ISSN:0306-0012    

DOI:10.1039/CS98514FX009

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

ISSN 0306--0012 CSRVBR 14(3) 197-356 (I 985) Chemical Society Reviews Vol 14 No 3 1985 Page Ligand Substitution Reactions of Squareplanar Molecules By Ronald'J. Cross 197 The Historical Development of Sodium Dodecyl SulphatePolyacrylamide Gel Electrophoresis By Larry R. Sherman and James A. Goodrich 225 Activation Parameters for Chemical Reactions in Solution By Michael J. Blandamer, John Burgess, and Jan B. F. N. Engberts 237 R. A. ROBINSON MEMORIAL LECTURE Potentiometric Titrations of Aqueous Carbonate Solutions By A. K. Covington 265 TIEDEN LECTURE Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin By A. G. Sykes 283 Hard-sphere Theories of lransport Properties By J. H. Dymond 317 The Royal Society of Chemistry London

ISSN:0306-0012    

DOI:10.1039/CS98514BX011

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

ISSN 0306-001 2 CSRVBR 14(3) 197-356 (1985) Chemical Society Reviews Vol 14 No 3 1985 Page Ligand Substitution Reactions of Square-planar Molecules By Ronald J. Cross 197 The Historical Development of Sodium Dodecyl Sulphate-Polyacrylamide Gel Electrophoresis By Larry R. Sherman and James A. Goodrich 225 Activation Parameters for Chemical Reactions in Solution By Michael J. Blandamer, John Burgess, and Jan B. F. N. Engberts 237 R. A. ROBINSON MEMORIAL LECTURE Potentiometric Titrations of Aqueous Carbonate Solutions By A. K. Covington 265 TILDEN LECTURE Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin By A. G. Sykes 283 Hard-sphere Theories of Transport Properties By J. H. Dymond 317 The Royal Society of ChemistryLondon Chemical Society Reviews EDITORIAL BOARD Professor K.W. Bagnall, B.Sc., Ph.D., D.Sc., C.Chem., F.R.S.C. Professor B. T. Golding, B.Sc., M.Sc., Ph.D., C.Chem., F.R.S.C. Professor G. Pattenden, Ph.D., C.Chem., F.R.S.C. Professor P. A. H. Wyatt, B.Sc., Ph.D., C.Chem., F.R.S.C. (Chairman) Dr. D. A. Young, Ph.D., D.Sc., C.Phys., M.Inst. P. Editor: K. J. Wilkinson, B.Sc., M.Phi1. Chemical Society Reviews (ISSN 0306-0012) appears quarterly and comprises approximately 20 articles (ca. 500 pp) per annum. It is intended that each review article shall be of interest to chemists in general, and not merely to those with a specialist interest in the subject under review. The articles range over the whole of chemistry and its interfaces with other disciplines.Although the majority of articles are intended to be specially commissioned, the Society is always prepared to consider offers of articles for publication. In such cases a short synopsis, rather than the completed article, should be submitted to the Managing Editor, Books and Reviews Section, The Royal Society of Chemistry, Burlington House, Piccadilly, London, W 1V OBN. Members of the Royal Society of Chemistry may subscribe to Chemical Society Reviews at E15.50 per annum; they should place their orders on the Annual Subscription renewal forms in the usual way. All other orders accompanied with payment should be sent directly to The Royal Society of Chemistry, The Distribution Centre, Blackhorse Road, Letch- worth, Herts.SG6 1HN England. 1985 annual subscription rate U.K. E45.00, Rest of World E47.50, U.S.A. $87.00. Air freight and mailing in the U.S.A. by Publica- tions Expediting Inc., 200 Meacham Avenue, Elmont, New York 11003. U.S.A. Postmaster: Send address changes to Chemical Society Reviews, Publications Expediting Inc., 200 Meacham Avenue, Elmont, New York 11003. Second class postage is paid at Jamaica, New York 11431. All other despatches outside the U.K. by Bulk Airmail within Europe, Accelerated Surface Post outside Europe. 0The Royal Society of Chemistry, 1985 All Rights Reserved No part of this book may be reproduced or transmitted in any form or by any means -graphic, electronic, including photocopying, recording, taping, or information storage andretrievalsystems- without writtenpermission from The Royal Society of Chemistry Published by The Royal Society of Chemistry, Burlington House, London, W1V OBN Printed in England by Richard Clay (The Chaucer Press) Ltd, Bungay, Suffolk

ISSN:0306-0012    

DOI:10.1039/CS98514FP013

出版商:RSC    

年代:1985

数据来源: RSC

ISSN:0306-0012    

DOI:10.1039/CS98514BP015

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

Ligand Substitution Reactions of Square-planar Molecules By Ronald J. Cross CHEMISTRY DEPARTMENT, GLASGOW UNIVERSITY, GLASGOW, G12 8QQ 1 Introduction Ligand exchange reactions of square-planar molecules are usually divided into three main groups-nucleophilic substitutions, electrophilic substitutions, and oxidative additions followed by reductive eliminations. Scheme 1 shows three reactions of one compound which would conventionally be respectively assigned to these types. 9 cl-SN HgCl,\IPtC12(PMez Ph), I + MeHgCl SE2 MeCl oxidative addition reductive elimination Scheme 1 The basic features of these three mechanisms have been understood for year^.^-^ Each pathway has generally been considered in isolation however, though to an extent this reflects the nature of the available data.For example, nearly all the mechanistic and kinetic studies on nucleophilic substitutions have been made on compounds of platinum or palladium, and very few on square-planar compounds of iridium or rhodium, whereas the reverse is nearer the truth when applied to oxidative additions. Well-proven examples of electrophilic substitution of square- planar molecules are rare, but many reactions have been assigned to this class on the basis of comparisons with other systems. J. D. Ruddick and B. L. Shaw, J. Chem. Soc. A, 1969, 2801, 2989. R. J. Cross and R. Wardle, J. Chem. Soc. A, 1970, 840. (a)F. Basolo and R. G. Pearson, ‘Mechanisms of Inorganic Reactions’ 2nd Edn., Wiley, New York,1967; (6) L. Cattalini, frog.Inorg. Chem., 1970, 13, 263. (a) M.H. Abraham, ‘Comprehensive Chemical Kinetics’, Vol. 12, ed. C. H. Bamford and C. F. H. Tipper, Elsevier, New York, 1973; (b) 0. A. Reutov, Tetrahedron, 1978, 34, 2827; (c) F. R. Jensen and B. Rickborn, ‘Electrophilic Substitutions of Organomercurials,’ McGraw-Hill, New York,1968. (a) J. P. Coliman and W. R. Roper, Adu. Organomet. Chem., 1968,7,53. (b)J. Halpern, Acc. Chem. Res., 1970, 3, 386; (c) J. K. Stille and K. S. Y. Lau, Acc. Chem. Res., 1977, 10, 434. Ligand Substitution Reactions of Square-planar Molecules Nucleophilic substitutions and oxidative additions have been the subjects of several recent investigations and it now appears that both processes are more complicated and span a wider range in their intimate mechanisms than had previously been supposed.Moreover, there are indications that there are areas of overlap in the operation of these routes, and possibly with the intimate mechanisms of some electrophilic substitutions and dissociative ligand replacements also. This article summarizes the mechanistic information on these reactions. This now indicates the existence of a broad range of available reaction pathways, and it is concluded that it may well be unrealistic and unhelpful to think in terms of the operation of three basic routes only. Even small changes in reaction conditions, solvents, or the nature of the reactants have the capacity to alter the initial bimolecular interaction, and hence the choice of which pathway a reaction follows.For convenience, the work is divided into three sections, based loosely on nucleophilic substitutions, electrophilic substitutions, and oxidative additions. It should be realized that the labels are formalisms, owing more to traditional ideas than to the true situation. 2 Nucleophilic Ligand Replacements Thanks to many studies on kinetically inert complexes of platinum(rI), ligand replacement at square-planar complexes is one of the best understood of all inorganic reaction mechanisms. There is general agreement that the reactions are associative and involve nucleophilic attack of the entering ligand (Y) at the metal, the 5-co-ordinate adduct passing through square-pyramidal and trigonal-bipyramidal stages (equation l).3A solvolysis step often competes with the direct replacement of equation 1, leading to rate law 2.The subsequent replacement of the co-ordinated solvent molecule by Y is fast. C X \/ +Y /pt\T C X +X rate = (k,+ k,[Y])[complex] (2) The trigonal-bipyramidal complex of equation 1 has sometimes been regarded as a reaction intermediate,3b with the two square-pyramidal species as transition states. Over the years, however, many 5-co-ordinate complexes of platinum(I1) and other d8 metal ions have been isolated and investigated, and whilst there are indeed trigonal-bipyramidal molecules amongst them,6 many are closer to square-E. A. Jeffery, Aust. J. Chem., 1973,26,219; E. J. Lukosius and K. J. Coskran, Inorg. Chem., 1975,14,1922; J.K. Stalick and J. A. Ibers, Inorg. Chem., 1969, 8, 1090 A. Gleizes, A. Kerkeni, M.Dartiguenove, Y. Dartiguenove, and H.F. Klein, Inorg. Chem., 1981,20,2372; R. Favez and R. Roulet, Inorg. Chem., 1981, 20, 1598. 198 Cross pyramidal geometry,’ so any or all of the 5-co-ordinate species of equation 1 might be regarded as intermediates. The reaction profile is therefore likely to resemble Figure 1. The pathways of the entering and leaving ligands are probably off-axis,* and the relative heights of the energy maxima dictate whether bond-making or bond-breaking determines the rate. IY Yt E C\ /y T Reaction co-ordinate Figure 1 A major complication of these ligand-substitution processes, pseudorotation of the 5-co-ordinate intermediates, first became apparent quite recently from studied of isomerization reaction^.^ The overwhelming majority of substitutions studies to date have been stereospecific [that is, the arrangement of the three other ligands, trans, T, and cis,C (Figure 1 and equation 1) remained unaltered), and this had been taken as evidence that pseudorotation did not operate during such processes.Isomerization reactions of square-planar molecules, usually catalysed by nucleophiles, are common, however, and the best understood mechanism for such geometry changes, consecutive displacement, simply involves two stereospecific ligand substitutions (equation 3) and no necessity for pseudorotation. Examination of the details of the two steps of equation 3 reveals a potential for the operation of a pseudorotation mechanism: one 5-co-ordinate intermediate is common to both steps (Scheme 2) and the operation or not of pseudorotation steps would depend ’W.J. Louw, D. J. A. de Waal, and G. J. Kruger, J. Chem. SOC..Dalton Trans., 1976,2364; K. M. Chui and H. M. Powell, J. Chem. SOC.,Dalton Trans., 1974,1879,2117; E. C. Alyea and D. W. Meek, lnorg. Chem., 1972,11,1029;N. K. Roberts and S. B. Wild, Inorg. Chem.,1981,20,1892,1900;G.Annibale, L. Canovese, L. Cattalini, G. Natile, M. Biagini-Cingi, A.-M. Manotti-Lanfredi, and A. Tiripiccio, J. Chem. SOC.. Dalton Trans., 1981, 2280; A. Albinati, P. S. Pregosin, and H. Ruegger, Angew. Chem., lnt. Edn. Engl., 1984, 23, 78. R. G. Pearson, ‘Symmetry Rules for Chemical Reactions’, Wiley-Interscience, New York, 1976, p.316. G. K. Anderson and R. J. Cross, Chem. SOC.Rev., 1980, 9, 185. Ligand Substitution Reactions of Square-planar Molecules only on the relative rates of the steps depicted. Moreover, many 5-co-ordinate 8 complexes are known to be fluxional." Not surprisingly, then, reports of isomerization by pseudorotation, though few at first and often controversial, are beginning to ac~rue.~ Scheme 3 shows a good example.' 'A comparison of the rates of the chloride-catalysed isomerization with those of individual substitution steps revealed that consecutive displacement could not be responsible, and the reaction presumably proceeded via pseudorotation. (Interestingly, DMSO also catalysed the isomerization and in this case the kinetics were compatible with consecutive displacement).AxB +6 -AxB-Ax0+A +A (3) A-B A A B A cis trans A AAx+A+---A&BA A cis B A)(;+BA A B 6 A ='AB AABA A trans Scheme 2 It follows that pseudorotation could accompany any ligand replacement steps, and at least one clear example of this may already have been described.12 The ring closure shown in reaction 4 is a replacement of C1- by NH2R. It proceeds without retention of configuration, and pseudorotation of a 5-co-ordinate intermediate is the most likely cause. lo E. J. Lukosius and K. J. Coskran, Inorg. Chem., 1975,14,1926; P. Meakin and J. P. Jesson, J. Am. Chem. SOC.,1974,%, 5751,5760; J. J. MacDougall, J.H. Nelson, and F. Mathey, Inorg. Chem., 1982,21,2145. L. F. Erickson, T. A. Ferrett, and L. F. Buhse, Inorg. Chem., 1983, 22, 1461.'' M. K. Cooper and J. M. Downs, J. Chem. SOC.,Chem. Commun., 1981, 381. Cross (N\pt/dmso N-0 represents glycine, sarcosine, or N,N-dimethylglycine Scheme 3 2+r + -CI-, (4) L -1 L With 5-co-ordinate d * species being commonly fluxional, by pseudorotation or some other me~hanism,’~ a question which must be asked is why many more non-stereospecific ligand-replacement reactions of square-planar molecules have not come to light in the past? The answer is almost certainly that the systems studied have been those which, for one reason or another, would suppress such a process. For example, in the interests of simplicity molecules with only one weakly- held ligand for the leaving group, X, are frequently employed; the trans ligands, T, are often chosen to assist the departure of X, by further weakening M-X or by having a preference for the trigonal plane of the trigonal bipyramid;14 and the use of chelating ligands which further cut down the scope for unwanted side- reactions, including isomerizations, is popular.It seems inevitable now, however, that many more examples of ligand replacement without retention of configuration will be discovered. Indeed it has been pointed out that the numerous stereospecific l3 I. Ugi, D. Marquarding, H. Klusacek, P. Gillespie, and F. Ramirez, Arc. Chem. Rex, 1971, 4, 288. l4 ReJ 8, p, 318. Ligand Substitution Reactions of Square-planar Molecules >-C +z 11 11 11 11 11 11 11 Cross replacements already described and assumed to conform to a mechanism like that in Figure 1 would be indistinguishable kinetically from more complicated systems involving rapidly fluxional 5-co-ordinate intermediates.' Overall then, the broadest picture of the intimate mechanism of associative nucleophilic ligand replacement at square-planar molecules is one where the resulting 5-co-ordinate species can have a number of energy minima, and may fluctuate between them, affording a choice of pathways before a group is eliminated. Equation 1 should be extended to Scheme 4 in the general case. 3 Electrophilic Substitutions and Dissociative Ligand Replacements When the incoming nucleophile (Y of Figure 1) is an organic group, R, from an organometallic reagent, the ligand replacement process is not normally regarded as a nucleophilic substitution, although if complete charge-separation occurs to form a carbanion, R-,then clearly it would be.(This may occur with, for example, organolithium compounds. 5, More commonly, charge separation is believed to be incomplete and a transition state involving a degree of bridging through the organic group is likely. The ligand exchange reactions are usually described as electrophilic substitutions at carbon, and the reaction pathways, SE2(open) or SE2 (cyclic), are shown in Scheme 5. Both involve second-order kinetics. The SE2 (cyclic) route proceeds with retention of configuration at R,whereas SE2 (open) can proceed with inversion or retention.The transfer of the organic group from mercury to palladium in reaction 5 proceeds with retention of configuration at carbon,16' whereas transfer of an (s>-( -)-(a-deuteriobenzyl) group from tin to a similar palladium@) complex in a polar solvent proceeded with inversion. 16' Both appear to be electrophilic substitutions. L 3i....@. .. .Mi f sE2 (Open) \ L,M-x + R-M' L3MR + M'X SE2 (cyclic) Scheme 5 K. Tatsumi, R.Hoffmann, A. Yamamoto, and J. K. Stille, Bull. Chem. SOC.Jpn., 1981,54,1857; F. Ozawa, T. Ito, Y. Nakamoro, and A. Yamamoto, Bulf. Chem. SOC.Jpn., 1981, 54, 1869. (a)J.-E. Backvall and B. Akermark, J. Chem.SOC.,Chem. Commun., 1975,82; (b)J. W. Labadie and J. K. Stille, J. Am. Chem. Soc., 1983, 105, 669. Ligand Substitution Reactions of Square-planar Molecules 1 IMe -HgCl Me ‘PdCL(NCPh)2 (5) The majority of studies on this type of process have been performed on organomercury or organotin cornpound~,~ and the consensus is that if an appropriate bridging group is present (X in Scheme 5), some degree of bridging will take place, tending towards a transition state of the SE2(cyclic) form. It is this route which is most appropriate to the square-planar complexes under discussion here. Whilst such electrophilic substitution reactions are rarely considered alongside the ligand-exchange processes described in the previous section, an obvious link exists since electrophilic attack at the carbon atom by a metal ion can equally be regarded as nucleophilic attack at the metal by carbon.An example is the reaction between cis-[PtCl,(PMe,Ph),] and cis-[PtMe,(PMe,Ph),] (see below, reaction 6). This produces, initially, only the cis isomer of [PtClMe(PMe,Ph),].” The authors postulated a cyclic transition-state, pointing out that retention of configuration at both platinum atoms was entirely consistent with what might be expected from a reaction that can be described as SE2with respect to the carbon atoms, and S,2 with respect to the platinum atoms. Similar reactions showed the expected second order kinetics.’* L CI P~-L -D 2cis-[PtCIMeL21 (6) + cis-[PtMe2L21 Me L Many transfers of organic groups from tin to platinum are also believed to follow SE2 (cyclic) routes (equation 7).The acceleration by electron-releasing substituents on R and retardation by electron-withdrawing groups is consistent with this interpretation (though Wheland intermediates are possible when R is aromatic). Interestingly, trifluoroacetate complexes of platinum are more reactive than chlorides, and six-centre cyclic intermediates could be involved here (equation 8).*’ A recent variation concerns the second order reaction between cis-[PtMe,(SMe,),] and [PtCl,(SMe,),], leading to trans-[PtMeCl(SMe,),].* ’ This l7 R. J. Puddephatt and P. J. Thompson, J. Chem. SOC.,Dalton Trans., 1975, 1810. R.J. Puddephatt and P. J. Thompson, J. Chem. SOC.,Dalton Trans., 1977, 1219.l9 C.Eaborn, K. J. Odell, and A. Pidcock, J. Chem. Soc., Dalton Trans., 1978, 357. 2o C.Eaborn, K. J. Odell, and A. Pidcock, J. Chem. Soc., Dalton Trans., 1979, 758. J. D. Scott and R. J. Puddephatt, Organometallics, 1983,2, 1643. Cross proceeds after preliminary loss of Me,S from [PtMe,(SMe,),]. Such ligand losses may not, however, be general requirements. Altogether, a great many reactions involving transfer of organic groups between e.g. Pt, Pd, Au, Hg, Ge, Sn, and Pb have been postulated as proceeding by sE2 (cyclic) routes,22 though reliable mechanistic evidence is often lacking. J L (7) [Pt(02CCF,),L2] +RSnMc, 6' '6 Ney C' If we regard the reactions as nucleophilic displacements at the 4-co-ordinate metal, the potential for geometry change at the intermediate/transition-state presumably exists, as it appears to do in the more conventional nucleophilic displacement reactions discussed in the last section.No clear examples have been pointed out, however, and it is conceivable that the transition state is too short- lived to allow anything other than stereospecific exchange. The steric constraints of two sites being involved in these interactions might further reduce opportunities for rearrangement, though it must be noted that one of the best examples to date of isomerization by pseudorotation of 5-co-ordinate platinum involves chelating ligands," and other geometry-change routes l3 may be less prone to steric constraint than classical pseudorotation.An added complication may arise from the proximity of the two metal atoms in some of the S,2 (cyclic) reactions described. A significant interaction is pos~ible,'~*~~and an entire range from &2 (cyclic) (no MM' interaction) through to oxidative addition (complete M-M' bond formation) can be envisaged. Scheme 6 illustrates this progression. Thus this one type of oxidative addition reaction at least is also mechanistically related to nucleophilic attack at square-planar complexes; reductive elimination (of M'X in Scheme 6) leads to the ligand- exchanged products. It is of interest that a comparative study of organic group- 2L J. P. Visser, W. W. Jago, and C. Masters, Red. Trav. Chim. Pays-Bas, 1975,94, 70 A. Segnitz, E. Kelly, S.H. Taylor, and P. M. Maitlis, J. Organomel. Chem., 1977, 124, 113; C. Eaborn, K. J. Odell, and A. Pidcock, J. Organomet. Chem., 1978, 146, 17; R. J. Puddephatt and P. J. Thompson, J. Organomel. Chem., 1979,166,251; Z. Dawoodi, C. Eaborn, and A. Pidcock, J. Organomel. Chem., 1979,170,95; C. Eaborn, K. Kundu, and A. Pidcock, J. Chem. Soc., Dalion Trans., 1981,933; 1223. 23 R. J. Cross in 'Mechanisms of Inorganic and Organometallic Reactions', Vol. 2, ed. M. V. Twigg, Plenum, New York, 1984, Ch. 5, p. 105. Ligand Substitution Reactions of Square-planar Molecules transfer reactions involving mixed alkyl-aryl complexes of gold(II1) and platinum(I1) led to the suggestion that aryl groups are more likely to transfer by S,2 mechanisms, whereas alkyl groups are more likely to exchange by oxidative addition/reductive eliminati~n,~~ a change that may simply reflect the position of the transition-state/intermediate along the ‘scale’ of Scheme 6.Presumably any degree of metal-metal interaction at the transition state will further reduce opportunities for geometry change to occur concurrently with the ligand exchange, and it seems reasonable to conclude that pseudorotation-type complications at the SE2(cyclic) family of reactions are likely to be rare. R I L3M-M’ I X SE2 (cyclic) oxidative add it i on Scheme 6 Another variation of SE2 reaction types is the involvement of nucleophilic catalysis: in the reactions under discussion a nucleophilic agent would approach the metal of the carbon-metal bond in M’R, thus activating the carbon to the electrophilic attack of M.When the catalysing or activating nucleophile is the eventual leaving-group, X, this could clearly lead to the cyclic transition-state already encountered, and would be virtually indistinguishable from cases where the interaction of M and R was synchronous or primary. A second pathway in the abstraction of the group X by M’ is available however (Scheme 7). There is growing evidence that a preliminary electrophilic attack by a metal ion at, for example, a co- ordinated halide can lead directly to its abstraction. An example is the action on [FeI(CO),(C,H,)] of AgBF,, which produces first an adduct [Fe(IAg)-(CO),(C,H,)] +,before AgI is eliminated.25 With square-planar platinum complexes also, several reactions involve silver(1) or mercury(I1) co-ordinating to ligand halide ions leading to their abstraction.26 Other electrophilic agents such as boron halide^,^' [Me30]BF,,28 or MeS0,F 29 act in a similar manner.(These last 24 J. K. Jawad, R. J. Puddephatt, and M. A. Staltori, Inorg. Chem., 1982, 21, 332. ”B. M. Mattson and W. A. G. Graham, Inorg. Chem., 1981,20, 3186. ’6 D. A. Duddell, P. L. Goggin, R. J. Goodfellow, M.G. Norton,and J. G. Smith,J. Chem.Soc. A, 1970,545; K. R. Dixon and D. J. Hauke, Can. J. Chem., 1971,49,3252; R. J. Cross and I. G. Phillips, J. Chem. Soc., Dalton Trans., 1982,2261; R. G. Goel and R. C. Srivastava, Can.J. Chem., 1983,61,1352; Z.-Y.Yang and G. B. Young, J.Chem. SOC.,Dalton Trans., 1984, 2019. ” P. M. Druce, M. F. Lappert, and P. N. K. Riley, J. Chem. SOC.,Dalton Trans., 1972,438; H. C. Clark, K. R. Dixon, and W. J. Jacobs, J. Am. Chem. Soc., 1968,90,2259; H. C. Clark and K. R. Dixon, J. Am. Chem. SOC.,1969,91, 596. 28 P. M. Treichel, K. P. Wagner, and W. J. Knebel, Inorg. Chim. Acta, 1972, 6, 614. 29 C. Eabotn, N. Farrell, J. L. Murphy, and A. Pidcock, J. Chem. SOC.,Dalton Trans., 1976, 58. Cross reactions provide interesting contrasts with some oxidative addition reactions of the same reagents discussed in the next section.) Loss of a ligand from 4-co-ordinate square-planar complexes produces a reactive S,2 (cyclic) RL~M++ XM’R----+ L ~+ M‘X (dissociative route) Scheme 7 14-electron species.These tend rapidly to add another group (possibly after isomerization of the T-shaped intermediate), producing the ligand exchange. Whilst proposals of such mechanisms have for some years been regarded as somewhat contro~ersial,~ many possible examples have acc~mulated,~~ and evidence presented for some recent examples at least is strong.31 cis-[PtCl(m-tol)( PEt,),] 2-[Pt(m-tol)(PEt 3)2] i”~~~~-o”~ tr~~~~-[PtCl(m-tol)(PEt3)J(9) Many of these reactions proceed without the agency of obvious electrophiles like Ag+, and loss of a halide has been regarded as more-or-less spontaneous. The leaving group will certainly be solvated once free, however, and prior co-ordination to solvent is likely. This type of interaction (of the co-ordinated halide) with solvent is closely related to electrophilic attack by a metal ion: the solvent molecules take the abstracting role of M’R in Scheme 7.Thus whilst this comparatively rare route to ligand exchange at square-planar complexes seems far removed from the ‘traditional’ routes of nucleophilic attack, the relationship to catalysed SE2 processes establishes a pattern of gradually changing reaction pathways which encompass all these types. Scheme 8 shows the scope of the initial interactions leading, by degrees, through the well-recognized ligand-exchange pathways of nucleophilic substitution, sE2 (cyclic), oxidative addition/reductive elimination, and the dissociative routes. Combined with the possible variations following nucleophilic attack (Scheme 4), the overall picture is already rich in choice.j0R. J. Mureinik, Coord. Chem. Rev., 1978, 25, 1. M. J. Blandamer, J. Burgess, and R. Romeo, Inorg. Chim. Acta, 1982,65, L179; M. J. Blandamer and J. Burgess, Pure Appl. Chem., 1982, 54, 2285. Ligand Substitution Reactions of Square-planar Molecules N XEN t L Scheme 8 Relationships between the primary interactions of E-N (E and N are electrophile and nucleophile, respectively) with square-planar MXL3, which can lead subsequently to replacement of X by another ligand 4 Oxidative Addition Reactions The ligand substitution is effected by the operation both of an oxidative addition step and a reductive elimination step, as in equation Since it is the modes of [PtMe,(PEt,),] + I, -[PtI,Me,(PEt,),] -[PtMeI(PEt,),] + Me1 (10) interaction of the reacting molecules which are being compared here, we concen- trate on the oxidative addition step.Although one type of oxidative addition reaction has already been related to the nucleophilic and electrophilic substitutions discussed in the last sections, the mechanistic variations available to reactions thus described are truly vast and further extend the range of interactions encountered. L4M + AB-L4MAB (1 1) Represented in general terms by equation 11, oxidative addition reactions have usually been classified into one of three types; concerted, SN2two-step, or free The free-radical mechanism is quite distinct from the paired-electron 32 J. Chatt and €3.L. Shaw, J. Chem. SOC.,1959, 705. 33 Ref: 8, p. 408. Cross processes being compared here and will not be discussed further (though it is worth noting that it can sometimes be difficult in practice to distinguish between the operation of this route and the SN2two-step mechanism 5c9. Concerted oxidative-addition leads to products with (initially) cis entering groups. It is typified by H, addition to Vaska’s compound (equation 12), and had H been likened to 0,or C,H, additions. This similarity has recently been amplified by the description of an ‘H, complex’, (l), which probably resembles an intermediate stage in a reaction like 12.34Whereas concerted trans addition is a symmetry-forbidden proce~,~*~~ cis addition is allowed. Often described in terms of overlap of a filled d,., or dyzorbital of the metal and an empty o* orbital of the adding molecule (Figure 2),8 this would be essentially an electrophilic attack at the metal and such concerted oxidative additions have usually been referred to as this.5 As Saillard and Hoffmann have pointed however, an overlap of a filled CT orbital of A-B with an empty metal acceptor-orbital must also be involved, representing a transfer of charge in the other direction, from A-B to the metal.(Both interactions weaken A-B and strengthen M-A and M-B, see Figure 2). These authors also suggest, because of the experimental requirements of co-ordinative unsaturation, that initial flow of electron density from AB to M might be more important than the reverse.In this description, then, the concerted oxidative addition, of, for example, H, to a square-planar molecule resembles nucleophilic attack at the metal, at least in the early stages. The formal similarity between simple addition of an q ligand and concerted oxidative addition has been emphasized previo~sly,~~though if two trans ligands of the metal are bent away from the entering group(s), the energy of the interaction appears to be greatly reduced.36 0 C 34 G.J. Kubas, R. R. Ryan, B. I. Swanson, P. J. Vergamini, and H. J. Wasserman, J. Am. Chem. Soc., 1984, 106, 451. ”P. S. Braterman and R. J. Cross, Chem. SOC.Rev., 1973, 2, 271. 36 J.-Y. Saillard and R. Hoffman, J. Am. Chem. Soc., 1984, 106, 2006. Ligand Substitution Reactions of Square-planar Molecules 0 *\L.yM L Figure 2 The SN~two-step route is probably the most difficult of the mechanisms to assess.Represented by Scheme 9, it can apply to the addition of dipolar molecules such as Me1 or HCl, and involves electrophilic attack at the metal Clearly the initial interaction is exactly opposite to the processes we have examined so far, all of which can be related to nucleophilic attack at the metal. Though uncommon, there are precedents for the same atom of a molecule acting as both electrophile and nucleophile in different reactions. Equation 13, for example, shows PCI3 acting as a n~cleophile,~~whilst equation 14 involves the same P atom in an acceptor role.38 [Ni(CO)4] + 4Pc13 -[Ni(PC13)4] + 4CO (1 3) PC13 + NMe3 CI3PNMe3 (14) The case of square-planar molecules is somewhat different, however, in that the donor orbital (presumably the filled dz2)and acceptor orbital QZ) have the same symmetry with respect to the entering group along the z-axis.Evidence for the operation of this SN2 two-step process is clearly worthy of close scr. tiny to 0 B- A I B 0 Scheme 9 37 W.C. Smith, Inorg. Synfh., 1960, 6,20. 38 R. H. Holmes and R. P. Wagner, Inorg. Chew., 1963, 2, 384. 210 Cross establish whether or not it can be regarded as established, so we shall examine the evidence in greater detail than in the previous sections. Many possible examples have been shown to be first order in both reagents.3948 Examples include methyl iodide addition to Vaska's c~mplex,~~*~~ and related 946iridi~m,~' rhodium, 40 or platinum compound~,4~*~~ and similar addition reactions of other polar molec~les.~~.~~ The order of reaction is not very helpful in itself in establishing the mechanism operating here, however, since it does not distinguish between two-step mechanisms like Scheme 9 (where the initial step is rate-determining) and concerted processes like Figure 2, or indeed some compromise between the two.Scheme 9 implicates a trans geometry of addition, but this can be misleading. Geometry change at intermediate cationic complexes, [ML4A] +,is a possible fast process, and examples are known.49 Thus 16-electron 5-co-ordinate species seem at least as likely to undergo complicating isomerizations as the 18-electron analogues met in the first section following nucleophilic interactions.Some octahedral platinum(1v) complexes, products of oxidative additions to square-planar Pt" species, were found to isomerize readily by ligand loss to form 5-co-ordinate cations.48 (It should be noted also that free-radical addition routes can lead to trans products.*) Clearly, then, product geometry is not definitive in establishing the mechanistic route. In practice many examples of trans addition of polar molecules have been detected 45s0--56 (equation 15 is an example 50) including some where chelating ligands would make geometry change Examples of cispS3 addition of polar molecules, including hydrogen halides and cases where neighbouring group participation (vide infra) is important, are, however, also recorded.' 7-60 Observation of the stereochemistry at A or B (Scheme 9 and Figure 2) should 39 P.B. Chock and J. Halpern, J. Am. Chem. SOC.,1966,88, 3511. 40 I. Douek and G. Wilkinson, J. Chem. Sac. A, 1969, 2604. 41 R. Ugo, A. Pasini, A. Fusi, and S. Cenini, J. Am. Chem. SOC.,1972, 94, 7364. 42 M. Kubota, G. W. Kiefer, R. M. Ishikawa, and K. E. Bencala, Inorg. Chim. Acta, 1973, 7, 195. 43 H. Stieger and K. Kelm, J. Phys. Chem., 1973, 290. 44 J. K. Jawad and R. J. Puddephatt, J. Organomet. Chem., 1976, 117, 297. "J. P. Collman and M. R. MacLaury, J. Am. Chem. SOC.,1974, %, 3019. 46 W. H. Thompson and C. T. Sears, Inorg. Chem., 1977, 16, 769.47 J. Burgess, M. J. Hacker, and R. D. W. Kemmitt, J. Organomet. Chem., 1974,72, 121. 48 T. G. Appleton, H. C. Clark, and L. E. Manzer, J. Organornet. Chem., 1974, 65, 275. 49 P. Meakin, R. A. Schunn, and J. P. Jesson, J. Am. Chem. SOC.,1974,%, 277; A. D. English, P. Meakin, and J. P. Jesson, J. Am. Chem. SOC.,1976, 98, 422. J. P. Collman and C. R. Sears, Inorg. Chem., 1968, 7, 27. J. P. Collman, D. W. Murphy, and G. Dolcetti, J. Am. Chem. SOC.,1973,95, 2687. 52 A. Morarskiy and J. K. Stille, J. Am. Chem. SOC.,1981, 103, 4182, 53 J. L. Paterson, I. T. E. Nappier, and D. W. Meek, J. Am. Chem. SOC.,1973,95, 8195. 54 D. Strope and D. F. Shriver, Inorg. Chem., 1974, 13, 2652. 55 F. M. Miller and B. L. Shaw, J. Chem. SOC.,Dalton Trans., 1974, 480.56 R. G. Pearson and C. T. Kresge, Inorg. Chem., 1981, 20, 1878, 57 E. M. Hyde and B. L. Shaw, J. Chem. SOC.,Dalton Trans., 1975, 765. 58 L. Vaska, J. Am. Chem. Sac., 1966,88, 5325. 59 H. Singer and G. Wilkinson, J. Chem. SOC.A, 1968, 2516. "D. M. Blake and M. Kubota, Inorg. Chem., 1970, 9, 989. 21 1 Ligand Substitution Reactions of Square-planar Molecules afford a means of distinguishing between the operation of concerted or two-step ionic routes. Concerted addition should involve retention of configuration, whereas the &2 two-step mechanism would require inversion. (Free-radical processes should lead to racemization). In practice the few studies that have been made with optically active organic halides 61p62 have led to no clear conclusion^.^^-^^ One problem is the potential involvement of free-radical processes, either intrinsically or via exposure to oxygen.64 As a general caveat, it should be noted that a comparative study of several oxidative addition reactions led to the conclusion that free-radical paths were often almost competitive with other routes.66 Operation of the SN2two-step mechanism in the presence of other anionic species should be expected to lead to the incorporation of these into the product.Scheme 10depicts a clear example of this.45 When the reaction with butyl bromide was performed in the presence of Cl-, the chlororhodium complex was isolated (subsequent halogen exchange was not responsible.) Acetonitrile solvates resulted from methyl tosylate reactions.On the other hand, addition of Me1 to [Ir(SCN)(CO)L,J (L = PPh, or PMePh,) in the presence of excess SCN- in dichloroethane, or to [IrCl(CO)L,J in the presence of C1-, resulted in no incorporation of the free anions in the products,61 and the addition of Me1 to Vaska's complex in the presence of l3II- involved no uptake of radioactive iodine,67 though the geometry of these additions is believed to be trans.50Either a one-step route must operate under these conditions, or intimate ion-pairs must be retained throughout. To complete the preliminary general view of the requirements of the SN2two-step mechanism, solvent effects must be considered. Obviously polar solvents should favour and accelerate this ionic route, and this appears to be the case.The magnitude of solvent effect on, for example, H, or 0, additions is less than on RX or HX additions, which might be expected to conform toScheme 9.39-41,43,44,47,52,68 Inevitably the effects are not straightforward, as the choice of solvent can affect the course of the reactions by differentially altering the rates of competing paths. 61 R. G. Pearson and W. R. Muir, J. Am. Chem. SOC., 1970,92, 5519. 62 J. A. Labinger, R. J. Braus, D. Dolphin, and J. A. Osborn, J. Chem. SOC..Chem. Commun., 1970, 612. 63 G. M. Whitesides and D. J. Boschetto, J. Am. Chem. SOC., 1971, 93, 1529. 64 J. S. Bradley, D. E.Connor, D. Dolphin, J. A. Labinger, and J. A. Osborn, J. Am. Chem. Soc., 1972,94, 4043; J. A. Labinger, A. V. Krarner, and J.A. Osborn, J. Am. Chem. SOC.,1973,95, 7908. 65 F. R. Jensen and B. Knickel, J. Am. Chem. SOC.,1971,93, 6339. 66 R. G. Pearson and P. E. Figidore, J. Am. Chem. SOC., 1980, 102, 1541. 67 P. B. Chock and J. Halpern, Proc. lOIh Int. Cot$ Coord, Chem., 1967, 135. K. Walper and H. 2.Kelm, Z. Phys. Chem. (Neue Folge), 1978, 113, 207. 212 Cross BuI N-N /Rh/ % N-N' N-N F-I U sdlv Cl Scheme 10 For example, cis addition of HX to Vaska-type complexes was found in benzene or toluene,68 but some trans addition is also apparent in MeOH, MeCN, H20,or DMF.60 Moreover, some solvents may exert other effects: DMF reacts with Me1 leading to a 20-fold increase in conductivity:' and casting some doubt on the suitability of this solvent for kinetic investigation.Already then it can be seen that there is not a clear-cut class of reactions adhering simply to the SN2two-step route, although a few systems do show strong evidence for the operation of an ionic mechanism compatible with Scheme 9. Further consideration of specific cases is needed to identify the intimate interactions involved. The suggestion that these oxidative addition reactions of organic halides and similar molecules proceed by nucleophilic attack at carbon originated in the first instance from the similarity of the activation parameters (particularly the large negative value of ASt) for Me1 and [IrX(CO)(PPh,),] 39 to those for the reactions of alkyl halides and tertiary amines. These latter reactions are well established as proceeding via linear SN2displacements at carbon, so a transition state like (2) seemed plausible.Later studies on related oxidative additions, however, revealed that the marked solvent effects on rate did not exactly parallel the change in solvent polarity, and the substituent effects on rates of addition of para substituted benzyl halides did not resemble those of their reactions with ~yridine.~~ The authors concluded that an asymmetric transition-state like (3) was more likely than a linear one, and explained the large negative AS$ and solvent effects by the marked deformations of the iridium complexes from planarity. A greater degree of Ir-C bond making than of C-X bond breaking was necessary to account for observed electronic effects (vide infra), and the variable degree of Ir X bond formation could usefully account for the previously mentioned ambiguities over retention or inversion of configuration at carbon.Ligand Substitution Reactions of Square-planar Molecules L HH LPPh3 (2) Activation volume measurements of the addition of Me1 or 0, to Vaska’s complex in several solvents provided more inf~rmation.~~ A V are negative, in keeping with a bond-making associative rate-determining step. The values for Me1 were not as great as for the Menschutkin reaction between Me1 and pyridine, and the authors considered that they fitted a linear transition-state such as (2) better than simultaneous formation of two bonds as in (3) (interestingly, they pointed out that Ir I CH, bond making would fit the data as well as Ir CH, I).The reactions of MeS0,F or MeSO,CF, with Vaska’s complex or47353954*69 [RhC1(Ph,PC,H6PPhC3H6PPh,)l 53 were also found to be in keeping with nucleophilic displacement of SO,F-or S03CF,- from carbon, and with a linear transition-state as in equation 16. The reactions were more rapid than with MeI, probably because SO,F-is a better leaving group. Altogether, then, the evidence in favour of operation of the SN2two-step route in Some examples is quite compelling, though a gradation of intermediate configurations ranging from (2) to (3) seems likely. Further comparative studies of such reactions both strengthen the case for this mechanism (Scheme 9) and add interesting extra detail./ Me x\ PPh, ‘\ I ,/’Ir OS0,F 69 D. Strope and D. F. Shriver, J. Am. Chem. SOC.,1973, 95, 8197. Cross Several studies of oxidative additions to iridium or rhodium complexes, [MX(CO)L,], found consistently that more basic or electron-donating ligands, L, (usually tertiary phosphines) increased the reaction rate.39-42.46*68 This is entirely consistent with increased electron-density on the metal atom enhancing nucleophilic attack by the metal on the substrate. The rates of reaction generally parallel the basicity of the metal atom, as determined from the extent of pro- tonation by benzoic acid.70 (It should be noted that tertiary phosphines exert a steric effect also:41,46 indeed when L is P(0-tol),, oxidative additions to [IrX(CO)L,] do not proceed at all.46) The effects of varying the halide, X, of [MX(CO)L,] are less easy to explain.For additions of H,, 02,39and hydrogen halides (which usually undergo cis additions)68 rates increase in the order of X = C1 < Br < I. Par- alleling increasing basicity at the metal,70 this could again be interpreted in terms of electrophilic attack at the metal. The order for the addition of organic halides, however, is X = F B C1 > Br > I, the reverse of that observed abo~e.~~*~~*~~The basis of an explanation may lie in the fact that the ligands L are usually trans in both the reactants and products, and probably do not change position during the course of reactions. X and CO on the other hand, are in the plane of entering H,, O,, or (cis)HX, and are displaced as the new bonds form.This is presumably also the case with transition states resembling (3) for organic halide addition,68 and it is quite conceivable that CO and X bend towards a trigonal- bipyramidal geometry even with a linear transition-state. If so it would be quite reasonable for L, and C0,X to exert their electronic effects in different ways, as is observed. It should be noted that the apparent conformality of the halogen effect in the H, or 0,additions could be misleading since, as we have seen, these interactions could well be nucleophilic. The relative effects on rate of altering the halide are not as great as those brought about by changing L.Changing the halide of the adding molecule RX has a relatively small but when R is aryl, it is found that electron-withdrawing substituents increase the reaction rate.71-73 This, too, is indicative of electrophilic attack by carbon on the metal, though a three-centre transition-state like (3) could still operate.72 CF31 fails to add to [RhX(CO)(PPh,),], whereas Me1 reacts readily.40 Reversal of the polarity of the C-I bond might explain this, and would lend support to the SN2two-step route as the general mechanism for organic halide addition, but steric or other factors could be involved. In some cases ligand loss from the square-planar molecules prior to the oxidative addition step has been shown not to and this is presumed to be so with the majority of reactions described above. A few examples have been described, however, where L is lost from [RhCIL,] 74 or [IrX(CO)L,] prior to addition.The increased lability of rhodium compounds or high temperatures in the iridium cases 'O A. J. Deeming and B. L. Shaw, J. Chem. SOC.A, 1969, 1802. 71 J. Blum, M. Weitzberg, and R. J. Mureinik, J. Organomet. Chem., 1976, 122, 261. 72 R. J. Mureinik, M. Weitzberg, and J. Blum, Inorg. Chem., 1979, 18, 915. 73 D. Milstein and J. K. Stille, J. Am. Chem. SOC.,1979, 101, 4992. 74 Y. Ohtani, M. Fujimoto, and A. Yamagishi, Bull. Chem. SOC.,Jpn., 1977, 50, 1453. Ligand Substitution Reactions of Square-planar Molecules were probably responsible. Though described as ligand loss, the process is most likely one of ligand displacement by solvent. The solvated species formed appear to undergo oxidative additions by the same type of mechanisms as described, though at different rates to their precursor^.^^,^^ An interesting variation is the iodide-catalysed methyl iodide addition to [RhI(CO)L,].75 When L is Ph,As or Ph,Sb (but not Ph,P), it is displaced by iodide and the anionic complex formed adds Me1 much faster than the neutral parent compound (Scheme 1 l), as might be anticipated for electrophilic attack at the metal.Whilst this type of system does not appear to be common, it can have profound effects when it operates. For example, dissociated triaryl-phosphine from [RhCl(CO)L,] reacts with Me1 to form [PAr,MeJI, and this iodide in turn co- ordinates to rhodium forming [RhClI(CO)L] -,which reacts much more rapidly than the original complex.76 An induction period sometimes observed for such reactions might be thus e~plained.~’,~~ McI, slow McI, fast1 1 IRhMeI,(CO)$l + I’ = [RhMcIjCO)L]-+ L [RhMe12(CO)Ll + L + 1-Scheme 11 Iodide catalysis of a different kind has been reported by Louw and co-worker~.~~.~’Rather than displace a ligand, I- adds to [Ir(cod)(phen)] +,and the 5-co-ordinate [IrI(cod)(phen)] reacts oxidatively more rapidly with Me1 (Scheme 12)77 or 02”than does the square-planar cation.(Indeed an earlier report indicated that Me1 would not react at all in the absence of I-.79) Activation parameters for the iodide-catalysed k, step resemble those for the k, step indicating the same type of transition-state configuration; reasonably SN2displacement of I -from carbon.Nucleophile catalysis of this sort has also been established for the addition of hydrogen halides to several square-planar iridium complexes. 56.79-8 Co-ordination of polar solvent molecules as well as halide ions enhance the 75 D. Forster, J. Am. Chem. SOC.,1975, W, 951. 76 S. Franks, F. R. Hartley, and J. R. Chipperfield, Inorg. Chem., 1981, 20, 3238. 77 D. J. A. de Waal, T. I. A. Gerber, and W. J. Louw, Inorg. Chem., 1982, 21, 1259. 78 W. J. Louw, T. I. A. Gerber, and D. J. A. de Waal, J. Chem. SOC.,Chem. Commun., 1980, 760. 79 G. Mestroni, A. Camus, and G. Zassinovich, J. Organomet. Chem., 1974, 73, 119. J. E. Chapman, D. J. A. de Waal, and W.J. Louw, J. Chem. SOC.,Chem. Commun., 1977, 845. T.V. Ashworth, J. E. Singleton, D. J. A. de Waal, W. J. Louw, E. Singleton, and E. Van der Stok, J. Chem. SOC.,Dalton Trans., 1978, 340. 216 Cross abstraction of H+ from HX, and it is interesting to speculate to what extent this effect might account for the acceleration of &2 two-step mechanisms by polar media. K[Ir(cod)(phen)l+ + I' 7[Ir(cod)(phen)Il [IrMeI(cod)(phen) 1 + I-Scheme 12 The possible importance of polar-solvent co-ordination in promoting two-step oxidative additions is given more emphasis by the discovery by Shaw and co- workers of neighbouring group participation in some systems. Oxidative additions of HC1, MeCl, MeBr, MeI, CCl,, Cl,, and PhCOCl to phosphine complexes of Rh', Ir', or Pt" are all enhanced when the phosphine is PMe,(o-MeOC,H,), compared to PMe,Ph, and nucleophilic attack by ligand oxygen at the metal, making it in turn more nucleophilic, is proposed as the explanation [See structure (4)].55*82983 Interestingly, no activating effect of these ortho-methoxy groups was found for H, addition to [IrCl(CO)L,], and although a low polarity transition-state could be the explanationYs7the view that H, approach actually resembles nucleophilic attack 36 is a reasonable alternative.Taking account of nucleophilic catalysis in oxidative addition reactions both weakens and strengthens the case to be made for the SN2 two-step route. When nucleophilic catalysis operates, even by solvent co-ordination, the species being 82 H.D. Ernpsall, E. M. Hyde, C. E. Jones, and B. L. Shaw, J. Chem. Soc., DuffonTrans., 1974, 1980. A. G. Constable, C. R. Langrick, B. Shabanzadeh, and B. L. Shaw, lnorg. Chim. Acta, 1982,65, L151. Ligand Substitution Reactions of Square-planar Molecules attacked by the electrophile is an 18-electron 5-co-ordinate molecule, and not the 16-electron square-planar complex under scrutiny. There are many examples of electrophilic attack at 18-electron species, and the process can be regarded as well established.8L87 It seems probable that some apparent examples ofthe SN2two-step route will be, in reality, assignable to this 18-electron route, thus reducing the number of authentic examples. On the other hand it seems clear that many can not be.Some proceed in non-polar solvents, where a significant solvent intereaction seems unlikely. In other cases no change has been noted, and no incorporation observed, when (potentially catalytic) anions have been present. Since there is good reason for believing that 18-electron species undergo closely related processes to these 16-electron molecule^,^^.^^ the case for electrophilic attack at least at some square-planar molecules is strengthened by the comparison. To this evidence we should now add the isolation of a number of compounds which can be described as L,M -E. These correspond to the transition state following electrophilic attack in the oxidative addition sequences described above. Examples include adducts of Vaska's complex and related molecules with BF, or B(C6F5)3, which are described in terms of Ir -B co-ordinate bonding.88 Also, there is evidence to indicate that many metal-metal bonded complexes containing 5-co-ordinate platinum or palladium should be described as electron-pair donation from the Pt or Pd atom^.^'-'^ Compound (5) is an example.Clearly it is not only simple species like H+ or CH3+ which behave as electrophiles to square-planar molecules. With the establishment (finally!) of the electrophilic attack route, we now have the curious situation that a square-planar molecule might undergo oxidative addition by a nucleophilic attack followed by electrophilic attack, or Dice versa! With the potential at intermediate stages for geometry change, and for gradations 84 J.P. Collman and W. R. Roper, J. Chem. Sac., Chem. Commun., 1966, 244. 85 A. J. Deeming and B. L. Shaw, J. Chem. SOC.A, 1970, 3356. 86 A. J. Hart-Davis and W. A. G. Graham, Inorg. Chem., 1970,9,2658. 87 A. J. Oliver and W. A. G. Graham, Inorg. Chem., 1970, 9, 243. R. N. Scott, D. F. Shriver, and D. Lehman, Inorg. Chim. Acta, 1970, 4, 73. 89 A. F. M. J. van der Ploeg, G. van Koten, and K. Vrieze, J. Organomet. Chem., 1982, 226, 93. 90 A. F. M. J. van der Ploeg, G. van Koten, K. Vrieze, A. L. Spek, and A, J. M. Duisenberg, Organometallics, 1982, 1, 1066. 91 A. F. M. J. van der Ploeg, G. van Koten, K. Vrieze, and A. L. Spek, Inorg. Chem., 1982, 21, 2014. 92 A. F. M. J. van der Ploeg, G. van Koten, and C.Brevard, Inorg. Chem., 1982, 21, 2878. Cross away from these classical extremes, the number of possible reaction pathways is again dramatically extended. One more variation needs now to be explored. Methanolic hydrogen chloride reacts with organoplatinum complexes to cleave R-groups, as in equation 17. Early studies indicated that the mechanism involved HCI CPtR2L2I -RH CPtRC1LJ HCI CPtC12L21 (17) oxidative addition of HCl to Pt (via H+ attack at the metal) followed by reductive elimination of RH.93 More recent studies on arylplatinum compounds found the reactions to be first order in [H'] and zero order in [Cl-1. The reaction rate was increased by electron-donating aryl sub~tituents.'~ The authors considered that Scheme 13 best accounted for their observations, the rate-determining step being proton attack at the Pt-C bond, a step consistent with the very high deuterium kinetic isotope effects observed.The 3-co-ordinate intermediates could well be solvated, but prior co-ordination of solvent or anion seems unlikely since the reactions are kinetically independent of [Cl-1. Direct attack of [H'] at the carbon atom, in these cases leading to Wheland-type intermediates (6),offers an alternative pathway, and we have now reached a situation identical to the elimination L Ar \/ -Pt H+. slow L Ar IArH Pt /" -L L\ CI -\+Pt L /\Ar I *O\ Pt /L solv /L 2. L/A*r Scheme 13 93 U. Belluco, M. Giustiniani, and M. Graziani, J. Am. Chem. SOC.,1967,89,6494. 94 R.Romeo, D. Minniti, S. Lanza, P. Uguagliati, and U. Belluco, fnorg. Chem., 1978, 17, 2813. Ligand Substitution Reactions of Square-planar Molecules pathways already depicted in Schemes 7 and 8, resultant on electrophilic attack at a co-ordinated ligand. p! ” L-Since electrophilic attack might take place at either the metal atom, ligand atom, or metal-ligand bond, it seems reasonable that migration of the attacking electrophile across this bond might occur in some cases. This would be difficult to prove, though a theoretical study has indicated that such migrations are feasible,” (though more facile at 5-co-ordinate 18-electron species), and hydrogen migrations from carbon to metal (a-eliminations) are common,96 though not always complete.Equations 18 and 19” show two equilibria which appear to involve such migrations. CT““: The base-catalysed rearrangement shown in equation 20 may proceed via migration of I and PMe, across a Rh-C bond,’* and several similar reactions of platinum complexes could well be related.” ” J. V. Ortiz, Z. Havlas, and R. Hoffman, Helv. Chim. Acfa, 1984, 67, 1.’‘ R. J. Cross in ‘The Chemistry of the Metal-Carbon Bond‘, ed. F. R. Hartley and S.Patai, John Wiley & Sons, New York, 1985, Vol. 2, p. 559. ’’ (a)C. Crocker, R. J. Errington, R. Markham, C. J. Moulton, K. J. Odell, and B. L. Shaw, J. Am. Chem. SOC.,1980,102,4373; (b)H. D. Empsall, E. M. Hyde, R. Markham, W. S.McDonald, M. C. Norton, B. L. Shaw, and B. Weeks, J. Chem. SOC.,Chem.Commun., 1977, 589. R. Feser and H. Werner, Angew. Chem., Int. Edn. Engl., 1980, 19, 940.’’ (a)N. J. Kermode, M. F. Lappert, B. W. Skelton, A. H. White, and J. Holton, J. Organomel. Chem., 1982, 228, C71; (b) J. R. Moss and J. C. Spiers, J. Orgunomet. Chem., 1979,182, C20 (c) N. J. Kermode, M. F. Lappert, B. W. Skelton, A. H. White, and J. Holton, J. Chem. SOC.,Chem. Commun., 1981, 698. Cross T Finally, the unusual oxidative addition of Me1 to a square-planar platinum complex (equation 21) might also involve migration across the Pt-C bond."' The possibility of these migrations, like the potential for geometry change at the various 5-co-ordinate intermediates we have met, all indicate caution in inferring mechanistic detail from product geometry.Me1BF1, -5 Concluding Remarks Though this survey is far from comprehensive and takes but a superficial look at some of the reaction types discussed, it is clear that a relationship between many types of reaction mechanism can be demonstrated, ranging gradually right from nucleophilic attack to electrophilic attack at the metal, and encompassing nucleophilic substitution, SE2(cyclic) interactions, oxidative additions, dissociative ligand exchange, and even some reactions of co-ordinated ligands. These descriptions must therefore be regarded as extremes and attempting to classify reactions simply as one of these types may be misleading. Scheme 14 summarizes the main pathways in stylized manner. Ligand X of [MXL,] is replaced by nucleophile, N (which can also be part of N-E or N-and E+).Evidence exists for the operation of all the pathways described in Scheme 14, though the number of choices will depend on the complexity of the interacting systems (e.g. L, could be three different ligands, creating divergence of some of the pathways and increasing the number of stereochemical options: a choice of leaving groups would lead to yet more variations). Exactly which pathway(s) any individual system follows may be difficult to predict, since it will depend on the nature of all the variables shown in Scheme 14,as well as on the hidden ones such as solvent (which can interact with the attacking species as well as the square-planar loo D. M. Grove, G. van Koten, J. N. Louwen, J. G. Noltes, A. L.Spek, and H. C. Ubbels, J. Am. Chern. SOC.,1982, 104,6609. 221 Ligand Substitution Reactions of Square-planar Molecules + z \ I -1 + u\ ?',i I 2-Z w;,1-1 2-Z-Xf f u-x -1 tf -1-1 Scheme 14Interactions of E-N (or E+and N-) with [ML,X], leading toreplacement of X by N Cross molecule). At present it would seem that much more work is needed before predictions of the reaction pathways followed by square-planar molecules can be made confidently, though an understanding of the range of available options is at least a step in the right direction.

ISSN:0306-0012    

DOI:10.1039/CS9851400197

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

The Historical Development of Sodium Dodecyl Sulphate- Polyacrylamide Gel Electrophoresis By Larry R. Sherman* and James A. Goodrich DEPARTMENT OF CHEMISTRY, UNIVERSITY OF SCRANTON, SCRANTON, PA 18510, U.S.A. Electrophoresis is probably the most widely used method of biochemical analysis. Its use in protein separation, molecular weight determination, and peptide mapping has enabled the characterization of many complex mixtures, including body fluids and cell extracts. Many individuals have contributed much time to the development of functional electrophoretic techniques. The development of the state-of-the-art technique for sodium dodecyl sulphate-polyacrylamide gel electrophoresis did not occur overnight but has slowly evolved throughout the course of the twentieth century.All electrophoretic techniques fall into one of two categories: moving boundary electrophoresis ’ or zone electrophore~is.~Techniques of moving boundary electrophoresis exploit the fact that similar molecules have charge properties which are also very similar. These similar molecules will move close together as a band during electrophoresis, and boundaries will be formed between substances with slightly different electrophoretic mobilities. Competent techniques of moving boundary electrophoresis require much too complicated and expensive equipment for regular laboratory use.4 Zone electrophoresis techniques are based on the fact that charged particles which are supported on a relatively inert and homogeneous solid or gel framework will migrate as separate zones depending upon their specific characteristic^.^ Theoretically, zone electrophoresis can achieve complete separation of all of the electrophoretically different components of a mixture. Many different supporting media have been applied to zone electrophoretic techniques, all of which have specific advantages and disadvantages.Of the supporting media in use today, polyacrylamide gels are probably the most versatile and extensively used. Electrophoresis has existed as a means of biochemical analysis for about fifty years. Experimentation with electrophoretic methods began around the turn of the ~entury.’*’~~7’Attempts to develop an electrophoretic method for separating proteins were unsuccessful until 1937when Tiselius separated proteins in a solution * Author to whom correspondence should be sent ‘ 0.Teague and B.H. Buxton, J. Exp. Med., 1907, 9, 254. C. W. Field and 0.Teague, J. Exp. Med., 1907, 9, 86. R. J. Wieme, ‘Agar Gel Electrophoresis,’ American Elsevier Publishing Co., Inc., New York, 1965. ‘A Biologist’s Guide to Principles and Techniques of Practical Biochemistry’, B. L. Williams and K. Wilson, American Elsevier Publishing Co., Inc., New York, 1975. D. J. Shaw, ‘Electrophoresis’, Academic Press, New York, 1969. C. W. Field and 0.Teague, J. Exp. Med., 1907, 9, 222.’H. Picton and S. E. Linder, J. Chem. Soc., 1892, 61, 148. Development of Sodium Dodecyl Sulphate- Polyacrylamide Gel Electrophoresis through electrophore~is.~*~ Tiselius' method used a moving boundary technique that allowed for the formation of initial sharp boundaries.8 Zone electrophoresis, as an analytical method, was not used until 1952, when two methods of zone electrophoresis were proposed; neither of these, however, provided a resolving power as great as that of the Tiselius method.In 1955, Smithies described a technique of zone electrophoresis which used a starch gel as the supporting medium.12 The resolving power of the technique in many cases was found to be equal, if not superior, to that of the Tiselius method. After the introduction of starch gels in 1955, experimentation began with other forms of gels as possible supporting media for zone electrophoresis. Raymond and Weintraub in 1959 introduced a polyacrylamide gel as a useful stable, flexible gel for zone electrophoresis.13 The gelling agent present in the polyacrylamide gel was named Cyanogum, and was formed through a polymerization cross-linking reaction between two organic monomers, acrylamide and N,N-methylenebisacryl- amide.The gel was found to be best for electrophoresis when three- to five-percent Cyanogum was added to acid or alkaline buffers (0.3Mto 0.OlM). Raymond and Weintraub found the gel, once formed, to be optically clear and colourless, flexible and elastic, stable, and completely insoluble in water.' Research with polyacrylamide gel advanced slowly after the introduction of Cyanogum gel. Along with co-workers, Raymond attempted to perfect his method of polyacrylamide gel electrophoresis and by 1962 an apparatus which they designed was being produced by the E-C Apparatus Corporation of Swathmore, Pennsylvania.The apparatus was a vertical gel electrophoresis cell which consisted of an upper and lower electrode chamber with cooling water channels embedded in the walls of the gel compartment.17 Raymond and his research group were not the only individuals performing research with PAGE. In 1962,Chang et al. were able to obtain clear resolution of at least twenty-five bands with a soluble protein preparation made from a mutant strain of Neurospora crassa.18 Only eighteen bands were obtained using a starch-gel technique.I8 Davis and Ronstein also contributed much to the early techniques of PAGE by developing improved buffer systems which allowed high-resolution separations of protein^.'^ The significance of pore size in PAGE had not been fully realized by 1962, but this rapidly changed.Raymond and Nakamichi had noticed that changes in the gel concentration often resulted in changes in the separation of some bands, and even A. Tiselius, Trans. Faraday SOC., 1937, 33, 524. A, Tiselius, Biochem. J., 1937, 31, 313. lo H. G. Kunkel, and A. Tiselius, J. Gen. Physiol., 1951, 35, 89. l1 H. G. Kunkel, and P. J. Slater, Proc. Soc. Exp. Med., N. Y., 1952, 80, 42. l2 0.Smithies, Biochem. J., 1955, 61, 629. l3 S. Raymond and L. Weintraub, Science, 1959, 130, 711. l4 S. Raymond and Yi-Ju, Wang, Anal, Biochem., 1960, 1, 391. l5 S. Raymond and M.Nakamichi, Anal. Biochem., 1962, 3, 23. l6 S. Raymond, M. Nakamichi, and B. Aursell, Nature, 1962, 195, 697. l7 S. Raymond, Clin. Chem., 1962, 8, 455. L. 0. Chang, A. M. Srb, and F. C. Steward, Nature, 1962, 193, 756. l9 B. J. Davis and L. Ronstein, Ann N.Y. Acad. Sci., 1964, 121, 321. Sherman and Goodrich the disappearance of others. He hypothesized that these effects were related to the pore size of the polyacrylamide gels.16 In 1963, Hjerten proved that the migration velocity of a protein in polyacrylamide gels depended not only upon the charge and molecular size of the protein, but upon the pore size of the By 1964, polyacrylamide gels of variable pore sizes were readily being made by varying the gel concentration.2 ’ Many variations and applications in the use of electrophoresis on polyacrylamide gels arose between 1964 and 1966.A majority of these fell into the area of discontinuous electrophoresis. Jovin et al. developed an apparatus which was suitable for preparative, temperature-regulated PAGE in discontinuous buffer systems.22 Through the use of this apparatus, complete separation of haemoglobins A and S was obtained from loads of haemolysate as large as 40 mg. Another apparatus for preparative, discontinuous electrophoresis on polyacryl- amide gels 23 resulted from slight modifications in the conventional vertical system of Smithies.24 This apparatus was capable of providing greater than seventy- percent recovery of proteins.23 Many other pieces of apparatus for discontinuous electrophoresis on polyacrylamide gels were also developed during this two year peri~d.~~-~~ The popularity of PAGE as an analytical method also grew rapidly between 1964 and 1966. Through the use of discontinuous zone electrophoresis on a ten-percent polyacrylamide gel researchers were able to separate soluble ribonucleic acid into four major fractions.30 Another group of researchers found that polyacrylamide gels could be used for electrophoretic sieving of intracellular particle^.^' This finding came about through the separation of the 30s and 50s ribosomes of Escherichia ~oli.~’ Polyacrylamide gel was found to be a good medium for micro- immunoelectrophoresis after proteins in human urine and serum were identified by PAGE using 2.8% acrylamide gel plates.32 PAGE also allowed the simultaneous determination of serum-haemoglobin binding capacity and haptoglobin type.33 The previous procedure required two different analyses.In 1966, Maizel published a description of a mechanical fractionator which produced electropharograms by extrusion of polyacrylamide gels through a narrow orifice in a continuous, sequential stream.34 The main point of his publication was that his fractionator could with ease produce electropharograms of 2o S. Hjerten, J. Chromatogr., 1963, 11, 66. “ J. Vos and H. J. van der Helm, J. Neurochem., 1964, 11, 208. 22 T. Jovin, A. Chrambach, and M. A. Naughton, Anal. Biochem., 1964,9, 351. 23 E. J. Devillez, Anal. Biochem., 1964, 9, 485.24 0.Smithies, Biochem. J., 1959,71, 585. ” C. Schwabe, Anal. Biochem., 1966, 17, 201.’‘ G. L. Wright and W. L. Mallmann, Proc. SOC.Exptl. Biol. Med., 1966, 123, 22. 27 R. C. Allen and D. J. Moore, Anal. Biochem., 1966,16,457. G. R. Stepherd and L. R. Gurley, Anal. Biochem., 1966, 14, 356. 29 L. J. Rogers, Biochim. Biophys. Acta, 1965, 94, 324. ’O E. G. Richards and W. B. Gratzer, Nature, 1964, 204, 878. ” S. Hjerten, S. Jerstedt, and A. Tiselius, Anal. Biochem., 1965, 11, 211. ” H. J. Keutel, C. R. Ammons, Jr., and W. H. Boyce, Invest. Urol., 1964, 2, 22. 33 T. G. Foris, R. E. Easterling, K. J. Nelson, and R. E. Budd, Am. J. Clin. Pathol, 1966, 46, 385. 34 J. V. Maizel, Jr., Science, 1966, 151, 988. Development of Sodium Dodecyl Sulphate- Polyacrylamide Gel Electrophoresis equal quality to those obtained by laborious manual sectioning.In one step of his procedure 0.05%sodium dodecyl sulphate (SDS) was pumped into the carrier-fluid inlet at a rate of 4 ml min-’ in order to carry the crushed gel.34 He used the SDS because of its powerful virus-dissociating ability, which he desired in his work with Adenovir~ses.~~ HeMaize1 only mentioned SDS four times in his p~blication.~~ obviously did not realize the future effect that SDS would have on PAGE but none-the-less he was the first to use it in association with polyacrylamide gel electrophoresis. SDS did not become prominent in electrophoresis until after 1970, but between 1966 and 1970 many PAGE techniques were developed.In 1967, refinements of electrophoresis on polyacrylamide gels, based upon the methods of Raymond and Weintraub,’ and Davis and Ronstein,” allowed higher resolution of normal serum protein^.^' The discontinuous electrophoretic method was modified so that large 22 mm gels could be used.36 These large gels were desirable for preparative electrophoresis. At the same time, an apparatus for preparative electrophoresis was developed for a loading of one gram of protein.37 Techniques for gel slicing38.39 and a technique for the preservation of polyacrylamide gels 40 were discovered. Other new types of apparatus for PAGE were also de~eloped.~’-~~ A method for estimating the molecular weights of proteins by PAGE was defined in 1967.45 Through use of the vertical PAGE method of Raymond and Weinstraub,’ calibration curves were set up comparing the ratio of the mobilities of known proteins in two different gel concentrations to the log of their molecular weights.45 From this curve, crude estimations of molecular weights could be made.A year later, a new method was published for the estimation of the molecular weights of proteins with a precision of & 4%.46In this work a calibration curve was prepared by plotting the molecular weights of well-characterized proteins against the slope of the line resulting from the log of the relative protein mobility versus the acrylamide gel c~ncentration.~~ These methods were later perfected and give fairly accurate res~lts.~~.~~ A technique for electrophoresis on a polyacrylamide concentration-gradient gel was devised to enable full separation of a mixture of proteins.49 The theory was that the gradual, constant variation in pore size would separate all sizes of proteins, but the first attempt was not very succe~sful.~~ In 1968, a pore-size gradient method 35 R. F.Ritchie, J. G. Harter, and T. B. Bayles, J. Lab. Clin. Med., 1966, 68, 842. 36 R. C. Peterson, J. Pharm. Sci., 1967, 56, 1489. 37 S. Hjerten, S. Jerstedt, and A. Tiselius, Anal. Biochem., 1969, 27, 108. H. C. Birnboim, Anal. Biochem., 1969,29, 498. 39 B. Garfinkle, Anal. Biochem., 1970, 38, 552. 40 I. Smith and J. B. Weiss, J. Chrornatogr., 1967, 28, 494. 41 M. DeMets, A. Lagosse, and M. Radaey, J. Chromatogr., 1969,43, 145.42 K. Felgenhauer, Biochim. Biophys. Acfa, 1967, 133, 165. 43 J. Wein, Anal. Biochem., 1969, 31, 405. 44 W. S. Bont, J. Geels, and G. Rezelman, Anal. Biochem., 1969, 27, 99. *’ J. Zwaan, Anal. Biochem., 1967, 21, 155. 46 J. L. Hedrick and A. J. Smith, Arch. Biochem. Biophys., 1968, 126, 155. 47 C. R. Parish and J. J. Marschalonis, Anal. Biochem., 1970, 34, 436. 48 D. P. Blatter and F. J. Reithel, J. Chromatogr., 1970, 46, 283. 49 J. Margolis and K. G. Kenrick, Biochem. Biophys. Res. Commun., 1967, 27, 68. Sherman and Goodrich was developed which successfully enabled the separation into several bands of two highly concentrated proteins.’’ This method was further perfected using a polyacrylamide gel gradient ranging from 5% to 2O%.’ An additional variation in PAGE techniques between 1966 and 1970 allowed the preparation of mixed acrylamide and agrose gels.52 These gels allowed for higher resolution and greater separation of protein fractions.After the first use of SDS in association with PAGE in 1966, Shapiro, Vinuela, and Maizel realized that it was possible to estimate the molecular sizes of polypeptides from the relative mobilities of their SDS-complexes on polyacrylamide gels. The method which they developed was rapid and versatile but had several flawss3 By 1969 the flaws were corrected and the method was used to determine the molecular weights of well-characterized proteins with an accuracy of at least Later in the same year the method was further perfected to determine molecular weights of proteins with an error of less than +6%.55 Sodium dodecyl sulphate is a powerful, negatively charged detergent.It binds to the hydrophobic regions of protein molecules and causes them to unfold into extended polypeptide chains. This frees the individual protein molecules from their associations with other proteins or lipid molecules and renders them freely soluble in the detergent solution.56 Whenever SDS is used, a reducing agent such as mercaptoethanol is usually added to break any S-S bonds present in the proteins.56 The SDS-solubilized proteins are associated with many negatively charged detergent molecules and, as a result, each protein migrates toward the positive electrode when a voltage is applied across the gel.56 Complete separation of all proteins occurs strictly according to size, regardless of their inherent solubilities in the aqueous solution.56 The importance of this compound in biochemical analysis can not be stressed enough.By using reducing agents, the correct molecular weights of proteins were determined by SDS-PAGE in 1972.” Indiscriminate use of non-reduced proteins and protein aggregates gave erroneous estimates for molecular weight determination by SDS-PAGE.” Later in the same year, the separation of human serum by SDS-PAGE was found to result in the resolution of twice as many component proteins.58 Another research group 59 validated the molecular weight estimates of several membrane proteins through the use of SDS-PAGE.Confidence in the analytical accuracy of SDS-PAGE was growing. During the following three years (1973-1975) SDS-PAGE expanded from isolated use by few researchers into one of the most common methods of ’O E. Epstein, Y. Houvras, and B. Zak, Clin. Chim. Acra, 1968, 20, 335. ’I G. G. Slater, Anal. Biochem., 1968, 24, 215. ” U. Ringborg, E. Egyhazi, B. Daneholt, and B. Larnbert, Nature 1968, 220, 1037. ”A. L. Shapiro, E. Vinuela, and J. V. Maizel, Biochem. Biophys. Rex Commun., 1967, 28, 815. 54 K. Weber and M. Osborn, J. Biol. Chem., 1969, 244,4406. ”A. K. Dunker and R. R. Rueckert, J. Biol. Chem., 1969, 244, 5074. s6 B. Alberts, D. Bray, D. Lewis, J. Raff, K. Roberts, and J. D. Watson, in ‘Molecular Biology of the Cell’, Garland Pub., Inc., New York, 1983.” I. P. Griffith, Biochem. J., 1972, 126, 553. 58 G. J. Brewer, E. Lopez-Corella, and M. E. Noelken, Cfin. Chim. Acta, 1972, 36, 574. 59 G. A. Banker and C. W. Cotrnan, J. Biol. Chem., 1972, 247, 5856. 229 Development of Sodium Dodecyl Sulphate- Polyacrylamide Gel Electrophoresis biochemical analysis. SDS-PAGE methods extend into all areas of electrophoresis. A technique for performing isoelectric focusing on proteins dissolved in SDS was developed.60 Another SDS-PAGE technique allowed the determination of the molecular weights of proteins at the nanomole level.61 These proteins had low molecular weights and were dissolved in a 0.1% SDS solution.61 Researchers isolated many proteins through the use of various SDS-PAGE methods during this same period, including the growth hormone (GH) and prolactin (PRL) from rat pituitary homogenates and cell fractions.62 Quantitative determinations of GH and PRL were possible because SDS-gel systems allowed for such discrete separation.62 The researchers involved were even able to estimate the degree of contamination present in GH and PRL separated by a PAGE method lacking SDS.62 The molecular weight of human erythropoietin was also determined by SDS-PAGE.63 SDS-PAGE allowed the preparative separation of milligram quantities of all of the major erythrocyte membrane proteins with a yield as great as 93%.64 Modifications of the SDS-PAGE methods were brought to near perfection by 1975.One simple modification eliminated the use of SDS in the gel and electrode compartment, limiting its use to the sample solution alone.65 Another method allowed direct visualization of protein bands in SDS-polyacrylamide gels.66 The procedure consisted of chilling the gels to 0-4"Cand observing the white opaque bands of proteins, thus eliminating the need for stains.66 Another research group found that sodium octylbenzene-p-sulphonatecould be used in place of SDS and PAGE, but the method was never extensively used.67 Although it had limitations, by 1975 SDS-PAGE was the best means for protein analysis.Electrophoresis on polyacrylamide gels with SDS can separate proteins from relatively complex mixtures. However, when more complex mixtures (generally containing greater than fifty different proteins) are separated by this one-dimensional method, closely spaced protein bands tend to overlap.It was for this reason that two-dimensional electrophoresis was developed. The theory behind two-dimensional electrophoresis is defined by the dimensions. In the most advanced methods, proteins are first separated according to their isoelectric points and then further separated according to their molecular weights. Electrophoresis performed in this manner assures complete separation of all of the proteins in a complex mixture. In 1969, Margolis and Kenrick published a method for two-dimensional electrophoresis which utilized polyacrylamide gels.68 In the first stage a low- concentration polyacrylamide gel was used to perform discontinuous electro- 6o D.W. Miller and S. C. R. Elgin, Anal. Biochem., 1974,60, 142. 61 T. Kato, M. Sasaki, and S. Kimura, Anal. Biochem., 1975,66, 515. A. Zanini, G. Giannattasio, and J. Meldolesi, Endocrinology, 1974,94, 594. 63 M. Dorado, J. Espada, A. A. Langton, and N. C. Brandan, Biochem. Med., 1974,10, 1. 64 H. Knuefermann, S. Bhakdi, and D. F. H. Wallach, Biochim. Biophys. Acta, 1975,389,464. 6' J. T. Stoklosa and H. W. Latz, Biochem. Biophys. Res. Commun., 1974,58, 74. 66 R. W. Wallace, P. H. Yu, P. J. Dieckert, and W. J. Dieckert, Anal. Biochem., 1974, 61, 86. "K. Tsujii and T. Takagi, J. Biochem. (Tokyo), 1975,77, 117. 68 J. Margolis and K. G. Kenrick, Nature, 1969, 221, 1056. Sherman and Goodrich phoresis, thus allowing the proteins to migrate with very little resistance.68 The second stage consisted of a gradient-gel electrophoresis.68 Separation resulting by this method was only slightly greater than that resulting from one-dimensional PAGE.A year later, researchers 69 proposed a two-dimensional polyacrylamide gel system which greatly improved the analytical separation of complex protein mixtures obtained from ribosomes. Through this method the protein mixtures of Escherichia coli ribosomes were separated into about fifty component^.^^ The procedure was rather widely used over the next five years in spite of its limited applicability. DeWachter and Fiers7' published in 1972 a method of preparative two-dimensional PAGE which was capable of separating complex mixtures of RNA molecules.The first dimension separation was executed on polyacrylamide acid gels in the presence of a high concentration of urea, and the second dimensional separation was performed on more highly concentrated polyacrylamide gels buffered at pH 8.70Another two-dimensional PAGE technique was developed in 1973 by Orrick et to separate extracted rat liver nuclei into about one hundred distinct proteins. In 1974, a two-dimensional system of electrophoresis for the analysis of ribosomal proteins was described.72 This system had several advantages over the previous systems. The first dimensional separation was based on the mobility of ribosomal proteins at pH 5 in 8M urea and 4% polyacrylamide. The second dimensional separation occurred on the basis of molecular weight, in the presence of SDS.72 High resolution of ribosomal proteins resulted from use of this method.In the same year, the two-dimensional PAGE system developed by Orrick 71 was modified to improve the separation of proteins from rat liver.73 The modifications included reducing the polyacrylamide concentration in the first dimension from 10% to 6% and substituting 8% polyacrylamide for a linear 8-10% polyacrylamide gradient in the second dimension.73 These modifications resulted in improved resolution of the protein bands. OFarrel174 in 1975 published a new method for high-resolution two-dimensional SDS-PAGE. In first dimensional separation the proteins were separated according to their isoelectric points, on isoelectric focusing gels made with polyacrylamide. In the second dimensional separation the proteins were further separated according to their molecular weights by means of a discontinuous SDS polyacrylamide gel system.With this technique, O'Farrell was able to resolve 1 100 different components from Escherichia coli. Proteins differing by only a single charge could be resolved and proteins comprising 10-4 to of the total protein content could be detected. The implications of this powerful method were obvious. 69 E. Kaltschmidt and H. G. Witmann, Anal. Biochem., 1970,36, 401. 70 R. DeWachter and W. Fiers, Anal. Biochem., 1972,49, 184. '' L. R. Orrick, M. 0.J. Olson, and H. Busch, Proc. Nut. Acud. Sci. USA, 1973, 70, 1316. 72 L. J. Mets and L.Bogorad, Anal. Biochem., 1974, 57, 200. 73 G. I. Busch, L. C. Yeoman, C. W. Taylor, and H. Busch, Physiol. Chem. Phys., 1974,6, 1. 74 P. H. OFarrell, J. Biol. Chem., 1975, 250, 4007. 23 1 Development of Sodium Dodecyl Sulphate- Polyacrylamide Gel Electrophoresis Lambin et al. devised a new method of SDS-PAGE useful for the determination of large molecular weight proteins in 1976.75The electrophoresis was performed on a 20 to 30% polyacrylamide gradient gel; and proteins, with molecular weights ranging from 10 O00 to 1 000 000, could be determined with good accuracy. In 1977, a micro-gel-electrophoresis technique, which permitted the routine analysis of proteins in levels as low as lW9 g was developed using SDS in the polyacrylamide gel system.76 It allowed the use of micro-samples to determine the molecular weights of proteins.76 Another technique was developed at the same time for the quantitative analysis of proteins on SDS-PAGE system.77 Olden and Yamada developed a similar technique for the direct detection of antigens on SDS- polyacrylamide gels.78 In 1978, a new system (which was entirely self-contained and highly efficient) was described for the preparative electrophoresis on polyacrylamide gels.79 Modifications developed in 1980 by preparative SDS-PAGE allowed improved separation of high molecular-weight proteins.80 In the next year, a new method was developed for the detection of nanogram quantities of proteins on SDS-polyacrylamide gels.” The method employed an ‘251-labelled reagent.81 In 1983, an improved method for the separation of low molecular-weight polypeptides was described 82 using a 10%to 18%linear gradient polyacrylamide gel containing 7M urea.With this method peptides whose molecular weights ranged from 1 500 to 100 000 were highly resolved.82 In the same year, picogram amounts of Escherichia coli DNA-polymerase were successfully detected through the use of a modified technique of SDS-PAGE.83 The modifications consisted of embedding fibrinogen in the gels and washing the detergents from the gels with aqueous isopropyl alcohol after electrophore~is.~~ After the introduction of O’Farrell’s astounding technique in 1975,74 two-dimensional SDS-PAGE became popular for it required very few modifications to function in most situations.O’Farrell’s technique was put to use in 1976, less than one year after it was published. Slight modifications were made in order to allow protein analysis of Escherichia coli and Salmonella typhimurium cell envelopes.84 The same researchers used the technique to separate plasma membrane proteins from HeLa cells.84 Another research group used the O’Farrell technique to analyse the non-histone chromosomal proteins of the HeLa ~el1.s.~~ More than 450 components were revealed, most of which were rare (less than 10000 copies per cell) and were not previously detectable in the cytoplasm.85 75 P. Lambin, D. Rochu, and J. M. Fine, Anal. Biochem., 1976, 74, 567. 76 J. S. Condeelis, Anal. Biochem., 1977, 77, 195.77 T. Asao, Anal. Biochem., 1977, 77, 321. 78 K. Olden and K. M. Yamada, Anal. Biochem., 1977,78,483. 79 J. J. Koziarz, H. Koehler, and T. L. Steck, Anal. Biochem., 1978, 86, 78. D. A. Hardman and J. P. Kane, Anal. Biochem., 1980, 105, 174. Y. W. Shing and A. Ruoho, Anal. Biochem., 1981, 110, 171.’* F. Hashirnoto, T. Hosigorne, M. Kanbayashi, K. Yoshida, and H. Sugano, Anal. Biochem., 1983,129,192. 83 A. Blank, J. R. Silber, M. P. Thelen, and C. A. Dekker, Anal. Biochem., 1983, 135, 423. 84G.Ferro-Luzzi-Ames and K. Nikaido, Biochemisrry, 1976, 15, 616. J. L. Peterson and E. H. McConkey, J. Biol. Chem., 1976, 251, 548. Sherman and Goodrich Addition of SDS to the sample preparation enhanced the reproducibility of gel patterns in the O’Farrell technique.86 The glass plates, which hold the second- dimension polyacrylamide gel, were slightly modified and ultracentrifugation was used to reduce clogging at the top of the isoelectric focusing gela6 In 1978, a procedure was developed for the determination of similar amino-acid composition among cellular proteins separated by two-dimensional gel electrophoresis.8 ’ A differential two-dimensional PAGE method was devised in 1979 for peptide mapping of heterogeneous protein samples.88 In the first dimension a mixture of denatured and the reduced proteins was separated on a SDS-polyacrylamide gel slab.In the second dimension each of the separated proteins was subjected to partial proteolysis and resolved into a characteristic pattern of peptides by a stacking technique.By means of this method, up to twenty individual proteins could be analysed at once.88 In the same year the polypeptide turnover rates in 100 lo3 Figure 1 Schematic representation of CHO plasma membrane polypeptide ‘map.’ Vertical bars dividing the map are based upon approximate pH values, while horizontal lines designate molecular weight. Major proteins of the CHO cell plasma membrane map are shown as black spots, while minor polypeptides or variable spots are shown in outline. Each one of the proteins was further identijied using the radioactive isotopes (Reproduced by permission from re$ 89) D. L. Wilson, M. E. Hall, G. C. Stone, and R. W. Rubin, Anal. Biochem., 1977, 83, 33. F. Cabral and M. M. Gottesman, Anal.Biochem., 1978, 91, 548. C. Bordier and A. Crettol-Jarvinen, J. Biol. Chem., 1979, 254, 2565. Development of Sodium Dodecyl Sulphate- Polyacrylamide Gel Electrophoresis Chinese hamster ovary cell plasma membranes were correctly determined through the use of the OFarrell technique (see Figure l).89Previously, turnover rates were determined through the use of one-dimensional systems of electrophoresis which resulted in considerable overlap of the bands.89 .-One dimensional discontinuous SDS-PAGE slab was successfully used to give linear molecular weight sepaiations from 2 500-90 000.90Slab SDS-PAGE was a strong improvement over the normal one-dimensional PAGE. Using two adjacent SDS-PAGE slabs, one coated with 2-mercaptoethanol and the other uncoated, showed the mobility of the reduced and non-reduced disulphide bonds in the pr~tein.~' Chao in 1980 described a technique which allowed high-precision comparisons of complex protein patterns from two different cell lines.92 The technique combined + Figure 2 Two-dimensional minislab gel containing yeast histones.Nine micrograms of yeasthistone were electrophoresed on an acetic acid-urea minislab gel. After staining and destaining of the minislab gel, the gel lane was excised; prepared for the electrophoresis and electrophoresed on a 15% polyacrylamide-sodium dodecyl sulphate minislab gel. The results are shown above. A one-dimensional electrophoresis did not dejnitely separate the yeast histone. The two- dimensional run adequately separated them into their four acetylated species (H2A, H2B, H,, and H,) and the H, species into its various protein species (A0-A4).(Reproduced by permission from ref.93) M.N.Horst and R. M.Roberts, J. Biol. Chem., 1979, 254, 5OOO. 'O B. L. Anderson and R. W. Berry, Anal. Biochem., 1983, 132, 365. 91 R.J. Allore and B. H. Barker, Anal. Biochem., 1984,137,523. Sherman and Goodrich a double isotope labelling procedure with two-dimensional PAGE.92 Lam and Kasper developed a procedure for examining sequence homology between two or more proteins in a heterogeneous protein mixture (see Figure 2).93 In the same year, two-dimensional PAGE was utilized to analyse human pancreatic This analytical procedure separated pancreatic fluid into thirteen individual proteins.Even the a1 and a2 chains of rat tail tendon collagen were ~eparated.'~ This occurred because the a2 chain binds appreciably to the SDS while the a1 has negligible binding. In 1982,Davie devised two two-dimensional polyacrylamide gel systems for the rapid analysis of his tone^.^^ In the first system, an acetic acid-urea or acetic acid- urea-Triton X-100minislab gel made up the first dimension and a polyacrylamide SDS minislab gel made up the second dimension. In the second system the first and second dimensional separations were simply switched. Both systems allowed for rapid, high-resolution analysis of modified histone species and variants. Heating the peptides with SDS buffer prior to electrophoresis is very popular.Hodges and Hirata 97 showed that it hydrolyses the protein and leads to many new spots which show greater intensity with a silver staining solution. A similar enhanced mapping of protease after partial hydrolysis for samples as small as 50 mg of protein was reported by Cleveland et al.98However, these authors were probably unfamiliar with work by Rittenhouse and Marcus," who showed that heating polypeptides to 110 "Cin SDS buffer prior to electrophoresis preferentially cleaved the aspartyl-prolyl peptide bond. Although the latter authors performed most of their work on fructose-1,6-bisphosphatase,the cleavage was specific and exhibited distinctly different PAGE patterns than proteins containing no aspartyl-prolyl peptide bonds.It is possible that either Hodges and Hirata or Cleveland's success might be due to this cleavage. In 1983, Tijssen and Kurstak developed an efficient two-dimensional SDS- PAGE method for the simultaneous peptide mapping of proteins contained in a mixture."' These two researchers found that the previous methods of peptide mapping 88*93 gave non-consistent results."' Their technique consisted of first separating the polypeptides by SDS-PAGE, then embedding the strip of gel obtained from SDS-PAGE perpendicular to the direction of electrophoresis in the stacking gel of a second gel system, into which proteolytic enzymes were loaded. The technique could also be performed in the Laemmli gel system"' with modifications.loo 92 K. H. Chao, R.G. H. Cotton, and D. M. Danks, Anal. Eiochem., 1980, 103, 33. "K. S. Lam and C. B. Kasper, Anal. Eiochem., 1980, 108, 220. 94 W. Bieger and G. Scheele, Anal. Biochem., 1980, 109, 222. 95 K. Kubo, Collagen Relai. Res., 1984, 4, 201. 96 J. R. Davie, Anal. Eiochem., 1982, 120, 276. 97 S. C. Hodges and A. A. Hirata, Clin. Chem., 1984,30, 2003. 98 D. W. Cleveland, Methods Enzymol., 1983, 96, 222. 99 J. Rittenhouse and F. Marcus, Anal. Biochem., 1984, 138, 442. loo P. Tijssen and E. Kurstak, Anal. Eiochem., 1983, 128, 26. '01 U. K. Laemrnli, Nature, 1970, 227, 680. 235 Development of Sodium Dodecyl Sulphate-Polyucrylumide Gel Electrophoresis Since electrophoresis was first put into practical use in 1937 by Tiselius *w9 it has constantly been under modification and improvement and has been used to identify all types of proteins and protein residues.However, with smaller and smaller samples, contamination also becomes more of a problem and Ochs lo2 discovered that many erroneous bands in SDS-PAGE work were due to skin proteins. Her work indicated that extreme care is essential for good analytical biochemistry. The proliferation of literature is an indication of the maturity of a method and specific reviews have started to appear. One by Spanos and Huebscher Io3 reviews the enzyme catalytic activity after SDS-PAGE and another by Sano Io4 covers the specific analyses of proteins. Raymond and Weintraub I3 introduced polyacrylamide as a stabilizing medium for zone electrophoresis and in the years since their discovery great advances have been made in the techniques. It is obvious that many more unique techniques can be expected in the future. ‘Of D. Ochs, Anal. Biochem., 1983, 135,470. lo3 Ad. Spanos and V.Huebscher, Methods Enzymol., 1983,91, 263. K. Sano, Med. Technol., 1982, 10, 443.

ISSN:0306-0012    

DOI:10.1039/CS9851400225

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

Activation Parameters for Chemical Reactions in Solution By Michael J. Blandamer and John Burgess DEPARTMENT OF CHEMISTRY, UNIVERSITY OF LEICESTER, LEICESTER, LE1 7RH Jan B. F. N. Engberts DEPARTMENT OF ORGANIC CHEMISTRY, UNIVERSITY OF GRONINGEN, NIJENBORGH 16, 9747 AG GRONINGEN, THE NETHERLANDS 1 Introduction Chemical reactions are not instantaneous; an ‘energy barrier’ separates reactants and products, each mole of reactant crossing this energy barrier in the process, reactants -products. Chemical kinetics probe details of these energy barriers by examining the dependence of rates of reaction on composition, temperature, and pressure. The results are summarized using partial differentials (e.g. aln k/ap at constant T; see below) which in turn characterize activation parameters.This review examines definitions and relationships between activation parameters for chemical reaction in solution. Chemical reaction is, in thermodynamic terms, an irreversible process, the direction of spontaneous change being determined by the Second Law of Thermodynamics. Accordingly, the product of affinity for reaction A and rate of change Jconforms to the condition’, A.J 2 0. Jequals dk/dt where d5 is the extent of chemical reaction in time dt. Intuition suggests that J is proportional to the affinity A, the driving force for reaction, such that J and A are related by a linear phenomenological equation; J = L.A. (L is a phenomenological coefficient.) This Ohm’s Law approach’ to chemical kinetics has merit but is rarely useful.Although J can be characterized by measuring the dependence of composition on time, the affinity cannot-no affinity meter is available commensurate with a voltmeter. Therefore the phenomenon of chemical reaction is conventionally described using the Law of Mass Action in which the ratio (J/V) {where Vis the volume) is related directly to the composition at time t by the differential equation (1-1), cj is the concentration of substance j, aj is the order with respect to j, and k is the phenomenological parameter called the rate constant. In this review we concentrate attention on the single reaction given in equation 1-2 where chemical substances W and Z are solutes in a solvent which is chemically inert in the sense that it is not involved in the stoicheiometric equation for the reaction; ‘sln’ identifies the solution state.I I. Prigogine and R. Defay, ‘Chemical Thermodynamics’ (trans. D. H. Everett), Longmans-Green, London, 1954. See for example, J. R. Partington, ‘A History of Chemistry’, MacMillan, London, 1964,volume 4, chapter 18. 237 Activation Parameters for Chemical Reactions in Solution W(sln) -Z(s1n) (1-2) At fixed Tandp, this reaction is characterized by a first-order rate constant which is independent of time. The chemical reaction is elementary, a single energy barrier separating reactants and products. Complexitie~~.~ arising from pre-equilibria, consecutive5 and parallel6 processes are not considered here. Rate constant k for reaction (cf.equation 1-2) is an intensive dependent variable defined by the independent variables T and p for reaction in solvent I,.In k = In k[T;p] (1-3) The dependences of In k on temperature at fixed pressure and on pressure at fixed temperature define corresponding isobaric and isothermal activation parameters. We comment below on their derivation and interpretation. Also we consider isochoric (constant volume) activation parameters. Two important themes dominate this review. First, the several conditions associated with a given activation parameter are defined using an extended symbolism. In this respect we apologize to the reader for the decoration of thermodynamic symbols. In our defence, we suggest that ambiguity may otherwise result.Possible no misunderstanding arises in the case of the familiar isobaric and isothermal activation parameters. However, for isochoric parameters we are concerned to establish the 'volume held constant'. The first theme has spilled over into a second theme in which we have been concerned to identify the standard (and reference) states associated with each activation parameter. Interest in isochoric activation parameters stems from a seminal paper7 by Evans and Polanyi published in 1936.These authors voiced a concern felt by all who study kinetics of chemical reactions in solution. When the dependence of rate constants on T and p is considered, one is aware that the properties of solvents and solvent- solute interactions depend on T and p.Evans and Polanyi wrote' (and we quote from page 893 of reference 7), 'Especial difficulty arises in solution from the interaction between solute and solvent, which depends strongly on temperature. This effect would be to some extent eliminated by measuring the temperature coefficients at constant volume, . . . . . .'. We have italicized three words because they indicate a compromise, prompting the calculation of isochoric activation parameters. Isochoric parameters have been calculated from data describing transport processe~,~*~ dielectric properties," spectroscopic properties," and chemical kinetics. B. Perlmutter-Hayman, Progr. Inorg. Chem., 1976, 20, 229. R. Koren and B. Perlmutter-Hayman, J. Phys. Chem., 1971, 75, 2372. See for example, M.J. Blandamer, J. Burgess, P. P. Duce, R. E. Robertson, and J. M. W. Scott, J. Chem. Soc.. Faraday Trans. I, 1981, 77, 1999. J. G. Winter, J. P. Barron, and J. M. W. Scott, Can. J. Chem.. 1975, 53, 1051. ' M. G. Evans and M. Polanyi, Trans. Faraday Soc., 1936, 31, 875. A. F. M. Barton, Rev. Pure Appl. Chem., 1971, 21, 49. S. B. Brummer and G. J. Hills, Trans. Furaday Soc., 1962, 57, 1816. lo G. Williams, Trans. Faraday Soc., 1964, 60, 1548. D. Griller, J. Am. Chem. Soc., 1978, 100, 5240. l2 E. Whalley, Adv. Phys. Org. Chem., 1954, 2, 93; Ber. Bunsenges Phys. Chem., 1966, 70, 958. Blandamer, Burgess, and Engberts 2 Thermodynamics A vital role is played in chemical kinetics by the Second Law of Thermo- dynamics. In this section we develop the point by considering a closed single- phase system wherein spontaneous chemical reaction 1-2 is taking place. At time 1, dG = -SdT i-Vdp -AdS (2-1) At fixed Tandp, spontaneous chemical reaction occurs in the direction which leads to a decrease in the Gibbs Function, G.Within a microscopic volume, characteristic of the total system, local fluctuations in composition sample the dependence of G on 5 at fixed T and p.Those fluctuations are favoured which are accompanied by a decrease in G. At a given stage in the reaction (i.e. fixed c), the thermodynamic properties are related (Figure 1). As the reaction proceeds so the volume V, enthalpy H, entropy S, and isobaric heat capacity C,change. Eventually (i.e.limit (t ----a)},the system attains chemical equilibrium, composition ceq, where G is a minimum and yqis characteristic of the system, Tandp.At equilibrium J = 0, A = 0 and ((aG/aC)T,}eq = 0. At equilibrium all local fluctuations in composition produce an increase in G. Nevertheless the thermodynamic variables H, S, V, and C, are not necessarily at extrema. In a particular system, Veq [ = ((dG/ap)T}eqJ may be a maximum; in another case it may be a minimum; in yet another case, at some intermediate value. With reference to equation 1-2, the volume of the system at limit (t -00)depends on the magnitudes and signs of the partial molar volumes of solutes W and Z and the solvent. The foregoing thermodynamic statements refer to macroscopic properties which are related to (partial) molar properties of chemical substances making up a system; Figure 2.The parent partial molar property is the chemical potential which for Figure 1 Thermodynamic variables as a function of G at fixed composition Activation Parametersfor ChemicaI Reactions in Solution solute j in solution (solvent = II) is given by13 equation 2-2 where mj is the molality ofj( = nj/nlM1) and where mi is the molality of all other solutes in solution: I I I sj =(as/ ---II I I II I 1 II I I I I II I I I I I I II II I I I I I I I II I I I I I II I I '--Cp, = Otij/JT)p Figure 2 Partial molar properties of substance jin a system containing ni moles of substance i (= 1,2,3,4 . .); the dotted lines indicate a Maxwell relation where limit (mj -0; mi -0) yj = 1 at all T and p.pje(Sln;T) is the standard chemical potential of solutejin solution at temperature Tand standard pressure po; i.e. an isobaric-isothermal standard state. Vjm(sln;T;p) is the partial molar volume of solutejat infinite dilution. From the differential of equation 2-2 with respect to pressure at constant temperature, and according to the definition of yj, limit (mi -0; mi -O)Vj(sln;T;p)= Vj=(sln;T;p) = Vj(s1n;mj = l;y, = 1;T;p) (2-3) Therefore the partial molar volume of j in an ideal solution where mj = 1 at temperature T and pressure p equals Vjm(Sln;T;p), the latter being Vj(sln; T;p) extrapolated to the limit of infinite dilution. l4 Similarly,'4 M.L. McGlashan, 'Chemical Thermodynamics', Academic Press, London, 1979. l4 J. E. Garrod and T. M. Herrington, J. Chem. Educ., 1969, 46, 165. 240 Blandamer, Burgess, and Engberts limit (mi -0; mi -0) Hj(sln;rp) = Hj"(s1n;T;p) = Hj(sln;mj = 1;yj = 1;T;p) (2-4) and At p = PO, Vjm(sln;T;p)= Vj"(sln;T), C,j"(sln;T;p) = C,j"(sln;T) and Hi"-(s1n;T;p) = Hje(sln;T). These equalities do not carry over to the chemical potentials and partial molar entropies of solutej because limit (mj -0) In mj = -co;the standard state is not the infinitely dilute solution. 3 Chemical Kinetics The general differential of equation 1-3 is dln k = [F];T (3-1)+ [y]:p Experimental data describing the dependence of composition on time are analysed to obtain an estimate of the true rate constant at given T and p.The latter two quantities are usually assumed to be error-free, i.e. the true temperature and true pressure. Equation 1-3 implies that a quantitative relationship exists between k, T, and p but this relationship is unknown; it is not defined by thermodynamics although the dependence can be described in thermodynamic terms. At this stage various equations are tested with the aim of describing the observed dependence."-** For reactions at constant pressure, the dependence of In k on T about In k(8)at temperature 8 may be expressed" by equation 3-2 where K is the SI unit of temperature, Kelvin. Ink = a1 + (a2K)[(l/T)-(l/e)] + a3ln (T/O) (3-2) Hence, (dln k/dT), = -a2K/T2 + a3/T (3-3) Similarly the dependence of k on pressure (at fixed T) may be fitted about k(x) at reference pressure 7~ using equation 3-4.Statistical analysis using least squares procedures yields estimates of the M. J. Blandamer, J. Burgess, R. E. Robertson, and J. M. W. Scott, Chem. Rev., 1982, 82, 259. l6 T. Asano and W. J. le Noble, Chem. Rev., 1978, 78, 407. W. J. le Noble, Rev. Phys. Chem. Jpn., 1980, 50, 209. S. D. Hamann, Rev. Phys. Chem. Jpn., 1980, 50, 147. l9 T. W. Swaddle, Rev. Phys. Chem. Jpn., 1980, 50, 231.'* R. van Eldik and H. Kelm, Rev. Phys. Chem. Jpn., 1980,50, 185. 2L B. S. El'yanov and E. M. Vasylvitskaya, Rev. Phys. Chem. Jpn., 1980,50, 169. 241 Activation Parameters for Chemical Reactions in Solution dimensionless quantities a, and b, for i = 1 to 3.Various statistical advantage^'^ follow if 0 and II are chosen near the middle of the experimental Tandp ranges. The simple polynomial in equation 3-4 can also be modified22 by replacingp and x by T and 0 respectively and used to fit the dependence of k on Tat fixedp. If 8 in equation 3-2 is set to 1 K, the result is the Valentiner equation.” If II in equation 3-4 is set to zero, the result is a simple quadratic23 in p. However, the latter procedure has been criticized24 on the grounds that (i) the equation predicts extrema in the dependence of In k on p and (ii) derived parameters at low pressures depend strongly on the number of experimental points at high pressures. A more satisfactory de~cription~~ is given by equation 3-6.(We have modified the original equation in reference 24 to express the dependence about k(n) at pressure II.) With reference to the dependence of In k on T, the Clarke-Glew equation25 for the dependence of equilibrium constants on T is readily modified to yield an equation for the dependence of In k in terms of molar enthalpies and molar isobaric heat capacities of activation (Section 6). A problem over dimensional analysis emerges in these fitting equations (cJ equations 3-2 and 3-4) concerning the units associated with rate constants. This problem is met by defining a dimensionless quantity ks; for a first order rate constant, k = k$/sand for a second order rate constant, k = ks/smol m-3 where s is the SI unit of time, second.A multitude of analytical procedures are therefore available for calculating the two partial derivatives in equation 3-1 for chemical reaction in a given solvent at temperature 0 and pressure n. At 8 and 11, the two partial derivatives are orthogonal, no direct relationship existing between the isobaric and isothermal quantities. 4 Properties of Solvents The volume of a closed system comprising liquid ll at temperature Tand pressurep is an extensive property. The molar volume V,* (= V/nl)is an intensive property defined by the intensive independent variables T and p; V1* = vl*[T;p] The general differential of equation 4-1 is dVl* = (aVl*/aT),dT + (aV,*/ap),dp (4-2) For reversible changes (i.e.equilibrium conditions), thermal (isobaric) expansivity, 22 M.J.Blandamer,J. Burgess, P. P. Duce, R. E. Robertson, and J. M. W. Scott, J. Chem. SOC.,Perkin 2, 1981, 1157. 23 J. B. Hyne, H. S. Golinkin, and W. G. Laidlaw, J. Am. Chem. SOC.,1966, 88, 2104. 24 T. Asano and T. Okada, J. Phys. Chem., 1984,88, 238. ”E. C. W. Clarke and D. N. Glew, Trans. Faraday Soc., 1966,62, 539. 242 Blandamer, Burgess, and Engberts al* = (l/V,*)(aV,*/aT), (4-3) and the (isothermal) compressibility, For stable phases, K,* > 0 but a,* can be positive, zero, or negative depending on the system. The internal pressure of liquid I,, ni = T(al*/K1*)-p (4-5) niis characteristic of a at defined T and p (Table 1). Table 1 Internalpressures of liquids at 298 K and 101 325 N m-2 Liquid lO-**Ili/Nm-2 Methyl alcohol 2.99 Ethyl alcohol 2.91 Acetonit rile 3.89 1,4-Dioxane 4.99 Hexane 2.39 Water 1.683 Water (273 K) -0.363 D2O 1.228 DzO (278 K) -0.617 taken from references 2629 According to equation 4-1, the molar volume of liquid I, at temperature 8 and pressure 71 is defined by V,*[B;x].If the temperature is changed from 8 to 8 + 60, the molar volume is defined by V,*[e + 68;~).Suppose that at temperature 0 + 68, the pressure is changed to 71: + 6n1,whereby the molar volume of liquid I, at [e;x]and [8 + 68; K + 671,) are equal.This isochoric condition can be expressed in the form, 6x,is characteristic of the liquid. The conditions operating either side of equation 4-6 are isobaric-isothermal but the equality is isochoric.Similar considerations may be given to a binary liquid mixture formed from n, and n2 moles of liquids I, and I,. The molar volume V,,, (= V/(n, + n,)) is defined by the independent variables, T, p, and x,; i.e. V,,, = V,,,[T;p;x,] where x2 = n2/(nl + n,) and x, = 1 -x,. Many changes can be rung amongst the variables T,p, and x,. If, at a given T and p, the excess molar volume of a mixture VmE> IV,* -V2*l,there will exist 26 M. R. J. Dack, Chem. SOC.Rev., 1975,4, 211. ”J. Amoros, J. R. Solana, and E. Villar, Muter. Chem. Phys., 1984, 10, 557. Data for water from J. V. Leyendekkers, ‘The Thermodynamics of Sea Water as a Multicomponent Electrolyte Solution’, Part 1, M. Dekker, New York, 1976. 243 Activation Parameters for Chemical Reactions in Solution pairs of mole fractions x2'and x2"where the molar volumes are equal, i.e.isochoric.At a given x2, V,,,is a function of T and p so that an isochoric condition analogous to equation 4-6 is, where 6n2is characteristic of the mole fraction composition x2. The isochoric condition in equation 4-7 refers to a mixture having defined mole fraction composition, i.e. a local isochoric condition. One can also envisage a global isochoric condition where over the range 0 ,< x2 < 1.0, there exist temperatures and pressures where the molar volumes are identical. 5 Phenomenological Kinetic Parameters According to the Arrhenius eq~ation,~'-~* an energy of activation E characterizes the isobaric derivative in equation 3-1; (ahk$/aT), = E/RT2 (5-1) E is a macroscopic phenomenological property and depends on T,p, and solvent.Explanations of the factors controlling E are offered in terms of molecular processes within a system. Chemical reaction is envisaged as proceeding by the pathway (mechanism) involving the lowest activation energy of all available pathways. For reactions in solution, the solvent plays a key role in determining this pathway. The isothermal dependence of rate constant on pressure (equation 3-1) defines an activation volume, AV which is also a macroscopic property of a system: (aln ks/ap), = -A VIRT (5-2) For a given chemical reaction E and A V characterize the orthogonal dependences of In k$ in a plot of In k$ against T and p. In another analysis we consider how In k$ depends on temperature not at constant pressure but where the pressure changes in the sense defined by equation 4-6, i.e.isochoric with respect to the molar volume of the solvent.The required partial derivative is, Similarly we consider the dependence of Inks on pressure not at constant temperature but where the temperature changes to hold V1* constant; 30 P. D. Pacey, J. Chem. Educ., 1981,58, 612. S. R.Logan, J. Chem. Educ., 1982, 59, 279. 32 K. J. Laidler, J. Chem. Educ., 1984, 61, 494. Blandamer, Burgess, and Engberts The latter two partial derivatives are related (cf: reference 33) to the isobaric and isothermal partial derivatives; Within the plot of In k$ against T and p, the two partial derivatives calculated by equations 5-3 and 5-4 are not orthogonal, being related through the properties of the solvent.By definition, (5-5) where E( V,*)is an isochoric (V,*) energy of activation. For solvolysis of t-butyl chloride in methyl at 298 K and 101 325 N mW2, E{V*(MeOH;l)) = 103.76 kJ mol-I and E = 94.14 kJ mol-’. The phenomenological approach to chemical kinetics has considerable merit in that no ‘apriori’ assumptions are made concerning the process of chemical reaction. Nevertheless links between activation parameters and the thermodynamic properties of solutes are tenuous. 6 Transition State Theory The wealth of data concerning the thermodynamic properties of solutes in solution offers a basis on which to build an analysis of kinetic data. Transition State Theory35 provides a route for analysis in these terms but at the expense of adopting a particular model for the activation process.Chemical reaction (cj equation 1-2) proceeds through a transition state, symbol #. Hence for chemical reaction in solvent I, and at temperature T and pressure p, w +) #-z (6-1) Reactant W and transition state # are in eq~ilibrium.~~ Hence, at time t, the thermodynamic condition is, If the solution is dilute, y+eq/yweq = 1 and m+eq/m,eq = cgeq/cWeq.If the 33 G. N. Lewis and M. Randall, ‘Thermodynamics’ (revised by K. S. Pitzer and L. Brewer) McGraw-Hill, New York, 1961, chapter 3. 34 G. J. Hills and C. A. Viana in ‘Hydrogen Bonded Solvent Systems’, ed. A. K. Covington and P. Jones, Taylor & Francis, London, 1968, p.261. 35 S.Glasstone, K. J. Laidler, and H. Eyring, ‘The Theory of Rate Processes’, McGraw-Hill, New York, 1941. Activation Parameters for Chemical Reactions in Solution transmission coefficent3' is unity (cJ:references 36 and 37) at all T and p, kS/T= (kes/h)'K"(sln;T) exp (6-3) A' G"(s1n; T) = RT In 'K"(sln;T)e = pz*(sln;T) -pw (s1n;T) (W Rate constant k$is determined by the molar volume of activation A' V" and the difference between the standard chemical potentials of reactant and transition state. The standard equilibrium constant, 'K", depends on temperature but not on pressure. By analogy with the van't Hoff equation for the dependence of K" on T, {ah (k$/T)/aT},= A'Hm(sln;T;p)/RT2 (6-5) where (cf:equation 2-4), A'H"(s1n;T;p) = H,"(sln;T;p) -H,"O(sln;T;p) (6-6) At p = p", the standard increase in molar enthalpy of activation, A'H"(s1n;T) = H,"(sln;T) -Hw"(sln;T) (6-7) Similarly, the reference molar volume of activation is given by, (dln k$/dp)T = -A' Vm(sln;T;p)/RT (6-8) where for the reaction in equation 1-2, A' V"(s1n;T;p)= V, "(s1n;T;p) -V,"(sln;T;p) (6-9) The reference molar enthalpy of activation, A'H" is dependent on both Tand p.The reference molar isobaric heat capacity of a~tivation,~~.~' A'C," = (dA'H"/aT), (6-10) Also, A*C,," may also depend on temperature but the statistical significance of a calculated dependence is often poor because it emerges from the fourth derivative of the input data, the dependence of composition on time.An important suggestion4' concerns the measurement of relative rates at T and T + AT of two otherwise identical systems. Consequently, one differential operation is incorporated into the experimental procedure. 36 H. A. Kramers, Physica, 1940, 7, 284. 37 B. Gavish and M. M. Werber, Biochemistry, 1979, 10, 1209. R. E. Robertson, Progr. Phys. Org. Chem., 1967, 4, 213. 39 M. J. Blandamer, R. E. Robertson, and J. M. W. Scott, Progr. Phys. Org. Chem., in press. ''W. J. Albery and B. H. Robinson, Trans. Faraday Soc., 1969,65, 980. Blandamer. Burgess, and Engberts The molar volume of activation AzVm also depends on temperature and pressure, striking evidence for these dependences being shown by kinetic data for hydrolysis of methyl p-nitrobenzene ~ulphonate,~' methyl bromide,42 and methyl acetate.43 The quantities defined by equations 6-10 and 6-11 are related to the partial differentials in the general differential of the equation, AfHw = AzHw [Q].Activation parameters, A*Vw and AzHw refer to the differences between the partial molar properties of reactants and transition states in ideal solutions under isothermal and isobaric conditions (cf. equations 6-6 and 6-9). 7 Isothermal and Isobaric Activation Parameters A diagrammatic repre~entation~~ of the activation process described by equation 6-4 is shown in Figure 3 where chemical reaction involves rupture of a chemical bond within W to form two fragments, identified collectively as product 2. I W-f bZ -t I-/ \ ..c 1 \-. m \ Y 0 \ &-rj --w Figure 3 Standard chemical potential as a function of bond iength A series of solutes are envisaged where the two parts of molecule W are separated by distance rj and the standard chemical potential is pj*(sln;T). The initial and transition states are characterized by re and pwO(s1n;T) and by rz and pz"(s1n;T) respectively. pz "(s1n;T) occurs at a maximum in the plot of pje(sln;T) against rP When rj > rz, pje(sln;T) decreases until, at rj = co, there are two quantities representing the standard chemical potentials of the fragments. The maximum at rf is the key feature although we rarely know either r+ or the detailed form of the plot between re and rf and between r+ and rw. All that we calculate from experimental kinetic data is the difference, A # G"(s1n;T).Comparable plots can be constructed (at least in principle) showing the *' J. L. Kurz and J. Y.-W. Lu, J. Phys. Chem., 1983,87, 1444. 42 B. T. Baliga and E. Whalley, J. Phys. Chem., 1969, 73, 654. 43 B. T. Baliga, R. J. Withey, D. Poulton, and E. Whalley, Trans.Furuday Soc., 1965, 61, 517. 44 F. R. Cruikshank, A. J. Hyde, and D. Pugh, J. Chem. Educ., 1977,54,288. Activation Parameters for Chemical Reactions in Solution dependence of Xj"(sln;T) on rj for X = H, C,, V, S. . . There need be no between the shape of these plots and that shown in Figure 3. For a given system, Xje(sln;T) may decrease gradually with increase in ri. In another system, Xj"(sln;T) may pass through a minimum, but not necessarily at rf .Where X = H, the overall dependence of Hj"(sln;T) on rj is likely to resemble that shown in Figure 3 on the grounds that A'G"(s1n;T) and A'H"(s1n;T) are, generally, of comparable magnitude. But the similarity is unlikely to extend to plots where X = Cp and X = V. The latter point is well established, various generalizations'6-21 being reported linking molar volumes of activation with the molecularity of reaction and changes in solvent-solute interactions during the activation process. The complexity of the dependence of Xj"on rj is clearly indicated by system^'^,^^ where ]Af V"(s1n;T;p)l < IA,V"(sln;T;p)l. The foregoing comments go some way to explaining why interpretation of trends in A'G" and rate constants tend to be more successful than in the case of derived parameters; the unique feature in Figure 3, the maximum, being the deciding factor.Closely related to these considerations is the observation that for a series of related substances in a given solvent or for one reaction in a range of solvents, plots of A'H" against A'S" (with p = p") are close to linear. The source of these isokinetic relationship^^^-'^ has been a matter for intense debate, although it has become clear that a proper statistical analysis of the data is mandatory before conclusions are drawn concerning the chemical significance of these relationships. Other correlations include an interdependence of molar volumes and entropies of a~tivation.~'The slope of the plot for reactions in aqueous solutions has been related to the number of neighbouring water molecules which break up into charged fragments, i.e.an ionberg-iceberg model.' No actual number value can be assigned to the standard chemical potential of a solute, and so derived parameters (i.e. A'G") are differences between standard chemical potentials. However, it is possible to examine trends in A'G"(s1n;T) for a given reaction in a range of solvents in the light of changes in the standard chemical potentials of reactant^.^^.^^ Considerable interest surrounds kinetic data for reaction in both aqueous solution and binary aqueous mixture^''-^^ because these systems provide convenient test-beds for treatments of solvent effects on rate constants for chemical reactions.At ambient pressure,^ N p",the integral term in equation 6-3 is ignored such that rate constant k$is simply related to A'G"(s1n;T). The kinetics of reaction in binary aqueous mixtures are examined by comparing the molar activation 45 W. J. Albery and B. H. Robinson, Trans. Faraday SOC.,1969,65, 1623. 46 R. A. Grieger and C. A. Eckert, J. Am. Chem. SOC.,1970, 92, 7149. 47 J. E. Leffler and E. Grunwald, 'Rates and Equilibria of Organic Reactions', Wiley, New York, 1963. 48 R. Lumry and S. Rajender, Biopolymers, 1970, 9, 1125. 49 0.Exner, Coll. Czech. Chem. Commun., 1964, 29, 1094; 1972, 37, 1425. J0 R. R. Krug, W. G. Hunter, and R. A. Grieger, J. Phys. Chem., 1976, 80, 2335, 2341. 51 M. V. Twigg, fnorg. Chem.Acta, 1977, 24, L84. 52 J. C. Phillips, J. Chem. Phys., 1984, 81, 478. s3 M. J. Blandamer and J. Burgess, Chem. SOC.Rev., 1975, 4, 55. s4 M. J. Blandamer and J. Burgess, Pure Appl. Chem., 1983, 55, 55. Blandamer, Burgess, and Engberts parameters in a mixture, mole fraction of organic cosolvent x2, and in aqueous solution. For a second order reaction between solutes i andj, A(aq -x,)A'G"(sln;T) = A(aq -x,)p+ "(s1n;T) -A(aq -x,)pi"(sln;T) -A(aq -x,)pje(sln;T) (7-1) Equation 7-1 highlights one of the major attractions of Transition State Theory.35 Kinetic data yield the quantity on the left-hand side of this equation and equilibrium thermodynamic data (e.g. solubilities) are analysed to obtain the dependence of standard chemical potentials of i andj on x2.By difference, the effect of solvent on the transition state is obtained./. IVOIYo EtOH 4 105 kJ mor' 0 10 20 30 VOIYo EtOH-Figure 4 Analysis of kinetic data for the dissociation of [Fe(bipy),(CN),] in water + methylalcohol mixtures; data from reference 61 An application of this procedure is shown in Figure 4, where the solvent effects on rate constants for dissociation of the non-electrolyte [Fe(bipy),(CN),] are represented in these terms.61 The left-hand side of Figure 4 emphasizes the greater stabilizing effect of added ethyl alcohol on the initial state. The right-hand side of Figure 4 emphasizes just how small these changes in solvation effects are in relation to the activation barrier for reaction. Figure 5 illustrates the data for a simple dissociation reaction of a non-electrolyte, this time for a series of non-aqueous solvents.Again the effects of solvents on initial and transition states are in the same ss M. J. Blandamer and J. Burgess, Coord. Chem. Rev., 1980, 31, 93. 56 M. H. Abraham, Progr. Phys. Org. Chem., 1974,11, 1. 5' J. B. F. N. Engberts, Pure Appl. Chem., 1982, 54, 1797. "J. B. F. N. Engberts in 'Water-A Comprehensive Treatise', ed. F. Franks, Plenum Press, New York, 1975, volume 6, chapter 4. 59 M. J. Blandamer and J. Burgess, Pure Appl. Chem., 1982,54, 2285. 6o M. J. Blandamer, Adv. Phys. Org. Chem., 1977, 14, 203. 61 M. J. Blandamer, J. Burgess, N. V. Reed, and P. Wellings, J. Inorg. Nucl. Chem., 1981, 43, 3245. Activation Parameters for Chemical Reactions in Solution direction, but this time it is the solvent effect on the transition state which tends to dominate.62 These examples from inorganic chemistry are linked to examples from organic chemistry through an interesting example from organometallic chemistry.The case concerns the bimolecular reaction (Figure 6) between tetraethyltin and mercury(I1) chloride in methyl alcohol + water mixture^.^^.^^ (The reference point for transfer parameters is 100% methyl alcohol in Figure 6, whereas the reference point is 100% water in Figure 4.) PC MeOH MeCN OMSO DMF Figure 5 Analysis of kinetic data for the dissociation of [Mo(CO),(bipy)] in a series of solvents; data from reference 62. (pc E propylene carbonate) R,Sn + HgClz-RHgCl + R,SnCl (7-2) In the footsteps of the classical work by Win~tein~'.~~ and ArnettY6' extensive studies of solvent effects in aqueous mixtures on activation parameters have been made of the water-catalysed hydrolysis of activated ester~~~,~' and arnide~;~'.~ Scheme 1.M.J. Blandamer, J. Burgess, J. G. Chambers, and A. J. Duffield, Transition Met. Chem., 1981,6, 156. M. H.Abraham, G. F. Johnston, J. F. C. Oliver, and J. A. Richards, J.Chem. SOC.,Chem. Commun., 1969, 930 64 M.H. Abraham, J. Chem. Soc. A, 1971, 1061. A. H. Fainberg and S. Winstein, J. Am. Chem. SOC.,1956,78, 2770. 66 S. Winstein and A. H. Fainberg, J. Am. Chem. SOC.,1957, 79, 2770. '' E. M.Arnett. W. G. Bentrude, J. J. Burke, and P. McC. Duggleby, J.Am. Chem. SOC.,1965,87, 1541. J. F. J. Engbersen and J. B. F. N. Engberts, J. Am. Chem. Soc., 1975,97, 1563. 69 H. A. J. Holterman and J. B. F. N. Engberts, J. Am. Chem. SOC.,1980, 102,4256. 'O W. Karzijn and J. B. F. N. Engberts, Red. Trav. Chim. Pays-Bas, 1983, 102, 513. 71 J. Haak and J. B. F. N. Engberts, in press. 250 Blandamer, Burgess, and Engberts -x ( MeOH 1 + 1.a TS + 10.1 7IS Et, Sn Hgc12 100 90 80 70 wt % MeOH-Figure 6 Analysis of kinetic data for the reaction between Et,Sn and HgCl, in methyl alcohol + water mixtures: reference solvent is a mixture where x(Me0H) = 0.999; data taken from reference 64 25 1 Activation Parameters for Chemical Reactions in Solution 0 0 I1 1 1'X'C-X2 + H20 4X C-OH + HX 2 Y ,N=C' 1 2X = R.Ar; x =-" I LN I H Scheme 1 Different kinetic patterns72 are observed for these reactions in water-rich typically aqueous (TA) and water-rich typically non-aqueous (TNA) mixtures.60 In TA-mixtures (e.g.t-butyl alcohol + water) A 'G" usually increases (assuming p = pa) continuously with increase in mole fraction of organic co- solvent. This simple pattern conceals eccentric if not capricious variation in the temperature and pressure dependences of the rate constant^.'^.^^ Quite generally, solvent effects on A' W and A'S" exhibit mirror-image patterns and extrema are located around the solvent composition where the co-solvent has enhanced water-water interactions to the greatest extent.However, prerequisite for this behaviour is a marked change in the hydrophobicity of reactants in the activation process.72 Therefore it is most likely that for reactions involving neutral substrates the changes in activation parameters with solvent composition reflect initial-state stabilization through hydrophobic interactions with the co-solvent. Interestingly, entropy changes often dominate relative rates describing changes in substituents in the substrates. Nevertheless, satisfactory correlations are obtained of substituent effects in terms of linear free-energy relationships, e.g. the Hammett equation.58 The underlying task involves establishing a link between, on the one hand, thermodynamic and kinetic data and, on the other hand, models describing the interactions at a molecular level between solutes and solvent molecules.Such an approach requires detailed insight into the roles played by dispersion, hydrogen- bonding, dipole-dipole . . . interactions and the contributions of these several interactions7 to the overall solvation parameters. Despite the formidable problems involved some progress has clearly been made. The dramatic dependence of activation parameters, particularly A' Cpm,on mole fraction composition of TA mixtures may point to the importance of microheterogeneity (or, pseudo-phase separation) across a narrow range of '* F. Franks, reference 58, 1973, vol. 2, chapter 1; 1975, vol. 4, chapter 1. 73 S. Goldman, Acc. Chern. Res., 1979, 12, 409. Blandamer, Burgess, and Engberts mixture cornpositi~ns.~~~~~ The marked dependence on composition of excess molar isobaric heat capacities of mixing,76 sound absorption77 properties, and light scattering properties78 of these mixtures are indicative of this tendency.The close relationship between trends in the kinetic parameters for reactions in these mixtures and in microemulsions79~80 is interesting in this respect. In aqueous mixtures where the co-solvent is hydrophilic (i.e.TNA mixtures), the hydrophobic character of the substrate is important but mechanistic interpretation of solvent effects on kinetic parameters may be complicated by preferential solvation Rate limiting deprotonation of carbon acids in several water- rich TNA systems has been studied and extrema in A'G" shown to occur in water- rich mixture^.^ 1*83It has been suggested that polarization of water molecules by dipolar organic solvents is partly responsible for the observed solvent effects.81 If chemical reaction involves ions, the treatment is slightly less satisfactory because thermodynamic equilibrium data yield the transfer chemical potential for a salt rather than the individual ions.Consequently additional extrathermodynamic assumptions are invoked to obtain single ion quantities. In the case of a 1:1 salt (= 3, A(aq -x2)p2"(sln;T) = Afaq -x,)p+"(sln;T) + A(aq -x2)p-"(sln;T) (7-3) Considerable progress has been made in the derivation of these single ion transfer parameters (cf: right-hand side of equation 7-3), the extensive sets4,ss for methyl alcohol +water mixtures being notable in this respect.Recent assignments of single ion transfer parameters are based on the assumption that A(aq- A(aq -x2)p0(Ph4P+;sln;T)= x,)p"(Ph,B-;sln;T), i.e. the TPTB assump- tion. Figure 7 shows the transfer chemical potentials for a small selection of ionss6 in water + methyl alcohol mixtures, being derived in all cases on the TPTB assumption. The derived parameters show the expected destabilization of simple ions such as K+, Cl-, OH-, and SO,2-as the proportion of methyl alcohol in the mixture increases. Again as expected, the di-negative sulphate ion is more markedly affected than the 1 +and 1-ions. Figure 7 also shows the importance of the nature of the ligand in an inorganic complex ion.Thus an increase in the methanol content 74 H. A. J. Holterrnan and J. B. F. N. Engberts, J. Org. Chem., 1983,48, 4025. "L. T. Kanerva and E. K. Euranto, J. Am. Chem. Soc., 1982, 104, 5419. 76 C. de Visser, G. Perron, and J. E. Desnoyers, Can. J. Chem., 1977, 55, 856. 77 M. J. Blandarner, reference 58, volume 2, chapter 9. 78 T. Kato, N.Ito, T. Fujiyama, and Y. Udagawa, Studies in Physical and Theoretical Chemisfry, 1982,27, 175. 79 M. J. Blandamer, J. Burgess, B. Clark, P. P. Duce, and J. M. W. Scott, J. Chem. Soc., Faraday Trans. I, 1984, 80, 739. M. J. Blandarner, B. Clark, J. Burgess, and J. M. W. Scott, J. Chem. SOC., Faraday Trans. I, 1984,80,1651. K. Rernerie and J. B. F. N. Engberts, J. Org. Chem., 1981, 46, 3543.82 K. Rernerie and J. B. F. N. Engberts, J. Phys. Chem., 1983, 87, 5449. 83 F. Hibbert and F. A. Long, J. Am. Chem. SOC., 1972,94, 7637. 84 M. A. Abraham, T. Hill, H. C. Ling, R. A. Schulz, and R. A. C. Watt, J. Chem. SOC., Faraday Trans. I, 1984, 80, 489. "0.Popovych, J. Phys. Chem., 1984, 88, 4167. 86 M. J. Blandamer, J. Burgess, A. Hakin, N. Gosal, S. Radulovic, P. Guardado, F. Sanchez, C. Hubbard, and E.-E. A. Abu-Gharib, submitted for publication. Activation Parameters for Chemical Reactions in Solution of the mixture destabilizes the [Co(NH,),(CO,)] cation but stabilizes the + [Co(phen),(CO,)] ion, where hydrophilic ammonia ligands have been replaced + by hydrophobic 1,lO-phenanthroline ligands. The dominance of ligand hydrophobicity over ionic charge is also shown by the data for iron@) cations included in Figure 7; the extent of stabilization by added methyl alcohol increases enormously as one goes from the very small gmi ligand through 1,lO-phenanthroline to the very bulky ligand derived from 2-benzoyl pyridine and 3,4-dimethylaniline (i.e.bsbMe,). The dominating influence of hydrophobic ligands carries through into the analysis of kinetic data in terms of solvent effects on initial and transition states, as shown in Figure 8. Here the relatively small effect of sot-/ "\1; MebsbFe ( Figure 7 Calculated dependence on solvent composition of single ion chemical potentials for various ions in methyl alcohol + water mixtures at 298 K and ambient pressure Blandamer, Burgess, and Engberts changes in solvent composition on the rate constant masks very large but nearly equal effects on the iron@) complex cation and the transition state.Strong preferential solvation of hydroxide ions by water means that the transfer chemical potential of hydroxide ions does not exert a marked kinetic effect in water-rich mixtures. The importance of solvation changes in kinetics of reaction between iron@) di- imine complex cations and hydroxide ions is dramatically demonstrated by trends in activation volumes. Despite the bimolecular nature of the rate-determining step, 85 kJ mol--10.5i TS OH’ IS Fe(phen(* 0 10 20 30 60 50 60 vol MeOHOh Figure 0 Analysis of kinetic data in terms of effects of solvent composition in methyl alcohol + water mixture on (a) Fe(phen),’+ ions, (6) OH-ions, and (c) the transition state at 298 K Activation Parameters for Chemical Reactions in Solution A' V" is in the range + 10 to +20 cm3 mol-' in aqueous s~lution.~' These positive values may be ascribed to release of electrostricted water from hydroxide ions.The variation of A' V" with solvent composition in water + methyl alcohol mixtures shows a striking dependence on the nature of the di-imine ligand. For the complex with a relatively small and moderately hydrophobic ligand, [Fe(hxsb)]*+, A' V" decreases from 13.4 in water to 7 cm3 mol-' in 85% methyl alcohol, but for the large -+and hydrophobic complex cation, [Fe(bsbMe2)I2 mentioned above, A' V" increases from + 11.1 to 27 cm3 mol-' over the same composition range.88 Recent experiments show that the dependence of A* V" on solvent for reaction between either [Fe(gmi)12 or [Fe(hxsb)I2 and hydroxide ions reflects structural effects in + + water + alcohol mixture^.^^**^ hxsb Me Me bsbMeZ Returning attention to molar enthalpies of activation, absolute partial molar enthalpies cannot be determined for solutes in solution.The outlook is much brighter when we turn attention to molar volumes of activation because partial molar volumes of solutes in solution can be determined. The same situation prevails for partial molar heat capacities which can be measured using, for example, a flow cal~rimeter.~~~~~In the absence of volumetric and heat capacity data, group additivity scheme^^^-^^ lead to estimates for C,j"(sln;T;p) and Vj"(sln;T;p). Analysis of kinetic data proceeds through the analogue of equation 7-1 re-expressed in terms of V-and C,-quantities.Where one or more of the reactants are J. Burgess and C. D. Hubbard, J. Chem. SOC.,Chem. Commun., 1983, 1482. 88 J. Burgess and C. D. Hubbard, J. Am. Chem. SOC.,1984, 106, 1717. 89 M. J. Blandamer, J. Burgess, C. D. Hubbard, and S. Radulovic, unpublished work. 90 P. Picker, P. A. Leduc, P. R. Philip, and J. E. Desnoyers, J. Chem. Thermodyn., 1971, 3, 631. 91 J. E. Desnoyers, C. de Visser, G. Perron, and P. Picker, J. Solution Chem., 1976, 5, 605. 92 N. Nichols, R. Skold, C. Spink, J. Suurkwesk, and I.Wadso, J. Chem. Thermodyn., 1976, 8, 1081. 93 G. Perron and J. E. Desnoyers, Fluid Phase Equilibria, 1979, 2, 239. 94 R. N. French and C. M. Criss, J. Solution Chem., 1981, 10, 713. <=)W(sln)+s Blandamer, Burgess, and Engberts ions, extrathermodynamic assumptions are again required to calculate ionic from salt proper tie^,"-^' e.g. V, "(s1n;T;p) and Cp+"(s1n;T;p). Analysis of kinetic data where chemical reaction involves the solvent is a little more complicated. Suppose reaction 6-1 is written, z -z (74) In dilute solutions, n(S) % n,,n,, and n,; the input quantity to the analysis is a first order rate constant describing a bimolecular process. But (at p 1:p"), A'G"(s1n;T) = pz*(sln;T) -pw"(sln;T) -p"(S;tT) (7-5) Here po(S;I;T)is the standard chemical potential of the solvent. If the first-order rate constants for reaction 7-4 are compared in two solvents S1 and S2 (e.g.H,O and D,O), the ratio k(Sl)/k(S2)is relatedg8 to the difference between the standard chemical potentials of the liquids, S1 and S2. If reaction 7-4 is studied in a mixed solvent formed by two liquids S1 and S3, where S3 is inert, analysis of the dependence of rate constants on solvent composition is more complicated in view of the different standard states which can be defined for solutes and solvents.The usual approach defines the chemical potentials for reactant W and transition state in terms of standard states in a solution formed by the mixture S1 and S2, using the pure liquid S1 for the standard state of S1.Therefore the dependence of rate constant on composition is accounted in part by the (non-ideal) properties of S1 in the mixture.This is a contentious subject, the arguments revolving around the extent of solvent involvement in the activation process and the amount of information which can be extracted from a first-order rate constant. The subject is complicated even further if chemical reaction is studied in a mixture of two solvents where there is a possibility of two parallel reactions involving solute W and either solvent. 8 Isochoric Activation Parameters The molar enthalpy of activation A'H"(s1n;T;p) describes the dependence of rate constants for a given reaction on temperature under isobaric conditions. We can also ask how the rate constant for this reaction depends on temperature, in the event that the pressure changes to hold constant the molar volume of the solvent.This isochoric condition is indicated by equation 4-6. The required partial derivative is, 95 R. N. French and C. M. Criss, J. Solution Chem., 1982, 11, 625. 96 F. J. Millero, Chem. Rev., 1971, 71, 147. 97 S. Cabani, G. Conti, and E. Matteoli, J. Chem. SOC.,Faraday Trans., 1978, 74, 2408. 98 M. J. Blandamer, J. Burgess, R. E. Robertson, K. M. Koshy, E. C. F. KO,H. S. Golinkin, and J. M. W. Scott, J. Chem. SOC.Faraday Trans. 1, 1984,80, 2287. 257 Activation Parameters for Chemical Reactions in Solution where, by dln kSK/T A+w(V1*)[TIVl*= RTZ A#w(V,*) is expressed in J mol-'. Rate constant k$ characterizes the change in composition under isobaric-isothermal conditions.Transition State Theory uses the isobaric-isothermal equilibrium condition in equation 6-2 where the chemical potentials of reactants and transition states are related to standard (or reference) chemical potentials under isobaric-isothermal conditions. Therefore the isochoric condition in equation 8-1 is extrin~ic~~-'~' to the reacting system. A*w(V1*) is a pseudo-isochoric activation parameter where the isochoric condition refers to the molar volume of the solvent. The dependence of rate constant on pressure at constant V1*is described by the partial derivative, By Afq( V,*), expressed in m3 mol-', is an extrinsic isochoric activation parameter.Equations 8-1 and 8-3 are rewritten in terms of the molar isobaric and isothermal activation parameters, AfV(V1*) = A'Hm (s1n;T;p) -(al*/K1*)TAf V"(s1n;T;p) (8-5) and A'p( V1*)= A' V" (s1n;Zp) -(K~*/al *)A 'H"(s1n; T;p)/T (8-6) Equation 4-5 is incorporated into these equations to produce two further equations; A'y(V1*) = A'Hm(sln;rp) -(nl*+ p)A'V"(sln;T;p) (8-7) and A'(p(V,*) = AfVa(sln;T;p) -A#H"(sln;T;p)/(n,* + p) (8-8) For liquids where I'll*g p, (cJTable 1) A'y(Vl*) = nl*A'(p(VI*) (8-9) The latter equation has an interesting form,lo0 resembling the classical 99 M. J. Blandamer, J. Burgess, B. Clark, R. E. Robertson, and J. M. W. Scott, J. Chem. SOC.,Faraday Trans.I, 1985,81, 11. loo J. R. Haak, J. B. F. N. Engberts, and M.J. Blandamer, J. Am. Chem. SOC.,in press. lo' M. J. Blandamer, J. Burgess, B. Clark, and J. M. W. Scott,J.Chem.SOC..Faraday Trans. I, 1984,80,3350. Blandamer, Burgess, and Engberts thermodynamic equation, w = -pdV. Also xl*, V1*, Azw(V,*), and Afcp(V1*) depend on temperature and pressure. For a reaction in binary aqueous mixtures where xl and V, depend on T, p, and x2, then so must A*v(V,) and A#q( V,,,) where V,,, refers to the molar volume of a liquid having a particular mole fraction composition. If kinetic data in aqueous solution form the re-ference, The quantities on the right-hand sides of equations 8-10 and 8-11 are isochoric (V,) parameters for a mixture and for water, i.e. local to each solvent system. The two derived quantities are differences between these local quantities; they do not measure differences under a global isochoric condition.The effects of added t-butyl alcohol on activation parameters"' for the neutral hydrolysis of p-methoxyphenyl2,2-dichloropropionateare summarized in Table 2. With increase in x2, the enthalpy of activation decreases, passes through a minimum and then increases, this being a common pattern for reactions in aqueous mixtures. The volume of activation decreases whereas Afw( V,) increases gradually. The contrast between the minimum in the isobaric parameter and the gradual change in the isochoric parameter prompted the suggestion that the latter are ~impler~~."~ The issue is far from settled. In fact, the and more f~ndamental.'~~ data in Table 2 identify problems in the interpretation of the dependence of activation parameters on solvent composition.A(aq -x2)AfHW measures the dependence of an isobaric property at 298 K; A(aq-x,)A'V" is the dependence of an isothermal quantity at ambient pressure. But as x2 changes so does the molar volume of the binary mi~ture.'~ x2)Afy(V,) isHence A(aq ---the dependence of local isochoric (V,) quantities where the pressure 6n2 in equation 4-7 is characteristic of each mixture. These considerations indicate additional complexities in the term, A(aq ---,x,)A'v( V,,,) rather than a simplification. Table 2 Isothermal, isobaric, and isochoric (V,) activation parameters for neutral hydrolysis of p-methoxyphenyl2,2-dichloropropionatein t-butyl alcohol -+ water mixtures at 298 K and ambient pressure x(t-butyl alcohol) 0 0.05 0.075 A(aq -+x2)Af H"/kJ mol-' 0 -10.5 -9.2 A(aq -+XZ)A# V"/cm3 mol-' 0 -31 -37 A(aq -+x~)A'w( J'm)/kJ mol-I 0 8.8 35.5 taken from ref.102 lo' H. A. J. Holterman and J. B. F. N. Engberts, J. Am. Chem. SOC.,1982, 104, 6382. lo3 B. T. Baliga and E. Whalley, J. Phys. Chem., 1967, 71, 1166. lo4 D. L. Gay and E. Whalley, J. Phys. Chem., 1968,72,4145; Can. J. Chem., 1970,48, 2021. Activation Parameters for Chemical Reactions in Solution The procedures leading to equations 8-1 and 8-3 can be repeated with reference to derived activation parameters. For example, using A' V*, (8-12) Here the derived quantity describes the dependence of A' V" on temperature in the event that the pressure changes to hold V1* constant.A similar equation describes the isochoric ( V,*) dependence of ArV" on ternperat~re.~~ For ethanoic acid in water,lo5 both ArV" and (aArV"/aT)at constant Vl* are < 0. Equation 8-12 can be rewritten as a partial derivative for A'Hm. Slightly more contrived is the partial derivative of In (k$K/T)with respect to T at constant A' V"; The derived quantitylo6 endeavours to account for differences in solvent densities around initial and transition states. 9 Discussion The kinetic isochoric (V,) and isochoric (V,*) quantities emerge from a drawing together of the isobaric-isothermal activation parameters for chemical reactions Figure 9 Isobaric and isothermal properiies; the link through isochoric conditions lo5 D.A. Lown, H. R. Thirsk, and Lord Wynne-Jones, Trans. Faraday SOC.,1975, 66, 57. Io6 E. F. Caldin, quoted in ref: 34. Blandamer, Burgess, and Engberts 18.019 A O, i8.oia 3Yr 2 2 -I--. 0 E m 25 18.011 \ 0 ON I Y # 1 '18.016 I 1 I I 2 4 6 8 ( T-273.15)/K Figure 10 Dependence on temperature at ambient pressure of molar volume for water and rate constant for soluolysis of t-butyl chloride; data from references 107 and 112 and the isobaric-isothermal volumetric properties of solvents (Figure 9). A key question concerns the extent to which the isochoric activation parameters (e.g. Afy(V1*) and Af~(Vl*)) satisfy the criteria described by Evans and Polanyi7 (Introduction).We take a pessimistic view. No simple relationship exists between intermolecular separation in liquids and their molar volume. At ambient pressure, there are pairs of temperature, one above and one below the temperature of maximum density (TMD), where the molar volumes of water (and D,O) are equal.lo7 Yet X-ray and neutron scattering data"* show that these equalities in molar volumes do not reflect identities in plots of pair correlation functions. 09-1 Further, rate constants for chemical reaction' 12,113 in water over a temperature range spanning the TMD show no surprising features (Figure 10). lo' G. S. Kell, reference 72, 1972, volume 1, p. 363. lo* A. H. Narten and H. A. Levy, reference 72, volume I, chapter 8.lo9 J. A. Polo and P. A. Egelstaff, Phys. Rev. A, 1983, 27, 1508. 'lo P. A. Egelstaff and J. H. Root, Chem. Phys., 1983, 76,405. 'I1 G. A. Gabella and G. W. Nielson, Mol. Phys., 1983, 50, 97. E. A. Moelwyn-Hughes, R. E. Robertson, and S. E. Sugamori, J. Chem. SOC.,1965, 1965. 'I3 W. J. Albery and J. S. Curran, J. Chem. SOC..Chem. Commun., 1972,425. 26 1 Activation Parameters for Chemical Reactions in Solution In a wider context, however, interest in isochoric activation energies has revived.loO Based on the definitions described in the previous section, interpretation of dependence on solvent composition and substrate is a topic of current research and will be the subject of future reports. The 'isochoric' condition is slightly unusual but offers a possibly new insight into chemical reactions in solution.If the compromise suggested by Evans and Polanyi raises new problems, it might be informative to direct attention to the internal pressure of the solvent, xi,bearing in mind that this quantity emerges in several equations reviewed above. This is not a new suggestion, many authors having commented on the role of internal pressure in kinetics of reactions in solution.114 The analysis described in the previous sections prompts the derivation of partial derivatives at constant xi; e.g. -01 I I I 16 TTi /bar Figure 11 Dependence on internal pressure for water at ambient pressure of rate constant for solvolysis of t-butyl chloride; data from references 28 and 105 114 M.R.J. Dack, J. Chem. Educ., 1974, 51, 231. Blandamer, Burgess, and Engberts Alternatively the dependence of rate constant on internal pressure can be explored115 (Figure 11) leading to an estimate of the partial derivative, 0 0.2 0.4 0.6 0.8 1.0 x2 -Figure 12 Dependence of inrernalpressure on mole fraction for binary aqueous mixtures; 0 = methyl alcohol; A = t-butyl alcohol; and = DMSO; data from reference 116 The dependences of ni on mole fraction x2 for several binary aqueous rnixtures1l6 and solutions are known (Figure 12) and there may be merit in examining the dependence of rate constants on x2 in terms of the associated dependences of k on ni (cf: reference 117). An interesting feature of aqueous solutions is the dependence of TMD on which means that the composition at which ni is zero also depends on the nature of the co-solvent.Moreover below a TMD, the internal pressure is negative. The significance of the latter is a matter for speculation in so far as the impact on the kinetics of chemical reactions in these systems. Presumably, negative internal pressures for aqueous solutions at low temperatures are linked to the repulsive characteristics of hydrogen bonding. When a hydrogen bond forms between two near-neighbour water molecules, their centres of mass move apart. The same argument applies 115 M. J. Blandamer, J. Burgess, and A. Hakin, unpublished work. '16 D. D. Macdonald and J. B. Hyne, Can. J. Chem., 1971,49, 611, 2636. 11' M. R. J. Dack, Aust.J. Chem., 1976, 29, 771. F. Franks and B. Watson, Trans. Faraday SOC.,1967, 63, 329. D. D. Macdonald, A. McLean, and J. B. Hyne, J. Solution Chem., 1978, 7, 63. M. V.Kaulgud, J. Chem. SOC.,Faraday Trans. I, 1979, 75, 2246. 12' Activation Parameters for Chemical Reactions in Solution when a weak (distorted) hydrogen bond is strengthened within liquid water. Recent12 models for liquid water emphasize the importance of fluctuations involving weak-distorted and strong-directional hydrogen bonds between water molecules. The impact of this equilibrium on the thermodynamic properties of solutes can be treated in terms of a medium-sensitive activity coefficient for a s01ute.l~~Interest in this development stems from applications of the model to initial and transition states, thereby estimating, for example, molar isobaric heat 25capacities of activation for reactions in water and aqueous 12' R.Lumry, E. Battistel, and C. Jolicoeur, Furuday Symp. Chem. SOC.,1982, 17, 93. 122 D. Mirejovsky and E. M. Arnett, J. Am. Chem. SOC.,1983, 105, 1112. E. Grunwald, J. Am. Chem. SOC.,1984, 106, 5414. M. J. Blandamer and J. Burgess, J. Chem. SOC.,Furuduy Trans. 1, 1985, 81, 1495. M. J. Blandamer, J. Burgess, and J. M. W. Scott, J. Chem. Soc., Faraduy Trans. 1, 1984,80, 2881.

ISSN:0306-0012    

DOI:10.1039/CS9851400237

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

R. A. ROBINSON MEMORIAL LECTURE Potentiometric Titrations of Aqueous Carbonate Solutions By A. K. Covington* DEPARTMENT OF PHYSICAL CHEMISTRY, THE UNIVERSITY NEWCASTLE UPON TYNE, NEI 7RU 1 Introduction When carbon dioxide dissolves in water, as is well known,' it forms a weak acid, carbonic acid H2C03, which dissociates to give hydrogencarbonate (bicarbonate) and carbonate ions. Only a small fraction of dissolved CO, forms carbonic acid and, depending in extent on pH, four forms can be present, namely, CO,, H2C03, HCO,-, and Co3,- thus complicating the usual dissociation process of a weak diprotic acid. The basic equations are summarized in Table 1. In view of the importance of the carbonate system to environmental, biological, and industrial processes, it has been much studied and is the subject of a book2 and several review^.^-^ Originally, our interest in the aqueous carbonate system arose from the possible role of carbonate impurity in the results for the ionization constants for H,O and D,O obtained from the cells: where M = an alkali metal and m,= 0.01, m, > 0.01 mol kg-'.From the temperature variation of the e.m.f. of cells I or I1 over the range, usually, of 0-55 "C, values for the enthalpy of ionization of H,O and D20 can be derived. For H20, AH+ = 56.61 kJ mol-' from cell I,6 whereas by calorimetric methods systematically lower values of 55.81 kJ mol-' have been found.7 For D,O the situation is reversed and the calorimetric value is higher. In searching for an explanation, suspicion fell upon the role of a systematic error in the hydroxide ion concentration (m resulting from absorption of atmospheric * This review is based on the third R.A. Robinson Memorial Lecture, 'The Carbonate-Bicarbonate System Revisited', given at the University of Singapore, Kent Ridge; the Universiti Sains Penang; and the University of Malaya, Kuala Lumpur, in January 1984. ' W. Stumm and J. J. Morgan, 'Aquatic Chemistry', Wiley, New York, 1970, chapter 4. R. E. Loewenthal and G. R. Marais, 'Carbonate Chemistry of Aquatic Systems', Ann Arbor Science Publ., Ann Arbor, Michigan 1976, pp. 102--8. J. T. Edsell, NASA Spec. Reporr No. 188, 1969, 15. D. M. Kern, J. Chem. Educ., 1960, 37, 14. Gmelin Handbuch der Anorganischen Chemie, Carbon, 8th Edition, Vol.C3, ed. R. J. Meyer, Verlag Chemie, Weinheim, 1973. A. K. Covington, M. I. A. Ferra, and R. A. Robinson, J. Chem. SOL..,Faraday Trans. I, 1977, 73, 1721.'G. Olafsson and L. G. Hepler, J. Solution Chem., 1975, 4, 127. Potentiometric Titrations of Aqueous Carbonate Solutions Table 1 The equilibrium distribution of solutes in aqueous carbonate solution (system closed to the atmosphere)' Species COz(aq), HzC03, HC03-, COz3-, H', OH-[HzCOJ*] = [Co~aq]+ Concentration condition CT = [HzC03*] + CHC03-] + [C032-] Ionization fractions [HzCO3*] = CTaO; CHC03-I = CTa1; [C03z-] = CraZ carbon dioxide in spite of stringent precautions to exclude it. The acquisition of a new automatic titrator provided the opportunity to investigate the potentiometric titration of hydroxide solutions contaminated with known additions of carbonate in an attempt to determine the lower limit of detection by this method.The titrator was unique in type in providing a true first derivative output, dE/dV, from measured potential difference (E) between sensor and reference electrodes with volume (V) delivered, rather than mathematically derived slopes. Our first derivative titration with this apparatus revealed an artefact, in that an additional maximum in the first derivative curve appeared between those expected for the protonation of carbonate to hydrogencarbonate and hydrogencarbonate to carbonic acid (Figure 1). Whilst attempting to locate an experimental origin of this unexpected feature, Robinson and I began looking into the calculation of first derivative titration curves and how the heights of the maxima varied with the concentration conditions of the titration.' Figure 2 shows the three expected maxima for the three protonation steps in a titration with acid.Alkali titrations are simply the reverse. Clearly, experiment and theory were discrepant and a systematic study was commenced to establish the reprqducibility of the experimental titration curves and the effect of varying conditions on the manifestation of the additional maximum. A. K. Covington, R. A. Robinson, and M. Sarbar, Anal. Chim. Acta, 1978,100, 367. Covington 7.77 8.07 8.30 8.50 Volume of HCI / dm3 Figure 1 Titrationof 10cm3of 0.2 mol dm-3 NaOH + 6 mg Na2C03with 0.25 mol dm-3 HCl 750 I I I I I I I I 600 I I I I I II II I I I I 450 I I I I d Inh OH' I CO;-+HCO,-I HCO,' + H2C03 I Idx I I I I I 300 I I I I I I I 1 I150 I I I wI 01 w 0 0.33 0.67 1 XW Figure 2 Theoretical differential titration curve for titration with HCl of 0.1 mol dm-3 NaOH + 0.1 mol dm-3 Na,CO,, x is the degree of advancement of the titration Potentiometric Titrations of Aqueous Carbonate Solutions 2 Experimental Titrations were carried out in a 25 cm3 cylindrical vessel thermostatted at 25 "C by circulating water in an outer jacket.The top of the vessel was sealed tightly with a lid containing ports for glass and reference electrodes, thermometer, nitrogen gas- entry, and titrant-entry.The titration solution was stirred by means of a Teflon- coated magnetic follower. The Mettler titrimeter (Zurich, Switzerland) comprised the modular units of a 10 cm3 burette, conversion, control, and electrometer units and display of the derivative titration curve (dE/d v)of dE/dpH on chart recorders. A variety of glass electrodes was used. Some of these were combination electrodes, but others were used with saturated calomel reference electrodes. Titrations were also carried out using a carbon dioxide gas electrode (Radiometer Type PS1-904- 123). Sodium hydroxide was carbonate-free solution (BDH, Poole). Hydrochloric acid solutions were prepared from BDH AVS ampoules.Sodium and potassium carbonates were AnalaR grade. Further experimental details are a~ailable.~ 3 Results Figure 3 shows the results of derivative titrations with 0.05 mol dm-3 HC1. Figure 4 shows the effect of varying the temperature. The additional maximum moves closer to that for hydrogencarbonate to carbonic acid at 5 "C from its position at 34567 Volume of HCl /dm3 Figure 3 Titration of0.l mol dm-3 NaOH + Na,CO, solutions with 0.25 mol dmS3HCl at various CO,'-/OH-mol %: (a) 5%, (b) lo%, (c) 25% A. K. Covington, R. A. Robinson, and M. Sarbar, Anal. Chim. Acta, 1981, 130, 93. Covington 25 "C,and disappears into the maximum for carbonate to hydrogencarbonate as the temperature approaches 55 "C.Figure 5 shows that the effect is present in a series of experiments at constant carbonate concentration instead of constant hydroxide with variations in carbonate/hydroxide ratio; with no hydroxide the effect is absent. Identical titrations were obtained if potassium was substituted for sodium, but with tetramethylammonium instead of an alkali metal the additional maximum was less apparent and the other two maxima were greater in height.If nitrogen was bubbled through the solution instead of passed over it, then no additional maximum is seen, presumably because of loss of carbon dioxide. This also occurs if hydrogen gas is bubbled through the solution, so a platinum hydrogen gas electrode does not show the extra maximum but other hydrogen-ion responsive electrodes do.Figure 6 shows the results with a rhodium-rhodium oxide pH-responsive electrode, which is slower in response than a glass electrode, so the new feature appears as a shoulder rather than a separate maximum. Successive titrations with a glass electrode newly brought into service show the same effect; as the electrode becomes conditioned its speed of response increases and the maximum becomes better defined. Otherwise, the results are independent of the type of glass electrode (and reference electrode) used. Figure 7 shows the titration curves obtained when a carbon dioxide gas electrode was used. The maximum in these curves coincides with the minimum between the second and extra maximum in the glass electrode titration curves. A point of 55'C 2345 Volume of HCl/dm3 Figure 4 Titration of0.l mol dm-3 NaOH + Na2C03(5 mol % C032-/OH-) with 0.05 mol dm-3 HCl ut 5, 25, and 55 "C Potentiometric Titrations of Aqueous Carbonate Solutions dEC)dV \ L 1 .1 4 5 6 2 3 4 1 2 30 1 2 3 Volume of HCt / dm3 Figure 5 Titration of 0.01 mol dm-3 Na,CO, (25 dm3)containing various amounts of NaOH at different mol % with 0.25 mol dm--3HCI: (a)20%, (6) 40%, (c) 125%,(d)no NaOH added t I I 1 I 1 I I 1 1 I 0 1 2 3 4 5 6 7 6 9 1 0 Volume of HCl/ dm3 Figure 6 Titration of 25 cm3 0.04 mol dm? NaOH + 0.006 mol dm-3 Na,CO, with 0.05 mol dm3 NaOH (1 cm3/4 min) using glass electrode (solid curve) and rhodium-rhodium oxide electrode (hatched curve) Covington1:1 II III tiI I II I _-_-------* '-----L""" 1234567 Volume of HCl/dm3 Figure 7 Titration of0.l mol dm-3 NaOH + Na,C03 (10% C.03!-/OH-mol%) with 0.05 mol dm-3 HCl using glass electrode (solid curve) and carbon dioxide gas electrode (hatched curve) inflection is found corresponding to the hydrogencarbonate-carbonic acid conversion.At higher temperatures, the carbon dioxide electrode maximum moves closer to the carbonate-hydrogencarbonate maximum in the pH titration. The extra maximum was also found when the entire titration of NaOH-Na,C03 was carried out with DCl in D,O at 5 and 25 "C.As in light water, it was not present above 55 "C. Addition of amounts of ethanol in the mol fraction range 0.024.20 produced changes in the titration curves.In the mol fraction range 0.134.20the extra feature was absent. It was also eliminated by the addition of t-butyl alcohol at mol fraction 0.1. The position of the extra maximum is changed if the acid titrant concentration is changed (Figure 8). If the rate of change of hydrogen ion concentration is kept constant for a diluter titrant by a compensating increase in the speed of delivery, then the extra maximum is in the same position in the two titrations. We then turned to alkalimetric titations lo of solutions containing dissolved carbon dioxide. These can be prepared very simply with a commercial soda-syphon bottle. In Figure 9 titration curves are shown for both glass and carbon dioxide electrodes. There are three maxima and a shoulder on the right-hand side of the central maximum in the pH titration.A shoulder in the carbon dioxide electrode derivative titration is located near the first maximum in the glass electrode titration. It is clear for the glass electrode titration in Figure 9 that the shoulder on the middle maximum lies exactly between the first and third maxima. In comparison with acid titrations, it is the middle maximum which is the additional feature and not the A. K. Covington and M. Sarbar, in preparation. 27 1 Potentiometric Titrations of Aqueous Carbonate Solutions ~~~~ 012345678 Volume of HCI /dm3 Figure 8 Effect of rate of titration on titration curves of 0.04 mol dm-3 NaOH + Na,COJ (5mol % COi-/OH-) with 0.05 mol dm-3 HCl.A, 1 cm3 HCl in 4 min; B, 1 cm3 HCl in 48 s shoulder, for it is the maximum in the CO, electrode titration which corresponds with the shoulder in the pH titration. Figure 10 shows the effect of varying the temperature of titration of C0,-water. At 5 "C, the new feature has moved towards the first maximum in the titration. Above 55 "C, the titration is that expected with the centre maximum of increased height. Figure 11 illustrates the effect of back titration with acid, and then a further back titration with alkali on the results at 5 "C, and indicates that the effects are entirely reproducible. n It It 1 , I 012345678 Volume of NaOH/dm3 Figure 9 Titration of 25 cm3 of 0.02 rnol dm-3 HCl + 0.0125 mol dm-3 of dissolved CO, solution with 0.1 rnol dm-3 NaOH (rate of addition 1 cm3 NaOH/4 min) using glass electrode (solid curoe) and carbon dioxide gas electrode (hatched curve) Covington 5 *c l l I k 1 1 & I " * 0 1 2 3 4 5 0 1 2 3 4 Volume of NaOH I dm3 Figure 10 Titration of 25 cm3 of0.022 mol dm-3 dissolved C02 with 0.25 mol dm-3 NaOH (rateof addition 1 cm3/48s) at 5,25, and 55 "C.At 55 "Csome C02 is lostfrom the solution due to lower solubility 0 1 2 3 4 56 789 Volume of HCI Idn Figure 11 Effect of bovine carbonic anhydrase on glass electrode titration of 25 cm3 0.04 mol dm-' NaOH + 0.008 mol dm-3 Na2C03.Solid curve, without carbonic anhydrase; hatched curve, with carbonic anhydrase (1 mg) added The slow kinetics of the hydration of carbon dioxide and dehydration of carbonic acid are well documented 3*4 (equation 9) Potentiometric Titrations of Aqueous Carbonate Solutions with kf = 0.03 s-l, k, = 20 s-I, and we considered whether this could give rise to a spurious maximum in the titration curves.The enzyme, carbonic anhydrase, speeds up these hydration-dehydration reactions, so the effect of addition of a small amount to the titration solution was investigated, taking care not to add the enzyme to solutions of extreme pH to avoid destroying enzyme activity. The results are shown for acid glass-electrode titration in Figure 11. For all titrations addition of carbonic anhydrase completely removes the extra feature. Neither Robinson or I liked the obvious conclusion that the new feature arose from the slow kinetics, so, assisted by R.N.Goldberg, who had had experience of computer simulation of liquid junction potentials,' computer modelling of titration curves was developed taking into account the slow kinetics in the system.12 The algorithm used is indicated in Figure 12. First the 'equilibrium' case with no slow steps was derived, then the carbonic acid concentration as a function of time was introduced in accordance with equation 9 and solved for [H'] numerically. Figure 13 shows that the only effect of the slow kinetics was to change the height of the maximum at pH about 8.5. To make sure that the same was true if the kinetics were even slower, the values were changed from their accepted values by the amounts shown in the Figure caption.Again only a change in the height of the maximum was observed, unless the rate of addition of alkali was speeded up, when some displacement of the maximum was observed, as expected, but no new features in the titration curve were found. Initial Condition Total [COz], initial [H'] Mass balance Charge balance I n time increments New mass balance = n volume increments of NaOH New charge balance Slow CO2 hydration 1I INew [H'], [H2CO3], [HC03-] etc. dECalculated *--etc. dt dt Figure 12 Flow chart of computer simulation of titration curves with slow kinetics H. S. Frank and R. N. Goldberg,J. Phys. Chem., 1972, 76, 1758. I2 A. K. Covington, R.N. Goldberg, and M. Sarbar, Anal. Chim. Acta, 1981, 130, 103. 274 Covington 0.0035 --0.0025 -0.0020 -0.0015 -0.0010 -0.0005 -0.0000 2 4 6 8 10 12 PH Figure 13 Calculated values of dpH/dt as a function of pH for titration of 0.01 mol of CO2 andO.O1 mol of HC1 with NaOH (rate of addition 1W6 mol/s). The thermodynamic, and kinetic rate, constants given in the text were used to calculate curve 2. Curve 1 was calculated by removing all time delays in C02 -H2C03 conversion. Curve 3 was obtained by setting kf = 0.015 s-l and kf = 10.0 s-l 4 Discussion The evidence presented above suggests that the new feature in the first derivative titration curves is a property of the titrated solution, which is detected by glass electrodes and certain other hydrogen-ion responsive electrodes, but not by the platinum-hydrogen gas electrode because the hydrogen gas sweeps carbon dioxide out of the solution.The position of the extra maximum between the carbonate and hydrogencarbonate equivalence points suggests that the new feature is the result of protonation of a novel species with pK intermediate between those for carbonate and hydrogencarbonate. The most likely structure for this complex ion is a singly charged ion, formed by or Potentiometric Titrations of Aqueous Carbonate Solutions The difference between these two processes is, of course, the hydration of carbon dioxide (equation 9). If the equilibrium constant associated with equation (11) is denoted by K3 then [H 3c206 -3 =K3[HCOJ-3 [H 2CO 31 (12) =(K3/K1KZ2)[H'] 3[C032 -I2 (13) and computer-simulated titration curves can be obtained (Figure 14).a moles H2C03 2ax moles NaOH where x = 0 to 1 the degree of advancement of the titration mass balance I charge balance I 1 [C032-] = flH'] chosen [H'] values -1 Figure 14 Flow chart for computer simulation of titration curve with presence of additional species Figure 15 shows the species distribution diagram for the carbonate system based on K3 = 1.2 x lo3 dm3 mol-l, since comparison of the computer simulation titration curves (Figure 16) with experimental dE/dpH curves l3 suggests K3 is about lo3from the height of the extra maximum. Theoretical carbon dioxide gas- electrode first-derivative titration curves are shown in Figure 17. The maximum in these curves at pH 11 is not seen experimentally (Figures 7 and 9) because the carbon dioxide concentration at this pH is well below the detection limit of the electrode.The most probable structure for the new anion species is two planar carbonate moieties linked by bridging hydrogen bonds to oxygen atoms. There is evidence for the existence of such strong hydrogen bonds. l4 A computer program generation l3 A. K. Covington and M. Sarbar, in preparation. l4 3. Emsley, Chem. Soc. Rev., 1980, 9, 91. Covington PH Figure 15 Species distribution diagram for the carbonate system based on K3 = 1.2 x dm3 mol-' in equation 9 dx 1 3 5 7 9 11 13 14 PH- Figure 16 Superimposed theoretical pH titration curves for dgferent values o K3.Read- ing upwards at pH 4 the curves refer to K3 = lo4, 5 x lo3, 3.5 x lo3, 2 x 103f, 1.5 x lo3, 1.2 x lo3, 5 x lo2, 2.5 x lo2,50, 0 dm3 mol-' of this structure is shown in Figure 18. The bond lengths of C-0 and H-0 were taken from Edsel13 and Brown et a1." The suggestion is related to sodium sesquicarbonate (Na2C03,NaHC03,2HC20), which exists as the mineral, trona. In the crystal structure of sodium sesquicarbonate,' 'two carbonate ions are linked through hydrogen bonds (O-H-0) with a bond length of 0.253 nm forming a complex ion species (HC206)3 -. Protonation of this species yields dimeric hydrogencarbonate ions and then the proposed new species (equation 14).C. J. Brown, H. S. Peiser, and A. Turner-Jones, Actu Cryst., 1949, 2, 167. Potent iome tr ic Titra tions of Aqueous Carbonate Sohtions d In [CO,] dx 1 3 5 7 9 11 13 14 PH -Figure 17 Superimposed theoretical CO2 gas electrode titration curves for dgferent values of K3. Reading upwards at pH 9 the curves refer to the values of K3 given in figure 16 .''/4/w Figure 10 Structure of the new anion species consisting of two planar carbonate moieties linked by three hydrogen bonds to the oxygen atoms Thus the suggested species is the form sesquicarbonate exists in near neutral pH aqueous solution. The existence of dimeric hydrogencarbonate ion and sesqui- Couington carbonate ion in aqueous solution may be difficult to prove. It is pertinent to enquire whether any other anomalous behaviour of the carbonate system has been reported.Kern4 and Edsell have drawn attention to inconsistencies in kinetic data for the hydration-dehydration reactions. Koefoed and Engel explained their results for the acid catalysis of the hydration reaction by invoking catalysis by a new species, trimeric carbonic acid formed as shown in equation 15. 0[+H+ 0 + HO OH \/HO-C-0-Ho-c-0-,C/OH I ,OH I 'OH 0 C .C /OHI 'OH 0 4-H+ /\OH 'OH HO Edsell pointed out that there were differences between the rate constants for the dehydration of carbonic acid depending upon whether the measurements were derived from studies at acid pH or at pH 6-8 as shown in Figure 19. Laser Raman spectra of carbonic acid solutions have been but no anomalous spectral lines were found.Abbott et aLz0 determined 13Cn.m.r. spectra 1.50 1.00 0.50 Figure 19 Variation of the rate constant for the dehydration of H,CO, with 1/T (ref3).measurements made in bufler (pH 6-8); 0measurements made at low pH (HCO; l6 J. Koefoed and K. Engel, Acta Chem. Scand., 1961, 15, 1319. l7 A. R. Davis and B. G. Oliver, J. Solution Chem., 1972, 1, 329. A. R. Davis and B. G. Oliver, Can. J. Chem., 1973, 51, 698. l9 Y. K. Sze, W. A. Adams, and A. R. Davis, in 'Chemistry and Physics of Aqueous Gas Solutions', The Electrochemical Society, New York, 1975, p. 42. 2o T. M. Abbott, G. W. Buchanan, P. Kruus, and K. C. Lee, Can. J. Chem., 1982,60, 1OOO. 21 C.W. Davies and L. J. Hudleston, J. Chem. SOC.,1924, 125,260. Potentiometric Titrations of Aqueous Carbonate Solutions and detected signals ascribed to CO,(aq), hydrogencarbonate, and carbonate ions. No direct evidence for carbonic acid was obtained but an unstable species was found with a shift, relative to TMS, or 151.3 p.p.m. compared to 161.3 p.p.m. for hydrogencarbonate and 163.5 for carbonate was found. The new species could be considered as and such triple ions have been reported to exist for a variety of acids in aqueous solution. The best known 21*22 is probably HF2-, but triple ion formation constants have also been determined for phosphoric 23*24 and iodic 25 acids. From solubility measurements, Kolthoff and Bosch 26 postulated the existence of a benzoic acid-benzoate 'inner complex', and Martin and Rossotti 27 have reported formation constants for monocarboxylic acid triple ions from pH titrations in perchlorate media.These data are collected in Table 2, from which it may be noted that the formation constant for the carbonate species is appreciably higher than those found previously. Table 2 Triple-ion formation constants Acid Triple-ion &/dm3 mol-' Ref: HF HF2-4.7, 3.86 21,22 HzPO~-*H~PO~ 3, 1.26 23, 24 HIOj H(IO 3)2 - 4 25 RCOOH" R*COOH*RCOO- 0.32, 0.46, 0.45, 0.58 27 R = H, Me, Et, Pr" Finally, a comment on the removal of the new feature in the titration by carbonic anhydrase is necessary. Although addition of carbonic anhydrase affects the kinetics of the hydration-dehydration reaction, it is also likely to affect the kinetics of formation of the new species. The existence of the new species shows up in the first-derivative titration curves when the pH of the solution is changed at an appropriate rate. The species concentration diagram (Figure 15) shows that 30% of the carbon dioxide is in the form of the new species at pH 6-8 based on comparison of experimental and theoretical titration curves of the same heights of the maximum. This could be misleading without recognizing the kinetic aspects of its existence.Although it should be possible to introduce into the computer modelling rate constants for the formation and decomposition of the new species, this has not yet been done.Owing to the physiological2* and technical importance of the new species, 22 H. H. Broene and T. DeVries, J. Am. Chem. SOC., 1947,69, 1644. 23 M. Selvaratnam and M. Spiro, Trans. Faraday SOC., 1965,61, 360. 24 K. L. Elmore, J. D. Hatfield, R. L. Dunn, and A. D. Jones, J. Phys. Chem., 1965,69, 3520. 25 A. D. Pethybridge and J. E. Prue, Trans. Faraday SOC., 1967, 63, 2019. 26 I. M. Kolthoff and W. Bosch, J. Phys. Chem., 1932,36, 1685. "D. L. Martin and F. J. C. Rossotti, Proc. Chem. SOC., 1959, 60. C. T. G. Flear, A. K. Covington, and J. C. Stoddart, Ann. Intern. Med., 1984, 144, 2285. 280 Covington further spectroscopic investigations would be valuable, and using modern instrumentation, a new study of the kinetics of the hydration and dehydration reactions.Acknowledgements. The results presented here are the work of Dr. M. Sarbar. Dr. R. N. Goldberg, during his sabbatical leave from the National Bureau of Standards, Washington, DC, devised the computer simulation program involving slow kinetics. Dr. M. N. S. Hill and Mr. I. McKeag helped with computer programs for species distribution and titration. Discussions with many visitors, especially Prof. R. H. Stokes and Prof. R. H. Wood are gratefully acknowledged. Dr. M. Spiro kindly read the text and suggested the addition of Table 2. Tribute. I first met R. A. Robinson when he was in R. G. Bates’ Electrochemical Analysis Section at the National Bureau of Standards in 1966 during my sab- batical leave. He was still a keen experimentalist with his isopiestic technique, which I learnt from him, but also he avidly devoured experimental e.m.f.results from M. Paabo, H. B. Hetzer, and myself as they were recorded. His consuming passion was the working over of experimental results and devising new theoretical treatments particularly for multielectrolyte problems. His sound knowledge of chemical principles and ‘thermodynamics and a shrewd intuition made scientific discussions with him catalytic and exhilarating. Perhaps the attribute I most admired was his tenacity of purpose in attacking seemingly intractable problems. 28 1

ISSN:0306-0012    

DOI:10.1039/CS9851400265

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

TILDEN LECTURE * Structure and Electron-transfer Reactivity of the Blue CopperProtein Plastocyanin By A. G. Sykes DEPARTMENT OF INORGANIC CHEMISTRY, THE UNIVERSITY, NEWCASTLE UPON TYNE, NEI 7RU 1 Introduction Plastocyanin is a single polypeptide protein of -99 amino-acids (M. Wt. 10 500) containing a single Cu active site with characteristic type 1 properties, including intense blue colour and small e.p.r. hyperfine coupling (A II close to 0.006 cm-') for the CU"state.'-6 It is involved in electron transport (E'370 mV at pH -7) between photosystems I1 and I of the chloroplasts in higher plants and More specifically its function is to transfer electrons from cytochromef(360 mV) to the chlorophyll-containing pigment P700' (520 mV) which is a component of photosystem I.Isolation procedures, requiring about one week, are referenced in specific papers. 2 Functions of Plastocyanin Photosynthesis takes place at highly convoluted thylakoid membranes inside the chloroplast. A thylakoid membrane encloses space so that it has an interior and exterior. Cytochrome f is a component part of the membrane-bound cytochrome b,/'complex, which also includes the Rieske Fe/S protein. It is now known that cytochromefis trans-membrane, with the major globular part of the protein (residues 1-250) containing the haem unit, in the interior of the thylakoid (the lumen). Plastocyanin is a mobile molecule also located in the interior. The release of plastocyanin after (mechanical) damage of the membrane, and without use of * Based on the lecture delivered at a meeting of the Dalton Division of the Royal Society of Chemistry, Scientific Societies' Lecture Theatre, London, on 14th March, 1985.H. C. Freeman, in 'Coordination Chernistry-21', ed. J. L. Laurent, Pergarnon Press, Oxford, 1981, pp. 29-5 1. A. G. Lappin, in 'Metal Ions in Biological Systems', ed. H. Sigel, M. Dekker, New York, 1981, Vol. 13, pp. 15-7 1.'0. Farver and I. Pecht, in 'Copper Proteins', ed. T. G. Spiro, Wiley, New York, 1981, pp. 151-193. D. Boulter, B. G. Haslett, D. Peacock, J. A. M. Ramshaw, and M. D. Scawen, Plant Biochemistry 11, ed. D. H. Northcote, University Park Press, Baltimore, 1977, Vol. 13, p. 1040. R. A. Holwerda, S. Wherland, and H. B. Gray, Annu. Rev. Biophys.Bioeng., 1976, 5, 363. J. A. Fee, Struct. Bonding (Berlin), 1975, 23, 1.'W. A. Cramer, W. R. Widger, R. G. Herrmann, and A. Trebst, TIBS, 1985, 125. W. Haehnel, Annu. Rev. Plant Physiol., 1984, 35,659. J. Barber, Plant Cell Environment, 1983, 6, 311. See also 'Advances in Photosynthetic Research', Proceedings 6th International Congress on Photosynthesis, Kluwar Academic Publishers Group, Netherlands, 1984 and previous volumes. ' D. L. Willey, A. D. Auffret, and J. C. Gray, Cell, 1984, 36, 555. D. L. Willey, C. J. Howe, A. D. Auffret, C. M. Bowman, T. A. Dyer, and J. C. Gray, Mol. Gen. Genef., 1984, 194,416. Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin detergent, is consistent with it not being membrane-bound.Its function as a diffusibIe electron carrier between cytochrome f and P700+, Figure 1, is comparable to that of cytochrome c in the electron transport of bacteria and in the respiratory chain.* High plastocyanin concentrations and shielding of surface charges appear to be necessary for the interaction of plastocyanin and P700' Electron transfer is linked with the generation of protons inside the thylakoid in the water splitting reaction (which involves Mn), and with proton transport for the exterior of the thylakoid by plastoquinol, thereby creating an electrochemical potential gradient for ATP synthesis. ADP ATPEXTER 10R nu ti+ ///,//,Q/, //~,M/,,bt3 PS 1 MEMBRANE -PQH, P 680 f P700 / ////// //// / ////, H+ INTERIOR Figure 1 Schematic representation of photosynthetic electron transport at the thylakoid membrane indicating the function of plastocyanin, PCu.Other abbreviations are Mn for the H20splitting complex, PQH2for plastoquinol, b,/f for the cytochrome complex, Fdfor ferredoxin, FNR for the ferredoxin NADP+ reductase, and ADP and ATPfor adenosine di- and tri-phosphates 3 Aims and Background Physical properties and the structure of plastocyanin form an important part of what follows. Mechanistic studies described are aimed at better understanding the active-site chemistry, as well as identifying binding sites on the surface of plastocyanin, and in the long term understanding just how electrons are transferred over long distances, with 10-15 A no longer regarded as exceptional. The active site of plastocyanin consists of a single Cu atom and four ligating amino-acid side- chains.Oxidation states I and 11, referred to here as PCu' and PCu" are involved in the redox cycle. A binding site is a region on the surface of the protein at which electron transfer with a redox partner occurs. Association of the partner at such a site prior to electron transfer to give a reactant pair (the equivalent of outer-sphere association in the reaction of two metal complexes), does not involve covalent bonding. This contrasts with the case of 0,-carriers and substrate binding (e.g. zinc) enzymes, where the active site and binding sites are one and the same, and bond formation occurs. The precise location of electron transfer binding sites is important in order to define the distance over which electrons are transferred. For metalloproteins having an irregular shape with the active site not necessarily at the centre of the molecule, with a non-uniform distribution of groups on the surface, Sykes and non-uniform distribution of charge (which will vary with pH) this is not trivial.Figure 2 which bears some resemblance to plastocyanin illustrates these features. Moreover although a high degree of specificity of binding site is required of natural redox partners, this need not be the case for reactions of proteins with non-natural redox partners, such as small inorganic complexes, when competing sites of varying relevance depending on their distance from the active site may contribute. Most proteins assume a globular shape, with charged residues on the outside. They are soluble in H,O, and non-aqueous solvents sometimes have disruptive effects.Thus dimethyl sulphoxide (80% V.V. with H,O) is known to unfold the Fe/S proteins, a property which has been exploited in the extrusion of active site ~1usters.l~ Figure 2 Representation of a metalloprotein. The two hypothetical binding sites indicated byarrows are different distances from the active site The biologically relevant pH for a metalloprotein is not always known with certainty, and for purposes of comparison a pH at or close to 7 is adopted. The pH inside the thylakoid is reported to be about 5.5, although lower values are sometimes indicated.Studies over a range of pH are therefore appropriate, with pH 7 relevant in the overview. At pH 7 aspartic and glutamic acid residues are acid dissociated and have 1-charges, and lysine, arginine, and (unco-ordinated) histidine are protonated and have 1+ charges. In addition, cysteine co-ordinated as thiolate has a 1-charge. Estimates of the total protein charge are approximate only since they take no account of local effects, such as H-bonding between adjacent residues, which can lead to the sharing of H+, and give abnormal acid dissociation (pKJ values. X-Ray crystallographic information from Freeman and colleagues on poplar leaf plastocyanin in both oxidation states have made it structurally one of the best l3 W. 0.Gillum, L.E. Mortenson, J. S. Chen, and R. H. Holm, J. Am. Chem. Soc., 1977, 99, 584. Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin understood metalloproteins.1i14 The question whether the same structure can be assumed to hold in solution is an important one. The n.m.r. method is probably the most powerful technique which can be used to answer this question, and the studies of Williams and colleagues on cytochrome c are exemplary in this context. About a half of the 104 amino acids have now been assigned in the 'H n.m.r. spectrum.15 It would appear that while the structure as a whole remains compact with retention of shape, there are some regions of looser structure which exhibit movement giving differences in solution and solid-state spectra.Studies on plastocyanin have also been carried out, and again the structures in the solid state and in solution appear to be very similar.'6~17 Other techniques which have been used in studies on blue Cu proteins include e.p.r.,' EXAFS,' and Resonance Raman Spectroscopy.20*21 Evolutionary aspects have also been ~onsidered.~.~~ Electron-transport metalloproteins have attained a high degree of efficiency; even when the thermodynamic driving force is small electron-transfer reactions are rapid and require rapid mixing or relaxation techniques to monitor their progress. In redox studies stopped-flow spectrophotometry is invariably used to monitor the formation or decay of the blue PCu" absorption at 597 nm (E 4 500 M-' cm-').The temperature-jump method continues to be comparatively neglected,23 in some part because rate laws are more complicated, making it difficult to quantify precisely bimolecular equilibration processe~.~~,~~ Because of the size and complexity of metalloproteins it is not generally meaningful at the outset to explore the electron-transfer reactivity between two such molecules without first carrying out exploratory studies. It is now customary to use inorganic complexes as probes for redox reactivity in an initial assessment of each metallopr~tein.~~~,~~ Once such an assessment has been carried out it is possible to turn to protein-protein reactions,27 and ultimately to reactions involving natural protein partners.28 Even so, the latter can have some problems l4 J.M. Guss and H. C. Freeman, J. Mol. Biol., 1983, 169, 521. G. Williams, N. J. Claydon, G. R. Moore, and R. J. P. Williams, J. Mol. Biol., 1985, 183, 447. I6 (a) D. J. Cookson, M. T. Hayes, and P. E. Wright, Nature (London), 1980,283,682, Biochim. Biophys. Acta, 1980,591,162; (6)P. M. Handford,H. A. 0.Hill, R. W.-K. Lee, R. A. Henderson, and A. G. Sykes,J. Inorg. Biochem., 1980, 13, 83. A. E. G. Cass and H. A. 0.Hill in 'Copper Proteins and Copper Enzymes', ed. R. Lontie, CRC Press, 1984, Vol. 1, pp. 63-91. l8 J. F. Boas, ref 17, pp. 662. l9 M. S. Co and K. 0.Hodgson, ref: 17, pp. 93-114. 'O T. M. Loehr and J. Sanders-Loehr,ref 17, pp. 115-156. " W. H. Woodruff, K. A. Norton, B. I. Swanson, and H. A.Try, Proc. Natl. Acad. Sci. USA, 1984,81, 1263.'' L. Ryden, in 'Copper Proteins and Copper Enzymes', ed. R. Lontie, CRC Press, 1984, Vol. 1, pp. 157- 182. 23 S. Wherland and I. Pecht, Biochemistry, 1978, 17, 2585. 24 M. Goldberg and I. Pecht, Biochemistry, 1976, IS,4197.'' S. K. Chapman, I. Sanemasa, A. D. Watson, and A. G. Sykes, J. Chem. SOC., Dalton Trans., 1983,1949. 26 S. K. Chapman, I. Sanemasa, A. D. Watson, and A. G. Sykes, ACS Symp. Ser. No. 211, ed. M. H. Chisholm, 1983, pp. 177-197.'' M. A. Augustin, S. K. Chapman, D. M. Davies, A. D. Watson, and A. G. Sykes, J. Inorg. Biochem., 1984, 20, 281. D. Beoku-Betts, S. K. Chapman, C. V. Knox,and A. G. Sykes, J. Chem. SOC., Chem. Commun., 1983, 1150; Inorg. Chem., 1985, 24, 1677. Sykes (as with cytochromefand plastocyanin), because rate constants are fast and at the upper limit of the stopped-flow range.4 Amino-acid Sequences Primary structure information is available for plastocyanin from 14 higher plants, 3 green alga (Chlorellafusca and Scenedesmus obliquw are referred to in this review) and 1 blue-green alga (Anabaena uariabilis), all of which have been completely seq~enced.~*'~+~~-~~In addition a further 42 plastocyanins have been partially sequenced (first 32-40 residues). Sequences which are particularly relevant to this review are shown in Figure 3. Of the 14 completed higher plant sequences 45 residues are invariant (52 with the exclusion of parsley which indicates a remark- able variability for this molecule).Sequence homologies are not as strong if the 3 algae are included when only 24 residues are invariant. Plant plastocyanins normally have 99 residues and algae as many as 105 for A. ~ariabilis.~' The invariant residues include His-37, Cys-84, His-87, and Met-92 which are co- ordinated to the Cu (see below). Variations are likely to be most extensive in the functionally least important regions of the protein. Although residues carrying charge are not always invariant there is with the exception of A. uariabilis conservation of overall charge, which is estimated to be between -8 and -10for PCu' at pH 7. The isoelectric point, PI -4.2 for spinach pla~tocyanin,~~ indicates charge neutrality at pH 4.2. At lower pHs the protein denatures.In sharp contrast A. uariabilis in the PCu' state has an estimated charge of +2 (from the sequence), and from its column behaviour a PI >7. Accordingly A. variabilis plastocyanin has quite different properties. The green algal plastocyanins have similar overall charges to those of the higher plants. The deletions at 57 and 58 are an unusual feature, which (surprisingly) have now also been observed for parsley plasto- ~yanin.~~ The high degree of sequence conservation is significant for a number of reasons. Firstly, it suggests that structural information obtained for poplar plastocyanin should be valid for other members of the family. For a fuller understanding, however, it is now desirable to have crystal structure information for plastocyanin from such diverse sources as parsley and A.uariabilis. For the present it is assumed that gross overall features of the structure are retained. The close similarity of 'H n.m.r. spectra for PCu' from four different sources are consistent with this.34 Secondly, it is likely that not just the amino acids at active site, but those constituting the binding site(s) for higher plant and green algal plastocyanins are 29 The parsley plastocyanin sequence has been determined, R. P. Ambler and A. G. Sykes, unpublished work included in Figure 3. 30 The Scenedesmus ob/iquus sequence has been determined J. M. Kelly and R. P. Ambler unpublished work included (with permission) in Figure 3. 31 J. A. M. Ramshaw, in 'Nucleic Acids and Proteins in Plants I, Encyclopedia of Plant Physiology', Vol.14A, ed. D. Boulter and B. Parthier, Springer Verlag, Berlin, 1982, pp. 229-240. 32 A. Aitken, Biochem. J., 1975, 149, 675. 33 J. A. M. Ramshaw, R. H. Brown, M. D. Scawen, and D. Boulter, Biochem. Biophys. Acla, 1973,303,269, see also ref. 59. 34 H. C. Freeman, V. A. Norris, J. A. M. Ramshaw, and P. E. Wright, FEBS Lett., 1978, 86, 131. h) 5 10 15 20~.~~iabilisG1u-Thr-Tyr-Thr-Val -Lys-Leu-G1 y-Ser-Asp-Lys-G1 y-Leu-Leu-Val -Phe-G1 u-Pro-A1 a-Lys-Leu-Thr-I le-Lys-Pro-G1 y-Asp 'w Spinach Fr. bean Pars1ey [Conservation] A. variabilis S.oblisuus Poplar Spinach Fr. bean Parsley [Conservation] A. variabilis S.oblisuus Poplar Spinach Fr. bean Parsley [Conservation] A.variabilis S.oblisuus Poplar Spinach Fr. bean Parsley [Conservation] A1a-Asn-Va 1-Lys-Leu-61 y-A1 a-Asp-Ser-G1 y-A1 a-Leu-Val -Phe-G1 u-Pro-A1 a-Thr-Val -Thr-I 1e-Lys-A1 a-G1 y-AspIle-Asp-Val-Leu-Leu-Gly-Ala-As~-Asp-Gly-Ser-Leu-Ala-Phe-Val-Pro-Ser-Glu-Phe-Ser-IJe-Ser-Pro-Gly-GluVa 1-61 u-Va 1-Leu-Leu-G1y-G1 y-G1y-Asp-G1y-Ser-Leu-A1 a-Phe-Leu-Pro-61y-Asp-Phe-Ser-Val -A1 a-Ser-61 y-G1u f Leu-G1 u-Va 1-Leu-Leu-G1y-Ser-G1 y-Asp-G1y-Ser-Leu-Va 1-Phe-Va 1-Pro-Ser-G1 u-Phe-Ser-Va 1-Pro-Ser-G1 y-61u a A1a-G1u-Val -Lys-Leu-G1y-Se r-Asp-Asp-61y-G1y-leu-Val -Phe-Ser-Pro-Ser-Ser-Phe-Thr-Val -A1 a-A1 a-61y-61u & tt tP? f 9 30 35 40 45 50 $Thr-Val-G1 u-Phe-Leu-Asn-Asn-Lys-Val -Pro-Pro-Hi s-Asn-Val -Val -Phe-Asp-A1 a-A1 a-Leu-Asn-Pro-Ala-Lys-Ser Ser-Va 1-Thr-Trp-Thr-Asn-Asn-A1 a-Gl y-Phe-Pro-Hi s-Asn-I 1e-Va I -Phe-Asp-Gl u-Asp-A1 a-Val -Pro-A1 a-61 y-Val z Lys-I1e-Va 1-Phe-Lys-Asn-Asn-A1 a-G1 y-Phe-Pro-Hi s-Asn-I1e-Val -Phe-Asp-61 u-Asp-Ser-I1e-Pro-Ser-G1 y-Val G1u-I1e-Val -Phe-Lys-Asn-Asn-A1 a-G1 y-Phe-Pro-Hi s-Asn-Val -Val -Phe-Asp-61 u-Asp-G1 u-I1e-Pro-Ser-G1 y-Val Lys-I 1e-Val -Phe-Lys-Asn-Asn-A1 a-G1 y-Phe-Pro-Hi s-Asn-Val -Val -Phe-Asp-61 u-Asp-G1 u-Ile-Pro-A1 a-Gly-Val $Lys-I1e-Thr-Phe-Lys-Asn-Asn-A1 a-G1 y-Phe-Pro-Hi s-Asn-I1e-Val -Phe-Asp-61 u-Asp-G1 u-Val -Pro-A1 a-G1y-Val t ttt t++t +4tt %-tt l? f? 55 60 65 70 75 gA1a-Asp-Leu-A1a-Lys-Ser-Leu-Ser-Hi s-Lys-G1 n-Leu-Leu-Met-Ser-Pro-G1y-G1 n-Ser-Thr-Ser-Thr-TW -Phe-Asp L"Asn-Ala-Asp-A1 a-Leu-Ser-* -* -Hi s-Asp-Asp-Tyr-Leu-Asn-A1 a-Pro-61 y-G1 u-Ser-Tyr-Thr-A1 a-Lys-Phe-Asp Asp-A1 a-Ser-Lys-Ile-Ser-Met-Ser-G1 u-G1 u-Asp-Leu-Leu-Asn-A1 a-Lys-G1 y-G1 u-Thr-Phe-G1 u-Val -A1 a-Leu-Ser % Asp-A1 a-Ala-Lys-Ile-Ser-Met-Ser-61 u-G1 u-Asp-Leu-Leu-Asn-Ala-Pro-G1 y-G1 u-Thr-Tyr-Lys-Val-Thr-Leu-Thr 5 Asp-A1 a-Val-Lys-Ile-Ser-Met-Pro-Gl u-G1 u-G1 u-Leu-Leu-Asn-A1 a-Pro-61 y-G1 u-Thr-Tyr-Val -Val -Thr-Leu-Asp Asn-A1 a-G1 u-Lys-Ile-Ser-* -*-G1 n-Pro-G1 u-Tyr-Leu-Asn-Gly-Ala-Gly-G1 u-Thr-Tyr-61 u-Val-Thr-Leu-Thr $ rpti-+ ft f-t tt 0 80 85 90 95 GA1a-A1 a-61 y-G1 u-Tyr-Thr-Phe-Tyr-Cys-G1u-Pro-Hi s-Arg-G1 y-A1 a-G1 y-Met-Val -G1 y-Lys-I1e-Thr-Val -A1 a-G1y b 2Thr-A1 a-G1 y-G1 u-Tyr-G1 y-Tyr-Phe-Cys-G1 u-Pro-Hi s-G1 n-G1y-A1 a-G1y-Met-Val -G1 y-Thr-I1e-Val -G1 n As n-Lys-G 1y-G1u-Tyr-Ser-Phe-Tyr-Cys -Ser-Pro-His-G1n-G1y-A 1a-G1y-Met-Va 1-G1y-Lys-Va 1-Thr-Va 1-Asn 2 G1u-Lys-G1 y-Thr-Tyr-Lys-Phe-Tyr-Cys-Ser-Pro-Hi s-G1 n-G1y-A1 a-G1 y-Met-Val -Gl y-Lys-Val-Thr-Val-ksn :Thr-Lys-Gly-Thr-Tyr-Ser-Phe-Tyr-Cys-Ser-Pro-Hi s-G1 n-Gly-A1 a-61 y-Met-Val-61 y-Lys-Val -Thr-Val -Asn 3G1u-Lys-G1 y-Thr-Tyr-Lys-Phe-Tyr-Cys-Glu-Pro-Hi s-A1 a-G1y-A1 a-61 y-Met-Lys-Gl y-GI u-Val -Thr-Val -Asn 'at f ti-+ f+ +f++ t t+t s-Figure 3 Flastocyanin amino-acid sequences referred to in this review.The asterisk (*) indicates deletions, $ positions exhibiting invariance for a// 17 completed sequences, and t additional positions exhibiting invariance for higher plant plastocyanins c % 3 Sykes conserved. In this context the conservation of negative charge at positions 42-45 and 59-61, and absence of charge in other regions is noted, Figure 3.Ironically the only higher plant plastocyanin for which the Asp-Glu-Asp-Glu sequence for residues 4245 is broken is for poplar (45 is Ser),14 while for parsley negative charge at positions 59-61 is not conserved which follows closely the deletions at 57 and 58.29 A. variabilis is clearly in a category on its own since only 42(Asp) of 42-45 and 59-41 is negatively charged, although residue 85(Glu) compensates towards retention of some negative charge in this locality.32 This could be significant as will be discussed later. Although no studies on green algal plastocyanins e.g. S. obliquus and C.fusca,have yet been carried out, these are now important examples in any systematic appraisal of reactivity, because of the versatility in sequence as compared to the higher plant plastocyanins.5 Crystal Structure Freeman and colleagues have determined the structure of poplar plastocyanin in the Cu" state to 1.6 A resolution. Relevant information is summarized only briefly here, and the papers of Freeman are strongly recommended for further reading. The Cu is co-ordinated to N-atoms of His-37 and His-87 and the S-atoms of Cys-84 and Met-92 in an irregular tetrahedral co-ordination geometry (Figure 4). Two of the bond angles at the Cu differ by more than 20" from a regular tetrahedron. The two imidazole Cu-N bonds at 2.10 and 2.04 A, and the thiolate Cu-S (Cys) bond at 2.13 A may be regarded as normal, but the thio-ether Cu-S(Met) distance (2.90 A) Figure 4 The active site of plastocyanin, PCu" Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin is sufficiently long as to raise questions as to its relevance.It is not detected by EXAFS meas~rements.~~ There are no important changes in the PCu" crystal structure at pH 4.2 as compared to 6.0, and the geometry of the active site does not change.' It is estimated that 36% by volume of the crystal is occupied by solvent HzO. Forty-four water molecules have been identified, but none of these is found at the active site or elsewhere in the interior of the protein.14 The molecule has the shape of a slightly flattened cylinder of approxi-mate dimensions 40 x 32 x 28 A, the 40 A distance corresponding to what is sometimes referred to as a north-south axis.The Cu atom is buried 6 A in the interior at the north end. There are eight strands of polypeptide chain which are connected by seven loops at the ends of the cylinder. Seven of the strands have substantial P-character, and strand five is irregular and contains the only helical structure (about 1.5 turns). As already mentioned S. obliquus, C.fusca,and parsley plastocyanins have deletions at 57 and 58. The two green algae retain a 2 -charge in this locality but parsley has only one negative charge at Glu-61 or Glu-59 if the two deletions are not included in the numbering. A normal view of the molecule which is often used is shown in Figure 5.The right-hand side, which includes the 42-45 and 59-61 negative patches already referred to, is sometimes referred to as the east side. Some care is required because rotation about the north-south axis could lead to ambiguity in description. All the charged residues and the majority of uncharged polar residues (Ser, Thr, Asn, and Gln) are exposed to solvent. The majority, but not all, of the non-polar and aromatic residues are buried within the molecule. It has been noted that the exposed edge of the His-87 imidazole ring is level with the molecular surface at the northern extremity. This partly exposed His-87 is surrounded by conserved non- polar groups, and constitutes the so-called hydrophobic patch. The Tyr-83 residue is exposed to solvent, Tyr-70 has one side exposed, whereas Tyr-80 is on the inside of the protein and is H-bonded to a peptide carbonyl group.There is a striking imbalance in charge on the surface of plastocyanin. None of the ten charged residues which are conserved in plant plastocyanins (eight Glu/Asp and two Lys) occur in the northern quarter of the molecule. It is important to note that the highly conserved 42-45 and 59-61 regions are concentrated in two kinks in the protein backbone. These occur either side of Tyr-83 and at pH -7 their negatively charged carboxylates are directed into the solvent and form an elongated region of negative charge. A structure analysis of poplar PCu' has been carried out at six pHs in the range 3.9 to 7.9. At pH 7 the co-ordination geometry is very like that of PCu".Active-site structural changes observed at lower pHs will be referred to later. 6 Spectroscopic Properties Studies on Cot'-substituted plastocyanin in which the Cu is replaced by Cot' lead to the assignment of the dominant 597 nm band (Figure 6) as S(Cys-84) +Cu" charge-35 R.A. Scott, J. E. Hahn, S.Doniach, H. C. Freeman, and K.0.Hodgson, J. Am. Chem. SOC.,1982,104, 5364. 290 Sykes Figure 5 The structure of poplar plastocyanin, PCu", as obtained by Freeman ',14 tran~fer.~~*~'As many as six other satellite bands have been reported at 464, 551, 739,838,971, and 1818 nm.38 Assignments made involve the cysteine and histidine ligands. While the S (Met-92) is believed to make a weak but definite contribution to the ligand field at the Cu atom, the analysis reported by Penfield et al.39does not reveal any S(Met-92) to Cu" charge-transfer component in the electronic spectrum.Additional detail (often ignored) is observed in the near-u.v. spectrum of PCu' and PCu'I, with peaks or shoulders at 284, 278, 273, 269, 266, 259, 252, and 248 nm (Figure 6).The peaks at 284 and 278 nm have been assigned to tyrosines, and the rest to phenylalanine residue^.^' Absorbances for PCu' are (for spinach) -70% those observed for the PCu" protein; PCu' does not absorb in the visible.41 The 'H and 3C n.m.r. method can be used to study amino acids close to the Cu 36 D. R. McMillin, R. C. Rosenberg, and H. B. Gray, Proc. Natl. Acad. Sci. USA, 1974,71,1339 and 4760.37 E. I. Solomon,J. Rawlings,D. R. McMillin, P. J. Stevens,andH. B. Gray, J.Am. Chem. Soc., 1976,98,8046. E. I. Solomon, J. W. Hare, and H. B. Gray, Proc. Natl. Acad. Sci. USA, 1976, 73, 1389. 39 K. W. Penfield, R. R. Gray, R. S. Himmelwright, N. C. Eickman, V. A. Norris, H. C. Freeman, and E. I. Solomon, J. Am. Chem. Soc., 1981, 103,4382. 40 J. W. Donovan in 'Physical Principles and Techniques in Protein Chemistry', ed. S. 3. Leach, Academic Press, New York, 1979, Part A, pp. 102-172. 41 E. L. Gross, G. P. Anderson, S. L. Ketchner, and J. E. Draheim, Biochim. Biophys. Acta, 1985, in press, and personal communication from Professor E. L. Gross. 291 Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin 3000 .-I €0 z \ 1500 260 280 300 nm 1 I I L 400 500 600 700 X/nm Figure 6 Visible absorbance spectrum for plastocyanin, PCu".For the U.V. range (inset) spectra arefor PCu' (-) and PCu" (---). The U.V. spectra4' are specijic to spinach plastocyanin, since aromatic composition is important active site in the reduced but not (due to line broadening) oxidized form of protein. Resonances which are most readily identified are those due to the methyl of the methionine, and the histidine, tyrosine, and phenylanlanine aromatic-ring protons.42 A number of N-H peptide signals remain unexchanged in D20 consistent with a compact inaccessible core to the protein. It has also been demonstrated that the Cu" at the active site of the type-1 proteins is inaccessible to solvent H,0.43 Adequate modelling of the tetrahedral Cu" site in low M.Wt.complexes is difficult, and although the intense blue colour has been reported for a tetrahedral pyrazolylborate complex having N2S2and N3Sco-0rdination,4~ and e.p.r. spectra have g-values that match those of the blue Cu proteins, their Cu hyperfine All values are normal rather than very small as for the proteins. The difficulties in precise modelling are the distorted tetrahedral angles and long Cu to thioether distance. 7 Reduction Potentials Values of &? in the range 347 to 395 mV have been reported for PCu"/PCu' at pH 7.0, which is high compared to the aqua Cu"/Cu' couple (115 mV) and corresponds to a stabilization of the Cut state.Until recently such values were determined using 42 E. L. Ulrich and J. L. Markley, Coord. Chem. Rev., 1978, 27, 109. 43 N. Boden, M. C. Holmes, and P. F. Knowles, Biochem. Biophys. Rex Commun., 1974, 57, 847; L. Avigliano, A. Finazzi-Agro, and B. Mondovi, FEBS Lett., 1974, 38, 205. 44 J. S. Thompson, T. J. Marks, and J. A. Ibers, J. Am. Chem. SOC., 1979, 101, 4180. 292 Sykes a mediator, generally the [Fe(CN)6]3 -/[Fe(CN),I4- couple,45 because of the slow response of proteins at electrode surfaces. Direct non-mediated electrochemistry has now been observed at an edge-orientated pyrolytic graphite electrode, which when subjected to a standard polishing procedure in air gives C-0 functional groups capable of interacting with the protein (25 pM) in the presence of Mg2+ (<5mM).46 By attaching positively charged Cr"' complexes to the graphite electrode surface the electrode becomes fully reversible to the plastocyanin couple, but not to cytochrome c which is positively charged.46 In 5 mM buffer/l mM KC1 solution at 3 "Cthe reduction potential for spinach is 375 mV.Katoh et ~1.~'first reported an increase in Eo with decreasing pH for spinach plastocyanin, which has been confirmed in kinetic studies with Figure 7, and potentiometric studies on marrow pla~tocyanin.~' At pH 4.2 the higher Eo of 430 mV is the result of changes at the active site of the Cu' protein. 350 1 I I 1 5 7 9 PH Figure 7 Variation of Eo with pH for parsley plastocyanin 8 Other Single (Type 1) Blue Cu Proteins All single type-1 proteins in the CU" state have in common the intense blue colour and exceptionally small hyperfine-splitting in the e.p.r.spectrum. Table 1 summarizes properties of some of these proteins.2,6 Other proteins of the type which have been characterized include planta~yanin,~~ mung bean blueY5 45 G. W. Pettigrew, D. A. Leitch, and G. R. Moore, Biorhim. Biophys. Acta, 1983, 725, 409. 46 F. A. Armstrong, H. A. 0.Hill, B. N. Oliver, and D. Whitford, J. Am. Chem. SOL..,1985, 107, 1473 and F. A. Armstrong, P. A. Cox, H. A. 0. Hill, B. N. Oliver, and A. A. Williams, J. Chem. Soc., Chem. Commun.,in press. 47 S. Katoh, 1. Shiratori, and A. Takamiya, J. Biochem. (Tokyo), 1962, 51, 32. 48 M.G. Segal and A. G. Sykes, J. Am. Chem. Sor., 1978, 100, 4585. 49 M. D. Scawen, E. J. Hewitt, and D. M. James, Phytochemistry, 1975, 14, 1225, and rcf 4, p. 12. K. A. Markossian, V. T. Aikcazyan, and R. M. Nalbandyan, Biochim. Biophys. Acta, 1974,359,47; V.T. Aikcazyan and R. M. Nalbandyan, FEBS Left., 1975,55272;and T. Sakurai, H. Okamoto, K. Kawahara, and A. Nakahara, FEBS Lett., 1982, 147, 220. 51 H. Schichi and D. P. Hackett, Arch. Biochem. Biophys.. 1963, 100, 183. 293 Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin ami~yanin,’~.’~ and basic blue from cucumber.55 In addition, multi- ma~icyanin,’~ copper oxidases such as the laccases, ceruloplasmin, and ascorbic acid oxidase have a type-1 Cu as well as type-2 and type-3 active site^.^,^^ As can be seen from Table 1 the type-1 proteins have a variety of different origins, and while their function almost certainly remains associated with electron transport, only plastocyanin is involved in photosynthesis. Many of the properties differ considerably from those of plastocyanin. The sequence of azurin from ten different bacterial sources has been determined and is also highly conserved.2 Crystal structure information on azurin from Pseudornonas aeruginosa (2.7 A resolution) 57 and of azurin from Alcaligenes denitrificans to 2.5 A has been obtained.58 The structure conforms to the plastocyanin model.Structure homologies between the plastocyanins and azurins have been noted.” The co-ordination spheres and position of the Cu ( -7 A buried) are also similar to plastocyanin.The most striking departure from the plastocyanin structure is the addition of a flap between residues 53 and 78. This flap, which includes some helical turns and seems to be an extension of the irregular fifth strand, hangs outside the body of the rest of the molecule in the region of the east site. Active site co-ordination of the Cu is to His-46, Cys-112, His-1 17, and Met- 121. The absorption maximum for azurin at 625 nm is appreciably shifted compared to that of plastocyanin at 597 nm. Additional weak co-ordination of an adjacent carboxyl of the peptide chain, which approaches to within -3.2 8, of the Cu, is possible. Azurin, like plastocyanin, has a northern hydrophobic surface.There is no negatively charged region and the charge is -2 and -1 for the two states, assuming only one of the two unco-ordinated histidines contributes a 1 + charge. Differences are to be noted in the case of stellacyanin which has no methionine,60 and umecyanin which although it has three methionines has none in the sequence after residue-74.61 In both cases therefore the fourth ligand is unlikely to be methionine.62 It appears that in the case of stellacyanin the fourth ligand may be a disulphide, which it has been suggested 63 is formed during the isolation procedure, and that two thiolate ligands are present in the original protein. This remains to be confirmed. Rusticyanin is remarkable in that in uiuo it is reduced by Fe2+,64 and it 52 Y.Morita, A. Wadano, and S. Ida, Agr. Biol. Chem., 1981,101,502; T. van Houwelingen, G. W. Canters, J. A. Duine, J. Frank, and G. Stobbelaar, Rev. Port. Quim., 1985, 27, 177. 53 J. Tobaria and Y. Harada, Biochem. Biophys. Res. Commun., 1981,101,502; and T. van Houwelingen, G. W. Canters, J. A. Duine, J. Frank, and G. Stobbelaar, Rev. Port. Quim., 1985, 27, 177. 54 A. Marchesini, M. Minelli, H. Merkle, and P. M. Koneck, Eur. J. Biochem., 1979, 101, 17. 55 M. Muraka, G. S. Begg, F. Lambrou, B. Leslie, R. J. Simpson, H. C. Freeman, and J. F. Morgan, Proc. Natl. Acad. Sci. USA, 1982, 79, 6434. ”See reviews in ‘Copper Proteins and Copper Enzymes’, Vol. 3, ed. R. Lontie, CRC Press, 1984. 57 E. T. Adman and L. H. Jensen, Jsr. J. Chem., 1981, 21, 8.58 G. E. Norris, B. F. Anderson, and E. N. Baker, J. Mol. Biol., 1983, 165, 501. 59 D. Boulter, B. G. Haslett, D. Peacock, J. A. M. Ramshaw, and M. D. Scawen, Int. Rev. Biochem., 1977, 13, 1. 6o C. Bergman, E.-K.Gandvik, P. 0.Nyman, and L. Stid, Biochem. Biophys. Res. Commun., 1977,77, 1052. 61 C. Bergman, PbD. Thesis, Chalmers University of Technology, Goteborg, 1980. 62 C. Bergan and P. 0.Nyman, unpublished work. 63 H. A. 0.Hill and W.-K. Lee, Biochem. SOC.Trans., 1979, 7, 733. 64 J. G. Cobley and B. A. Haddock, FEBS Lett., 1975, 60, 29. 294 Table 1 A comparison of properties of single blue Cu proteins Protein Source M.Wt. No. of amino-acids pZ E'/mV hm.x.(&)/nm(/M-lcm-") Plastocyanin Chloroplasts, plants/algae 10 500 99 4.2" 370' 597 (4500) Azurin Pseudomonas aeruginosa ' 14 OOO 128 5.4 330' 625 (4800) Stellacyanin Lacquer tree' 2OOOOf 107 9.86 184 608 (4080) Rusticyanin Thiobac.ferro-oxidans 16 OOO 159 9.1 6808 597 (1 950) Umecyanin Horse-radish roots 14600 125 5.85 283 610 (3 400) Spinach. 'At pH 7. Other bacteria also. 'At pH 7. 350 mV at pH 5. Rhus vernicifera. 40% carbohydrate. pH 2. Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin normally functions at pH 2, at which pH no negatively charged residues can be present on the surface. Plastocyanin is denatured at pH < 4. The high for rusticyanin (680 mV) 65 has not so far been explained. The close proximity of Cys- 127, His-132, and Met-137 in the sequence implicates these residues in binding the CU.~~There are four other histidines, two methionines, and a number of aspartates in the sequence, one or more of which could also be co-ordinated to the CU.~~ Kinetic studies involving umecyanin and rusticyanin are at present underway.9 EXAFS Studies Solution and crystal studies for plastocyanin have yielded values in satisfactory agreement with Freeman's X-ray crystallographic Cu-N(His) and Cu-S(Cys) distances, Table 2.67 The long Cu-S(Met) distance is not detected by EXAFS measurement^.^^ Information obtained for a~urin,~~.~'stellacyanin,68 and ~mecyanin,~~is also indicated in Table 2. Co-ordination of the Cu" to two histidines (average CU-N distance 1.99 A) and one thiolate Cu-S (average distance 2.12 A) is indicated from the fitting.Upon reduction the Cu-N and Cu-S distances increase by -0.05 A and -0.10 A respectively. A reasonable description of the redox process might therefore be that there is little angular rearrangement of ligands and only small changes in the metal-ligand bond distances. The change in u.v.-visible spectrum observed for UCu" on adjusting the pH from 7.0 (peak at 610 nm) to 10.7 (peak at 580 nm) is not reflected in any differences in EXAFS bond distances, which remain (within experimental error) 1.99 and 2.13 A respectively. This suggests some minor change, possibly the approach of a fifth ligand (an amine?), which does not establish itself as a fully co-ordinated group. Alternatively a pH-controlled conformational change effective at the Cu" active site could be the explanation. Table 2 EXAFS solution studies.In each case a satisfactoryjt is obtained for two histidines and one cysteine co-ordinated to the Cu. Bond lengths for Cu-N (average) and Cu-S are given Oxidized Reduced Cu-N(His)/A Cu-S(Cys)/A Cu-N(His)/A Cu-S(Cys)/A PCu" 1.97 2.11 2.05 2.22 ACU" 1.97 2.2 2.00 2.22 scu" 2.04 2.11 2.07 2.25 UCu'l' 1.99 2.13 2.03 2.21 pH 7.5. Identical results (k0.03A) at pH 10.5 65 W. J. Ingledew, Biochim.Biophys. Acta, 1980,590,141. 66 R. P. Ambler and W. J. Ingledew, unpublished results, personal communication Dr. W. J. Ingledew. "T. D. Tullius and K. 0.Hodgson referred to in ref: 19. T. D. Tullius, P. Frank, and K. 0.Hodgson, Proc.Natl. Acad. Sci. USA, 1978,75, 4069. 69 S. K. Chapman, J. McGinnis, J. D. Sinclair-Day, A. G. Sykes, P.-I. Ohlsson, K.-G. Paul, and W. H. Orme-Johnson, to be published. Sykes 10 Apoplastocyanin Apoplastocyanin has been prepared by 7h dialysis of 0.1 mM spinach PCu' against 50 mM KCN and 50 mM phosphate buffer at pH 7.1 under argon.70 Thiourea at pH 4-5 has been used successfully to remove Cu' from az~rin.~ Crystals of poplar PCu" have been soaked in a sequence of solutions to effect the Cu" to Cu' reduction (ascorbate), and then cyanide (0.15 M) for much longer time intervals (5,17, and 72 h) to remove the Cu' at pH 5.3 in 5 M phosphate b~ffer.'~ The crystal structure of the poplar apoplastocyanin to 1.8 A resolution resembles that of the holoprotein, thus suggesting that the geometry of the type-1 site is imposed by the p~lypeptide.~~ A rotation of the His-87 ring by 180" appears to facilitate access to the Cu site, and re-entry of the Cu by a reverse process in a trap-door type mechanism has been proposed.Quantitative kinetic study of the reformation of the Cu protein is not easy as has been illustrated by studies of McMillin and colleagues on the reconstitution of azurin CU".~' One of the problems is the form in which the free Cu is made available at the pHs under investigation. In the azurin studies imidazole and 1-methylimidazole buffers (0.1 M) in the pH range 7-9 were used, with 1 mM Cu" and apoprotein at 2 x l@'M. Under these conditions it has been estimated that -90% of the Cu" exists in solution as the tetrakisimidazole complex. Uptake of Cu occurs in a stepwise fasliion, and at least two intermediates have been proposed.In the reconstitution of spinach apoplastocyanin, thionein has been used to complex free Cu", and Cu' (thiourea),' was found to be a convenient source of CU'.~' No kinetic studies were reported. 11 Inorganic Complexes as Redox Partners It is preferable to use substitution inert complexes. Even when there is only a small thermodynamic driving force reactions are rapid and well into the stopped-flow range. The Co"'/Co" couple is sometimes an exception because of its unfavourable self-exchange characteristics. Reduction potentials for complexes employed as redox partners for type-1 proteins, in most cases at pH 7, are listed in Table 3.73 Both states of [Ru(NH,),py] ,+/'+ and [Fe(CN),I3-/"- have been used, where the reaction is driven to completion in the desired direction by having the inorganic complex in sufficiently large excess.Complexes such as [Fe(edta)12-, [C~(terpy>~]~+,and [Co(phen),I2 +,although labile, can be retained in solution by having an excess (say 3 :1) of chelating ligand present. Incorrect interpretation of kinetics can result if a reaction does not proceed to >90%completion or the full rate laws are not used. A particularly striking example of this is the [Fe(CN),]"- reduction of cytochrome ~(III).~" 70 S. Brutsch, H.-J. Hartmann, and U. Weser, Inorg. Chim. Acta, 1984, 92, 147.71 J. A. Blaszak, D. R. McMillin, A. T. Thornton, and D. L. Tennent, J. Biol. Chem., 1984, 259, 2822.''T. P. J. Garrett, D. J. Clingeleffer, J. M. Guss, S. J. Rogers, and H. C. Freeman, J.Biol. Chem., 1984,259, 2822. 73 S. K. Chapman, I. Sanemasa, and A. G. Sykes, J. Chem. SOC.,Dalton Trans., 1983, 2549. 74 J. Butler, D. M. Davies, and A. G. Sykes, J. Inorg. Biochem., 1981, 15, 41. 297 Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin Table 3 Reduction potentials of inorganic couples (P)relevant to studies with type-1 Cu proteins PjmV [Fe(edta)] '-I2-a 120 [C~(terpy)~]~ 270+I2 + [Ru(NH~)sPYI~ 273+'2 + [C~(phen)~]3+/2 + 370 [Fe(CN)6] 3-/4-410 [(NC)sFeCNCo(CN)s J 5-/6-* 460 [Ru(NH3)spyI3 +/2+ 273 [CO(C204)313-/4-570 [Co(dipic)2] '-I2-' 747 (I edta probably quinquedentate with H20in sixth position.Ref:80. Re-determined by N. H. Williams and J. K. Yandell, Ausr. J. Chem., 1983, 36,2377. Earlier value 400 mV edta = ethylenediaminetetra-acetate;terpy = terpyridine; py = pyridine; phen = 1,lO-phenanthroline; dipic = pyridine-2,6-dicarboxylate With the complex [Co(4,7-DPSphen)J3 -, where 4,7-DPSphen is 4,7-disphenylsulphonate- 1,lO-phenanthroline, difficulties have been experienced in obtaining reproducible data, and in interpreting results in a self-consistent manner.' This complex is therefore excluded from the present discussion. 12 Kinetic Studies A range of buffers (-10-'M) have been used for pHs in the range 4-10 relevant to metalloprotein reaction^.^^ Normally there is satisfactory reproducibility in buffer overlap regions. Ionic strengths are generally adjusted to 0.10 M with NaCl, and the temperature is 25 "C unless otherwise stated.Protein concentrations of lW5M are widely used, and can be as low as lW7M for the cytochromes which have intense redox-state-dependent Soret bands. Use of the stopped-flow method as opposed to conventional spectrophotometry also helps to conserve protein. Inorganic complexes, e.g., [Fe(cN)6l3- in equation (l), are used in > 10-fold excess of the protein. First-order plots give kobs,from which the dependence kobs = k[Fe(CN)2-] can be demonstrated. This establishes the simple rate law (2), Rate = k[PCu'][Fe(CN)36-] (2) where k is the second-order rate constant. ''(a)A.G. Lappin, M. G. Segal, D. C. Weatherburn, and A. G. Sykes, J. Am. Chem. SOC.,1978,101,2297, and (b) recent studies J. D. Sinclair-Day and A. G. Sykes, unpublished work. l6 See e.g. ref: 28 and preceding papers in this series. Sykes Rate constants for the [Fe(CN)6I3 -and [Co(phen)313 oxidations of PCu' + from parsley, spinach, and French bean are in good agreement with a spread of less than a factor of two in each case, Table 4.48*77*78Conservation of charge at 8-, 9-, and 9-respectively for the PCu' proteins is noted. Rate constants for PCu' from A. variabilis, charge 2+, indicate a different pattern consistent with the different overall charge.79 Table 4 A comparison of rate constants (25 "C)forthe [Fe(CN)6l3-(kFe)and [C~(phen)~]~+(kc,) oxidation of plastocyanin PCu'from different sources at pH 7.5, I = 0.10 M (NaCl) Source of PCu' kF,/M-' S-' kco/M-' S-' kF,/kc, Parsley French Bean Spinach 94 OOO 58 OOO 85 OOO 3000 4 700 2 500 31 12 34 Anabaena variabilis 650 OOO 680 950 With [Co(phen)3I3+ as oxidant, rate constants kobsgive a less than first-order dependence on [Co(phen)$ '1 on increasing the latter to -3 x 10-3M.48 Instead equation (3) holds Kk,, [Co"'] (3)kobs = 1 + qco"'] and the reaction is said to exhibit limiting kinetics where in the present case the limit would only be attained at much higher [Co(phen)$ '3.Equilibrium and rate constants K and k,, defined in (4) and (9, PCU' + CO"' A PCU', CO"' (4) PCU', CO"' PCU" + CO" (5) can be obtained from a graph of (kObs)-lagainst [Co(phen)z+]-'.Although a satisfactory fit is obtained, the rate law may not be as simple as indicated, and in keeping with later discussion, a linear dependence of kobson [Co"'] may remain at high [Co"']. Data for parsley,48 ~pinach,~~~~~ and French bean78 PCu' give a satisfactory fit to (3), with KIM-' at 25 "C 167 and 389 for parsley and spinach respectively, but with A. uariabilis PCu' a plot of kobs against [Co(phen);+] is linear, and flCo(phen)i+] is not influential in the denominator of (3), i.e. Kis small. In such instances second-order rate constants (k) can be equated to Kk,, in a two-step process (4) and (9, which is perfectly reasonable as long as rate constants for the association process are very much greater than ket.This interpretation is supported by studies with [Fe(CN),13 -and l7 J.D. Sinclair-Day and A. G. Sykes, to be published. G. C. King and P. E. Wright, unpublished work. 79 J. A. Chambers, M. P. Jackman, J. D. Sinclair-Day, M. J. Sisley, and A. G. Sykes, to be published. 299 Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin [(NC)SF~CNCO(CN)~]-as oxidants for parsley PCu' when limiting kinetics are not observed. However the AH% for k are negative (-2.9 and -3.3 kcal mol-' respectively) consistent with two-stage processes involving association (K), which presumably has a negative A@, prior to electron transfer (k,t).80In fact with [Co(phen)3I3+ as oxidant an additional step has to be included alongside (4) and (9,with modification of (3), as will emerge later. The importance of electrostatics, and its influence on reactions of the type (4) is illustrated in these studies.In addition to the studies with [Fe(cN)6l3- and [(NC)5FeCNCo(CN)5]5 -limiting kinetics are not observed with [Co(dipic)2] -, or [Co(bipy)2(02CMe)2] as oxidants or with [Fe(CN)6]4- and [RU(NH~)~PY]~ + + as reductants for PCU".~~ Excluding the case of [C0(4,7-DPSphen)~]~ the [Co(phen)3] study provides -+ the only example so far of limiting kinetics with plastocyanin. Values of K obtained are small and the fact that the solution composition changes on replacing a 1:1 by a 3: 1 electrolyte raises some questions.However K increases significantly on decreasing the ionic strength, making it more easily dete~table.~~ The converse also applies and Kis not detectable at Z = 0.5 M.82 Also relevant are experiments with more highly charged redox inactive complexes [Pt(NH3)6I4+ and [(NH&Co*NH2- CO(NH~)S]'+,~~which are found to associate strongly with plastocyanin (see below). The two stages as in (4) and (5) are now regarded as well established. Other examples of limiting kinetics have been reported with [2Fe-2S] and 2[4Fe-4S] ferred~xins,~~ with cytochrome bSg4 and, recently, cytochrome f.28 Those for the ferredoxins with complexes ranging from 5 + to 2 + are the most complete yet obtained clearly illustrating the effect of charge. The cytochrome f study is of interest because a positively charged locality on a negatively charged protein is involved.Also it is (at present) the only example involvilig a negatively charged complex and a positively charged locality on a protein (there are no examples of limiting kinetics with stellacyanin or cytochrome c). Earlier studies reporting limiting kinetics which have more recently been questioned include, the oxidation of [Fe(CN)6]4-with cytochrome ~(III),'~ stellacyanin Cu' with [C~(edta)]-,~' azurin Cu' with [Fe(CN)6I3-(and the reverse), 73 and [Fe(CN)6I4- with PCU".~'A procedure for estimating the local effective charge on a protein surface from association constants has been reported.86 Results obtained are consistent with structural information.There are two alternative explanations to (4)---(5), which give rate laws of the same empirical form as (3).8' One of these is readily dismissed. It involves an initial S. K. Chapman, I. Sanemasa, A. D. Watson, and A. G. Sykes, J. Chem. SOC.,Dalton Trans., 1983,1949. 81 See comments in ref: 80. R. A. Holwerda, D. B. Knaff, H. B. Gray, J. D. Clemmer, R. Crawley, J. M. Smith, and A. G. Mauk, J. Am. Chem. SOC.,1980, 102, 1142. 83 F. A. Armstrong and A. G. Sykes, J. Am. Chem. SOC.,1978,100,7710; F. A. Armstrong, R. A. Henderson, and A. G. Sykes, J. Am. Chem. SOC.,1979, 101, 6912 and 1980, 102,6545. 84 S. K. Chapman, D. M. Davies, C. P. J. Vuik, and A. G. Sykes, J. Am. Chem. SOC.,1984, 106, 2692. M.J. Sisley, M. G.Segal, C. S. Stanley, 1. K. Adzamli, and A. G. Sykes, J. Am. Chem. SOC.,1983,105,225. 86 S. K. Chapman, J. D. Sinclair-Day, A. G. Sykes, S.-C. Tam, and R. J. P. Williams, J. Chem. SOC.,Chem. Commun., 1983, 11 52. Ref: 2, p. 49. 300 Sykes 'activation' of the protein, here represented as P P*, followed by reaction of P* with the redox partner. A stationary-state treatment for P* gives an equation of the form (3), from which the rate constant for P --+ P* can be obtained. Since different values of this rate constant are obtained with different redox partners the mechanism is clearly untenable. The second alternative sometimes described as the 'dead-end' mechanism, is more difficult to dismiss and remains a kinetic ambiguity.This requires (for example) [Co(phen),13+ to associate at one binding site to give a completely redox inactive form. The redox reactivity is maintained by the [Co(phen)J3+ reacting with the remaining protein at an alternative site in a redox process which does not give observable association. Measurement of proton n.m.r. spectra of PCu' in the presence of analogue redox inactive Cr"' complexes have so far provided no support for conformational changes of the kind required by the dead-end It seems reasonable therefore that discussion should proceed in terms of (4) and (5) until evidence in support of this alternative is obtained. 13 Information from N.m.r. Studies The suggestion that different oxidant binding sites are utilised according to charge on the redox partner has been further established by high resolution 'H n.m.r.spectroscopy. The effect of redox inactive complexes [Cr(CN),I3 -,[Cr(phen)J3 +, and [~~(NHS),]~' (0.i-1.2 mM) on the n.m.r. of PCu' (-3.5 mM) has been investigated.', Since [Cr(phen),13+ (K= 176 M-') exhibits competitive inhibition for [Co(phen)J3+ it can be assumed that the two associate at the same site on PCu'.' The paramagnetic Cr"' complexes induce local line-broadening effects and indicate preferred sites for association. Such experiments provide evidence for association of [Cr(CN),I3 -close to His-87 at the northern hydrophobic patch near to the Cu (which is 6 A from the surface), whereas [Cr(phen)J3+ and [Cr(NH,)6]'+ associate at a site more distant from the Cu and close to Tyr-83.The latter is close to the conserved negatively charged 4245 and 59-61 regions. Similar behaviour is observed for plastocyanin from three sources, parsley, French bean, and cucumber. Invariance and high conservation of non-polar amino-acid residues close to His-87 has also been noted. The results indicate a high degree of specificity in the binding. Since line broadening is dependent on the inverse sixth- power of the distance of the amino-acid from the paramagnetic centre, the His-87 and Tyr-83 residues are likely to be close to the respective binding sites. Cytochrome ~(II) (charge 8+) also induces line broadening of Tyr-83 and evidence for association K = 1.1 x lo3 M-I has been reported with French bean PCU'.~~From kinetic studies however, with parsley PCU''*~ there was no curvature of the kind implicit in (3) and it was concluded that K < 150 M-I, I = 0.10 M.These results for non-physiological protein reactants of impressively high opposite charges are of considerable interest even though the magnitude of K remains in doubt. A value of K < 150 M-' indicates considerable mismatch of charge. G. C. King, R. A. Binstead, and P.E. Wright, Biochem. Biophys. Acta, 1985, 806,262. 89 M. A. Augustin, S.K. Chapman, D. M.Davies, A. D. Watson, and A. G. Sykes,J.Inorg. Biochem., 1984, 20, 28 1. Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin 14 Effect of pH on Reactivity of PCu' On decreasing the pH from 7.5, rate constants for the [Fe(CN),13- and [Co- @hen)J3+ oxidation of PCu' decrease dramatically to zero or a value close to zero.48 The apparent retention of up to 10% reactivity in some cases', at low pHs may be due to the difficulty in determining accurately rate constants at pH < 5.The contribution is in any case small and, if real, does not affect the discussion to follow. The dependence on [H'] assuming a complete switch-off is summarized by (6) where the constants are as defined in (7)--(8), H+PCu'& H+ + PCu' (7) PCu' + oxidant -% products (8) It is now clear that the pK, from studies with [Co(phen),I3+ are 0.64l.8 units higher than those obtained with [Fe(CN),I3- as oxidant, Figure 8.90 An active site pK, of 4.9 determined some time ago by n.m.r.for spinach PCu' was assigned to protonation and dissociation of Hi~-87.~ More recently n.m.r. values78992 for other plastocyanins have been determined, Table 5. Conditions of ionic strength and temperature show some minor variations. In all cases, however, there is satisfactory agreement with the [Fe(CN),] -kinetic pK,s. Confirmation that protonation and dissociation of His-87 is implicated has come from X-ray crystallography. The approach here has been to repeat diffraction measurements and refine calculations for crystals of poplar PCu' prepared at six different pHs from 7.8 to 3.8. The only detectable differences are at the Cu active site. The Cu atom is seen to move away from His-87 and towards Met-92. The Cys-84 side chain follows the Cu atom while the positions of His-37 and Met-92 remain unchanged.At each pH the bond lengths determined are the mean of contributions from the protonated and unprotonated forms. The increase in the Cu-N (His-87) distance to -3.4 A is sufficient to accommodate a proton on the imidazole N, atom. For energetic reasons oxidation of three-co-ordinate Cu' to Cu" is expected to be difficult. The higher pK,s for [Co@hen),l3' can be accounted for by including a second acid dissociation constant &', for a process occurring at the binding site used by [Co@hen),I3 +. Accordingly there are, for positively charged reactants, two protonations one at the active site A and the other at the binding site B. Assuming 90 J. D. Sinclair-Day, M.J. Sisley, A. G. Sykes,G.C. King, and P. E. Wright, J. Chem. Soc.,Chem. Commun., 1985, 505. 91 J. L. Markley, E. L. Ulrich, S. P. Berg, and D. W. Krogman, Biochemistry, 1975, 14, 4428. 92 C. L. Kojiro and J. L. Markley, FEBS Leu., 1983, 162, 54. 302 Sykes 0 4.0 6.0 8.0 PH Figure 8 Variation of rate constants k(M-'s-') at 25 "C (relative scale) for the oxidation of parsley PCu' with [Fe(CN)$-(A)and [Co(phen),13+ (0) Table 5 Acid dissociation constants pK, values (25 "C)for plastocyanin PCu'from different sources as determined Sy n.m.r. and kinetic studies with [Fe(CN),]'-and [Co(phen)3I3+ respectively as oxidants PCu' Source N.m.r. [Fe(CN)6] 3- [Co(phen)3] + Parsley 5.7 5.5 6.1 Spinach 4.9 4.9 5.7 French Bean 4.8 4.6 5.4 Anabaena variabilis 5.1 4.8 5.5 the two protonations to be independent the reaction is shown in Scheme l.90 Protonation at A gives redox inactive protein.From this scheme the expression (9) is derived. kiKaK8' + k2Ka'[H+]k= KaKa' + Ka'[H+] + Ka[H+] + [H+I2 (9) The experimental data can be fitted to (9) with K, fixed at the value determined by n.m.r. Figure 9 indicates a best fit for parsley PCu' with [Co(phen)J3+. Values of pK,' obtained are for parsley (5.8), spinach (5.6), French bean (5.7) and A. vuriubilis (5.7). For reactions with [Co(phen)J3 + protonation at B is a major contributing factor, whereas active-site protonation is the predominant and possibly only influence on the [Fe(CN)613 -oxidation.The behaviour observed is consistent with different binding sites for [Fe(CN),]' -and [Co(phen)J3 +,which from the n.m.r. line-broadening studies in the presence of redox inactive Cr"' complexes were designated as close to His-87 Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin K. H~PAB3HPA +H+ HPB~PH++ K., P + oxidant -% products kHPB + oxidant A products Scheme 1 20 c (I) ci10 Y P s 5 6 7 PH Figure 9 Variation of rate constant k(M-' s-') for the oxidation of parsley PCu' by [Co(phen),]'+, Z 0.20 M (NaCl), with pH(.). The broken lines are obtainedfrom thefit of = data and indicate the infuence of binding site (upper) and active site (lower) protonations.The solid line indicates the overalljt of data to equation 9 (north) and Tyr-83 (east). Values of pK,' close to 5.7 are high for protonation at a single carboxylate residue, and could be accounted for by proton sharing between two adjacent carboxylates. There are a number of carboxylates close to Tyr-83, most notably for plant plastocyanins the highly conserved 4245 patch. Since the 59-41 negative patch is not conserved for parsley plastocyanin this may make a less significant contribution than might previously have been supposed. Protonation of acidic residues will decrease their affinity for positively charged [Co(phen),13+ in the association step prior to electron transfer. Also of interest is the response of A. variabilis plastocyanin since there are far fewer negatively charged residues, and only 42 of 4245 is a carboxylate, Figure 3.We note, Sykes however, the close proximity of Glu-85 which like Asp-42 is close to Tyr-83, and could provide an adequate site for association of [Co(phen),]'+ and for protonation. Relevant distributions of negative charge on the east side of poplar and A. uariabilis plastocyanin are indicated in Figure 10. Poplar A. variabilis Figure 10 Distribution of negatively charged carboxylate residues on the east side (normal view) of poplar and A. variabilis plastocyanins as seen from the south east of the molecule with the Cu' and Tyr-83 ring aligned With regard to the higher pKas for parsley plastocyanin, sequence information has indicated some striking differences compared to other plastocyanins, most notably the deletion of Met-57 (normally invariant) and residue-58, which are -10 A from the active site, and the occurrence of Pro-60 which gives a bend in the peptide chain.Plastocyanin from the algal sources S. obliquus and C.fusca. are known to have deletions at positions 57 and 58, and will be the subject of a further study in order to understand more fully these effects. Of further interest is the observation that all other single Cu (type- 1) proteins investigated including azurin, stellacyanin, umecyanin, and rusticyanin do not display active-site protonation as observed for plast~cyanin.~' Clearly some very delicately balanced mechanism is applicable to give rise to such different behaviour of the plastocyanin Cu' active site.15 The Effect of pH on Reactivity of PCu' With [Fe(CN),I4- as reductant for parsley PCu" the effect of decreasing the pH (7.5 to 4.5) on rate constants is small, Figure 11, and in sharp contrast to behaviour observed for [Fe(cN),]'- with PCU'.~~,~~ The implication of these results is that A!?' for the protein increases with decreasing pH as already indicated (Figure 7). Microscopic reversibility requires that [Fe(CN)6]4- and [Fe(CN),]' -react at the same site (or sites), and that the ratio of rate constants (the redox equilibrium constant) at any one binding site is the same. With [Ru(NH,),~~]~+,~~ and (presumably) other positively charged reductants yet to be tested, a significant effect of pH is observed, Figure 12.A fit of the kinetic results gives a rate constant k, for protonated protein which is 36% of k, for unprotonated protein (4.2 x lo5M-' s-'), and a pKa of 4.95.The behaviour observed is consistent with [Fe(CN),I4- 93 J. McGinnis, J. D. Sinclair-Day, and A. G. Sykes in 'Biochemical and Inorganic Aspects of Copper Coordination Chemistry', ed. K. D. Karlin and J. Zubieta, Adenine Press, 1985. 305 Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin reacting at the adjacent north site, which is distant from and only slightly influenced by protonation(s). In contrast [Ru(NH,),py]' reacts at least partially at the east + site which is susceptible to protonation, most likely protonation at the 42-45 patch.I 1 1 5 6 7 8 PH Figure 11 The variation of rate constants (25 "C)for the reactions of parsley plastocyanin PCu' + [Fe(CN),I3-(O),and [Fe(CN),]'-+ PCu" (A) with pH, I = 0.10 M (NaCl) The above approach has been applied to reactions of PCu" with other proteins, where it is of course essential to have independent information (from studies with inorganic complexes) that pH does not effect the reactivity of the second protein and give rise to ambiguities in interpretation. It has been shown that the reaction of PCu" with the high-potential Fe/S protein (hipip) from Chromatium vinosum, charge -3 at pH 7, is independent of pH (5.0-8.5) implicating the adjacent (north) site as binding However with cytochrome ~(II)94 and cytochrome ~(II)28 both give significant pH effects which are more extensive than those observed for [RU(NH,)~~~]'+.With cytochrome ~(II) the rate constant for reaction of the protonated form is close to zero, and the pK, 4.95.With cytochromefln) (Figure 13)kH is -10% of k,, and the pK, is 5.07.28These findings strongly suggest use of the remote (east) binding site. In the case of cytochrome &I) this is perfectly consistent with the overall charge of 8+ and circle of lysine residues around the exposed haem edge. With regard to cytochromef(11) the position is less certain since the structure is not known. However, in spite of the small overall negative charge (apparent from column behaviour), evidence has accumulated for the presence of a functional positive patch, presumably close to an exposed haem edge on the protein.The sequence has indicated pairs of basic lysine residues at five places in the chain, and it is tempting to speculate that these are brought together in 94 S. K. Chapman, C. V. Knox,and A. G. Sykes,J. Chem. SOC.,Dalton Trans., 1984, 2775. 306 Sykes 4 6 8 PH Figure 12 The effect of pH on rate constants (25 "C)for the [RU(NH~)~~~]~+reduction of PCu"at Z = 0.10 M (NaCl); buffers-acetate (m), mes (A)and Tris/maleate (0) the tertiary structure to form a positive patch capable of interacting with the negative patch on plastocyanin, its natural partner.' The pK,s of around 5.0 observed in the above studies involving PCu" are in contrast to values (pK,') of -5.7 obtained for protonation at the binding site in the [Co(phen),13+ oxidation of PCu'.It is puzzling that similar values are not observed since the Cu charge would not have been expected to be influential at the distance of the Tyr-83 binding site, even though the connecting peptide is conserved. Using near-u.v., fluorescence, and c.d. measurements, plastocyanin from higher plants including spinach and poplar has been shown to undergo conformational changes upon reduction and lowering of the pH.41 Fluorescence technique is par- ticularly effective since plastocyanin contains only a few tyrosines (three for spinach and two for poplar) and no tryptophans. Each of the tyrosines is located in a different region making it possible to determine which parts of the molecule under- go conformational changes.In addition Tyr-83, which is exposed to solvent, has been chemically modified to nitrotyrosine which is non-fluorescent. The results obtained show that the east face of the molecule which incorporates Tyr-83 and Tyr-80 Structure and Electron-transfer Reactivity of the Blue Copper Protein Plustocyanin 11 I 1 4.0 6.0 8.0 PH Figure 13 The eflect of pH on the cytochrome f(rr) reduction of parsley PCu" at 25 "C,I = 0.10 M undergoes conformational change upon reduction, and that the effects observed are pH dependent. These results contrast with the crystallographic information which indicates nearly identical PCu' and PCu" structures at neutral pH.' The solution effects observed are very much lessened by addition of 100 mM CaC1, or 2.7 M (NH4)2S04, and an explanation may be related to the fact that crystallization was from 2.7 M (NH,)2S0.+.Conformational changes could explain the different pK,s for PCu' (5.7) and PCu" (5.0)which have been assigned to protonation at the east site, and for the simplest most consistent explanation involve the same residue. In the wider context the effects observed are important in so far as the natural function of the protein is concerned, since the affinity of cytochromef(r1) and PCu" for each other prior to electron transfer has to be reconciled with less affinity required after electron transfer, so that the proteins separate efficiently. In other words the conformational changes identified could well promote differential binding of the oxidized and reduced forms of plastocyanin to the redox partner.Further information is required, and in particular studies on A. variabilis plastocyanin, which are in progress, could be extremely helpful. 16 Competitive Inhibition This is observed in the [Co(phen),13+ oxidation of PCu' in the presence of redox inactive complexes [Cr(phen),13 +, [Co(NH,)J3', [Pt(NH3)6]4+, and [(NH,),C~-NH,CO(NH,)~]~+.The effect stems from competitive association at the binding site (or sites) used by [Co(phen),]'+. Inhibition by [Cr(phen),13 + is an important link with n.m.r. experiments already referred to. Blocking with the 3 + complexes is not sufficiently extensive, however, to indicate clearly the effectiveness Sykes at high 3 + concentrations.With the 4 + and 5 + complexes on the other hand (here designated B), it is clearly established that blocking at high concentrations is incomplete, Figure 14. The extent of the effect (recently verified 77) appears to be independent of the size and charge of B and for both 4 + and 5 + complexes the adduct PCu', B retains 50% reactivity with [Co(phen),13 at pH 5.8. Interestingly, + a similar influence of protonation is observed as with inhibition by metal complexes. At relatively low [Co(phen),13 +,when aC~(phen),~ '3 as in equation 3 can be neglected, the reactions (lo)-( 12), PCu' + Co"' 3products (10) PCu' + B PCu', B (1 1) kPCu', B + Co"' -A products (12) gives a dependence shown in equation 13, and the variation of second-order rate constants kexpwith (B) can be studied.Values of association constants K (and KB)in Table 6, are consistent with charge being important. To avoid acid dissociation of [Pt(NH3)6]4+ (pK, 7.1) with formation of a 3 + complex, a pH of 5.8 is adopted to give maximum effectiveness. There is no similar problem with the 5+ complex which remains undissociated to a W Y 9 s! I I0. Figure 14 The blocking effect of redox-inactive [Pt(NH3)J4+ and \(NH,),CoNH,-Co(NH,)J5 + on the [Co(phen)J3 oxidation of parsley plastocyanin, PCu . Rate constants determined at 25 "C,pH 5.8, Z = 0.10 M (NaCl) Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin higher pHs, but for comparison it is sometimes convenient, as in Figure 13, to work also at pH 5.8. Consistent with the electrostatics the 4 + and 5 +complexes give the biggest association constants.Because of its spherical symmetry and high charge density (as well as ease of preparation), [Pt(NH3)6]4+ is probably the most appropriate inhibitor to select. Table 6 Association constants (K)for inorganic complexes with parsley plastocyanin, PCu', at 25 "C,I = 0.10 M (NaC1) a From data in Figure 13. 1.6 x lo4 M-'at pH 7.5 It has been observed in other related studies of the [2Fe-2S] and 2C4Fe-41 ferredoxins with inorganic complexes that there is complete blocking by redox- inactive complexes such as [Cr(en),13 +.An important question is raised therefore in the case of plastocyanin by the observation of only partial inhibition i.e k, is not zero.There are two possible explanations. The first is that because the negative charge in the vicinity of Tyr-83 of plastocyanin is widely distributed it is possible to retain some reactivity of the PCu', B adduct in equation 13. This requires that two positively charged complexes can be accommodated simultaneously at the east site. The second is that reaction corresponding to k, is at the adjacent north site, even though in the n.m.r. experiments [Cr(phen)J3 line broadening of the His-87 + resonances was not observed. As long as there were two prominent negative patches 42-45 and 59-61 either side of Tyr-83 the first of these remained a strong possibility.Now that the sequence of parsley has been determined and it has been demonstrated that 59-61 is no longer invariant (and is only 1 -), this assignment is perhaps less likely, particularly as rate constants and the reactivity pattern for parsley plastocyanin is so similar to that for other higher plant plastocyanins. For these reasons the reaction of [Co(phen),13+ with parsley PCu'may occur 50% (in the case of parsley plastocyanin) at the north site, with the rest of the reaction at the east. Whether for this to hold it is reasonable that a single proton should completely switch off reactivity in a locality (B) of considerable negative charge is a key question. Evidence for a conformational change has been presented from fluorescence experiments, and this might help provide a satisfactory explanation.It has been found that KBfor association of [Pt(NH3)6]4+ with PCu' decreases to zero as the pH is decreased.', Experiments aimed at determining the effect of pH on K and k,, for [Co(phen),13 + oxidation of PCu' are difficult due to the smallness of K. The effect of protonation on the [Ru(NH3),py12+ reduction of PCu" can likewise be explained by reaction at both the north and east sites. Both the cytochrome C(II)~~and cytochrome f(xI)28 reductions of PCu" are substantially inhibited by [Pt(NH3)J4+. At pH 5.8 the former gives a (maximum) 310 Sykes 73% blocking effect. The rapidity of the cytochromef(r1 j reaction necessitated the reaction being carried out at 10 "C, I = 0.20 M (NaCl).Under these conditions complete blocking appears to hold, Figure 15, with KB= 1600 M-'. As was concluded also from [H '3 effects, both cytochromes have much greater specificity for the east site. Complementary matching surfaces in the case of cytochromefand plastocyanin would be expected to give higher specificity, with comparatively large surface contact areas. I 1 1 2 4 6 1O"PtIVl (MI Figure 15 The effect of redox-inactive [Pt(NHJ6I4+ on the cytochrome f(u) reduction of parsley PCu" at 10 "C,pH 5.8, I = 0.20 M (NaCl) Since limiting kinetics are not observed in the [Co(phen),13+ oxidation of A. oariabilis PCu' it is hardly surprising that [Pt(NH3),I4' does not inhibit the reaction. Analysis of the effect of pH on rate constants has indicated that here also -50% of reaction is at the east site (pK, 5.7).There is no effect of [Pt(NH3),I4 + on the [Co(dipic),] -oxidation of parsley PCu' consistent with reaction at the north site.73 The increase in rates for the [Fe(CN),I4- and Hipip(r) reduction of PCu" in the presence of [Pt(NH3)6]4+ can be explained by these reactants using the east as well as the north sites in the presence of associated [Pf(NH3),l4+, and/or reactant ion pairs such as [Pt(NH3)6]4+, [Fe(CN),I4- exhibiting different behavio~r.~~.~~ 17 Electronexchange Rate Constants In a recent study of the line-broadening observed at 50 "C in the proton n.m.r. spectrum of a partly oxidized solution of Pseudomonas aeruginosa azurin an electron self-exchange rate constant of 2 x 10, M-' s-' has been reported." A variety of values from 2.8 x 1W2 to 8 x lo7 M-' s-l have been obtained using the Marcus treatment for a range of redox partner^.'^?'^ The value obtained compares 95 G.W. Canters, H. A. 0.Hill, N. A. Kitchen, and E. T.Adman, J. Mugn. Reson., 1984, 57, 1. 96 D. Cummins and H. B. Gray, J. Am. Chem. SOC.,1980, 102,4360. 97 A. G. Mauk, R. A. Scott, and H. B. Gray, J. Am. Chem. Soc., 1980, 102,4360. 311 Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin well with 9 x lo5 M-'6' at 20"C obtained by Wherland and Pecht from studies on protein-protein reaction^.^ An earlier value reported for bean plastocyanin is +2 x lo4 M-' s-' 98 If indeed the exchange of plastocyanin is so slow then it is tempting to relate the difference to the different charge distributions over the protein surfaces.The existence of negatively charged regions on plastocyanin has been construed as evidence for the importance of electrostatic interactions in the reaction with other redox partners. The repulsive effect of two such regions could provide an explanation of the slow self-exchange, although exchange uia two hydrophobic north sites would remain a reasonable alternative. A preliminary value of the self-exchange rate constant for stellacyanin of I x 105 M-1 s-1 using an e.p.r. method 99 compares with values previously reported using the Marcus treatment from 6 x lo3 M-' s-' for electron transfer with Pseudomonas aeruginosa cytochrome c551, to 2.9 x lo4 M-' s-l with cytochrome c, 1.7 x lo5 M-' s-l with [Ru(NH3),py13+, 2.3 x lo5 M-' s-' with Fe(edta)J2-, and 3.0 x lo5 M-' s-' w ith [Co(phen),13+ 18 Modifications Reduction of French bean PCu" by hexa-aqua Cr2+ gives a product which it has been demonstrated has Cr"' attached.'OO*lO' Since there is no binding of a solution of hexa-aqua Cr"' with PCu' at pH -5 the reaction falls within the classification of inner-sphere electron transfer.From thermolysin proteolysis experiments on the product obtained at pH 7 using labelled Cr2+, it has been concluded that the label is contained in the peptide fraction containing amino- acid residues 40-49.'O1Co-ordination of the Cr at one or two carboxylates in the 42-45 patch is favoured.The Cr"' modified protein exhibits reactivity consistent with modification at the 42-45 patch, with a net slowing down of the reaction with positively charged redox partners such as [Co(phen),13 and+ [RU(NH,),~~]~+,'~~as well as cytochrome cg4and cytochromeS,28 but no effect is observed on the reaction with [Fe(CN)613-, [Co(dipic),J -, and Hipip Fe/S pr~tein.~**~~However, there are features which cast some doubt on the whole approach. Since [Cr(H20),13+ has a pK, of 3.8, attachment of an aqua Cr"' moiety to a protein at pH -7 must be viewed with some concern. Formation of Cr"' conjugate-base forms with a resultant labilizing effect on the normally inert co- ordination sphere could mean that the Cr"' does not remain attached at the point of Cr2+ attack.Experiments at pH 5.8 moreover indicate the presence of at least two different Cr*'*-modified forms are present. Other Cr" complexes having pro- tective ligands might usefully be explored here. Unfortunately the Cr" complex of the tetradentate macrocyclic ligand 1SaneN, (1,4,8,12-tetra-azacyclopentade-'13 J. K. Beattie, D. J. Fenson, H. C. Freeman, E. Woodcock, H. A. 0.Hill, and A. N. Stokes, Biochim. Eiophys. Acfu, 1975, 4435,109. 99 S. Dahlin, B. Reinhammar, and M. T. Wilson, Inorg. Chim. Acta, 1983, 79, 126. loo 0.Farver and I. Pecht, Eiochemisfry, 1982, 21, 1885. lo' 0.Farver, Y. Shahak, and I. Pecht, Biochemistry, 1982, 21, 1885. Io2 S. K. Chapman, C. V. Knox, P. Kathirgamanathan, and A.G. Sykes, J. Chem. SOC., Dalton Trans., 1984, 2769. 312 Sykes cane), [Cr( 15aneN,)(H20),I2 +,which reacts inner-sphere with [2Fe-2S] and 2[4Fe-4S] ferred~xin,"~ reacts by an outer-sphere mechanism with PCu". Spinach plastocyanin has been chemically modified using a water soluble car- bodi-imide to form an amide bond between a protein carboxyl group and an amine group of ethylenediamine, equation 15.'04 protein-C0,-+ NH,C2H4NH3+-protein-CONHCzH4NH3+ (15) Four distinct chemically modified products containing 2.1, 3.2,4.1, and 6.3 mol of ethylenediamine per mol of plastocyanin were separated by gel electrophoresis and ion-exchange chromatography. O5 The location of the modified residues was determined for the fraction containing 3.1 mol of ethylenediamine.A two-fold enrichment of the 14C-labelled ethylenediamine was found in the tryptic peptide containing residues 31-55. The modifications give an increase in reduction po- tential of +40 mV. The effect of ethylenediamine modification of plastocyanin on electron donation by plastocyanin to P700+ in photosystem I particles has been studied.lo6 The reduction of such particles by unmodified plastocyanin requires the presence of divalent cations such as Mg+ to screen the negative charges on the two reactants and hence facilitate interaction. lo' Although the chemically modified plastocy- anins bind more strongly with PSI, it has been concluded that the 42-45 region is probably not the binding site for P700+.'05 The effect of cytochromefmodifi- cations on reactivity with plastocyanin are also being explored.lo8 Evidence for cytochromef(~~) reacting at the remote Tyr-83 site of PCuu has been obtained from the effects of pH, [Pt(NH,),I4+, and Cr"' modification.28 The occurrence of the haem-containing globular part of cytochrome f (Figure 16), and plastocyanin in the inner thylakoid suggests that the two are able to orientate and dock in an electrostatically controlled process.It is often assumed that because two binding sites have been identified for isolated plastocyanin, that the same two sites must be biologically relevant, the one in the reaction with cytochromefand the other with P700'. This is possible and even likely, but has yet to be established. The hydrophobic north surface may alternatively serve solely to orientate plastocyanin by associating favourably at the thylakoid surface.A further type of modification should be mentioned, which is providing much additional important information. The groups of Gray and Isied have attached Ru"' to metalloproteins so that fixed-site long-distance electron transfer between metal centres separated by distances > 10 A can be studied. Two examples have so far been reported and others are being investigated. The approach is to attach lo' I. K. Adzamli, R. A. Henderson, J. D. Sinclair-Day, and A. G. Sykes, Inorg. Chem., 1984, 23, 3069. lo4 K. 0.Burkey and E. L. Gross, Biochemistry, 1981,20, 5495. lo' K. 0.Burkey and E. L. Gross, Biochemistry, 1982, 21, 5886.lo6 T. Takabe, H. Ishikawa, and S. Niwa, J. Biochem., 1983,94, 1901. lo' T. Takabe, H. Ishikawa, and S. Niwa, J. Biochem., 1984,%, 1813. lo' K. Takenata and T. Takabe, J. Biochem., 1984, %, 1813. Structure and Electron-transfer Reactivity of the Blue Copper Protein Plastocyanin Thylakoid membrane Figure 16 Schematic representation of the trans-membrane orientation of cytochrome f based on the occurrence of the extended stretch of hydrophobic residues 250-271, and the high (22%) charge composition of the 1-250 section (Ref. 11) (NH&Ru'' to the His-35 of cytochrome c,~O~*''Oand the His-83 of azurin.11'*112 The Run' of the fully oxidized adduct is then reduced in situ by flash photolysis Io9 or pulse radiolysis,' lo when the slow subsequent (first-order) intramolecular electron transfer between the Ru" and Fe" (30 s-')'09 or Cu" (1.6 s-')"~ is observed over distances of -12 A defined in crystallographic studies.Only by extending the range of such studies will it be possible to explore fully the rela- tionship of rate constants to distances, and comment more meaningfully on the relative merits of direct as opposed to through atom (via the peptide chain) electron transfer (both of which may be relevant), and comment on the part which intervening groups such as aromatic residues play. In this same context molecules containing an electron donor and electron acceptor linked by a rigid non-conjugate bridge are being studied to obtain relevant information.1'3-117 Many of these points were addressed by Gray in his recent Centenary Lecture.In the experiments with Ru-modified proteins the sites of attachment are not the binding sites relevant to biological electron-transfer, but sites determined by the presence of histidine residues suitable for modification. In future work there is no lo9 D. G. Nocera, J. R. Winkler, K. M. Yocum, E. Bordignan, and H. B. Gray, J. Am. Chem. SOC.,1984, 106, 5145. S. S. Isied, C. Kuehn, and G. Worosila, J. Am. Chem. SOC.,1984, 106, 1722. N. M. KostiE, R. Margalit, C.-M. Che, and H. B. Gray J. Am. Chem. Soc., 1983, 105, 7765. R. Margalit, N. M. KostiE, C.-M. Che, D. F. Blair, H.-J. Chiang, I. Pecht, J. B. Shelton, J. R. Shelton, W. A. Schroeder, and H. B. Gray, Proc. Natl. Acad. Sci. USA, 1984,81, 6554.L. T. Calcaterra, G. L. Closs, and J. R. Miller, J. Am. Chem. SOC.,1983, 105, 671. 'lo J. R. Miller, L. T. Calcaterra, and G. Closs, J. Am. Chem. Soc., 1984, 106, 3047. C. A. Stein, N. A. Lewis, and G. Seitz, J. Am. Chem. Soc., 1982, 104, 2596. 'I6 D. N. Beratan and J. J. Hopfield, J. Am. Chem. SOC.,1984, 106, 1584. 'I7 N. S. Hush, M. N. Padon-Row, E. Cotsaris, H. Oevering, J. W. Verhoeven, and M. Heppener, Chem. Phys. Lett. in press. Sykes reason why the carboxylates of the 4245 patch should not be modified by attachment of metals. It is also worth noting that in plastocyanin from the algae S.obliquus and A. uariabilis residue 59 is a histidine which is close to Tyr-83 and of interest therefore as a centre for modification. Acknowledgement. The author is indebted to the patience and enthusiasm of his research group and those associated with it, and to many colleagues who have conveyed some of their own interest in the subject area of this Tilden Lecture review.

ISSN:0306-0012    

DOI:10.1039/CS9851400283

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

Hard-sphere Theories of Transport Properties By J. H. Dymond DEPARTMENT OF CHEMISTRY, GLASGOW UNIVERSITY, GLASGOW G12 8QQ 1 Introduction A detailed study of transport properties of fluids and fluid mixtures is important not only for the solution of problems involving heat and mass transfer but also for the development of our understanding of molecular motions and interactions in such systems. For monatomic gases at low densities, the coefficients of viscosity, thermal conductivity, and diffusion can be accurately calculated at any temperature using exact kinetic theory expressions based on the work of Boltzmann, Enskog, and Chapman (see re$ 1) and methods have been devised2n3 for the direct determination of the pair potential energy functions of these substances from experimental transport data.However, such methods cannot be applied to monatomic fluids at high densities or to polyatomic fluids because there is at present no formal theory which allows an exact evaluation of transport properties in terms of a realistic description of the molecular interactions. An alternative approach, which has led to significant progress towards a successful molecular theory of transport properties in dense fluids, is the use of the computer simulation method of molecular dynamic^.^^^ This can be applied in different ways. Firstly, in an attempt to simulate real fluids under given conditions of temperature and density, transport coefficients are evaluated for a system of molecules interacting with a specified form of potential energy function.The function most widely used is the well-known Lennard-Jones (124) potential which relates the interaction energy to the separation of a pair of molecules according to equation 1: V(r) = 4c[(o/r)l2 -(a/r) where parameters E and CT represent the depth of the attractive well and the separation at zero energy. The self-diffusion coefficient of a fluid is then calculated from the integration of the velocity autocorrelation function: G. C. Maitland, M. Rigby, E. B. Smith, and W. A. Wakeham, ‘Intermolecular Forces’, Clarendon Press, Oxford, 1981.’J. H. Dymond, J. Chem. Phys., 1968,49, 3673. D. W. Gough, G. C. Maitland, and E. B. Smith, Mol. Phys., 1972, 24, 151. B. J. Alder and T. E. Wainwright, J. Chem.Phys., 1959,31,459.’A. Rahman, Phys. Rev., 1964, 136, A405. Hard-sphere Theories of Transport Properties where the average is over all particles over a set of initial times, or from the mean- square displacement using the Einstein expression: D = lim -:X(t) -x(0) ; (3) i+m 6t I’ Calculation of the self-diffusion of argon, the simplest atomic fluid, has been made5-’ in this way for a number of different temperatures and densities. For molecular fluids the (12-6) potential function is used to represent the interactions between the nuclei in neighbouring molecules as in the ‘two-centres’ computations of the self-diffusion coefficient fluorine, chlorine, bromine, and carbon dioxide * and of nitr~gen,~ and the ‘three-centres’ calculations of the self-diffusion coefficient for carbon disulphide.’ The shear viscosity and thermal conductivity coefficient may also be calculated by a steady-state molecular dynamics method llvl by expressing these coefficients in either the Einstein form or in terms of an autocorrelation function.The problem is the significantly greater computing time required for the evaluation of these transport coefficients, which are properties of the system as a whole, compared with the self-diffusion coefficient for which the diffusion of each individual molecule can be determined and the average taken. Thus, for a similar precision in the results, the molecular dynamics computations need to be carried out for about N times as long, where N is the number of particles considered. As an indication of accuracy, calculated viscosity coefficients of simulated argon l2 had a statistical error of 15 per cent.Transport coefficients can also be calculated by non-equilibrium molecular dynamics methods. Recent studies 143 l5 indicate that this is a more economic way of computing liquid viscosities, but the uncertainty in the reported results is still about 10 per cent. As a result of such computational studies, it is possible, by suitable choice of molecular parameters, to obtain a reasonably satisfactory fit to the experimental data, considering the uncertainties in the experimental measurements and in these computations. However, there are disadvantages to this general approach. It is expensive of computer time because of the necessity to evaluate numerically the transport coefficients for each substance considered [for homonuclear diatomics, for example, there is an additional (dimensionless) parameter, the ratio of the bond- length to the diameter of each ‘atom’] for several temperatures and densities in order to determine the molecular parameters and the dependence of the transport coefficients on the experimental variables.Furthermore, it should be noted that, D. Levesque and L. Verlet, Phys. Rev. A, 1970, 2, 2514.’D. M. Heyes, J. Chem. SOC.,Faraday Trans. 2, 1983, 79, 1741. a K. Singer, J. V.L. Singer, and A. J. Taylor, Mol. Phys., 1979, 37, 1239. P. S. Y. Cheung and J. G. Powles, Mol. Phys., 1975,30,921. lo D. J. Tildesley, Mof.Phys., 1983, 48, 129.B. J. Alder, D. M. Gass, and T. E. Wainwright, J. Chem. Phys., 1970, 53, 3813. E. M. Gosling, I. R. McDonald, and K. Singer, Mof. Phys., 1973, 26, 1475. W. T. Ashurst and W. G. Hoover, Phys. Reu. A, 1975, 11,658. I4 D. J. Evans, Phys. Reo. A, 1981, 23, 1988. Is D. Fincham and D. M. Heyes, Chem. Phys., 1983,78, 425. Dymond even if exact agreement was obtained with experimental data over a wide range of experimental conditions, it would not necessarily follow that the assumed form of potential energy function accurately represented the interactions of the real molecules. The second general application of the molecular dynamics method is the simulation of assemblies of molecules interacting with somewhat over-simplified forms of potential energy function in order to establish a sound physical basis for the development of a successful theory of transport properties in dense fluids.For example, the computations of Alder and Einwohner 16917 on the free-path distribution for hard-spheres, which interact according to U(r) = 0 r > Q (4)U(r) = a3 r < Q and square-well molecules, for which the interaction potential is showed that molecular motion proceeds by a succession of small diffusive steps and not by a relatively small number of jumps whose length is approximately equal to the intermolecular spacing, as is implicit in the activation model of Eyring.18 Furthermore, they showed that the Brownian motion approximation, which postulates that the molecules undergo many ‘collisions’ involving the attractive part of the potential (soft collisions) between successive repulsive interactions (hard collisions) and which was used by Rice and co-workers l9 as a basis for a theory of transport properties, is unsatisfactory even at a high pressure and at low temperature.What is required is a theory based on a reasonably realistic description of the trajectory of the molecules which can be used as a physically motivated and accurate approximation to the more formal theories. Such a theory is the van der Waals theory, which has served well for equilibrium properties. The van der Waals model of a fluid is of an assembly of molecules having a weak long-range attractive energy and a hard-core repulsive energy, as illustrated in Figure l(a).For real systems, the dependence of the pair interaction potential energy on molecular separation has the familiar shape shown in Figure l(b). The potential does have a steep repulsive part and the range of the attractive part can be considered large relative to the interparticle spacing at densities greater than the critical density. The attractive energy then forms a uniform attractive energy surface, and the molecules will move in straight lines between core collisions. This l6 B. J. Alder and T. Einwohner, J. Chem. Phys., 1965,43, 3399. ”T. Einwohner and B. J. Alder, J. Chem. Phys., 1968,49, 1458. S. Glasstone, K. J. Laidler, and H. Eyring, ‘The Theory of Rate Processes’, McGraw-Hill Book Co.Inc., New York, 1941.l9 S. A. Rice and A. R. Allnatt, J. Chem. Phys., 1961, 34, 2144. Hard-sphere Theories of Transport Proper ties (a) Van der Waals Model (b) Realistic Pair Potential Function Figure 1 Comparison of a realistic pair potential energy curve with that given by the van der Waals model (Reproduced by permission from Physica, 1974,75, 101) description of the molecular motion is expected to be correct at tempera-tures greater than the attractive energy well-depth or, approximately, the criti- cal temperature, when the kinetic energy will exceed the attractive potential energy. An extremely important consequence, for the van der Waals theory of transport properties is that it is equivalent to the hard-sphere theory, providing that the core sizes are allowed to decrease as the temperature increases to reflect the somewhat soft repulsive energy of real systems.This is the justification of the present widely- accepted method of interpreting transport coefficient data on the basis of the hard- sphere model. In the first part of this paper, the expressions are given for the transport coefficients of dense assemblies of smooth hard-spheres and of rough hard-spheres. In the following sections, these hard-sphere theories are applied to the rare gases, to metals, to molecular fluids, and to mixtures. Although the shear viscosity and thermal conductivity coefficients are of greater significance from the chemical engineering point of view, theoretically it is the diffusion coefficient which has proved the most important in the development of theories in dense fluids.This arises because it is the simplest transport property to treat theoretically and also Dymond because of the greater accuracy with which it can be calculated for a given intermolecular potential energy function. 2 Transport Coefficients for a Dense Hard-sphere Fluid A kinetic theory for transport coefficients of a dense hard-sphere system has been given by Enskog.20 In a dense system, the collision rate is higher than in a dilute system because the diameter of the molecule is no longer negligible compared with the interparticle distance. The Enskog theory of diffusion assumes that the high density system behaves exactly as a low density system except that the collision frequency in increased by a factor of g(a), where g(o) is the radial distribution function at contact for spheres of diameter o.The solution of the Boltzmann equation valid at low density is merely scaled in time to give the ratio of the diffusion coefficient D, at high number density n relative to that at low density, subscript zero: g(o)is obtained from computer simulation studies and is given by the Carnahan- Starling equation: 21 where 5 = b/4V for a molar volume V, and b = 27cNo3/3. Do is related to the number density no at temperature T by the expression Do = (3/8n0x02)(xkT/rn)* (8) where rn is the molecular mass and k is the Boltzmann constant. For diffusion the particles themselves must move, but for viscosity and thermal conductivity there is the additional mechanism of collisional transfer whereby momentum and energy can be passed to another molecule upon collision. The Enskog theory for the viscosity qE and the thermal conductivity h, in terms of the low density coefficients accordingly contains additional terms: 3L,/h, = [l/g(o)+ 1.2b/V + 0.755g(o)(b/V)2] (10) where the low density coefficients are given to first-order approximation by where C, is the molecular heat capacity at constant volume.2o D. Enskog, Kungl. Svenska. Vet.-Ak. Handl., 1922, 63,No.4. 21 N. F. Carnahan and K. E. Starling, J. Chem. Phys., 1969, 51, 635. Hard-sphere Theories of Transport Properties In order to apply equations 6,9, and 10for the calculation of dense gas transport coefficients, it is necessary to assign a value to the core size.In the original application of this method,22 values for cr for the rare gases were obtained by fitting p VT data to the van der Waals equation of state. It was found that the calculated high density transport coefficients differed by less than 10 per cent from the experimental values. Now the Enskog theory is based on the molecular chaos approximation. A sphere is considered as always colliding with other spheres approaching from random directions with random velocities from a Maxwell-Boltzmann distribution for the appropriate temperature. However, molecular dynamics calculations 2324 have shown that there are correlated molecular motions in hard-sphere systems.At high densities, the principal correlation effect is back-scattering, whereby a sphere closely surrounded by a shell of surrounding spheres is most likely to have its velocity reversed on collision with its neighbours and this leads to a decreased diffusion coefficient. At intermediate densities, there is a different correlation effect associated with an unexpected persistence of velocities which leads to an enhanced diffusion coefficient. The resulting corrections to the Enskog transport coefficients have been computed by Alder, Gass, and Wainwright for systems of 108and 500 particles, with the diffusion coefficients extrapolated to infinite systems on the basis of hydrodynamic theory. The density dependence of the corrections is illustrated in Figure 2, where Vo,given by No3/$, is the volume of close-packing of spheres.For Vo/Vup to about 0.5, corresponding to dense gases at densities up to 2.5-times the critical density, the corrections to Enskog theory for the viscosity and thermal conductivity coefficient are less than 10 per cent, but for diffusion the corrected coefficient is significantly greater than the Enskog value at densities corresponding to 1.5-to 2-times the critical density. At the highest densities, approaching the onset of solidification, the corrections arising from back-scattering result in the exact hard-sphere diffusion coefficient being lower by about 40 per cent, and the viscosity coefficient being higher by a similar amount. To obtain exact expressions for the dense hard-sphere transport coefficients in terms of the low density coefficients, equations 6, 9, and 10 must be multiplied by the appropriate correction factor from Figure 2 at the given reduced volume.With core sizes determined from equilibrium data by extrapolation to infinite temperature, quantitative evidence for the existence of these correlated motions in real systems was obtained by analysis of self-diffusion coefficients of methane 25 and of carbon dioxide.26 3 Application of Exact Smooth Hard-sphere Expressions: Self-Diffusion A. Monatomic Gases and Methane.-It was realised that there were uncertainties 22 J. H. Dymond and B. J. Alder, J. Chem. Phys., 1966,45, 2061. ”B. J. Alder and T. E. Wainwright, ‘The Many Body Problem’, ed.S. K. Percus, Interscience Publ. Inc., New York, 1963. 24 B. J. Alder and T. E. Wainwright, Phys. Rev. Lett., 1967, 18, 988. ”J. H. Dymond and B. Alder, J. Chem. Phys., 1968,48, 343. l6 J. H. Dymond and B. J. Alder, Ber. Bunsenges. Phys. Chem., 1971,75, 394. Dymond 0.70.I 0.3 VO/" Oe5 Figure 2 Ratio of the exact hard-sphere transport coefficients to the Enskog coefjcients given by molecular dynamics calculations, ref. 11 (Reproduced by permission from Physica, 1974,75, 103) in determining the core size from equilibrium data and different methods were proposed *' for comparing calculated and experimental transport coefficients without a prior estimation of core size. A quantity D* which is independent of molecular diameter was defined according to: D* = (nD/noDo)(V/v,)f (13) D* can be calculated from theory by writing where (DID,) is the computed correction to Enskog theory.D* can also be calculated from experimental data on the assumption that the real fluid is behaving like an assembly of hard spheres, since on substituting for the hard-sphere expressions for n,D, and V,, D* = 5.030 x lo8 (M/RT)*D/Vf (1 5) 27 J. H. Dymond, Physicu, 1974,75, 100. 323 Hard-sphere Theories of Transport Properties From equation (14), D*is a function of V/Vo;from equation (15), D*is a function of V for a given substance at a given temperature. To test whether this smooth hard-sphere theory can satisfactorily account for the density dependence of the experimental measurements at a given temperature, D*from theory, equation (14), is plotted against log (V/Vo)and D* from experiment, equation (15) is plotted against log (V).If these curves are superimposable laterally then the hard-sphere theory does represent the density dependence of the data, and the range of applicability of the theory can be established. Furthermore, V, can be obtained from points where the curves coincide. In the absence of extensive accurate diffusion coefficient measurements for the rare gases, accurate methane data 28,29 obtained using the n.m.r. spin-echo technique have been used 27-31 to test the applicability of the smooth hard-sphere theory. It was assumed initially, and subsequently confirmed, that methane is a polyatomic molecule to which the rough hard-sphere theory (see Section 4) applies with a coupling factor of unity.It was shown that the experimental points at these temperatures from 1.7-times the critical temperature, T,, down to 1.2 T,lie within 5% of the smooth hard-sphere values down to densities about 0.8-times the critical density. A subsequent experimental study was carried out by Harris and Trappeniers3' on methane at 110, 140, and 160 K. They found the reduced diffusivity D* isotherms fell on a common curve when plotted against reduced density n* (equals no3) with the core sizes given in Table 1, in agreement with the smooth hard-sphere predictions, except at the highest densities (n* >0.86) where 2.0 D* 1.0 0.0 0.2 0-4 0.6 0-8 1.0 n* Figure 3 Reduced diffusion coefJicients for methane (Reproduced by permission from Physica, 1980, lMA, 268) 20 P.H. Oosting and N. J. Trappemiers, Physica, 1971, 51, 418. 29 K. R. Harris, Physica, 1978,94A, 448. 30 K. R. Harris and N. J. Trappeniers, Physica, 1980, lMA, 262. 31 J. H. Dymond and T. A. Brawn, Proc. Symp. on Transport Properties of Fluih, Nat. Eng. Lab., East Kilbride, H.M.S.O., 1979. Dymond Figure 4 Reduced diffusion coeficients at high density for methane and ethene (Reproduced by permission from Physica, 1980, lMA, 269) the experimental values are significantly higher. A similar conclusion was obtained by analysis of the self diffusion data for ethene obtained by Arends, Prins, and Trappenier~,~~with the core sizes given in Table 1.This is illustrated in Figures 3 and 4. This discrepancy at high density casts doubt on the validity of the model. However, recent molecular dynamics studies by Easteal, Woolf, and Jolly 33 of the self diffusion coefficient in a hard-sphere system concluded that although the Table 1 Hard-sphere diameters CzH4 T/K o/nm T/K o/nm 110.00 0.3745 123.15 0.4150 140.00 0.3695 173.15 0.4080 160.00 0.3655 223.15 0.4026 223.15 0.3595 273.15 0.3985 298.15 0.3540 298.15 0.3966 323.15 0.3520 32 B. Arends, K. 0.Prins, and N. J. Trappeniers, Physicu, 1981, lWA, 307. 33 A. J. Easteal, L. A. Woolf, and D. L. Jolly, Physicu, 1983, 121A,286; ibid., 1984, 127A, 344. Hard-sphere Theories of Transport Properties computed corrections to the Enskog theory were dependent on the number of molecules considered in the calculation, the number dependence was significantly lower than that previously reported by Alder, Gass, and Wainwright.” By taking small increments in density, the dependence of (DID,) on reduced density was obtained.Their results are compared with previous computations in Figure 5. I I I J I I I I I I I I I 0 13- 8 0 12- 7 4 t # L s- I8 IIILIIIII,, 15 17 19 21 23 25 2.7 29 31 3.3 35 37 39 Figure 5 Density dependence of DID,. Filledsymbols, ref. 33: V,128particles: .,250particles:A,432 particles. Open symbols, ref. 11: V 108 particles: A, 500 particles: 0,infinite system.Hatched symbols, ref. 34: B, 108 particles: A,500 particles: 0,4 OOO particles(Reproduced by permission from Physica, 1983, 1211A,289) The solid line is given by the following equation, where the coefficients have been rounded off to give significant figures only: DID, = 0.7144 + 2.8786 -0.82236’ -10.93c3 (16) Using this correction to Enskog theory, Easteal, Woolf, and Jolly found that D for methane obtained from experiment was in excellent agreement with the smooth hard-sphere predictions over the whole density range, as shown in Figure 6. The core sizes are given by the following equation, with rounded values for the coefficients, o/nm = 0.397 95 -2.765 x l@T/K + 3.420 x lO-’ (T/K)’ (1 7) These values are lower than those in Table 3, but they agree to better than 1%with values obtained from the density of methane at the freezing point using the expression for randomly close-packed hard-~pheres.~~ 34 B.L. Holian and co-workers cited by W. G. Hoover and W. T. Ashurst in ‘Theoretical Chemistry’, ed. H. Eyring and D. Henderson, Academic Press, New York, 1975, Vol. 1, p. 24. 35 R. 0.Watts and I. J. McGee, ‘Liquid State Chemical Physics’, Wiley, New York, 1976, 162. Dymond o/nm = 0.1161 1 (V/cm3 mol-')+ (1 8) The smooth hard-sphere model has been used36 as a basis for the calculation of rare-gas self-diffusion coefficients. Core sizes were derived from densities at the freezing pressure and adjusted at temperatures close to the triple point, as described in Section 6 on viscosity.The calculated values generally agree with the experimental results to within the large experimental uncertainty of the measurements and in fact provide a more reliable estimate of this property for these substances. 30 0 00 0 80 96-0 00 0 92-00 I 11111l11111111111111, B. Liquid Metals-The applicability of the smooth hard-sphere theory for describing the self-diffusion coefficients of liquid metals was investigated by Protopapas, Andersen, and Parlee.37 These authors used the correction factors of Alder, Gass, and Wainwright.'' The core size at the melting point was obtained 38 on the assumption that the packing fraction at the melting point, t,, equal to 7cno3/6, has the same value of 0.472 for all metals.The temperature dependence of the core diameter was derived from consideration of the average distances of closest approach for repulsive collisions of real molecules. This leads to the expression 38 a/o, = [1-B(T/ Trn)+]/( 1-B) (19) where subscript m refers to the melting point and B is a constant with a value of 0.112 for all metals. The predicted self-diffusion coefficients are in close agreement with the measured values as shown in Table 2 for values at the melting point for 13 metals. 36 A. J. Easteal and L. A. Woolf, Physica, 1984, 124B, 182. 3' P. Protopapas, H. C. Andersen, and N. A. D. Parlee, J. Chem. Phys., 1973, 59, 15. P. Protopapas and N. A. D. Parlee, High Temp. Sci., 1974,6, 1. Hard-sphere Theories of Transport Properties Table 2 Comparison of experimental melting point self-diffusion coeficients with the predictions of the hard-sphere theory * Experimental Calculated D/1C9 m2s-' Metal Li 7.00 7.01 Na 4.22 4.24 K 3.82 3.85 cu 3.96 3.40 Rb 2.62 2.68 Ag 2.55 2.77 Zn 2.05 2.55 Cd 1.78 2.00 Hg 1.17 1.07 Ga 1.72 1.73 In 1.74 1.77 Sn 2.05 1.96 Pb 1.68 1.67 * ReJ 37.The hard-sphere theory also satisfactorily reproduces the temperature de- pendence of the self-diffusion coefficient as illustrated for liquid sodium in Figure 7, which is based on Figure 3 of re$ 37. 4 Rough Hard-sphere Model for Polyatomic Fluids The motion of a polyatomic molecule in a real liquid has been shown by Chandler4' to be related to the motion of a particle in a rough hard-sphere fluid.It is assumed that the motion is determined primarily by those parts of the intermolecular potential that are short-ranged and steeply repulsive. This is considered valid at densities above twice the critical density where attractive interactions will play only a minor role. For polyatomic molecules there is the possibility of changes in angular momentum as well as in translational momentum upon collision and Chandler 42 showed that coupling between translational and rotational motions led to the result that the diffusion coefficient for a rough hard-sphere fluid DRHSwas related to that for a smooth hard-sphere fluid DSHS: where 0 < A < 1. A was stated to be rigorously independent of density and furthermore assumed to be temperature independent also.There is thus a lowering of the self-diffusion 39 R. H. Meyer and N. H. Nachtrieb, J. Chem. Phys., 1955, 23, 1851. *' 0.S. Ozelton and R. A. Swalin, Phil. Mug.,1958, 18, 441. D. Chandler, J. Chem. Phys., 1974, 60,3500. 42 D. Chandler, J. Chem. Phys., 1975,62, 1358. Dymond 12 I I 1 I 1 11 100 200 300 T I’C Figure 7 Comparison of experimental self-dffwion coefficients for sodium with calculated hard-sphere values (solid line). Experimental: ---, ref. 39; ---, ref. 40 coefficient as coupling produces an additional mechanism for molecular velocity relaxation. The initial application of this rough hard-sphere theory was to carbon tetrachloride The temperature-dependent core size was determined by matching along isotherms the logarithmic derivative of the experimental diffusion coefficient with respect to density with that predicted by the theory.For ease of application, DE calculated using the Alder, Gass, and Wainwright correction to Enskog was represented by an analytical expression quadratic in reduced density no’.A satisfactory fit to the high pressure measurements of McCool and Woolf4’ at different temperatures was given with a constant value of A of 0.54 and with core sizes given by: o/nm = 0.5270[1 -0.057(T/K -283.2/283.2)] (21) Since then accurate measurements of self-diffusion coefficients have been made for several polyatomic fluids by the n.m.r. spin echo technique and the data interpreted in terms of the rough hard-sphere model.In place of the smooth hard- sphere diffusion coefficient expression of Chandler:* the simpler relationship given O3 M.A. McCool and L. A. Woolf, J. Chem. SOC.,Faraday Trans. 1, 1972, 68, 1971. Hard-sphere Theories of Transport Properties earlier by Dymond44 has been generally used. Some of the results are collected in Table 3. Table 3 Translational-rotational coupling factors, A, for diffusion Compound T rangelK 0 rangelnm A Ref: Methane 110-198 0.372-0.346 1.o 33 Carbon tetrafluoride 235-348 0.45 14.439 1.o 45 Trifluoromethane 168-250 0.3984378 0.61 & 0.04 46 Fluorotrichloromethane 341460 0.5034.490 0.64 & 0.01 47 Chlorot rifluoromethane 303-348 0.460-4.456 0.90 & 0.02 48 Carbon tetrachloride 283-328 0.5274522 0.54 42 Tetrameth ylsilane 298-373 0.568-0.563 0.59 & 0.03 49 Benzene 303433 0.5124.505 0.77 & 0.05 49 Perfluorocyclobutane 323473 0.5654.554 0.92 & 0.06 50 Sulphur hexafluoride 240-319 0.487 1.o 45 Sulphur hexafluoride 296-398 0.478-0.472 0.97 51 C yclohexane 3 13-383 0.554-4.551 0.78 & 0.07 52 Methylcyclohexane 203-298 0.578-0.574 0.26-0.52 53 Pyridine 303423 0.494-4.490 0.62-1.05 54 For the substituted methanes, the extent of translational-rotational coupling is in the order CCl, > CHF, > CFCl, > CF,Cl > CF, as might generally be expected from consideration of molecular interlocking which is most evident with carbon tetrachloride and decreases as the chlorine is replaced by fluorine atoms.The coupling factor of trifluoromethane is however difficult to explain since both methane and tetrafluoromethane behave as smooth hard-sphere molecules. For the compounds in Table 3, the factor A is generally temperature independent. However, for trifluoromethane at 142 K, A is found to be 0.38, significantly lower than the value found at higher temperatures. This was attributed to either increased translational-rotational coupling in this dipolar fluid (1.62 D) or to the effect of attractive interactions. The temperature variation of A for methylcyclohexane can be explained in terms of the increased departure from spherical shape of the molecules on going from cyclohexane, for which the model ** J.H. Dymond, J. Chem. Phys., 1974,60, 969. *’ J. H. Dymond, J. Chem. SOC.,Faraday Trans. 2, 1972,68, 1789. 46 F. X. Prielmeier, E. W. Lang, and H.-D. Ludemann, Mof. Phys., 1984,52, 1105. 47 J. DeZwaan and J. Jonas, J. Chem. Phys., 1975,62,4036. 48 K.R. Harris, Physica, 1978,93A, 593. 49 H. J. Parkhurst, Jr. and J. Jonas, J. Chem. Phys., 1975,63,2698. 50 R.J. Finney, M. Fury, and J. Jonas, J. Chem. Phys., 1977,66, 760. J. DeZwaan and J. Jonas, J. Chem. Phys., 1975,63,4606.’* J. Jonas, D. Hasha, and S. G. Huang, J. Phys. Chem., 1980,84, 109. ’’J. Jonas, D. Hasha, and S. G. Huang, J. Chem. Phys., 1979,71, 3996. 54 M.Fury, G. Munie, and J. Jonas, J. Chem. Phys., 1979,70,1260. 330 Dymond works remarkably well, to methylcyclohexane. The results for pyridine can be compared with those for benzene for these molecules have nearly identical shapes and moments of inertia.However, pyridine has a significant dipole moment (2.2 D) and the molecules can hydrogen-bond. The effect of these intermolecular interactions will decrease as the temperature is raised, and this is reflected in the increase in A values. At high temperature, A attains the smooth hard-sphere value of 1,which is unexpected by comparison with benzene which has an A value of 0.82. The predicted density dependence of D for the compounds in Table 3 is in very close agreement with experimental measurements except at high densities corresponding to V,/V > 0.66 where the experimental values are higher than predicted. The failure of the rough hard-sphere theory in this region arises from the fact that the smooth hard-sphere system becomes metastable at these densities. More recently, Easteal and Woolf 36 have used their values for the corrections to Enskog theory (Figure 5) to determine the dependence of A on density and temperature.The core sizes were determined from molar volumes at the freezing pressure. They found that for carbon tetrachloride, using the data of McCool and Woolf,4’ the factor A is temperature independent, as found by but density dependent. This is illustrated in Figure 8. This result is at variance with the postulate of Chandler that A should be rigorously density independent. 0.52 I I I I I I 1 0*43 0-45 047 0.4 9 Figure 8 Density dependence of A for carbon tetrachloride.9,283.2 K: 0,298.2 K:0,313.2K: A,328.2 K (Reproduced by permission from Physica, 1984, 124B,187) Strong density dependence is also observed for 1,2-dichloroethane, mesitylene, and octamethylcyclotetrasiloxane. For benzene, A is strongly temperature dependent as well as density dependent. However, for carbon disulphide, where the departure from spherical shape is predicted 42 to render the rough hard-sphere model invalid, it is found that the experimental self-diffusion coefficients are in close agreement with values predicted on the basis of this model with a density 33 1 Hard-sphere Theories of Transport Properties independent and temperature independent A factor of 0.765 & 0.02.For the similarly shaped but dipolar acetonitrile, A is temperature dependent, decreasing as the temperature is lowered, but still density independent. A similar result is found for deuteromethanol, where the temperature dependence is significantly greater. For those molecules where A is found to have a strong density dependence, it might be concluded that the model is invalid. However, another possibility is that the core sizes for transport properties at these low reduced temperatures are not given by equation 18 (see Section 6B). A small variation in the core size leads to a significant change in the density dependence of the calculated diffusion coefficient at high densities. Further studies are required to produce an agreed set of core sizes for these molecules. 5 Diffusion Coefficients in Binary Mixtures A.Mutual Diffusion Coefficients-The mutual diffusion coefficient, (0,2)E, for a binary dense smooth hard-sphere mixture can be calculated by an extension of the Enskog method used for self-diffusion coefficients of dense fluids. At high density, is related to the low density coefficient by the unlike pair distribution function at contact g,,(o): where n, and n, are the number densities of the particles of molecular masses rn, and rn, and with molecular diameters Q, and 0,. The low density mutual diffusion coefficient is given by the expression 55 The initial application of these expressions was to trace gas diffusion in dense gases,56 using core sizes determined from pVT data and g,,(o) values from the approximate expression given by Lebowit~.~’ The qualitative features of the results were that (i) when the trace gas had the higher molecular mass the measured diffusion coefficient was significantly higher than the calculated value but that (ii) when the trace gas had the lower molecular mass the diffusion coefficient was less than predicted.The features were understandable in terms of the correlated events previously described for pure systems, which are neglected in the Enskog theory. The positive deviations arising from a vortex flow pattern are expected to be enhanced by a more massive diffusing particle because of its larger momentum relative to that of the solvent molecule.On the other hand, for a lighter trace gas particle there is an increased probability of back-scattering. These effects were ’’S. Chapman and T. G. Cowling, ‘The Mathematical Theory of non-uniform Gases’, Cambridge University Press, Cambridge, 1970. s6 J. H. Dymond and B. J. Alder, J. Chem. Phys., 1970,52,923. ”J. L. Lebowitz, Phys. Rev.A, 1964,895, 133. Dymond investigated quantitatively 58i59 by computer simulation studies for systems of a single test particle in a solvent for selected size and mass ratios to give values of the correction factor (Dlz)sHs/(DIZ)E.The exact smooth hard-sphere diffusion coefficient (D12)SHSis then given by Instead of previous approximate estimate^,'^ g12(o)was given by 6o where gii(o)is given by yi2 gii(0) = -1 +-+-3yi 1 -5 2(1 -5)2 2(1 -5)3 where 6 equals C ni7coi3/6and yi = (oicj+ o,&)/oi.For applicatidn to systems involving polyatomic fluids, effects of translational- rotational coupling are included by expressing the rough hard-sphere mutual diffusion coefficient (D12)RHS in terms of the smooth hard-sphere coefficient 61 (Dl 2)RHS = A 1 2(D1 2)SHS (27) where A12 is the coupling factor between the unlike molecules. For nearly ideal binary liquid mixtures, it was shown by Bertucci and Flygare 61 that the calculated mutual diffusion coefficient was in excellent agreement with experiment over the whole composition range. However, the calculations were based on the assumption that the mass and size ratios were exactly equal to one and the value of (D12)SHS/(D12)Eobtained for trace amounts of solute was used at all concentra- tions.To account more precisely for the actual molecular size and mass ratios, Czworniak, Andersen, and Pecora62 assumed that, in the absence of molecular dynamics calculations at intermediate concentrations, the correction factor in mixtures with mole fraction x1 of component 1 was given by Core sizes for the pure components were derived from self-diffusion coefficient data. They applied this theory to their results obtained from laser light scattering and concluded that the rough hard-sphere theory was accurate for both spherical and 58 P. T. Herman and B. J. Alder, J. Chem. Phys., 1972, 56, 987. 59 B. J. Alder, W. E. Alley, and J.H. Dymond, J. Chem. Phys., 1974, 61, 1415. 6o N. F. Carnahan and K. E. Starling, ‘Abstracts of Invited Lectures for the van der Waals Centennial Conference on Statistical Mechanics’, North-Holland Publ. Co., Amsterdam, 1973. 61 S. J. Bertucci and W. H. Flygare, J. Chem. Phys., 1975, 63, 1. 62 K. J. Czworniak, H. C. Andersen, and R. Pecora, Chem. Phys., 1975, 11, 451. Hard-sphere Theories of Transport Properties very non-spherical molecules in ideal and moderately ideal solutions. Non-ideality was taken into account by using the relationship where y, is the activity coefficient of component 1. D,, was determined at any concentration by dividing the experimental mutual diffusion coefficient at that concentration by the thermodynamic factor, for comparison with the calculated (D12)sHs.Values obtained for A12, assumed to be dependent only on the nature of the components and not on their proportions in the solutions, were in the range 0.5 to 0.65 for C6H,,-C6H,CH3, C~H&~HSCH~,C6H1,-CC14, C6H6<6H12, CC14<&6, cCl4-Cs2, CC14-CH3COCH3, C6H6-CH3COCH3 with a Value Of 0.89 for C6H6-n-C,H16.In order to provide a more rigorous test of this theory, Dymond and W00lf~~ measured tracer diffusion coefficients for five different solutes in n-hexane at 298 K at pressures up to 400 MPa. These limiting intradiffusion coefficients are theoretically identical to mutual diffusion coefficients at low solute concentration. A comparison with rough hard-sphere values showed remarkable agreement and it was found that the assumption that A,, was equal to A for the pure solvent was valid for benzene, toluene, and even carbon disulphide tracers but that for acetonitrile tracer A,, was approximately 20% lower than A.For the exact determination of A12, it is essential that values for the correction factor (D12)sHs/(D,,)Eshould be obtained at closely spaced mass ratios and size ratios to overcome the errors involved in interpolating the limited computer results. Protapapas and Parlee 64 showed that the results of Alder, Alley, and Dymond 59 could be interpolated quite accurately on the basis of a semilogarithmic plot. Using these correction factors, diffusion coefficients calculated on the basis of the smooth hard-sphere theory for gases diffusing in liquid metals were found to be in good agreement with experiment where the latter were self-consistent.In order to remove this uncertainty of interpolation, Dymond, Easteal, and Woolf 65 have recently studied tracer diffusion of seven solutes in octamethylcyclotetrasiloxane at 323 K at Table 4 Core sizes and A12 values with OMCTS af 323 K A12 Tracer a/nm V/V, 1.607 1.565 1.503 CH,OH 0.363 0.31 0.27 0.26 CH,CN 0.410 0.29 0.29 0.28 C2H,0H 0.422 0.24 0.21 0.16 cs2cc14 0.428 0.516 0.32 0.26 0.30 0.21 0.23 0.16 c-C6H12 0.546 0.23 0.22 0.16 c-C8H16 0.586 0.22 - - J. H. Dymond and L. A. Woolf, J. Chem. Soc., Faraday Trans I, 1982,78,991. 64 P. Protapapas and N. A. D. Parlee, High Temp.Sci., 1976,8, 141. 65 J. H. Dymond, A. J. Easteal, and L. A. Woolf, Chem. Phys., submitted. 3 34 Dymond pressures up to 59 MPa and reported values for the correction factor for the actual size and mass ratios for the individual systems. The derived values for the translational-rotational coupling factors A , ,, together with the core sizes, are given in Table 4. All the A,, values are small, implying considerable rotational- translational momentum transfer between solute and solvent. For the more spherical solute molecules, A , is density dependent. These results for A,, are significantly different from the values obtained for other non-electrolyte systems from measurements of mutual diffusion coefficients. Several studies have been made 66*67*69-74 on different systems using the chromatographic peak-broadening method at atmospheric pressure over a wide range of temperature.The data were in close agreement with the calculated rough hard-sphere values for all the systems st~died,~~-~~ which included as solutes, rare gases, methane, neopentane, carbon tetrachloride, tetra-alkyl tins (where the alkyl group was methyl, ethyl, n-propyl, n-butyl, or n-decyl) and a variety of solvents including benzene, cyclohexane, n-hexane, n-octane, n-decane, n-tetradecane, acetone, methanol, propan-2-01, butan- 1-01, and octan-1-01. The solute core size was determined from the tracer diffusion in one solvent at a given temperature (298 K). A stricter test with measurements for aromatic hydrocarbons in cyclohexane up to its critical temperature concluded71 that the rough hard- sphere theory was adequate over the whole of this temperature range.Evans, Tominaga, and Ravis 67 considered A,, to have different but fixed values for each of the three classes of systems (i) monatomic solute and solvent species for which A,, is 1, (ii) monatomic solute and polyatomic solvent species for which A12 should be unity, but was found to be 0.78 for an optimum fit of mutual diffusion coefficient data, and (iii) polyatomic solute and solvent species for which they derived a value of 0.7 for A12.These A,, values cover the calculated range of molecular roughness with the lower value of 0.7 corresponding to uniform mass distribution throughout the molecule.74 However, the correction factors were obtained by interpolation of the limited computer results together with some additional simulation values which appear to have a large uncertainty.Furthermore, the core sizes for monatomics were determined from self-diffusion data at temperatures far below the temperature of the actual mutual diffusion measurements, so the A,, value should not be taken as exact. Tracer diffusivity results for small crown ethers in cyclohexane 72 have also been satisfactorily interpreted in terms of the rough hard-sphere theory. The authors suggest that the disk-like shape of the ethers is averaged out by rapid molecular rotation. For larger crown ethers diffusing in n-decane and n-tetradecane, the theory has limited SUCC~SS.’~ 66 J.H. Dymond, J. Phys. Chem., 1981,85, 3291. 67 D. F. Evans, T. Tominaga, and H. T. Davis, J. Chem. Phys., 1981, 74, 1298. S. H. Chen, H. T. Davis, and D. F. Evans, J. Chem. Phys., 1981,75, 1422. 69 S. H. Chen, H. T. Davis, and D. F. Evans, J. Chem. Phys., 1982,77, 2540. 70 S. H. Chen, D. F. Evans, and H. T. Davis, AIChE J, 1983,29,640. 71 C. K. J. Sun and S. H. Chen, AIChE J, in press. 72 H. C. Chen and S. H. Chen, Chem. Eng. Sci., in press. 73 H. C. Chen and S. H.Chen, ind. Eng. Chem., Fundam., in press. 7* M. Baleiko and H. T. Davis, J. Phys. Chem., 1974, 78, 1564. Hard-sphere Theories of Transport Properties B. Inter-and Intradiffusion Coefficients away from the Zero Concentration Limit.- The advantage of the rough hard-sphere theory is that it can be applied to intra- (tracer) diffusion and inter-(mutual) diffusion in binary fluid mixtures over the whole composition range.Harris and Woolf 75 calculated tracer diffusion coefficients for each component in five binary liquid mixtures, based on the equation of Sandler and Mason76 It was found generally that the values of the coupling factor obtained by comparison of the calculated tracer diffusion coefficient with the measured coefficient for each of the two components were in close agreement over nearly all the composition range. Furthermore, these values agreed reasonably well with the A12 values obtained from limiting diffusion studies in these systems. However, the expression used for gI2((3)was incorrect, and the correction factors used to calculate the hard-sphere results were given by the equation of Czworniak, Andersen, and Pecora 62 and based on the assumption that the correction factor for mutual diffusion was a linear function of composition.For an accurate calculation of all the diffusion coefficients in a binary mixture, computer simulation results are required for the corrections to the Enskog expressions at different compositions. Easteal and Woolf 77 have recently investigated the effects of differing mass ratios (range 1-10) and core size ratios 0.5 a3 s-0.1 -aI 1-0 1 1 1 I 1 1 I1 I I I -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 In(WM,1 Figure9 The mass dependence of the intradiffusion ratio for an equimolar hard-sphere mixture at various reduced volumes, V/V,.V, 1.5; .,1.6; 0,1.8; 0,2.5; a,3.0; A, 4.0 (Reproduced by permission from Chem. Phys., 1984,88, 105) 75 L. A. Woolf and K. R.Harris, Chem. Phys., 1978,32, 349. 76 S. I. Sandler and E. A. Mason, J. Chem. Phys., 1968,48, 2873. 77 A. J. Easteal and L. A. Woolf, Chem. Phys., 1984, 88, 101; corrigenda (in press). 336 Dymond (range 1-4) in a V/Vorange from 1.5 to 4 on the diffusion coefficients in an equimolar mixture. The ratio of the correct smooth hard-sphere intradiffusion coefficient to the Enskog coefficient for component 2 to that for component 1 [denoted by (D2/Dl)Jis given in Figure 9 for an equimolar mixture with o1= o2 to illustrate the mass dependence. Values at selected reduced volumes are presented in Table 5.The results show that differing size ratios are more important than differing mass ratios. Table 5 Predicted intradiffusion ratios in an equimolar mixture v/vo (a) (b) 1.5 0.986 3.10 1.6 1.034 2.83 1.7 1.060 2.62 1.8 1.068 2.46 2.0 1.101 2.26 2.5 1.134 2.10 3.0 1.150 2.02 Attempts to obtain (Dl2)SHS/(D12)E for calculation of interdiffusion coefficients in the equimolar mixture were unsuccessful. It was proposed that for mixtures with a small departure from ideality this correction factor could be taken as the mean of the factors for the intradiffusion coefficients. A comparison of (D&M/(D12)E with values predicted by the Czworniak, Andersen, and Pecora equation 62 showed reasonable agreement at V/Vo= 1.6, but successively poorer agreement at V/Vo= 1.7 and 1.5.This reinforces the need for accurate computer studies on different mixtures. Measured inter-diffusion and intra-diffusion coefficients for 1 1 binary liquid mixtures were analysed and values calculated for (A1)2 and (A2)1. For mixtures where there was no strong specific interaction, there was a good correlation between A,, the ratio of A,, to the mean of (A1)2 and (A2)1, and the thermodynamic factor (i31nal/i31nxl),,,, though these were not identical (see corrigenda, re$ 77). The ratio of (D,/DJCfrom the simulations agreed with the measured ratio of the intra-diffusion coefficients within the combined uncertainties of calculation and experiment, except for mixtures containing an associated component.6 Viscosity Coefficients A. Monatomic Fluids at Supercritical Temperatures.-Analysis of dense gas viscosity coefficient data on the basis of the smooth hard-sphere model can be carried out in an analogous manner to the analysis of diffusion coefficient data described in Section 3. A quantity q* is defined by Hard-sphere Theories of Transport Properties where qEis the Enskog dense gas value, (q/qE) is the computed correction to Enskog theory, and (qE/qo)is given by equation 9. Values of q* can be obtained from experimental data by substitution of the hard- sphere expressions to give q* = 6.035 x lo8 qVf/(MRT)f (32) The range of applicability of this model is tested by superimposing curves of q* versus log (V/ V,) from theory, equation 31, and q* versus log V from experiment, equation 32.Using extensive measurements at above critical densities for neon,78 arg~n,~~-~lkrypton, 80*82 and xenon,8o it was shown 27 that the density depend- Table 6 Comparison of calculated smooth hard-sphere viscosity coeficients with experiment Argon at 308 K Krypton at 323 K ViscositylmPa s Viscosiry/mPa s -P/bar Calc. Expt. P/bar Calc. Expt. 6060 31.05 31.37 (ref: 84) 6 540 57.92 57.40 (ref: 83) 5 835 29.94 30.08 6 020 53.08 53.10 5 540 28.50 28.68 5 560 49.06 49.35 5 290 27.35 27.50 5000 44.28 44.95 5 055 26.20 26.3 8 4 560 40.70 41.70 4 800 24.97 25.13 4 030 36.52 37.30 4 590 24.01 24.1 5 3 540 32.72 33.32 4 100 21.72 21.83 2 930 28.1 1 28.75 3 540 19.14 19.20 2 480 24.74 25.20 3 020 16.84 16.73 2 005 21.16 21.50 2 500 14.51 14.34 1755 19.27 19.37 2 355 13.87 13.66 1 990 12.20 11.88 1755 11.08 10.86 2 079 21.71 22.10 (ref: 82) 1403 9.39 9.22 1 347 16.07 16.33 1060 7.73 7.62 88 1.7 12.12 12.41 994.0 7.38 7.30 603.0 9.44 9.79 883.5 6.82 6.76 415.8 7.36 7.63 726.5 5.99 5.99 308.3 6.03 6.19 625.5 5.44 5.45 244.7 5.2 1 5.26 496.0 4.69 4.74 193.0 4.59 4.47 389.5 4.13 4.13 302.0 3.67 3.62 ”N.J. Trappeniers, A. Botzen, H. R. Van Den Berg, and J. Van Oosten, Physica, 1964,30,985. l9 A. Michels, A. Botzen, and w.Schuurman, Physica, 1954, 20, 1141.8o E. G. Reynes and G. Thodos, Physica, 1964,30, 1529. J. A. Gracki, G. P. Flynn, and J. Ross, J. Chern. Phys., 1969, 51, 3856. N. J. Trappeniers, A. Botzen, J. Van Oosten, and H. R. Van Den Berg, Physica, 1965,31,945. Dymond ence of the data at above critical temperatures was very satisfactorily represented by the hard-sphere theory at densities from above twice the critical density down to about 1.2-times the critical density. Since then accurate experimental measure- ments have been made for krypton at 323 K83 and for argon at 308 K84*85at pressures up to 6 OOO atm, where the density approaches the point of solidification. These provide a much more critical test of the theory. The density dependence of these measurements, together with the earlier data, is compared with that given by the hard-sphere theory in Figure 10. Although the computed corrections to Enskog theory are less well known than the corresponding corrections to the diffusion coefficient, nevertheless it can be concluded that the smooth hard-sphere theory gives a very satisfactory fit to the viscosity coefficient data at densities down to 1.2- times the critical density.This corresponds, in the case of krypton data at 323 K, to a pressure range from 6 500 atm down to 250 atm in which the viscosity coefficient changes by a factor of eleven. For argon at 308 K, the data are closely fitted by the theory from a pressure of 6 OOO atm down to 300 atm, with a factor of nine variation in the viscosity.A comparison with the calculated values is given in Table 6 and the I I I *T 50-1I* 40-I I 30-'I;t*I 110 0-*o o-0-A I I I 0.5 1.0 1.5 ln VIVO Figure 10 Variation of q* (equation32) with logarithm of reduced volume. Valuesgiven by the hard-sphere theory are denoted by * with error bars. Experimental data for argon 0,ref. 79; e,ref. 84; 0,ref. 85; +,ref. 93:for krypton A,ref. 83; A, ref. 82. Solid line is given by equation 34 83 J. Vermesse, M. Provansal, and J. Brielles, Physica, 1978, 92A,282. 84 J. Vermesse and D. Vidal, C.R. Hebd. Seances Acad. Sci. Ser. B., 1973, 277, 191. 85 N. J. Trappeniers, P. S. Van Der Gulick, and H. Van Den Hoof, Chem. Phys. Lett., 1980,70,438. Hard-sphere Theories of Transport Properties I I I AT % 5 0 '0 0+ 0 0 0 -5 I I 1 0.2 0.4 0.6 v,/v Figure 11 Percentage deviation of experimental viscosity data from values calculated on the basis of hard-sphere theory for argon at 308 K and krypton at 323 K.Key as for Figure 10 deviations shown in Figure 11, as a function of reduced density, demonstrate that the fit is generally better than the uncertainties in the measured viscosity coefficients. Values obtained for the core sizes are summarized in Table 7. Table 7 Molecular core sizes (nm) for the rare gases TIK 173 223 298 323 348 Argon 0.334 0.328 0.320 0.318 0.316 Krypton 0.344 The core sizes have an estimated uncertainty of less than 0.5%. The values for argon are higher than those given earlier 27 which had a greater uncertainty because the viscosity data did not at that time extend to the high densities necessary to define the diameter closely.These core sizes for argon can be expressed in the form Dymond Q = 00[1 -B(T -TO)/TO] (33) where CJ,, is the hard-sphere diameter at reference temperature To.For a reference temperature of 300 K, the value of B for argon is 0.080. These core sizes can be compared with diameters obtained by application of the hard-sphere theory to gas solubilities,86 which correspond to temperatures approximately equal to the well- depth of the pair potential. In view of the uncertainties in the computed corrections to Enskog theory, the results given by the rare-gas data at densities greater than 1.2-times the critical density can be considered as the exact hard-sphere results.The solid line in Figure 10 can be expressed by the equation 1/q* = C ai(Vo/V)‘ (34) i=O with the values for the coefficients a, given in Table 8. From this, the corrections to Enskog theory are given by the equation. with coefficients aj listed in Table 8. An alternative appr~ach,~’ based on liquid viscosity coefficient data, compared data for methane 88 with values calculated using the Enskog expression with core diameters determined from the expression (equation 18)for randomly close-packed hard-spheres at the freezing point o/nm = 0.116 11 (V/cm3 mol-’)* (18) where Vis the molar volume at the freezing pressure obtained from the density data of Cheng, Daniels, and Crawf~rd.~’ This gave the correction to Enskog theory q/qE as a polynomial in V/V, with coefficients listed in Table 8.(The coefficients have been rounded off here to the appropriate number of significant figures.) Table 8 Coeficients of the equations for q* and (q/qE) 00 a1 a2 a3 a4 a5 a6 1/T* 0.044 55 2.1789 -5.9822 -6.421 40.258 -51.208 21.39 (qE/q)(this work) 0.975 1.86 -17.56 94.9 -269.13 363.2 -189.51 (q/qE) (ref: 87) 5.023 -46.748 205.41 -432.18 430.62 -155.98 86 E. Wilhelm and R. Battino, J. Chem. Phys., 1971, 55, 4012. A. J. Easteal and L. A. Woolf, Physica, 1984, 124B,173. D. E. Diller, Physica, 1980, lWA, 417. 89 V. M. Cheng, W. B. Daniels, and R. K. Crawford, Phys. Rev., 1975, B11,3972.341 Hard-sphere Theories of Transport Properties The results obtained from liquid methane data are compared with the correction factors calculated from rare-gas data and with the computed corrections to Enskog theory in Figure 12. The hard-sphere valuesg0 are a combined result of extrapolations of computations for a square-well system and interpolations of the earlier results for a 108 hard-sphere system. The uncertainty is estimated to be between 5% and 7%. 1.3 1.0 0.3 0.5 0rlv,lv Figure 12 Density dependence of q/qE Vertical lines with error bars, hard-sphere theory, ref.90; ---from liquid methane data, ref. 87; -from rare-gas data, this work This close agreement supports the conclusion of previous studies "vg2 that methane behaves as a smooth hard-sphere fluid with regard to transport properties, and provides a reliable estimate of the corrections to Enskog theory.Furthermore, it illustrates that the hard-sphere theory can be satisfactorily applied to fluids at temperatures below the critical temperature where non- uniformities in the attractive potential energy surface for real fluids have been shown in computer simulation studies to have only a small effect on the molecular trajectories. B. Monatomics at Subcritical Temperatures-Easteal and Woolf *' have recently applied the corrected Enskog theory to the viscosities of the liquified rare gases. 90 J. P. J. Michels and N. J. Trappeniers, Physica, 1980, lMA, 243. 91 J. H. Dymond, Chem. Phys., 1976, 17, 101.92 J. J. Van Loef, Physica, 1978, %B, 34. Dymond The corrections to Enskog theory were based on the use of methane as a model smooth hard-sphere fluid, as described in the above section, and core diameters calculated from liquid densities along the freezing curve according to equation 18. The calculated results are compared with experimental data for kryptong5 and xenong6 in Figure 13, which is based on Figure 3 of their paper. 1.1 fl, .---3 0 +O I 0.5 0.6 0.7 0.8 0.9 1.0 1.1 T/Tc Figure 13 Ratio of experimental viscosity coefjcients to values calculated on the basis of the hard-sphere theory with core sizesgiven by equation 18. Argon a,ref. 94; 0,ref. 93; krypton V,ref. 95; xenon 0,ref. 96 It is found that for argon at temperatures from about 0.7-times the critical temperature Tc to 1.2 Tc the agreement is better than 3%, which is within the combined uncertainties of the corrections to Enskog theory and the experimental uncertainties.For krypton and xenon, the deviation is about 10%at 0.8 Tc but within the estimated probable uncertainty of the experimental data. It is apparent that at lower reduced temperatures there is a systematic and increasing discrepancy between experimental data and values calculated by this application of the smooth hard-sphere theory. This is explained 87 by a breakdown of equation 18 for these liquids as the temperature approaches the triple point. Values calculated for the core diameters of argon to give agreement at these low reduced temperatures were given by the equation CT = CT,, for TR > 1.5 CT = opRafor 1.0 < TR < 1.5 where TR is the temperature reduced by the triple point temperature and CT,, 93 A.De Bock, W. Grevendonk, and W. Herremann, Physicq 1967,37, 227. 94 W. N. Haynes, Physicu, 1973, 67,440. 95 A. Michels and C. Prins, Physicu, 1962, 28, 101. 96 S. A. Ulybin and V. I. Makarushkin, High. Temp. (USSR), 1977, 15, 430. 343 Hard-sphere Theories of Transport Properties obtained from density data, was given by the following expression (here rounded off to give significant figures): ap/(nm) = 0.409 36 -1.0492 x lO-’ (T/K) + 5.491 x (T/K)’ -1.117 x (T/K)3 (37) The ratio R, was found to vary with temperature according to the equation R, = 0.4102 + 1.2941T~-0.9611T~~+ 0.2402T~~ (38) The Q values so derived agree to within 1% with the values previously obtained by Dymond ’’from fitting liquid argon viscosity coefficients. Application of the same modifications to the core diameters, equations (36) and (38), lead to a significant improvement to the viscosity data fit for krypton and xenon with the Q values from densities along the freezing curve given by the expressions Krypton: o/(nm) = 0.417 40 -4.389 x 1p(T/K) + 7.944 x lO-’ (T/K)’ (39)Xenon: o/(nm) = 0.449 60 -2.988 x 10-4 (T/K) + 3.468 x lo-’ (T/K)’ 2.8 I I I I I I 1 2 -6 2 4 2.2 2 .o 1.8 1*6 ~1.4 1 -0 > l a 2 C.S.= CS A.G.W --+/.\:\Lo-. -.-.-.- 0.8 0-6 I I I 0.15 0.20 0.25 0.30 0.35 0.60 0.45 0.50 k Figure 14 The ratio of the viscosity coefficient q for the smooth hard-spherejuid and for various metals to the Enskog theory approximation qE,plotted as a function ofpacking fraction, 5.The circles are hard-sphere molecular dynamics results (ref. 11) and curve HS is a smoothed representation of these results. The other curves are obtained from analysis of experimental data for liquid metals Cfor data references, see ref. 98) (Reproduced by permission from Chem. Phys., 1975,8, 21) 97 J. H.Dymond, Physica, 1975,79A,65. Dymond C. Liquid Metals-The smooth hard-sphere theory has been applied to the viscosity coefficients of liquid metals,’* using core diameters determined as in Section 3B.The authors obtained smooth values for the correction factor (q/qE)by using the observation of Alder, Gass, and Wainwright l1 that the product of the self-diffusion coefficient and the viscosity coefficient for a smooth hard-sphere system varies slowly with packing fraction. These ratios of exact to Enskog viscosity coefficient are compared with values obtained from experiment for several metals in Figure 14. Although these curves do not coincide exactly, there is generally close agreement with the theoretical curve, with the exception of antimony and zinc which are significantly different. The authors suggest that the caesium curve should be taken as the universal (q/qE)curve for metals. This leads to a greatly improved fit to the liquid metal viscosity data at low temperatures and, for 15 of the 23 metals studied, the agreement over the complete temperature range was within the typical scatter of the measurements.Whether the theory is applicable or not depends on the position of the metal in the Periodic Table, as shown in Table 9. Table 9 Applicability of the hard-sphere theory for viscosity IA IIA VIII IB IIB IIIB IVB VB Li 0.060 i Na iMg A1 0.095 0.065 0.050 Rb Ag Cd 0.148 0.126 0.097 cs Au Hg 0.169 0.137 0.110 The dashed line represents the dividing line between the elements for which the theory is accurate, those below and to the left, and those for which it is not. The number given is the radius (nm) of the ion when all valence s and p electrons have been removed.The metals for which agreement is poor were either transition metals for which accurate data were difficult to obtain because of the high melting-point, or else elements having less metallic character, appearing at the top of the Groups and to the right of the rows. It appears that for metals having two or more valence electrons in s and p orbitals, there is a critical value of 0.073 nm for the ionic radius such that, for all metals with a radius greater than this, the viscosity is accurately described by the hard-sphere theory. 98 P. Protapapas, H. C. Andersen, and N. A. D. Parlee, Chem. Phys., 1975,8, 17. Hard-sphere Theories of Transport Properties D. Polyatomic Fluids.-For a system of fairly spherical polyatomic molecules at densities greater than twice the critical density, Chandler 42 showed that the viscosity coefficient is equivalent to the rough hard-sphere viscosity coefficient qRHs.When account is taken of the effect of changes in the angular momentum as well as changes in the linear momentum of a particle upon collision, then it is found that the rough hard-sphere coefficient is directly related to the smooth hard-sphere coefficient: where C is assumed to be constant. It obeys the inequality and equals one when coupling between angular and translational motions is absent. Most tests of the rough hard-sphere model for viscosity have been made using the full equation where (q/qE)is the Alder;Gass, and Wainwright computed correction to Enskog theory.Values of the core size were obtained either from fitting the high density diffusion coefficient data for the fluids or from plots of ln(l/q) uersus In p, from which the slope was determined and 0 derived using the smooth hard-sphere expressions for fluidity given by Dym~nd.~~ Values for the core diameters agreed closely with values obtained from self-diffusion coefficient data. Typical values for the translational-rotational coupling factor are given in Table 10. Table 10 Translational-rotational coupling factor Cfor viscosity Compound T rangelK 0 rangelnm C Ref: Chlorotrifluoromethane 303-348 0.460-4.458 0.77 f0.02 48 Carbon tetrachloride 283-328 0.527-0.522 1.74 42 Tetramethylsilane 298-373 0.540-4.555 1.39 99 Benzene 303433 0.514-O.506 1.32 99 Perfluorocyclobutane 323423 0.5584.554 1.23 50 C yclohexane 3 13-383 0.5554.55 1 1.41-1.31 52 Meth ylcyclohexane 223-298 0.578-0.574 3.90-2.48 53 Pyridine 303423 0.499-0.492 1.49-1.22 54 The coupling factor is practically temperature independent for those molecules which can be considered pseudospherical but shows a marked temperature dependence where there is a significant departure from spherical shape or where the molecules can hydrogen-bond. The rough hard-sphere model of transport properties has been treated in a 99 H.J. Parkhurst, Jr. and J. Jonas, J. Chem. Phys., 1975,63,2705. Dymond different way by Dahler with the derivation'OO*'O' and solution102*'03 of an appropriate kinetic equation. The transport coefficients depend on the internal mass distribution, characterized by the moment of inertia which in reduced form is given by k=-41 mcZ The dimensionless moment of inertia can have values from zero when the mass is at the centre, to two-thirds when the mass is evenly distributed over the surface of the sphere. The coefficient of viscosity can be written lo4in terms of k and the reduced volume V/Vo.It is found that (qRH&/qSHShas a maximum value of 1.64and, more important, is constant to within 2% for a given value of k over the range of V/V, from 1.5 to 2.5.This supports the result obtained by Chandler4' that the rough hard-sphere coefficient is proportional to the smooth hard-sphere coefficient, though in Chandler's theory there is no way of evaluating the proportionality constant.The disadvantage of the Dahler theory is that it overemphasizes the role of inelastic collisions. Generally, the values derived for the translational-rotational coupling factor derived from viscosity are greater than unity as postulated by Chandler.42 However, for chlorotrifluoromethane Harris 48 obtained the figure of 0.77 for C which he showed to be not unreasonable since application of the slip and stick boundary conditions of the Stokes-Einstein equation leads to the inequality where A is the coupling factor from self-diffusion. More recently, Easteal and Woolf 36 have used their calculated corrections to the approximate Enskog theory, based on methane data, to determine the density and temperature dependence of the translational-rotational coupling factor for relatively simple polyatomic fluids.They find that the coupling factor may have a strong density dependence, as illustrated in Figure 15 for carbon tetrachloride. For other liquids such as benzene, the coupling has a strong temperature dependence in addition, as shown in Figure 16. The core sizes for these molecular fluids were calculated from the molar volumes at the freezing pressure, equation 18, which as in the case of monatomic fluids (Section 6B) may not be appropriate at these low reduced temperatures. Further work is required to establish conclusively whether the translational-rotational coupling factors do have such a strong density and temperature dependence.If this is indeed the case, it contradicts the basic postulate of Chandler and the rough hard- "' W. Condiff, W. Lu, and J. S. Dahler, J. Chem. Phys., 1965,42, 3445. lo' B. J. McCoy,S. I. Sandler, and J. S. Dahler, J. Chem. Phys., 1966, 45, 3485. lo* M. Theodosopulu and J. S. Dahler, .I.Chem. Phys., 1974,60, 3567. '03 M. Theodosopulu and J. S. Dahler, J. Chem. Phys., 1974, 60, 4048. S. F. Y. Li, Ph.D. Thesis, University of London, 1984. Hard-sphere Theories of Transport Properties I I -> I 3.3 - 0% C 3.1 - 2.9 - 2.7 - 2.5 - 2.3 - - 2.1 0.43 0.4 0.47 0.49 E Figure 15 Density dependence of the translational-rotational coupling factor for viscosity for carbon tetrachloride. V, 283.2 K, 0,298.2 K, 0,313.2 K; A, 328.2 K (Reproduced by permission from Physica, l984,124B, 187) I 1 I I I 1 I J k.41 OA2 0.43 0.44 0.45 0.46 0.47 0.48 e Figure 16 Density dependence of the translational-rotational coupling factor for viscosity for benzene.V,288.2 K; 0,298.2 K; 0,313.2 K; A, 328.2 K, 0,333.2 K (Reproduced by permission from Physica, 1984, 124B,188) Dymond sphere theory is not appropriate. However, for the purpose of data correlation, the model can still be retained and the dependence of the coupling factors on temperature and density allowed to remain. E. Binary Mixtures.-Shear viscosities for mixtures of argon + methane, calculated by Kandiyoti and McLaughlin”’ on the basis of the smooth hard- sphere theory using Thorne’s extension ”to the Enskog theory, were found to be in poor agreement with experiment.However, Jhunj hunwala, Boon, Frisch, and Lebowitz Io6 found good agreement using this theory with measured viscosities for argon + krypton mixtures. As pointed out by M~Donald,’~’ this agreement was somewhat fortuitous in view of the fact that the core diameters were derived from viscosity coefficients for the pure liquids using the approximate Enskog theory. When the computed corrections for correlated motion l1 were taken into account, the core sizes were found to be close to values obtained from the position of the first peak in the structure factor. For the calculation of mixture viscosities, the correction factors to the Thorne-Enskog expression were taken as equal to the factors for the single component system at the same packing fraction.The calculated viscosities were then in closer agreement with experiment, but this too was fortuitous because the Percus-Yevick approximation was used for the radial distribution function at contact. This approximation can be readily removed using correct expressions for g,,((r),60 but a rigorous test of the applicability of the smooth hard-sphere theory for mixture viscosities awaits the accurate computation of the correction factors. 7 Thermal Conductivity Coefficients A. Monatomic Gases at Supercritical Temperatures.-It is convenient to test the applicability of the smooth hard-sphere theory for interpretation of thermal conductivity data by considering the function h* defined by: where (hlh,) gives the computed correction to Enskog theory,” (h,/ho)is the ratio of Enskog dense hard-sphere thermal conductivity coefficient to the dilute hard- sphere value, equation 10, and h* is core size independent.Substitution of the hard-sphere expressions leads to the following relationship for a monatomic fluid which behaves as an assembly of hard spheres: h* = 1.610 x lo* hV*(M/R379* (44) This theory can be tested, using the extensive experimental measurements at high lo’ R. Kandiyoti and E. McLaughlin, Mol. Phys., 1969, 17, 643. Io6 N. Jhunjhunwala, J. P. Boon,H. L. Frisch, and J. L. Lebowitz, Physica, 1969,41, 536. lo’ I. R. McDonald. Physica, 1973,65, 630. Hard-sphere Theories of Transport Properties pressures and at temperatures above the critical temperature for argon 108~109and krypton,10g for which values for the core sizes have been obtained by application of the hard-sphere theory to viscosity coefficient data, Table 7.There are thus no adjustable parameters, and h* from experiment, equation 44, can be compared directly with h* from theory, equation 43, by plotting versus In (V/Vo).The results are illustrated in Figure 17, which shows very close agreement over the density range from about 0.8-to 2.5-times the critical density. At higher densities, the experimental results are lower than the hard-sphere predictions. This may possibly be due to errors in the computed corrections to Enskog theory. Although recent calculations for a 108-particle system agree closely with the earlier results," the number dependence of the results has not yet been established.Resolution of this discrepancy therefore awaits the results of further computer studies. I I I I 20 m A* 0 15 01 0 10 0 0. 5 I 1 A comparison of calculated thermal conductivities with experimental values at densities below 0.8-times the critical density shows the predicted values to be lower A. Michels, J. V. Sengers, and L. J. M. Van de Klundert, Physica, 1963,29,149. lo9 R. Tufeu, D. Vidal, M. Lallemand, and B. Le Neindre, High Temp.-High Press., 1979, 11, 587. 'lo J. P. J. Michels and N. J. Trappeniers, Physica, 1981, lWA, 299. 1. Dymond and this difference increases as the density is decreased.This is attributable to neglect of intermolecular attractions which become significant at lower densities. These differences can be empirically related" to the reduced temperature and reduced volume. There is an additional factor with regard to the thermal conductivity and that is the anamolous behaviour in the critical region. The smooth hard-sphere theory, modified to account for the effects of intermolecular attractionsg7 is unable to reproduce this behaviour. This is not unexpected, but it is interesting that deviations begin to appear at temperatures as high as 1.7 T,. This effect has been confirmed in a recent accurate experimental study.' l1 B. Polyatomic Fluids-The thermal conductivity coefficient for a rough hard- sphere fluid has been treated by Theodosopulu and Dahler.'02*103 Li'04 has evaluated their expressions and shown that although the translational and rotational contributions vary quite significantly with change in the moment of inertia, the reduced total thermal conductivity, h*, given by analogy with equation 43 as varies by less than 10%with change in the moment of inertia over the whole density range.To test Dahler's theory for the thermal conductivity it is first neces-sary to establish values of volume V, and coupling factor C from analysis of viscosity coefficient data in terms of Chandler's rough hard-sphere model. Since the theories of Chandler and Dahler are mutually consistent for viscosity of rough hard-sphere systems, a value for the dimensionless moment of inertia, k,can be derived from C and the thermal conductivity calculated and compared with experiment.Li lo4 applied this method to n-hexane at 298 K, for which he found C = 1.45, V = 78 x 1W6m3 mol-', k = 0.44,and n-octane at 298 K for which C = 1.7, V = 105 x 1W6m3 mol-', k = 0.66. The calculated thermal conductivity coefficients agreed with measured values for n-hexane to within 5% over the density range for which the smooth hard-sphere model is stable (corresponding to pressures up to 150 MPa). For n-octane, the differences were somewhat greater but still less than lo%,which is remarkably good in view of the simplicity of the model. 8 Correlation and Prediction of Transport Coefficients From a chemical engineering viewpoint, it is essential to be able to make accurate "' C.A. N.de Castro and H. M. Roder, J. Rex Nat. Bur. Stand., 1981,86, 293. 35 1 Hard-sphere Theories of Transport Properties predictions of thermophysical properties. The most satisfactory representation of experimental data is one which is based on theory. As discussed above, the physically realistic hard-sphere models lead to a satisfactory fit of experimental transport coefficient measurements for dense fluids and their mixtures where the molecules are reasonably spherical in shape. The problem lies in the transition to a metastable state that occurs for hard-sphere systems at high densities. For many real fluids this density corresponds to a pressure far below the experimental freezing pressure at a given temperature.However, the methods used to demonstrate the applicability of the hard-sphere theories for the transport properties can be successfully extended to give correlation/prediction schemes of high accuracy at all densities. A. Self-Diffusion Coefficients.-On the basis of the rough hard-sphere theory, the reduced self-diffusion coefficient DRHSis given by If the coupling factor is density independent and temperature independent, DRHs is just a function of molar volume for a given fluid at a constant temperature. Plots of D&s (or log D&) uersus log V for different isotherms will therefore be superimposable laterally, and the amount by which the curve at a given temperature has to be moved to superimpose it on a curve at a reference temperature TRleads to a value for VO(r)/YO( TR).” Typical results, for tetramethylsilane, are shown in Figure 18.The curves for different temperatures are superimposable on the single curve given by data at the reference temperature of 373.2 K, not only over the density range for which the hard-sphere theory is valid (up to 150 MPa at 298.2 K), but over the whole density range (for pressures up to 400MPa). Values derived for Vo(T)/(Vo(TR)were as follows: TIK 298.2 323.2 348.2 373.2 V,(T)/~O(TR) 1.043 1.033 1.01 4 1.OOo Once the reference curve has been established for a given fluid, self-diffusion coefficients at other temperatures and densities can be accurately predicted. B.Viscosity Coefficients.-A method analogous to that described above for self- diffusion coefficients can be used for the successful correlation and prediction of viscosity coefficients over the whole density range. A quantity q’ was defined as 104qVfI(MQ3 in the cgs system of units, or more generally, as q’ = 9.118 x lO’qV$/(MRq* (48) 3. H. Dymond and T. A. Brawn, Proc. 7rh Symp. Thermophys. Prop., Am. SOC.Mech. Engrs.,New York, 1977,660. Dymond I I I 0.4 0.3 D* 0.2 0.1 2.05 2.10 2.15 log v' Figure 18 Correlation of experimental self-diffwion coefficient data for tetramethylsilane at different temperatures and pressures, based on the 373.2 K isotherm. D& is defined in equation 15 and V' = V-V,(T,)/V,(T). A, 298.2 K; 0,323.2 K, a,348.2 K; 0,373.2 K (Reproduced by permission from Proceedings of a Symposium on Transport Properties of Fluids, National Engineering Laboratories, East Kilbride, H.M.S.O.,1979) For the density region where the rough hard-sphere theory is applicable, q' will be proportional to (qsHs/qo)(V/Vo)f and so will depend only on (V/ V,) for a given fluid at a given temperature, providing that the translational-rotational coupling factor for viscosity is density- and temperature-independent.Plots of q' (or of log q') uersus log V using data for a given compound at different temperatures should be superimposable on the curve obtained for any reference temperature. The amount of adjustment gives a value for Vo(T)/Vo(TR).Results obtained for carbon tetrachloride and for tetramethylsilane showed that the curves were superimposable not only over the density range for which the rough hard-sphere theory was applicable, but over the whole density range.This method also gives an excellent correlation I2 of the viscosity data for large aspherical molecules such as bicyclic hydrocarbons, and has been successfully applied to the correlation of viscosity data for liquid normal alkanes, aromatic hydrocarbons, and for their binary mixtures.l1 '-' A typical plot is shown in Figure 19, for n-hexane. 'I3 J. H. Dymond, K. J. Young, and J. D. Isdale, Int. J. Thermophys., 1980, 1, 345. 'I4 J. H. Dymond, J. Robertson, and J. D. Isdale, Int. J. Thermophys., 1981, 2, 133. J. H. Dymond, J. Robertson, and J.D. Isdale, Int. J. Thermophys.,1981, 2, 223. 'I6 J. H. Dymond, N. F. Glen, and J. D. Isdale, Inr. J. Thermophys., in press. Hard-sphere Theories of Transport Properties I I I 1 I I 2.00 2.05 2.10 215 log V' Figure 19 Correlation of experimental viscosity coefficient data for n-hexane at different temperatures and pressures based on the 373.2 K data. q' is defined by equation 48, V' = V*Vo(Ta/(Vo(T). 373.2 K0,298.2 K; a,323.2 K;0,348.2 K; .,(Reproduced by permission from Int. J. Therrnophys.,1980,1, 364) C. Thermal Conductivity Coefficients.-On the basis of the rough hard-sphere theory of Dahler,102i103 the thermal conductivity coefficient of a fluid can be represented by the general equation: where A. is given by equation 46 and cl, c2, and c3 are algebraic functions of the dimensionless moment of inertia, k.As shown by Li'04 the dependence of the thermal conductivity on k is weak. For this model system, k is temperature independent and for a real fluid the temperature dependence is likely to be small. Substitution for A. and Vo in equation 45 allows h* to be calculated from experimental measurements: h* = 1.936 x 107kV*(M/R7)* (50) By analogy with D* for diffusion and q' for viscosity, h* is expected to be a function only of (V/ Vo).Plots of h* uersus log V at different temperatures for a given fluid Dymond should therefore be superimposable on the curve for a reference temperature. The relative shift along the log I/axis provides a value for the ratio of the V, values at the different temperatures.Li lo4 has tested this approach using very accurate measurements on n-hexane, n-octane, benzene, and cyclohexane, using the lowest isotherm as reference in each case. A very satisfactory correlation was obtained, with values for V,(T)/V,(T') in close agreement with values obtained by Dymond l1 3--1 for the same liquids by interpretation of viscosity coefficients on the basis of the rough hard-sphere theory. Since h* is so weakly dependent on k, there is the possibility of a universal correlation for h*. This was investigated by Li lo4using accurate results for eleven hydrocarbons over a wide range of thermodynamic states. The results are shown in Figure 20, with the 307 K isotherm for n-hexane as the reference curve.The V, value at this temperature was taken as 72.64 x 1W6 m3 mol-'. 1 I < 100 50 Qo B 1.o 115 20 2.5v/ vo Figure 20 Reduced thermal conductivity versus reduced volume for eleven hydrocarbons (Reproduced by permission from re$ 104) The universality of this reduced plot for hydrocarbons is striking, especially in view of the wide range of temperature and pressures at which the measurements were made. Though the deviation of some individual points from the best curve is slightly greater than the uncertainty estimated on the basis of the measured thermal conductivity and density, it is apparent that this near universality will provide a very good estimate of the thermal conductivity for members of the n- alkane series at different temperatures and pressures.A similar result is to be expected for other homologous series. Hard-sphere Theories of Transport Properties 9 Conclusions Significant progress towards a successful molecular interpretation of transport properties in dense fluids and their mixtures has resulted from consideration of hard-sphere theories. The hard-sphere model, with a temperature dependent core size, gives a simple yet physically reasonably realistic description of molecular trajectories in the dense fluid state. The transport coefficients of monatomic species can be satisfactorily reproduced by the smooth hard-sphere theory. For pseudospherical polyatomic species, the derived translational-rotational coupling factors appear to be in general accord with expectations for the molecules con- cerned.However, a fuller discussion of these factors and their dependence on density and temperature must await more accurate computer calculations of the corrections to the approximate hard-sphere transport coefficients. Furthermore, for a rigorous examination of the limits of applicability of the hard-sphere theories for transport properties it is essential to have very accurate experimental data over a wide range of temperature and pressure for spherical, pseudospherical, and indeed non-spherical molecular fluids and their mixtures. Although the hard-sphere model is only an approximation, at the present time it provides the most satisfactory basis for the interpretation, correlation, and prediction of transport properties of dense fluids and their binary mixtures.

ISSN:0306-0012    

DOI:10.1039/CS9851400317

出版商:RSC    

年代:1985

数据来源: RSC