摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1941-1951 Hydration of Polar Interfaces A Generalised Mean-field Model Stephan Kirchner and Gregor Cevc* Medizinische Biophysik, Technische Universitat Munchen , Klinikum r.d.1. , lsmaningerstr. 22, D-81675, Munchen 80, Germany A generalized non-local electrostatic model has been proposed for the description of the hydration of arbitrary polar surfaces, including interfaces with a finite thickness. This model is suitable for the description of complex biological surfaces, such as the surfaces of lipid bilayer membranes. It is designed so as to resemble as closely as possible the Gouy-Chapman diffuse double-layer theory, for the sake of the simplicity of model use. The molecular meaning of the model parameters is discussed and the chief determinants of the surface hydration are identified. The concept of simple solvent polarization is shown to be less suitable for the description of the interfacial hydration than the local excess-charge density approach, which corresponds to a generalized, sub- molecular polarization. A general scheme for the calculation of the hydration between two thick, structured interfaces has been developed.The effects of surface structure on the hydration-dependent interfacial repulsion have been investigated. The magnitude and the range of the hydration pressure are shown to increase dramat- ically as a consequence of the water penetration and binding into the interfacial region. Interfacial swelling and dynamics, consequently, may affect the properties of, and the interactions between, structured surfaces.In most current descriptions of hydration phenomena it is customary to treat the interface between the aqueous sub- phase and the hydrophilic surface as a sharp water-perturbing boundary. In their seminal theory of hydration MarEelja and Radii:' have assumed, for example, that the reason for the occurrence of various hydration effects is the inability of the mutually coupled water (layers) near an infi- nitely thin interface to respond locally to the surface-induced structural perturbations. The concept of spatially varying water-order parameter has emerged from this. Early extensions of such a hydration model have retained essentially the same phenomenological picture. Correspond- ingly, their emphasis has been on the elucidation of the most relevant water-waterz or water-surface3 coupling mecha- nisms.Later, the picture of perturbed water structure was reformulated in terms of the distribution of '~ater-defects'.~,~ Various solvent-polarization concepts have also been devel- ~ped.~.~ is the treatment ofA more recent de~elopment~.~ surface polar residues and their associated local-excess charges as the chief source of interfacial hydration. This latter approach permits studies of interfacial hydration as a func- tion of the surface polarity and its spatial distribution.'-'' There is still confusion, however, about the most convenient and reliable formulation of surface-hydration theory. Even the precise significance of various model parameters is as yet unclear.The principal ideas of this paper are similar to those out- lined in ref. 10; here they are extended and formalized in more detail. Moreover, a rationale is given for the practical use of an electrostatic mean-field hydration model. We also propose the application of such a model for the extraction of interfacial polarity profile data from measured hydration force data. Details of this latter application and the corre- sponding computing protocols are described separately,' as are the effects of lateral surface structure.12 Here it suffices to say that, to a good approximation, for the thick interfaces such effects can be neglected. Standard Landau Theory of Hydration One of the most commonly used hydration models was pro- posed by MarEelja and Radik.' This model is based on the Landau postulate for the Helmholtz energy F = (A/C) (q(x)* + A2[dq(x)/dxI2) dx (1)r where A and C are two adjustable model parameters. An early modification of this model3 was aimed at facilitating the identification of the basic hydration-force sources and to permit molecular interpretation of the model predictions.(A more general but related ansatz is given in ref. 13.) d, in eqn. (1) is the separation between two interacting surfaces (the 'interlamellar water layer thickness'), each with an area A; A is the decay length of order parameter q. Boundary condi- tions cause the order parameter value at all polar surfaces to attain a non-zero value (qbulk= 0).The optimum value of order parameter is obtained from eqn. (1) by minimizing the Helmholtz energy. The result permits the hydration (disjoining) pressure between two hydrated surfaces to be derived from the simple thermodyna- mic relation, ph(d,) = (l/NAA)(dF/dd) [or for unit area: ph = (dF/dd)].This yields approximately the magnitude of po being determined by the boundary con- ditions. The 'Landau solution' to eqn. (1)is rather general. In spite of this, its agreement with experimental results is excellent. Owing to its entirely phenomenological origin, however, it is also dificult to interpret at the molecular level. However, an even more severe deficiency of the simplistic hydration-model approach is the assumed constancy of the hydration decay length A.All simple hydration models pos- tulate that this model parameter is determined only by the intrinsic properties of the medium and that it is independent of the interfacial properties. In contrast to this, experiments show that the measured decay lengths are highly variable. For example, the decay length of so-called hydration force between the fluid lamellar phosphatidylcholine multibilayers (L,-phase) is nearly twice as large as the corresponding decay length of this lipid in gel LBr-phase.14 A new mechanism is, therefore, needed to account for this variability. This can be based on the allowance for lateral' 5, l6 or transversal*-" interfacial structure. With this latter idea in mind we have introduced an exter- nal, hydration-inducing perturbation, h, which is spread over a region of finite thickness.(This represents a generalisation of the existing mean-field models of hydration for the case of spatially smeared interfaces.) An example of such a system is phospholipid bilayers in water. The boundary conditions are now no longer specified by the external field itself, but can be determined from the electroneutrality condition. Molecular Basis of the Hydration and Discreteness of Charge Effects All polar molecules have a non-uniform electric charge dis- tribution, even if the whole molecule is uncharged. ‘Local excess charges’ are, therefore, always present in such mol- ecules. This pertains to essentially all molecules which form interfaces as well as to the water molecules.The sites and the strength of water binding to a hydro- philic surface are determined largely by the quantum-mechanical fields that originate from the surface polar residues. Macroscopic fields which stem from the net surface charges or from the surface dipoles and higher multi-poles are weaker by one to two orders of magnitude than the very short-range, local fields that arise from the atomic local excess charges. Consequently, the former are much less important for the hydration of polar surfaces than the latter.? This is seen from the detailed computer simulations of surface hydration. These show that the whole water molecules as well as individual water OH-bonds follow closely the direction of local, atomic electric fields rather than the direction of Cou- lombic or dipolar surface fields.” On the other hand, the distributions of water molecules around the polar residues in protein crystals clearly show that the primary reason for water binding is hydrogen bonding to such residues.’* The principal trends in surface hydration, consequently, can be learned from the detailed electrostatic calculations on the atomic scale.Corresponding fields, or physical quantities related to these fields, as well as the corresponding inter- action potentials are thus suitable order parameters for the electrostatic description of surface hydration. This is tantamount to saying that the proximity of a polar surface alone may perturb the interfacial water structure.This causes the distribution of local excess charges on the bound water molecules to differ from the corresponding bulk values. This results in the accumulation of water-associated local-excess charges which compensates the oppositely charged local-excess charges on the polar residues. This is true for all polar residues in the contact with water and causes the electrical fields near such residues, and near the polar surfaces, to be extremely short-ranged. Computer simu- lations of the water binding to an isolated polar group clearly show this.Ig It is therefore reasonable to describe the polarity of a hydrophilic surface in terms of the surface electrostatics. The corresponding hydration can then be treated as a screen- ing process.Before extending these considerations to the real systems it is worthwhile to remember the basics of standard Gouy- Chapman theory of the charged surfaces in an electrolyte solution. Such theory can be derived from a Helmholtz energy expression that is very similar to (l),“*’if the decay length A is replaced by the Debye screening length A,,. The Gouy-Chapman theory is therefore a useful model for the construction and interpretation of the electrostatic theories of 7 This is to say that the contributions of standard macroscopic electrostatic polarization to the interfacial hydration is, in the first approximation, negligible. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 +-3 ---1 Lid-+* -I -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 distance Fig.1 (a) The distribution of surface-associated net charges (-, +) and the corresponding counterion clouds (curves) near an array of the anionic phosphatidylglycerol, A, or zwitterionic phospha-tidylacholine headgroups, B, in contact with a 0.1 molar monovalent electrolyte solution. The decay length value is 1 nm. (b) The distribu- tion of the water-associated local excess charges near a charged, A and non-ionic, B but hydrophilic, surface in water; the decay-length value of 0.1 nm gives the order of magnitude of the molecular-order decay length in water. hydration. By action of the net surface charges a region of non-zero local ion charge density, the so-called ionic diffuse double-layer, is created near a charged surface.’ The total charge density in such a surface-induced ionic diffuse double layer thus is always identical in magnitude, but opposite in sign, to the total structural surface electric charge.If the separation between two individual net surface charges is smaller than the average range of Coulombic inter- action [Debye screening length A, @ J(area per charge)] it is normally sufficient to consider only surface averages. A uniform surface charge density model then adequately replaces the more realistic discrete-charge approach [Fig. l(a)]. Surfaces with an equal density of positive and negative charges in such a situation behave as if they were elec-troneutral, owing to the mutual compensation of the oppositely charged groups on each surface.No interfacial repulsion is therefore observed between two electroneutral surfaces.? If the average intercharge separation far exceeds the Debye screening length, however, each individual surface charge tends to interact with its proximal ions independently, or nearly so [Fig. l(b)]. Clouds of the positive and negative ion charges then accumulate near the anionic and cationic surface sites, respectively.$ In such a situation even the sur- t Counterion distribution is always relatively uniform; the counterion concentration near a layer of charges is higher, however, than near a layer of zwitterions. In the ‘unscreened’ case pertaining to pure water with a very short characteristic decay length the inter- action of the individual charged segments with their associated counter charges is nearly spatially independent.This is the reason why lipid headgroup dipoles do more than just polarize the water molecules macroscopically. Indeed, the significance of the surface- induced water-dipole reorientation in such systems is rather limited. Hydration of the surface polar groups, consequently, is mirrored in the intra-molecular rather than multi-molecular polarization of the surface-perturbed water molecules. $ If one still wants to work with surface averages, and wishes to neglect the effects of interfacial correlations, the averaging procedure must be done separately for the positive and negative surface charges. J. CHEM. SOC.FARADAY TRANS., 1994, VOL. 90 -repulsion w attraction +-+-+ +-+-+ -+-+-+-+-+ Fig. 2 Schematic representation of the ionic charge distribution near two surfaces with a low density of two equally frequent, but different, types of net surface charge. faces with no net charge may repel or attract each other elec- trostatically, depending on the mutual positions of surface-charge lattices. This is schematically illustrated in Fig. 2. It is clear, however, that these interactions are weakened by the smearing of the charge lattices. Analogously, even in the absence of ions, non-zero local density of the local excess charges exists on the water mol- ecules that are contained in a small, surface-perturbed water volume fraction. This is principally a consequence of the interactions between the surface local excess charges and the water-associated local excess charges.Such interactions effec- tively mimic the screening of the former by the latter type of charges. Modified hydrogen bonding between the surface polar residues, surface-bound, and other water molecules are all manifestations of such local charge interaction pheno-mena. Indeed, any water binding to a polar residue that involves a charge transfer also tends to displace or shift the charges on the surrounding water molecules. Consequently, any such binding leads to at least partial screening of the surface local excess charges. Water alone, therefore, may give rise to the effects that resemble closely the screening of surface charges in an electrolyte solution. This is true on the appropriate scale, at least.The water-associated local excess charges that screen the local excess charges on the polar residues of a non-charged (i.e. zwitterionic) hydrophilic surface are always arranged in a number of distinct, but mutually nearly independent local maxima [Fig. lB(b)]. The size of such maxima is much smaller than the size of the individual phospholipid head- groups. It is also smaller than, or at best comparable to, the thickness of surface adsorbed water layers. The hydration of non-ionic polar surfaces, consequently, is not explicable in terms of simple macroscopic dipolar polar- ization or in terms of the water-dipole ordering alone. Such hydration is imaginable, however, in terms of the redistri- bution of local excess charges on the water molecules located near the hydrophilic surface.This may, but need not, give rise to some dipolar polarization as well. The distribution of water-associated local excess charges in the MarEelja-Gruen-Cevc approximation thus plays the same rde as the distribution of net ionic charges in the surface electrostatic models. Therefore, standard equations of the diffuse double-layer theory can also be adapted for the description of surface hydration. The similarity between Gouy-Chapman theory and the mean-field theory of hydra- tion is shown explicitly in Table 1. It is noteworthy that any approach based on the electro- static mean-field theory is macroscopic.This means that it is crucial to make a careful distinction between the molecular mechanism and theory. Quantities that appear in such a theory are not directly related to the atomic properties of the investigated system. In particular, if one uses the polarization vector (P)approach, the value of P is insensitive to the size of the solvent molecules. Consideration of the finite-size molecu- lar dipole orientation is then impermissible and misleading. Generalized Non-local Electrostatic Landau Theory of Hydra tion Our present formulation of the generalized theory of hydra- tion involves the following assumptions: (1) The Helmholtz Table 1 generalized Gouy-Chapman theory distribution of net surface- [pel(x)] and ion-charges [pi(x)] P(X) = Pedx) + Pi(x) electrostatic potential and electric field dE(x)/dx = P(X)/EE~ d$eI(x)/dx =z -E(x) d2$e1(x)/dx2= -P(X)/EEO linear Poisson-Boltzmann approximation for a planar, infinitely narrow, charged surface def dz$el(X)/dx2= $el(x)/'i d2E(x)/dx2= E(X)/'; $el(X) = (Gel 'd&~o)exP(-x/'d self-consistent spatial distribution of the ionic charges near a single charged surface def -rpi(x) dx = gel= E(x = 0) = EE0$:](X = 0) Helmholtz energy of a charged surface in ionic solution Fel = -3A(EEo/& $,",(x)+ ';C$:,(x)12lW Comparison of Gouy-Chapman and mean-field theories of hydration generalized theory of hydration distribution of surface polarity- [pp(x)] and water-associated local excess charges [p,(x)] PAXI = P,(X) + PJX) hydration potential and hydration (polarization) field dEh(x)/dx = Ph(X)/[EOEm(l-d$h(x)/dx = -Eh(X) d2$h(x)/dx2 = -Ph(X)/[EmEO(l-linear 'Poisson-Boltzmann ' approximation for a planar, infinitely narrow polar surface def d2$h(x)/dx2 = $h(x)/A2 d2Eh(x)/dx2= Eh(x)/A2 $h(X) = (ap A/&m EOk'xP(-x/A) self-consistent spatial distribution of the water-associated local excess charges near a single polar interface def -rp,(x) dx = oP= E,E~(~-E,/E)E,,(x = 0) = E,EO(l -E,,/&)$;(X = 0) Helmholtz energy of a polar surface in water Fh= -$A[E~E,/(~-E,/E)A~]p(x) + A2c$;(X)l2 -2('i/EEO)$el(X)P(X) dx -2[A2/E, -E,/E)l$(X)Ph(X)dx linear Poisson-Boltzmann equation for a charged interfacial linear Poisson-Boltzmann equation for the interfacial hydration zone with finite width potential of an interface with a finite width d211/e,(x)/dx2= $eLX)/'i -PeI(X)/&&O d2$h(X)/dX2= I(lh(X)/AZ-PP(~)/&O -Em/E) The meaning of various symbols is explained in the text.energy of a hydrated system can be described by a Landau- type order parameter expansion ; the coupling between water molecules is given by the fluctuation term -~4~(q’)~,which is proportional to the (medium specific) decay length value A. (2) The Helmholtz energy functional contains a linear contri- bution from the external interfacial field, h(x)= Eh(x) F = C c{q(~)~+ A2[q’(x)I2-q(x)h(x))dx (3) d, being the separation between the interacting interfaces. (3) The physical interpretation of model parameters is based on the assumption that hydration involves an electrostatic screening process.The Euler-Lagrange equation correspond- ing to eqn. (3) is therefore similar to the Poisson-Boltzmann equation. There are, however, some modifications of the con- stants. In eqn. (3) an arbitrary interface of finite thickness is con- sidered. This introduces a second length scale into the model. This allows for the different values of hydration decay length and, in our opinion, is essential for the understanding of experimentally determined hydration force. The generalized mean-field theory of hydration then pro- vides a means for studying of the interaction between two (thermally) smeared interfaces in a polar (associated) fluid medium which transmits the interaction.Steric contributions are neglected in this model but could easily be included.? Lateral surface inhomogeneity is also not considered here but is the centre of our interest in another paper.12 In the following, we thus confine our interest to the quan- tities which are averaged parallel to the plane of the interface. This introduces surface area, A, as a factor in some of our model results. The key to the understanding of the theory used in this paper is the concept of hydration as a screening process. This corresponds to using the following Poisson equation for hydration potential, $,, : (4) This states that the sources of hydration potential are given by the distribution of the external local excess charges, pp, and that they are screened by the internal local excess charges on the solvent molecules; the distribution of the latter is given by p,.[This distribution should be pro- portional to the Boltzmann factor exp(-q$,.JkT).] E~ is the permittivity of vacuum, E the static relative permittivity, and E, the corresponding high-frequency part. The somewhat strange factor on the right-hand side of eqn. (4) stems from the theory of non-local electrostatic^.^^^ In the field picture it includes the quantum modes arising from fluctuations of the polarization field in the so1vent.20n~b In the linear approximation, similar to Gouy-Chapman theory, the screening charge, p,, is proportional to the hydration potential. Comparing the corresponding form of eqn.(4): A2(d2$,/dx2) -$h = -Kpp, with the Euler-Lagrange equation, of eqn. (3), which is: A2(d2q/ dx2)-q = -h/2, then yields W,)= W/2W F{$:(x) + A2C$h(X)I2 -2Kh(x)Pp(x)dx (5) t It is possible to include such effects by introducing a polarity profile which explicitly depends on the thickness d, of the inter- lamellar water layer: p,(x) = pp(x; dw).This is without any influence on the formal development of our model. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 where and A is the total surface area investigated. As is shown in Appendix A, the minus sign pertains to all interfaces with a finite thickness. The plus sign is valid only when ppis a &function. The actual hydration potential is given by the solution to the differential equation A2(d2$Jdx2) -$h = -Kpp (7) The appropriate boundary conditions are discussed further in the text.The expression for the Helmholtz energy can be simplified by using eqn. (7) and a partial integration: F(d,) = --;[‘pp(x)$h(x)dx + surface terms (8) By the virtue of our boundary conditions the contribution from surface terms is zero. This term is thus omitted in the following discussion. The Helmholtz energy written in the form of eqn. (8) can be derived directly from the theory of non-local electrostatics. Appendix C illustrates how this is done. Field vs. Potential Approach For many years, the solvent polarization vector was con- sidered to be the natural order parameter of the mean-field theory of hydration.As is shown in Appendix A, identical model resuls are obtained, however, if the scalar quantities pp and $h are used instead. If the interfacial hydration is viewed in terms of water polarization, the former, field approach is appropriate. In the concept advocated in this work, which deals with the distorted local charge distribution as the basic hydration-associated variable, the hydration potential is to be given preference over the hydration field. Such a choice brings the advantage of using a scalar, direction-independent rather than a vectorial basic quantity. Consideration of the hydration potential, $h , rather than the hydration field also allows a straightforward derivation of the boundary conditions for t,bh, by the use of the condition of electroneutrality. Moreover, as is shown in Appendix C, it facilitates the formal comparison between the mean-field theory of hydration and the mean-field theory of surface elec- trostatics.[In particular, the approximation inherent in the use of eqn. (5) is better perceivable in such a derivation.] Note the following formal differences between the vectorial (polarization) and scalar (potential) approach to the surface hydration theory : the corresponding expressions differ by a factor +A2, which appears in the potential equations, the signs + and -being valid for pp 3 0 and pp # 0, respec-tively.t Interfacial Structure Effects Hydrophilic residues are never located all in one plane [cf: Fig. 3(a)]. Structural and/or dynamic smearing of the inter- facial region is thus often quite appreciable.The conse-quences of this smearing for the surface hydration can best be assessed by comparing the effective thickness of the polar t This is a direct consequence of: ( 1) the fact that the spatial varia- tion of any order parameter occurs on the length scale of A and (2) the fact that potential and field are related through a derivative. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Cs 0 -0.4 0.8 1 I 0.4 I-0.41 "I Id\ I h9 Pfl") / 0 -1.2 -0.8 -0.4 0 0.4 d/nm Fig. 3 Crystal structure of (a) the phosphatidylethanolamine layers at room temperature (from ref. 27) and (b) of the phos-phorylethanolamine crystals at 123 K (from ref.25). (c) The calcu- lated surface local-excess charge density, pp, and (6) the surface hydration potential, t+hb, of the latter. [The illustrated profiles were determined by means of eqn. (11) and (13.) To align panels (a) and (b),the phosphorus atoms were positioned at (0,O).The polarity peak that stems from the polar groups on the diacylglycerol is not shown, owing to the lack of firm information on the corresponding local excess charge density. Inclusion of this peak would give rise to two maxima in the interfacial polarity profile. Decay length used for potential calculations was A = 0.075 nm; higher A-values would cause the interfacial thickness to become even greater. surface region, d,, with the range of the surface-induced ord- ering in water, A ('solvent-order decay length ').We have recently measured the range of the water-mediated interactions between hydrated polar groups directly. This was achieved by so-called 'molecular rulers '. The pH-titration of such bifunctional water-soluble sub-stances of precisely known composition is studied potentiometrically2' or calorimetrically.22 By means of molecular modelling programs the separation between the identical terminal titratable polar groups is determined with an accuracy of better than 0.05 nm.$ From this length and the corresponding separation-dependence of the measured (de)protonation constant the solvent-dependent contribution to the Helmholtz energy was determined. This was again done as a function of the separation between the titrated polar groups.This yielded directly the range of the water- $ Previous attempts to use similar methods for the determination of A have given erroneous and too large values. This was chiefly owing to the ad hoc estimates of the molecular ruler length and to the fact that experimental data from different sources were used. 1945 mediated interactions, and thus a tentative value for the water-order decay length. For a series (n = 24) of different hydrophilic solutes we have found the hydration range of molecular rulers consist- ently to be smaller than 0.1 nm: A = 0.086 f0.003 nm, when E, = 2 was used. Even for the highest reasonable choice of the high-frequency relative permittivity, E, = 5, the water-order decay length value was still quite small: A = 0.144 f0.002 nm between 4 and 85 "C.? Although it may seem strange that the measured hydration decay length of water is smaller than the size of an individual solvent molecule (ca.0.25 nm) this result is in perfect agree- ment with the most recent theoretical results of Matyu~hov.~~ These show that the actual solvation decay length in polar liquids should be of the order of one-half of the solvent size, A z 0.5~.Some of the problems that arise in the non-local electrostatic theories of hydration thus might be due to the use of too large order decay values for water (A 2 a). At this point the ideal 'macroscopic' character of the cur- rently used simplified hydration theories is immediately clear.Many such theories invoke the propagation of an external perturbation of the solvent-order parameter throughout the bulk solvent on the length scale of A. The molecular graini- ness is typically neglected in such theories. The many-body effect, which is called 'hydration', is thus described by a smooth mean field which is also allowed to vary on a sub- molecular length scale. One must be therefore alert to avoid overly simplistic arguments and misleading conclusions based on such models. The explanation of the interfacial hydration solely in terms of simple 'dipole orientation' of water mol- ecules near the polar surface is one example of this. Indeed, the interfacial water layer thickness in phospho- lipid multilamellae, for example, is quite large; it may appre- ciably exceed the bulk value of A.To account for the resulting interfacial structure effects a fixed value of the surface local excess charge density, o,, should be replaced by the corresponding surface polarity profile, p,(r). In the sim- plest approximation this is achieved by introducing its one- dimensional kin, p,(x). In order to find such a spatial polarity profile, the magni- tude and the distribution of the individual local excess charge densities on all polar surface residues has to be known. These densities can be evaluated for each polar group or atom, r, from the corresponding entity charge, Q,, and volume, V,. The standard relation pp,, = Q,/K is used for this purpose. Individual local excess charge values can stem from suitable computer simulation^^^ or, even better, from direct meas~rements~~[cf.Fig. 3(b)].S The required volume values can deduced from Pauling radii (corrected for the effects of thermal smearing). Finally, the integral surface polarity profile is determined by summing up all contributions from the polar residues and by the subsequent surface averaging over molecular area, A, pp(r) = A, ' 1A, ~p,r(r) (9) r where A, = v,2/3 and the prime signifies that only polar groups that are not compensated directly by mutual intra- surface charge-transfer processes are included in the sum. The t Since all these values pertain to the dissolved substances it is impossible that the smallness of A could be due to the lateral- structure effects, which have repeatedly been invoked to explain the small A-values measured with the multilamellar lipid lamellae in the gel phase or for some DNA systems.$ If required and known, the differential physical accessibility to water, 0 d a, < 1, of the individual polar groups, moreover, can also be accounted for: pp,,= x, Q,/K. latter may arise from intra-surface hydrogen bonds or from other direct intra-surface interactions. (This means that only polar residues free to bind water are important for the surface hydration.) According to our data analysis, the relevant water-order decay length A is much smaller than the typical thickness of the phospholipid/water interface: d, z4 to 11 x A.The value of A thus being much smaller than the total length of the common phospholipid polar headgroups, it would seem that every realistic hydration model should allow for the dis- creteness of surface polar residues. The Poisson equation should, consequently, be solved in three dimensions. In this contribution we are primarily concerned with the energetics of surface hydration, however. We therefore neglect the effects of lateral surface inhomogeneity. This is justified in the first approximation at least.? With appropriate precautions the area integration then can be done in advance. This allows working with suitable surface averages without restricting the reliability of the qual- itative model conclusions.” Eqn. (9) then becomes r rx+ax A complex three-dimensional problem has thus been mapped into one dimension solely by means of eqn.(10) and a solu- tion to eqn. (7).$ The result of such a procedure is shown in Fig. 3(c). It is based on the local excess charge information measured for the model phosphatidylethanolamine ‘membrane’: phos-phorylethanolamine crystals at low temperature (123 K, ref. 25). To get the polarity profile shown in this figure each local excess charge value, Qi, was assumed to occupy a volume of qi= 4nRi3/3, where Ri is the van der Waals radius, and to be spread thermally in accordance with the experimentally determined value2 of the corresponding Gaussian Debye- Waller factor. The corresponding charge density values were then normalized with regard to the lipid area.The latter was taken to be constant, A, = 0.56 nm2, for the sake of simpli- city. The surface profile of a lipid layer was thus approx- imated by x exp[ -(7)I] dy where ri is atomic position, Rithe relevant van der Waals radius and ai the measure of the isotropic thermal mean-displacement of an atom i. Since the value of A is small com- pared to the intermolecular distances the absolute value of the local excess-charges were used. Boundary-value Formulation For practical applications it is more suitable to reformulate the theory of surface hydration directly as a boundary value problem. It is therefore convenient to introduce the Green’s function corresponding to eqn. (7). This function is given by t This is less true for a vector order parameter which is also sensi- tive to the effects of changing direction.Hydration models based on the concept of water polarization (vector) are thus more sensitive to lateral inhomogeneity than our present model which uses water binding energy or potential (scalars) as the basic variables. 1For a more realistic study of intersurface interactions it is advan- tageous to know and consider the positions of all polar residues on the interacting surfaces. The discreteness of water binding sites as well as interfacial correlation effects then may become impor-tant.12,15,16,26 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 the solution to d2G(x, y)/dx2 -G(x,y),1A2= 6(x -,v) (12) and relates the spatial profiles of interfacial charge and hydration potential by $h(X) = r.I.3 Y)[l-Kpp(Y)l dy (13) The actual form of Green’s function is determined by the boundary conditions.These must be specified in order to make the solution to eqn. (7) unique. The appropriate boundary conditions are easily derived from the usual condition of system electroneutrality. In the linear, one-dimensional approximation this means that one should have: j p, + p, x 1$h -KPP= 0. With eqn. (7) one then gets 1&(0) = t&(dw) for the first derivatives of the hydra- tion potential. For the identical surfaces this implies 9N)= 4ww) = 0 (14) owing to the system symmetry. By extending this argument one can claim the same boundary condition for any two sur- faces in the one-dimensional approximation.Eqn. (12) together with eqn. (14) determines the Green’s function of our model system. In the general case of two interacting interfaces separated by a solvent layer of thickness d, one then has (15) This expression is suitable for the calculation of all ther- modynamic quantities of our current interest, such as the Helmholtz energy of hydration or the hydration pressure. The Helmholtz energy, for example, can be written as a ‘matrix element’ (16) Likewise, the hydration pressure between both surfaces of interest is calculated from Eqn. (16) explicitly invokes parameters d, and A. It also depends on the separation dependence of p,. This clearly shows that the generalized mean-field theory of hydration contains two length scales: the solvent-order decay length A and the ‘typical interfacial thickness’ d, which depends on the actual form of the surface polarity profile p, .In principle, it should thus be possible to use a set of experimental hydration pressure data in order to deduce the spatial profile of surface hydration potential; from the latter, the surface polarity profile could ultimately be obtained. The fact that surface hydration potential and surface polarity profile are connected through a second derivative or double integration, however, restricts the intrinsic resolution of such an approach [cf. eqn. (7)]. The general Green’s function eqn. (15) is of little practical use. The reason for this is that the hydration pressure equa- tions are much too complicated if they are expressed in terms of this function.More suitable for the evaluation of the surface polarity profile is a conventional ‘linear superposition’ approx-imation. In this approach, the hydration pressure between J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 two (interacting) interfaces at a distance d, is calculated from the change of the Helmholtz energy which results from bring- ing two single interfaces from infinity to a separation dW/2. Fig. 3 illustrates the results of such a calculation. A more detailed description is given in ref. 11, where we derive the surface polarity profile, pp, of a phosphatidylcholine bilayer from the measured hydration force data.? In any case, the problem of a suitable starting interfacial polarity profile must first be solved.In this context it is con- venient to realize" that the application of the Green's func- tion to a polarity profile can be considered as the action of a self-adjoint operator. Therefore, every continuous function which fulfils appropriate boundary conditions can be written as a series expansion in terms of the eigenfunctions C,,(x)of Green's operator a, KPp(4 = c A"Cfl(4 (18)n=O With eqn. (8) and (18) it then follows owing to the orthonormality of eigenfunctions. Eigen-functions that correspond to eqn. (15) and pertain to our model are simple cosine-functions : n = 0, 1, 2, . . . (20) and have eigenvalues 12 UW = 0, 1, 2, . .. (21)A,,= -dt + (n7~A)~ Although the eigenvalue expansion seems to be quite simple one has to realize that both the Fourier coefficients A,, as well as the eigenvalues A,, depend on the interlamellar water layer thickness d, .Practical applications of the expansion (18) are discussed in detail in ref. 11. Discussion We have previously shown that many features of atomic and molecular hydration can be described in terms of a 'mean- field quantum mechanical model of hydration'.6 This was obtained by generalizing and modifying the non-local electro- static model of an ice-like water that was initially introduced by Onsager and Dupuis2* and later extended by Gruen and MarEelja.4 For the sake of convenience, all such models were devised so as to resemble as closely as possible the Gouy- Chapman diffuse double-layer theory.In this paper we discuss in detail the model generalizations which also allow for the interfacial structure effects. The simplifying assumptions of our current model are : First, a continuum solvent model with just one characteristic correlation (or order-decay) length is used. Secondly, the solvent parameters are taken to be independent of separation. (This is probably true for the very short correlation lengths and intramolecular modes considered in this work : librations and vibrations of the water molecules are unlikely to change t In ref. 11, the wrong boundary conditions are used. This affects just the Green's function, however, and has no influence on the resulting p,-profiles.The reason for this is that at all experimentally accessible distances such profiles are much greater than zero. There- fore, no reconstruction of the p,-profile near a boundary is possible. Beyond the boundaries, however, the profile is independent of the boundary conditions. much with the system hydration. This is true for the solvent- order decay length A as well as for the high-frequency rela- tive permittivity E, .) Thirdly, only a one-dimensional surface polarity profile is considered. No account is thus made for the lateral surface structure effects. This assumption is clearly an oversimplification which is relaxed in our next paper.I2 Fortunately, it does not affect our qualitative conclusions, however, owing to the scalar nature of the order parameter used.The formal parallelisms between the generalized Gouy- Chapman29 and the generalized mean-field hydration model8 are given in Table 1.It shows that all crucial equations of the non-local electrostatic hydration model closely resemble the corresponding equations of surface electrostatics. This simi- larity indicates that in both cases a similar physical mecha- nism is at work: the electrical screening of the interfacial charges. The only exceptions are expressions which depend on the distribution of the water-associated excess charge density, which contain a factor (1 -E,/E) instead of a simple relative permittivity E. This difference is a result of an 'ad hoc' electrostatic representation of the interactions between water molecules. This factor is the smallest possible tribute to the quantum- mechanical nature of molecular hydration.20 It ensures that the surface-induced accumulation of the water-associated local excess charges, p,,,(r),and the hydration-dependent field Eh(r) both disappear if the solvent structure is neglected. Water susceptibility for the interaction with the surface polar residues then, of course, also attains a zero value.In such situations, the aqueous sub-phase acts as a simple dielectric with E, -+ E. However, normally the situation is different. Polar surfaces immersed in water start to bind the solvent molecules. While doing so, they swell in all directions. In the majority of cases, the swelling proceeds chiefly, but not exclusively, in the direc- tion perpendicular to the hydrophilic surface.14 In the initial stages of water uptake by the phospholipid bilayers, for example, the molecular area' and the thickness of the hydrated headgroup region3' both increase strongly. For the phospholipids with two acyl chains the hydration-induced area expansion is up to 0.2 nm2 in the gel phase and up to 0.3 nm2 in the fluid lamellar phase, precise values depending on the lipid type and experimental conditions.The accompany- ing change in the interfacial thickness is estimated to be between 0.2 nm and 0.8 nm.I2 These values compare nicely with the thickness of the polar region that was deduced from the lipid crystal data (cf:Fig. 3).An assumed interfacial thickness of ca. 1 nm is thus cer- tainly not an exaggeration. This implies that between 30 and 75% of the 'interbilayer water layer thickness' can be reached, and possibly swept, by the hydrated lipid heads. These heads, consequently, must contribute to the total inter- facial repulsion at least at short and intermediate separations. It is important to realize, however, that this is not a standard, hard-core, steric repulsion discussed previously by Simon and co-worker~.~'It is also not identical to the protrusion force studied by Israelachvili and Wenner~trom.~~ The repulsion described in this work is driven and mediated by the polar headgroup hydration. In the absence of water our model reveals no net interfacial repulsion.If such a repulsion did exist dry lipid crystals would be unstable. Fig. 3 suggests that the interfacial fine-structure effects are masked in the surface potential and interfacial force profiles. The latter profiles are always smoother than the underlying polarity distribution profile. This is due to the integration which must be performed in order to obtain the surface hydration potential from the known surface-charge distribu- tion. The irregularities in damping are also a consequence of the fact that our present Landau form of the expression for the Helmholtz energy contains a gradient term which sup- presses the effects of all small-scale variations. In previous sections we have argued that Gouy-Chapman diffuse double- layer thesry is based on a very similar Helmholtz energy functional. From this theory and numerous computer simula- tions of the ionic double layers it is known that the surface potential profile is very insensitive to the fine details of the charge distribution in the interfacial region.33 Our previous suggestion” that the interfacial polarity profile is mirrored in the interfacial ‘hydration force’ thus should be interpreted properly. Rather than being a simple mirror, the interfacial force is an integrator of the overall surface hydrophilicity.However, this ‘integrator’ is relatively insensitive to the fine interfacial structural details. To illustrate the influence of a surface polarity profile and this thickness on the hydration phenomena, we have calcu- lated the hydration pressure for several model profiles: a box (with a variable width b), an exponentially decaying profile (with several decay lengths dp), and a Gaussian profile (with varying thickness ndJ2).All these models, their correspond- ing analytical expressions, and the results of our hydration force calculations are given in Fig. 4-6, respectively. They were all obtained by assuming that A = 0.1 nm. Comparison of the results from Fig. 4-6 shows that the ‘thickness’ of surface polarity profile may influence the final hydration pressure in a number of ways. For a box-like inter- face it only leads to an increase in the pre-exponential factor po. This is due just to the renormalisation of the effective 0.6 .-0.3 0.0 I I I II I I (b110 I I I I I I I I 1 0 1 2 3 4 d,/nm Fig.4 Model calcu lati ons for a box prof ile giv en by p,(x) = Q(@b - - -x)O(x) + 8[x (d, b)]8(dW-x)}, where x = 0.. d,, 8 is the usual step-function and b is the box width. (a)Polarity profile, p,(x) and (b) calculated hydration pressure as a function of the inter- lamellar water layer thickness, d,. Lines (from top to bottom) given forb = 0.25,0.15, 1.0, 0.08 and 0.04 nm. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 0.0 n h X vs’ Fig. 5 Model calculation for the exponentially decaying surface polarity profile given by p,(x) = N(d,)p,(?), with p,(?) = exp(-d,/2dp)cosh[(x -dW/2)d]-exp(-d,/d,) with the normal-ization constant N(d,) = Q/I$p,(?) dx.(a)Polarity profile pp(x) and (b)calculated hydration pressure as a function of interlamellar water layer thickness and exponential decay constant d, . Both were evalu- ated by means of the commercially available software package MAPLE V. (-) Total polarity profile and (---) polarity profile of a single interface. distance between the interfaces. However, a box-like polarity profile does not affect the apparent decay length of hydration pressure. On the contrary, for the exponential as well as for the Gaussian surface polarity profile, the decay length of hydration force is modified by the thickness of the interfacial region. In the case of an exponential surface polarity profile the result is essentially the same as that reported in ref.10: the calculated hydration pressure contains three terms. One depends on the water-order decay length A, one on the decay length of the surface polarity profile, d,, and the third on a mixture of both. The hydration pressure as a function of the interlamellar water layer thickness at large distances is always determined by the larger of these two characteristic length parameters. The results for the Gaussian surface polarity profiles are more complicated by also reveal the existence of two different decay regimes. At short distances the spatial decay of hydra- tion pressure is nearly exponential, even for a Gaussian polarity profile. The characteristic decay length of hydration force then increases with the interfacial thickness. Even an interfacial thickness which is only one-half of the water-order decay length increases the effective range of hydration pheno- mena appreciably. At large distances all profiles are parallel.Over small intervals the corresponding curves can be approx- imated by exponentials. The point at which this becomes pos- sible gets larger with increasing thickness of the surface polarity profile. In Fig. 5 the hydration pressure profiles for surfaces with an exponential polarity profile are shown. The pressure value J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 1.2 , 1 X 1o-2 d,/nm Fig. 6 Model calculation for a Gaussian surface polarity profile: PPH= exp{ -Cx -(~~p/2)12/(ndp/2)2}+ exp( -{x -Cd, -(.4/2)21}/[nd,/2I2).A, Polarity profile pp(x)and B, hydration pressure between two interacting surfaces with such polarity profile as a function of the interlamellar water layer thickness d,.(ndJ2) = (a)0.4, (b)0.3,(c)0.2, (d)0.1, (e) 0.05 and cf)0.02. (9)exp(d,jA) where A = 0.1 nm. diverges at short separations. However, if the area under the polarity profile decreases with d, +0 this divergence disap- pears (not shown). The latter situation is illustrated in Fig. 6 for a Gaussian surface polarity profile of variable height. For such a profile the hydration pressure at low distances goes to zero. We believe that the reality lies somewhere between these two limiting cases but closer to the latter. At short distances, which correspond to a low total water content, one does not expect the surface polarity profile to have a constant height.Indeed, if the total surface charge was a constant non-zero value, lipid drying would be nearly impossible. On the other hand, at large distances (i.e. at high water content) the surface charge distribution and accessibility is probably independent of the water content between the interfaces. This question of normalization is only of minor importance for practical pur- poses since differences in the calculated hydration pressures occur only at small distances. Realistic model calculations should allow for interfacial swelling during water uptake. The neglect of this phenome- non may provoke quantitatively false conclusions such as an underestimation of the effective decay length of the hydration force.However, the principal trends are always the same. We believe that our conclusions are relevant for most, if not all, hydrophilic systems. Interfacially bound water in such systems is known either to increase the average separation between the individual polar headgroups and the mobility of polar residues on such headgroups or else to shift the polar- apolar interface away from the solvent and into the ‘surface depth’. A more detailed account of these effects, as well as a discussion of the corresponding temperature variations, will be published elsewhere. Solvation force measurements in non-aqueous solvents34 imply an apparent correlation between the ‘solvation force decay length’ and the size of the solvent molecule.Our con- clusions are not necessarily borne out by such results. First, the interfacial swelling, and thus the interfacial thickness, is also likely to depend on solvent size; solvent partitioning and binding in the interfacial region are the reasons for this. Sec- ondly, from the three experimental points measured to date no general conclusions can be drawn. We believe that the validity of our conclusion is hardly affected by the neglect of the lateral surface structure. This is not surprising since the results of all models that are based on the vectorial order parameters are far more sensitive to the lateral surface structure than the models based on the use of scalar order parameters.Indeed, the corresponding insensi- tivity of the main conclusions of this study has been directly confirmed in an investigation in which the variations of the surface polarity parallel and perpendicular to the surface plane have been allowed for simultaneously.’2 In summary, we have shown that it is possible to describe and understand the hydration of polar surfaces either in terms of the surface hydration potential or else, but less pref- erably, in terms of its associated hydration field. We have derived several equations which relate these two basic quan- tities and have shown that they are formally identical to the results of standard electrostatic diffuse double-layer theory. Based on our model calculations, as well as on the experimen- tal data of other authors, we have concluded that the thick- ness of the polar membrane region (d, > 1 nm) is much greater than the typical water-order decay length (A % 0.1 nm).We suggest that any change of the interfacial thickness should modify appreciably the surface polarity profile and the hydration-dependent intermembrane repulsion. This pro- vides a rationale for the explanation of the measured hydra- tion force data. Financial support by the Deutsche Forschungsgemeinschaft (under grants Ce 2/1, Ce 19 5/1-1 and SFB 266/C8) is grate- fully appreciated. We would also like to thank A. A. Korny-shev for very stimulating discussions. Appendix A: Hydration in the Field and Potential Approaches In the field approach the Helmholtz energy of the hydration is described by the general expression’ F = s {El(x) + A2[VEh(x)l2-2Eh(x)Ep(x))dx (A1) Eh is the vectorial order parameter and E, the external per- turbing field.Auxiliary constant r is defined as r = -+A[E~E,(~ + _+A/2K,the use of positive and -E,/E)]/~A* negative signs being described in the main text. By minimizing eqn. (Al) in three dimensions the following Euler-Lagrange equation is obtained A2AEh-Eh = -Ep -vr\(VAEh) (A21 where A indicates the vector product. Since Eh = -vrl/h E, = -v$ ho 043) it also follows from eqn. (A2) that V(A2Arl/, -rl/h + $ho) = 0. This is equivalent to A2A+hh-rl/h = -lCIho + c where c is a constant. After the introduction of $co = $ho -c eqn. (A3) can be recast in the following form? A2A$h -$h = -$to (A4) which corresponds to the Euler-Lagrange equation of func- tional The Helmholtz energy of the investigated system can thus be described in two, almost equivalent, ways.First, the vecto- rial surface hydration field can be used as an independent system variable and a basic order parameter; secondly, this r61e is taken by the scalar surface hydration potential. To obtain two consistent sets of differential equations that describe the thermodynamic optimum of the system one should, furthermore, require that the boundary conditions in both cases are consistent. This implies that Vn $h lav = Eplav (A61 where n is the outer normal direction at the boundary dV. This relation connects the boundary conditions in the field and potential approaches.From the definition (A3) it is clear that the potential $h is a mean-field potential which includes contributions from the external as well as internal fields. What remains to be done is to find a connection between the pre-integral factors in the Landau expansion for the Helmholtz energy, when the latter is expressed in terms of the surface hydration field and hydration potential, respectively. To achieve this goal, a series of formal manipulations on the functionals F and I;* is made. The results of these manip- ulations are then combined with Euler-Lagrange equation for the surface hydration potential$ to get Starting with eqn. (Al) in three dimensions, setting again -Eh= -v$h, Ep = -Vt,bh0, r = ~~e,(l E,/E)/~, and per- forming partial integrations with regard to v$h and v$ho, one gets F = r bA$h(A2A$h -$h -k 2$h0) d3x + l,(1.-2$ho)v$h dS (A8) Combination of eqn.(A7) and (A8) then yields I-/. The same procedure applied to eqn. (A5) gives /. /. Now, F as well as F* describe the thermodynamic behav- iour of the same physical system. These two quantities, there- fore, must be identical, up to a constant term. This also pertains to their dimensions. Expressions (A9) and (A10) consist of sums only. The previous requirement is thus also for all individual terms. In order to find the connection between r and r*it is, consequently, enough to compare all t,$ho is a short notation of KPp. $ Owing to the fact that the constant difference between $h and t,$z depends only on the choice of the zero point of potential, and has no physical significance, the potentials $,, and t,$z from now on are taken to be identical.J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table A1 Prefactors r and r*in 1 and 3 dimensions n=l n=3 equivalent terms. In the following, we use the volume inte- grals as an example. Substituting $hoA$h = $ho($h -$ho)/h2 [from eqn. (AT)] into eqn. (A9) gives + l>$h -2$ho)V$h dS (A11) If the potential $ho is non-zero, one gets, by comparison of eqn. (A10) and (All), r*= -T/A2; however, in the case of vanishing potential, $ho = 0,r*= +r/A2. Explicit expressions for the constant r are given for some cases in Table Al. The absolute values of all constants in the non-local electrostatic model are given in this table for the case of non-zero surface potential or external field (hf 0).In the one-dimensional case, the surface area A becomes a multiplicational factor owing to the fact that the area integra- tion is done in advance. The derivation given in this appendix is based on the use of one, standard thermodynamic minimization requirement and on the simple electrostatic relations between the local fields and potentials. No reference is made to the dimensions of the investigated system or to its boundary conditions. Final model results, consequently, are applicable to the isolated surfaces in water as well as to the interacting surfaces. Appendix B: External Hydration Potential and the Surface Polarity Profile In previous publication^^.^.^ the one-dimensional field approach was used.The external field was then assumed to be confined to the polar surfaces only, i.e. E, =f16(x + d/2) +f2qX-42).3 In the generalized model discussed in this work such an assumption would lead to rather unphysical situations, such as an infinitely high electrostatic potential in all space. To avoid this difficulty eqn. (A3) is useful. In the present case it gives E, = -KVp. In the one-dimensional approx- imation discussed in3 it corresponds to E2 + A2(E’)2+ ~EKAcT, (W if the density p is assumed to be purely a surface term. From the relation f(x)d’(x) = -f’(x)d(x) one gets: h2E” -E = E’KAo,[G(x + d/2) + 6(x -d/2)].However, the delta func- tions contribute only at the boundaries; integration across each surface thus affords the appropriate boundary condi- tions for the field derivative, E’. Within a sign, these are iden- tical to those given in ref. 3. In such a special case the distinction between the surface hydration potential or the surface charge density is somewhat arbitrary. After all, Poisson’s equation implies that a step- function-like potential is related to the charge density through 6’. With properly adjusted constants both interfacial descriptions are thus possible and consistent with each other. However, as soon as the hydrated interface becomes an interphase and attains a finite thickness, the interpretation of J. CHEM. SOC.FARADAY TRANS., 1994, VOL. 90 i+!ie0 as an electrostatic potential is no longer possible. For the thick interfaces (‘interphases’) only the terminology based on the charge distribution is appropriate. Appendix C: Generalized Theory of Hydration and Non-local Electrostatics The simplest method of obtaining eqn. (8) for the Helmholtz energy of hydration from the theory of non-local electro- statics is to begin with which is the general starting point of any theory of screening. Eqn. (Cl) relates the Fourier transforms of the potential, $(q), of the charge distribution p(q), and the (spatially varying) relative permittivity c(q). This relation is derived in nearly every textbook on solid-state physics (cf.ref. 35). Although the actual form of E(q) is not known this function has some very general features based on its physical proper- ties.(See ref. 36 for a thorough discussion of this aspect.) The simplest approximation for the relative permittivity of a polar fluid is given by so-called ‘single pole approximation’, which, together with eqn. (C2),results in Since q2$(q) is the Fourier transform of -A$(x), eqn. (C3) after the transformation into real space gives the integro- differential equation -A2A$(x) + $(x) = -A2 p(x) + -1 17exp(-iqx) dq ‘Q EEO (C4) This result is very similar to eqn. (7),except for the existence of the integral term. Neglect of this term together with the general electrostatic relation F x $(x)p(x) d3x then yields eqn. (8) for the Helmholtz energy, In the light of this deriva- tion the main simplification of the mean-field hydration theory is thus the use of a simplified relation between the charge distribution and the electrostatic potential.The differences in constants that appear in eqn. (7) and in the approximate equation eqn. (C3) are not important from the practical point of view. The reason for this is that E z 80 and E, z 2, so that (1 -E,/E) x 1. Furthermore, the given ‘derivation’ totally neglects the anisotropy of the system, (C2) pertaining to a homogeneous medium. Note that (C2) is only one special possible form of E(q). This means that even the most general or exact hydration model that is based on the concepts of non-local electro- statics relies on several ad hoc assumptions.? We are not t There is another possibility to derive the free energy of hydration within the framework of the non-local electrostatic model.This approach (ref. 12) works in q-space and uses a more general expres- sion for E. The hydration potential in such an approach is formally calculated for a very general Green’s function. For the numerical cal- culations, however, it is necessary to use a truncated Green’s function which is nearly identical to ours. aware of any first-principle arguments in favour or against a given plausible choice of the required model constants. It was, therefore, solely for the sake of convenience to keep the same definitions of constants as in our earlier papers, such as ref. 6. References 1 S. MarEelja and N.RadiE, Chem. Phys. Lett., 1976, 42, 129. 2 S. MarEelja, Croat Chem. Acta, 1977,49, 347. 3 G. Cevc, R. Podgornik and B. ZekS, Chem. Phys. Lett., 1982,91, 193. 4 D. W. R. Gruen and S. MarEelja, J. Chem. Soc., Faraday Trans. 2, 1983, 79, 225. 5 G. Cevc and D. Marsh, Biophys. J., 1985,47,21-31. 6 G. Cevc, Chem. Scr., 1985,2597. 7 G. Cevc and J. M. Seddon, in Surfactants in Solution, ed. K. L. Mittal and P. Bothorel, Plenum Press, New York, 1986, vol. 4, pp. 243-255. 8 G. Cevc and D. Marsh, Phospholipid Bilayers, Wiley, New York, 1987. 9 G. Cevc, Biochim. Biophys. Acta, 1990,1031-3, 3 11-382. 10 G. Cevc, J. Chem. SOC.,Faraday Trans., 1991,87,2733. 11 S. Kirchner and G.Cevc, Langmuir, submitted for publication. 12 M.Hauser, A. A. Kornyshev and G. Cevc, 1994, submitted for publication. 13 R. Podgornik, Chem. Phys. Lett., 1989, 163, 531. 14 R. P. Rand and V. A. Parsegian, Biochim. Biophys. Acta, 1990, 988,351. 15 A. A. Kornyshev and S. Leikin, Phys. Rev. A, 1989,40,6431. 16 A. A. Kornyshev and S. Leikin, Phys. Rev. A, 1991,44, 1156. 17 K. Zakrzewska, in Physical Chemistry of Transmembrane Ion Movements, ed. G. Spach, Elsevier, Amsterdam, 1983, pp. 45-66. 18 N. Thanki, J. M. Thornton and J. M. Goodfellow, J. Mol. Biol., 1988,202,637. 19 (a)A. Pullman, B. Pullman and H. Berthod, Theor. Chim. Acta, 1978, 47, 175; (b) A. A. Kornyshev, in The Chemical Physics of Solvation, ed. R. R. Dodonadze, E. Kalman and A. A. Korny- shev, Elsevier, Amsterdam, pp. 77-1 18. 20 (a) A. A. Kornyshev, J. Chem. Soc., Faraday Trans. 2, 1983, 79, 651; (b) R. R. Dogonadze, A. A. Kornyshev and A. M. Kuznet- sov, Theor. Mat. Fiz., 1973, 15, 127. 21 G. Schwarzenbach, Pure Appl. Chem., 1970,24, 307. 22 M. Hirth and G. Cevc, to be published. 23 D. V. Matyushov, Chem. Phys., 1993,173, 199. 24 G. Peinel, Chem. Phys. Lipids, 1975, 14, 268. 25 S. Swaminathan and B. M. Craven, Acta Crystallogr. B, 1984, 40, 511. 26 S. Leikin and A. A. Kornyshev, J. Chem. Phys., 1990,92,6980. 27 M. Elder, P. Hitchcock, R. Mason and G. G. Shipley, Proc. Royal SOC. London, A, 1977,354, 157. 28 L. Onsager and M. Dupuis, in Electrolytes, ed. B. Pesce, 1962, p. 27-46. 29 G. Cevc, S. Svetina and B. ZekS, J. Phys. Chem., 1981,85, 1762. 30 C. A. Helm, P. Tippman-Krayer, H. Mohwald, J. Als-Nielsen and C. Kjaer, Biophys. J., 1991,60, 1457. 31 T. J. McIntosh, A. D. Magid and S. A. Simon, Biochemistry, 1989, 28, 17. 32 J. N. Israelachvili and H. Wennerstroem, Langmuir, 1990,6, 873. 33 S. L. Carnie and G. M. Torrie, Adu. Chem. Phys., 1984,56, 141. 34 T. J. McIntosh, A. D. Magid and S. A. Simon, Biochemistry, 1989,28,7904. 35 N. W. Ashcroft and N. D. Mermin, Solid State Physics. Holt-Saunders, Philadelphia, International edn., 1976. 36 A. E. Blaurock, and T. J. McIntosh, Biochemistry, 1986,25,299. Paper 3/05964B; Received 5th October, 1993

ISSN:0956-5000    

DOI:10.1039/FT9949001941

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1953-1959 Kinetics of Self-replicating Micelles J. Billingham and P. V. Coveney Schlumberger Cambridge Research, High Cross, Madingfey Road, Cambridge, UK CB3 OHG Recent experiments which achieved the autopoiesis of caprylate micelles by aqueous alkaline hydrolysis of ethyl caprylate have shown that the kinetics of this process are highly non-linear. There is an extended induction period during which the concentration of micelles remains small; at the end of this period, ethyl caprylate is consumed and micelles form rapidly via an autocatalytic reaction. In this paper, we investigate two macroscopic kinetic models for this process. In the first, we specifically include the equilibrium critical micellar concentration for caprylate anions and require that self-replication of micelles only occurs beyond this point.In the second, we study the properties of a non-linear model which is capable of accounting for the very sharp growth in total caprylate concentration as a function of time, without making any assumptions concerning equilibrium. Although both of these models have limitations, they provide insight into what features a more realistic model must have. We conclude by formulating a mesoscopic model that provides a much more detailed description of the micro- scopic processes of micelle formation, and which observed react ion kinetics. 1. Introduction The synthesis of autopoietic systems in the laboratory is cur- rently under investigation.? The motivation for this work originates in a definition of the minimal conditions necessary for a system to be called living, proposed by Maturana and Varela.' In brief, they define autopoiesis as a process whereby a system which possesses well defined boundaries is capable of self-replication.It can be argued that the micellar system that we shall describe here is indeed such an autopoietic system and therefore can be regarded as fulfilling this cri- terion for minimal life.2,3 In the present paper, we shall study the kinetics of this system in some detail. The most obvious feature of the reaction is that there is a well defined induction time prior to very rapid growth in the production of micelles. We begin by briefly summarising the experimental techniques employed, and then describe our theoretical analysis of the non-linear kinetics of self-replication.We conclude by outlin- ing a mesoscopic approach which may provide a more realis- tic model of the kinetics of micelle formation than the macroscopic models that we describe here. 2. Experimental Methods and Observations The basic experimental set-up is very simple. Immiscible ethyl caprylate and a concentrated (3 mol dm-3) aqueous solution of sodium hydroxide are stirred at 150 rpm and heated under reflux, typically at temperatures close to 100°C. Any alcohol produced in the reaction boils off under reflux. The concen- tration of ethyl caprylate and the total caprylate anion concentration are conveniently determined by FTIR spec-troscopy. The concentration of the developing micellar struc- tures is determined from time-resolved fluorescence q~enching.~ It is found that for a well defined period after the start of reaction very little activity takes place, as measured by changes in the concentrations of the aforementioned species.However, at the end of this quiescent period the reaction sud- denly takes off at a dramatic rate: all of the ester is consumed and the production of micelles proceeds apace, as illustrated in Fig. 1. The final state of the system, after about 34 h, is a homogeneous clear liquid. Experimentally, the induction A group at the Institut fur Polymere at the E.T.H. in Zurich is actively researching this area.' we believe will provide a quantitative description of the period is found to depend strongly on both the temperature and the initial concentration of caprylate ions.An important quantity is the critical micellar concentration (c.m.c.) of the caprylate surfactant system. The c.m.c. is defined as the concentration of monomers above which micelles are formed. Note that this is an equilibrium property of a micellar system, and therefore not necessarily relevant to the experiments currently under discussion. In addition, it is notoriously difficult to measure c.m.c.s unambiguously, not only because the results are strongly dependent on which technique is used for making the measurements, but also because micelle clusters are actually present at low concentra- tions below the notional c.m.c.One simple way of measuring c.m.c.s makes use of the cloud point in a surfactant system as the concentration of monomers is steadily increased. For the surfactant described above, the c.m.c. was found by this method to be 0.1 mol dm-3, under the conditions pertaining in this experiment. The number of caprylate monomers per micelle determined experimentally is roughly n = 63. The ester dissolves in the micelles, where it is rapidly hydrolysed to form more sur- factant and hence micelles. It is apparent that the micelles are self-replicating insofar as they act as a cross-catalyst for the hydrolysis of ester in the bulk of the aqueous phase, rather than being restricted to the macroscopic ester/water interface as would be the case in their absence. The aqueous caprylate micelles formed can be reversibly transformed into vesicles by decreasing the pH to 6.5.These have been observed using freeze-fracture electron microscopy, and have a radius of around 150 nm. The same effect can be achieved by bubbling CO, through the solution. Note also that use of caprylic anhydride in place of the ethyl caprylate ester leads to hydrolysis at lower pH, whereby vesicles are formed directly. 3. Theoretical Analysis In purely qualitative terms, it is simple to account for the behaviour of this system, as described in the previous section. However, it is of considerable theoretical importance to be able to furnish a more detailed account of the processes involved in this example of autopoiesis.For example, from the point of view of prebiotic chemistry one would like to be able to furnish estimates of induction times and timescales for the period of rapid reaction. The modelling approach described in this paper also serves to highlight the basis for the unusual time-dependent properties of self-assembling supramolcular micellar systems in general. As such, it should be of general interest inter alia to those working on the kinetics of self-replicating systems.' Let EC represent ethyl caprylate, C, the caprylate anion monomer, and C,, the micelle formed from caprylate anions, assumed as in ref. 2 to be monodisperse with n = 63. From a theoretical standpoint, the assumption of monodispersity is, as will become clear in this work, a rather strong one.In broad terms, the following processes occur, EC is con- verted to C via two possible routes. In the first, the step EC -P C occurs directly through alkaline hydrolysis in the presence of excess hydroxide. The C produced in this manner can then form C, in a process which, if it were at equilibrium, would only proceed if the concentration of C exceeds the c.m.c. Once Cnstarts to appear in the system, unreacted EC is solubilised within the micelles, and is then hydrolysed. If this last process is fast, its effect is to cross-catalyse the pro- duction of C (and, of course, indirectly C, itself) thereby catalysing the production of micelles. Overall, therefore, the production of micelles is autocatalytic in that, once some are formed, they accelerate their own rate of formation.In the following subsections we analyse two models for the kinetics of micelle formation. Although we shall see that neither of these models is entirely satisfactory, an understand- ing of the difficulties that arise in connection with each scheme tells us a lot about the features which a more com- plete model should have. 3.1. Model with known C.M.C. The reaction scheme for this model is rate = 0; for CCl [Clc.rn.c. C, + EC C, + C; rate = k2[EC][Cn] (14 Here, square brackets denote the concentration of the given chemical species. The c.m.c. is written as [C]c.m.c,.The three steps in reaction (I) represent : uncatalysed hydrolysis of ethyl caprylate, EC, to produce the caprylate monomer, C, by pseudo-first-order kinetics, assuming that this takes place in the aqueous phase where hydroxide ion is present in large excess compared to the ester [reaction (Ia)]; formation of a micelle, C,, from n caprylate monomers, C [reaction (Ib)]; and hydrolysis of ethyl caprylate, EC, to produce the capry- late monomer, C, catalysed by the presence of micelles, C, [reaction (Ic)]. The uncatalysed formation of micelles directly from capry- late monomers is assumed to be possible only when the caprylate monomer concentration exceeds the c.m.c.([C] > [C]c.m.c.).Until this occurs, the only reaction which proceeds is the simple pseudo-first-order decomposition of the ethyl caprylate. Note that these processes are not intended to rep- resent the stoichiometric reactions themselves.For example, we are not suggesting that n caprylate monomers combine simultaneously to produce a micelle. The second reaction step is a simple representation of the overall uncatalysed process of micelle formation. Note that our assumption of pseudo-first-order kinetics is also justified by the close agree- ment that we obtain with the experimental results. It is clear J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 that for 0 < t 6 t,,,.,., where Eqn. (1) and (2)tell us that the caprylate monomer concentra- tion, [C], grows until t = tc.m.c.. When t = t,,,.,., the capry- late monomer concentration reaches the c.m.c. ([C] = [C],.,.,), and the remaining reaction steps start to proceed.The results of the experiment, where tc.m.c,x 33 h, [C]c.m.c.= 0.1 mol dm-3, n z63 and [EClo z 1.425 mol dm-3, suggest that k, 6.1 x s-'. These values are all deduced from Fig. 1. Note that, because the ester and aqueous alkaline solution together comprise a biphasic system, the interfacial area between the immiscible fluids is an important parameter influencing the numerical value of the rate constant k,, which can thus be expected to vary from one experimental set-up to another if different volumes of the phases or rates of stirring are used.6 For t > tc.m,c,,the reaction rate equations are dCEC1--k,[EC] -k,[C,][EC]dt These equations are non-linear, and do not have a closed- form solution. It is, however, straightforward to obtain a numerical solution using the fourth-order Runge-Kutta method (see, for example, ref.7). We can simulate the experi- mental results shown in Fig. 1 by using the parameter values: k, = 6.1 x s-l, k, = s-l, k, = 0.19 dm3 mol-' s-l, [C]c.rn.c. = 0.1 mol dm-3, [EC], = 1.425 mol dm-3, n = 63. This value of k, has been determined experimentally, and is given in ref. 2. The size of k, determines the rate at which micelles are produced once the caprylate concentration exceeds the c.m.c. The value given above leads to good agree- ment of the model with the experimental results. The exact 1.5-* 25 1U-EUE" 1.2 ----20 5 E0 E 4---.2 0.9--15 s cC .-c 0 c .-.-. I.-6 0.6-'0 2 4-s0.3---5 -w-is =:JP -w 0zo.0-: : : -: .: . : ' i-0 'E J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 value of k, is not critically important, since any value of this order of magnitude gives similar results. The predicted micelle and total caprylate concentrations are illustrated in Fig. 2 and 3 for [C], = 0 and [C], = 0.02 mol dm-3, respectively. These should be compared with Fig. 1, which shows the experimental results. The observed and theoretical results are in good agreement. At first sight, we appear to have a very successful mathe-matical model for the kinetics of micelle formation. The problem is that, because the model is by nature very largely empirical, we have actually learnt very little. We have con-firmed that it is possible to model this autopoietic system in a piecewise fashion by assuming that ethyl caprylate is hydro-lysed by hydroxide ion to produce caprylate monomers until the c.m.c.is reached, when micelles start to form. These then rapidly catalyse their own production, thereby exhausting the supply of the ester. However, by adopting this piecewise approach, our understanding of the coupled nature of the overall process has not been addressed. At the heart of the problem is the phenomenon of a well defined c.m.c., which this model makes no attempt to explain, but simply takes for granted. The requirement that the pro-duction of further micelles, and the hydrolysis of ester within such micelles, may occur only when [C] > [C]c,m.c, is undoubtedly only a first approximation.It is not clear a priori whether the rate of micellar-catalysed hydrolysis is slow compared to the rate at which micelles are formed, itself a non-equilibrium process for which the assumption of equi-librium is merely an approximation. The assumption of a thermodynamic equilibrium for one or more steps within a given kinetic scheme is a familiar one s Oa6 t V -time/h Fig. 2 Total caprylate (---) and micelle (-) concentrations when no caprylate is present initially, predicted from the model of reaction (I) with k, = 6.1 x lo-' s-', k, = lop4 s-', k, = 0.19 dm3 mol-' s-l, [C]c,m,c,= 0.1 mol drnp3, [EC), = 1.425 mol dmF3, n = 63 1 E 1.5 i. I ' ,--L-__--___--'L_-_-_---------------_25 7 ,U E-;1.2 ---20 5 u .. E 0 --.E'= 0.9 --152 .-c -C 2 c c2 0.6 --10 6 0 0 Q, --Z 0.3 -5 - :0 2-P 9 o.o ,--_--------7 __________---------Q1 I ,,I, 1.; 0 which is used to simplify the mathematical analysis of the resulting reaction rate equations.It is by no means obvious, however, that such an assumption is generally justified. An alternative approach is to try to formulate a global non-equilibrium model wherein all the steps are coupled and which does not explicitly include a c.m.c., but where the con-centration of micelles remains small for a well defined induc-tion period, after which the concentration grows rapidly. This type of kinetic scheme describes what is known as a clock reaction.Examples of simple model clock reaction schemes, where the induction period arises from the interaction of the various reaction steps rather than by its explicit inclusion in the model, have recently been studied in a series of papers.'.' In the next section, we propose a clock reaction model for autopoietic micelle formation. 3.2. Clock Reaction Model The model that we propose is very similar to the model of reaction scheme (I). It is given by EC --* C; rate = k,[EC] (114 nC +C,; rate = k,[C] (IIb) 2C, + nEC +3C,; rate = k2[EC][CJ2 (IIc) These three simple reaction steps represent : uncatalysed hydrolysis of ethyl caprylate, EC, to produce the caprylate monomer, C [reaction (IIa)] ;formation of a micelle, C, ,from n caprylate monomers, C [reaction (IIb)] ; and autocatalytic production of a new micelle, C,, from n ethyl caprylate mol-ecules, EC [reaction (IIc)].The first step is the same as that in reaction (I), whilst the rate expression for the second is slightly different since we do not explicitly include a c.m.c. The third step requires some explanation. Since in reaction scheme (11) we have not included a c.m.c. explicitly, the uncatalysed production of micelles from monomers must take place very slowly if we are to have a long induction period before a significant concentration of micelles is formed. If we were simply to modify reaction scheme (I) by setting [C]c.m.c, to zero, and making k, much smaller, there would be no mechanism for the rapid production of micelles.This leads us to postulate an autocatalytic step, whereby micelles catalyse their own production, rather than cross-catalysing the pro-duction of monomers, as in reaction (I). Finally, from our previous analysis of model clock reaction schemes, we know that a cubic autocatalytic step is both realistic and leads to a more clearly defined induction period than a quadratic auto-catalytic step (rate = k,[EC][C,]). Note that the autocatalytic step should not be treated as corresponding to an elementary process. We are not suggest-ing that tens of ethyl caprylate molecules interact with two micelles to produce three micelles in a single collisional inter-action. As in many other kinetic schemes, this step should be interpreted as representing the overall effect of a complex sequence of more elementary processes.These more elemen-tary processes are described in more detail in the model we discuss in Section 4. The reaction rate equations for the kinetic scheme (11)are -=dCEC' -k,[EC] -nk,[EC][C,12dt dCcl -k,[EC] -nk, [C] (4)dt dtdccnl -k,[C] + k2[EC][C,]2 1956 As before, although these equations have no closed-form solution, we can obtain solutions numerically using the fourth-order Runge-Kutta method. However, for this set of equations, we can also obtain a useful asymptotic solution for the case where the catalysed hydrolysis of ethyl caprylate proceeds much faster than the uncatalysed hydrolysis (k,[EC]g + k,). We summarise the results here and give more details in the Appendix.We can show that there is then a well defined induction period where the micelle concentration is small and the domi- nant reaction step is the slow, uncatalysed hydrolysis of ethyl caprylate to produce caprylate monomers. Meanwhile the uncatalysed production of micelles from caprylate monomers proceeds very slowly, and the autocatalytic step more slowly still. At the end of the induction period, the autocatalytic step rapidly becomes dominant, and the ethyl caprylate is con- sumed to produce micelles. Once the ethyl caprylate has been consumed, only the very slow, uncatalysed combination of monomers into micelles can proceed. The asymptotic analysis described in the Appendix allows us to determine the duration of the induction period for given values of the parameters. We have chosen the values of k,, k,, [EC], and n to be as in Section 3.1. However, as we explained above, the value of k, needs to be much smaller than before in order to have a long induction period.The asymptotic analysis shows that we must take k, = 2.0 x s-l in order to achieve agreement with the observed 33 h long induction period. Fig. 4 shows the numerical solution of eqn. (4) for [C], = 0, and the other parameter values taken as follows: k, = 6.1 x s-l, k, = 2.0 x s-l, k, = 0.19 dm6 mol-2 s-l, [EC], = 1.425 mol dm-3, n = 63, This numerical solution is consistent with the asymptotic solution, and shows that the model can reproduce the behaviour seen in the experiment when no caprylate is present initially.Note that, although the concentration of micelles appears to be constant in Fig. 4 and 5 once the induction period is over, there is actually an extremely slow uncatalysed conversion of caprylate monomer to micelles. Fig. 5 shows the numerical solution of eqn. (4) for [C], = 0.02 mol dm-3. This shows that the duration of the induction period is reduced to around 28 h, consistent with the asymp- totic solution, as we would expect, but not in quantitative agreement with the experimentally measured induction period of around 25 h. The duration of the induction period, to, predicted by the model as a function of [C],, is shown in Fig. 6, along with the experimental values. We can understand the discrepancy between the model and the experimental observations by investigating whether the -.rL.E" 0.9 t-2 Y 0.6 0.31-Q) I I 10 .E 40 50 60 time/hc, Fig. 4 Total caprylate (---) and micelle (-) concentrations when no caprylate is present initially, predicted from the model of reaction (11) with k, = 6.1 x lo-' s-', k, = 2.0 x lo-* s-l, k, = 0.19 dm6 molP2 s-l, [EC], = 1.475 mol dmP3, n = 63 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 c0 tirne/hFig. 5 Total caprylate (---) and micelle (-) concentrations when [C] = 0.02 mol dm-3 initially, predicted from the model of reaction (11) with the parameters given for Fig. 4 model effectively has a c.m.c. associated with it. Fig. 7 shows the behaviour of the total caprylate concentration, [C],,, = [C] + n[C,], predicted by the model for various initial capry- late concentrations, [C],.Clearly, the value of [C],,, at the end of the induction period varies as [C], varies. We need [C],,, = [C]c.m.c.at the end of the induction period, irrespec- tive of the value of [C],, if the model is to reproduce the experimental observations. It is clear that, in the present model, regardless of how much caprylate monomer is present initially, there is always a finite induction time needed for the uncatalysed step to produce enough micelles for the autocat- alytic step to become significant. 3025 L 4 i 5 1~I I ,,I,, 0 0 25 50 75 100 125 150 175 200 [C],/rnmol dm-3 Fig. 6 Induction time, to, predicted by the model of reaction (11) with the parameters given for Fig.4, as a function of [C],. (A) Experimental values; (M)c.m.c. 1.80 1.60 1.40 m E 1.20 1.00 0.80 21 0.60 o, 0.40 0 10 20 30 40 50 60 time/h Fig. 7 Total caprylate concentration, [C],,,, for various values of the initial caprylate monomer concentration, [C], , predicted from the model of reaction (11) with the parameters given for Fig. 4. [Cl0/mol dm-3: (a) 0, (b) 0.02, (c) 0.06, (d) 0.1, (e) 0.2. The horizontal dotted line represents the expected value of the c.m.c. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 We conclude that the model of reaction (11) is able to reproduce the long induction period observed experimentally, but that it does not agree with the experimentally observed c.m.c., incorrectly predicting that a finite induction period persists for any initial caprylate monomer concentration, [C],.1° One reason for this may be that the model does not include the possibility of micelles being converted back to monomers.4. Mesoscopic Model It should be evident that the models described above are very much macroscopic and semi-empirical in nature. A more detailed, microscopic treatment would be preferable, in which we consider the kinetics of each 'elementary step' in the process of micelle formation. This would enable us to relax many of the assumptions invoked in Section 3, including that of the monodispersity of micelles. Such an approach has recently been proposed by Carr et al.for the study of multi-component micelle kinetics in the absence of chemical reac- tions." These authors argue that the well known Becker-Doring equations (which provide the theoretical basis underpinning the generally very successful classical nucle- ation theory" and the theoretical description of the kinetics of a variety of thermodynamic phase transitions) may be used to study the process of micellization under non-equilibrium conditions.' Moreover, the long-time properties of this system provide a description familiar from equilibrium ther- modynamics." We are not aware of any other attempt to model micellar kinetics in this fashion, although some earlier and less general work was based on the same fundamental approximations.l4 Strictly speaking, the Becker-Doring theory is mesoscopic rather than microscopic, for reasons we shall explain shortly. The basic assumption of the Becker-Doring theory is that clusters of particles (in this case micelles) change their sizes through a series of one-step processes in each of which a given cluster grows or shrinks by one monomer molecule at a time. The general kinetic process in Becker-Doring theory can be written as with r ranging from one to infinity. Here a, and b,+l are the rate coefficients for the forward and reverse steps, respec- tively. The reaction rates are given by the law of mass action, and lead to an infinite system of coupled non-linear differen- tial equations a, dc,/dt = -Jl -1J, r= 1 dc,/dt = Jr-l -J,; for r > 1 (5) for the concentrations, c, = [C,], of each size r of cluster, where Note that the total caprylate concentration defined by (7) is a constant (dp/dt = 0),as we would expect.One point of physical significance which emerges from an analysis of the Becker-Doring equations [eqn. (5)] is the concept of metastability. Rigorous mathematical analysis for the case of nucleating vapours shows that there is a certain critical cluster size above which all growth rates remain small for an exponentially long time (the induction period) prior to rapid growth of larger cluster^.'^.^^ This is consistent with experimentally observed nucleation behaviour, and is used in the modelling of nucleation and crystal growth.Note that the assumption of single-particle accretion and fragmentation is a special case of the discrete coagulation-fragmentation equa-tions which can be used to model more general processes, but at considerably more computational expense. '' The Becker-Doring formalism can readily be extended to handle the kinetics of the experiments studied here. To include the effect of ethyl caprylate hydrolysis, both catalysed and uncatalysed, we add the following irreversible steps EC +C; rate = koe, EC + C, 4C + C,; rate = k,ec, for r > rcrit (IV) where e = [EC] and rcrit is some critical cluster size below which catalysis of ethyl caprylate hydrolysis is not possible. This constitutes a minimal modification of the Becker-Doring scheme.The modified Becker-Doring equations are then given by de/dt = -J, dc,/dt = Jr-l -J,; for r > 1 where In this case, the total caprylate concentration defined by m p = [c],,, = e + 1rc, r= 1 is an invariant of the kinetics. If we are to implement this model in a numerical fashion we need some way of estimating the plethora of rate coeffi- cients that arise in these equations. In principle, this can be done through an appeal to equilibrium statistical mechanics and diffusion theory. It is important to recognise that all of these rate constants implicitly contain information on the size (or, equivalently, the surface area) of the micellar clusters. This model, defined by its infinite set of rate equations [eqn. (S)], is mathematically very complicated to study and has yet to be explored fully, but we hope that it will be the subject of future work.However, preliminary numerical calculations provide encouraging evidence that this model does contain the correct features to describe self-replicating micelles. Note also that we can develop a continuum version of this discrete set of ordinary differential equations, which is a partial differential equation in terms of the variables r and t, coupled with an ordinary differential equation for cl. The detailed form of this continuum limit is not as easy to deter- mine as it appears at first sight. However, we know that an integral over the range of cluster sizes must be involved, from the form of the discrete Becker-Doring equation for c,.Such equations can have finite time singularities that can be analysed by asymptotic techniques, as shown in ref. 18. These singularities would correspond to a well defined induction period, similar to that which we analyse in the Appendix for eqn. (4). In other words, there is a good chance that we can construct an asymptotic, metastable solution, of the form shown to exist in ref. 16. Some rigorous analysis along these lines is already in progress.” Note that the more macroscopic chemical kinetic models which we have invoked to account for both ettringite nucle- ation during cement hydrationg and the formation of micelles from monomers in Section 3, most likely emerge as crude mean-field approximations to the mesoscopic theory described in this section.However, even the Becker-Doring equations do not provide a truly microscopic model, as they say nothing about the role of fluctuations on the distribution of cluster sizes; they are concerned only with the average behaviour of such distributions. We thank Pier Luigi Luisi for many stimulating discussions; P.V.C. also acknowledges his hospitality during several visits to E.T.H. We are also indebted to Peter Walde for his help in clarifying many aspects of the experimental work. We are grateful to Jack Carr and Oliver Penrose for sharing their ideas on the application of the Becker-Doring equations to the kinetics of micelle formation, and to Denver Hall for some helpful comments.Appendix Asymptotic Analysis We begin by defining the dimensionless variables x = CECl/~EClO~Y = ccl/cEclo z = [C,]/[ECl0; z = kot (Al) In terms of these variables, eqn. (4) becomes dx _---x -&-1nxz2dz dY -= x -Icnydz _-dz -& -lXZ2 + Icydz subject to the initial conditions x(0) = 1, y(0) = a, z(0) = 0, where a = [C],/[ECl0; E = ko/k2[EC];; u = k,/k, (A3) Here, a is the dimensionless initial concentration of caprylate monomers, E is a measure of the rate of the uncatalysed decomposition of ethyl caprylate relative to the rate of the autocatalytic step, and K is a measure of the rate of the uncatalysed production of micelles from caprylate monomers relative to the rate of the uncatalysed decomposition of ethyl caprylate.Since eqn. (A2) shows that d(x + y + nz)/dz = 0, we can eliminate y and arrive at dx----x -&-lnXz2dz dz ---E -‘xz2 + 1c(1 + a -x -nz)dz We are interested in the case E << 1, when the uncatalysed rate of decay of the ethyl caprylate is slow compared with the rate of the autocatalytic step. We will consider first the problem when a = 0(&li3).A suitable rescaling of the vari- ables is given by z = ,51/3i; x = 1 + &‘/3X = E2/3-.z, a = &‘/3a (A5) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 At leading order as E +0, eqn. (A4) become subject to X = 0, Z = 0 at i = 0. Clearly, X --i, and hence d2 --j2 + K(ii + 7)di We can now scale K out of this equation by writing 2 = Ic1/3z.7 = K-1/3., a = Ic-1/3~ (A@5 so that dZ--Z2+A+TdT subject to Z = 0 when T = 0.The solution of this simple non-linear equation becomes unbounded, Z + 03, at finite time T = To for all positive values of A. Since Z is a scaled, dimensionless version of the micelle concentration, the time, To, corresponds to the end of the induction period, when the micelle concentration grows rapidly. This is all that we need to know from the asymptotic solution. We can easily calculate the function To(A) numerically by integrating eqn. (A9) and determining when Z becomes large for any given value of A. The function To(A) is illustrated in Fig. Al. Since A is a scaled, dimensionless version of the initial concentration of caprylate monomers, this allows us to determine the duration of the induction period as a function of CClO * We can repeat the above analysis for the case a = 0(1), which is equivalent to A 9 1.We again find that there is a singularity in the leading order solution of the micelle con- centration. However, in this case, we can determine a simple expression for the time at which this singularity occurs, which shows that The curve n/2A1I2 is also shown in Fig. Al, and is clearly in good agreement with the numerically calculated curve To for sufficiently large values of A. If we let to be the duration of the induction period, in terms of the physical variables, 2.0 1.6 Y3 1.2 \ L. 0.8 0.4 t 1 0.0 I I II 0.0 2.5 5.0 7.5 10.0 A Fig. A1 The scaled, dimensionless induction time, To (-) and 7~/2A’’~(---), the asymptote for A 9 1 J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 7r (A 12)to -2(k k, [EC] [C] o) ’2 for k, < k2[EC]i and [Cl0 = O([EC],). Note that T,(O)z 2, so that for ko 3 k,[EC]i and [C], = 0. It is this equation that allows us to determine the value of k, from the given values of to,k,, k, and [EC], in the experiment with [Cl0 = 0. References 1 F. Varela, H. Maturana and R. Uribe, Biosystems, 1974,5,187. 2 P. Bachmann, P. L. Luisi and J. Lang, Nature (London), 1992, 357,57. 3 P. L. Luisi, in Thinking about Biology, ed. W. Stein and F. J. Varela, Addison-Wesley, New York, 1993. 4 A. Malliaris, J. Lang and R.Zana, J. Chem. SOC., Faraday Trans. 1,1986,82, 109.5 S. Colonna, G. Fleischakar and P. L. Luisi, Self-reproduction of Supramolecular Structures, Proc. NATO Advanced Research Workshop Maratea, Italy, 1993, Elsevier, Amsterdam, in the press. 6 P. L. Luisi, personal communication. 7 W. Press, S.Teukolsky, W. Vetterling and B. Flannery, Numeri-cal Recipes, Fortran Version, Cambridge University Press, 1986. 8 J. Billingham and D. J. Needham, Philos. Trans. R. SOC.London, A, 1992, 340, 569; J. Billingham and D. J. Needham, J. Eng. Math., 1993, 27, 113. 9 J. Billingham and P. Coveney, J. Chem. SOC., Faraday Trans., 1993,89,3021. 10 F. Mavelli and P. Walde, unpublished results. 11 J. Carr, 0.Penrose and J. Wattis, unpublished results. 12 Z. Alexandrowicz, J. Phys. A: Math. Gen., 1993, 26, 655; S. Toschev, in Crystal growth: An Introduction, ed. P. Hartmann, North-Holland, Amsterdam, 1963. 13 R. Becker and W. Doring, Ann. Phys., 1935,24,719. 14 E. Aniansson and S. Wall, J. Phys. Chem., 1974, 78, 1024; E. Aniansson, Ber. Bunsenges. Phys. Chem., 1978,82,981. 15 J. Ball, J. Carr and 0.Penrose, Commun. Math. Phys., 1986, 104, 657. 16 0.Penrose, Commun. Math. Phys., 1989,124,515. 17 K. Binder, Phys. Rev. B, 1977, 15, 4425; Z. Melzak, Trans. Am. Math. SOC., 1957, 85, 547; J. Spouge, Math. Proc. Camb. Philos. SOC.,1984, 96,351. 18 C. Budd, B. Dold and A. Stuart, SIAM J. Appl. Math., 1993, 53, 718. 19 J. Wattis, unpublished results. Paper 4/00087K; Received 6th January, 1994

ISSN:0956-5000    

DOI:10.1039/FT9949001953

出版商:RSC    

年代:1994

数据来源: RSC

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J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1961-1966 Micellisation and Gelation of Triblock Copolymer of Ethylene Oxide and r-Caprolactone, CLnEmCLn in Aqueous Solution Luigi Martini, David Attwood,* John H. Collett, Christian V. Nicholas, Siriporn Tanodekaew, Nan-Jie Deng, Frank Heatley and Colin Booth Manchester Polymer Centre, Departments of Chemistry and Pharmacy, University of Manchester, Manchester, UK M 13 9PL Three triblock copolymers of ethylene oxide and E-caprolactone, nominally CL,E,,CL, , CL4EgOCL4 and CL,E,,CL, have been prepared and characterised. The micellar and surface properties in aqueous solution of the copolymers with CL-block lengths of four and six were investigated as a function of temperature and concen- tration using surface tension and static and dynamic light scattering techniques.Reversible gelation on cooling solutions of CL&g&L, was observed at critical concentrations and temperatures ranging from 130 g kg-' at 25°C to 300 g kg-' at 80°C. The micellisation and gelation properties of triblock co-poly(oxyethylene/oxypropylene/oxyethylene)s, E,P,E, (where E represents an oxyethylene unit and P an oxypropylene unit) have been extensively studied in recent years.'-9 In an extension of this the oxypropylene unit was replaced with the more hydrophobic oxybutylene unit, B, to form a series of E,B,E, copolymers, the use of which avoids many of the problems related to sample purity and repro- ducibility which are associated with the anionic polymeris- ation of propylene oxide.6 Members of both series of triblock copolymers form micelles in dilute aqueous solution and thermally reversible gels at higher concentrations. Gelation results essentially from the packing of micelles acting as hard spheres and can be effected either by heating from a low tem- perature or cooling from a high temperature, so-called 'hot' and 'cold' ge1ati0n.I~ Gelation on heating occurs whilst micelles are being formed and is a consequence of the close packing of the micelles at sufficiently high concentration to prevent micellar translational motion.The influential factor governing gelation on cooling is the significant increase in hydration of the oxyethylene units of the micellar fringe as the temperature is decreased.', COpOlymerS such as E106P6,E106 (F127), which form gels at temperatures between ambient and body temperature, have been widely studied for their potential in the formula- tion of implants for the controlled delivery of drugs (see, e.g.ref. 14). These systems offer the possibility of implant forma- tion in situ by the subcutaneous injection of a mobile solu- tion, thus avoiding the necessity for surgical implantation. However, their poor biodegradation characteristics might necessitate surgical removal of the implant after drug release. In an attempt to address this problem, block copolymers have been synthesised incorporating poly(ecapro1actone) which is known to be subject to degradation in viuo by hydrolytic chain scission involving the ester linkages.' 5*16 We report here an investigation of the solution properties of a series of CL,E,CL, copolymers (where CL represents E-caprolactone).Although a limited number of compounds of this type have been synthesised previ~usly,~~-'~ their associ- ation properties in aqueous solution have not been reported. In view of the role of micelles in the gelation of block copoly- mers, light scattering methods have been used to examine micellisation in dilute aqueous solution and changes in micel- lar properties on increase of temperature and concentration. Experimental Materials To remove any hydroxy acid formed by ring opening, E-caprolactone (Aldrich 99%) was stirred over 2,4-diisocyanate- 1-methylbenzene (Fluka) for at least 24 h, then fractionally distilled under reduced pressure (bp 96-98 "C, 5 mmHg) directly onto fresh CaH, .Polyethylene glycol 4000 (Fluka) was evacuated at 80 "C (1 mmHg) for 75 h to remove residual traces of water. Cop1ymerisation The block copolymers were prepared by using polyethylene glycol 4000 [or-hydro, o-hydroxypoly(oxyethylene), E,,] to initiate the polymerisation of ecaprolactone at 180 "C in the absence of added catalyst; the method used was that of Cerrai et a1.I9 The E-caprolactone (CL), was inserted by syringe into an ampoule containing a pre-weighed quantity of dried E90 under dry N, and sealed after evacuation. Poly- merisation was carried out at 180°C for 30 h, after which the product was recovered from the ampoule using dichloro- methane which was subsequently removed by evacuation.Purification was effected by extracting repeatedly with hexane to remove any poly(CL) initiated by traces of mois- ture. The product was subsequently subjected to prolonged evacuation to remove any remaining volatile substances. The overall compositions of the copolymers were deter- mined by 'H and 13C NMR (Bruker Spectrospin AC-300E, 75 or 300 MHz, CDCl, solvent) and their molar masses by gel permeation chromatography (GPC) [tetrahydrofuran solvent ; columns calibrated with poly(oxyethy1ene) standards]. The three samples are denoted CL,E,,CL,, where n = 2,4, or 6. These formulae are based on overall composition from NMR combined with an E-block length of 90 units.Details of the molecular characterisation of the samples by GPC and NMR are given below. GPC curves obtained for the three copolymers contained narrow peaks, corresponding to M,, in the range 5000-6000 g mol-', and A?w!l@n in the range 1.10-1.15 (see Table 1). These values of MW//l@"are similar to that found for the precursor PEG4000, showing that no degradation (chain scission) occurred under the conditions used for copolymer- isation. The GPC curve of sample CL,E,,CL, also con-tained a small peak (< 5% by area) centred on Mpk= 450 g mol-',which was assigned to homopoly(CL) impurity, initi- ated by moisture. No homopolymer was detected in the other two samples. Assignments for relevant 'H and 13C resonances are listed in Table 2.'H NMR spectra were used to measure the overall composition (see Table 1) by comparison of the inte- grated resonances of the methylene protons of the E block with those of the CL block. A similar analysis of the inte- J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Molecular characteristics of the copolymers mol% E "MR) copolymer MwIMn (GW 'H 3c wt.% E (NMR)(average) mol% E* (I3CNMR) Mn (13CNMR) An (formula) CL2E90CL2 1.12 95.8 96.3 90.5 25 4420 4430 CL4E90CL4 1.15 90.7 91.5 79.8 6 4870 4690 CL6E90CL6 1.15 87.5 87.2 72.8 3 5330 5420 grated resonances of the methylene carbons in the I3C NMR num plate suspended from a calibrated torsion balance. The spectra confirmed these compositions (see Table 1).usual precautions were taken to ensure cleanliness and the The I3C spectra of the three copolymers contained clear water was triply distilled from alkaline permanganate solu- evidence of oxyethylene hydroxy ends (E*, resonances a* and tion. The accuracy of measurement was checked by frequent b* of Table 2) as well as carboxypentamethylenehydroxy measurement of the surface tension of water (71.0 nN m-'; ends (CL*, resonances 5* and 6* of Table 2). Comparison of expected at 30 "C,71.2 mN m- I). Solution temperatures were integrals gave the mole percentages of E* ends listed in Table maintained at 30 k 1"C by means of a thermostatted water 1. If all ends (E* and CL*) have equal reactivity towards jacket. Surface tension readings were measured at intervals addition of CL units, then the probability of finding an E* until consistent values were obtained.end after reaction with 2n CL units should be simply 0.5": i.e. mol% = 25, 6 and 1.6 for n = 2, 4 and 6, respectively. Given Light Scattering the experimental uncertainty of determination of the mol% of E* ends (+2), the results obtained for the copolymer samples Static light scattering was measured at temperatures in the are as expected. range 30-50 "C (_+1 "C) by means of a Malvern PCSlOO Integrals of the resonances of end-group carbons and back- instrument with vertically polarised incident light of wave- bone carbons were used to obtain the overall number- length 488 nm supplied by a 2 W argon-ion laser (Coherent average molar masses listed in Table 1.These values of &%, Innova-90). Solutions were clarified by repeated ultrafiltra- are in good agreement with the values expected from the con- tion through 0.1 pm filters, the final filtration being directly ditions of preparation, as indicated by their nominal formu- into the cleaned scattering cell. The intensity scale was cali- lae. brated against filtered benzene. Refractive index increments The mol% of triblock copolymers in the samples, as calcu- were measured over the temperature range 30-50 "C lated from mol% of E* ends, were ca. 94, 88 and 50% for ( & 0.5 "C) using an Abbe 60/ED precision refractometer CL,E,,CL,, CL,E,,CL, and CL,E,,CL, , respectively. In (Bellingham and Stanley Ltd). view of the low purity of CL,E,,CL,, this copolymer was Dynamic light scattering measurements were made by not studied further.means of the Malvern instrument described above combined with a Malvern K7027 auto-correlator using 60 linearly spaced channels with a far-point delay of 1024 sample times. Cloud Point Measurement of scattered light was at an angle of 90" to the Aqueous solutions of the copolymers (2 wt.%) in small tubes incident beam. The data were analysed either by the were slowly heated (0.5 K min-') in a water bath to 100°C CONTIN method to obtain information on the distribution and clouding was observed visually. The cloud points quoted of decay times or, if appropriate, by a single-exponential fit of below were the mean of two determinations. the correlation curve.Surface Tension Gelation Characteristics Surface tensions (7) of dilute aqueous solutions were mea- A solution of copolymer of known concentration was sured by the Wilhelmy plate method using a roughened plati- enclosed in a small tube and observed over the temperature Table 2 Assignments for 'Hand NMR spectroscopy: E,CL, and CL,E,CL, a* 61.5 b* -72.4 C 3.6 70.4 d -69.0 e 4.1 63.2 2 2.2 33.9 3 1.5 25.2 4 1.2 24.4 5 1.5 28.2 6 3.9 63.9 5* -32.1 6* 3.6 62.2 HOCH,CH2[OCH,CH21,-,0CH2CH20[C0CH,CH2CH2CH2CH20]~-ICOCH2CH,CH2CH,CH,0H(diblock) a* b* c c de 23456 2 3 4 5* 6* . . .OCH ,CH 2[OCH ,CH 23, -,OCH ,CH,O [COCH ,CH ,CH ,CH ,CH,O], -COCH ,CH ,CH ,CH ,CH ,OH (triblock) ed cc de 23456 2 3 4 5* 6* J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 range 5-50°C. The change from sol to gel (or uice versa), determined by inverting the tube, defined the gel temperature to within f1 K. Results and Discussion Preliminary measurements of the in vitro degradation of CL~E~OCL~in aqueous solution at 37°C have shown a decrease of molar mass (from GPC) of ca. 20% over a period of 16 weeks. The extent of the reduction of molar mass over the timescale of the measurements of this study (not exceed- ing 2 days from the preparation of a polymer solution) was less than 0.4% and it was considered that any influence of degradation on the results was negligible. Cloud Points The cloud points of 2 wt.% aqueous solutions of the copoly- mers were 65 and 55 "C for CL,E,,CL,, and CL&,oCL6.Surface Tension Plots of surface tension, y, of solutions at 30°C against log c (where c is concentration in g dmP3) are shown in Fig. 1. Equilibrium readings were obtained within 8 h for all solu- tions. The plot obtained for CL&,oCL6 shows a single clear transition point at c = 0.010 g dm-3, at which the surface tension attained a constant value (yc.m,c.= 50.6 mN m-'), assumed to be the critical micelle concentration (c.m.c.). The corresponding plot for CL,E,,CL, is less easily interpreted. Behaviour of this type has been observed previo~sly~,~~ and attributed to a range of compositions within the sample. In the present case the composition range will be wide, including as it does diblock copolymers as well as a range of CL chain lengths in the triblock copolymers (n = 1-10, average n = 4).The surface tension became roughly constant (y = 50.9 mN m-') at a critical concentration of c = 0.050 g drnp3. The unfiltered aqueous solutions of this copolymer were clear, suggesting that the homopoly(CL) impurity, thought to be present in CL,E,,CL,, was solubilised by the copolymer micelles. As a consequence, the onset of micelle formation will occur at a lower concentration and the critical concen- tration quoted above should be regarded as a minimum value. The slopes of the y us. log c plots for CL,E,,CL, and CL~E~OCL~well below the critical concentrations were used 60 0 0 c I2 55 + 0 E--. 02-50 -3 -2 -1 0 1 log(c/g d~n-~) Fig. 1 Surface tension us.log c for aqueous solutions of block copolymers at 30 "C : (@) CL,E,,CL,; (+) CL,E,,CL, 1963 to calculate approximate values of excess surface concentra- tion, r, by use of the simple form of the Gibbs absorption isotherm r = -(l/RT) (dy/d In C) (1) and hence the area per molecule in the full monolayer, a, from a = i/m, (2) where N, is Avogadro's constant. The values of Q were 1.5 and 1.4 nm2 for CL,E9,CL, and CL&&L6, respectively, which are similar to those of other triblock copolymers with long oxyethylene chains. For example, copolymers E,,P,,E,, and E,,B, ,E5, in aqueous solution have values of 1.4 and 1.3 nm2, respectively, at 30 0C.10,21 Dynamic Light Scattering Dilute solutions (2-4 g drn-,) of each of the copolymers were examined at 30°C by dynamic light scattering.The results were analysed by the constrained regularisation CONTIN technique developed by Provencher22 to provide information on the nature of any association. The size distribution of any aggregates present in solution was determined from the dis- tribution of decay rates and hence of apparent diffusion coef- ficients, Dapp,by application of the Stokes-Einstein equation rh, app = kB T/(6nqDapp) (3) where rh,app is the radius of the hydrodynamically equivalent hard sphere corresponding to Dapp,k, is the Boltzmann con- stant and q is the viscosity of water at temperature T. The results from the CONTIN analysis are presented in Fig. 2 in the form of (a) intensity and (b) weight distributions of log(?-,,app).The distributions for both CL,E,,CL, and CL,E,,CL6 were narrow, indicative of a closed association. There was evidence in the intensity distribution of CL,E,'CL, of an extremely small proportion of material in the form of large particles; the presence of these particles could not be detected when the dynamic scattering data were expressed in the form of a weight distribution of log rh,app). Their influence was considered to be negligible. Values of Dapp for CL,E,,CL6 at concentrations below 20 g dm- and over the temperature range 30-50 "C were deter- mined from single exponential fits of the correlation curves. Extrapolation of the data to infinite dilution yielded the Do values listed in Table 3.The radii of the hydrated micelles, rh (rh = [( l/rh)=)]-'), as calculated from the Stokes-Einstein equation, were constant between 30 and 50 "C (see Table 3). Static Light Scattering Plots of the scattering function K'c/(S -S,) against c for solutions of CL,E,,CL, at 30, 40 and 50°C are shown in Fig. 3; S is the intensity of light scattered from a solution at 90" relative to the scattering from benzene and S, is the corre- sponding value for water. The constant K' was calculated using the values of refractive index increments, dn/dc, in Table 3. The temperature derivative of dn/dc (-2 x lov4 cm3 8-l K-I) of this copolymer was identical to that obtained previou~ly'~.~~ for aqueous solutions of di- and tri- block copolymers of oxyethylene and oxybutylene.The dis- symmetries, Z, of the scattering envelopes, as determined by the ratio of intensities at scattering angles of 45" and 135", were close to unity (2< 1.10 & 0.05) indicative of small par- ticles. The pronounced curvature of the plots of Fig. 3 is a conse- quence of interparticle interference which was accounted for, as in previous work,"-' by treating the micelles as 2923*24 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 I I I I I I B 0 1 2 3 lodr,, app/nm) Fig. 2 Dynamic light scattering from aqueous solutions of block copolymers at 30 "C. Normalised, A, intensity distributions and, B, weight distributions of the logarithm of apparent hydrodynamic radius obtained for (a)CL,E,,CL,, c = 4 g dm-3; (b) CL,E,,CL4, c = 5 g dm-j.hard spheres and using the scattering equation in the form K'c/(S -S,) 1: l/QA?, (4) where is the mass-average molar mass of the micelles and Q is the interparticle scattering (the intraparticle scattering factor being unity for small spheres). For moderate concen- trations of uniform hard spheres, Vrij25 has suggested that Q can be calculated from the Carnahan-Starling equation26 1/Q = "1 fw2-V(44 -+2)1(1-(5)+)r4 where 4 is the volume fraction of equivalent thermodynamic uniform spheres calculated from the actual volume fraction of copolymer in micelles in the system by applying a volume swelling factor (6, = swollen volume relative to dry volume). The adjustable parameters are A?, and 6,.In applying eqn. (5)concentrations were converted to a volume basis assuming a density of dry polymer, p, of 1.10 g dm-3, irrespective of temperature. Fig. 3 shows approximate fits to the experimen- I I I I I D I 1 I I I 0 20 40 60 80 100 c/g dm-3 Fig. 3 Static light scattering function K'c/(S -S,) us. c for aqueous solutions of CL,E,,CL, at (e)30, (A) 40 and (7)50°C and (+) CL,E,,CL, at 30°C. The curves were calculated using the Carnahan-Starling equation as described in the text. tal data obtained with 6, values of 2.8, 2.5 and 2.3 at 30, 40 and 50 "C, respectively. Data points for the lowest concentra- tions were possibly affected by micellar dissociation and were given less weight than those for higher concentrations (c 3 10 g dmr3).Thermodynamic hard-sphere radii, rt , were calcu- lated from 6, and A? using I, = (36, MW/47CN,p)f'3 (6) and are listed in Table 3 together with the association numbers of the micelles calculated from N = NJmicelle)/A? w( molecule) (7) The results in Table 3 show an increase of the molar masses and thermodynamic radii (rt) of micelles of CL~E,OCL~with temperature rise but a constancy of their hydrodynamic dimensions as measured by rh . Similar results have been reported for a number of oxyethylene/ oxypropylene and oxyethylene/oxybutylene triblock copoly- mers.1-5,10,12,27 The effect is due to the dehydration of the micelles with increase of temperature which counteracts the increase in anhydrous size due to micellar growth in such a way that the hydrodynamic radius does not show any signifi- cant change with temperature.Table 3 shows the decrease with temperature of the hydrodynamic swelling factor, 6, [calculated from the ratio of the volumes of swollen (vh = 47cnr,3/3) to anhydrous (V, = A?,/N, p) spheres] which pro- vides evidence for micellar dehydration. Previous workers have shown similar decreases of micellar hydration by this means'-4 and also from changes in the intrinsic viscosity2' Table 3 Micellar properties" of aqueous solution of block copolymers CL,E,CL, T dnldc ', DO 'h 'h. apg NWcopolymer /"c /cm3 g-' 10-5Mw ,hm cm2 s-l /nm /nm 6, 30 0.144 -----8.6 -CL4E90CL4 CL6E90CL6 30 0.143 2.07 38 6.0 2.9 9.8 9.9 13 40 0.138 3.13 58 6.7 3.4 10.4 -10 -750 0.134 4.16 77 7.1 4.3 10.1 ~~ -~-a dnldc = refractive index increment (k0.002 cm3 g-'); M, = molar mass (k10% g mol- I); N, = association number (k15%); rt = thermodynamic radius (+ 1 nm); Do = limiting diffusion coefficient (k0.5x lo-' cm2 s-'); rh = hydrodynamic radius from Do (k1 nm); 6, = hydrodynamic swelling factor ( f2).Intensity-average value estimated by the CONTIN method from results on dilute solutions (4-5 gdmP3). J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 and in the fluorescence quantum yields of polarity-sensitive probes.28 Light scattering measurements on aqueous solutions of CL,E,,CL, were restricted to 30 "C and to concentrations of less than 20 g dm-3. In view of the scattered data in a limited concentration range and the evidence of dissociation at the lowest concentrations (Fig.3), it was not meaningful to evalu- ate 6, and M,,,by application of the Carnahan-Starling equa- tion. Gelation Characteristics The sol-gel diagram for solutions of CL6EgoCL, is illus- trated in Fig. 4. The dashed line through the data points defines approximately the sol-gel transition on cooling solu- tions of given concentration, or alternatively the gel -+ sol transition on heating. No lower gel -+sol transition was observed on further cooling the solutions of concentrations represented by the data points of Fig. 4to 0°C. Previous work".' 2,24,29*30 has shown that the gelation of oxyethylene/oxypropylene and oxyethylene/oxybutylene copolymers can be broadly explained by assuming that the critical gel concentration (c.g.c) is equivalent to the critical concentration for close packing of the micelles acting effec- tively as hard spheres, i.e.C.g.C. = (2"2/8ri,)( 1024M/NA)= 0.292M/& (8) In eqn. (8), M is the molar micellar mass in g mol- ',rhs is the equivalent hard sphere radius in nm, and c.g.c. is in g dmP3. Application of the equation to the gelation of CL,E,,CL6, assuming that the values of A?, of Table 3 can be directly related to hf,yields rhs values in reasonable agreement with the r, values from static light scattering. For example, the c.g.c. for CL~E~OCL~ at 30°C is 165 g dm-3 which leads to an equivalent hard sphere radius of rhs = 7.2 nm compared with an r, value from light scattering of r, = 6.0 nm.Gelation of solutions of CL&oCL6 by cooling from a high temperature, commonly known as hot gelation,' will be accompanied by a negative standard enthalpy of gelation. If, as is thought, gelation is a consequence of the aggregation of spherical micelles, then it is possible to determine the ther- modynamic quantities for the gelation process. The standard states for gelation are micelles in solution at unit molarity and the micelles in their gel state. The equations by which the I I I I I / / /.80 / / 9 60 / /L-/ / /sol / / / // e'/ 20 / 1 I I I I 100 150 200 250 300 clg kg-' Fig. 4 Gel-sol diagram for aqueous solutions of CL,E,,CL, thermodynamic quantities can be obtained are AgelGe = R (c.g.t.)ln(c/N) (9) and AgelH* = R[d In c/d (c.g.t.)-'] (10) where c.g.t.is the critical gel temperature of a solution of concentration c [expressed in (mol chain) dmW3], and N is the aggregation number. The units of the thermodynamic quantities are J (mol micel1es)- ' or J (mol chains)-' on divid- ing by N. Gibbs energies of gelation from eqn. (9) for CL,EgoCL6 at 30, 40 and 50°C were -17.7, -19.1 and -20.4 kJ (mol mice1les)-'. AgelHo,as calculated from the gradient of the linear plot of In c against (c.g.t.)-' was -17.3 kJ (mol mice1les)-'. Values of similar magnitude were reported for hot gelation of oxyethylene/oxybutylene triblock copoly-mer~.~~,~'Conversion of these values to units of J (mol chain)-' using the aggregation numbers of Table 3 yields very low values, i.e.the gelation of a micellar solution of a triblock copolymer of caprolactone and oxyethylene, as with that of micellar solutions of oxyethylene/oxypropylene31.32 and oxyethylene/~xybutylene~~copolymers, is almost an athermal process. This work was generously supported by the Wellcome Trust and SERC. Research studentships were provided by the Science and Engineering Research Council (L.M.), the Insti- tute for the Promotion of Teaching Science and Technology, Thailand (S.T.) and the Colloid Fund of the University of Manchester (N.J.D.).Professor Provencher kindly provided copies of the CONTIN programme for analysis of the dynamic light scattering data.Dr. R. H. Mobbs and Mr. K. Nixon gave valuable assistance with the preparation and characterization of the copolymers. References 1 Z-K. Zhou and B. Chu, Macromolecules, 1988,21, 2548. 2 Z-K. Zhou and B. Chu, J. Colloid Znterface Sci., 1988,126, 171. 3 G. Wanka, H. Hoffman and W. Ulbricht, Colloid Polym. Sci., 1990,268,101. 4 W. Brown, K. Schillen, M. Almgren, S. Hvidt and P. Bahadur, J. Phys. Chem., 1991,95, 1850. 5 N. K. Reddy, P. J. Fordham, D. Attwood and C. Booth, J. Chem. Soc., Faraday Trans., 1990,86, 1569. 6 L. Yang, A. D. Beddells, D. Attwood and C. Booth, J. Chem. Soc., Faraday Trans., 1992,88, 1447. 7 G-E. Yu, Y-L. Deng, S. Dalton, Q-G. Wang, D. Attwood, C. Price and C. Booth, J. Chem. Soc., Faraday Trans., 1992, 88, 2537.8 W. Brown, K. Schillen and S. Hvidt, J. Phys. Chem., 1992, 95, 6038. 9 P. Linse and M. Malmsten, Macromolecules, 1992,25, 5434. 10 Y-Z. Luo, C. V. Nicholas, D. Attwood, J. H. Collett, C. Price and C. Booth, Colloid Polym. Sci., 1992,270, 1094. 11 C. V. Nicholas, Y-Z. Luo, N-J. Deng, D. Attwood, J. H. Collett, C. Price and C. Booth, Polymer, 1993,34, 138. 12 Y-Z. Luo, C. V. Nicholas, D. Attwood, J. H. Collett, C. Price, C. Booth, Z-K. Zhou and B. Chu, J. Chem. Soc., Faraday Trans., 1993,89, 539. 13 I. R. Schmolka, J. Biomed. Mater. Rex, 1972,6, 571. 14 C. J. Tait, J. B. Houston, D. Attwood and J. H. Collett, J. Pharm. Pharmacol., 1987,39,57. 15 C. G. Pitt, A. R. Jeffcoat, R. A. Zweidinger and A. Schindler, J.Biomed. Mater. Res., 1979, 13, 497. 16 Y. H. Bae and S. W. Kim, Adv. Drug Delivery Rev., 1993,11,109. 17 R. Perret and A. Skoulios, Makromol. Chem., 1972,156, 143. 18 R. Perret and A. Skoulios, C. R. Acad. Sci. (Paris), 1969, 268, 230. 19 P. Cerrai, M. Tricoli, F. Andruzzi, M. Paci and M. Paci, Polymer, 1989,30,338. 1966 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 20 21 Z. Yang, S. Pickard, N-J. Deng, R. J. Barlow, D. Attwood and C. Booth, Macromolecules, submitted. K. N. Prasad, T. T. Luong, A. T. Florence, J. Paris, K. Vaution, M. Seiller and F. Puisieux, J. ColIoid Interface Sci., 1979, 69, 28 29 J. C. Gilbert, C. Washington, M. C. Davies and J. Hadgraft, Int. J. Pharm., 1987,40,93. P. Bahadur, P. Li, M. Almgren and W. Brown, Langmuir, 1992, 8, 1903. 22 23 24 25 26 27 225. S. W. Provencher, Makromol. Chem., 1979,180,201. A. D. Bedells, R. M. Arafeh, Z. Yang, D. Attwood, F. Heatley, J. C. Padget, C. Price and C. Booth, J. Chem. Soc., Faraday Trans., 1993,89, 1235. S. Tanodekaew, N-J. Deng, S. Smith, Y-W. Yang, D. Attwood and C. Booth, J. Phys. Chem., 1993,97,11847. A. Vrij, J. Chem. Phys., 1978,69, 1742. N. F. Carahan and K. E. Starling, J. Chem. Phys., 1969,51,635. D. Attwood, J. H. Collett and C. J. Tait, Int. J. Pharm., 1985, 26, 25. 30 31 32 A. D. Bedells, R. M. Arafeh, Z. Yang, D. Attwood, J. C. Padget, C. Price and C. Booth, J. Chem. Soc., Faraday Trans., 1993, 89, 1243. G-E. Yu, Y-L. Deng, S. Dalton, Q-G. Wang, D. Attwood, C. Price and C. Booth, J. Chem. SOC., Faraday Trans., 1992, 88, 2537. Y-L. Deng, G-E. Yu, C. Price and C. Booth, J. Chem. Soc., Faraday Trans., 1992,88, 1441. Paper 4/0813H ;Received 9th February, 1994

ISSN:0956-5000    

DOI:10.1039/FT9949001961

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1967-1972 I967 EPR/ENDOR Characterization of Radicals produced in the Photopolymerization of a Dimethacrylate Monomer Elena Selli, Cesare Oliva and Giorgio Termignone Dipartimento di Chimica Fisica ed Elettrochimica e Centro C.N.R.,Universita di Milano, via Golgi 19, I20133 Milano, Italy The formation of trapped radicals under UV irradiation of ethylene glycol dimethacrylate in the presence of different amounts of photoinitiator, as well as radical decay at different temperatures (90-150 "C)after the end of irradiation, have been studied by electron paramagnetic resonance (EPR) spectroscopy. A fitting procedure of the EPR signals revealed that the nine-line EPR spectrum can be attributed to the propagating radical, under- going a fast exchange process between two conformations.This radical also gives an ENDOR spectrum even at room temperature, thus suggesting that the polymer structure is essentially solid. At least one different radiFal species is present in highly photo-cross-linked samples. At temperatures above 100 "C, the hyperfine structure of the nine-line EPR spectrum is partly washed out, owing to a spin-spin exchange phenomenon between radicals. This becomes more evident with increasing degree of polymerization and cross-linking during radical decay kinetic runs and also affects the rate of exchange between the two radical conformations. Radicals produced during the photoinduced polymerization of methacrylate monomers have been thoroughly investigated by EPR spectroscopy.' Sufficiently high concentrations of long-lived radicals were obtained in early studies2 by addi- tion of difunctional monomers to methyl methacrylate.A densely cross-linked polymer network can thus be created. which hosts trapped radicals, exhibiting a nine-line EPR pattern. Variations of the EPR spectrum with temperature and the fact that the same pattern could also be obtained from UV, y-or X-irradiation of poly(methy1 metha~rylate)~-~ caused spe- culation about the radical assignment. The propagating free radical reported in Scheme 1 is now universally accepted to be the sole originator of the nine-line spectrum,*-' which arises from the hyperfine interaction of the unpaired electron with the freely rotating methyl group and with the p-methylene group, which is constrained in a certain conforma- tion of the polymer chain.However, good matches were obtained between the experi- mental EPR patterns and simulations based on different hypotheses involving constraint of the CH, group. The EPR pattern could, in fact, be simulated from a superposition of spectra due to two stable conformations," as a Gaussian dis- tribution of the dihedral angles about the most stable confor- mati~n,'.'~ as the result of exchange broadening due to hindered oscillations between two stable conformations,' ' or, finally, by a composite of the above models.' 371 In order to obtain more information, eventually supporting one of the above hypotheses, a different approach has been carried out in the present work.Following the recent studies y3 -CH,-C' I C ol" '0 I R 0 CH3 II I R = CH,-CH,-O-C-C=CH, (DMA) Scheme 1 reported by us on radicals trapped in photopolymerized and photo-cross-linked multiacrylate systems and on their ther- mally induced decay,16-' the EPR spectra of radicals trapped in a UV-irradiated difunctional methacrylate monomer, ethylene glycol dimethacrylate, have been recorded both under irradiation and during the post-irradiation radical decay at different temperatures (90-1 50 "C). The experimental EPR patterns have been fitted by an automatic non-linear least-squares procedure. Moreover, ENDOR spectra have been recorded for the first time with this photo- polymerized system.Experimental Materials Monomer and photoinitiator were commercial products. Ethylene glycol dimethacrylate (2-methylprop-2-enoic acid, ethane- 1,2-diyl ester), DMA (Aldrich), was washed twice with 2 mol dm-3 NaOH to remove inhibitor and then washed several times with saturated aqueous NaCl solution. It was successively dried over anhydrous sodium sulfate and molec- ular sieves 4A and stored at 4°C in the dark. The photoini- tiator, 2,2-dimethoxy- 1,2-diphenylethanone (BASF), was used as received. Sample Preparation The monomer, either pure or mixed with photoinitiator (0.3- 5.0 wt.%), was sealed under vacuum in quartz EPR tubes. In radical formation kinetic runs the EPR tubes were irra- diated directly in situ in the EPR cavity.The previously described apparatus and experimental procedure were employed.'* Photopolymerized DMA samples for radical decay and ENDOR studies were prepared by pre-irradiating the EPR tubes outside the spectrometer cavity, under the already reported' 6,1 experimental conditions. A double-bond con-version degree of around 63% was reached in the presence of 1-5% of photoinitiator, as revealed by analysis of residual unsaturations, carried out by Raman spectroscopy on a Perkin-Elmer Model 1720 FTIR spectrometer. The band at 1641 cm-' corresponding to the C=C stretching mode was monitored,20 using the band at 1729 cm-' due to the car- bony1 group as an internal standard. ENDOR analysis was carried out with the samples employed for radical decay kinetic studies, which had been stored at -18"C in the dark.EPRFNDOR Spectroscopy and Fitting Procedure EPR spectra under irradiation were recorded at 25°C by means of a Varian E-line Century Series EPR spectrometer, while EPR and ENDOR spectra of pre-irradiated samples were recorded at different temperatures on a Bruker ESP 300 EPR/ENDOR spectrometer, equipped with an EN1 3100LA RF (200 W) Power Amplifier. In both instruments, the tem- perature of the sample was kept constant at the desired value to within & 10C.16-18 EPR digitized spectra were fitted according to the pro- cedure already reported,' 9*21yielding width, hyperfine split- ting, g factor, spectral area of each overlapping EPR pattern and also parameters of linewidth variation resulting from dynamic processes involving radicals.The radical concentration, assumed to be proportional to the numerical integrated area of the corresponding EPR pattern, was in the range 10-3-10-2 mol dm-3, according to calibration of the two instruments by means of a Varian strong pitch. The best ENDOR signal was obtained with a microwave power of 6.3 mW and 10 dB (200 W) RF power attenuation. The RF modulation depth was kept to 100 kHz to achieve a good resolution. Results EPR Spectra at 25°C under Irradiation The well known nine-line spectrum reported in Fig. 1, typical of propagating methacrylate radicals (see Scheme l), was obtained at 25°C under UV irradiation in situ of DMA samples containing different amounts of photoinitiator. The shape of the spectrum did not change significantly with either irradiation time or photoinitiator content in the photoreac- tive mixture.Moreover, spectra identical both in shape and in intensity were recorded immediately after the light was turned off at the end of each radical formation kinetic run. Very good fittings of the experimental EPR spectra were obtained (see Fig. 1) by assuming that they result from the interaction of the unpaired electron with the three completely equivalent hydrogen atoms [with hyperfine coupling constant (hfcc), a3H = 22.7 f0.1 G] and, at the same time, with the Fig. 1 EPR spectrum at 25°C recorded under irradiation in situ of a DMA sample containing 0.3 wt.% of photoinitiator.Irradiation time: 450 min. (a) Experimental spectrum; (b) least-squares computer-synthesized spectrum. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 two P-methylene hydrogen atoms, characterized by a mean value of the hfcc, u~~ = 10.6 & 0.1 G, undergoing a fast chemical exchange. The central line of the latter multiplet is broadened by a contribution AWexchx 5.3 G to which the intrinsic linewidth AWo x 4.1 G is added. AWo increased slightly with irradiation time, i.e. as the polymer structure became more rigid and entangled, owing to further poly- merization and cross-linking. The concentration of radicals, R', responsible for the nine- line EPR spectrum increased continuously with irradiation time, as shown in Fig.2, being more than one order of mag- nitude lower in samples containing no photoinitiator. Photo- polymerization of DMA was quite slow in this case. Fig. 2 also shows that greater amounts of photoinitiator produced an increase in radical concentration. However, a maximum value was reached in the presence of 3% photoini- tiator, while a higher photoinitiator content was less effective in this respect. EPR Spectra at Different Temperatures The shape of the EPR spectrum of DMA irradiated in situ at 25°C did not change significantly in the temperature range from -120 to + 100°C. The fittings of the EPR spectra reveal that AWexchincreased only by ca. 7% if the tem-perature was lowered from + 100"C to -120 "C. In contrast, at higher temperatures (120-150 "C) some modifications were observed in the EPR spectral shapes.In fact, much better fittings of the experimental EPR spectra could be obtained by assuming that they are the super- position of the usual nine-line hyperfine structured pattern and a single-line pattern with the same g-value, having a line- width of around 10 G at 150°C. The mole fraction of rad- icals, S', giving this latter EPR pattern increased with temperature, being cu. 0.2 at 150 "C. In the framework of this fitting model, the exchange broadening, A Wexch,decreased, being about 30% less than in the absence of the single-line EPR pattern. Note that two new lines appeared on both sides of the EPR spectra with samples irradiated outside the spectrom- eter cavity, which are more homogeneously polymerized to a relatively high degree of conversion.At temperatures above 100"C, the two new lines also appeared in the EPR spectra of 250 200 h v)4-.-C :150 v m2? U$ 100 L rn 4-.-t 50 0 fi -ma 200 400 600 irradiation tirne/rnin Fig. 2 EPR nine-line pattern integrated area (arb. units) as a func- tion of irradiation time for DMA (A) pure or photopolymerizing in the presence of (a)0.3, (0) 3.0, (A)5.0 wt.% of photoinitia- 1.0, (0) tor J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Fig. 3 EPR spectrum at 120°C of DMA pre-irradiated in situ at 25°C in the presence of 0.3% photoinitiator (same sample as in Fig. 1). New EPR lines in the experimental spectrum (a) are indicated by arrows.(b) Least-squares computer-synthesized spectrum. samples pre-irradiated in situ, as shown in Fig. 3. They did not disappear if samples were cooled again to room tem-perature. Radical Decay Radical decay, investigated at 90-150°C in DMA samples behaviour was also reported recently by other authors.22 The results of the fitting procedure indicate that the mole fraction of S' radicals, giving the single-line EPR pattern, increased continuously during radical decay kinetics. This also occurred at 90°C, as shown in Fig. 5, although no single-line pattern could be detected in the EPR spectrum at the beginning of radical decay. The single-line spectrum rep- resented up to 90% of the whole integrated area at the end of radical decay at 150 "C.Fig. 5 also shows that, while the hyperfine-structured EPR pattern decreased continuously at 90-1 50 "C, the single-line spectrum increased continuously with decay time at 90 and Q 0.4 .-R J.a-5 0.2 \/ -c--E x.C ...n 0 100 300 400 time/min A) 90"C, (0,0)120kc,(m, 0)150°C. ,. Fig. 4 EPR spectra of DMA pre-irradiated in the presence of 1.0%photoinitiator at various times during radical decay at 150°C (noisy trace) and least-squares fittings of their central parts. Maximum spectral intensity was normalized. (a) 0, (b) 50, (c) 130, (d)310 min. 11 12 13 14 15 16 radiofreq u ency/M Hz Fig. 6 ENDOR spectrum of pre-irradiated DMA (3.0% photoinitiator) at (a) 150 K and (b)room temperature 120"C, while at 150°C it reached a maximum value and then decreased. The fitting of the EPR spectra also revealed that AWexchof the hyperfine-structured spectrum decreased during each radical decay kinetic run.A greater amount of photoinitiator in the photoreactive mixture caused a slight enhancement in the rate of radical termination, as already observed and discussed in previous studies on similar systems." ENDOR Spectra 'H ENDOR of pre-irradiated DMA (see Fig. 6)was detected with the magnetic field set at the centre of the EPR spectrum. Different settings always gave ENDOR patterns character- ized by an intensity roughly proportional to the intensity of the nine-line EPR pattern. At the lowest attained temperature (150 K) the ENDOR spectrum [Fig.qa)]was composed of a narrow singlet, over- lapping a broader feature. This pattern is qualitatively similar to that already rep~rted~~*" at similar temperatures with hexane- 1,Bdiol diacrylate, tetraethylene glycol diacrylate and butane-1,Cdiol diacrylate. However, in the present case, at variance with the previously investigated systems, an ENDOR broad band was also detectable at room tem-perature [Fig. qb)],the width of which was the mean of the linewidths measured at 150 K (see Table 1). Discussion Radical Formation under Irradiation At 25°C the EPR spectra detected under irradiation (Fig. 1) are identical to those obtained after the light had been switched off. This confirms that in both cases the observed nine-line EPR pattern is due to the propagating radical (see Scheme l), which is already trapped in the polymer matrix Table 1 ENDOR results sample photoinitiator content (%) T/K 6"/MHz rb/A 0.6 150 1 .OO9-0.194 4.3 -7.4 295 0.6 5.1 3 150 0.95-0.2 4.4-7.4 295 0.65 5.0 a 6, ENDOR peak-to-peak linewidth (maximum dipolar constant value).r, unpaired electron-proton distance. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 during irradiation. No reversible phenomena, such as those occurring by switching off and on the light in the presence of methyl methacrylate,' have been observed with the inves- 5923 tigated difunctional monomer. The fact that a maximum radical concentration value is obtained in the presence of 3% photoinitiator (Fig.2) demon-strates, as already discussed,18 that this amount of photoini- tiator represents in this case the optimum balance between a greater number of simultaneously initiated radical chains and the parallel increase of radical-terminating encounters, which are more probable at higher radical concentration. Also a filter effect, increasing with increasing photoinitiator concen- tration, could play a role in this respect, by reducing signifi- cantly the penetration depth of the radiation impinging on the sample. However, this effect should not be predominant, as the same extent of double-bond conversion (ca. 63%) was reached in the presence of different amounts of photoinitia-tor. Exchange between Radical Conformations Good fittings of the experimental EPR spectra have been obtained (see Fig.1 and 3) by assuming that the CH, group of the propagation radical (Scheme 1) undergoes a fast exchange process, causing a line-broadening phenomenon. The most likely explanation is that the two C,-H bonds are subject to hindered oscillations between two possible radical conformations, R,' and R,' , corresponding to two orienta- tions of the CH, group with respect to the C,-C, bond. The exchange time, z/s, between these two conformations can be evaluated from AW,,,,,/G, the exchange contribution to the width of the EPR lines characterized by a total nuclear spin quantum number, rn, = 0. The following equation has been employed :' I ye I = 17.61 x lo6 s-' G-' is the magnetogyric ratio, a, and a,, are the hyperfine coupling constants of the two protons involved in the exchange process. We have estimated a, = 15.1 G and a,, = 8.1 G, according to calculations' based on the assumption that in the two oscillating radical chain con- formations the dihedral angles of the two C,-H bonds rela- tive to the 7~ orbital of the unpaired electron are 60 k 5".This assumption is also strengthened by the fact that a mean value, ii,, = 11.6 G, is obtained with these two values, rather close to mean values of about 11 G obtained from the fitting procedures. The exchange time, z, is around 22 ns in the temperature range between -120 and + 100 "C, with an exchange activa- tion energy practically equal to zero.At higher temperatures, in contrast, the exchange phenomenon becomes faster (z z 14 ns at 150°C). However, z values do not seem to decrease with temperature according to an Arrhenius plot, as the exchange activation energy apparently increases continuously with increasing temperature, being around 20 kJ mol-' at 120- 150°C. This effect, which has already been observed in similar system^,'^ is clearly related to major modifications occurring in the polymeric structure. The glass-transition temperature of this polymer has been evaluated' very recently as ca. 140°C. Spin-Spin Exchange At temperatures higher than 100°C the EPR spectra are the superposition of the hyperfine-structured pattern, due to the exchange between conformations R,'and R2*, and the single- line pattern, due to the s' radicals.The mole fraction x(S') J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 increases during radical decay kinetic runs (Fig. 5), which are accompanied by further polymerization and cross-linking in the dark.16,26 Moreover, S' radicals decay at 150°C, but at a slower rate than R' radicals. Similar experimental evidence was observed by us in our previous EPR studies on pre-irradiated multifunctional acry- lates. A single-line pattern superposed on a hyperfine-structured pattern was attributed to radicals trapped in dense, highly cross-linked polymeric regions. 16-' In fact, spin exchange between radicals separated by distances com- parable to molecular diameters could be responsible for the lack of hyperfine splitting in the single-line spectrum. At higher temperatures, higher spin-spin exchange frequencies correspond to narrower EPR singlets.27 The single-line spectra observed in pre-irradiated DMA samples may thus be correlated with the fact that the polymer is not homogeneous.The propagation radical of Scheme 1 can undergo spin-spin exchange through its rigid polymeric surroundings. This effect is more evident at higher temperatures, as in previously investigated systems. l6 On the other hand, the presence of clusters of radicals has been detected in y-irradiated DMA6 and methyl metha~rylate.~ The increase in single-line mole fraction with radical decay, that is, with methacrylate double-bond conversion, and the slower decay of the single-line can be well explained by this model. However, in the case of pre-irradiated DMA the con- centration of s' radicals increases with time at high tem-peratures (Fig.5), while the total radical concentration ([R']+ [S.]) decreases. This implies that the fraction of propaga-ting radicals undergoing spin-spin exchange increases as the polymer becomes more entangled, owing to further poly- merization and cross-linking in the dark. Also the variation in EPR spectral shapes observed28 in the absence or presence of monomer in UV-irradiated poly(methy1 methacrylate) samples can be easily explained according to this model. Interplay between Dynamic Processes During radical decay kinetic runs at 90-150°C the rate of exchange k = 7-l between the two conformations, R,' and R2', of the propagating radical increases, together with an increase in the mole fraction of these radicals giving the single-line EPR pattern.Fig. 7 shows that the exchange time 25 1 I I I I I I 1 r i1 I 1 I I 1 I I 1 J 0 0.2 0.4 0.6 0.8 X(S7 Fig. 7 Exchange time between radical conformations R,' and R2', r/ns, us. mole fraction x(S'). Data have been calculated from the EPR spectra recorded during radical decay kinetic runs at 90°C (open symbols), 120"C (half-solid symbols) and 150"C (solid symbols). Amount of photoinitiator: (0,a)5.0%. a,0)1.0%; (A, A, A) 3.0%; (U, 0, values, z, for pre-irradiated samples containing different amounts of photoinitiator at various temperatures, are clearly correlated with the corresponding x(S') values.This means that the exchange Rl'+R2' does not involve R' radicals alone, but it can also occur through a intermolec- ular pathway involving S', according to the following equa- tion : R,' + S*=R2' + S' (1) Evidence for this reaction was also obtained in a similar system," with $3') values varying over a much smaller range. The present results clearly show that at low x(S') values the rate of exchange, z-l,undergoes a small enhance- ment due to reaction (I), while it increases for @') + 1. Presence of Different Radicals The propagating radical of Scheme 1 is thus responsible for both the hyperfine-structured line pattern and the superposed single-line pattern.However, in some EPR spectra, recorded with highly photo-cross-linked samples, two new lines appear on both sides of the usual pattern (Fig. 3). The presence of these lines, occasionally also reported by other author^,^^.^' was interpreted as an improbable superposed doublet with a splitting of 12.8 mT.29 We also think that these lines are not due to the propaga- ting radical, but to a different species, N', which is generated after long irradiation. This is also suggested by the observa- tion that the two extra lines never appear in spectra recorded during monomer irradiation in situ, where the irradiation on the sample is not uniform, owing to the shape of the EPR cavity. Furthermore, they appear and become more evident if the samples are kept at high temperatures for a certain time, thus allowing further polymerization and cross-linking in the dark, as well as chain transfer.However, all attempts to fit the EPR spectra assuming the presence of another superposed pattern, carried out in order to identify the second radical species N', did not give com- pletely reliable results, mainly because the shape of the central part of the experimental EPR spectrum does not change in an understandable manner when the two new lines appear. The most plausible hypothesis on N' is that it consists of the radical -CH2-C'(CH3)-CH,-, i.e. a mid-chain radical also undergoing a chemical exchange phenomenon, involving the two pairs of two equivalent C,-H bonds. The hfcc values, u~~ and a2H, obtained from the fitting procedure are close to those found for the propagating radical of Scheme 1.This mid-chain radical could be easily generated by homolytic chain scission in the a position to the carbonyl group. Its presence in similar systems has already been rep~rted.~"~' Also the delocalized allylic radical CH,"'C(CH3)=CH-, which has been proposed to be present in y-irradiated poly(methy1 rnetha~rylate),'~ is compatible with the spectral fitting. However, it should not be generated easily in the present case by UV irradiation, as this would imply a C-C bond scission in the polymer chain. In contrast, the radical y3 y3 -CH2-CdH----CdH2-I I C0,R C0,R which could easily be obtained by hydrogen abstraction from the polymer chain,14 should be discarded, as it is not compat- ible with the experimental EPR spectra on the basis of our fitting procedure.Radical Decay Kinetics During post-irradiation heat treatments, the decay of the total radical concentration is accompanied by an increase in the fraction of propagating radicals undergoing spin-spin exchange, as shown in Fig. 5. Thus an R' -+ S' step should be included in the mechanism in order to account for the experi- mental picture, together with the mutual termination steps involving the radicals R', S' and N, which should occur according to bimolecular reactions. Unfortunately, in this case we are not able to evaluate the rate constants of the single steps from the integrated areas of the EPR signals, which are supposed to be proportional to the radical concentrations.In fact, the amount of N' radicals cannot be evaluated from the EPR spectra with sufficient accuracy. ENDOR Analysis The trapped radicals, although affected by the dynamical phenomenon [see eqn. (I)], are essentially embedded in a solid phase. The ENDOR spectra (Fig. 6), which are typical of a solid matrix, strongly support this hypothesis. In fact, they can be interpreted, as in the previous case^,'^.'^ as due to matrix nuclear spins (protons), which interact with the unpaired electron spin by hyperfine coupling. A lower limit for the distance between them can be estimated using the equation : 6 = 80/r3 (2) where r is the proton-electron distance in 8, and 6 is the dipolar constant in MHz.6 is less than the experimental ENDOR linewidth. At 150 K the narrow singlet can thus be attributed to an interaction between the unpaired electron and protons at a distance of ~7.48, away. The broader ENDOR feature can be attrib- uted, using the same model, to an interaction between the unpaired electron and more closely placed protons, i.e. situ-ated about 4.3 A from the electron. At room temperature thermal vibrations would destroy the order in the sample, and the unpaired electron would interact with protons at a mean distance of about 5 A. Furthermore, the relationship between the intensities of the ENDOR and nine-line EPR patterns suggests that they are due to the same species, although the isotropic hyperfine couplings measured by EPR are no longer detectable by ENDOR.Conclusions Propagating radicals (Scheme 1) are trapped within the poly- meric structure produced by UV irradiation of difunctional methacrylates. The experimental nine-line EPR spectrum results from the interaction of the unpaired electron with the three completely equivalent hydrogen atoms of the methyl group and with the two P-methylene hydrogens, which undergo a fast chemical exchange between two different con- formations. The very minor changes observed in the EPR spectrum in the temperature range -120-+ 100 "C (although its shape is affected by a dynamic process) and the fact that a matrix ENDOR spectrum is detectable even at room temperature lead to the conclusion that radicals are surrounded by an essentially solid polymeric structure.A spin-spin exchange phenomenon between radicals trapped at relatively short distances within a rigid network can be observed at temperatures above 100"C, leading to the partial washing out of the hyperfine structure in the EPR spectrum. The fraction of S' radicals undergoing spin-spin J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 exchange increases with the degree of polymerization and cross-linking during radical decay kinetics, as expected. Moreover, the presence of S' radicals induces an enhance- ment in the rate of chemical exchange between the two con- formations R,' and R,' of the propagating radical, thus suggesting that this latter process could occur through an intermolecular pathway also involving S' radicals. Finally, at least one radical species other than the propaga- ting radical is formed by chain transfer in highly photo-cross- linked samples.We thank Prof. I. R. Bellobono for suggesting this research area, Dr. M. Barzaghi for helpful discussions and Dr. A. Giussani for preparing samples and recording some EPR spectra. This work was financially supported by Minister0 dell'universita e della Ricerca Scientifica e Tecnologica and by Consiglio Nazionale delle Ricerche through Progetto Finalizzato Chimica Fine. References 1 B. RAnby and J. Rabek, ESR Spectroscopy in Polymer Research, Springer-Verlag, Berlin, 1977. 2 N. M. Atherton, H. Melville and D. H.Whiffen, Trans. Faruday SOC.,1958,54, 1300; J. Polym. Sci., 1959,34, 199. 3 I. D. Campbell and F. D. Looney, Austr. J. Chem., 1962,15,642. 4 A. T. Bullock and L. H. Sutcliffe, Trans. Faraday SOC., 1964,60, 625. 5 F. Szocs and K. Ulbert, J. Polym. Sci., Part B, 1967,5, 671. 6 J. Zimbrick, F. Hoecker and L. Kevan, J. Phys. Chem., 1968, 72, 3277. 7 W. Kaul and L. Kevan, J. Phys. Chem., 1971,75,2443. 8 M. C. R. Symons, J. Chem. SOC.,1963,1186. 9 M. Iwasaki and Y. Sakai, J.Polym. Sci., Part Al, 1969, 1537. 10 M. Kamachi, M. Kohno, D. J. Liaw and S. Katsuki, Polym. J., 1978, 10, 69. 11 M. Kamachi, Y. Kuwae, S. Nozakura, K. Hatada and H. Yuki, Polym. J., 1981, 10,919. 12 M. Kamachi, Adv. Polym. Sci., 1987,82, 207. 13 M. E. Best and P. H.Kasai, Macromolecules, 1989,22,2622. 14 J. PlaEek and F. Szocs, Eur. Polym. J., 1989, 11, 11 49. 15 Y. Tian, S. Zhu, A. E. Hamielec, D. B. Fulton and D. R. Eaton, Polymer, 1992,33, 384. 16 I. R. Bellobono, C. Oliva, R. Morelli, E. Selli and A. Ponti, J. Chem. Soc., Faraday Trans., 1990,86,3273. 17 C. Oliva, E. Selli, A. Ponti, I. R. Bellobono and R. Morelli, J. Phys. Org. Chem., 1992,5,55. 18 E. Selli, C. Oliva, M. Galbiati and I. R. Bellobono, J. Chem. SOC., Perkin Trans. 2, 1992, 1391. 19 E. Selli, C. Oliva and A. Giussani, J. Chem. SOC., Faraday Trans., 1993,89,4215. 20 B. Chu and D. Lee, Macromolecules, 1984, 17,926. 21 M. Barzaghi and M. Simonetta, J. Magn. Reson., 1983,51, 175. 22 S. Zhu, Y. Tian, A. E. Hamielec and D. R. Eaton, Polymer, 1990, 31, 1726. 23 J. Shen, Y. Tian, G. Wang and M. Yang, Makromol. Chem., 1991,192,2669. 24 N. M. Atherton, Principles of Electron Spin Resonance, Ellis Horwood, London, 1993, ch. 9. 25 D. Li, S. Zhu and A. E. Hamielec, Polymer, 1993,34, 1383. 26 E. Selli, I. R. Bellobono and C. Oliva, Makromol. Chem., 1994, 195,661. 27 Yu. N. Molin, K. M. Salikhov and K. I. Zamaraev, Spin Exchange, Springer-Verlag, Berlin, 1980, p. 49. 28 R. E. Michel, F. W. Chapman and T. J. Mao, J. Chem. Phys., 1966,12,4604. 29 F. Szocs, J. Appl. Polym. Sci., 1986,32, 5673. 30 K. Hatada, T. Kitayama, E. Masuda and M. Kamachi, Makro-mol. Chem., Rapid Commun., 1990, 11, 101. 31 J. F. Kircher, F. A. Sliemers, R. A. Markle, W. B. Gager and R. I. Leininger, J. Phys. Chem., 1965,69, 189. 32 D. D. Leniart, J. S. Hyde and J. C. Vedrine, J. Phys. Chem., 1972,76,2079. Paper 4/01560F ;Received 15th March, 1994

ISSN:0956-5000    

DOI:10.1039/FT9949001967

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1973-1977 Dissolution of Amorphous Aluminosilicate Zeolite Precursors in Alkaline Solutions Part 2.T-Mechanism of the Dissolution T. Antonic, A. Ci2mek and B. Subotic Ruder BoSkoviC Institute, P.O. Box 1016,41001Zagreb, Croatia The influence of the initial mass of the solid phase and concentration of NaOH on the kinetics of dissolution of an amorphous aluminosilicate precursor having an Si : At molar ratio of 1.178 : 1 has been studied by measuring the change in the aluminium and silicon concentrations in the liquid phase during dissolution at 80°C.Analysis of the results obtained indicated that only the outside surface and not the internal surface (pore system) is relevant in the dissolution process. The process of dissolution is controlled by two reactions: a forward one, whose rate is proportional to the outer surface area, S, of the solid phase exposed to the action of OH-ions from the liquid phase, and a backward one, whose rate is proportional to the surface area, S, and to the concentration of reactive silicate and aluminate species from the liquid phase.In many cases, the dissolution rate of amorphous alumino- silicate precursor is the rate-determining step of the crys- tallization of zeolites from amorphous aluminosilicate gels. 1,2 Hence knowledge of the mechanism and kinetics of disso- lution of the precursor is necessary for a detailed kinetic analysis of zeolite crystallization. Our previous study of the dissolution of differently prepared amorphous aluminosilicate zeolite precursors having various Si : A1 molar ratios, in 0.2 mol dm-’ NaOH solution at 80°C showed that the ratio of molar concentrations of silicon and aluminium in the liquid phase is constant during the dissolution and equal to the molar Si : A1 ratio of the dissolving precursor, i.e.the disso- lution occurred in a congruent fashion.’ Kinetic analysis of the change in Si and A1 concentrations in the liquid phase during the dissolution showed that the rate of dissolution is directly proportional to the surface area, S, of the solid exposed to alkaline solution and under~aturation,~ i.e. Although the results obtained by numerical solution of eqn. (1) were in excellent agreement with measured values for all analysed prec~rsors,~ the abovementioned conclusions were made on the basis of dissolution experiments performed under one set of conditions, i.e.dissolution of 0.5 g of precur- sor in 200 cm’ of 0.2 mol dm-3 NaOH solution at 80°C. For this reason, the aim of this work is the study of other relevant factors such as the effects of starting amount of dissolving precursor and concentration of NaOH solution on the kinetics of dissolution in order to obtain a better understand- ing of the mechanism of the dissolution process. Experimental The amorphous aluminosilicate precursor PAP 1 was used as the dissolving solid phase in all experiments. The precursor PAPl ([Si : All = b = 1.178) was prepared as follows:’ Al(OH), (8.22 g, Baker) was dispersed in 10 cm’ of distilled water and NaOH (10 g) was added.The suspension was stirred with heating until the Al(OH), was dissolved com- pletely. The solution was diluted with distilled water to 100 cm’. Sodium silicate solution was prepared by dilution of 14 cm’ of water-glass stock solution (8.15 wt.% Na,O, 25.9 wt.% SiO,, 65.95 wt.% H20) with distilled water to 100 cm3. The temperature of the sodium aluminate and sodium silicate solutions was then thermostatically controlled at 25 “C before t Part 1 :ref. 3. mixing. Then, 100 CM’ of the sodium silicate solution was poured (within 10 s) into a 600 cm3 plastic beaker containing 100 cm’ of the sodium aluminate solution stirred with a mag- netic stirrer. The system (precipitated gel dispersed in the mother liquor) was stirred for a further 10 min and was then transferred into a stainless-steel reaction vessel preheated at 80°C and mixed at the same temperature with a magnetic stirrer for 1 h.Thereafter, the gel was centrifuged to separate the liquid from the solid phase. After removal of the clear liquid phase above the sediment (wet amorphous solid), the solid phase was redispersed in distilled water and centrifuged repeatedly. The procedure was repeated until the liquid phase above the sediment was at ca. pH 10. The washed solid was dried at 105°C for 24 h. The dried solid was pulverized in an agate mortar. In order to follow the dissolution process, a determined amount (0.3-2 g) of the solid was added into a stainless-steel reaction vessel containing 200 cm3 of stirred 0.125, 0.2, 1 and/or 2 mol dm- NaOH solution preheated at dissolution temperature (80 “C).The reaction vessel was provided with a thermostatically controlled jacket and fitted with a water-cooled reflux condenser and a thermometer. The reaction mixture was stirred with a Teflon-coated magnetic bar (L = 5 cm, q5 = 0.95 cm) driven by a magnetic stirrer at 510 rpm. At various times, td, after the beginning of the dissolution process, 5 cm3 aliquots of the suspension were drawn off (by pipette) to prepare samples for analysis. The point at which the solid was added to the preheated NaOH solution was taken as time zero of the dissolution process. Aliquots of the reaction mixture drawn off at given dissolution times, t,, were centrifuged.The clear liquid phase was used for the analysis of silicon and aluminium concentrations in the liquid phase. Equilibrium (saturation) concentrations C,,(eq) of alu- minium and C,(eq) of silicon, which correspond to the solu- bility of the precursor PAPl at given conditions were determined by measuring the A1 and Si concentrations in the liquid phase at t, = 4 h. The concentrations C,, and C,,(eq) of aluminium and CSi and C,,(eq) of silicon in the liquid phase were measured by colorimetric method^.^,^ Results and Discussion Kinetic analysis of dissolution of various compounds6-’ including amorphous aluminosilicates ‘g2 and zeolites”-’’ indicated that the dissolution is controlled by at least two processes : (i) Forward reaction caused by breaking of surface bonds due to the action of solvent and formation of soluble species that leave the surface of the dissolving solid.The rate, (dC/dt,),, at which the soluble species (solvated ions and/or molecules) leave the solid phase is assumed to be propor- tional to the surface area, S, of the solid exposed to the action of solvent, i.e. (dcldt,), = klS (2) (ii) Backward reaction, i.e. reaction of the soluble species from the liquid phase on/with the surface of the dissolving solid. The conventional kinetic arg~ments'~ applied to a chemically controlled dissolution of solute, A, B, CaAbf(aq)+ bB"-(aq), lead to: (dC/dt,), = -k2 SC" (3) where C = CA or C = C, and n = a + b.Hence, dC/dt, = (dC/dtd)l + (dC/dtd)z = k,S -k, SC" = k,S[C(eq)" -C"] (4) However, eqn. (4)fails to explain the kinetic form: dC/dt, = kdS[C(eq) -c]" (5) used for the analysis of the kinetics of dissolution of many solids7 including zeolites.' '-' Our earlier study of the kinetics of dissolution of zeolites has shown that the dissolution takes place in accordance with the model proposed by Davies and Jones," and hence the kinetics of dissolution can be expressed as:12,13 dC/dtd = kd SICAl(eq) -CA,l[CSi(eq) -cSi Ib (6) Since the power, n, in eqn. (5) is closely related to the surface integration step (e.g. formation of the bonds relevant for the crystal structure of the dissolving solid, by chemical reaction of the species from the liquid phase on the surface of the ~olid),~.' it is certain that the concentration dependence in eqn.(6) is the consequence of the backward step of the disso- lution process. The latter is characterized by a chemical reac- tion between silicate and aluminate anions from the liquid phase on the surface of the dissolving zeolite crystals and the formation of Si-0-Si and Si-0- A1 bonds characteristic of the appropriate type of zeolite. It can be assumed that the above considered reaction between silicate and aluminate anions from the liquid phase is catalysed by the specific ord- ering of Si and A1 atoms on the surface of zeolite crystals. On the other hand, although the mechanism of the forward reac- tion is the same for both dissolution of zeolites and amor- phous aluminosilicates [see eqn.(2)], a linear relationship between log(dC/dt,) and logS[C(eq) -C]" with n = 1 (see ref. 3) indicates that the backward reactions during the disso- lution of amorphous aluminosilicates in hot alkaline solu- tions can be expressed as : (dC/dt,), = k2SC (7) and hence, dC/dt, = k1S - kzSC (8) where C = C,, or C = Csi. Since in equilibrium: k,S = k2 SC(eq) (9) eqn. (8) can be transformed to the form: dC/dt, = k, s[C(eq) -c]= k, S[C(eq) -c] (10) This leads to an assumption that the backward reaction described by eqn. (7) is not controlled by mutual chemical reactions between silicate and aluminate anions from the liquid phase on the surface of the solid phase (gel), but by another type of surface reaction which will be discussed later.J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 The abovementioned considerations show that both the forward [see eqn. (2)] and backward reactions [see eqn. (3) and (7)], are directly proportional to the surface area, S, of the solid exposed to action of solvent. Also, most models of the dissolution processes suggest that the rate of dissolution is directly proportional to S.'*7-8711-1 Some authors have predicted that the surface area, S, can be expressed as a function of mass, mu,of the undissolved solid. Truskinovskiy and Senderov' and later Mydlarz and JonesI6 proposed that the surface area of the solid exposed to solvent is propor- tional to the 2/3 power of mu,i.e.S = G!(mu)2'3 (11) On the other hand, Cook and Thompson2 assumed that owing to the porosity of amorphous aluminosilicate zeolite precursors, the surface area, S, of the solid exposed to solvent is directly proportional to the mass, mu,of the undissolved solid, i.e. S = pm, (12) and hence, the rate of dissolution is also directly proportional to mu.Our previous analysis of the kinetics of dissolution of amorphous aluminosilicate zeolite precursors3 led to the con- clusion that the rate of dissolution is directly proportional to the surface area S [see eqn. (1) and (lo)], and that the surface area can be expressed as : S = a(mJ2i3 = a[mg -mG(L)]2/3 (13) However, our conclusion was made on the basis of a study of the kinetics of dissolution for constant mg ,constant concen- tration of solvent and constant temperature (see Introduction), so that it is necessary to examine the relations between mu,S and dm,(L)/dt, under different conditions in order to confirm the relations expressed by eqn.(1)and (13). Fig. 1 shows the change in the mass, mG(L), of dissolved solid during heating of different amounts, mg,of the precur- sor PAPl in 0.2 mol dm-3 NaOH solution at 80°C. Since the dissolution occurred in a congruent fashion, the mass m,(L) was calculated as:3 wAL) = [CAI M(A1)' + Csi M(Si)11/2 (14) The 'plateau' of the dissolution curves [mG(L) = mG(L),, see Table 11 is determined by the initial amount, mg,of the pre- F a -2.0 -1.6 m I E -1.2 --.n ?.{ 0.8 f O.li0.0 0 10 20 30 40 50 60 t,/min Fig.1 Change in the mass, m,(L), of the dissolved solid during the dissolution of the amorphous aluminosilicate precursor PAP 1 in 0.2 mol dmP3 NaOH solution at 80°C. td is the time of dissolution. The initial mass, m:, of the precursor PAPl was 1 (O),1.65 (a),2 (O), 2.5 (m) and 3 (A) g dmP3. Solid curves represent the m,(L) us. t, functions calculated by numerical values of rn: ,Kd (see Table I) and mG(eq)= 2.18 g dmP3 as appropriate constants. The horizontal dashed lines are explained in the text. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Numerical values of the 'plateau' concentration, m,(L) = mG(L)&,, and constant K, in eqn. (17) that correspond to the kinetics of dissolution during heating of different amounts, mg , of the precur- sor PAPl in 0.2 mol dm-3 NaOH solution at 80°C 1.00 1.00 0.220 1.65 1.65 0.215 2.00 2.00 0.200 2.50 2.18" 0.225 3.00 2.18" 0.21 1 ~ ~~~~~~~ " mC(L), = mG(eq)= 2.18 g dm-j is the solubility of the precursor PAPl in 0.2 mol dm-3 NaOH solution at 80°C (see Table 1 in ref.3). cursor and its solubility, m,(eq), in 0.2 mol dm-3 NaOH solution at 80°C (see Table 3 in ref. 3). It is evident that m&), = mg for mg < m,(eq) and that m&), = mG(eq) for mg 2 m,(eq) (see Fig. 1 and Table 1). To determine the rela- tions between dm,(L)/dtd, mg -mJL) and mG(eq) -m&), each of the five mG(L) us. td functions (see Fig. 1) was graphi- cally differentiated at the point of constant m&) [and thus constant m,(eq) -mG(L); intersection between each of the five m,(L) us.td functions and dashed horizontal line]. Then, each set of the differentials drn,(L)/dt, [that determined at the points of constant mG(L)] was plotted against the corre- sponding values of mu = mg -mG(L) (Fig. 2) and (mJ2I3 = [mg -mG(L)]2'3, respectively (Fig. 3). Fig. 2 and 3 show that dmG(L)/dtd is not a linear function of mu, but that the rate of dissolution is directly proportional to (mu)213for each con- sidered constant undersaturation, m,(eq) -m&). Hence, where, in accordance with eqn. (1) and (13), the slopes K, of the straight lines in Fig. 3 are given by = kda[mG(eq) -mG(L)l = Kd[mG(eq) -mG(L)l (16) Fig.4 shows that K is a linear function of the under-saturation [mG(eq) -mG(L)], and that the numerical value of the slope Kd (=0.22 g-2/3 min-') is very close to the values of K, (see Table 1) which correspond to the kinetics of disso-lution presented in Fig. 1. The values of Kd presented in I 0.7 I 0.61 .-C E 0.5 -mI5 0.4 -0--.2 0.3tPih 0.2; ELU 0.1 -0.0 I 0.0 0.4 0.8 1.2 1.6 2.0 2.4 ImG -mG(L)l/g dm-3 Fig. 2 dm,(L)/dt, us. mu = m: -m,(L) plots which correspond to the dissolution of the precursor PAPl at different undersaturations : m,(eq) -mG(L) = 1.78 (O),1.58 (a),1.38 (O),1.18 (H)and 0.98 (A) g dm-j. The concentration of NaOH was 0.2 mol dm-3 and the temperature of dissolution was 80 "C.1975 0.7 0.6 m 0.5 w 0,> 0.4 //I/ /I 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 [mG -mG(L)]2/3/g2/3 dm-' Fig. 3 dm,(L)/dt, vs. = [mg -m,(L)]2/3 plots which corre- spond to the dissolution of the precursor PAPl at different under- saturations: m,(eq) -m,(L) = 1.78 (O),1.58 (*), 1.38 (0)and 0.98 (A) g dm-3. The concentration of NaOH was 0.2 mol dm-3 and temperature of dissolution was 80 "C. Table 1 were calculated by the procedure explained earlier.3 The results presented in Fig. 1-4 undoubtedly confirm that the rate of dissolution is directly proportional to the surface area, S, and the undersaturation as expressed by eqn. (1).The linear relationship between dm,(L)/dt, and [mg -m&)] 2/3 and at the same time, the non-linearity between drnG(L)/dtd and [mg -m&)] indicate that only the outside surface (solid/liquid interface) and not the internal surface (pore system) of the particles of the investigated solids is relevant in the dissolution process.Hence, the kinetics of dissolution can be expressed as : Very good agreement between the measured values of mG(L) (symbols in Fig. 1) and the values of mG(L) calculated by numerical solution of eqn. (17) (curves in Fig. l), using the corresponding values of mg, m,(eq) and Kd (see Table I), confirms this conclusion. It is evident from eqn. (8)-(10) that Kd = ak, is directly proportional to the rate constant k, of the backward reaction and that the product &mG(eq) is directly proportional to the rate constant, k,, of the forward reaction of the dissolution process.0 0.36 t1 c /c/ 0.32 ; 0.28 : I.E 0.24; 7 0.20 1 E 0.16 \ r 0.12; 0.00 1' 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 [m,(eq) -m~(L)l/gdmW3 Fig. 4 Values of constant K in eqn. (15) and (16) plotted against the -corresponding undersaturations : &(eq) -mG(L) - 0 0 10 20 30 40 50 60 t,/min Fig. 5 Change in the mass, m,(L), of the dissolved solid during the dissolution of the amorphous aluminosilicate precursor PAP 1 in 0.125 (O), mol dm-3 NaOH solution at 0.2 (a),1 (a)and 2 (0) 80°C. Solid curves represent the m,(L) us. t, functions calculated by numerical solution of eqn. (17) using the corresponding numerical values of mg ,K, and m,(eq) (see Table 2) as appropriate constants. For a better understanding of the reactions which control the dissolution process, the kinetics of dissolution of the pre- cursor PAP 1 in NaOH solutions of different concentrations were analysed by eqn.(17). The very good agreement between the values of mG(L) measured during the dissolution of the precursor PAP1 in NaOH solutions of different concentra- tions at 80°C (symbols in Fig. 5) and the values of m,(L) calculated by numerical solution of eqn. (16) (curves in Fig. 5), using the corresponding values of mg,mG(eq) and Kd (see Table 2), show that the variation in NaOH concentration does not affect the mechanism of dissolution, i.e. the kinetics of dissolution can be in all cases expressed by the differential equation, eqn.(16). The values of mG(eq) were determined experimentally and the values of Kd were calculated from the log[dm,(L)/dt,] us. log[mL -mG(L)]2/3[mG(eq)-m,(L)] plots by the procedure described earlier.3 The data in Table 2 show that the value of Kd does not depend on the NaOH concentration and that the value of m,(eq) increases with the increase of NaOH concentration. Based on these findings, the process of dissolution of amorphous aluminosilicate precursors in NaOH solutions can be explained as follows: The action of OH- ions from the liquid phase on the solid/liquid interface causes breaking of the surface Si-0-Si and Si-0-A1 bonds of the precur- sor and formation of soluble aluminate and silicate species.Owing to agitation of the suspension, soluble silicate and alu- minate species so formed leave the solid/liquid interface and tend to be homogeneously distributed throughout the bulk of the liquid phase. The rate of formation of the soluble silicate and aluminate species is assumed to be proportional to the number of OH- ions that act to the unit surface area of the Table 2 Numerical values of the measured equilibrium amounts, m,(eq), of the dissolved solid and of the constant K, in eqn. (17) that correspond to the kinetics of dissolution of the amorphous alumino- silicate precursor PAPl in NaOH solutions of different concentra- tions (CNaOH)at 80°C; m: is the initial mass of the precursor in the suspension C,,,,/mol dm - mglg dm - m,(eq)/g dm - Kd/g-213 min - 0.125 2.5 1.66 0.185 0.2 3.0 2.18 0.211 1 6.0 5.39 0.205 2 10.0 6.34 0.185 J. CHEM.SOC. FARADAY TRANS., 1994, VOL. 90 precursor. Hence, the rate at which the soluble silicate and aluminate species leave the solid/liquid interface (forward reaction) increases with increasing concentration of NaOH, and is directly proportional to the surface area, S, exposed to the action of OH- ions, as is expressed by eqn. (2). The dependence of the rate of the forward reaction on the concen- tration of NaOH in the liquid phase is determined by the change of S and mG(L) under the given conditions. Previous analysis of the degree of Si polycondensation in the liquid phase showed that the liquid phase contained silicate anions in both monomeric and dimeric forms with predominant monomeric forms.Some of the silicate and aluminate anions from the liquid phase return to the solid/liquid interface, where they react with surface silicon and aluminium ions forming a new surface layer of the solid phase. Phase analysis of the solid residues showed that no phase transformation occurred during the dissolution, i.e. that the solid phase formed by the backward reaction has the same structural properties as the starting amorphous aluminosilicate precur- SO^.^ The constant Si: A1 molar ratio in the liquid phase during the dissolution which is the same as the Si : A1 molar ratio of the solid phase indicates that the solid phase formed in the backward reaction has a chemical composition identi- cal to that of the initial solid phase.Therefore, based on the linear relationship between dmc(L)/dtd and m,(eq) -m,(L), it can be concluded that the silicate and aluminate anions from the liquid phase do not react with one other at the surface of the dissolving solid, but only with the terminal OH- groups of the solid phase forming new Si-0-Si and Si-0-A1 bonds characteristic for amorphous aluminosilicates. Taking into consideration the abovementioned assumptions it can be expected that the rate of the backward reaction is directly proportional to the concentration of the reactive species in the liquid phase (silicate and aluminate anions, expressed as the molar concentrations CAI of aluminium and CSiof silicon) and the ‘concentration’ of terminal OH- groups on the surface of the solid phase (which is assumed to be pro- portional to the surface area, S, i.e.[OH-], = KS), as expressed by eqn. (7). Under the given experimental condi- tions the rate constant Kd z k, is assumed to be dependent only on the kinetic energy of the reacting species, and thus is independent of the concentration of NaOH. The values of K, in Table 2 confirm such an assumption. Otherwise, the value of K, is a function of the properties of the solid phase (chemical comp~sition,~ particulate characteristics) and is assumed to be dependent on experimental conditions (temperature, mode and rate of agitation, design of vessel etc.).It is evident that the rate of forward reaction decreases owing to the decrease of the surface area, S [caused by the decrease of the mass mu,see eqn. (12)] and that the rate of the backward reaction increases owing to the increase of the concentration of reactive species in the liquid phase during the dissolution process. At the moment when both of the reactions have the same rate, the dissolution process achieves the equilibrium expressed by eqn. (9). The validity of eqn. (8), (10) and (17), which are derived on the basis of the above considered model of the dissolution process, for the kinetic analysis of the dissolution process and for the mathematical description of the change in CAI, CSi and m,(L) during the dissolution, indicates that the above considered model is rele- vant for the process of dissolution of dehydrated amorphous aluminosilicate precursors in NaOH solutions.Conclusion The influence of the initial mass, mg,of the solid phase on the kinetics of dissolution of the amorphous aluminosilicate precursor PAPl (Si : A1 = 1.178 : 1) in 0.2 mol dmP3 NaOH J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 solution at 80°C was studied. Analysis of the change in the mass, mG(L), of the dissolved precursor showed that the rate of dissolution is directly proportional to the external surface area, S, and undersaturation, as expressed by eqn. (17), i.e. dmG(L)/dtd = KdS[mG(eq) -m&)], where S = V.[mG(eq) -mG(L)]2’3. The simple relation between the rate of disso- lution, Rd = dmG(L)/dtd, and undersaturation, m,(eq) -m,(L), indicated that the dissolution process is controlled by two reactions: (RJl = klS = &mG(eq)S (forward reaction) and (Rd)2 = -k$mG(L) = -Kd Sm,(L) (backward reaction).This model has been evaluated by analysis of the kinetics of dissolution of the precursor PAPl in NaOH solu- tions of different concentrations. The analysis showed that: (i) the rate of the forward reaction is controlled by breaking of the surface Si-0-Si and S-0-A1 bonds owing to the action of OH-ions from solution. The rate of the forward reaction depends in a direct way on the concentration of solvent as indicated by the increase of the value of mG(eq) with increasing concentration of NaOH (see Table 2).(ii) The rate of the backward reaction is controlled by the formation of new Si-0-Si and Si-0-A1 bonds between the silicate and aluminate anions from the liquid phase and surface silicon and aluminium atoms. Under the given conditions, the rate of the backward reaction indirectly depends only on the concentration of NaOH by the change of the concentration of reactive species in the liquid phase, but the rate constant k, x Kd does not depend on the concentration of NaOH (see Table 2). The values of mG(L) calculated by numerical solu-tion of eqn. (17) are in excellent agreement with the experi- mentally obtained values of mG(L). This shows that the kinetics of dissolution can be described mathematically by eqn. (17), and hence confirms the proposed model of disso- lution.Although the above considered model was successfully applied in the simulation of the synthesis of zeolite A from differently aged, as-created expanded aluminosilicate gels,22 it is clear that, at times, this model can be used strictly for mod- elling and simulation of zeolite synthesis from dehydrated aluminosilicate powders. However, it is our opinion that the experimental experience and theoretical considerations arising from this study will be helpful in further studies of the kinetics of dissolution of as-created, expanded aluminosilicate gels. The authors thank the Ministry of Science and Technology of the Republic Croatia for its financial support. Glossary b Molar Si : A1 ratio of the zeolite Concentration of soluble species (A, B, Al, Si) in the liquid phase C(eq) Equilibrium (saturation) concentration of soluble species (A, B, Al, Si) in the liquid phase dC/dtd Differential change in the concentration of soluble species in the liquid phase kl Rate constant of the forward reaction k, = kd Rate constant of the backward reaction 1977 Kd = akd Rate constant of the dissolution process 4 Initial mass (at td = 0) of the solid phase in the suspension mG(eq) Mass of the dissolved solid which corresponds to its solubility mG(L) Mass of the solid phase dissolved up to any time, td mG(L), Mass of dissolved solid which corresponds to the ‘plateau’ of the dissolution curves shown in Fig.1 m” Mass of undissolved solid M(Al), Mass for the precursor PAPl which contains 1 mol of A1 (see Table 1 in ref.3) M(Si), Mass of the precursor PAPl which contains 1 mol of Si (see Table 1 in ref. 3) S Surface area of the solid phase exposed to the action of solvent td Time of dissolution a Proportionality constant in eqn. (1l), (12) and (16) B Proportionality constant in eqn. (12) References 1 L. M. Truskinovskiy and E. E. Senderov, Geokhimiya, 1983, 3, 450. 2 J. D. Cook and R. W. Thompson, Zeolites, 1988,8, 322. 3 T. Antonik, A. Ciimek, C. Kosanovik and B. Subotik, J. Chem. SOC.,Faraday Trans., 1993,89, 1817. 4 M. L. Blanchet and L. Malaprade, Chim. Anal., 1960,42, 603. 5 G. Valence and S. Marques, Chim. Anal., 1967,49, 275. 6 C. H. Bovington and A. L. Jones, Trans. Faraday Soc., 1970,66, 764.7 A. L. Jones and H. G. Linge, Z. Phys. Chem. NF, 1975,95,293. 8 H. Sverdrup, P. Warfwinge and 1. Bjerle, Vatten, 1986,42,210. 9 R. Wolast and L. Chou, in Physical and Chemical Weathering in Geochemical Cycles, ed. A. Lerman and M. Meybeck, Kluwer, Dordrecht, 1988, p. 11. 10 R. G. Compton and K. L. Pritchard, Philos. Trans. R. SOC. London, A, 1990,330,47. 11 A. Ciimek, LJ. Komunjer, B. Subotik, M. Siroki and S. RonEe-vik, Zeolites, 1991, 11, 258. 12 A. Ciimek, LJ. Komunjer, B. Subotik, M. Siroki and S. RonEe-vik, Zeolites, 1991, 11, 810. 13 A. Ciimek, LJ. Komunjer, B. Subotic, M. Siroki and S. RonEe-vic, Zeolites, 1992, 12, 190. 14 G. H. Nancollas and N. Purdie, Q. Rev. (London), 1964,18, 1. 15 C. W. Davies and A. L. Jones, Trans. Faraday SOC., 1955, 51, 812. 16 J. Mydlarz and A. G. Jones, Chem. Eng. Sci., 1989,44, 1391. 17 A. L. Jones, G. A. Madigan and I. R. Wilson, J. Cryst. Growth, 1973,20,93. 18 C. N. Litsakes and P. Ney, Fortsch. Miner., 1985,63, 135. 19 P. Gohar and M. Cournil, Muter. Chem. Phys., 1986, 14,427. 20 H. Sunada, A. Yamamoto, A. Otsuka and Y. Yonezawa, Chem. Pharm. Bull., 1988,36, 2557. 21 D. Elenkov, S. V. Vlaev, I. Nikov and M. Ruseva, Chem. Eng. J., 1989, 41, 75. 22 B. Subotik and J. BroniC, in Proceedings of the Ninth Interna- tional Zeolite Conference, ed. R. von Ballmoos, J. B. Higgins and M. M. J. Treacy, Butterworth-Heinemann, Boston, 1992, p. 321. Paper 3/040391; Received 12th July, 1993

ISSN:0956-5000    

DOI:10.1039/FT9949001973

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1979-1982 Effects of Hydrogen and Deuterium Concentration on Measurements of the Solubility and Diffusivity of Hydrogen Isotopes in Yttrium Takeshi Maeda, Shizuo Naito,' Masahiro Yamamoto and Mahito Mabuchi Institute of Atomic Energy, Kyoto University, Uji, Kyoto 61 1, Japan The solubility and diffusivity of hydrogen and deuterium in polycrystalline a-yttrium have been measured in the temperature range 1073-1273 K and at hydrogen and deuterium concentrations, 8 (H :Y and D :Y, atomic ratio), of 0-0.44.The measured solubility obeys the relationship p = k[8/(1 -O)]', where p is the hydrogen pressure and k is a constant independent of 8. The measured diffusion coefficients for hydrogen and deuterium increased with 8.The experimental result has been explained by a model in which a hydrogen atom can occupy a pair of two nearest-neighbour tetrahedral sites of the hcp a-yttrium lattice and move almost freely between the two sites. The yttrium-hydrogen system can retain the hcp a-phase structure in a wide range of temperature and hydrogen con- centration.1-6 The a-phase region extending up to a hydrogen concentration 8 = 0.24 at even 4 K has attracted much research interest because it is closely related to the occurrence of hydrogen pairing?y6-' which was first proposed as a pos- sible cause of the low-temperature resistivity anomaly observed in the yttrium-hydrogen system. At high tem-peratures, however, the hydrogen pairing can no longer be expected to persist and hydrogen atoms are likely to be unpaired.6*'2 In addition, the a-phase region extends up to larger values of 8 as the temperature increases. This makes it possible to study the solubility and diffusivity in a wide range of 6 without paying special attention to additional com-plications resulting from hydrogen ordering and the phase boundary.The purpose of this paper is to find factors that affect the 8 dependence of the solubility and diffusivity in hcp a-yttrium. Several studies have been reported on the solubility of hydrogen and deuterium in a-yttri~m.'-~*'~ Some of the reported values of ~olubility,~~~ however, show considerable deviations from Sieverts law at small 8. In addition, a change in the reported enthalpy of solution of hydrogen with 8 has been shown to exhibit a spread of values over the range 0-0.69 eV.I3 The cause of this observed inconsistency still seems to be unclear.Several researcher^'^-^' have reported mea- surements of diffusion coefficients (D) for hydrogen and deu- terium in a-yttrium. There has been, however, no systematic study of the 8 dependence of D although in some metals other than a-yttrium, effects of 8 on D have been investi- gated.20*21In the fcc yttrium hydride, an observed increase in D with 8 has been related to the sites occupied by hydrogen atoms.22 Decreases in D with 8 in bcc niobium and tantalum have been discussed on the basis of an elastic interaction between the hydrogen atoms.20*2' In the present study we have measured changes in the solu- bility and diffusivity with 8.The 8 dependence of the mea- sured solubility is compared with a model of solution that involves sites available to hydrogen atoms and an interaction between the hydrogen atoms in yttrium. We then discuss a model of diffusion that incorporates the factors of interaction and site occupation, and compare it with the 8 dependence of the measured diffusivity. Experimental Values of the diffusion coefficient, D,were calculated from the rate of gaseous hydrogen absorbed by a yttrium sample and the solubility was calculated from the final amount of hydro- gen absorbed. The apparatus and procedures for measure- ments have been described previo~sly.'~.~~ To obtain D at different values of 8, we repeated the measurement after increasing the hydrogen pressure, p, in a specimen chamber.Values of 8 were defined, for particular values of D obtained from each measurement, as the average of 8 estimated before and after the measurement. The sample used and the heat treatment employed were the same as described previously.' ' Measurements were made in the temperature range 1073-1273 K in steps of 50 K and at hydrogen concentrations of 0.02-0.44. Surface processes were found to affect the measured hydro- gen absorption rate. The values of D were corrected to allow for these effects, as shown previo~sly.'~*~~ Results and Discussion Sohbaity Relationship between Hydrogen Pressure and Hydrogen Con- centrat ion When 8 4 1, Sieverts law has been found to apply to 8 and p.6923*24We are concerned with the solubility at specific values of 8 and consider a relationship that incorporates a consideration of the sites available to hydrogen atoms in the hcp or-yttrium and of the interaction between the hydrogen atoms, both factors which play crucial roles in the relation- ship at finite 8.The relationship has been derived in terms of the chemical potentials, pHZfor hydrogen in the gas phase and pH for hydrogen in yttrium where pH, = 2pH (1) The expression of pH2 is well kn~wn.~*~~ Adopting the lattice- gas model and using the mean-field approximation for the interaction between hydrogen atoms, we can write pH as6i24 pH = pi + w8 + k, T In -e r-8 where pi is the part of the chemical potential pHthat corre- sponds to the energy of hydrogen atoms in yttrium, w is a parameter that characterizes the hydrogen-hydrogen inter-action and r is the number of sites available to a hydrogen atom per yttrium atom in the hcp yttrium lattice.From eqn. (1) and (2) we have p=k -(1 (3) k = k' exp(2w8/kBT) (4) where k' is a constant independent of 8. A little care is needed in choosing the value of r. Hydrogen atoms occupy tetrahedral (T) sites in hcp cr-yttri~m~,~,~-’ (Fig. 1) and the number of the T sites is twice that of yttrium atoms. Now the distance between the nearest-neighbour T sites, which form a T-T pair (Fig. I), is c/4 (where c is the lattice constant along the c axis), i.e.0.14 nm. Variations of this distance corresponding to changes of temperature and 8 are small and can be ignored under the experimental condi- tion in the present study. This distance is rather small as compared to the separation of two hydrogen atoms in metals.6 This suggests that two hydrogen atoms cannot simultaneously occupy the T-T pair and only one of the T sites in it is therefore available to a hydrogen atom. We may thus assume that r = 1. At larger r, the hcp structure is unlikely to be retained and changes to the fcc stru~ture~,~ e.g. at r = 2. The problem of values of r other than unity will be mentioned later. We make a comment here on w. The assumption that one T-T pair is available to only one hydrogen atom means that w is strongly repulsive for nearest-neighbour hydrogen atoms.In eqn. (2) and (3) the values of w should therefore be regard- ed as a long-range part of the interaction, which has been discussed with regard to the origin of spinodal decomposition in some metal-hydrogen system^.^.^' 324 Interpretation of the Measured Solubility To discuss the solubility and to compare critically the result obtained in the present study with those reported earlier, we consider a k-8 plot instead of conventional p8 plots. An In p8 plot in particular shows only insufficiently clearly the extent of deviations of the solubility from eqn. (3). Fig. 2 shows values of k computed from measured values of p and 8 and through eqn. (3), where we have put r = 1.To obtain the values of k precisely at different temperatures we have plotted k on a logarithmic scale. The values of k at small 8, i.e. 8 < 0.1, coincide with those reported previo~sly.’~ At small 8, the difference between the values of k for hydrogen and deu- terium comes from the differences in the partition functions for H, and D, and in the partition functions for hydrogen and deuterium atoms in yttrium.” As can be seen from Fig. 2, values of k obtained in the present study are almost independent of 8. Reported values have been read off graphically from the literat~rel-~ and some of these values have been plotted in Fig. 2. In contrast Fig. 1 Tetrahedral (T) sites and octahedral (0)sites in the hcp a-yttrium.(.)Yttrium atoms, (T) tetrahedral sites and (0)octahedral J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 m5 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 0.5 0 0 Fig. 2 8 dependence of k at various temperatures computed from measured values of p and 8 by using eqn. (3) and (4) with r = 1. A, Hydrogen and, B, deuterium. (a) 1073, (b)1123, (c) 1173, (6)1223 and (e) 1273 K. (0,0)This study, (---) Begun et aL3 (*..-) Yanno-poulos et al.’ and (-.-) Lundin et al.’ The reported values plotted in this figure have been read off graphically from plots in the literature. to the values of k obtained in the present study, the reported values show a complicated 8 dependence, particularly at small 8. This inconsistency can also be seen in comparison of the change in the enthalpy of solution of hydrogen with 8.The enthalpy change has been summarized12 for the earlier reported data, for which its 8 dependence has been assumed to be linear. Since this assumption is equivalent to eqn. (4), we can make a comparison in terms of w in eqn. (4).It may be seen that w w 0 for the result of the present study and w = f0.04,’ 0.43,, 0.693 and 0.11 eV12 for the previously reported values.’ The origin of this inconsistency in k and w is presently not clear. All the data except the last one” mentioned above, which has been obtained from calorimetric measurements, have been obtained from measured isotherms. A possible origin may be the influence of impurities such as oxygen and nitrogen that were absorbed by samples in the course of experiments.In fact, it has already been reported that oxygen and nitrogen could cause complicated changes in k in the niobium-and tantalum-hydrogen sys terns.’ 5-2 In the present study we used an ultra-vacuum apparatus in order to prevent impurities from being absorbed by the sample during measurements. We have shown above that the solubility experimentally obtained in this study can be explained for values of r = 1 and w = 0 in eqn. (4). Note, however, that there remains an alternative possibility of explaining the solubility for values of r # 1 and w # 0. In fact, we can show that the experimental result in the present study can also be reproduced if w = -0.05 eV and r = 1.2. (The corresponding computed lines are not shown in Fig.2 because they are horizontal, almost straight lines and would reduce the clarity of the figure.) This value of w = -0.05 eV corresponds to the long- range elastic interaction energy in the yttrium-hydrogen system.6 The negative value, i.e. indicative of the attractive interaction, is required for w to cause spinodal decomposition to occur in the ~ystem.~,~~.~~ It is, however, not clear whether the spinodal decomposition is mainly due to the elastic inter- action in the yttrium-hydrogen system, since yttrium metal has a transition point at 1758 K and its corresponding effect on the phase transition in the system cannot be ruled out. A further discussion on the value of r has been given in the sites. Only a pair of nearest-neighbour T sites (T-T pair) and two of the.0 sites next to these T sites are shown. The thin dotted lines literature.6.28 There is, however, no evidence for r = 1.2 in the indicate reference of a tetrahedron and an octahedron site. The thick solid line is a T-0-T path and the thick dotted line is a T-T-0-T case of hcp cr-yttrium. Thus, it is difficult to conclude from path. only the solubility data that we can determine the particular J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 values of M' and r that reproduce the experimental result. These will be determined after the 8 dependence of the diffu- sion coefficient is discussed. Diffusivity Digusion Coeficients The values of diffusion coefficients have been measured under a hydrogen concentration gradient and the diffusion coeffi- cient values obtained are therefore chemical diffusion coeffi- cient~.~~~~*~~.~~These are related by 29-31 (5) r = rvf (6) where 2 is the jump length, r' is the jump rate, V is the site- availability factor, which is 1 -8, e.g.for r = 1 [eqn. (3)], and f is a mobility correlation factor3' or physical correlation factor,29 indicative of the presence of short-range order due to interactions between hydrogen atoms3' or can represent an additional distortion of the chemical potentialz9 other than that caused by the concentration gradient. The term d(p,/k, T)/aIn 0 in eqn. (5) is called the thermodynamic fa~tor~~-~land r in eqn. (6) represents the effective jump fre- quency. Since values of 0 mainly influence (i) the thermodynamic factor d(pH/k, T)/aIn 8, (ii) the site-availability factor V and (iii) the correlation factor f, we further consider these three factors.In regard to (i) we have from eqn. (2) (7) In the case of (ii), since we have used the mean-field approximation for the hydrogen--hydrogen interaction, we have V = 1 -0/r (8) The presence of a T-T pair (Fig. 1) requires a modification of eqn. (8). The result of quasielastic neutron scattering measurement16 has shown that the rate of hydrogen atom jump between the two T sites in the T-T pair is much larger than that between the 0 and T sites and between the 0 and 0 sites. This is consistent with the theoretical calculation of potential barriers between the various sites available to hydrogen atoms in or-yttrium: that is to say 0.16 eV between the T and T sites in the T-T pair, 0.33-0.46 eV between the 0 and T sites and 0.85 eV between the 0 and 0 sites.32 The large rate of the T-T jump makes it possible for hydrogen to jump through the T-T-O-T path (the thick dotted line in Fig. 1) with a considerable additional rate to jumps through the T-O-T path (the thick solid line in Fig.11, which mainly contribute to the long-range diffusion of hydrogen. We will now calculate for r = 1, i.e. when only one of the T sites in a T-T pair can be occupied by a hydrogen atom, and where the probability is that the hydrogen atom on the T site will find, through either of the two paths, an empty T site in other T-T pairs.For the T-O-T path this probability is 1 -8 and the T-T-O-T path it is, to a crude approximation, a8(1 -O), where O(1 -8) is the probability that the hydrogen atom on the T site finds no empty sites in other T-T pairs but finds an empty site through the other T site in the T-T pairs, and where a is a factor that takes into account the extra T-T jump necessary for the T-T-O-T path. The value of a may be near to but less than unity. We then have V = 1 -0 + a0(l -8) = (1 -0x1 + ae) (9) where the equation has an extra term 1 + a8 in addition to eqn. (8) with r = 1. (iii) The 8 dependence of f is rather complicated and numerical calculations are needed to estimate its precise value.z9-31 We will assume here that correlation is small and put f= 1 for the following reason.In the yttrium-hydrogen system the elastic interaction is one order of magnitude smaller than in other metal-hydrogen systems6 and the mag- nitude of the resulting short-range order, which is responsible for ~orrelation,~' should be small. In addition, the mobility correlation factor should deviate less from unity than the tracer correlation fa~tor.~ Thus, the diffusion coefficient can be written as with the modification of the site-availability factor eqn.(8)] and D = riZ(i + ae) (1 1) with the modification but without the interaction (W = 0). lnterpretation of the Measured Diflusivity Fig. 3 shows values of D measured at various temperatures and values of 8. In order precisely to see the values of D at different temperatures we have plotted D on a logarithmic scale.Measured values of D for hydrogen and deuterium increased with increasing 8. At high temperatures, e.g. at 1273 K, a rather large scatter in D could not be avoided owing to the difficulty in controlling the hydrogen pressure precisely for several seconds at the beginning of the mea~urement.~~ We can now compare measured values of D with eqn. (10) and (11).The solid lines in Fig. 3 show values of D computed from eqn. (ll),where a = 0.8 and rAzhas been adjusted so that D computed at 8 = 0.05 coincides with those reported previo~sly'~and the ratio of D for deuterium and hydrogen is 1/J2. The computed 0 dependence is consistent with the observed increase in D with increase of 8.The adopted value of a = 0.8 seems reasonable on the following considerations. The potential barrier between the T sites in the T-T pair has been calculated as 0.16 eV,32 which would be smaller if relax-ation of metal atoms around the hydrogen atom is con-~idered,~~and is small enough to allow almost free jumps between the T sites at high temperatures. Since the value of a is the factor that takes into account the effect of this T-T jump, and reduces to unity when this jump is completely free, the value of a may be taken as slightly less than unity. A A B 2.0c 0.3 I I I I I I I I I I I 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 0.5 0 0 Fig. 3 0 dependence of D measured at various temperatures for A, hydrogen and B, deuterium.The solid lines have been computed from eqn. (11) with a = 0.8.Symbols as Fig. 2. discussion of a possible dependence of a on temperature and 8 is, however, beyond the scope of this paper. In order to reproduce measured values of D by using eqn. (10) we need a value of I larger than unity and a value of w of the order k,T, which is too large as a magnitude of hydrogen-hydrogen interactions in metal-hydrogen systems. Moreover, values of r > 1 and w > 0 cannot reproduce the measured solubility: a value of w c0 is required to repro- duce the measured solubility if r > 1. It is thus impossible to give a reasonable explanation of the measured diffusivity and solubility by using eqn. (3), (4) and (10). A similar result can also be obtained by introducing improved approximations to the interaction such as with the quasi-chemical approx- imati~n.~~.~' A long-range hydrogen-hydrogen interaction factor seems to be less important to high-temperature solu- bility and diffusivity values in the case of the yttrium- hydrogen system, in contrast to the cases of the niobium- and tantalum-hydrogen systems, where 1on.g-range elastic interaction plays a key role in the 8dependence of the diffusi- vity and occurrence of the phase transition.20,21 An observed increase in D with 8 in fcc yttrium has been discussed and its cause ascribed to a partial hydrogen occupation of 0 sites.22 In the hcp yttrium, however, the jump rate is smaller for the 0-0jump than for the 0-T and an increased 0-site occupation is unlikely to make an appreciable contribution to measured values of D.In addition, the fraction of hydrogen atoms on the 0 sites in fcc yttrium has been shown to decrease with increasing tem- perat~re.~~We cannot, therefore, apply the model proposed to explain the increase in D with 8 in fcc yttrium directly to the experimental result obtained in the present study. In conclusion, a model is proposed in which a hydrogen atom occupies a pair of two nearest-neighbour T sites and the hydrogen atom makes jumps between these two T sites with a great frequency that can give an explanation of the 8 dependence of the measured solubility and an increase in measured values of D with 8. References C.E. Lundin and J. P. Blackledge, J. Electrochem. SOC., 1962, 109,838. L. N. Yannopoulos, R. K. Edwards and P. G. Wahlbeck, J. Phys. Chem., 1965,69,2510. G. M. Begun, J. F. Land and J. T. Bell, J. Chem. Phys., 1980,72, 2959. J. E. Bonnet, C. Juckum and A. Lucasson, J. Phys. F: Met. Phys., 1982, 12, 699. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 5 J. P. Blackledge, in Metal Hydrides, ed. J. P. Blackledge and G. G. Libowitz, Academic, New York, 1968. 6 Y. Fukai, The Metal-Hydrogen System, Springer, Berlin, 1993. 7 I. S. Anderson, J. J. Rush, T. Udovic and J. M. Rowe, Phys. Rev. Lett., 1986, 57, 2822. 8 M. W. McKergow, D. K. Ross, J. E. Bonnet, I. S. Anderson and 0.Schaerph, J. Phys. C, 1987,20, 1909. 9 I. S. Anderson, N. F.Berk, J. J. Rush and T. J. Udovic, Phys. Rev. B, 1988,37,5358. 10 F. Liu, M. Challas, S. N. Khanna and P. Jena, Phys. Rev. Lett., 1989,63,1396. 11 0.Blaschko, J. Less-Common Met., 1991, 172-174, 237. 12 G. W. West, E. F. W. Seymour, C. T. Chan, D. R. Torgeson and R. G. Barnes, Phys. Rev. B, 1991,44,9692. 13 P. G. Dantzer and 0.J. Kleppa, J. Chem. Phys., 1980, 73,5259. 14 0. N. Carlson, F. A. Schmidt and D. T. Peterson, J. Less-Common Met., 1966,10, 1. 15 F. Frisius, H. J. Lahann, H. Mertins, W. Spalthoff and P. Wille, Ber. Bunsenges. Phys. Chem., 1972,76,1216. 16 I. S. Anderson, A. Heidemann, J. E. Bonnet, D. K. Ross, S. K. P. Wilson and M. W. McKergow, J. Less-Common Met., 1084,101, 405. 17 P. W. Fisher and M. Tanase, J. Nucl. Muter., 1984, 122-123, 1536.18 L. Lichty, R. J. Schoenberger, D. R. Torgeson and R. G. Barnes, J. Less-Common Met., 1987, 129, 31. 19 T. Maeda, S. Naito, M. Yamamoto, M. Mabuchi and T. Hashino, J. Chem. SOC., Faraday Trans., 1993,89,4375. 20 J. Volkl and G. Alefeld, in Hydrogen in Metals I, ed. G. Alefeld and J. Volkl, Springer, Berlin, 1978. 21 H. Wagner, in Hydrogen in Metals I, ed. G. Alefeld and J. Volkl, Springer, Berlin, 1978. 22 U. Stuhr, H. Wiph, B. Frick and A. Magerl, 2. Phys. Chem. NF, 1989,164,929. 23 S. Naito, J. Chem. Phys., 1983,79, 3113. 24 R. H. Fowler and E. A. Guggenheim, Statistical Thermodyna- mics, Cambridge University Press, Cambridge, 1939. 25 P. Kofstad, W. E. Wallace and L. H. Hyvonen, J. Am. Chem. SOC.,1959,81, 5015. 26 J. A. Pryde and C. G. Titcomb, J. Phys. C, 1972,51293. 27 B. Siege1 and G. G. Libowitz, in Metal Hydrides, ed. J. P. Black- ledge and G. B. Libowitz, Academic, New York, 1968. 28 G. Boureau, J. Phys. Chem. Solids, 1981,42,743. 29 G. E. Murch, in Diflusion in Crystalline Solids, ed. G. E. Murch and A. S. Norwick, Academic, Orland, 1984. 30 D. A. Faux and D. K. Ross, J. Phys. C, 1987,20,1441. 31 D. A. Reed and G. Ehrlich, Surf. Sci., 1981,102,588. 32 B. J. Min and K. M. Ho, Phys. Rev. B, 1992,45,12806. 33 C. Elsasser, K. M. Ho, C. T. Chan and M. Fahnle, J. Phys.: Condens. Matter, 1992,4, 5207. 34 J. A. Goldstone and J. Eckert, Solid State Commun., 1984, 49, 475. Paper 41007625; Received 7th February, 1994

ISSN:0956-5000    

DOI:10.1039/FT9949001979

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1983-1986 Heterogeneous Catalysis in Solution Part 27.t-Reaction between Titanium(ll1) and Triiodide Ions Catalysed by Platinum Shaorong Xiaoz and Michael Spiro* Department of Chemistry, Imperial College of Science, Technology and Medicine, South Kensington, London, UK SW72AY The rate of the reaction between titaniumfiii) chloride and triiodide ions in an acid chloride medium has been studied in the absence and presence of a rotating platinum disk. At low concentrations of triiodide the catalytic rate at platinum was found to be first order in 13-, zero order with respect to Ti"' and H+, and proportional to the square root of the rotation speed of the disk. These results pointed to diffusion-controlled catalysis, as did the low activation energy of 19 kJ mol-' as compared with 40 kJ mol-' for the uncatalysed reaction.All these findings are consistent with an electrochemical interpretation of the catalytic mechanism, as was shown by the current-potential curves determined for the two reactants at the same reduced platinum surface. Provided that the voltammograms for Ti"' had been carried out in the presence of the same concentration of K! as in the reaction mixtures, the rates and mixture potentials determined electrochemically agreed well with the catalytic rates and potentials measured experimentally. The fact that quite different results were obtained when no KI was present in the TiCI, solution provides further confirmation for the modified form of the additivity principle.The redox reaction 2Ti"' + I, -+2Ti" + 31-(1) in aqueous hydrochloric acid is a slow process whose kinetics have been studied by several workers.'*2 An unusual feature of this reaction is that it can be homogeneously catalysed by certain quinones, phenazines and quin~xalines~,~ in concen- trations as low as lop7 to lop5 mol 1-'. The mechanism appears to depend on the catalyst4 and one case has been investigated in detail.5 Reaction (I) has also been found to be catalysed heterogeneously by metallic platinum.6 This was explained by an electrochemical mechanism whereby the elec- tron passed from Ti"' to the iodine via the noble metal. The present study aims to test this mechanism quantitatively. Theory As in the case of several other metal-catalysed redox reac- tion~,~,*the electrochemical mechanism can be tested by combining electrochemical and kinetic studies.The principle is illustrated in Fig. 1 where anodic currents are taken as positive and cathodic currents as negative. Curve (a) depicts the increase in current when a solution of Ti"' is oxidised electrochemically at a given platinum surface while curve (b) shows the variation of current with potential when a solution of iodine in KI solution is reduced electrochemically. When both Ti"' and iodine are present together in the solution, the two curves can be added algebraically provided they have been obtained in circumstances which correspond to those in the mixt~re.~,~ The platinum surface thus takes up a mixed or mixture potential Emixat which the anodic current Zmix on curve (a)exactly balances the cathodic current I Imixon curve I (b).By Faraday's law, the mixture current is directly pro- portional to the rate of the reaction between Ti"' and iodine on the platinum surface, as given by eqn. 1 umix = I,,JnFA (1) where n is the number of electrons cancelled out in the overall reaction equation [i.e. n = 2 for eqn. (I)], F is the t Part 26: Ref. 7. Department of Chemistry, Guangxi Teachers College, Nanning, Guangxi 530001,People's Republic of China. Faraday constant and A is the surface area of the platinum. If vmix, derived from purely electrochemical experiments with the separate reactants, agrees with the catalytic rate vCatfrom kinetic measurements of the reaction mixture, and if Emix obtained electrochemically also agrees with the potential E,,, taken up by the platinum catalyst during the reaction, then the catalysis has clearly proceeded by a purely electrochemi- cal mechanism.In order to control the hydrodynamic conditions, it is useful to present the platinum surface in the form of a large horizontal disk set in an inert trumpet-shaped former which rotates about a vertical axis." The thickness, 6, of the Nernst diffusion layer at the surface is then given by the Levich -2 -EjV vs. SCE -4 --8 t Fig. 1 Voltammograms at 10 mV s-' with the reduced platinum disk rotating at 9 Hz for the oxidation of (a') 23.7 mmol 1-' TiCl, and (a) 23.7 mmol I-' TiCI, in 0.1 mol 1-' KI, and (b) for the reduction of 0.630 mmol 1-' 1,-in 0.1 mol I-' KI. All solutions were at 25°C and also contained 0.1 mol 1-' HC1 and 0.8 mol I-' KCl.equation" 6 = 0.643D1/3v1/6f-1/2 (2) where D is the diffusion coeficient of the diffusing species, v is the kinematic viscosity of the solution and f is the rotation speed in Hz. Diffusion-controlled currents and diffusion- controlled catalytic rates vary inversely with S and are there- fore directly proportional to the square root of the rotation speed. Experimenta1 All solutions were made up with Milli-RO and Milli-Q de- ionised water (Millipore). The titanium(@ chloride was a BDH product, low in iron, which also contained ca. 0.049 g ZnC1, per ml.The Ti"' concentration was determined by standardizing with pure iron.', All other reagents were BDH AnalaR. The geometrical area of the platinum disk was 12.19 cm2. A saturated potassium chloride calomel electrode (SCE) was used as the reference electrode and a large platinum foil as the counter electrode. Before each experiment the platinum surface was polished with a suspension of 0.3 pm alumina in water, washed, and electrochemically cleaned by cycling it at 50 mV s-l between -0.2 and +1.7 V us. SCE in nitrogen- saturated 0.5 mol 1-' sulfuric acid while it was rotated at 9 Hz, until reproducible voltammograms were obtained. For the preparation of a reduced surface, the potential was dis- connected at 0.2 V and the electrode preconditioned at 0.2 V for 20 s, 1.7 V for 20 s and finally 0.2 V for 600 s.The disk was then thoroughly washed and stored in a desiccator. All the experiments were carried out in a thermostat bath, usually at 25.0 & 0.1 "C. Electrochemical experiments were carried out in a three-compartment cell' and the catalysed runs in a similar two-compartment cell.' The background electrolyte was normally a mixture of 0.1 mol 1-' HCl (to reduce the extent of Ti"' hydrolysis), 0.1 mol 1-' KI (to keep the iodine complexed as I,-) and 0.8 mol 1-' KCl (to main- tain a high and constant ionic strength). In the kinetic runs the background electrolyte and reactant solutions were ther- mally equilibrated before being mixed. In the catalysed runs the disk was allowed to attain the bath temperature by being spun for 15 min in the thermostatted background solution before the reactants were added.Nitrogen was passed through the solutions beforehand and the experiments were carried out under a nitrogen atmo-sphere. The reaction was followed by removing samples (0.5 or 1 ml) at regular intervals and diluting them with 10 ml of 0.1 mol 1-' KI solution. The absorbance A of the triiodide ions was then measured at the band maximum wavelength of 352 nm on a Perkin-Elmer Lambda 2 spectrophotometer. The applicability of Beer's law was confirmed. In the catalysed runs the potential adopted by the platinum disk was recorded each time us. the SCE reference. Results and Discussion Homogeneous Kinetics For both the homogeneous and the catalysed reactions, plots of In A us.time were normally linear for 30-60 min. The slopes, obtained by least-squares fitting, gave the first-order (with respect to 13-) rate constants, k. At a constant initial I,-concentration of 0.202 mmol 1-', k was found to be pro- portional to the initial concentration of TiCl, over the range 8 to 47 mmol 1-'. However, when the initial TiCl, concentra- tion was fixed at 23.7 mmol 1-', k declined gently as the initial concentration of triiodide increased from 0.1 to 0.6 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 mmol 1-'. All these results could be fitted, with an average deviation of less than 5%, by the equation -d[I,-]/dt = (9.6 x 10-3)[13-][TiC13] + (7.1 x lop7) x [TiCl,] (3) where the square brackets refer to concentrations in mol 1-' and the time t is in s.The first term on the right-hand side was always the larger one under our conditions. The rate of reaction fell almost inversely on raising the HCl concentra- tion, which suggests that TiOH2+ is the main reactant even though only ca. 5% of the Ti"' is present in this form in the medium empl~yed.'~ There was a lesser fall on increasing the concentration of KI. The activation energy between 9.8 and 25.0"C for the reaction between 0.202 mmol 1-' I,-and 23.7 mmol 1-' Ti"' was found to be 40 kJ mol-'. Johnson and Winstein2 obtained a similar rate law which they interpreted as indicating rate-determining reactions between TiOH2+ and both I,-and I,.For the same back- ground conditions of 0.1 moll-' HC1,O.l moll- ' KI and 0.8 mol 1-KCl and also at 25 "C, their kinetic equation was of the same form as eqn. 3 but with different rate constants, namely -d[I,-]/dt = 0.103[13-][Ti"'] + (1.92 x 10-5)[Ti"'] (4) This difference may be attributed to the presence of ZnC1, in the BDH TiCl, solution employed. Experiments with concen- trations of I,-and Ti"' similar to those used in ref. 2, but to which additional amounts of zinc chloride had been added, led to lower rates, as Fig. 2 shows. As the curve rises steeply at low ZnCl, concentrations, a much higher rate of reaction would be expected for the zinc chloride-free solutions employed by Johnson and Winstein. Catalysed Kinetics Reaction (I) was always faster in the presence of the spinning platinum disk, consistent with heterogeneous catalysis by platinum.In order to evaluate the catalytic component in these 'heterogeneous' experiments, their rates and those of the corresponding homogeneous runs were expressed in terms of the number of moles of triiodide reacting per second, (u'), by the equation 0' = kV[13-] (5) where V is the volume of the solution (normally 354 ml) and [I3-] is the initial concentration. The areal catalytic rate at 31 I 0 1 2 3 [Zr1Cl,]/l0-~ rnol dm-3 Fig. 2 Homogeneous first-order rate constant khom us. concentra-tion of zinc chloride, for a reaction mixture containing 8.3 mmol 1-' TiCl,, 2.52 mmol 1-' 13-, 0.11 moll-' KI, 0.1 moll-' HC1 and 0.82 moll-' KCl at 25 "C J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 the surface of the platinum [in (mol I,-) m-2 s-'1 was then given by ucat = -Yhom)/A (6) Expressing the catalytic rate in this way involves no precon- ceptions about the kinetic form of the catalytic reaction. It should be borne in mind, however, that ucat depends on the difference between two rates of comparable magnitude and is therefore uncertain by ca. & 10%. When heterogeneous runs were carried out with the same initial concentrations of reactants as for the homogeneous runs, the catalytic kinetics were quite different. Thus, with [I3-] = 0.202 mmol 1-', u,,, was found to be completely independent of the Ti"' concentration over the range 8-47 mmol 1-'.However, when the initial concentration of TiC1, was kept constant at 23.7 mmol 1-', u,,, increased linearly with [I3-] according to the equation u,,Jmol m-2 s-' = (2.92 x lop6)+ (3.17 x 10-2)[13-] (7) The catalysed reaction was therefore first order in I,- and zero order in Ti"'. Unlike the homogeneous reaction rate, ucat was independent of the hydrogen ion concentration when it was varied from 0.05 to 0.2 mol 1-'. However, it decreased from 1.83 x lo-' to 1.02 x mol m-2 s-' when the KI concentration was raised from 0.1 to 0.2 mol 1-' and stayed at the lower value for KI concentrations of 0.3 and 0.5 mol 1-' (the ionic strength being kept constant by appropriately lowering the amount of KCl). As shown in Fig. 3, ucat increased proportionately with the square root of the rotation speed.This is a clear indication of diffusion control, a conclusion supported by the low activa- tion energy of 19., kJ mol-' obtained between 0.202 mmol 1-' I,-and 23.7 mmol dm-, Ti"' over the range 9.8-25 "C.It follows that the first-order (with respect to I,-) catalytic rate constant is given by the equation', where D is the tracer diffusion coefficient of I,-in the medium employed. Combination with eqn. 2 leads to u,,, = 1.555D213v-"6f'I2[I3 -3 (9) Taking the viscosity of the supporting electrolyte medium at 25°C as 0.8888 x lop3 kg m-l s-' '' and its density as 1.0493 g ml-' l6 gives v = 0.8470 x lop6 m2 s-'. The resulting value of D from the lower plot of Fig. 3 is 7 N €5-E4 u) 03 1 0 0 1 2 3 4 5 f 1 /2/H~1/2 Fig.3 Catalytic rate at 25 "C us. the square root of the disk rotation speed, for solutions containing 23.7 mmoll-' TiCI, ,0.1 mol 1-1 KI, 0.1 mol I-' HC1, 0.8 KC1 mol 1-' and (0)0.202 mmol 1-' triiodide or (m) 4.04 mmol 1-triiodide 1985 1.02 x m2 s-'. Allowance for the correction + 0.145(0/~)~/~][l + 0.298(D/~)'/~ gives D = 1.07 x lo-' m2 s-'. This is in reasonable agreement with the value of 1.13 x m2 s-l obtained by Newson and Riddiford," also in the presence of 0.1 mol 1-' KI. In most heterogeneous runs the catalyst potential E,,, rose in the early stages and then declined. In other cases, E,,, ini-tially stayed constant before decreasing while, with higher I, -concentrations, E,,, decreased throughout the experi- ments.The initial values of E,,, fell as the TiC1, concentra- tion increased and rose as the I,- concentration increased. These findings are explained in the next section. Electrochemical Experiments If the catalytic mechanism is an electrochemical one, the cata- lytic rates and potentials should be predictable from electro- chemical experiments with the two reactants. Voltammograms were therefore determined for appropriate solutions of TiCl, and I,-in the normal supporting electro- lyte medium. Two examples are depicted in Fig. 1. Here the mixture potential, Emj,obtained from curve (a) for 23.7 mmol 1-1 Ti111 and curve (b)for 0.630 mmol 1-' I,-was 274 mV us. SCE while the initial potential E,,, measured in the catalysed reaction mixture was 280 mV.Furthermore, the rate umix cal-culated from the mixture current of 4.26 mA in Fig. l by means of eqn. 1 was 1.81 x mol m-2 s-l while the mea- sured catalytic rate u,,, evaluated from eqn. 6 was 1.83 x mol m-2 s-'. This good agreement for both the potential and the rate would be diflicult to explain by any catalytic mechanism other than an electrochemical one in which the electrons are transferred from the Ti"' reductant to the I, -oxidant through the platinum catalyst. Fig. 4 shows that similar goad agreement between umix and u,,, was obtained in many other sets of experiments. The con- cordance found between Emix obtained from the voltam- mograms and E,,, measured in the reaction mixtures is demonstrated in Fig.5. It must be emphasized that all the above electrochemical data were based on voltammograms for TiC1, solutions con- taining 0.1 mol 1-' KI, the same KI concentration as in the reaction mixtures. Quite different voltammetric curves were obtained for solutions of TiC1, without KI, as curve (a') in Fig. 1 illustrates. This difference arose from the strong adsorption of iodide ions on the reduced platinum surface, a wcat/l 0-5 mol rn-2 s-I Fig. 4 uCaJvmix vs. uCat for experiments in which the following parameters were varied: 0,TiCl, concentration; 0,I,-concentra-tion; 0,KI concentration; .,HC1 concentration and A, tem-perature. The symbols, x, refer to values of umix obtained from voltammograms for TiCI, solutions containing no KI.The dashed lines represent the 10% uncertainty limits. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Xi IX -200 --300 0 ' 100 0 200 °300 140C E,,JrnV vs. SCE Fig. 5 Emixus. E,,, for experiments in which the following param- eters were varied: 0,TiCl, concentration; e,I,-concentration; 0, KI concentration. The symbols x refer to values of Emixobtained from voltammograms for TiCl, solutions containing no KI. The straight line has a slope of unity. well attested phenomenon.20*21 It was confirmed in the present work by a cyclic voltammogram taken after immers- ing the platinum disk in a typical reaction mixture, which showed a large anodic peak at ca. 1.3 V which disappeared in the second sweep.If curve (a') rather than curve (a) in Fig. 1 is combined with the I,-curve (b), Emixbecomes 152 mV, completely different from the E,,, value of 280 mV. More- over, the larger Imixvalue of 7.72 mA leads to a correspond- ingly larger umix of 3.28 x lo-' mol mM2 s-', some 79% greater than the experimental value of ucat.Similar disagree- ment in other cases is clearly indicated by the data points marked with crosses in Fig. 4 and Fig. 5. This is further con- firmation that the original principle of the additivity of current-potential curves22 should only be applied in the modified form given by Creeth and Spi1-0.~ This states that current-potential curves can be added only if they have been obtained in circumstances which correspond to those of the mixture.It remains to show how the observed catalytic kinetics follow directly from the electrochemical curves. This is demonstrated in Fig. 6 where all currents have been plotted as positive. The intersections of the I,- reduction curves (bl)-(b3) with the Ti"' oxidation curves (al) or (a2)therefore mark the respective mixture potentials and mixture currents. Inspection of the diagram makes it clear that, for the low I,- concentration curves (b,) and (b2),the intersections with both (al) and (a2)lie in the limiting-current plateau regions of the I,-curves. Thus Imixand umix, and hence ucat,are indepen- dent of the concentration of TiCl, . Since the limiting currents are proportional to [I3-], umix and hence uCatare first order in I,-.Moreover, limiting currents vary inversely with the thickness, 6, of the diffusion layer and therefore umix and ucat are proportional to the square root of the disk rotation speed. On the other hand, when [I3-] becomes sufficiently large [curve &)I, the intersection mixture point with curve (al)in Fig. 6 lies below the limiting-current plateau. It follows that umix and thus uCatwill rise less than proportionately with [I3-] at high concentration as can be seen, for example, by comparing the slopes of the two lines in Fig. 3. Inspection of Fig. 6 also makes it easy to understand why Emix,and hence E,,, , were found to rise with increasing I, -concentration and fall with increasing concentration of Ti"'. The electro- chemical interpretation of the catalytic mechanism therefore allows us to explain satisfactorily the various aspects of the catalysis by platinum of the reaction between Ti"' and I,-.-0.4 -0.2 0 0.2 0.4 E/V vs.SCE Fig. 6 Voltammograms at 10 mV s-' with the platinum disk rotat- ing at 9 Hz for the oxidation of TiCl, [(al)23.7 and (a2)47.3 mmol 1-'1 and the reduction of I,-[(b,) 0.135; (b2)0.202 and (b,) 0.630 mmol l-']. All solutions were at 25°C and also contained 0.1 mol I-' KI, 0.1 moll-' HC1 and 0.8 mol I-' KCI. We thank Guangxi Teachers College, Nanning, P. R. China for granting leave of absence to S.X. and the Chinese Govern- ment for an overseas scholarship. References 1 D. M. Yost and S. Zabaro, J. Am. Chem. SOC., 1926,48,1181.2 C. E. Johnson Jr. and S. Winstein, J. Am. Chem. SOC., 1951, 73, 2601. 3 P. A. Shaffer, J. Phys. Chem., 1936,40, 1021; Cold Spring Harbor Symposium on Quantitative Biology, Cold Spring Harbor Labor- atory, New York, 1939, vol. VII, p. 50. 4 C. E. Johnson Jr. and S. Winstein, J. Am. Chem. SOC., 1952, 74, 755. 5 C. E. Johnson Jr. and S. Winstein, J. Am. Chem. SOC., 1952, 74, 3 105. 6 M. Spiro and A. B. Ravno, J. Chem. SOC., 1965,78. 7 R. 0.Farchmin, U. Nickel and M. Spiro, J. Chem. SOC., Faraday Trans., 1993,89, 229, and references therein. 8 M. Spiro, Catal. Today, 1993, 17,517. 9 A. M. Creeth and M. Spiro, J. Electroanal. Chem., 1991, 312, 165. 10 M. Spiro, in Comprehensive Chemical Kinetics, Vol. 28: Reac-tions at the Liquid-Solid Interface, ed. R. G. Compton, Elsevier, Amsterdam, 1989, ch. 2. 11 V. G. Levich, Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, NJ, 1962, p. 69. 12 A. I. Vogel, A Textbook of Quantitative Inorganic Analysis, Longmans, London, 1943, p. 391. 13 R.L. Pecsok and A. N. Fletcher, Inorg. Chem., 1962, 1, 155; Ya. I. Turyan and L. M. Maluka, J. Gen. Chem. USSR, 1983,53,222 (260).14 L. L. Bircumshaw and A. C. Riddiford, Quart. Rev. Chem. SOC., 1952, 6, 157. 15 R. H. Stokes and R. Mills, Viscosity of Electrolytes and Related Properties, Pergamon, Oxford, 1965, pp. 91, 105, 110. 16 International Critical Tables, ed. E. W. Washburn, McGraw- Hill, New York, vol. 111, 1928, pp. 54, 88, 89. 17 J. Newman, J. Phys. Chem., 1966,70,1327. 18 M. Spiro and A. M. Creeth, J. Chem. SOC., Faraday Trans., 1990, 86,3573. 19 J. D. Newson and A. C. Riddiford, J. Electrochem. SOC., 1961, 108, 695. 20 A. T. Hubbard, R. A. Osteryoung and F. C. Anson, Anal. Chem., 1966,38,692. 21 M. Spiro and P. L. Freund, J. Electroanal. Chem., 1983,144,293. 22 C. Wagner and W. Traud, 2.Elektrochem., 1938,44,391. Paper 4/00653D; Received 2nd February, 1994

ISSN:0956-5000    

DOI:10.1039/FT9949001983

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1987-1991 X-Ray Photoelectron Spectroscopy, Temperature-programmed Desorption and Temperature-programmed Reduction Study of LaNiO, and La,NiO, +6 Catalysts for Methanol Oxidation Jacques Choisnet Centre de Recherche sur la Metiere Divisee, Unite Mixte CNRS, Universite d 'Orleans-Crystallochimie,Faculte des Sciences , Universite d 'Orleans, F-45067 Orleans Cedex 2, France Nevena Abadzhieva, Plamen Stefanov and Dimitar Klissurskif Institute of General and Inorganic Chemistry, Bulgarian Academy of Sciences, Sofia 1040,Bulgaria Jean Marc Bassat Centre de Recherche sur la Physique des Hautes Temperatures, CNRS, ID Avenue de la Recherche Scientific, F-45071 Orleans Cedex 2,France Vicente Rives* Departamento de Qulinica lnorganica, Universidad de Salamanca , Facultad de Farmacia, 37007Salamanca, Spain Lev Minchev Institute of Kinetics and Catalysis , Bulgarian Academy of Sciences, Sofia 1040,Bulgaria An X-ray photoelectron spectroscopy (XPS), temperature-programmed desorption (TPD) and reduction (TPR) study of LaNiO, and La,Ni04+d perovskites has been carried out.The existence of at least two different forms of oxygen in these compounds is shown by both oxygen reactivity (TPD and TPR) and XPS characterisation. XP spectra have also revealed a surface enrichment in lanthanum and oxygen. TPR profiles have shown a reduction of LaNiO, through the formation of La,Ni,O, as an intermediate compound. Above 450 "C,LaNiO, and intergrowth nickelates (La,NiO, and La2Ni04+&) undergo a final reduction to metallic Ni and La,O,.Between 200 and 400°C all three compounds exhibit a high catalytic activity in the total catalytic oxidation of methanol. ABO erovskite mixed oxides are a subject of intensive stud;'! Their most outstanding feature is their capacity for partial substitution of A and B sites, which results in many structurally similar compounds. Moreover, the trend towards producing an intergrowth of ABO, perovskite layers with A0 rock-salt layers has resulted in new mixed oxides, such as (ABO,),AO (p = 1-3) phases,, which show a lower dimen- sionality of structure compared with the '3D' character of the so-called 'ReO,' octahedral network. This is another reason for studying their different physico-chemical properties.In addition, the discovery of high-temperature superconduc- tivity in La,CuO, +d phases has stimulated intensive studies of the structure and physical properties of oxides with K,NiF,-type structure. It is now well known that La,NiO,+, exists over a broad range of oxygen its structural, electric and mag- netic properties are very sensitive to the amount of non-st oichiome tric oxygen present .6-9 Perovskite-type oxides are known to be efficient catalysts for a large number of chemical reactions.'*-'' Most of them are excellent catalysts for complete oxidation.2~'0~"~'7 Their behaviour in catalytic partial oxidation reactions has also been investigated.', Oxidation of methanol is a very conve- nient test reaction for characterisation of the redox, as well as the acid-base, properties of oxide-type catalyst^.'^.'^ In view of this, an XPS, TPD and TPR study of LaNiO, and La,NiO,+, (6 < 0.16) has been performed in parallel with a study of their behaviour towards methanol oxidation.Mixed nickelates are of particular interest, as the presence of Ni3+ f Also at: Departamento de Quimica Inorganica, Universidad de Salamanca, Facultad de Farmacia, 37007-Salamanca, Spain. and their oxygen non-stoichiometry could be related to their catalytic properties and oxygen reactivity. Experimental La,NiO, was obtained from a 1 :1 stoichiometric mixture of La,O, and NiO, heated in air in the temperature range 930-1130°C. Two successive annealings at 1130°C for 15 h, with intermediate re-grinding, were necessary to complete the solid-state reaction. In order to achieve a maximum value for 6 in La,NiO,+&, a modified sol-gel method,,' using lanthanum and nickel nitrates as precursors, was followed. The gel was steadily heated in air up to 900°C.The resulting powder was further annealed in an oxygen flow at 1150 "C for 10 h. LaNiO, was synthesized by coprecipitation of lanthanum and nickel hydroxides.21 The precipitate was steadily cal- cined in oxygen up to 950"C, with a final annealing at this temperature for 15 h. The phase purity of the specimens was monitored by X-ray diffraction in a Siemens D500 instrument, using Cu-Ka radi-ation. Specific surface areas, as determined by the BET method, were in the range 1-2.5 mz g-'.TPD of oxygen was carried out in the temperature range 25-80O0C, at a heating rate of 25 "C min- in an He flow (60 ml min- I). TPR experiments were performed using a Micromeritics TPR/TPD 2900 apparatus, at a heating rate of 10°C min-', using a 5 vol.% H,-Ar mixture and calibrating the instru- ment by checking hydrogen consumption during CuO reduction. The amount of sample, heating rate and gas flow were chosen to ensure a good resolution of component peaks. XP spectra of fresh and tested samples were recorded with a VG Escalab I1 instrument, using Mg-Ko! radiation (1253.67 eV). Finally, the heterogeneous catalytic oxidation of meth- anol was performed by a flow method with a 4 ml min-' flow rate of the reaction mixture, 4 vol.% methanol in air.Analysis of the reaction products was performed using the hydrogensulfite (for formaldehyde) and chromatographic methods.22 Results and Discussion Structural Peculiarities The fully oxidized, Ni3 +-containing LaNiO, sample, exhibits, as previously ~hown,~',~~ a slightly distorted perovskite-like rhombohedra1 cell, i.e. a = ap,/2 = 5.395 8, and a = 60" (a, is the parameter of the simple cubic perovskite-type unit cell). The thermal stability of this perovskite depends on the tem- perature and surrounding atmosphere during calcination. The stability is high in air, as LaNiO, undergoes decomposi- tion only above 1130 "C, according to the following irrevers- ible reaction: 2LaNi0, + La,NiO, + NiO + 30, At moderate temperatures (200-430 "C) in a hydrogen flow, a progressive elimination of oxygen takes place, leading to the oxygen-deficient LaNiO, -phases, and further to the strongly reduced defect perovskite, LaNiO, .24 Consequently, catalytic tests on LaNiO, have been performed at tem-peratures below 450 "C in an oxidizing atmosphere.La,NiO, is another example of the 1 : 1 intergrowth of ABO, perovskite and A0 rock-salt-type layers, Fig. 1. The La,NiO, +, structure consists of p-type-doped NiO, layers alternating with rock-salt-type La,O, +,layers of variable oxygen content, the sequence along the c axis being Ni0,-La,O, +, . When prepared in air or in an oxygen flow, La,NiO,+, shows the K,NiF,-type tetragonal unit cell.Only slight variations of the cell parameters are observed, depend- ing on the preparation conditions: the value of c is somewhat larger when the oxygen in excess reaches a value close to 0.18 (cmaX= 12.71 A, vs. 12.67 8, for air-prepared La,NiO, 25,26). Several structural studies have elucidated the role of the oxygen con tent. 7-29 It has been demonstrated that the a ~a 0 Ni 00 o exc. 0 ""b p 4 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 occurrence of a tetragonal unit cell depends to some extent on Ni2++Ni3+ ~xidation.~' The air-prepared La,NiO, usually contains some non-stoichiometric oxygen. The nature and exact location of the extra oxygen atoms have produced some controversies. The existence of superoxide (02-)or per- oxide (0,2-)anions has been proposed. Stoichiometric La,NiO, (6 = 0) can be obtained only after annealing in an argon or nitrogen flow, i.e.in an inert atmo- sphere. Its crystal lattice is orthorhombic, a x b w upJ2, c = 12.547 A. Moreover, the La : Ni ratio can tolerate some variation (La3 vacancies in the La0 layers).26 Finally, the + actual oxygen content is controlled not only by the prep- aration conditions (oxygen, air or inert atmosphere), but also by the La : Ni stoichiometry. XPS Characterisation A study of the photoelectron spectra of 'fresh' samples and those used in methanol oxidation was carried out, in order to obtain information on their surface composition. The La 3d core-level spectra show split lines with maxima at 835.3 f0.2 and 838.1 f0.3 eV for fresh LaNiO,, air-prepared La,NiO, and La,NiO,+, .This agrees with values reported previ~usly.~' The position and shape of the peak remain unchanged after the catalytic experiments. The 0 1s peaks are broad and asymmetric for the three samples. This result is consistent with the presence of more than one type of oxygen species in the surface layer. This is clearly concluded from the peak deconvolution of the 0 1s spectra of samples LaNiO, and La,NiO,+, (Fig. 2 and 3, respectively), which points to the existence of three peaks. In view of the possible presence of surface impurities, the attribution of the high- energy (532 eV) peak to oxygen in the sample is not definite. On the basis of previous the low-energy peak can be ascribed to a lattice 0,-anion, whereas the other two peaks probably originate from chemisorbed 0-and adsorbed OH groups.There is a slight, but significant differ- ence between the binding energies (Ebs) of lattice oxygen in LaNiO, and La,NiO,.,, (528.1 and 529.1 eV, respectively); this can be related, at least in a qualitative way, to the non- equivalence of the lattice oxygens in the perovskite and inter- growth structures. 526 528 530 532 534 E,IeV Fig. 1 1 : 1 intergrowth of ABO, perovskite (P) and A0 rock salt Fig. 2 Deconvolution analysis (. ...) of the 0 Is signal of sample (RS) type layers in La,NiO, LaNiO, ('used' sample) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 I L I 526 528 530 532 534 E,IeV Fig.3 Deconvolution analysis of the 0 1s signal of sample La,Ni04+d (‘used’ sample) The atomic surface concentration was determined in terms of the La :(La + Ni) and 0 : (La + Ni) ratios, Table 1. As a typical result, a systematic enrichment in La and 0 surface concentrations with respect to the bulk values is observed whichever oxide (perovskite or intergrowth) is considered. The La enrichment is not influenced by the catalytic process, whereas the 0 enrichment (in the intergrowth-type oxides only) varies slightly and reaches approximately the same value, 2.24, for air-prepared La,NiO, and La,NiO,+ 6. Such an observation is in agreement with previous results obtained for similar compound^,^ where significant differences between the bulk and surface concentration have been reported.A tentative hypothesis based on the structural pecu- liarities of the perovskite family can be proposed. The overall structure of any perovskite-like phase is a combination of ‘BO,’ and ‘AO’ atomic planes, i.e. ‘NiO,’ and ‘Lao’ in the nickelates studied here. Consequently, a modification in La and 0 concentrations can be related to some changes in the distribution of the ‘NiO,’ and ‘Lao’ planes. In this way, the La and 0 enrichment of the surface observed here is likely to be due to a preferential distribution of ‘Lao’ planes in the layers close to the surface. Obviously, this is a qualitative assumption, but it is consistent with the available crys- tallochemical data for perovskite-like phases.Finally, it can be assumed that surface oxygen in these compounds is bonded in at least two different ways, which probably correspond to two different forms of adsorbed oxygen. Generally speaking, the existence of more than one form of oxygen is characteristic also for some oxides which exhibit catalytic activity for complete oxidation of organic compounds, namely c0304, NiO and Cr,O, .36 Moreover, it is well known that the low-temperature adsorption of oxygen Table 1 Surface atomic concentrations in LaNiO,, La,NiO, and La,NiO,+, samples, as determined by XPS LaNiO La,Ni04 La,NiO, + ratio fresh used fresh used fresh used La :(La + Ni) 0 : (La + Ni) 0.71 1.82 0.71 1.80 0.81 2.24 0.81 2.40 0.81 2.22 0.80 2.31 results in ‘weakly bound’ forms, for which the bonding energy value is characteristic of chemisorbed oxygen and consequently shows a fairly high reactivity. Reactivity of Oxygen (TPD and TPR) The TPD curves of oxygen from fresh LaNiO,, La,NiO, and La,NiO,+, are shown in Fig.4. The desorption peaks are rather broad, especially for LaNiO, . Desorption maxima are recorded at 280-320 “C and 450 “C for air-prepared ‘La,NiO,’, and at 400°C (this peak being well defined) and 480°C for La,NiO,+,. LaNiO, shows a desorption maximum at 320-380°C. From these results, it can be assumed that two different forms of oxygen (at least) exist on the catalyst surface, in agreement with the XPS results men- tioned above. Fig. 5 illustrates the oxygen desorption from the same cata- lysts after use in the catalytic tests, i.e.in methanol oxidation. It clearly shows a lower amount of evolved oxygen. More- over, the TPD traces for the intergrowth samples are very similar. There is a desorption maximum at ca. 450°C. A well defined desorption maximum has not been observed, however, for LaNiO, . Note that after the catalytic tests, the desorption maxima at lower temperatures, which are ascribed to the most weakly bound oxygen, practically disappear. This is indicative of a strong modification of the catalysts during the catalytic reac- tion. Evidently, the stationary state of all catalysts studied is noticeably different from the initial one. Undoubtedly, part of 100 300 500 700 T/“C Fig.4 TPD profiles of ‘fresh’ (a) La,NiO,, (b) LaNiO,,, and (c) LaNiO, samples 100 300 500 700 TIcC Fig. 5 TPD profiles of ‘used’ (a) La,NiO,, (b) LaNiO,,, and (c) LaNiO, samples /-\ .........-............. ... -_.i-.'' ..-.............. I801 I I I a I I I I I I 100 200 300 400 500 600 700 TI"C Fig. 6 TPR profiles of 'fresh' (a) LaNiO,, (b) La,NiO, and (c) La,NiO, +d samples the most reactive oxygen is lost during the catalytic oxidation of methanol. A similar effect has been observed in our pre- vious studies on the catalytic oxidation of methanol on superconducting YBa,Cu,O, -x (orthorhombic phase), which can also be considered to be a defective perovskite-type com- pound.,, LaNiO, and intergrowth nickelates have shown noticeably different behaviours during the TPR experiments.~~Studies carried out by Wachowski et ~1 on. reduced LaMeO, (Me = Fe, Co, Ni) showed that all three perovskite- like oxides do not reduce directly to Me and La,O,, but form intermediate oxygen-deficient structures. According to Crespin et ~l.,~'reduction of LaNiO, occurs at low tem- perature (300 "C) according to the reaction: 2LaNi0, + H, -+La,Ni,O, + H,O Our TPR results (Fig. 6) are in full agreement with this state- ment. To make the comparison easier, the TPR traces have been referred to one unit of the reducible metal, i.e. nickel. For LaNiO, two different peaks are clearly detected, with maxima at 385 and 511 "C. Hydrogen consumption for the first peak corresponds to 0.50 mol H, (mol catalyst)-', i.e.one electron (mol catalyst)-'. For the second peak, the ratio is 0.99 mol H, (mol catalyst)-', corresponding to two elec- trons (mol catalyst)-'. So, reduction yields La,O, and metal- lic Ni. The first peak, corresponding to the one-electron reduction process, would then correspond to the formation of La,Ni,O,. The TPR curves of both La,Ni04+d and air-prepared La,Ni04 show weak maxima at ca. 380"C, which can be ascribed to removal of non-stoichiometric oxygen, and corre- spond to 0.085 and 0.105 mol H, (mol catalyst)-', respec-tively. Reduction at higher temperatures is practically identical in both cases, with broad maxima at 610-660°C (undoubtedly formed by several overlapping peaks in the case of sample La,NiO,), with areas corresponding to consump- tion of 1.043 and 0.933 rnol H, per mol of the corresponding nickelate.These values indicate a practically complete trans- formation of both samples to La,O, and metallic Ni. Catalysis of Methanol Oxidation The conversion degrees of CH,OH to CO, CO,, HCHO or other by-products were determined after attaining a regime corresponding to a steady state of the catalyst. CO and H, were not found in the reaction products. As can be seen from the data summarized in Table 2, the main reaction product for all of the catalysts tested here was CO,. Over the whole temperature range studied, LaNiO, , La,NiO, and J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 2 Oxidation of methanol on LaNiO,, La,NiO, and La,NiO, ox ygen-containing products catalyst temperature/"c methanol conversion (Yo) HCHO CO, LaNiO, 200 40.3 0.5 39.8 300 51.4 1.6 49.8 370 85.9 2.5 83.4 400 89.0 4.5 84.5 450 90.0 5.0 85.0 La,NiO, 200 33.8 1.5 32.3 300 64.6 2.0 62.6 400 72.0 2.0 70.0 450 75.3 2.0 73.3 La2Ni0,+d 200 70.1 0.0 70.1 300 80.4 0.3 80.1 350 90.8 0.5 90.3 370 97.0 0.6 96.4 400 99.8 0.7 99.1 La2Ni0,+d behave as highly efficient catalysts for the com- plete oxidation of methanol.During our previous studies on the mechanism of ammonia oxidation over oxide-type catalyst^,^' we have found a distinct correlation between the binding energy of oxygen in oxide-type catalysts and their activity in complete oxidation. Boreskov et have shown that for a large series of complete oxidation reactions a simple relationship holds between the activation energy for the reaction (E,) and the binding energy of oxygen (Eb) in the surface layer of the cata- lyst : E, = I?,fbEb where b is a constant.The TPD curves for oxygen desorption from LaNiO,, La,NiO, and La,NiO,+, clearly show the existence of easily desorbable (i.e.weakly bound), highly reactive oxygen. Our further studies on methanol heterogeneous catalytic oxidation have shownI8 that selectivity to formaldehyde or CO, formation, i.e. to partial or complete oxidation, largely depends on the binding energy of oxygen in the surface layer of the catalysts and on the surface acid-base properties.The TPD and TPR studies of LaNiO,, La,NiO, and La2Ni04+6 are indicative, as already mentioned, of the exis- tence of weakly bound (and therefore highly reactive) oxygen in all three compounds. This is essential for catalytic activity during complete oxidation reactions, and is fully consistent with the results reported in the present study. Note that the catalysts studied show a high activity with respect to total oxidation, even at temperatures as low as 200 "C. Under the reaction conditions chosen, a similarity in the catalytic behaviour of all three nickelates has been observed, despite the structural peculiarities and different oxygen stoichiometries of the initial 'fresh' compounds. On the basis of the TPD and TPR data for the fresh and tested catalysts, it can be tentatively assumed that surface alterations seem likely to happen during the catalytic reac- tion, resulting not only in surface reconstruction, but also in changes in the surface stoichiometry.This could be the reason for a similarity in the catalytic behaviour of LaNiO, , La,NiO, and La,NiO, + The methanol oxidation reaction is very sensitive to the nature of the surface sites present in oxide-type catalysts. According to Wachs et al. surface redox sites (capable of being reduced and oxidized) primarily form formaldehyde, as J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 1991 well as methyl formate and dimethyl ether; surface acid sites, Lewis as well as Brsnsted, facilitate the formation of dimethyl ether, and surface basic sites yield CO and CO, as the reac- tion products.” The compounds studied exhibit a high activ- ity with respect to methanol oxidation to carbon dioxide.This pathway of methanol oxidation could be related to the 6 7 8 9 C. N. R. Rao, P. Ganguly, K. K. Sin& and R. A. Mohan Rao, J. Solid State Chem., 1988, 72, 14. R. R. Shartman and J. M. Honig, Muter. Res. Bull., 1989, 24, 1375. T. Freltoft, D. J. Buttrey, G. Aeppli, D. Vakmin and G. Shirane, Phys. Rev. B, 1991,44, 5046. J. D. Jorgensen, B. Dabrowski, S. Pei, D. R. Richards and D. G. predominantly basic character of the catalysts. In this context, the results of Ai and Suzuki should also be noted.40 These authors have found an acceleration in the total oxida- tion of phenol with increasing surface basicity for a large series of complex oxide catalysts.According to Sei~ama,~’the catalytic activity of per- 10 11 12 13 14 15 Hinks, Phys. Rev. B, 1989,49,2187. T. Seiyama, Catal. Rev.-Sci. Eng., 1992, 34, 281. B. Viswanathan, in ref. 1, p. 271. K. Ichimura, Y. Inoue and I. Yasumori, in ref. 1, p. 301. T. Shimizu, in ref. 1, p. 289. J. L. G. Fierro, Catal. Rev.-Sci. Eng., 1992,34,321. T. R. N. Kutty and M. Avudaithai, in ref. 1, p. 307. ovskites in total oxidation reactions is mainly dependent on component B oxides, and the activity sequence is similar to those of single B oxides. So, the activity of the La-Ni per-ovskites in the complete oxidation of methanol should re-semble, to some extent, the activity of nickel@) oxide.It is well known that NiO catalyses the complete oxidation of 16 17 18 19 D. B. Hibbert, in ref. 1, p. 325. R. J. H. Voorhoeve, in Advanced Materials in Catalysis, ed. J. J. Burton and R. L. Garten, Academic Press, New York, 1977, p. 129. D. G. Klissurski, Proc. 4th Znt. Congr. on Catalysis, Moscow, 1968, Akademiai Kiado, Budapest, 1977, vol. 1, p. 477. I. E. Wachs, G. Deo, M. A. Vuurman, H. Hu, D. S. Kim and methanol to carbon dioxide in the temperature range studied here. 20 J-M. Jehng, J. Mol. Catal., 1993, 82,443. M. Crespin, J. M. Bassat, P. Odier, P. Mouron and J. Choisnet, J. Solid State Chem., 1990,84, 165. 21 M. Crespin, P. Levitz and L. Gatineau, J. Chem. SOC., Faraday Conclusions 22 Trans.2, 1983,79, 1181. D. G. Klissurski, J. Pesheva, Y. Dimitriev, N. Abadzhieva and L. XPS studies of LaNiO,, La,Ni04 and La2Ni04+d have Minchev, in New Developments in Selective Oxidation, ed. G. shown a noticeable difference between their surface and bulk Centi and F. Trifiro, Elsevier, Amsterdam, 1990, p. 287. compositions. XP spectra have evidenced a surface enrich- ment in lanthanum and oxygen. The existence of at least two different forms of desorbable oxygen has been demonstrated by both TPD and XPS studies. A significant difference in the stoichiometry and oxygen 23 24 25 A. Wold, B. Post and E. Banks, J. Am. Chem. Soc., 1957, 79, 491 1. P. Levitz, M. Crespin and L. Gatineau, J. Chem. SOC., Faraday Trans. 2, 1983,79, 1195. J. Choisnet, J.M. Bassat, H. Pillier, P. Odier and M. Leblanc, Solid State Commun., 1988,66, 1245. reactivity between the initial ‘fresh’ and the tested catalysts has been observed. This is indicative of surface alterations 26 D. J. Buttrey, P. Ganguly, J. M. Honig, C. N. R. Rao, R. R. Shartman and C. N. Subbana, J. Solid State Chem., 1988, 74, during the catalytic reaction, until a steady state of the cata- lyst is reached. LaNiO, and the intergrowth nickelates (La,NiO, and 27 28 233. P. Odier, Y. Nigara and J. Coutures, J. Solid State Chem., 1985, 56,32. P. Odier, M. Leblanc and J. Choisnet, Muter. Res. Bull., 1986, La,Ni04 +a) have shown a high efficiency for complete oxida- 21, 787. tion of methanol. This can be related to the relatively low binding energies of oxygen in their surface layers, i.e.a high reactivity of surface oxygen. 29 30 P. Odier, J. M. Bassat, M. Crespin and J. Choisnet, Jpn. J. Appl. Phys., Ser. 2, 1989, 129. Y. Uwamino, T. Ishizuka and H. Yamatera, J. Electron Spec- trosc. Relate. Phenom., 1989, 34. D.K. acknowledges a sabbatical grant from Ministerio de Educacion y Ciencia (Madrid, Spain, ref. SAB92-0302 and 31 32 33 J. L. G. Fierro, J. Catal., 1984,87, 126. J. L. G. Fierro and L. G. Tejuca, Appl. Su$. Sci., 1987,27,453. L. G. Tejuca and J. L. G. Fierro, Thermochim. Acta, 1989, 147, SAB94-0020). 34 361. J. L. G. Fierro, in ref. 1, p. 195. 35 K. Tabata, I. Matsumoto and S. Koshiki, J. Muter. Sci., 1987, References 22, 1882. 1 J. Twu and P. K. Gallagher, in Properties and Applications of Perooskite-type Oxides, ed. L. G. Tejuca and J. L. G. Fierro, Marcel Dekker, New York, 1992, p. 1. L. G. Tejuca, J. L. G. Fierro and J. M. D. Tascon, in Advances in Catalysis, ed. D. D. Eley, H. Pines and P. B. Weisz, Academic Press, New York, 1989, vol. 36, p. 237. A. F. Wells, Structural Inorganic Chemistry, Clarendon Press, Oxford, 1984, p. 602. B. Dabrowski, J. D. Jorgensen, D. G. Hinks, S. Pei, D. R. Richards, H. B. Vanfleet and D. L. Decker, Physica C, 1989,99, 2 3 4 36 37 38 39 40 41 B. Halpern and J. E. Germain, J. Catal., 1975, 37,44. L. Wachowski, S. Zielinski and A. Burewicz, Acta Chim. Acad. Sci. Hung., 1981, 106,217. St. Kynev, D. Klissurski and E. Vateva, Commun. Znst. Phys., Bulg. Acad. Sci., 1962,9, 57. G. K. Boreskov, V. V. Popovskii and V. A. Sazonov, in Scientific Bases for Prediction of Catalytic Action, Proc. 4th Int. Congr. on Catalysis, Nauka, Moscow, 1970, p. 343 (in Russian). M. Ai and S. Suzuki, Bull. Jpn. Petrol. fnst., 1974, 16, 118. T. Seiyama, in ref. 1, p. 215. 162. D. E. Rice and D. J. Buttrey, J. Solid State Chem., 1993, 105, 197.5 Paper 3/07433A; Received 17th December, 1993

ISSN:0956-5000    

DOI:10.1039/FT9949001987

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1993-1998 Addition of Manganese to Iron Catalysts supported on Silicalite-I and its Effect on CO Hydrogenation Gopal Ravichandran, Debasish Das and Dipak K. Chakrabarty* Solid State Laboratory, Department of Chemistry, Indian Institute of Technology, Bombay 400076, India The addition of manganese to iron catalysts supported on silicalite-1 increases the selectivity of the catalysts to alkenes in CO hydrogenation. The catalysts were prepared by impregnating the support with metal nitrates followed by calcination and in situ reduction in hydrogen. The Mossbauer spectra of the calcined samples showed that the addition of manganese reduced the size of the cr-Fe,O, particles. This was confirmed by XRD and TPR results. The active phase consists of Hagg carbide and some oxides of Fell', the latter being responsible for the increased alkene formation.The role of manganese is to reduce the particle size of the iron oxide precursor, making carburization unfavourable. This leads to an increase in the amount of the oxide phase in the catalyst, thereby increasing the selectivity to alkenes. Recently there has been renewed interest in Fischer-Tropsch (FT) synthesis. The focus has been on selective conversion of synthesis gas to feedstocks for chemical industry rather than to liquid fuel.',, One such important aspect is the selective synthesis of C2-C, alkenes. However, FT synthesis yields a wide spectrum of products from methane to waxes, and the design of an appropriate catalyst to obtain specific products is of vital importance.Zeolite-supported FT catalysts are known to show unusually high specificity for lower hydrocar- bons or aromatics. The formation of lower hydrocarbons can be achieved by termination of chain growth by containing the active metal particles inside the small pores of the zeolite^.^-^ However, the nature of the zeolite support has a strong influ- ence on the product selectivity. Thus, while acidic zeolite such as ZSM-5 show poor selectivity to alkenes and favour the formation of gasoline-range hydrocarbon^,^,^ catalysts sup- ported on silicalite yield alkenes selectively.' A comparison of silicalite, mordenite and ZSM-5 supported cobalt catalysts has shown that Co/silicalite has very low methanation activ- ity and very high selectivity for C2-C4 alkenes.' Very high selectivity to lower alkenes has also been reported on potassium-promoted Fe/silicalite catalysts.' It has been claimed that the addition of manganese oxide to precipitated iron catalysts yields a catalyst with a high selectivity to low-molecular-weight alkenes.'0-'2 Although there is considerable interest in the use of zeolites in the FT reaction, and zeolite-supported iron and cobalt catalysts have shown very good selectivity to lower alkenes, no study had been reported on the effect of manganese on the behaviour of zeolite-supported iron or cobalt FT catalysts until we report- ed the results on CO hydrogenation over iron-manganese catalysts supported on silicalite-1 and zeolite ZSM-5.' A comparison of our results with unsupported iron-manganese catalysts showed that the zeolite-supported catalysts have better selectivity to alkenes.The aim of this work is to study the influence of systematic manganese addition to iron catalysts supported on silicalite- 1 in an attempt to understand the role of manganese. Experimental Silicalite-1 was synthesized according to a method described in the 1iterat~re.l~ Impregnation was carried out by adding appropriate amounts of 0.45 mol dm-3 metal nitrate solu- tions to 10 g of the freshly calcined support. The slurry was stirred continuously on a water bath and the excess of solvent was removed slowly under vacuum. The solid material was then crushed, dried at 120 "C for 12 h and finally calcined at 450°C in air for 8 h to convert the metal nitrates into oxides.The catalysts were designated as Fe(x)/Sil and Fe-Mn(x, y)/ Sil, where x and y indicate the wt.% of Fe and Mn, respec- tively. The X-ray diffraction (XRD) patterns of the catalysts were recorded using a Philips PW-1820 diffractometer with nickel-filtered Cu-Kcr radiation at a scanning rate of 2" min-'. Temperature-programmed reduction (TPR) of the catalysts was studied in a conventional flow apparatus, as described previously.' The transmission Mossbauer spectra of the catalysts in their calcined form and after use were obtained using a PC-based multichannel analyser. A 5 mCi 57Co(Rh) source was used in the constant-acceleration mode.The spectrometer was calibrated with a standard a-Fe absorber. The spectra were fitted using a computer program. Mossbauer spectra of the reduced catalysts could not be recorded as they were pyrophoric. CO hydrogenation was carried out in a high-pressure flow reactor (BTRS-Jr., Autoclave Engineers, USA) at 21 atm. The detailed experimental set-up for the synthesis gas conversion and the analytical procedure were described elsewhere.' The calcined catalysts (1 g, particle size 180-300 pm)were loaded in the reactor and reduced in situ in a flow of hydrogen (20 cm3 min -') at 450 "C for 10 h before CO hydrogenation was carried out. The conversion of CO on the various catalysts did not change much after ca. 1 h of reaction.The data reported in the tables are those obtained after 6 h on stream. Results and Discussion XRD Studies The XRD pattern of the silicalite-1 support showed that it was highly crystalline and free from impurities. The XRD patterns show the presence of a-Fe,O,. The intensity of the M-F~,O, peaks increased with the iron content from 5 to 20 wt.%. In contrast, the manganese-promoted Fe-Mn(x, y)/Sil catalysts showed only peaks that are characteristic of the support. The absence of the peaks for oxides of iron and manganese may be due to their very small particle size. For unsupported iron and manganese oxides, which were pre- pared by calcining the corresponding nitrates at 450 "C, strong peaks for a-Fe203 and fi-MnO, respectively, were noted.The unsupported Fe-Mn (1 : 2) catalyst showed only weak lines due to a-Fe,O, and p-(Mnl -%FeJ203 indicating poor crystallinity.' 5*16 This indicates that the addition of Mn 1994 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Mossbauer parameters of calcined Fe(x)/Sil catalysts reduces the particle size of iron oxide in unsupported Fe-Mn catalysts. A similar effect appears to be responsible for the 6 A Heff areaabsence of the XRD lines of the metal oxides for the Fe- catalyst component /mm s-' /mm s-' /kG (Yo)Mn(x, y)/Sil catalysts. It may be concluded that the addition of Mn increases the dispersion of iron oxide. Fe(S)/Sil a-Fe,O, 0.44 0 503 77.4 The catalysts used did not show any XRD lines other than SPO" 0.26 0.87 -22.6 those due to the support.There was also some loss in crys- Fe( lO)/Sil a-Fe,O, 0.44 0 502 86.9 SPO" 0.15 0.68 -13.1tallinity of the support. Fe(20)/Sil a-Fe,O, 0.39 0 506 97.9 SPO" 0.13 0.66 -2.1 Miissbauer Studies " Superparamagnetic oxide of iron. The room-temperature Mossbauer spectra of the calcined catalysts containing various amounts of iron are shown in Fig. 1. All three samples show superposition of a six-line size is found to be 15 nm on Fe(S)/Sil, 17 nm on Fe(lO)/Sil pattern of large particles of a-Fe,O, and a central doublet and >18 nm on Fe(20)/Sil samples. due to supermagnetic iron oxide (SPO).The area ratios of the The incorporation of manganese was found to decrease the six-line pattern and the superparamagnetic doublet are given average particle size of the iron oxide particles as the area of in Table 1.The area fraction of the six-line pattern increased the six-line pattern due to large a-Fe,O, particles was found with the iron content. Thus, the average particle size of iron to decrease with the addition of manganese (Fig. 2). The area oxide increased with iron content, as expected. According to ratios of the six-line pattern and the doublet are given in Kiindig et d.,"the average particle size of iron oxide can be Table 2. Thus, with 20 wt.% manganese added to the cata- estimated from the area ratio of the six-line pattern to the lyst, the sextet spectra completely disappeared, leaving only superparamagnetic doublet. The estimated average particle ..1oo.c 100.0 99.8 99.8 99.6 99.6 99.4 99.4 .-99.2 99.2 1 . *. 99.0 99.0 100.0 100.0 99.8 h h$ 99.8 S 99.6 v v c C .-0 .o 99.4v) v).% 99.6 .-E 6 99.2 c 4-z 2 99.099.4 98.8 98.699.2 ..* :. s.-.. 100.0 -100.0 -99.8 -99.6 -99.6 -99.2 -It99.4 -98.8 -99.2 -98.4 -99.0 -98.0 -98.8 -97.6 -98.6 -97.2 I I I I f I I I 98.4 I I I I I I I I 1 -12 -9 -6 -3 0 3 6 91;-12 -9 -6 -3 O 3 6 9 12 velocity/rnrn s-' velocity/rnm s-' Fig. 1 Mossbauer spectra of calcined Fe(x)/Sil catalysts: (a) Fe(5)/ Fig. 2 Mossbauer spectra of calcined Fe-Mn(x, y)/Sil catalysts: (a) Sil; (b) Fe(lO)/Sil and (c) Fe(2O)/Sil Fe-Mn(l0, 5)/Sil; (b) Fe-Mn(l0, lO)/Sil and (c) Fe-Mn(l0, 20)/Sil J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 2 Mossbauer parameters of calcined Fe-Mn(x, y)/Sil cata- lysts 6 A Heff area catalyst component /mm s-' /mm s-l /kG (%) Fe-Mn(l0, 5)/Sil a-Fe,03 0.39 0 498 68.0 SPO" 0.28 0.85 -32.0 Fe-Mn(l0, lO)/Sil a-Fe,03 0.44 0 503 64.0 SPO" 0.28 0.87 -36.0 Fe-Mn( 10, 20)/Sil SPO" 0.3 1 0.83 -100.0 " Superparamagnetic oxide of iron. the doublet. This clearly shows that addition of manganese increases the dispersion of iron oxide in the catalyst precur- sor. The Mossbauer results also show that the a-Fe203 phase is actually present as small particles in the calcined Fe- Mn(x, y)/Sil catalysts, although XRD could not detect this phase. TPR Studies Fig. 3 shows the TPR spectra of the Fe(x)/Sil and Fe-Mn(x, y)/Sil catalysts and that of bulk a-Fe,O, .a-Fe,O, was found to undergo complete reduction in a single step under the experimental conditions and the peak maximum was at 600°C.However, the TPR spectra of the supported catalysts showed two peaks and the reduction temperature was lower. We attribute this lowering of the reduction temperature in our catalysts to the smaller particle size of the iron oxide on the silicalite support. This is corroborated by the fact that in manganese-promoted catalysts, where the iron oxide particle size is reduced with increasing manganese content, the reduction begins at an even lower temperature. The appearance of the two TPR peaks indicates that iron oxide either undergoes a two-step reduction process or it is located at two different sites with different reducibility.The first peak can be assigned to the reduction of a-Fe203 located outside the silicalite pores. This is clear from the 100 200 300 400 500 600 700 800 T/"C Fig. 3 TPR spectra of the calcined samples: (a) Fe-Mn(l0, O)/Sil, (b) Fe-Mn(20, lO)/Sil, (c) a-Fe,O,, (d) Fe-Mn(l0, 5)/Sil, (e) Fe-Mn(l0, lO)/Sil, cf)Fe-Mn(l0, 20)/Sil figure which shows that the intensity of this peak increases with increase in iron content from 10 to 20 wt.% as more oxide particles will be outside the silicalite pores at higher loading. The second peak we speculate as due to the reduction of iron oxide located inside the silicalite pores. In the Fe-Mn(x, y)/Sil system we also observed two TPR peaks. The first peak is assigned to the reduction of a-Fe,O, .The intensity of the first peak decreased with increasing man- ganese content from 5 to 20 wt.% in the catalysts. The second peak is shifted to an appreciably lower temperature than that in Fe(x)/Sil catalysts. Although we did not notice the pres- ence of any other phase in the XRD patterns, the possibility of the presence of very fine particles of fi-(Mnl-,Fe,),O, cannot be ruled out as such a phase has been reported in the calcined Fe-Mn sarnple~.'~-~~The intensity of the second TPR peak increased with manganese content, indicating the formation of the Fe-Mn mixed phase. CO Hydrogenation Eflect of Iron Oxide Loading The performances of the catalysts for CO hydrogenation was studied from 275 to 300°C at 21 atm.The results for the Fe(x)/Sil catalysts at 275°C are given in Table 3. The CO conversion per gram of iron increased with iron oxide par- ticle size in the calcined catalysts. This is possibly because the larger iron oxide particles are easily carburized in the reac- tion atmosphere. Mossbauer studies of the Fe(x)/Sil catalysts (Fig. 4, Table 4) showed increased carbide formation in the order Fe(S)/Sil < Fe( lO)/Sil < Fe(20)/Sil The increase in CO conversion with the increasing forma- tion of iron carbide is not unexpected as it was also observed Table 3 CO hydrogenation Fe(x)/Sil catalysts (T=275"C;P=21atm;CO:HZ= l;GHSV= 1200h-') Fe(S)/Sil" Fe( lO)/Sil Fe(20)/Sil CO conversion 22.7 8.7 14.3 CO converted to [pmol (g Fe)-'s-'] CO, (molYo) hydrocarbons (mol%) 2.0 10.6 1.2 5.9 4.4 17.0 hydrocarbon distribution (wt.?h) c, CZ c3 c4 C,(alkene) C,(alkene) C,(alkene) c5+ O/P* 14.2 2.5 12.8 1.5 23.2 2.0 17.9 26.1 9.0 11.2 2.7 11.1 1.1 19.6 1.5 13.9 39.0 8.4 12.4 8.9 6.4 4.7 20.3 8.9 8.4 30.2 1.6 " GHSV = 920 h-'.Alkene :alkane ratio in C,-C4 fraction. Table 4 Area fraction of Hagg carbide and superparamagnetic oxide in the used catalysts Hagg carbide superparamagnetic catalyst (X-Fe,C,) oxide Fe(S)/Sil 75 25 Fe( 1 O)/Sil 85 15 Fe(20)/Sil 89 11 Fe-Mn( 10, 5)/Sil 80 20 Fe-Mn( 10, lO)/Sil 79 21 Fe-Mn( 10, 20)/Sil 71 29 1996 100.0 99.8 99.6 99.4 J 100.0 h S 99.8 v C 0.-v) --99.66 !2+ gg.4199.2 *..--.... .. . -.... .... .. *....:-... ..-at. --:* *. f..... . J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 It is still uncertain whether iron carbide or iron oxide is responsible for alkene formation. According to Itoh et aL2 iron carbide, Fe2C, is the most favourable iron species for alkene production. Our catalysts did not have this carbide phase. Our results show that a large amount of z-Fe,C2 is formed and this favours the formation of alkanes. Although CO conversion increased with the amount of this carbide, it took place at the expense of alkene selectivity. This suggests that the formation of alkenes is favoured by the oxide phase containing Fe"'. Reymond and co-workers26-28 observed very high CO hydrogenation activity in the presence of Fe,O, but they did not report the alkene selectivity of their catalysts.Itoh et al.25 found MnxFe3-x04 to have good alkene selectivity . Effect of Addition of Manganese Conversion us. time on stream plots are shown in Fig. 5. The catalytic activity remains more or less constant after the first hour. The results of CO hydrogenation on Mn oxide pro- moted iron catalysts are shown in Table 5. Addition of Mn was found to improve both CO conversion and the selectivity of the catalysts to alkenes. However, methane selectivity remained almost unchanged by Mn addition and the amount of C, + fraction increased substantially. The alkene selectivity of Fe(x)/Sil catalysts rapidly reached a steady state whereas this took 3-4 h for the Fe-Mn(x, y)/Sil catalysts (Fig.6). If alkene formation is favoured by the Fe"' oxide phase, this phase must be formed more readily in the Fe(x)/Sil catalysts but slowly in the FeMn(x, y)/Sil catalysts. Perhaps the active phase in alkene synthesis is finely divided Fe,O, and 99.0 I -8 -6 -4 -2 0 2 4 6 8 velocity/mm s-' Fig. 4 Mossbauer spectra of used Fe(x)/Sil catalysts: (a) Fe(S)/Sil; (b)Fe(lO)/Sil and (c) Fe(20)/Sil i0, I I I I I I 0123456 by other workers. Raupp and Delgass18 noticed that the time on stream/h increase in activity of supported iron catalysts parallels their Fig. 5 CO conversion us. time on stream plots at 275 "C: D,increased carbide content and a similar observation was Fe( lO)/Sil; ., Fe-Mn(l0, lO)/Sil; Fe(20)/Sil; 0,Fe-Mn(l0, 5)/Sil; 0, 20)/Sil10,Fe-Mn( ,, made by other worker^.'^-'^ In the low-temperature synthesis gas reaction, the final form of catalysts are either Hagg (x) or hexagonal close- packed (E) carbides and only at temperatures >500°C is cementite phase (Fe,C) found.23 Callejea et al.also noted the presence of only the Hagg carbide phase in Fe/ZSM-5 cata- lyst~.~~However, in Mossbauer spectra we observed the pres- ence of some oxides of Fe"'. Although XRD of the catalysts did not show any carbide, Mossbauer spectra clearly showed Hagg carbide, suggesting that the latter is formed only on the surface layer. While an increase in iron loading in Fe(x)/Sil catalysts led to increased CO conversion, the alkene selectivity decreased.Thus, Fe(20)/Sil showed a drastic decrease in alkene selec- tivity, indicating the high hydrogenation activity of this cata- lyst. The selectivity of the catalysts to alkenes can be correlated with the particle size of the iron oxide precursor. Catalysts that initially contained larger iron oxide particles showed higher CO conversion and gave more alkane pro- ducts. 16 , a--0-I I a 0 I I I I I I Fig. 6 Alkene :alkane ratio us. time on stream plots a 275 "C: D, Fe(lO)/Sil; ., Fe-Mn(l0, lO)/Sil; Fe(20)/Sil; 0,Fe-Mn(l0, 5)/Sil; 0,b,Fe-Mn( 10, 20)/Sil J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 5 CO hydrogenation on Fe-Mn(x, y)/Sil catalysts (P = 21 atm; CO :H, = 1; GHSV = 1200 h-l) Fe-Mn(l0, 5)/Sil Fe-Mn(l0, lO)/Sil Fe-Mn( 10, 20)/Sil catalyst temperature 275 300 325 275 300 325 275 300 325 CO conversion/pmol (g Fe)-' s-' 6.7 28.4 47.7 13.9 32.8 69.6 23.8 64.3 102.3 CO converted to CO, (molyo) 0.7 4.4 10.8 2.7 5.5 13.1 3.5 15.9 29.1 hydrocarbons (mol%) 4.5 17.7 26.4 7.7 19.0 38.9 12.9 28.4 41.4 HC distribution (wt.Yo) c, 9.3 13.3 18.2 9.3 13.6 23.7 8.6 10.5 23.0 2.6 9.3 13.0 2.3 4.8 15.3 2.0 3.1 11.1c2 C,(alkene) 17.4 9.7 6.1 13.0 11.1 1.6 12.7 11.0 3.2 0.6 1.8 6.6 0.9 1.o 10.9 0.9 0.9 6.2c3 C,(alkene) 29.3 25.0 20.4 23.6 24.0 13.3 23.3 21.3 17.7 c4 2.9 14.1 12.9 1.1 2.9 12.5 1.2 1.2 11.7 C,(alkene) 18.6 4.5 4.0 17.0 15.5 2.6 17.9 16.1 4.6 c5 + 19.4 22.4 18.7 32.7 27.3 20.1 33.5 36.0 22.6 0 : P" 10.7 1.6 0.9 12.5 5.8 0.5 13.1 9.3 0.9 a Alkene : alkane ratio in C,&, fraction.MnxFe, -x04for the Fe(x)/Sil and Fe-Mn(x, y)/Sil catalysts, respectively, as these phases have been reported to be active -. .. * in alkene synthesis.25 These phases could be formed from r-._.-Fe,O, under the reducing conditions in the reactor, in which 100.0 case Fe,04 is formed readily and MnxFe3-x04 slowly. It is, however, not possible to confirm this speculation as the XRD results did not show the presence of these phases, possibly because of their extremely small size. 99.8 The Mossbauer spectra of the Fe-Mn(x, y)/Sil catalysts are shown in Fig. 7. These samples were collected after 6 h on stream at the reaction temperature.Catalyst precursors with 99.6larger iron oxide particles contained a higher ratio of the carbide phase. The amount of Hagg carbide present in these catalysts decreased with Mn loading (Table 4). This is because Mn reduces the particle size of iron oxide and small 99.4' %particles of iron oxide are difficult to carburize. Although the amount of Hagg carbide decreased continuously with Mn 100.0loading and CO conversion initially dropped at 5 wt.% Mn, further addition of Mn resulted in an increase of CO conver- 99.8 hsion. This behaviour is different from that of Fe(x)/Sil cata- $lysts where CO conversion was found to increase with the -99.6 amount of Hagg carbide in the catalysts. This indicates that .-0 in manganese-promoted iron catalysts, the amount of Hagg .-s 99.4 carbide is not the only phase responsible for CO conversion.5 It is possible that in addition to iron carbide, some mixed E 99.2 CIiron manganese phases may also be responsible for the increased conversion. 99.0 The alkene selectivity of the Mn-promoted iron catalysts supported on silicalite 1 was found to be higher than that for 98.8' .. .-, . .-.. . .unpromoted catalysts (Fig. 6). This increase in alkene selec- tivity with decreasing carbide formation further supports our view that alkene formation possibly takes place on the iron oxide. In Mn-promoted ultrafine iron particles the MnxFe3-x0, phase was found to be the preferable structure for high alkene ~electivity.'~ Thus it appears that in Mn- 99.2 -promoted iron catalysts, Mn plays an important role by reducing the iron oxide particle size and thereby making the 98.8 -particles difficult to carburize, which in turn increases the alkene selectivity.1Although using higher reaction temperatures increased CO 98.4 conversion, this has a negative effect on alkene selectivity 1 I 1 I I I I 1(Table 5). The use of higher temperatures increases the alkane 98.0 ! content and also gives a large amount of CO, in the product. -8 -6 -4 -2 0 2 4 6 8 velocity/mm s-'CO, is possibly formed by the parallel water gas shift reac- tion which is accelerated at higher temperature. Using a high Fig. 7 Mossbauer spectra of Fe-Mn(x, y)/Sil catalysts: (a) Fe-temperature also enhances the hydrogenation of the alkenes Mn(l0, 5)/Sil; (b)Fe-Mn(l0, lO)/Sil and (c) Fe-Mn(l0, 20)/Sil 1998 J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 initially formed, thus increasing the amount of alkanes in the product. 8 9 V. U. S. Rao and R.J. Gormley, Hydrocarbon Process, Int. Ed., 1980,59, 139. M. Peukert and G. Linden, Proc. 8th Int. Congr. Catal., Verlag Chemie, Weinheim, 1984, vol. 2, p. 135. Conclusions 10 B. Biissemeier, C. D. Frohning and B. Cornlis, Hydrocarhon 1. Addition of manganese to silicalite-supported iron cata- 11 Process, Int. Ed., 1976,55, 105. H. Kolbel and K. 0.Tillmetz, US Patent 4,177,203, 1979. lysts gives increased alkene selectivity in CO hydrogenation. 2. The active phase of the catalysts consists of Hagg carbide and oxides of Fe"'.3. The role of manganese is to reduce the particle size of the iron oxide precursor, making it difficult to undergo car- 12 13 14 J. Barrault, C. Forquy and V. Perrichon, Appl. Catal., 1983, 5, 119. D. Das, G. Ravichandran, D. K. Chakrabarty, S. N. Piramanay- agam and S. Shringi, Appl. Catal., 1994, 107, 73. C. V. V. Satyanarayana and D. K. Chakrabarty, Appl. Catal., 1990,66,1. burization. This increases the amount of the iron oxide phase 15 D. Das, G. Ravichandran, D. K. Chakrabarty, unpublished in the catalysts. 4. The oxide of iron and the mixed iron-manganese oxide present in the catalysts are possibly responsible for their increased alkene selectivity. 16 17 work. G. C. Maiti, R. MaIessa and M. Baerns, Appl. Catal., 1983, 5, 151.W. Kiindig, H. Bommel, G. Constabaris and R. H. Lindquist, Phys. Rev., 1966, 142, 327. This work was supported by a research grant from the 18 19 G. B. Raupp and W. N. Delgass, J. Catal., 1979,58,348; 361. H. P. Bonzel and H. J. Krebs, Surf: Sci., 1980,91,499. Department of Science and Technology, New Delhi. 20 21 H. P. Bonzel and H. J. Krebs, Surf: Sci., 1982,117,639. H. J. Krebs, H. P. Bonzel, W. Sebwarting and G. Gafaer, J. References 22 Catal., 1980,63, 226. D. J. Dwyer and H. Hardenbergh, J. Catal., 1984,87,66. R. Snell, Catal. Rev. Sci. Eng., 1987,29, 361. M. Janardanrao, Ind. Eng. Chem. Res., 1990,29,1735. H. H. Nijs, P. A. Jacobs and J. B. Uytterhoeven, J. Chem. SOC., Chem. Commun., 1979, 180. S. Kawi, J. R. Chang and B. C. Gates, J. Am. Chem. SOC., 1993, 115,4830. P. L. Zhou, S. D. Maloney and B. C. Gates, J. Catal., 1991, 129, 315. C. D. Chang, W. H. Lang and A. J. Silvestri, J. Catal., 1979, 56, 268. P. D. Caesar, J. A. Brennan, W. E. Garwood and J. Ciric, J. 23 24 25 26 27 28 K. B. Jensen and F. E. Massoth, J. Catal., 1985,92, 109. G. Callejea, A. de Lucas, R. van Grieken, J. L. Pefia, A. Guerrero-Ruiz and J. L. G. Fierro, Catal. Lett., 1993, 18, 65. H. Itoh, S. Nagano, K. Takeda and E. Kikuchi, Appl. Catal., 1993,%, 125. J. P. Reymond, P. Mkriandeau and S. J. Teichner, J. Catal., 1982, 75, 39. F. Blanchard, J. P. Reymond, B. Pommier and S. J. Teichner, J. Mol. Catal., 1982, 17, 171. B. Pommier, J. P. Reymond and S. J. Teichner, Stud. Surf: Sci. Catal., 1984, 19, 471. Catal., 1979,56, 274. Paper 3/07535D; Received 23rd December, 1993

ISSN:0956-5000    

DOI:10.1039/FT9949001993

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1999-2000 FARADAY COMMUNICATIONS Microwave Synthesis of the Colloidal Poly(N4sopropylacrylamide) Microgel System Mary Murray, David Charlesworth, Linda Swires, Phillip Riby, Janice Cook, Babur 2. Chowdhry, Martin J. Snowden" School of Biological and Chemical Sciences, University of Greenwich, Woolwich, London, UK SE 18 6PF The preparation of monodisperse colloidal microgel particles of poly(N-isopropylacrylamide) by the use of microwave radiation is reported. The total synthesis time has been reduced from 6 h (conventional method) to less than 1 h (microwave method). The physicochemical characteristics of the microwave synthesized microgel are similar to those of conventionally prepared samples. This is the first report of the synthesis of a particulate colloid using microwave energy. Microwave radiation has been used for the initiation of a variety of different chemical reactions including S,2 type synthesis* and polymerisation processes e.g.for preparation of polyurethanes2 and p~lyamides.~This communication reports the first successful microwave synthesis of a colloidal microgel. The physical properties of the poly(N-isopro-pylacrylamide) (NIPAM) microgel system have received con- siderable attention in the recent literature. Studies reported include the reversible flocculation of the dispersion4,' and uptake and release characteristics, particularly with regard to polymers6 and heavy-metal ions.7 We have prepared poly(N1PAM) aqueous microgels using two different methods : (a)The conventional method by the free radical emul- sion polymerisation of NIPAM in water at 70°C, in the presence of N,N'-methylenebisacrylamide [(CH, = CH-CO-NH),CH,; from BDH Chemicals] as a cross-linking agent, following the procedure described by Pelton and Chibante.* Briefly the monomer was dissolved to a final concentration of 5 g 1-' with the cross-linker 0.5 g 1-1 and the initiator, ammonium persulfate, 0.5 g 1-'.The prep- aration took 6 h; the reaction mixture was thermostatted at 70 "C and stirred under an N, atmosphere. (b)A new method using microwave radiation for the syn- thesis of the microgel in a CEM MDS 2100 microwave cavity operating at 2450 MHz with a maximum power output of 1000 W. The cavity was equipped with a pressure transducer to allow continuous pressure monitoring within the CEM- lined digestion reaction vessel and a fibre-optic temperature probe to allow temperature control.These cavities are tradi- tionally used for digestion of solid samples for analytical pur- pose~.~Unlike most traditional synthetic routes the magnetron, or heat source, can be cycled in a feedback loop with reference to either the pressure, since the vessels are sealed, or the temperature within the vessel. Pressures can be varied from atmospheric pressure up to 200 psi? while tem- peratures of up to 200°C can be achieved. Heating within microwave fields is normally caused by either dipole rotation or ion migration. Since water is the continuous medium here, this mechanism is extremely effi- cient.The magnetron feedback was based on a pressure of 1.01 x lo5 Pa i.e. the magnetron cycled on and off so as not 7 1 psi = 6894.76 Pa. to exceed this limit. These conditions were chosen as they most closely resemble those used in traditional thermal- heating procedures. The reaction was carried out at 70 "C for 1 h using 400 W microwave power. The total volume of the reaction mixture was 75 ml and the stoichiometry of monomer to cross-linking agent identical to that for the free radical method (a). Transmission electron microscopy (TEM) showed the microgels prepared by both methods to be monodisperse spheres with mean diameter 380 & 28 nm for the convention- ally synthesized and 360 f25 nm for the microwave-prepared samples.The temperature dependence of the particle diameter of poly(N1PAM) microgel was determined turbidimetrically using a Perkin-Elmer Lambda 2 spectro- photometer connected to a programmable temperature- scanning water bath at a scan rate of 1 K min-'. The temperature in the measuring cell was monitored using a platinum thermocouple temperature probe. The turbidity of the dispersions was measured against distilled water in the range 20-50°C. Fig. 1 shows the change in turbidity at 547 nm as a function of temperature, for both heating and cooling scans. On cooling, the microgels re-expand to their original size. There is a good correlation between the tran- sition temperature obtained from the maximum of the first derivative of the turbidity measurements (34.9"C) and the value obtained from high-sensitivity differential scanning calorimetry (HSDSC) (35.6"C) for the microwave-synthesized microgel.This shows that the process(es) at the phase tran- sition are similar. The results from TEM, DSC and turbidity measurements suggest indeed that the structures of the microgels produced by methods (a) and (b) are similar. For both samples, the decrease in hydrodynamic diameter with increasing temperature is a consequence of the increase in the Flory interaction parameter, 2, for poly(N1PAM) in water. This facilitates more polymer-polymer contacts, hence the particles contract, forcing out solvent from the interstitial spaces.HSDSC measurements11,12 on the poly(N1PAM) microgel were carried out using a MicroCal MC-2D ultrasensitive DSC, with the DA2 software package for data acquisition and analysis supplied by the instrument manufacturer. Doubly deionized water provided the reference for all the measurements. The endothermic phase transitions exhibited by poly(N1PAM) using both synthetic methods are shown in 2000 om 01 I 0 10 20 30 40 50 60 TlOC -m .... 01 I 0 10 20 30 40 50 60 TrC Fig. 1 Turbidity of a 0.1% dispersion of poly(N1PAM) at 547 nm as a function of temperature; (m) heating and (0)cooling at 60 and -60 K h-', respectively, for (a) conventionally produced and (b) microwave-produced microgel Fig. 2 and the associated thermodynamic parameters are listed in Table 1.Clearly there are differences in the thermo- grams and this is reflected in the results derived from the mea- surements given in Table l. It should be noted that repeated heating and cooling scans were superimposable suggesting that the transitions are genuinely thermo-reversible. The ther- modynamic parameters for both samples are similar in terms of T, and AH,,, values. However the AT,,, of the conven- tionally produced microgel is ca. 60% greater than that of the E c I Y r b, 2.5 7 cp -20 30 40 50 T/"C Fig. 2 Temperature dependence of the partial excess specific heat capacity of the colloidal poly(N1PAM) microgel system in doubly deionised water at a concentration of 0.5 wt.%.The HSDSC record- ings shows the heating scans for (a)conventionally prepared and (b) microwave-synthesized microgel at a scan rate of 60 K h-'. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Microcalorimetrically recorded thermodynamic parameters for poly(N1PAM) microgels at a scan rate of 60 K h-thermodynamic conventionally microwave-parameter produced microgel produd microgel TZC 34.8 35.6 AHcaJJ g-' 24 23 AHvH/cal mol- ' 97400 167OOO ATI,,/oC 6.0 3.7 Cp,max/J g-' K-' 3.1 5.2 T, is the temperature at which the excess specific heat is a maximum (CpVmax);AHca,is the calorimetric enthalpy; AHvH the van't Hoff enthalpy and ATl,* the half-width of the transition at +Cp,max. corresponding value for the microwave-synthesized material.In addition the base molar unit (AHv,.JAHca,,using corre- spondingly appropriate units) has a significantly greater value in the case of the microwave-produced gel (1800 u) compared to the conventionally synthesized microgel (ca. lo00 u). These differences together with the differences in Cp, values appear to suggest that, in fact, the phase transition for the microwave-synthesized material has a higher cooperatively than the conventionally produced microgel. The T, values for both microgels were independent of scan rate (10, 30 and 60 K h-'). The values for the thermodynamic parameters had a standard deviation of 5% for microgels produced at different times using the two methods except for the T, which was always the same to within fO.l "C.Note that, because of the nature of the microgel, samples prepared even by the conven- tional method, at different times, will have slightly different thermodynamic parameters.More recent microwave results indicate synthesis times of as little as 12 min and the production of novel microgels at elevated pressure. Further reports of these findings and an outline of how the mechanism of the polymerisation process is effected by microwaves will be reported in a subsequent paper. Financial support for a PhD Studentship (M.M.) from the University of Greenwich postgraduate student bursary is gratefully acknowledged. This paper is released by the Bio- polymer section of the SMPG group of the University of Greenwich. References 1 R.Gedye, F. Smith, K. Westaway, H. Ali, L. Baldisera, L. Laberge and J. Rousell, Tetrahedron Lett., 1986,27,279. 2 H. Jullien and H. Valot, Polymer, 1985,26, 506. 3 S. Watanabe, K. Hayama, K. H. Park, M-A. Kakimoto and Y. Imai, Makromol. Chem., Rapid Commun., 1993, 14,481. 4 M. J. Snowden and B. Vincent, J. Chem. SOC., Chem. Commun., 1992,16,1103. 5 M. J. Snowden, N. Marston and B. Vincent, Colloids Surf., 1994, in the press. 6 M. J. Snowden, J. Chem. SOC., Chem. Commun., 1992,11,803. 7 M. J. Snowden, D. Thomas and B. Vincent, Analyst (London), 1993,118,1367. 8 R. H. Pelton and P. Chibante, Colloids Surf, 1986,20,247. 9 Introduction to Microwave Sample Preparation, ed. H. M. King- ston and L. B. Jassie, American Chemical Society, Washington, DC, 1988. 10 P. J. Flory, Principles of Polymer Chemistry, Cornell University Press, 1953. 11 J. M. Sturtevant, Annu. Rev. Phys. Chem., 1987,38,463. 12 S. C. Cole and B. Z. Chowdhry, TIBTECH., 1989,7,11. Communication 4/016985; Received 22nd March, 1994

ISSN:0956-5000    

DOI:10.1039/FT9949001999

出版商:RSC    

年代:1994

数据来源: RSC