+ entering the aqueous phase by measuring the current from the reduction of Cu2+ on the ring electrode. These kinetic studies allow us to conclude that the reaction takes place on the interface between the two liquids, and to determine the mechanism and rate-limiting step of the reaction.EXPERIMENTAL GENERAL The rotating diffusion cell and apparatus have been described previously.’ The Millipore filter disc is treated with clearing solution (33% n-hexane, 33% 1,4-dioxane and 34% 1,2- dichloroethane) to collapse the pores, leaving a small untreated disc in the centre; it is on this small central disc that the reaction takes place. We have improved the procedure for making the disc by mounting the filter on a lathe and then painting on the clearing solution using a paint brush and a cylindrical template.In this way good well centred discs can be made. The ‘ring’ electrodes were made by evaporating gold on to the Millipore filter surfaceW. J. ALBERY, R. A. CHOUDHERY AND P. R. FISK 55 through a mask. Instead of making a complete ring, we found it easier to make an arc that subtended ca. 70". Two such arcs were evaporated around each disc, so that there was a replacement if the first arc failed. Electrical contact was made by a strip made of evaporated gold strip and then of painted silver running to the outer circumference of the disc and then up the side of the rotating cylinder as shown in fig. 1 . This strip was insulated from the solution by painting it with Perspex cement. The counter-electrode was made of platinum gauze and the reference electrode was a saturated calomel electrode (SCE).To reduce Cu2+ the ring electrode was potentiostatted at -0.4 V; all potentials are reported with respect to SCE. The collection efficiency' of the ring-disc depends on the geometry. The radius of the disc, r , , and the internal and external radii of the arc, r2 and r,, respectively, were measured by using a travelling microscope on the lathe. Measurements along at least 10 diameters were made. The angle subtended by the arc was measured by making an enlarged photograph of the assembly. The collection efficiency was calculated in two ways. In the first method average values of the radii were calculated and the usual formula' was then applied.In the second method the formula was applied to each segment in turn and the overall collection efficiency found by summing the contributions from each segment. No significant difference was found between the results from the two methods. When the pH is less than 4 a given flux produces a smaller change and therefore special precautions need to be taken in using the pH-stat to follow the reaction. A Burr-Brown 3627 amplifier was fitted to the top of the glass electrode to act as an impedance converter, thereby reducing pick-up in the leads to the electrode. All chemicals were of AnalaR grade, except for the Acorga P50 and 4-nonylphenol, which were kindly supplied by Dr R. F. Dalton of ICI. RESULTS AND DISCUSSION RING-DISC TECHNIQUE The new ring-disc technique was tested in two ways.First the cell was.filled with 0.2 mol dm-3 K2S0,; an aliquot of Fe(CN):- was added to the inner compart- ment and the flux measured by the arc electrode and by measuring Fe(CN);- spectrophotometrically in samples taken from the outer compartment. In the second method 1,4-diaminobenzene was added to the inner compartment; the flux of this compound could be simultaneously measured by oxidising it on the arc electrode and by titrating it with the pH-stat. In both experiments good agreement was found between the flux measured by the arc electrode and that measured either spec- trophotometrically or by the pH-stat. RESULTS FOR EXTRACTION Fig. 2 shows typical results for the flux,j, for the extraction reaction as the oxime concentration, the metal concentration and the pH are varied.At low concentrations of oxime or metal the reaction is first order in both oxime and metal. However, as the concentration of oxime or metal is raised the reaction rate reaches a limit. This type of behaviour is typical of a surface reaction where the surface becomes saturated. The results at pH 3 show that the rate is slower by a factor of 3 compared with the rate at pH4. Experiments at p H 2 showed that the extraction rate was decreased by a further factor of 2 compared with the rate at pH 3. The Levich equation for the rotating-disc electrode states that the thickness of the hydrodynamic boundary layer, Z,, is given by5 where Y is the kinematic viscosity, D is the diffusion coefficient and W is the rotation speed in Hz.56 SOLVENT EXTRACTION OF COPPER [HL]/rnrnoi dmP3 20 c 6 [Cu2+]/rnmol dmP3 Fig.2. Typical results for the extraction reaction at a rotation speed of 2.9 Hz. In A [Cu"] was 10 mmol dm-3 and the pH was as follows: X, 4.0; 0, 3.0. In B [HL] was 67 mmol dmP3 and the pH was 4.0. We have shown'-4 that the flux,j, is usually given by an equation of the form j - ' =j;l + aZ,/Dc (2) wherejo is the flux at infinite rotation speed, a. is the area of the pores divided by the geometric area and c is the concentration of a reactant. The second term in eqn (2) describes the effect on the flux of transport through the diffusion layers. By plotting j - ' against W-'I2 one can extrapolate to find j,, which describes the flux at infinite rotation speed where mass transport in the diffusion layers is insignificant. Fig.3 shows typical results plotted in this way for the extraction reaction at p H 4 for a series of different oxime concentrations. Reasonable straight lines are found. We have added the product, CuL2, to the inner compartment to see if the extraction rate was inhibited by the product. Addition of CuL2 up to a concentration of 60 mmol dm-3 made no significant difference to the rate. RESULTS FOR STRIPPING Fig. 4 shows typical results for the stripping reaction in 3.0 mol dm-3 H2S04. These results have been plotted using a modified form of eqn (2):W. J. ALBERY, R. A. CHOUDHERY AND P. R. FISK 57 0.0 0.0 0.2 0.4 0.6 0.0 (W/Hz)-l’* Fig. 3. Typical results for the extraction reaction plotted according to eqn (2).The pH was 4.0 and [Cu”] was 10 mmol dmA3. [HL] in mmol dm-3 was as follows: 0, 13; X, 20; 0, 100. c l j = c / j o + aZ,/D (3) where c is the bulk concentration of CuL2. It can be seen that as c is varied the gradients of the different lines are the same, and this agrees with eqn (3). If the reaction at the interface was first order in CuL2, then all the lines would have a common intercept. This is not found. We may conclude first that the kinetics of the reaction at the interface are significant, and secondly that the order of the reaction with respect to CuL2 is less than unity. Similar plots are found for the results in 1.5 mol dmP3 H2S04. Fig. 5 shows intercepts from these experiments plotted against c. The linear variation with c corresponds to a rate-limiting step at the interface that is zero order in CuL2.It is satisfactory that the intercepts of the plots for the two different acid concentrations are in good agreement and correspond to the diffusion of CuL, through the filter. It is clear that the zero-order rate depends on the acid concentration; it is faster in 3 mol dm-3 H2S04, where the fluxes are close to transport control. The variation of the stripping rate with the concentration of H+ is shown in fig. 6. The kinetic step at the interface is roughly first order in acid. We have also found that the stripping reaction in 1.5 mol dm-3 H2S04 is inhibited to some extent by the addition of free oxime. Fig. 7 shows results for two different58 SOLVENT EXTRACTION OF COPPER QO 0.2 0.4 0.6 0.8 ( W / Hz)-”’ Fig.4. Typical results for the stripping reaction in 3 mol dm-3 H,S04, plotted according to eqn (3). The [CuL,] in mmol dmP3 were as follows: 0, 10; V, 36; A, 65; 0, 100; X, 161. values of c ; only modest effects are observed even for concentrations of L as large as 300 mmol dmP3. LOCATION OF THE REACTION It has been suggested that the reaction takes place entirely in the aqueous phase8 by a mechanism in which a limited amount of ligand would dissolve in the aqueous phase and there complex the copper before returning to the organic phase. In the stripping direction CuL, would dissolve in the aqueous phase and then dissociate. Using stopped-flow spectrophotometry we have measured k,, the second-order rate constant for complex formation, to be ca.lo5 dm3 mol-’ s-I. This value implies that the reaction length would be smaller than the diffusion length of the rotating disc. Under these conditions the flux for extraction would obey the following equation: j = (k,D[cu’+])’”[L]. j = ( ~ , D ) ’ ” [ C U L ~ ~ . The flux for stripping would be (4) ( 5 )W. J. ALBERY, R. A. CHOUDHERY AND P. R. FISK 59 8 0 1 I I so 100 1 so 200 0 1 [CuL,]/mmol dm-3 concentration of H2S04 in mol dm-3 was as follows: X, 1.5; 0, 3 . Fig. 5. Intercepts of plots, similar to those shown in fig. 4, plotted against [CuL,]. The 40 30 - m N I E - g 20 : 10 01 I I I 0 1 2 3 [ H,SO,]/mol dm-3 Fig. 6. Rate of the stripping reaction at a rotation speed of 4 Hz plotted against [H,S04]; the [CuL,] was 100 mmol dmP3.60 SOLVENT EXTRACTION OF COPPER A 1 [HL]/mmol dmP3 [HL]/mmol dm- Fig.7. Effect on the rate of the stripping reaction of the addition of free ligand to the organic phase. The rotation speed was 2.5 Hz and [H2S04] was 1.5 mol dm-3. In A [CuL,] was 10 mmol dmV3 and in B it was 100. The orders with respect to the reactants in these equations do not agree with those found above. This model does not explain the limiting rates observed in the extraction and the zero-order rate with some inhibition by HL in stripping. We therefore conclude that the reaction does not take place in the aqueous phase, but does take place on the interface. THE KINETIC MODEL We propose the following model for the interfacial reaction: organic 2HL HL HL CUL, KL k , L. k, k3 k - I k-2 k-3 interface HL CuL+ === HL,CuL' CuL, F= aqueous cu2+ cu2+ H+ H+ 2H' 2H+ We assume that at equilibrium each of the species HL, CuL' and CuL2 absorb on the interface according to a Langmuir isotherm and that the constant for HL is KL.W.J. ALBERY, R. A. CHOUDHERY AND P. R. FISK 61 Steady-state analysis of the model gives the following expression for the flux j , where j is positive for extraction and negative for stripping: $1 $2 $3 where K , = k,fk-, n is the number of sites on the interface in mol ern-,, xHL is the fraction of sites occupied by HL, rn, is the surface concentration of Cu2+ in the aqueous phase, co is the surface concentration of CuL, in the organic phase and 1, is the surface concentration of HL in the organic phase. The fraction, xHL, is given by: empty HL CuLt CuL, As indicated, the left-hand side of eqn (6) contains three terms corresponding to the three transition states. If one of the transition states is clearly rate limiting, then its term will dominate the left-hand side of eqn (6).The right-hand side of this equation describes the thermodynamics of the system. It will be zero at equilibrium. The first term will dominate for irreversible extraction giving a positive value of j ; the second term will dominate for irreversible stripping giving a negative value of j . Turning to eqn (7) for xHL, as indicated, the left-hand side describes the competition for the sites, when it is governed by thermodynamics. The terms in j on the right-hand side describe how the thermodynamic distribution may be pertur- bed by reaction taking place on 'the interface.Substitution of eqn (7) in eqn (6) followed by elimination of xHL gives such a complicated result that it cannot be used for mechanistic diagnosis. A better procedure is to obtain simpler expressions by assuming that one of the terms on the left-hand side of eqn (6) is dominant. The results for irreversible extraction and stripping are collected in table 1. THE RATE-LIMITING STEPS Inspection of the results in table 1 show that it is unlikely that transition state 2 is rate limiting. In the extraction direction, unless the Kimo term is significant, the reaction would be first order in rn, throughout; on the other hand if that term is significant, then the flux would pass through a maximum as rnoincreased. Thus this expression cannot explain the limiting flux observed in fig.2. In the stripping direction a similar argument applies to the variation of the flux with co. The reaction is first order in co unless the last term in the bracket is significant, and, if it is, then the flux would pass through a maximum as c, increased. In fact the reaction is zero order in c,. The remaining expressions for extraction in table 1, E$l and ES3, do contain terms that can explain the observed rate laws; each expression has a term that is first order in rn, and first order in lo and a term, k3, that gives a common limit at high concentrations of either Cu2' or of HL. Similarly the remaining expressions for stripping, SSl and SS3, both contain the required zero-order term k-,. In table 2 we collect together various inequalities that are required for the different combina- tions of an extraction and a stripping expression; these are based on the dominance of the terms in eqn (6) and on the insignificance of the penultimate terms in E$3 and S$1.The fact that the zero-order limits observed in the extraction and stripping62 SOLVENT EXTRACTION OF COPPER Table 1. Expressions for the flux from eqn (6) and (7) dominant term in irreversible extraction eqn (6) n / j = irreversible stripping - n / j = Table 2. Inequalities for combinations of extraction and stripping expressions expressions inequality however reactions are comparable means that at first sight the E$l, S f l and E$3, S33 combinations are unlikely. However, as we shall see below it may be that k, is not responsible for the zero-order limit in extraction.In that case it is possible to have the E$l, S$l combination. The E$3, S$l combination is ruled out because the change in acid concentration means that the inequality changes in the wrong direction. The reverse is true for the most likely combination, EZl, S$3, where the change in acid concentration alters the inequality in the correct direction. As one drives a sequence of irreversible steps harder the rate-limiting transition state will be found earlier in the sequence. To evaluate the rate constants we need a value for n, the number of sites. From the geometry of the oxime ligand we estimate that n = 0.5 nmol ern-?. (8) Using this value, in the stripping direction, from the data in fig. 5 we can find a value for kPl in 1.5 mol d ~ n - ~ H,SO4: kl = 60 s-’.(9) The data in fig. 6 show that this step is roughly first order in H’. The inhibition of the reaction by HL is too small to be certain about which other term is responsible. In the extraction direction there is no product inhibition so we can ignore the co term in ES1 in table 1. Fig. 8 shows plots of the intercepts,j,’, from thej-’/ W-”’ plots for series of experiments at constant bulk [Cu2+] plotted against [HLI-’.W. J. ALRERY, R. A. CHOUDHERY AND P. R. FISK 63 Table 3. Analysis of data in fig. 8. [CU2+] gradient KLk, KL PH /mmol dm-3 /ks cm-’ /dm3 mol-’ ms-’ /dm3 mol-’ 4 10 1.6 4 100 1.4 3 10 8 3 100 CQ. I 2.5 1.6 2.8 12 15 8 - Reasonable straight lines are obtained. Results for the gradients are collected in table 3 .First of all, at pH 3 we find that as expected from the first term in E$l the gradient is inversely proportional to [Cu”]. Comparing the experiments at [Cu”] = 10 mmol dm-, we find that increasing acid decreases the rate. In their respective acidity ranges both k , and k - , vary with [H+]. This means that there must be two parallel routes, and the simplest hypothesis is k , k , I HL + Cu2+ 3-* L- + Cu2’ + H’-+ CuL’ + H+ extraction: k-1 stripping: H++CUL+ ;-* HCUL~+ --* HL+CU~+. In the extraction direction one would then find that Substitution of eqn (10) in ES1 and ignoring the co term gives In the results discussed above the H’ term dominated giving a k , step that was first order in Cu” and inhibited by H’. At large concentrations of Cu” (100 mmol dm-‘) and at pH4, this term becomes small.The results in fig. 8 and table 3 show that the gradients are very similar. From the gradients we can conclude that the two terms are approximately equal at pH 4 when m,, = 10 mmol dmP3. Hence k - , / k , , == 100. For reactions close to diffusion control, this seems a reasonable result. Using eqn (10) and ( 1 1) we can calculate the values of K L k , given in table 3. Reasonably constant values are found. Inspection of eqn (1 1) shows that the limiting reciprocal flux at high concentra- tions of Cu2 ’ and HL is given by the sum of l / k , and l / k,. Unfortunately our data are not precise enough to make an unambiguous distinction between these two terms. In either case we find k, or k3 == lo2 s-l. (12) If the k , term is negligible then eqn ( 1 1) shows that we can find K , from the intercept on the x axis. Results are given in table 3.Again reasonably constant values are found. Furthermore the value of k , in eqn (12) is close to the value to be expected for the dissociation of an acid of pK 9. In the bulk homogeneous phase the pK of Acorga P50 is 9.5.964 SOLVENT EXTRACTION OF COPPER 0.3 - I 0.2 5 E u? 1 - !< 0.1 0.0 A I I I I .o 0 0.05 0.1 0 01 5 0.20 [HL]-l/drn3 rnmol-' 0.0 I I I I I 0 5 10 15 20 [HL]-'/dm3 rnol-' Fig. 8. Intercepts from plots, similar to those shown in fig. 3, plotted against [HLI-'. In A the pH was 4.0, and in B it was 3.0. The concentrations of Cu2+ in mmoldm-3 were as follows: (A) 0, 10; X, 100; (B) 0, 10; X, 100. Although more work is required on the fine details of the mechanism, the salient features are clear.Transition-state one is the most rate limiting in both the extraction and stripping directions. IMPLICATIONS FOR EFFICIENT SOLVENT EXTRACTION First of all from the results in fig. 2 and table 3 we can see that when the oxime concentration is > 150 mmol dmP3 the rate reaches a limit. This concentration is therefore the optimum oxime concentration, and is close to the concentration actually used in practice of 200 mmol d ~ n - ~ . ' ' In the extraction direction the limiting rateW. J . ALBERY, R. A. CHOUDHERY AND P. R. FISK 65 as given by eqn (8) and (12) is ca. 50 nmol cm-2 s-'. Under typical extraction conditions the concentration of Cu2' is 0.1 mol dm",'' and the radius of the droplets, r, is ca.100 pm." The transport limited flux, jL, is given by j , = D[cu~+]/ r == 100 nmol cm-2 s-I. Hence the system is close to being governed by the mass transfer of Cu2* to the interface. In the stripping direction we have found in 1.5 mol dm-' H,SO, that the zero- order rate as given by eqn (8) and (9) is ca. 30 nmol cm-- s-'. A similar argument suggests that under these conditions the system is again evenly balanced between kinetic and transport control. Increasing the acid concentration above 1.5 mol dm-3 would therefore lead to no significant increase in the rate of stripping since mass- transfer control would become dominant. Therefore this concentration of acid, which is the one used in practice, is probabIy the optimum concentration. We thank the S.E.R.C. and I.C.I. for financial support. We are grateful to Dr R. F. Dalton for helpful conversations. We thank Mr M. J. Pritchard for making the rotating diffusion cells, Dr M. .I. Lee for making the evaporated-ring electrodes and Mr L. R. Svanberg for assistance in pH-stat measurements. ' W. J. Albery, A. M. Couper, J. Hadgraft and C. Ryan, J. Chem. SOC., Faraday Trans. 1, 1974,70, ' W. J. Albery, J. F. Burke, E. B. Leffler and J. Hadgraft, 3. Chem. SOC., Faraday Trans. I , 1976, ' W. J. Albery and J. Hadgraft, J. Pharm. Pharmacol., 1979, 31, 65. ' V. G. Levich, Pbysicochemical Hydrodynamics (Prentice-Hall, New Jersey, 1962). 1124. 72. 1618. W. J. Albery and P. R Fisk, Hydrometallurgy, 1981, F5, 15. W. J. Albery and M. L. Hitchman, Ring-Disc Electrodes (Clarendon, Oxford, 1971). W. J. Albery and S. Bruckenstein, Trans. Faraday Soc., 1966, 62, 1920. R. J. Whewell, M. A. Hughes and C. Hanson, in ISEC'77 (Canadian Institute of Mining and Metallurgy, 1979) vol. 21, p. 185. J. S. Preston and R. J. Whewell, S. Inorg. NucC. Chem., 1977, 39, 1675. l o R. F. DaIton, personal communication. " J. Giles, C. Hanson and H. A. M. Ismail, in Industrial and Laboratory Nitrations, A.C.S. Symp. Ser. No. 22, ed. L. F. Albright and C. Hanson (A.C.S., Washington D.C., 1976), chap. 12.

ISSN:0301-7249    

DOI:10.1039/DC9847700053

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. Soc., 1984, 77, 67-74 Separation of Metal Ions by Ligand-accelerated Transfer through Liquid Surfactant Membranes BY DARSH T. WASAN* AND ZHONGMAO M. Gut Illinois Institute of Technology, Chicago, Illinois 606 16, U.S.A. AND NORMAN N. LI UOP Inc., Des Plaines, Illinois 60016, U.S.A. Received 5 th December, 1983 The rate of extraction of heavy-metal ions is greatly accelerated by the presence of a ligand in the aqueous solution containing the metal ions. The ligand effect on interfacial mass-transfer rates has been defined by measuring the rate of extraction of cobalt by di-2-ethylhexyl phosphoric acid using sodium acetate as ligand in a modified Lewis cell. The effect of a surfactant such as polyamine on mass transfer at liquid/liquid interfaces has been investigated and is found to be quite significant.This interfacial resistance to metal extraction by surfactant-membrane processes must be taken into account when modelling such systems. Since the discovery of liquid surfactant membranes for the separation of hydro- carbons over a decade ago,’ this novel separation technique has been widely studied. It appears that liquid membranes may potentially become effective tools for the separation and purification of many substances. In recent years many authors have reported their studies on the recovery and enrichment of valuable heavy metals2-* and the removal of trace contaminants from waste water.’”’ The formation of liquid surfactant membranes and the general separation process have been described elsewhere.” For metal-ion extraction in the liquid-membrane system, the process can be facilitated by utilizing the mechanism of carrier-mediated tran~port.’~”~ In this type of facilitation, an ion-exchange reagent is incorporated in the membrane phase to carry the diffusing species across the membrane to the receiving phase. As an example, the extraction of cobalt is achieved according to the following chemical reactions: extraction: 2HR + Co2+ $ CoRz + 2H+ org.aq. org. aq. (1) stripping: 2H’ + CoR2 G Co2’ + 2HR aq. org. aq. org. where HR represents the protonated form of a liquid exchange agent which is used as the carrier or ‘transport facilitator’. In this system, extraction [eqn (l)] occurs at the membrane/external-aqueous-phase interface while stripping [eqn (2)] occurs at the membrane/internal-aqueous-phase interface.The cobalt is effectively concen- trated in the encapsulated phase of the emulsion by the continuous permeation of hydrogen ions from the encapsulated phase to the external phase. T Permanent address: Institute of Atomic Energy, Academia Sinica, Beijing, China. 6768 LIGAN D-ACC ELE RATED METAL- ION EXTRACT10 N continuous encapsulated extraction stripping Fig. 1. Mechanism of ligand-accelerated liquid-membrane extraction. M = metal, L = ligand and MR = cxtractant. A kinetic study has shown that the process of the extraction of cobalt by di-2-ethylhexyl phosphoric acid (D2EHPA) is s10w.l~ This has also been shown by the published kinetic data for the extraction of cobalt by a liquid surfactant mem- brane.l 5 In our recent experiment on the liquid-membrane extraction of cobalt we found that the introduction of certain anionic ligands (such as acetate) to the aqueous solution containing Co2+ greatly accelerated the extraction rate,16 This phenomenon coincides with the effect found by some other authors. ''-I9 The ligand effect combined with the previously discussed mechanism of carrier- mediated transport becomes the mechanism of ligand-accelerated liquid-membraoe extraction, illustrated in fig. 1. In a liquid-surfactant-membrane system, surfactant is usually incorporated into the membrane phase for its stability. Adsorption and orientation of surfactant molecules at the membrane/aqueous interface lead to the formation of dense, viscous interfacial films which often offer considerable resistance to metal-ion transfer through a liquid-surfactant-membrane system.. In order to elucidate the effect of ligands on the liquid-surfactant-membrane extraction of heavy-metal ions, interfacial mass-transfer rates were determined for the extraction of cobalt(i1) by di-2-ethylhexyl phosphoric acid using a stirred liquid-liquid contactor (Lewis cell). The effects of different ligands on the kinetics of the extraction and the influence of the surfactant on the interfacial resistance to mass transfer were examined in the present study. EXPERIMENTAL LIQUID-MEMBRANE EXPERIMENTS The liquid-membrane phase was composed of 20-40 g dm-3 ECA 4360, 2-5'10 (v/v) D2EHPA and LOPS. ECA4360 (a non-ionic polyamine, from Exxon) was added as a surfactant, D2EHPA (di-2-ethylhexyl phosphoric acid, from Sigma) was used as an extractant and LOPS (low-order paraffin solvent, from Exxon) was used as membrane solvent and hadD .T. WASAN, Z . M. GU AND N. N. LI 69 an average molecular weight of 180, a specific gravity of 0.799 and a viscosity of 2.6 cSt at 60 O F (ca. 289K). The internal-phase concentration of the liquid membrane was 50-200 g dm-3 H2S04, which served as a stripping agent. The external aqueous phase of the liquid-membrane system was a CoSO, solution containing 1000 ppm Co2+. The initial pH value was adjusted to 5.0. The water-in-oil emulsion was prepared by mixing a 50 cm3 solution of the internal aqueous phase with a 50 cm3 solution of the oil membrane phase in a Waring blender for 2 min at ambient temperature.The prepared emulsion was examined microscopically and the internal droplets were found to be < 1 pm in diameter. The emulsion (40 cm3) was then added to a 400 cm3 vessel containing 200 cm3 of the CoSO, solution to be extracted. The system was stirred by a variable-speed mixer equipped with a marine-type impeller; the mixing speed was 200 r.p.m. Samples of the raffinate were taken periodically and analysed with a Beckman U.V. spectrophotometer for cobalt concentration. During the experiments, the feed solution was preconditioned with different ligands, such as acetate, tartrate, salicylate, succinate and formate, to investigate their effects on the mass-transfer rate. INTERFACIAL MASS-TRANSFER MEASUREMENTS All interfacial kinetic studies were conducted in a Lewis cell.The Lewis cell consisted of a cylinder 10 cm in diameter and 8 cm high. The cylinder was constructed of two 4 cm long glass pipes of 10 cm id., which were clamped between two flat end plates. These and all other metal parts inside the cell were made of stainless steel. The two glass sections were separated by a circumferential baffle, which, together with the central baffle, divided the cell into two identical halves, each of 250 cm3 volume, the interfacial area (the annular gap) being 27.3 em'. The two stirrers of the two phases were driven by two variable-speed d.c. motors (from Boding Electric). The stirring-speed range was 0-300 r.p.m. In order to obtain meaningful results, mass-transfer data for different systems should be compared for the same pH value.Therefore a pH controller (from Cole-Parmer) was used to control the pH of the aqueous phase. In each run the 250 cm3 organic phase contained LOPS as solvent and 5% (v/v) D2EHPA as extractant, and the 250 cm3 aqueous phase was a CoCI, solution containing 500 ppm Co2+. The pH value of the aqueous phase was maintained at 4.6 f 0.1 during the course of experiment. The ligand effect was examined by adding different ligands at various concentrations to the aqueous phase. The effect of surfactant on interface mass transfer was investigated using different con- centrations of ECA 4360. RESULTS AND DISCUSSION Several ligands were tested and their effects on the liquid-membrane extraction kinetics of cobalt are shown in fig. 2. Among these ligands, acetate was found to be the most effective.With no ligand in the aqueous feed solution it took ca. 15 min for 80% cobalt recovery, while only 2min were needed for 98% recovery in the presence of 0.1 mol dm-3 acetate in the continuous aqueous phase. An examination of the ligand effect reveals that the selected ligands act as phase-transfer catalysts and accelerate the transfer of the metal ions from one phase to Some author^'^,'^ have pointed out that some hexa-aquo-metal complexes are very inert kinetically, so that the extraction of metal ions from the aqueous phase to the organic phase is limited by the speed of the release of water molecules. However, the introduction of certain anionic ligands to the aqueous phase may accelerate the extraction rate significantly. It is assumed that the added ligand replaces the coordinated water molecules surrounding the metal ions to form a70 LIGAND-ACCELERATED METAL-ION EXTRACTION 1000 n 800 v t N 0 c 2 600 .- CI Y E LOO s 200 c V 0 2.0 L.0 6.0 8.0 10.0 tlmin Fig.2.Effect on the kinetics of different ligands in the external phase: X, no ligand; 0, acetate; A, succinate; 0, formate; 0, tartrate (all ligand concentrations 0.1 mol dm-3). thermodynamically less stable but a kinetically more labile complex with the metal ions [CO(H20)6]2+ +2Ac- CO(H~O),.(AC-)~ +2H20. Such an intermediate ligand-metal complex reacts rapidly with an organic extractant such as D2EHPA and/or with the surfactant at the interface between the membrane phase and the aqueous phase to form either a binary complex CO(H,O),.(AC-)~ +2HR C O R ~ +2Ac- +4H2O aq- org.binary aq. aq. complex or a ternary complex C O R ~ + R'NH2 R'H~N-CO-R~ ternary complex where HR is D2EHPA and R'NH2 is polyamine. The whole extraction process is accelerated in this manner. The equilibrium extraction experiments on the distribution coefficients of Co" as a function of the hydrogen-ion concentration with and without the addition of acetate to the aqueous solution as well as our n.m.r. and visible absorption spectral observations revealed that the ligand does not enter the organic-membrane phase. 16,20,2 1 Thus the thermodynamic equilibrium for extraction has not been changed by the addition of the ligand to the aqueous phase. INTERFACIAL MASS-TRANSFER STUDY Several organic ligands were tested to examine their effects on the kinetics of the extraction of cobalt by D2EHPA. In all the cases studied, 0.03 mol dm-3 of different ligands were added to the aqueous phase.The stirring speed of both phases was 150 r.p.m.D. T. WASAN, Z . M. GU AND N. N. LI 71 500 4 00 t 'b 300 0 0 C r- .- 2 zoo U e u c 8 I00 1 1 1 1 1 0 0.5 1 .o 1.5 2 .o t l h Fig. 3. Effect of various ligands (0.03 mol dm-3) on the kinetics of cobalt extraction: A, no ligand; 0, salicylate; A, formate; 0, succinate; 0, acetate. Table 1. Mean value of overall mass-transfer coefficients, K,, and the interfacial resistance to mass transfer, Fi, within the first hour of mass transfer for the extraction of cobalt by D2EHPA with the addition of 0.03 moldrnn3 of different ligands to the aqueous phase ligand k,/ I o - ~ cm s-' yi/ IO* s cmP3 - salicylate formate succinate ace tat e 0.094 105.7 1.64 5.0 3.5 1 1.7 5.34 0.8 6.09 0.5 The kinetic curves for the extraction of cobalt(i1) on the addition of different ligands to the aqueous phase are shown in fig.3. The mean value of the overall mass-transfer coefficients within the first hour of extraction, K,, and the related interfacial resistances, Fi, for different ligands in the aqueous phase were calculted and the values are given in table 1. The sequence of the ligand effect for the different ligands is: acetate > succinate > formate > salicylate. These data show that the ligand effect of the different ligands is in good agree'ment with that found in our liquid- membrane study of the extraction of cobalt(I1) (fig. 2).Acetate is confirmed as being the best ligand for accelerating the extraction. The effect of ligand concentration on the kinetics of the extraction of cobaIt(I1) by D2EHPA is shown in fig. 4. Here the average interfacial resistance, Ti, calculated within the first hour of mass transfer is plotted as a function of the concentration of sodium acetate, which acts as the ligand.72 LIGAND-ACCELERATED METAL-ION EXTRACTION [acetate]/mol dtn-.j Fig. 4. Inte,rfacial resistance as a function of sodium acetate concentration. In the present system there is no surfactant other than D2EHPA (extractant) in the organic phase and acetate (ligand) in the aqueous phase. Both D2EHPA and acetate exhibit weak surface activity and their relative concentration at the water/oil interface is favourable for cobalt extraction.Therefore the estimated interfacial resistance should be attributed to the extraction reaction occurring at the interface. In the absence of a ligand in the aqueous phase Ti is as high as 10.57 x lo3 s cm-I ; it decreases to approximately zero after >0.025 mol dm-3 acetate is added to the aqueous phase, as shown in fig. 4. This result indicates that the ligand effect changes the slow interfacial chemical reaction to a very fast reaction. From fig. 4 it can be seen that the ligand effect increases sharply when the concentration of acetate in the aqueous phase is <0.01 rnol dmP3. The ligand effect reaches a maximum ( i e . the minimum value of interfacial resistance) near 0.025 mol dm acetate and then remains constant over a wide range of acetate concentration.Since the initial concentration of Co2' in the aqueous phase is 500ppm ( i e . 0.0083 moi dm - 3 ) , the 0.025 mol dm-3 acetate in the aqueous phase is approxi- mately three times as high as the molar concentration of Co7+ ions. This implies that the reaction for the extraction of cobalt(1r) by D2EHPA at the water/oil inter- face is accelerated after 2 or 3 coordinated water molecules surrounding the Co2+ ions are replaced by acetate ions. A further increase in sodium acetate concentration (>0.2 mol dm-3) slightly decreases the ligand effect. This can be explained by the competitive extraction of sodium with cobalt. The effect of surfactant on the interfacial mass transfer has been reported to be significant in many previous s t ~ d i e s .~ ~ - ~ ' In our study of extraction by a liquid surfactant membrane, ECA4360, a non-ionic polyamine, was used as surfactant to stabilize the liquid membrane. The influence of this surfactant on cobalt extraction was also in:-cstigated. With the presence of a surfactant in the organic phase, note that for the extraction process at the water/oil interface the interfacial resistance to mass transfer results from chemical kinetic resistance as well as from the interfacial barrier caused by surfactant orientation at the interface hindering the passage of solute across the interface. Also, it has been shown in fig. 4 that with the addition of >0.025 mol dm-3 acetate to the aqueous phase the interfacial resistance to mass transfer because of chemical reaction may be overcome by means of a ligand effect.2.0 I I E c 1.0 vi m 0 I L- D.T. WASAN, Z . M. GU AND N. N. LI 73 1 o-2 [ECA4360]/mol dmP3 Fig. 5. Interfacial resistance as a function of surfactant concentration. In our study of the effect of surfactant on interfacial mass transfer, we added 0.1 rnol dm-3 acetate to the aqueous phase in each run. By doing this we could retard the interfacial resistance to mass transfer as the result of a surfactant layer at the interface by excluding the resistance of a chemical reaction. The interfacial resistance Ti due to ECA4360 is now plotted against the concentration of ECA4360, as shown in fig. 5. It is seen from fig. 5 that in the range of low ECA4360 concentration (< I 0-' mol dm-') fi increases slowly with increasing ECA4360 concentration.When ECA4360 in the oil phase is >5.0 x lo-' rnol dmP3, Ti rises sharply and then remains approximately constant. This can be interpreted as follows: In the range of low ECA4360 concentration (< lop3 rnol dm-'), ECA4360 adsorbed at the interface is far from saturation. There exists no rigid surfactant film at the interface; therefore Ti in this region rises slowly with ECA4360 concentration. In the region from 5.0 X to 1 .O x lo-* mol dm-3 ECA4360, the interface appears to be packed with ECA4360 molecules, forming a dense, rigid interfacial barrier through which the solute must pass. Therefore, Ti rises sharply in this region. Once a densely packed monolayer (or multilayer) of surfactant is formed at the interface, Ti reaches a maximum and any further increase in ECA4360 concentration does not significantly contribute to the rigidity of the interfacial film.A substantial constant value of Fi is maintained. We find from fig. 5 that the interfacial resistance due to a surfactant such as polyamine is as high as 2500 s cm-' at a surfactant concentration of ca. 0.01 mol dmP3. This suggests that for liquid-membrane metal extraction, which is accelerated by the ligand effect, the major resistance to mass transfer is concentrated on the peripheral surfactant layers of the emulsion globules, i. e. the interfacial surfactant layer offers the predominant barrier to mass transfer for the liquid-surfactant- membrane system. The formation of highly viscous interfacial films during extraction in the presence of surfactant was confirmed by the interfacial viscosity measurements recently made in our laboratory.20 Based on this experimental finding, a model of diffusion- controlled mass transfer for the liquid-surfactant-membrane system, in which the rate of the extraction reaction is increased by means of the ligand effect and the74 LIGAND-ACCELERATED METAL-ION EXTRACTION major resistance to interfacial mass transfer is from the surfactant layer, has recently been developed by us and the details of this model are discussed el~ewhere.~’ This work was supported by an EPA grant awarded to the Industrial Waste Elimination Research Center at Illinois Institute of Technology.’ N. N. Li, U.S. Patent 3 410 794, 1968.E. L. Cussler and D. F. Evans, J. Membr. Sci., 1980, 6, 113. E. L. Cussler, AIChE J., 1971, 17, 405. R. M. Izatt, M. P. Biehl, J. D. Lamb and J. J. Christensen, Sep. Sci. Technol., 1982, 17, 1351. K. H. Lee, D. F. Evans and E. L. Cussler, AIChE J,, 1978, 24, 860. J. W. Frankenfeld, P. P. Cahn, and N. N. Li, Sep. Sci. Technol., 1981, 16, 4, 385. A. Hochhauser, and E. L. Cussler, AZChE Syrnp. Ser., 1975, 71, 136. N. N. Li and A. L. Shrier, in Recent Developments in Separation Science (CRC Press, Cleveland, OH, 1972), vol. 1, p. 163. T. Kitagawa, Y. Nichikawa, J. W. Frankenfeld and N. N. Li, Environ. Sci. Techno!., 1977, 11,602. ’ I R. P. Cahn and N. N. Li, Sep. Sci., 1974, 9, 505. E. S. Matulevicius, and N. N. Li, Sep: Fur$ Methods, 1975, 4, 73. l 3 N. N. Li, J. Membr. Sci., 1978, 3, 265. l4 M. L. Brisk and W. J. McManamey, J. Appl. Chem., 1969, 19, 109. I s J. Strzelbicki and W. Charewicz, Sep. Sci. Technol., 1978, 13, 141. ‘ T. P. Martin and G. H. Davies, Hydrometallurgy, 1978, 2, 315. 10 Z. Gu, R. M. Kurzeja, D. T. Wasan and N. N. Li, paper presented at the Am. Inst. Chem. Engr. Meeting, Los Angeles, 1982. P. R. Subbaraman, Sr. M. Cordes and H. Freiser, Anal. Chem., 1967, 41, 1878. H. L. Finston and Y. Inone, J. Inorg. Nucl. Chem., 1967, 29, 199. Metallurgy, 1979), vol. 21. Meeting, Washington D.C., 1983. 18 l9 H. Eccles, G. J. Lawson and D. J. Rawlence, in ISEC’77 (Canadian Institute of Mining and 20 Z. Gu, R. M. Kurzeja, D. T. Wasan and N. N. Li, paper presented at the Am. Inst. Chem. Eng. 2 ’ P. Becher, Emulsion, Theory and Practice (Reinhold, New York, 2nd edn, 1965), p. 15. 22 S. Ross, E. S. Shen, P. Becher and H. J. Ranato, J. Phys. Chem., 1959, 63, 1681. 23 H. ‘Eccles, G. J. Lawson, D. J. Rawlence, in ISEC’77 (Canadian Institute of Mining and 24 A. H. Ghanern, W. I. Higuchi and A. P. Sirnonelli, J. Pharm. Sci., 1969, 58, 165. 25 V. Surpuriya and W. I. Higuchi, J. Pharm. Sci., 1972, 61, 375. 26 T. Yotsuyangi, W. I. Higuchi and A. H. Ghanem, J. Pharm. Sci, 1973, 62, 41. 27 Z. M. Gu, H. F. Zhang, D. T. Wasan and N. N. Li, paper presented at the Am. lnst. Chem. Eng. Metallurgy, 1979), vol. 21, p. 203. Meeting, Denver, 1983.

ISSN:0301-7249    

DOI:10.1039/DC9847700067

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. Soc., 1984, 77, 75-84 A General Model to Account for the Liquid/Liquid Kinetics of Extraction of Metals by Organic Acids BY MICHAEL A. HUGHES" Schools of Chemical Engineering, University of Bradford, Bradford, West Yorkshire AND VLADIMIR ROD Czechoslovak Academy of Sciences, Prague, Czechoslovakia Received 9 th November, 1983 A model based on two-film theory is developed for the case of the rate of extraction of a divalent metal from an aqueous acid phase with an organic acid HR held in a second immiscible solvent phase. The model involves a reaction zone of variable thickness so that the case of reaction at an interface of molecular dimensions can be accommodated as well as the case of reaction extending into the diffusion film on the aqueous side of the interface.Four parameters are used, one involving a partition coefficient for the acid, one involving diffusivities in the films together with the two-film mass-transfer coefficients. Rate data from three techniques used in laboratory liquid/liquid contacting are fitted by the model. The important commercial liquid/liquid extraction systems for the metals copper, cobalt and nickel involve contacting an aqueous acid phase with some organic acid, HR, held in a diluent.' Typically, HR is the hydroxyoxime LIX64, SME529, P5000 for copper or di-2-ethylhexylphosphoric acid for cobalt and nickel. Several papers describe the kinetics of extraction in these systems, but a variety of concentration conditions, in both the aqueous and organic phases, have been employed together with different contacting techniques.The latter range from the single-drop experi- ment2 through the constant-interface stirred cell3 to the rotating diffusion cell.4 Danesi' has shown how a combination of experimental technique with concentration conditions can result in true chemical-kinetic control or true mass-transfer control or mixed control. Rod et aL6*' have proposed a model for mass transfer with a fast reversible reaction and product extraction and have applied it to the extraction of copper(I1) by hydroxyoximes. It is now necessary to show how this model is generally applied and also how examples proposed by other workers are specific cases of the general model. THE MODEL The concentration profiles for this model are shown in fig. 1. The concentrations shown at the interface are arbitrary; in some cases a high interfacial concentration may exist if the extractant is surface active.It is taken that reaction must be at the interface and/or extending out into the aqueous diffusion film. Note that as P H R -+ 00 and P M R 2 - 00 then the profiles for cHR and c M R ~ , in the aqueous phase, are coincident at zero. Also, under these conditions, the cH and cM profiles in the aqueous phase become linear, as shown by the dotted lines in fig. 1. In fig. 1 A d is the diffusion-film thickness and Ar is the reaction-zone thickness. 7576 EXTRACTION OF METALS BY ORGANIC ACIDS organic aqueous I I I I For a divalent metal M2+: M2'+2HR MR,+2H' K E X = Z M R 2 ~ k + / ~ M 2 + C ; R . (4) Reaction (2) or (3) may be rate controlling. In the derivations, superscript bar will indicate the organic phase, subscript i will denote an interface condition and N will denote a flux.The film coefficients will be shown as k, for organic and ka, for water. D is a diffusivity within the films. It can be shown that if reaction (2) is rate determining then: (i) by Astarita's method: (ii) for the organic phase: CHR,i = CHR- N H R / k H R , ~ CMR2,i = CMR2 + N H R / 2 k M R 2 , 0 (iii) for the aqueous phase:M. A. HUGHES AND V. ROD 77 Table 1. Special cases of the general model values of key parameters particular case reaction in the film finite finite finite equilibrium reaction in the film a3 finite co reaction at the interface co a3 finite instantaneous reaction at the inter- 00 a3 face (Chapman's model) Some special cases may be noted which are summarised in table 1.The model of Chapman et a1.' is of particular interest but is only one special case, for under their assumed conditions then kR+ a, e = kRDHJPLRKHR+ 00, PHR+ 00, K E X is finite, thus eqn (5) transforms to: - 1 =o. ck,iCMRz,i K E X c i R , i C M , i Eqn (6) and (7) remain as before. Eqn (8) transforms to cHR = 0. (13) Eqn (9) transforms to c M R ~ = 0. Eqn ( 10) transforms to CM,i = cM - 0.5 NHR/ kM,aq. (14) (15) Eqn (11) transforms to cH,i = CH -k NHR/ kH,aq. (16) It may be noted here that if reaction (3) is the rate-determining step then eqn ( 5 ) becomes: but the other equations remain as before. IMPORTANT PARAMETERS OF THE MODEL The most sensitive parameters in the model are: together with PHR.Their values decide the location of the reaction and characteristics of the transfer process; table 2 illustrates this in a general way.78 EXTRACTION OF METALS BY ORGANIC ACIDS Table 2. Location of the reaction and characteristics of the transfer process P H R 0, or 6; particular case description of process finite finite reaction in the film diffusion coupled with kinetics of reaction in the film finite +co equilibrium reaction in the film diffusion coupled with equili- brium in the film -bm finite reaction at the interface diffusion and reaction kinetics at the surface +m --*a instantaneous reaction at the diffusion and equilibrium at the interface surface THE POSSIBILITY OF BULK PHASE REACTION In order to consider the possibility of reaction in a bulk aqueous phase, the thickness of the reaction zone j must be considered.Now: (18) only if i> 1 can reaction occur in the bulk phase. Suppose that the partition coefficient of the extractant was relatively low at ca. 100 and the mass-transfer coefficients relatively high at kHR+, = kHR,, == m s-l then with CHR = kmol m-2 s-l which i s too low for practical purposes. Extractants of this nature, which react in the bulk, would be of no practical use. kmol mP3 eqn (18) gives N H R , i < 3 x MATHEMATICAL TREATMENT OF THE SIMULTANEOUS EQN (5)-(11) The implicit function. for NHR is: F[ NHR,Cj,(KEX, K H R , PHR, PMRZ,kR,Dj)(kaq, ko)] = (19) in which cj is the bulk concentration.and Dj the molecular diffusivity of species j . The function is therefore made up of: (1) flux, (2) concentration and (3) physical and hydrodynamic parameters.The physical parameters are regrouped to give: in which el = k R D H R / P h R & R and e2= DHRPMR~/DMR~PHR. The ratio D~/DHR refers to a transferring speciesj with diffusivity Dj, and this ratio is relatively easy to obtain from generalised correlations: in any case the flux N H R is not very sensitive to this ratio. Thus in any problem KEX, D H R P M R 2 / D M R 2 P H R and D , / D H R are known or may be estimated for a given system and the data from the technique (be it single drop, stirred cell etc.) may be fitted by the model optimising the best value of O,, k,, and k,. It is k,, and k,, the hydrodynamic parameters, which change from one technique to another.A computer program is written using the Runge-Kutta-Merson method for numerical integrations and the Marquardt method for the optimisation technique to give parameter estimation. In the case of HR= hydroxyoxime, the programM. A. HUGHES AND V. ROD 79 Table 3. Most important parameters of F [eqn (19)] dictated by positiorl of rate and bulk concentrations far from equilibrium, e.g. initial k,, 0, ko near to equilibrium, e.g. in real KEX, k,, KEX, 8 , K E X rates contactors includes the chemical model of Whewell and Hughes'' to calculate the thermo- dynamic concentrations, cHR and cH+, cM2+. A reasonably large number of points taken from kinetic experiments on a particular system can be fitted to the model. Alternatively, the values of constants making up certain parameters can be estimated or measured separately and the parameters can be inserted into the model to calculate fluxes which can be compared with experiment.THE SENSITIVITY OF THE MODEL TO THE PARAMETERS The sensitivity of the model to the parameters depends on whether the rate is measured near to equilibrium or far away from equilibrium together with the bulk concentration conditions ; the most important parameters for the varying conditions are highlighted in each case in table 3. The behaviour of the model can be demonstrated using assumed parameter values and selected concentrations for the aqueous metal ion, the aqueous proton and the 'free' organic ligand, HR. In fig. 2 the flux (or extraction rate) is seen to depend upon the extractant concentration at variable values of the rate parameter 8,.As the values of 61 increase, the rate approaches the maximum theoretical diff usion-controlled transfer curve A. This theoretical curve A would take on new positions in the plot when the cM2+, k,, and k,, values are altered. Note that with increasing extractant concentration the extraction rate is approaching the region where the mass transfer of metal ions is the rate-controlling step. Only at very low values of is chemical control possible, and for < The dependence of the extraction rate on the concentration of the metal ion is shown in fig. 3. As cM2+ increases the rate approaches the limit of k,cHR, and for a given cM2+ value the flux is higher as the el increases. Again chemical control becomes significant when 61 becomes very small, e.g.ca. The importance of the influence of the reverse reaction is partly measured in the KEX value, and for set values of all the parameters this influence on the rate is illustrated in fig. 4, where cHR and KEX are varied. As expected, for a given cHR value the rate increases as KEX increases, chemical control is forced upon the system when KEX becomes very small and, in any case, as cHR increases the diffusion- controlled limit at 2 kaqcM2+ is approached. The sensitivity of the flux to the parameters can be best summarised in fig. 5 , in which a fractional change in flux produced by a fractional change in a parameter is plotted. The left-hand side of the graph represents excess metal in the aqueous phase and the right-hand side represents excess extractant in the organic phase.The sensitivity of the flux with respect to the mass-transfer coefficient k,, increases (or near) the model is not very sensitive to this parameter. or less.80 EXTRACTION OF METALS BY ORGANIC ACIDS 0 20 40 60 cHR/g mol m-3 Fig. 2. Dependence of the flux of HR on the parameter 8, and the concentration of HR in the organic bulk phase. 8, = ( a ) lov6, ( b ) (c) lo-'' and ( d ) 2k,,, c, *+ kCH, 0 1 2 3 Fig. 3. Dependence of the flux of HR on the parameter 8, and the concentration of metal in the aqueous bulk phase. 8, = ( a ) lop6, ( b ) loe8, (c) lo-'' and ( d ) 10-l2. with the extractant concentration and with the ratio koC~~/2kaqC~2+. On the other hand, the sensitivity with respect to k, decreases with increasing cHR and the ratio above.A point on the graph at cHR = 20 kg mol m-3, corresponding to a value of 1 .O for p = k&HR/2kaqCM2+, is a stoichiometric point for the cM2+ value chosen for this calculation. It is now seen that the sensitivity of the flux to kaq is high if p >> 1 and its sensitivity to k, is high if p << 1. The sensitivity of the flux to is a maximum if p = 1. These observations demonstrate that in order to obtain good estimates ofM. A. HUGHES AND V. ROD 81 er,Jg moI m-3 Fig. 4. Dependence of the flux of HR on the value of log K,, and the concentration of HR in the organic bulk phase. log KEX = ( a ) 1 .O, ( h ) 2.0 and ( c ) 3.0. 20 40 60 c I q R l g mol m-3 Fig. 5. Dependence of the rate of change in flux of HR on the fractional change in the parameters ( a ) k,, ( b ) kaq and ( c ) 8,.the three major parameters of the model then experimental data should be obtained from three different regions. Experiments in the region cM2+ >> cHR will provide good estimates of k, and experiments in the region cHR >> cM2+ will provide good estimates of kaq. The reaction rate parameter O1 is best estimated if the experimental conditions are such that82 EXTRACTION OF METALS BY ORGANIC ACIDS 0 f l 5 Fig. 6. Typical fit of the model (solid line) to experimental points from the rising-drop experiment. The oxime concentration is constant at 20 vol '/o HR and the aqueous copper concentration is 8 g dm-3. [H2S04]/g dm-3 = (a) 2, ( b ) 3.5, ( c ) 5, (d) 8 and (e) 12. 0.08 m I Q E - E" 3 0.OL 5 U 0 L 00 800 1200 r/min Fig.7. Typical fit of the model (solid line) to experimental points from the gauze-cell experiment. The oxime concentration is constant at 20 vol % HR and the aqueous copper concentration is 8 g dm-3. [H2S04]/g dm-3 = ( a ) 1, ( b ) 2, ( c ) 4, (d) 6 and (e) 8. APPLICATION OF THE MODEL TO DATA FOR THE LIX64N +CUSO~ + H2SO4 SYSTEM We have tested this model on the LIX64N +CuS04 + H2S04 system using data from two entirely different techniques of contacting the two phases but using bulk concentrations in both phases which are of commercial interest. In particular, the pH range is commercially more realistic than that adopted by Albery and F i ~ k . ~ The model was fitted to the initial rate data from the single-drop experiment^,^ see fig. 6.Rate data may be obtained over more extensive times using a 'gauze cell': where a fixed volume of organic phase is continually stirred at an interface, of known area, with an aqueous phase of constant composition continuously flowing throughM. A. HUGHES AND V. ROD 83 Table 4. Parameter estimates for copper extraction systems data Cu + LIX64N gauze cell 7.0 x 6.7 3.3 11.0 Cu + LIX64N rising drops 7.0 x 150 100 11.0 Cu + P5000 6.8 X 10.4 21.8 1 .o membrane cell (Albery and Fisk) 0 50 100 150 200 c,,/mmol dm-3 Fig. 8. Fit of the model to the data from the rotating diffusion cell. Data reported by Albery and F i ~ k . ~ Curve B, the concentration of aqueous copper is constant at 10 mmol dmP3 but HR is varied. Curve A, the concentration of HR is constant at 68 mmol dmP3 but aqueous copper is varied; the pH is 4.1.the cell and in contact with the organic phase at that interface. Data from these experiments, which involve concentrations in the same range as those for the single drop, have been reported elsewhere.’ The model fitted these data, see fig. 7. The parameters are reported in table 4. In the gauze cell the rate of mass transfer is controlled by diffusion with chemical reaction. The parameters O,, k, and k,, are determined with confidence because the data are measured in concentration-time ranges which allow the model to be sensitive to all three parameters. The model is not sensitive to e2 in this range. It is probable that the relatively low k, and k,, values are caused by inefficient stirring near to the interface.In the case of the rising-drop experiments the rate is mainly controlled by chemical reaction. Because these are initial rate data the range over which they are measured means that the rate is not so sensitive to k, and kaq, so these are not as well determined as in the case of the gauze-cell work. Note that the value of if it is determined independently for the drop data alone. The model appears successful especially since it accounts for rates measured both at initial times and near to equilibrium. We now turn to the experiments of Albery and F i ~ k , ~ who used a rotating diffusion cell to study the extraction of copper with P5000 from slightly acid media. The present model also accounts for their results, see fig. 8. In table 4 the value of 8, is is 6.9 x84 EXTRACTION OF METALS BY ORGANIC ACIDS greater than that found for the Cu +LIX64N system; this is to be expected since P5000 has a lower partition coefficient than LIX64N.l o A theoretical value of k, = 1 1.4 can be calculated for this system using the classical equation for a rotating disc, developed by Levich. So the value of 10.4 found by optimisation of the parameters is satisfactory. The relatively low value of k, shows that there is a diffusion resistance but it is not possible to say if this is due to the membrane itself or some film on the organic side of the membrane. In all the above cases the equation involving the addition of the first ligand [eqn (2) and thus (S)] gave the best fit. ' P. J. Bailes, C. Hanson and M. A. Hughes, Chem. Eng., 1976, 86. ' R. J. Whewell, M. A. Hughes and C. Hanson, J. Inorg. Nucl. Chem., 1975, 87, 2323. C. A. Fleming, Narl Insr. Merafl., Repub. S. Afr., Rep. no. 1793, 1976. W. J . Albery and P. R. Fisk, in HydrornetaNurgy '81 (SOC. Chem. Ind., London, 1981), F5/1-F5/ 15. P. R. Danesi and R. Chiarizia, in Critical Reviews in Analytical Chemistry, ed. B. Campbell (CRC Press, Boca Raton, Florida, 1980), chap. 10, p. I. V. Rod, Chem. Eng. J., 1980, 20, 131. V. Rod, L. Stmadova, V. HanEil and Z. Sir, Chem. Eng. J., 1981, 21, 187. M. Bhaduri, C. Hanson, M. A. Hughes and R. J. Whewell, in ISEC'83 (American Institute of Chemical Engineers, 1983), p. 293. l o R. J. Whewell, M. A. Hughes and C. Hanson, in ISEC'77 (Canadian Institute of Mining and Metallurgy, 1979), vol. 21, p. 185. ' W. Chapman, R. Caban and M. Tunison, Am. Inst. Chem. Eng. Symp. Ser., 1975, 71, 152.

ISSN:0301-7249    

DOI:10.1039/DC9847700075

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 85-96 The Concept of Interfacial Reactions for Mass Transfer in Liquid/ Liquid Systems BY WALTER NITSCH Lehrstuhl fur Technische Chemie I, Technische Universitat Munchen, LicKtenbergstraBe 4, 8046 Garching, Federal Republic of Germany Received 15 th December, 1983 Interfacial reactions during reactive mass transfer between liquid phases are the central point of this contribution. In order to go from the general problem to- identify the site of the reaction and the rate-controlling step, a kinetic treatment of interfacial reactions is proposed that considers the individual processes of all the species involved. This concept, together with a new method for the determination of individual transport coefficients, leads to an efficient concept of resistances and to the possibility of treating chemically coupled systems (coextraction).Finally, the pronounced effects of adsorption layers are discussed with respect to diffusional- and interfacial-controlled mass transfer. The literature concerning the kinetics of liquid/liquid reactions has greatly increased in volume during the last decade,’.* indicating a pronounced interest in chemical-extraction systems. However, until now it has been difficult or impossible to nominate a system for which the kinetic features are known and accepted: The 20-year-long discussion concerning kinetics in dithizone and the various disagreements about kinetics in Purex6-8 are typical of the state of controversy. We have been studying the fundamentals of liquid/liquid reactions for nearly twenty years, during which time we have identified the following problem areas which give rise to the present unsatisfactory state of knowledge of the subject: ( 1 ) a lack of agreement or certainty concerning suitable experimental methods to provide kinetic conclusions, (ii) ‘overall treatments’ of the measured results, (iii) uncontrolled effects of surfactants and (iv) incomparability of systems for methodical reasons.Our concepts and results concerning and surrounding the problem of interfacial reactions are summarized in the following sections. LIQUID/LIQUID REACTIONS AS HETEROGENEOUS SYSTEMS A water phase loaded with metal ions and in contact with a solvent phase loaded with an extracting agent leads to a typical liquid ion-exchange reaction: M2+ +2m+ +2H’ which obviously contains (in the interference of a chemical reaction with transport processes) the characteristics of heterogeneous reactions.In table 1 the kinetic features of various two-phase systems are compared. The differences in the nature of the transport processes are evident. However, in addition to their having small enthalpies and often well defined stoichiometric relations,’ liquid/ liquid reactions are characterized, first of all, by the appearance of gradients for reactants and products in both phases. It is in this aspect that the most pronounced familiarity is established with heterogeneous processes of membrane transport. 8586 INTERFACIAL REACTIONS Table 1. Comparison of various two-phase heterogeneous systems important site of system transport gradients reaction solid/fluid pore diffusion fluid phase surface gas/liquid fluid dynamic +diffusion liquid phase liquid phase liquid/ liquid fluid dynamic +diffusion both phases liquid 1, liquid 2 or interface qf I I 8 I I I I liquid gas l i q u i d 1 l i q u i d 2 Fig.1. (a) Scheme of concentration gradients for (a) an instantaneous irreversible reaction (gas/liquid) and (b) an interfacial reaction (liquid/liquid). THE SITE OF REACTION In relation to the fluid-dynamic nature of the transport processes, liquid/liquid systems are similar to liquid/gas systems, but if one considers the literature concern- ing reactions in these two types of system a decisive difference is evident. While gas/liquid reactions are always treated as occuring inside the liquid phase (homogeneous reactions),"" for liquid/liquid reactions the concept of interfacial, i.e. heterogeneous, reactions is the usual mode.172 This remarkable situation calls for an explanation. Without a systematic consideration of mass transfer accompanied by chemical reaction the problem of homogeneous or interfacial reaction can be explained by looking at the two heterogeneous reactions Aliquid 1 + Bliquid 2 * Cliquid 2. A gas/liquid reaction exclusively inside the liquid phase is realized only in the case of the instantaneous irreversible reaction (Hattarnodel)" between A and Bgas, because A is completely depleted at the plane of the reaction at a definite distance from the interface [fig. l ( a ) ] . In all other regimes the reactants A and B will meet together not only in the bulk but also at the interface, which means that interfacial reactions are not to be excluded.The degrees of conversion in the bulk phase and at the interface, however, will depend on the kinetic properties of the system. The case of a pure interfacial reaction is established if reactant A is exclusively soluble in one phase and reactant B is exclusively soluble in the other, which means that the interface must be the only locale of reaction [fig. I(b)]. Proceeding fromW. NITSCH 87 Table 2. Distribution data of typical gaseous reactants and extractants system gas/ water system solvent/ water 02/ water 32 dithizone, CC14/ water 1.5 x 10' COz/ water 1 9 2 dithizone, CHC13/water I o4 H2S/water 3.9 x lo-' LIX"/paraffin/ water ca.lo4 SOJwater 2.5 x tributylphosphate/paraffin/ water 3 x lo3 a 2-Hydroxy-5-f-octylacetophenone oxime. 1L 10 1 2 1 / ' ! / I / I / I I / I / I I d d .r I P I I- / I 0 200 LOO 600 800 1000 1200 n, (r.p.m.) Fig. 2. Influence of forced convection on the initial flux ri into CCI4 for the complexation of zinc ions with dithizone. [ZnJ/mmol ~ m - ~ : (a) lop2, (b) lop4 and (c) 5 X Filled symbols, free falling drops; open symbols, stirred cell. Initial concentration of HDz = 1.25 x mol dm-3, pH 5. this extreme kinetic situation the transition to reactions in the bulk phase and their degree will depend at first on the distribution coefficients of B and/or A between both phases. Table 2 shows a comparison of the distribution coefficients for typical gas-phase reactants Bgas with typical solvent-phase reactants Bliquid.The values of the coefficients demonstrate that the 'solubility' of typical extracting agents in the aqueous phase is extremely low compared with the gas-phase reactants, which means that interfacial reactions are more probable in liquid/liquid than in liquid/gas systems. In a real kinetic situation, however, interfacial reactions are only to be identified if they are rate-controlling: (i) fluxes must be independent of the forced convection (plateau rates), (ii) specific fluxes must be independent of the area and (iii) plateau rates should be sensitive to surfactants. The behaviour of the zinc/dithizone systemI2 is an example of such an identified interfacial reaction (see fig. 2 and fig. 8). However, in the case that transport processes88 INTERFACIAL REACTIONS are rate-determining, which means that under the influence of forced convection identification of the site of reaction requires indirect methods. THE RATE-CONTROLLING STEP The basic problem in the kinetic treatment of individual liquid/liquid reactions is identification of the rate-controlling step (diffusion or reaction).The most usual (and until now probably the only applicable) method for the identification of the rate-determining step is the measurement of mass transfer for different forced convections, as realized in different types of stirred cell^.'^-^^ In addition to the serious problem caused by impuritiesI7 brought about by the long time of phase contact, such stirred cells should be calibrated to ensure that the kinetic conclusions are valid.For the stirred cell. used in our investigations we know, from the so-called calibration measurements of ‘diffusional’ heat transfer and physical mass transfer, that the transfer rates or coefficients have a linear dependence on the stirring rate if the stirring ratio is kept constant.18 Therefore we can be sure that the appearance of plateaus in the rate plots (see fig. 2 ) shows that chemical reactions are rate- determining. Without such a calibration the plateau rates may be caused by the fluid-dynamics of the type of stirred cell being used. KINETIC TREATMENT OF INTERFACIAL REACTIONS AT LIQUID/LIQUID BOUNDARIES Sinks (reactants) and sources (products) of concentrations located at the interface point to an interfacial reaction.For such kinetic situations the relevant set of equations corresponds to the scheme shown in fig. 3. For each component one individual transport equation of the type may be applied, together with the rate equation of the interfacial reaction, derived from the analysis of the plateau rates The individual fluxes ri, are coupled with stoichiometric mass balances. equilibrium condition for the interfacial reaction must be applied: For transport processes to be rate-determining, instead of the rate equation the This set of equations [eqn (1) and (2) or (1) and (3)], characterized by the consideration of the individual fluxes, substitutes the usual descriptive overall and proposes a physico-chemical treatment of interfacial reactions. TRANSPORT PROCESSES The general problem of the above-mentioned kinetic treatment is that the inter- facial concentrations of the individual species c: and the individual transport coefficients pi are unknown quantities.Because interfacial concentrations c: areW. NITSCH 89 w a t e r solvent Fig. 3. Scheme of gradients for a liquid ion-exchange reaction at the interface. not measurable, values for the individual transport coefficients are necessary to solve the set of equations. In this context it is remarkable that in the numerous publications concerning the kinetics of liquid/liquid reactions at droplets very seldom has an attempt been made to use the relevant engineering literature2’-’* containing so-called correlations that would be suitable for calculating individual transport coefficients.However, for mass transfer in stirred cells, especially for the prototype used in our work, efficient correlations for calculating p do not exist. Therefore we have developed a new approach to the individual coefficients. The applied concept was originally elaborated for the system uranyl nitrate, nitric acid and tributylpho~phate,~’ but it should be applicable in general for the case when transport processes are rate-determining. For the concentration region of transport-controlled mass transfer, the set of eqn ( I ) and (3) can be solved numerically with reasonable assumptions for the values of the different transport coefficient^.^^ Thereby, with the equilibrium constant [eqn (3)] the interfacial con- centrations c: may be calculated.For the particular concentration region in which, for one (or more) of the reactants or products, the condition cT<< c, remains established in spite of strong variations in the assumed coefficients, the corresponding transport coefficient is accessible from measurements using the simplified equation PI = ri,/c,. In table 3 are compared individual coefficients for different systems measured in the same stirred cell for equal stirring numbers in the water phase and with Re, = Re,. The values are close together, and are thus suitable to describe the time dependence of the concentrations in the respective systems, which shows that the evaluation method applied on the basis of eqn (1) and (3) is justified. A further proof concerns measurements of mass transfer at droplets in the system uranyl nitrate, nitric acid and tributylphosphate.Using the published correlations for the state of circulating droplets the calculated individual coefficients are in a good agreement with measured values,” which also confirms the method proposed above. In addition, with such physico-chemical treatments of diff usion-controlled interfacial reactions it is possible to prove a proposed kinetic configuration and to identify the effects of impurities and of interfacial instabilities, by comparing individual coefficients of different systems. INTERFACIAL REACTIONS As mentioned above, the rate equation for an interfacial reaction demands an analysis of plateau rates (see fig. 2). In such a manner, for the liquid ion-exchange90 INTERFACIAL REACTIONS Table 3. Individual transport coefficients related to stirred cells of the same type at Re, = Re, a,h pw/ lo3 cm s-' solute phases 8.5 12 25 H,O/ CC1, 7.0 toluene'" H,O/ hexane 8.7 toluene" H20/ toluene 2.92 Cd2' H20/C14, HDz 5.0 uo;+ 23 H20/ hexanec ~~ ~~~ pol lo3 cm s-' solute phases 5.7 HDP H20/CC14, ChCl3 3.8 ZnDz, l 2 H20/CCi4 1.78 H20/ hexane, T H20/ hexane, T &' 6.84 ' n, = 300 min-'. The effects of different stirrers are elimi- nated.' HDz = dithizone, KO = U02(N03)22T, Kx = HN03T, T = tributyiphosphate. r = 1 . 1 mol d ~ n - ~ . of zinc and cadmium ions in water, in contact with a solvent phase loaded with dithizone, we found for conditions of unilateral equilibrium the rate equation12 + [Zn2']* [HDz]* W+I* n = k (4) The simplest mechanism which agrees with this kinetic equation is the three-step consecutive reaction K ; HDz a Dz-+H+ fast Zn2'+Dz- A ZnDz+ slow ZnDz' +Dz- - ZnDz2 fast occuring at the interface, which means c= Kgk.In order to compare the velocity constant k with the usual scale for the rate of homogeneous reactions it is necessary to make assumptions concerning the unknown interfacial properties: because the interfacial activity of the species involved (HDz, Me2+, MeDz2) is weak or negligible, equating the bulk concentration with the concentration in the adsorbed state seems to be justified. Note that inside the phases for the state of the plateau rates the concentration gradients are negligible. More critical is the value of the dissociation constant KZ. Following the suggestions of interfacial chemistry3' the assumption KD = K& should be justified and therefore the values for khomo in table 4 are calculated with the 'water value' for KD.However, an attempt to understand the result keel, = 100 kcHC13 (see table 4) for both cations leads to the interpretation that Kg is dependent on the nature of the interfa~e.~' Nevertheless, recalculation into the scale of homogeneous reactions shows that the accessible interfacial reaction could be very fast. This aspect is of interest in the kinetics of permeation through biological membranes.W. NITSCH 100 80 60 40 20 91 - - - - - X Table 4. Heterogeneous [eqn (4)] and derived homogeneous constants khomo for measured interfacial reactions cation solvent i/ 1 0 - ~ cm s-' ~q,,,,/cm~ s-' mmol-' Cd2+ CCl, 2.94 Cd2+ CHC13 0.03 Zn2 + CCl, 0.42 Zn2 + CHC13 0.004 1.47 x lo9 1.5 x lo7 2.1 x lo8 2 x lo6 0 1 Zn N C C ' L ; interfacial kinetics mixed kinetics transport processes I I Znhq I I I 1 I 1 2 3 4 5 6 7 8 9 10 PH Fig, 4.Transport resistances for the zinc/dithizone system for different pH values. Parameter: concentrations [Zn] - [HDz] in mol dmP3. OVERLAPPING OF TRANSPORT AND REACTION In principle, with the relevant set of equations and the corresponding kinetic parameters one may calculate fluxes and time dependences of concentrations. However, in order to survey the behaviour of a given system a suitable concept of resistances would be desirable, aiming at the separation of reaction and diffusion. Such a concept is possible when the interfacial concentrations c? can be calcu- lated.27 Using, for example, the metal-ion concentration in the dithizone system as the key component, the relation EM2+] - [M2+1* 1()00// I - T - [ M2 +] - [ M2 +] & ( 5 ) defines an actual measure of the transport resistance because the numerator corre- sponds to the actual gradient and the denominator is the gradient at equilibrium at the interface, i e .a transport-controlled process. The example for the zinc/dithizone system in fig. 4 shows the influence of pH and metal-ion concentration on the transport resistance I,. In this calculation, the second term in eqn (2) for the back-reaction is derived with eqn (4) applying the kinetic-equilibrium condition.12 In addition to the desirability of such a kinetic92 INTERFACIAL REACTIONS survey for a given system, these calculations are of interest because they suggest the possibility of realizing chemical control merely with a decrease in concentration (see fig.2) or increase in pH. COEXTRACTION The two liquid/liquid reactions (bars indicate species in the solvent phase) UO;' + 2NOT + 2T - U02( N03)22T H++NOT+T--+ HN03T are competing for the extractant tributylphosphate, which means that the system is chemically coupled. The kinetic treatment of such a coextraction system is possible with the above-mentioned principles if one assumes that the interface is the site of both reaction^.^^"^ The decisive experimental results concerning this coextraction are the linear dependences of the fluxes on the stirring speed for all the participating species, which means that transport processes are rate-determining. Therefore the appropri- ate set of equations contains the equilibrium conditions at the interface for both reactions [HNO,T]* K - - [H']*[NOJ*[T]* together with transport equations for all the individual fluxes by analogy with eqn (1).Applying the above-mentioned concept, it is possible to obtain the necessary individual coefficients for this system and therefore to calculate the time dependences of all the concentrations. One outstanding result of these calculations is the strong coupling of both reactions which is evident at high uranium concentrations. The nitric acid concentra- tion overshoots its equilibrium value in the course of mass transfer of uranium and nitric acid into the solvent phase very markedly." This significant result of the numerical calculation is in agreement with the corresponding measurements (fig.5), thus helping to confirm the proposed kinetic mechanism, and it shows that in the case of interfacial reactions chemically coupled systems can be treated. A very important application of these kinetic results concerns the design of extraction columns. Until now the design of columns for reactive systems has been very empirical, because both important influences (kinetics and back-mixing) are unknown. Therefore knowledge of the detailed kinetics of a system represents a new approach to the calculation of concentration profiles, to the treatment of back-mixing effects and to the optimization of chemical separations. ADSORPTION LAYERS Decades ago, mass transfer at liquid/liquid boundaries was suggested as a model for biological permeation; at the present time mass transfer through monolayers between different liquid phases is of interest for liquid-membrane technology.In the context of this contribution it should be emphasized that the relations to such membrane processes are closely connected with the kinetics of mass transfer.W. NITSCH 93 280 c 24 0 200 X h 120 2‘ v 80 40 0 60 120 180 240 300 t/min Fig. 5. Calculated (lines) and measured (open symbols) concentrations of ( a ) HNO,T(Kx) and ’(b) U02(N03),2T(Ko) for the mass transfer of UO’,+ ( c = 0.5 mol dm-3) and HN03 ( c = 2.4 mol dmP3) from water into hexane loaded with tributylphosphate [TI = I . 1 mol dm-3. Stirred cell: n, = 300 r.p.m.Initial deviations show interfacial instabilities; (I) (11) and (111) indicate different values for PT. In liquid/liquid permeation systems (water/adsorption-layer/solvent) the effects of surfactant layers are pronounced, but these effects are mostly of a fluid-dynamic nature. In this connection fig. 6 shows a very elaborate example of the influence of adsorption layers on liquid/liquid mass transfer for the case of transport limitation (stirred cell).32 Some peculiarities of fluid-dynamic behaviour in stirred cells should be emphasized. In the presence of surfactants, the state of the strongest depression of the rate (fig. 5 ) corresponds to rigid behaviour of the interface produced by a macroscopic gradient in the interfacial tension ‘spread’ over the whole interface. However, at a characteristic stirring number, connected with each individual surface coverage, the coefficient increases steeply, corresponding to a critical shear stress where the layer detaches from the edge of the interface (see sketch in fig.7), leading to the appearance of an undisturbed fluid flow at the periphery of the interface. In this fluid-dynamic region the true interfacial resistance is ‘covered’ by the rate-controlling diffusion step and therefore not recognizable. In spite of this fact knowledge about the fluid-dynamic mechanism with respect to the empirical behaviour of fluid-dynamic effects is important in order to identify true interfacial resistance. Limited to the case that interfacial reactions influenced by the monolayer are rate-determining, the true interfacial resistance is accessible.The zinc/dithizone system is again a suitable example.33 The typical behaviour of such a permeation system is markedly different compared with the fluid-dynamic effects: plateau rates indicate the reaction-controlling region, and the sensitivity of the plateau rates to the surfactant concentration indicates that an interfacial process is taking place (see fig. 8). In this context it should be emphasized that the separation of the fluid- dynamic and chemical effects of surfactants requires a measurement of mass transfer at variable forced convections.94 INTERFACIAL REACTIONS I I I I I 1 1 0 100 200 300 n, (r.p.m.) Fig. 6. Individual transport coefficient pw for the transfer of toluene into an aqueous phase in the presence of insoluble poly(ethy1enoxide) at the interface.Parameter: reciprocal coverage in A’ per monomeric unit. Highest line, pure interface; lowest line: rigid interface; intermediate lines as follows: +, 41.7; D, 44.2; 0, 47.6; a, 51.5; 0, 59.5; V, 66.8; 0, 85.2; 0, 94.5; +, 114.0; X, 168.4, R > n c n 5 “c Fig. 7. Scheme showing the fluid-dynamic state of the interface below and above the critical stirring number. The mechanism of such interfacial barriers has not been investigated until now. One interesting feature seems to be that in the case of an ionic interfacial reaction interfacial potentials are acting, because anionic layers decrease the rate of the interfacial reaction while cationic layers lead to its increase.34 The study of permeation through layers at the liquid/liquid boundary is in its infancy.To ‘catalyse’ its progress different chemically controlled systems occuringW. NITSCH 95 30 60 90 120 150 n,/min-' Fig. 8. Initial fluxes ri for the complexation of zinc with dithizone ([HDz] = 1.25 x [Zn] = 5 x dodecylsulphate ( mol dm-3, pH 5) at the water/toluene interface in the presence of sodium mol dm-3) for various concentrations of sodium chloride, c/mol dm-3: +, 0.01; 0, 0.05; 0, 0.1; X, 0.15; 0, 0.2; A, 0.3; 0, 0.5. at the interface are necessary in order to recognize and survey the different and decisive features of such processes. CONCLUSIONS Though a very small number of liquid/liquid reactions seem to have been thoroughly explained kinetically, it is the impression of the author that interfacial control in such systems will occur rather frequently.For proceedings in this undeveloped field the introduction of an efficient and generally accepted type of stirred cell seems to be important so as to enable a comparison between different investigations to be made. Another catalysing feature should be the substitution of each overall treatment by an approach which involves individual fluxes. Finally, it is important to take account of the effects of surfactants, not only in the context of permeation but, more importantly, for the evaluation of experimental results. Without definite knowledge of a sufficiently pure interface, results are always doubtful. See the various Proceedings of the International Solvent Extraction Conferences (Roc.ISEC). C. B. Honaker and H. Freiser, J. Phys. Chem., 1962,66, 127. * P. R. Danesi and R. Chiarizia, C.R.C. Crit. Rev. Anal. Chem., 1980, 10, issue 1 .96 INTERFACIAL REACT10 NS H. Watari and H. Freiser, J. Am. Chem. Soc., 1983, 105, 191. W. Nitsch and K. Hiliekamp, Chem.-Zrg., 1972, 96, 245. F. Baumgartner and L. Finsterwalder, J. Php. Chem., 1970, 74. 108. ' D. E. Horner, J. C. Mailen, D. W. Thiel, T. C. Scott and R. G. Yates, Ind. Eng. Chern. Fundarn., 1980, 19, 103. ' M. F. Pushlenkov, N. N. Shchepetilnikov, G. I. Kuznetsov, F. D. Kasimov, A. L. Yasnovitskaya and G. N. Yakovlev, in ISEC '74 (Society of Chemical Industry, London, 1974), vol. 1, p. 493. ' Y. Marcus and A. S. Kertes, in Ion Exchange and Solvent Extraction of Metal Complexes (Wiiey, London, 1969).G. Astarita, in Mass Transfer with Chemical Reactions (Elsevier, Amsterdam, 1967). I0 ' I P. V. Danckwerts, in Gas-Liquid Reactions (McGraw-Hill, New York, 1970). I' W. Nitsch and B. Kruis, J. inorg. Nucl. Chem., 1978, 40, 857. l 3 J. B. Lewis, Chem. Eng. Sci., 1954, 3, 248. J. Bulicka and J. Prochazka, Chem. Eng. Sci., 1976, 37, 13'7. l 5 H. Sawistowski and L. J. Austin, C'hem.-Ing-Tech., 1967, 39, 224. l6 P. R. Danesi, R. Chiarizia and A. Saltelli, J. Inorg. Nucl. Chem., 1976, 38, 1687. l7 W. Nitsch, M. Raab and R. Wiedholz, Chem.-ln,c.-Terh.. 1973. 44. 1026. l 9 G. Petrich, in ISEC '80 (Ass. des IngCnieurs sortis de I'Universite de Liege, 1980), vol. I , session 20 J. A. Golding and V. N. Saleh, in ISEC '80 (Ass. des Inginieurs sortis de I'Universiti de Likge, 21 H. Brauer, in Stoflaustausch einschlieplich chemischer Reaktionen (Verlag Saulgnder, Aarau und 22 A. E. Handlos and T. Baron, AIChE J., 1957,7, 127. 23 W. Nitsch and A. van Schoor, Chem. Eng. Sci., in press. 24 A. van Schoor, Doctoral Thesis (Technical University of Munich, 1980). 2 5 K. D. Heck, Doctoral Thesis (Technical University of Munich, 1974). 26 K. Matt, Diploma Thesis (Technical University of Munich, 1980). 27 A. Hoffmann, Doctoral Thesis (Technical University of Munich). 28 A. v. Imhof, Doctoral Thesis (Technical University of Munich). 28 W. Nitsch and U. Schuster, Sep. Sci. Technol., in press. 14 W. Nitsch and J. Kahni, Ger. Chem. Eng., 1980, 3, 96. 18 SA, pp. 80-42. 1980), vol. I , session 2A, pp. 80-194. Frankfurt, 197 1 ). J. T. Davies and E. K. Rideal, in Interfacial Phenomena (Academic Press, New York, 2nd edn, 1963). 30 3 1 W. Nitsch and 0. Sillah, Ber. Bunsenges, Phys. Chem., 1979, 83, 1105. 32 W. Kremnitz, Doctoral Thesis (Technical University of Munich, 198 I). 33 T. Michel, Diploma Thesis (Technical University of Munich, 1983). 34 W. Nitsch and K. Roth, Colloid Polym. Sci., 1978, 256, 1182.

ISSN:0301-7249    

DOI:10.1039/DC9847700085

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984,77, 97-104 Facilitated Transport across Liquid/ Liquid Interfaces and its Relevance to Drug Diffusion across Biological Membranes BY NICHOLAS BARKER,? JONATHAN HADGRAFT" AND PAUL K. WOTTON Department of Pharmacy, University of Nottingham, University Park, Nottingham NG7 2RD Received 22nd November, 1983 The rotating diffusion cell has been used to study the facilitated transport of a dianionic dye, Resorcin Brown R, across a solid-supported liquid membrane. A pH gradient provides- the chemical driving force for the co-transport mechanism. The carrier molecules incorporated into the liquid membrane were hydroxypropylamines and hydroxybutylamines. The transport mechanism was shown to be saturable. The amines also transported salicylate anions, and the proposed mechanism may be suitable for transporting anionic drug molecules across biological membranes.A further commercially available amine, Ethomeen S 12, was also found to be capable of increasing the flux of salicylate across lipid membranes, and this compound may have potential in skin preparations. In order to increase the efficiency of solvent extraction processes, solid-supported liquid membranes have been investigated recently.'.' Various workers have been able to utilise a pH gradient to facilitate the transport of ionic species from one aqueous compartment across a non-polar organic phase to a receptor aqueous phase against the ion concentration gradient. Either co- or counter-transport mechanisms are possible. In both cases a pH gradient is often the driving force, although inorganic anions have been used to facilitate cation flux in a co-transport scheme.3 We have developed this principle in order to facilitate the transport of anionic drugs across the skin.In commercial solvent extraction systems there are not many constraints on the choice of the pH gradient, and often the difference may be from 2 to 12. However, in the case of skin and other biological membranes there are severe limitations and any proposed scheme must operate within narrow limits. Since the surface of the skin is slightly acidic, pH4.2-5.6, and the lower layers of the skin are at physiological pH 7.3-7.4, these are the pH extremes under which the transport mechanism must pera ate.^ However, we should be able to design a system which utilises this inbuilt pH gradient to facilitate the transfer of anionic drugs which normally do not penetrate the skin.The potential of this technique has been assessed using a model system and the rotating diffusion cell has enabled us to simulate the lipids of the skin in a well defined in vitro m0de1.~ The epidermal barrier is simulated by using a Millipore filter impregnated with isopropyl myristate, a liquid representative of skin lipids.6 The facilitated transfer scheme is represented in fig. 1. To effect transfer, a carrier molecule is introduced into the isopropyl myristate and at the lower pH becomes protonated at the interface. In this form it combines with the least hydrophilic anion present to form an ion pair. The ion pair partitions into the bulk lipid phase and diffuses down its concentration gradient to the opposite interface.In the t Present address: Smith Nine & French Ltd, Welwyn Garden City, Hertfordshire AL7 IEY.98 phosphate buffer at pH 5 MeOr-' H corresponds to in vivo venicle at pH 5 FACILITATED TRANSPORT IPM plus carrier phosphate buffer at pH 7.4 :Or- \ OH- N - R, - R, - N : MeOr- +H,O I stratum corneum treated with carrier viable epidermis at pH 7.4 Fig. 1. Schematic diagram of the facilitated transport of MeOr. interfacial region at the higher pH, the carrier molecule deprotonates and the anion is released. The carrier is then free to diffuse back to'the other interface and repeat its role. Various criteria will govern the relative efficiency of the transport. The ideal carrier should have a pK, between 5 and 7.4, have a high partition coefficient and be water insoluble.Accumulation in the interfacial region will be improved if the carrier has slight surfactant properties; however, a compound with strong surface- active properties will cause problems owing to emulsion formation at the interface with concomitant interfacial breakdown. From the cosmetic and pharmaceutical standpoint the carrier must also be non-volatile, non-toxic, non-sensitising and inert to the different skin constituents. In previous studies we have shown that there are some substituted amine derivatives such as N-substituted bis(2- hydroxypropy1)amines which may fulfill the above criteria.6 In previous work Methyl Orange was used as the model anion; in this study we have investigated ionised salicylate, since this is often used as a model drug, and Resorcin Brown R, a dianionic species.This dye was chosen since it has structural resemblances to a potential topical drug, disodium cromoglycate. The structures are presented in fig. 2. EXPERIMENTAL The mono-substituted amines were prepared by documented techniques. N,N-bis(2- hydroxypropy1)octadecylamine ( 1) was prepared by the method described by Boivin,' and N, N- bis(2-hydroxybutyl)hexadecylamine (2) and N, N- bis(2-hydroxybutyl)octadecylamine (3) were synthesised using the method of Perrault.* N-(2-hydroxypropyl)bis(octadecyl)amine (4) was prepared by refluxing 2-hydroxypropylamine with 1 -bromoctadecane in chloroform with an excess of anhydrous potassium carbonate.Any quaternary ammonium compounds formed were removed by filtration and the product was distilled at reduced pressure. TheN. BARKER, J . HADGRAFT A N D P. K. WOTTON 99 OH 8 SO,Na OH Fig. 2. Structures of (I) Methyl Orange (MeOr), (11) Resorcin Brown R (RBR) and (111) disodium cromoglycate. Table 1. The carrier amines amine boiling point/"C formula (pressure/mmHg) N, N-bis(2-hydroxypropy1)octa- I 8H37N(C H2C H(oH)C H3)2 21 1 (0.5) decylamine (1) N, N-bis(2-hydroxybuty1)hexa- c ,6H,3N(CH2CH(OH)C2HS)2 199 (0.4) decylamine (2) N, N-bis(2-hydroxybuty1)octa- C18H37N(CH2CH(0H)C2H5)2 239 (0.2) decylamine (3) decy1)amine (4) N- (2 - hydroxypropyl)bis(octa- (CH 18H37)2NCH2CH(OH)CH3 221 (0.2) purity of the amines was checked using i.r. and n.m.r. spectroscopies. The amines and their distillation temperatures are given in table 1.Resorcin Brown R (RBR) was supplied by Hopkins and Williams, Methyl Orange (MeOr) and sodium salicylate by B.D.H.; all were recrystallised before use. Ethomeen S12 is a tertiary amine derived from soya-bean oil with an unsaturated C,8 alkyl chain and was supplied by Akzo Chemie, U.K. Isopropyl myristate (IPM) was supplied by Croda chemicals and has a refractive index gradient of I .4346 at 25 "C. The rate of transfer of the solutes across a filter impregnated with IPM was studied using a rotating diffusion cell. This cell uses the hydrodynamics of the rotating-disc system to impose a known pattern of convective flow on either side of the filter. The rotation of the cell produces stagnant diffusion layers of known thickness on both sides of the filter. It is thus possible to100 FACILITATED TRANSPORT ( W / H z ) - ' ' ~ Fig. 3.Relationship between the inverse flux, J, and the square root of the rotation speed, W, for RBR with (2) at a concentration of 0.01 mol dm-' as the carrier. see whether diffusion across these layers is in any way rate-limiting. In d 1 experiments 1 pm pore-size mixed cellulose ester filters were used which were impregnated with carrier solution in IPM by saturating the filter and carefully removing the excess solution with a tissue; in previous work this has been shown to be reproducible. The pH in both compartments was maintained using phosphate buffer. The rate of appearance of the solutes was monitored continuously using a flow-through cell in a spectrophotometer.A typical experimental determination is shown in fig. 3, where the influence of rotation speed on the transfer rate of RBR using (2) as a carrier is illustrated. In all discussions following, the flux quoted is the effective flux at infinite rotation speed, i.e. there is no contribution from the stagnant diffusion layers. In the preliminary experiments with the carriers that were synthesised, equal concentrations of the solute were placed in the donor and receptor compartments. This was to ensure that any breakdown of the membrane integrity would be immediately apparent. RESULTS AND DISCUSSION In all the experiments with RBR the p H gradient was maintained using phosphate buffer, the ionic strength of which was kept constant.In previous studies we have observed that at high ionic strengths the transport rate is modified. This is possibly due t o salting-out effects or because there is competition between the other anions and the dye anion for transfer sites at the interface. In all the studies with the synthesised amines the flux of RBR without the carrier present was negligible. The initial studies conducted with RBR compared the transfer rates achieved using the most efficient carrier described previously for Methyl Orange, compound (1). RBR was transported far less readily, which may be predicted if the carrier forms the 2 : 1 stoichiometric associate with the dianion. The results are given in fig. 4. The flux of RBR using this carrier was too low to be feasible for use in topical preparations and alternative amines were studied.(2) and (3) co-transported RBR against its concentration gradient far more readily than (1) (fig. 4). This result is difficult to rationalise as there are unlikely to be any significant pK, or lipophilicity differences between the bis(2-hydroxypropy1)amines and the bis(2-hydroxybuty1)amines. TheN. BARKER, J. HADGRAFT AND P. K. WOTTON 101 3 0 0 r c1 0.0 5 0.1 300r E E 7 1 0 Ep. ... [carrier]/mol dm-' Fig. 4. Relationship between dye flux and carrier concentration: V, (l), MeOr; A, (l), RBR; M, (2), RBR; 0, (3), RBR. 1 I 5 10 [carrier]/mmol dm-3 Fig. 5. Relationship between dye flux and carrier concentration: 0, (3), RBR; W, (2), RBR; A, (4), RBR. enhanced activity may possibly be attributed to a complex interfacial phenomenon related to the ion-association process.The transport rates at low carrier concentra- tions are shown in fig. 5 . (4) also transported RBR at low concentrations, but its low solubility in IPM precluded its evaluation at higher concentrations. However, it was less efficient than its mono-substituted counterparts. The influence of the RBR concentration was investigated (fig. 6); it appears that the coupled transport flux tends towards a limiting value, suggesting that a form of saturation carrier kinetics is occurring. A similar hypothesis has been tested by others9 The results may be analysed using a derivative of the Michaelis-Menten approach to enzyme kinetics. The classical constants V,,, and K in the enzyme analysis now reflect the maximum attainable dye flux and an affinity constant between the RBR and the carrier.A double reciprocal plot for RBR with (3) as the carrier is shown in fig. 7.102 FACILITATED TRANSPORT [RBR]/pmol dm-3 Fig. 6. Relationship between RBR flux and KBR concentration: 0, 0.01 mol dm-3 (3); A, 0.01 mol dm-3 (2); m, 0.1 mol dm-3 (1). ([RBR]/prnol dm-3)-' Fig. 7. Michaelis-Menten-type relationship; reciprocal RBR flux and reciprocal RBR con- centration for 0.01 mol dmP3 (3). One of the most commonly used model drugs is salicylic acid. Since the interfacial transfer kinetics have already been studied," we investigated the facili- tated transport of ionised salicylate. Fig. 8 shows that it is possible to facilitate the transport. However, salicylate is transported far less readily than RBR by the bis(2-hydroxybuty1)amines investigated.The cause of this reduction is probably the difference in the hydrophobicities of the two substrates and the stabilisation of the ion pair in the interfacial region. Compound (l), the less efficient carrier, transported the two anions equally, but on the basis of the stoichiometry required to produce a neutral ion pair we would expect salicylate to be transferred more efficiently.N. BARKER, J. HADGRAFT AND P. K. WOTTON 103 150- N I I 0 0.05 0.1 [carrier]/mol dm-3 Fig. 8. Relationship between salicylate flux and carrier concentration: a, (2); A, (3); W, (1). 2.5 - T N I E 1 0 0.005 0.0 1 [salicylate]/mol dm-3 Fig. 9. Relationship between salicylate flux and salicylate concentration for 0.: 1 mol cfrn -' Ethomeen S12. The lower linear relationship is diffusion without carrier transport and the upper curve is a combination of diffusion plus carrier transport.In order to develop a facilitated transport scheme for commercial use it is necessary to use materials that are cosmetically and pharmaceutically acceptable. We have therefore investigated the ability of Ethomeen 512 to facilitate the transfer of ionised salicylate across an IPM-impregnated filter. In these experiments the substrate was not initially present in the receptor phase and we were not concentrating it against its concentration gradient as in the previous work (although we have shown that Ethomeen S12 is capable of achieving this). This enabled us to produce a better representation of the use in viva To minimise the effect of transfer of un-ionised salicylate we used a pH gradient of 6.0-7.4 with the pH being maintained using a pH-stat.Diffusion in a system without carrier present occurred t o a small extent as indicated in fig. 9. However,104 FACILITATED TRANS PORT the flux obtained in the presence of 0.1 mol dmP3 Ethomeen S12 in IPM was at least an order of magnitude greater. The shape of the curve in fig. 9 has been reported previously for systems where diffusion and carrier transport occur simultaneously.' ' The results produced using this carrier and experimental conditions indicate that this type of phenomenon may be usefully utilised in a scheme to transfer anionic drugs across biological membranes. In preliminary work using a rabbit model we have shown that the penetration of ionised salicylate across intact skin can be enhanced by at least an order of magnitude using facilitated transfer and the amine carriers that we synthesised. There are few reports in the literature where this type of mechanism has been used to advantage in the delivery of drugs.In a study of the percutaneous absorption of indomethacin [( 1 -p-chlorobenzolyl-5-rnethoxy-2-methylindol-3-~1) acetic acid] an enhanced penetration rate at pH 6.2 was attributed to the formation of an ion- pair complex.12 This is possible since the pK, of indomethacin is 5.2 and bis(2- hydroxypropy1)amine is present in the preparation. It is therefore possible that facilitated transport mechanisms may have been used fortuitously to deliver drugs across biological membranes. We thank the S.E.R.C. for a studentship for N.B. and the S.E.R.C. and Fisons Pharmaceuticals for a CASE award to P.K.W. I P. R. Danesi, E. P. Horowitz, G. F. Vandergrift and R. Chiariza, Sep. Sci. Technol., 1981, 16, 201. ' P. R. Danesi, E. P. Horowitz and P. Rickert, Sep. Sci. Technol., 1982, 17, 1183. F. Caracciolo, E. L. Cussler and D. Fennell-Evans, AIChE J., 1975, 21, 160. M. Katz, in Design of Topical Drug Products: Pharmaceutics in Drug Design, ed. E. J . Ariens (Academic Press, London, 1973), vol. IV, p. 97. ' W. J. Albery, J. F. Burke, E. B. Leffler and J. Hadgraft, J. Chem. SOC., Faraday Trans. I , 1976,72, 1618. N. Barker and J. Hadgraft, Int. J. Pharm., 1981, 8, 193. ' J. L. Boivin, Can. J. Chem., 1958, 36, 1405. G. Perrault, Can. J. Chem., 1967, 45, 1063. T. Shimbo, M. Sugiura, N. Kamo and Y. Kobatake, J: Memhr. Sci., 1981, 9, 1. l o R. H. Guy and J. Hadgraft, J. Colloid Interface Sci., 1981, 81, 69. ' K. D. Neame and T. G. Richards, Elementary Kinetics of Membrane Carrier Transport (Blackweil Scientific Publications, Oxford, I972), p. 54. l 2 T. Inagi, T. Muramatsu, H. Nagai and H. Terada, Chem. Pharm. Bull., 1981, 29, 1708.

ISSN:0301-7249    

DOI:10.1039/DC9847700097

出版商:RSC    

年代:1984

数据来源: RSC