摘要:

Moderated Copolymerization and its ApplicationsThe Transfer Reaction between Styryl Radicals and Carbon TetrabromideBY CLEMENT H. BAMFORDDept. of Inorganic, Physical and Industrial Chemistry,University of Liverpool, Liverpool L69 3BXReceived 26th April, 1976It is proposed to apply the term “ moderated ” to a copolymerization in which one monomer (B)is present in very low concentration. Moderated copolymerization is a useful technique for studyingrelatively fast reactions between -B radicals and active reagents, for example transfer agents.The “ moderating.” monomer (A) is chosen so that MA radicals have much lower activity. Theincidence of MB radicals in the propagating chains is thus greatly reduced.The technique has been applied to measurement of the transfer constant for reaction of styrylradicals with carbon tetrabromide, with methyl methacrylate as moderating monomer.This quantityis too large to permit accurate measurement by studies of conventional type on the styrene+CBr4system. A value of 50.9 has been obtained for the transfer constant at 60T, a figure which is muchlower than that published by Thomson and Walters. We discuss possible reasons for the discrepancy,including the influence of non-terminal units in the propagating radicals. The use of moderatedcopolymerization in studying effects of this kind is described.Conventional copolymerization kinetics show some inadequacies in moderated copolymerizationunder conditions of high transfer, and the appropriate expressions for degrees of polymerization arederived.It is well known that carbon tetrahalides reduce the rate of styrene polymerization.A similareffect with CBrS occurs in moderated copolymerization. We suggest that these findings may beattributable to complex formation between styryl radicals and the halide.The experimental problems associated with measurement of transfer constantsof highly reactive compounds have been appreciated for many years.pointed out the necessity for limiting the extent of reaction in experiments of con-ventional type to a value equal to the reciprocal of the anticipated transfer constantand Fuhrman and Mesrobian subsequently remarked that their value of 39 for thetransfer constant of vinyl acetate with carbon tetrabromide is “minimal and theactual value may be closer to 200 ”.Thomson and Walters have considered chaintransfer with carbon tetrabromide in the polymerization of styrene and suggest thatthe published values of the transfer constant at 60°C (1.36-2.7) 2 y 4-6 are much toolow on account of the relatively high conversions (5-10 %) reached in the determina-tions. Thomson and Walters reported that if conversion is limited to 0.5 ”/o thetransfer constant assumes a value of 420 i- 60 (independent of temperature).We have recently been concerned ’ with the synthesis of styrene + chloropreneblock copolymers by free radical processes involving the block copolymerization withchloroprene of polystyrene carrying CBr, terminal groups. The preformed polymerwas prepared by polymerization in the presence of carbon tetrabromide, so that forour purposes the transfer constant of CBr, was an important parameter.A value ofthe transfer constant close to 400 was not compatible with our results and furtherinvestigations were desirable.The basic practical difficulties encountered in evaluating the transfer constant C,Walling2802806 MODERATED COPOLYMERIZATION AND ITS APPLICATIONSfrom studies of the polymerization of styrene, St, in the presence of carbon tetra-bromide and application of the Mayo equation may be readily appreciated. Dataon the dependence of the number average degree of polymerization, P,, on [CBr,]are required. When [CBr,] is sufficiently high to remain effectively constant at smallmonomer conversions, P , is low and the polymers are difficult to isolate and charac-terise.On the other hand, with [CBr,] sufficiently low to give tractable polymers,the concentration of carbon tetrabromide decreases so much during reaction, evenwith the lowest monomer conversions practically feasible, that values of C, deducedby conventional methods are gross underestimates. Thomson and Walters demon-strated that the apparent value of C, is strongly influenced by the conversion in therange 0.5-5 %. In determinations of C, they limited the conversion to 0.5 % andassumed that the average molar ratio [CBr,]/[St] during reaction was one-half of theinitial value (ie. that the carbon tetrabromide had effectively been completely con-sumed at 0.5 % conversion; experimental evidence for this view was presented).These workers isolated their (generally low) polymers by freeze drying from benzenesolution or precipitation in methanol and determined P , mainly by viscometry withthe aid of a [y] -P, relation which they had established on the basis of vapour pressureosmometry.A relatively simple procedure for determining large transfer constants could bebased on copolymerization.The idea is to copolymerize the monomer B underexamination with monomer A in the presence of the transfer agent S ; A is chosento have a relatively low transfer constant with S, and B is present in low concentra-tion. The incidence of B radicals in the propagating chains is therefore small, sothat in spite of the high reactivity of these radicals in transfer with S, the overallextent of transfer is not large and convenient values of P, may be obtained.As aconsequence, C, may be determined by conventional methods without undue experi-mental difficulty. We propose to call this type of copolymerization, in which themonomer under investigation is diluted with a large excess of a second monomerwhich is relatively inert towards the reagent involved (e.g. the transfer agent), “moder-ated copolymerization ”, the monomer present in excess being the “ moderatingmonomer ”. Additional possible applications of moderated copolymerization maybe envisaged, some of which will be mentioned later. The kinetics of such copoly-merizations may depart significantly from those of conventional copolymerizationand we include a consideration of the kinetics of a moderated copolymerization in thepresence of a highly active transfer agent.EXPERIMENTALMethyl methacrylate (MMA) was chosen as the moderating monomer since its transferconstant with carbon tetrabromide is relatively low, 0.27 at 60°C according to Fuhrman andMesro bian .The two monomers were purified by conventional methods and carbon tetrabromide wassublimed in vacuum before use.Mixtures of 9 cm3 methyl methacrylate+ 0.1 cm3 styrene (measured at 25°C) were com-polymerized at 60°C with azo-bisisobutyronitrile as initiator (1.3 x g) in the presenceof predetermined concentrations of carbon tetrabromide. Standard procedures were em-ployed : reaction mixtures were completely degassed in vacuum and copolymerization wascarried out in inactive light. After heating at 60°C for 45 (series I) or 60 (series I1 and 111)min, reaction mixtures were cooled rapidly and poured into a 20 fold excess of precipitantfor the polymer.In series 1 methanol, and in series 11 and I11 h e ~ a n e , ~ were the precipitants.The polymers were reprecipitated from benzene solution and dried in vacuum.Number average molecular weights were determined with the aid of a Hewlett-PackardMembrane Osmometer. A few determinations were made viscometricalfy using the [q] - FC . H. BAMFORD 2807relation of Fox et aL9 In the range of molecular weights for which this relation was cali-brated, the results agreed satisfactorily with those based on osmotic pressures.The initial conditions at 60°C are summarised in eqn (1).[St] = 0.091 mol dm-3; [MMA] = 8.85 mol dm-3; [azo-bis-isobutyronitrile] =8 .2 9 ~ mol dm-3 ; JJ = 1 . 1 6 ~ lo-* mol d ~ n - ~ s-I. (1 1In (l), 9 represents the rate of initiation; it is derived from the data of Bamford andJenkins.l’RESULTS A N D DISCUSSIONSince the reactivity ratios of methyl methacrylate and styrene are similar (seebelow) the copolymers, like the monomer feed, will contain only a low proportion ofstyrene ( ~ 2 %) so that the mean monomer unit weight will effectively be equal tothe molecular weight of MMA. This value has been used in calculating degrees ofpolymerization from molecular weights. Table 1 summarizes the experimental dataon degrees of polymerization.TABLE 1 .-DEGREES OF POLYMERIZATIONInitial concentrations/mol dm-3 : styrene 0.091, methyl methacrylate 8.85, azo-bisiso-butyronitrile 8.29 x ; 60°C.Reaction times/min : series I, 45 ; series I1 and 111, 60.Estimated standard deviations are shown.103[CBr4]/mol dm-3 10-3 L series3.817.620.002.004.006.908.0013.816.020.01 1 .oo18.002.1651.2997.744+ 0.3803.288+0.0831.876f 0.0641.3O4+ 0.1 131 .lo1 & 0.0390.737k0.0230.666+ 0.0260.5 1 8 0.0260.847k0.0280.550 f 0.007III111I1I1I1I1I1I1I11I11Values of 1 04pn, with estimated standard deviations for the experiments of seriesI1 and 111, are presented in fig. 1 for a range of values of [CBr,]. We believe thatseries I1 and 111, in which polymers were precipitated into hexane, provide the mostreliable data ; the least squares straight line for the combined results of these series isshown in fig.1. In series I the polymers were precipitated into methanol, in which,according to Fox et aZ.,’ polymers with H, < 200 are soluble. The correspondingpoints in fig. 1 have been corrected to allow for loss of low molecular weight speciesin this way; they are in satisfactory agreement with the results of series I1 and 111.The slope of the least squares line for l/pn against [CBr,] isThe conventional Mayo- type expression for the degrees of polymerization ofcopolymers obtained in the presence of a transfer agent is given in eqn (3), in whichr, and rB are reactivity ratios and CA and C, are transfer c0nstants.l In the presentexperiments A = MMA, B = St and S = CBr,.0 = (8.95k0.22) x mol-l dm3.(22808 MODERATED COPOLYMERIZATION AND ITS APPLICATIONSFrom eqn (3)so that CB is readily calculated from a knowledge of Q and the reactivity ratios andtransfer constants. Following BontA et d . 1 2 we take rA = 0.470 and rB = 0.500, andfrom Fuhrman and Mesrobian From eqn (l), (2) and (4) wethen find a valueCA = 0.27 at 60°C.CB = 50.9f1.8 ( 5 )for the transfer constant of styrene to CBr, under our conditions. This value issmaller than that obtained by Thomson and Walters by a factor >8.20- -15- -I l l l l l l l l l l l l l l l l l l I l l l l l0 5 .LO .I 5 .20 25lo3 [CBr4]/mol dm-3FIG. I .-Dependence of 1 /pn on LCBr,] in moderated copolymerization of styrene and methyl meth-acrylate at 60°C.Initial concentrations/mol dm-3 : styrene 0.091, methyl methacrylate 8.85, azo-bis-isobutyronitrile 8.29 x lo-,. series I, x series 111, other data series 11. Estimated standarddeviations for series I1 and IT1 are shown.5 10 15 2 0 ~ t ' ~ " " ' ' ' ~ ' ~ ~ ' r ' 0lo3 [CBr41/rnol dm-3centrations as for fig. 1.FIG. 2.-Dependence of conversion on [CBr,] (series 11). Reaction time 1 h, 60'C. Initia! conC. H. BAMFORD 2 809In view of the nature of this result we now examine our procedure for possiblesources of experimental error. (i) Consumption of CBr, during reaction. The mono-mer conversions AM are shown in fig. 2. If each polymer molecule formed involvesreaction of one molecule of CBr, (a reasonable approximation under our conditions)the change in concentration of CBr, will be AM/Fn.Inspection of the values infig. 1 and 2 shows that the consumption of carbon tetrabromide does not exceed4.2 % and is generally significantly smaller than this. We conclude that consumptionof carbon tetrabromide does not play an important part in our experiments. (ii)Consumption of styrene during reaction. From the copolymer composition equationit follows that the ratio ([A]/[B]) copolymer = -46. Thus the maximum conversionof monomer B is (3.6 x 8.85 x 10-2)/46 = 6.93 x 10-3 mol dm-3. This is -7.6 % ofthe initial concentration and so is not of prime importance. (iii) Possible errors inCA. The term in CA in eqn (4) is - 30 % of the first term in braces.Thus the valueof CB estimated from eqn (4) is not very sensitive to CA. For example, if CA = 0,the value of CB calculated from eqn (4) would be 75.6, which is still much less than thevalue estimated by Thomson and Walter~.~ (iv) Changes in 9 during reaction.The half-life of azo-bisisobutyronitrile at 60 is > 16 h,13 so that changes in concentra-tion of the initiator (and hence changes in 9) are unlikely to be significant in ourexperiments, and in any case they would have relatively little influence on the results.Thus there do not seem to be any obvious sources of experimental error whichcan account for the difference between our findings and those of Thomson andWa1te1-s.~ However, the “ styryl ” radicals reacting with carbon tetrabromide arenot identical in the two cases.In our system, the penultimate units, and indeed mostof the other units (excluding the terminal styryl) would be methyl methacrylate, whileThomson and Walters were concerned only with the homopolymerization of styrene.A penultimate unit of methyl methacrylate would certainly tend to reduce the reac-tivity of the radical towards carbon tetrabromide by diminishing the electron densityat the carbon atom with the unpaired spin.14 No evidence for a penultimate uniteffect has been found in the copolymerization of methyl methacrylate and styrene,which is described with considerable precision by two reactivity ratios [cJ ref. (12)].Although transfer with CBr, may be more sensitive than addition of MMA l4 itseems unlikely that such a penultimate unit effect in transfer would be very large,since it would have to be relayed from the -COOCH3 group to the terminal carbonthrough two saturated carbon atoms. Further, no effect of this type would operatein the block copolymerization studies already mentioned ’ which first drew ourattention to the large transfer constant postulated by Thomson and Walters.A penultimate unit effect would be expected to manifest itself in a dependence ofthe observed transfer constant CB,obs on the ratio [B]/[A] in moderated copolymeriza-tions, since with increasing fB]/[A] the number of styryl radicals having penultimatestyrene (B) units will increase.If there is an effect of this kind in the chain transferof styryl radicals with carbon tetrabromide it is reasonable to suppose that it is con-fined to penultimate units and is independent of the nature of other units in the chain.On this basis, making the further assumption (supported by experimental evidence l’)that there are no penultimate unit effects in propagation, we may show that theobserved transfer constant is given byin which CBA and CBB are the transfer constants for styryl radicals having penultimateunits of methyl methacrylate and styrene, respectively2810 MODERATED COPOLYMERIZATION AND ITS APPLICATIONSDetermination of CB,obs over a range of values of [B]/[A] by the moderated copoly-Experiments with different types of moderating monomers would also throw lightmerization technique would enable CBA and CBB to be evaluated.on this matter.KINETICSDEGREES OF POLYMERIZATIONConsiderations of the behaviour of a moderated copolymerization under condi-tions of high transfer reveal inadequacies in the conventional Mayo-type equation(3).Suppose that C, = 0 ; as [S] is increased a point will be reached at which effec-tively all B radicals undergo transfer rather than propagation (or termination).Further increase in [S] will then have little effect on the reaction; under suitableconditions homopolymers of A will be formed with a size distribution which reflectsthe distribution of sequence lengths of A units in the copolymerization of A and Bin the absence of S . These conclusions are not compatible with eqn (3), since thisequation (with CA = 0) predicts p, + 0 as [S] + a.In the derivation of eqn (3)it is assumed that the ratio of the concentrations of the two types of propagating radi-cal -A and -B is not changed by the presence of the transfer agent. In the majorityof systems hitherto studied this is a good approximation; however, in a moderatedcopolymerization under conditions of high transfer, the rate of transfer of -5radicals with S may be comparable to the rate of propagation of these radicals,although the reaction products are pgymers (mainly poly-A) of appreciable size.We now derive an expression for P , in the copolymerization of monomers A andB without introduction of the above assumption. We consider that A is present inlarge excess and that termination is effectively byldisproportionation of -A radicals.The kinetic scheme is shown in eqn (7).I 4 2 Rka .R+A -+Akb . R+B -+ BkaaA+A -+Ak+B -+ Bkab ,kba .~ + A - + AkbbB+B --+ Bkfa ri+s;-+ P+SkfbB + S -+ P + ikrsS+A +AS+B+ BA4-A -+ 2P.krb .kC. H . BAMFORD 281 1By assuming stationary values for [R], [A], [B], [i] we may derive the expression (8)for P,in whichRA = + LB1RB = [Al+rBIB1F$ = ka,[A]/(Sk,)*= krb[Bl/(kra[Al +krb[BI)*Ft is evidently the degree of polymerization of the product obtained by homopoly-merization of monomer A under the prevailing conditions of [A] and 9, in theabsence of transfer. Eqn (8) is the result of approximating a more complex completeexpression in the following ways. (i) A term in RB[A]/pi has been omitted from thenumerator since under practical conditions this will be negligible compared withRA[A]+RB[B].(ii) Similarly a term in ~A~&B[A]/F$ has been omitted from theexpression in braces in the denominator as being generally insignificant. (iii) It hasbeen assumed that P n 9 1.Under conditions of the present experiments the terms in [S] in the numeratorand the term in [S12 in the denominator of eqn (8) are unimportant, so that eqn (8)may then be rewritten in the same form as eqn (3) withIn a moderated copolymerization [A] 9 [B] so that unless rA or rA/rB Q 1, eqn (9)is equivalent to P,O = p$, as would be anticipated.When the extent of chain transfer is very high eqn (8) predicts behaviour which isconsistent with the intuitive views already outlined.For purposes of illustrationsuppose CA = 0 ; then at high [S] eqn (8) becomesThe expression in braces in eqn (10) is the mean sequence length of A units in thecopolymerization in the absence of transfer, so that the physical significance of eqn(10) is clear. At very high [S] when C, # 0, Pn falls off to very small values by virtueof the term in [S]'.RATES OF REACTIONIt has long been known that carbon tetrahalides reduce the rate of polymerizationof styrene.15-17 More recently, Thomson and co-workers 3* l 8 reported retardationby carbon tetrabromide and bromotrichloromethane of styrene polymerizationinitiated by azo-bisisobutyronitrile at 45 and 60°C and thermally at 80°C. Fig. 2indicates that carbon tetrabromide also behaves as a retarder in moderated copoly-merization, the results presented resembling those referred to for the homopoly-merization of styrene.3+ 15-18 A variety of explanations for the retardation has beenadvanced, e.g.the low reactivity of radicals such as CCl3 towards styrene l7 and therelative inactivity of the adduct radicals CCl3CH2CHPh ; l7, l9 Breitenbach andKarlinger l 6 have suggested that during polymerization of styrene in the presence o2812 MODERATED COPOLYMERIZATION AND ITS APPLICATIONScarbon tetrachloride or tetrabromide at high temperatures a retarder is formed,perhaps hydrogen chloride or bromide.In the author's opinion no explanation on these lines can account for the shape ofthe curve in fig. 2. There are two main problems. (i) While low concentrations(< 5 x lW3 mol dm-3) of carbon tetrabromide cause marked reductions in rate,increases beyond -7 x rnol dm-3 produce little additional retardation. Qualita-tively similar behaviour is evident in the thermal polymerization of styrene at 60°C inthe presence of bromotrichloromethane 17- l 8 and in the polymerization of styrenewith carbon tetrabromide as additi~e.~ In agreement with our views, Thomson andWalters 3 9 l8 remark that their results are not consistent with conventional retardationkinetics.(ii) Although increase in [CBr,] above 7 x mol dm-3 produces littlechange in the rate of polymerization (fig. 2) it gives rise to a proportional increase inchain transfer, evidenced by a corresponding reduction in the degree of polymeriza-tion (fig.1). We therefore find it difficult to believe that there is a direct relationbetween retardation and the extent of the transfer process, as in conventional retarda-tion kinetics. To stress this paint, we note that the fraction of styryl radicals under-going transfer with CBr, under our conditions is - rBCB[CBr4]/[MMA] which for[CBr,] = 7 xmol dm-3) the fraction is still < 6 %. If retardation were connected with chain trans-fer it should increase monotonically with [CBr,] over the whole range studied.We propose that the phenomena described above can be explained in ternis ofcomplex formation between styryl radicals and carbon tetrabromide [eqn (1 l)]. Thishypothesis does not seem to have been considered previously, although it is very muchin line with current views.20rnol dm-3 is -2 %.At the highest value of [CBr,] used (20 xK--.'st + CBr4 + -(Sf***CBr4)*. (1 1)It is necessary to assume that the complexed radicals are less reactive in propagationand transfer (so that termination is relatively more important) and that complexationis effectively complete at low values of [CBr,]( -7 x in our experiments).On this basis, the shape of the curve in fig. 2 , and the related results mentioned, areimmediately understandable.Complex formation between styryl radicals and carbon tetrahalides is chemicallyreasonable. Aromatic hydrocarbons are known to form donor-acceptor complexeswith carbon tetrahalides,21 and it is likely that CBr, in styrene solution may existlargely as a weak CBr,*..St complex.Polystyryl radicals are more powerfulelectron donors than styrene, so that strong competitive radical complex formationwith acceptors is to be expected. The ionization potentials of styrene 22 and thebenzyl radical 2 3 are 8.40 and 7.27 eV, respectively ; that of the polystyryl radical islikely to be somewhat lower and close to 7.0 eV. Thus the difference in ionizationpotential between styrene and the polystyryl radical is of the order of 1.4 eV or135 kJ mol-l (32 kcal mol-l). A portion of this relatively large energy differencewould be available to promote styryl radical + carbon tetrabromide complex formation.Approximate calculations show that inoderate values of - AG; + AG; (- 25 kJmol-l or 6 kcal mol-l) give the required extent of radical complexing, AG; and AGSbeing the standard free energy changes for complexation with CBr, of the styrylradical and styrene, respectively.We conclude that the postulated complexation ofstyryl radicals is energetically acceptable. Similar arguments apply to other systemscontaining olefins and electron acceptors. For example, it is well known that styreneand maleic anhydride form a donor-acceptor complex ; 24 nevertheless, in the copoly-merization of these two compounds preferntial complex formation between styrylradicals and maleic anhydride would be expected.moC. H . BAMFORD 2813In the styrene +carSon tetrabromide system, complex formation may involve inter-action between aromatic rings of the radicals and the halide, the process being rapidcompared to propagation or transfer.Intervention of a second CBr, molecule isnecessary for chain transfer of a complexed radical (in contrast to intra-complexreaction) since, as we have seen, transfer increases monotonically with [CBr,] in therange of complete radical complexation. Olah and Svoboda 2 5 have demonstratedthe ainbident nature of the triphenylcarbenium ion in some hydride transfer reactions,nucleophilic attack taking place at the accessible para ring position as well as at themore hindered carbenium centre. A related situation may exist with the styrylradical ; the radical centre is strongly hindered and attack by CBr, at a para positionin the ring seems feasible. Chain transfer in systems of this type may therefore bemore complex than has hitherto been thought.The hypothesis of complexed styryl radicals introduces kine tic complications whichmerit experimental exploration.These arise at low [CBr,], when both free and com-plexed radicals are present, each species having its own reactivity. No complicationsare apparent in the results of Thomson and Walters relating to P , determina-tions for [CBr,],/[St], < lo-, (i.e. in the range of [CBr,] over which the rate of poly-merization depends on [CBr,]). These experiments measure ratios of propagationand transfer rate coefficients, hence the apparent simplicity may imply that bothcoefficients are similarly affected by complexation. Additionally, in the experimentsof fig. 2 there are no apparent complications for [CBr,] < 7 x mol dm-3.Thepropagation reaction of styryl radicals with methyl methacrylate would be expectedto be slowed down by complexation with CBr, to a greater extent than the corre-sponding reaction with styrene. It is possible that the complexed radicals in themoderated copolymerization tend to react with styrene rather than methyl metha-crylate.A comparison of fig. 2 with fig. 6 of Thomson and Walters shows that the equili-brium constant K of reaction (11) has a smaller value in our systems. As alreadymentioned the reacting " styryl " radicals are different in the two investigations byvirtue of their different non-terminal residues. The smaller K in our experimentswould be consistent with a penultimate unit effect arising from methyl methacrylate.Secondly, the extent of retardation in our experiments (-20 %) is smaller than thoseobserved by Thomson and colleagues 3* (-50 %) and by Dunn et a1.l' (-67 %).This is probably a reflection of the lower styrene content of our systems.CONCLUSIONThe experiments described suggest that moderated copolymerization is a convenienttechnique for studying rapid transfer reactions.It appears capable of providinginformation about the magnitude of the relevant transfer constants and also about themechanism of the transfer process, including the influence of non-terminal units.I wish to thank my colleagues Professor A. Ledwith and Dr. D. Margerison forI am also grateful to Mr. K. Linge for carrying out their most helpful suggestions.the experimental work.C.Walling, J. Amer. Cheni. Soc., 1948, 70, 2561.N. Fuhrman and R. B. Mesrobian, J. Amer. Chein. Soc., 1954, 75, 3281.R. A. M. Thomson and I. R. Walters, Trans. Faraday Sac., 1971, 67, 3046.J. W. Breitenbach, 0. F. Olajand and A. Schwindler, Monatsh, 1960, 91, 205.C. H. Bamford and M. J. S. Dewar, Disc. Furaday SQC., 1947, 2, 314.R. A. Gregg and F. R. Mayo, J. Amer. Chem. Sac., 1953, 75, 3530.1-82814 MODERATED COPOLYMERIZATION AND ITS APPLICATIONSP. Hilton, Ph.D. Thesis (University of Liverpool, 1976).C. H. Bamford in Reactivity, Mechanism and Structure in Polymer Chemistry, ed. A. D. Jenkinsand A. Ledwith (Wiley, New York, 1974), chap. 3.T. G. Fox, J. B. Kinsinger, H. F. Mason and E. M. Schuele, Polymer, 1962, 3,71.A. E. Platt in Encyclopedia of Polymer Science and Technology, ed. N. M . Bikales (Wiley, NewYork, 1970), vol. 13, p. 1975.lo C. H. Bamford and A. D. Jenkins, Trans. Faraday SOC., 1962,58, 1212.l2 G. Bonth, B. M. Gallo and S. Russo, J.C.S. Faraday I, 1973, 69, 328.l 3 C. E. H. Bawn and S. F. Mellish, Trans. Faraday Soc., 1951, 47,1216.l4 C. H. Bamford, A. D. Jenkins and R. Johnston, Trans. Faraday SOC., 1958,55,418.l5 H. Suess, K. Rlch and H . Rudorfer, 2. phys. Chem. A, 1937, 179, 361.l6 J. W. Breitenbach and H . Karlinger, Monatsh, 1951, 82,245.l7 A. S . Dunn, B. D. Stead and H. W. Melville, Trans. Faraday Soc., 1954, 50, 279.l8 D. A. J. Harker, R. A. M. Thomson and I . R. Walters, Trans Faraday SOC., 1971, 67, 3057.l9 H. N. Friedlander and M. S. Karasch, J. Urg. Chem., 1949, 14, 239.2Q See, e.g., C. H . Bamford in Molecular Behaviour and the Development of Polymeric Materials,ed. A. Ledwith and A. M. North (Chapman and Hall, 1975), chap. 2.l G. Briegleb in Elektronen Donator Acceptor Komplexe (Springer-Verlag, Berlin, 1961).22 W. C. Herndon, J. Amer. Chem. SOC., 1976, 98, 887.23 F. P. Lossing, Canad. J. Chem., 1971, 49, 357.24 See, e.g., P. Hyde and A. Ledwith in Molecular Complexes, ed. R. Foster (Logos Press, 1974),25 G . A. Olah and J. J. Svoboda, J. Amer. Chem. Soc., 1973, 95, 3794.chap. 2, p. 174.(PAPER 6/812

ISSN:0300-9599    

DOI:10.1039/F19767202805

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Attachment of Particles to a Liquid Surface(Capillary Theory of Flotation)BY A. SCHELUDKO,* B. V. TOSHEV AND D. T. BOJADJIEVDepartment of Physical Chemistry, University of Sofia, Sofia, BulgariaReceived 12th June, 1975On the basis of the theory of capillarity, the process of formation of a wetting perimeter when aspherical particle touches a planar liquid surface is analysed taking into account the line energy ofthis perimeter. The minimum size of particle which can float is calculated and an accurate estimateis made for the minimum time of touching of particle and surface. The kinetic energy of collisionbetween an air bubble and the particles is used to calculate the maximum size of particles which canremain attached for flotation. Flotation data suggest that a lower limit for the size of isolated par-ticles which can be floated is of the order of 1 pm and a comparison of this radius with the theoreticallimit gives a value of dyn for the line energy of the wetting perimeter.Predictions of theflotation region in terrns of particle size and contact angle using this energy do not conflict withpractical findings.toFlotation has long been used as an efficient method for the concentration of mine-rals. However, the rate determining steps of this process have not yet been established.It is therefore convenient to examine the role of forces of attachment and removalbetween particles and a liquid surface under the simplest conditions.The theory of these forces, which we shall call the capillary theory of flotation,originated with the work of Nutt and was further developed by ourselves.2 Thedetermination of the contact time by Evans,3 and in a sense the work of Derjaguin andDukhin on the hydrodynamic removal of particles by a current flowing around abubble, may also be regarded as part of the following capillary theory.Variousassumptions relating to the processes preceding contact of a particle and an air bubbleare introduced here on an ad hoc basis and their future development will shape thecomplete theory of interaction of particles with liquid surfaces.1. FORMATION OF A THREE PHASE CONTACTWhen a particle encounters a bubble, a layer of liquid separates them as a resultof hydrodynamic resistance. Thinning and rupture of this layer precede the forma-tion of a three phase contact.This process is described in ref. (5), and the measure-ment of the critical thickness for the rupture of the layer is reported in ref. (6). Thetime required for thinning of the layer until rupture occurs was calculated in ref. (7).In these investigations the meniscus of the liquid was pressed against a planar solidsurface ; this corresponded to the interaction of a large particle with a large bubble.The hydrodynamic resistance diminishes as the size of the particle is reduced sothat for small particles as in flotation, it is assumed that contact with a planar surface(large bubble) occurs with no hydrodynamic resistance. This is equivalent toSmoluchowski’s assumption in his classical theory of the fast coagulation of colloidalparticles.* Instead, another rate determining barrier for attachment is introduced.In the approximation to follow, three phase contact grows from a point and passes2812816 CAPILLARY THEORY OF FLOTATIONthrough extremely small radii of the wetting perimeter.For cases of this type (fig. I)the equilibrium of the forces tangential to the surface of the sphere is expressed bythe formulaK0 2 3 - 0 1 3 = o12 cos er-- C O S ~ (1.1) rwhere otj are the surface tensions (1, liquid ; 2, air ; 3, solid) and Or is the wettingangle for a perimeter of radius Y. The central angle a, which defines the position ofthe particle with respect to the undisturbed liquid surface, is also the angle betweenthe solid surface and the plane containing the wetting perimeter, and IC is the lineFIG.1 .-Three phase contact of a sphere which enters phase 2 from phase 1.tension of this perimeter ( x / r has the sense of a two dimensional capillary pressuredirected towards the centre of the wetting perimeter for IC > 0). The term IC is morefully discussed in a following paper. A special case of eqn (1.1) for a drop wettinga planar solid surface can be easily obtained in the form 023 - 013 = o12 cos Or+ K / Y ,by minimising the free energy of the system and taking K into account. In this casea = 0 and the wetting perimeter lies under the liquid, with the result that the signpreceding I C / ~ is the reverse of the sign in eqn (1.1).* The complete formula (1.1) hasrecently been thermodynamically derived.Eqn (1.1) shows that the wetting angle, generally speaking is a function of the sizeof the wetting perimeter.For large values of Y, this dependence disappears and eqn(1 .I) assumes the general form of Young's lawwhere 8 is the wetting angle for r + a, which is generally found for macroscopicwetting perimeters. For a sphere, as in fig. 1, Y = R sin a, and (1.1) can be written6 2 3 - 6 1 3 = o12 cos e (1.1')cos e,.-cos 6 = Icctg a j m . (1 -2)Here and in the remainder of the discussion, 023 -cI3 is represented by o12 cos 6 onthe basis of eqn (1.1') and o12 is now denoted by o. The right hand side of eqn (1.2)increases indefinitely with decreasing cc, whereas the left hand side is limited by thevalue of 1 -cos 6 for 8, = 0. When a is smaller than a certain critical value a,, threephase contact cannot occur spontaneously.The critical value x = ac, above which(a > cc,) the wetting perimeter grows spontaneously, is given byRoctg a, = -(1- cos 6). (1.3)K* It should be noted that owing to the presence of a in eqn (1 .l), the last term disappears for rigidcapillaries or cylinders immersed in a liquid, since c( = go", and the entire force of the two dimensionalcapillary pressure is directed perpendicular to the solid surfaceA. SCHELUDKO, B . V . TOSHEV A N D D. T. BOJADJIEV 2817The situation that arises is similar to the situation on formation of a new phase, sothat the wetting perimeter for a = a, may be regarded as the nucleus of a new phasesurface between phases 2 and 3 and a line between 1, 2 and 3.To overcome theresistance to the formation of this nucleus, it is necessary to apply either a pressingforce of the sphere on the phase surface G 2 f, or an energy U 2 A,, wheref, is themaximum resisting force and A , is the work of reversible isothermal formation of thisnucleus.The forcef, is easily estimated knowing that for cc = a,, 8, = 0. In ref. ( 1 ) and(2), the approximationf = 2nrocosp (1.4)(fig. 1) was used for the force deforming the planar liquid surface on introduction ofa solid sphere. It was later shown lo that this formula is correct for the small particlesthat are typical of foam flotation. In the case under consideration with a = a, and0, = 0, the angle with the normal to the surface is p = 90-a, and with r = R sin awe obtainf = 2nRa sin2 a.(1 -5)Substitution of a = a, from eqn (1.3) givesfc = 2nRo l+ -(l-cos 0) . i r 3’For given values of CT, IC and 8, the forcef, has a maximum value off,,, = nR,o for R, = IC/O(~ -COS 0). (1.7)The formation of a three phase contact is “ most difficult ’’ for particles having theradius R = R,. Introduction of R, from eqn (1.7) gives the condition (1.3) in theformctg Q, = R/Rm (1.3’)and instead of (1.6) we obtain(1.6’)There are two limiting caes(R/R,J2 9 1 ; fc = 2noR&/R (1 . , ‘ I )(R/R,)2 < 1 ; fc = 2nR0. (1 . , I ” )If we assume that x/o is of the order of the thickness of the transition layer bat weenphases, then for the particles that are dealt with in flotation, with size considerablyexceeding molecular dimensions, the condition (1.6”) is always fulfilled.The elementary work of expansion of a three phase contact can be expressed inthe formanddA = - ~ w [ ~ ( c o s ~ , - C O S 0)- ~/r]dZ (1.8)where dl is an element of linear expansion on the surface of the sphere.In the squarebrackets is given the force acting along unit length of the perimeter of wetting. Sucha way of expressing the force moving the perimeter of wetting on a solid surface hasalready been exploited in ref. (5) without taking account of ~ / r 2818 CAPILLARY THEORY OF FLOTATIONBy taking r small for nucleating contact and R/Rm @ 1 then 8, M 0 and dl M drso that eqn (1.8) can be simplified todA = ~ ~ Y [ J C / Y - O ( ~ -COS O)]dr.KlrC = o(i -cos e).(1.9)(1.10)The value of A goes through a maximum (A,) at Y = r, given byThe condition (1.10) coincides with the condition (1.3) because when r = r, = R sin a,is small ctg a, x l/sin a,.By integrating eqn (1.9) between the limits r = 0 andr = rc we obtainA , = nr,K: = nlc2/a(l -cos 9). (1.11)Eqn (1.1 1) is identical to the well known expression for the work of formation ofa two dimensional nucleus rcL,/2 because the length of the perimeter of wetting L, inthe nucleating contact is 271rc.2. LIMIT OF FLOTABILITY OF SMALL PARTICLESIt is clear from practical experience that particles smaller than a few microns can-not be captured in foam flotation (see section 5). Taking into account the economicimportance of the flotation of small particles, we can fairly confidently assume thatthis limitation cannot be overcome by variation of the usual parameters, i.e.bubblesize, wetting angle, and agitation. For some time, therefore to avoid this difficulty,the particle size has first been increased by mutual coagulation or by combinationwith larger particles or droplets of an inert material.The only explanation known to us for the limit in the flotability of small particleswas suggested by Derjaguin and Dukhin on the entrainment of small particles bythe current flowing round an ascending bubble. If N is the number of particles lyingin the path of the ascending bubble, only a certain fraction of these, AN, will collidewith it. For the usual ascent velocity of bubbles in flotation, it was found byDerjaguin and Dukhin thatwhere R B is the radius of the bubble.For particles that normally exhibit optimumflotability, with R - 10-20 pm, AN/N has a value of a few tenths. These particlesare nevertheless recovered in full, apparently because of the large number of bubblespassing through the suspension. For smaller particles (e.g. R = 2-3 pm), therefore,a severalfold increase in the number of bubbles and/or a decrease in RB should leadto a satisfactory recovery. As was indicated earlier, however, this apparently does notgive the expected result. The limited flotability of small particles is probably due tosome other, more radical cause, for example a resistance to the formation of thenucleating contact. This resistance may be overcome either by the weight of theparticle, G > A, or by the kinetic energy of the impact between the particle and thebubble, U > A,.As will be shown later, under normal flotation conditions U is con-siderably greater than the potential energy of the wieght of the particle and is thereforethe determining factor. Assuming, again ad hoc, that the flow of liquid around thesurface of the ascending bubble does not control the rate determining step for collec-tion, we focus attention only on those AN particles which come into contact with thebubble surface. In the limits of a complete theory the number of attached particleswill be given by the product of the probability for contact ANIN, the probability forattachment and the probability for non-detachment of the attached particle.In the present paper we shall be concerned with preparing a basis for estimatingANIN = 3R/RB (2.1A .SCHELUDKO, B . V . TOSHEV A N D D . T . BOJADJIEV 2819only the last two probabilities. It would seem from recent papers ' ' 9 l2 that eqn (2.1)for the probability of contact needs some revision.The energy U for central collision, is equal to mV2/2, where m = 4nR3p/3 ( p isthe density difference between the particle and the liquid) and V is the sedimentationvelocity of the particle in relation to the ascending bubble. Since the sedimentationvelocity of small particles is usually much smaller than the ascent velocity of thebubbles in flotation, Yis approximately equal to the latter. It is also easy to showthat the mean kinetic energy for all types of collision is half of the value for centralcollisions.* Taking all this into account, we find that the smallest particle that iscapable of overcoming A , is given by the conditionmV2/4 = A,.(2.2)Together with eqn (1.1 l), this leads to the following expression for the radius of thisparticle3 K)+. V2pa(l - cos 6 ) Rmin =Taking V = 20 cm s-l, p = 2 g ~ r n - ~ , G = 50 dyn cm-' (see discussion of theseparameters in section 5) and assuming, again on the basis of flotation practice, thatflotation stops at approximately Rmin = 1 x cm we can estimate K from eqn (2.3).For the wetting angles 8 that normally occur in flotation, i.e. between 20 and 40°, itis found that K is between 2.8 x and 5.6 x dyn.Corresponding values forp = 3 g ~ m - ~ are 3.5 xThe success of the assumed limiting role of the work of formation of the threephase nucleation contact in flotation can be judged by the correctness of the valuesobtained for the line tension. The available data on ic are unfortunately ratheruncertain. Thus Langmuir l3 obtained a value of K = 6.5 dyn from liquid lenses ata liquid/air boundary. later reduced this valuevery considerably to 2 x dyn. Pethica l6 estimates that the quantity ic/a is ofthe order of 10-2cm. Very recent experimental results obtained by Torza andMason l7 for the coalescence of two drops of different liquids place K in the rangefrom 6 x to 6 x dyn. Though these last values are closer to those obtainedby us, it is doubtful whether this can be regarded as reliable confirmation of ourhypothesis.In fact, K (like a) is determined by the composition of the phases, and itis unsafe to apply the results for one system to another. For this reason it would beinteresting to do a direct " flotation " experiment, without the hydrodynamic entrain-ment of particles. For example, if particles in a suspended drop are allowed to fallon the liquidlair boundary, the kinetic energy of the collision for small particles willbe negligible in comparison with the potential energy forcing them against the phaseboundary. The corresponding gravitational force G = 4xR3pg/3 (where g is theacceleration due to gravity) will lead to attachment at the three phase contact whenG > fc, and to non-attachment when G < fc.The transition between the two condi-tions occurs at G = fo or according to eqn (1.6") for particles having the radiusand 6.8 x dyn.Harkins l4 and Buff and SaltsburgR, = (30R&/2pg)*. (2.4)For treated glass spheres with p E 1 g ~ m - ~ , Q = 50 dyn cm-I and 8 = 20" assumingK = 5 x cm for R, leading to an R, of-3 x Such particles would be large enough for their attachment or non-dyn would give a value of - 2 xcm.* A deeper analysis of the current flowing around a bubble may change the coefficient 3 in frontof mV212 in eqn (2.2)2820 CAPILLARY THEORY OF FLOTATIONattachment to the surface of a suspended drop to be observed under the microscope.*The replacement of the gravitational interaction by the considerably stronger kineticenergy of impact between the particle and the surface of a bubble in flotation isobviously the reason for the reduction of the “flotation limit” by an order ofmagnitude.3.DURATION OF THE IMPACT OF A PARTICLE WITH A BUBBLEThe duration of the impact of a particle with a liquid boundary is important in theprocesses responsible for the formation of the three phase contact. The impact timeis shortest when a three phase contact is unable to form. The particle simply deformsthe surface of the bubble, but remains separated from it by the liquid film and is thrownback by the capillary forces resulting from this deformation. This shortest time Tisincreased on formation of the three phase contact, and if the recovery force is in-sufficient to remove the particle, T becomes infinite.A necessary condition for theattachment of the particle in the phase boundary is obviously a sufficiently large valueof T,FIG. 2.-Deformation of a plane liquid surface by a sphere. (a) according to EvansY3 (h) with amonotonically changing curvature.Evans estimated the time T as follows. He assumed that the particle forms afilm of uniform thickness? over the entire surface that is immersed in the opposingphase [fig. 2(a)]. If the depth of immersion of the particle is ho as in fig. 2(a) theincrease in the surface area of the liquid will be xhi, and the increase in the free surfaceenergy will be xh,2o. The capillary recovery force will therefore be d(xh20)/dhi =2noho and the half-period of the harmonic oscillation of the particle in the surfaceis thusTE,TANS = J x m I 2 ~ (3.0since T = n/Jf/nzh,.However, this model is improbable, since the stressed liquid surface should deformsmoothly, as shown in fig.2(b). In this case, for the unruptured film, when a < ccc,If0 E h, and from an analysis of work by Derjaguin and James 2o h can be takenas RB sin2 a, where B is a complicated expression which is shown in section 4. Therscovery force isf = 2nRo sin2 a as in eqn (1.5) and this leads to the formulaHere nz is the mass of the particle andf = 2naho.T = JxmB,l2o = JBT,,,,,. (3.2)* These predictions have been confirmed in experiments by Mingins and Scheludko, the results ofwhich are reported in a following paper.’* In brief, the value obtained there for x is close to the onecalculated above from the lower limit of flotability.j.Evans’ film was evidently a thick film in the sense of the absence of a disjoining pressure, and wasformed because of the hydrodynamic resistance to thinningA . SCHELUDKO, B . V. TOSHEV AND D. T . BOJADJIEV 282 1If all possible collisions are taken into ilccount, Tis increased by J3/2 so that for areasonable value of B E 10 this time is approximately four times as great as TEvASS.Friction was ignored in the above treatment, which thus refers to undamped oscil-lation. An extension of Evans' work in this respect showed that damping is negli-gible.21 We shall therefore disregard friction later (section 4) in the discussion of theelastic collision of a particle with a liquid surface.4.REMOVAL OF A PARTICLEEffective flotability is possible if a particle forms a three phase contact when itencounters a bubble, and the forces acting on it are subsequently unable to remove itfrom the phase boundary.The removal of the particle is inevitable if its weight G is greater than the maximumforce of attachmentf,,,. According to eqn (1.4),fis determined by the angle p andthe wetting perimeter Y = R sin a, which are functions of G at equilibrium (f+ G = 0).iFIG. 3.-Deformation of a plane Iiquid surface by an attached heavy sphere.In the case under consideration (fig. 3), /?-cx+8 = 90". Moreover, the line energyIC can now (after attachment) be disregarded if we exclude excessively small values of 6and regard the wetting angle as a constant.Accordingly,f = 2nRo sin a sin(& cx) (4.1)has a maximumfmax = 27cRo sin2 8/2 at cc = 8/2Thus when G > --fnlax the particle will be removed, and the upper limit of flotabilityis given byThe estimation of G for a = 8/2 is facilitated by the fact that for the wetting angles of<40" that are normally found in flotation, the volume of the part of the sphere abovethe wetting perimeter is small in comparison with the volume of the whole sphere.This fraction, which is equal to (1 -cos 8/2)2 (2+cos 8/2)/4, has a value of only- 4 x It is therefore possible to use the expression for a totallyimmersed sphere, namelyfor 8 = 45".G = 4zR3pg/3. (4.4)From eqn (4.1), (4.2) and (4.3), therefore, we obtain the gravitational limit of flotqt' c1 ion-= /e sin 812.(4.52822 CAPILLARY THEORY OF FLOTATIONAs detailed in the discussion later and as shown elsewhere 2 v 23 this result overestimatesthe higher flotability limit.It was assumed earlier that the forces of removal in flotation are much greaterthan the weight of the particles. This assumption is justified, since the forces resultingfrom the encounter of a particle with a bubble are still considerably greater than G.In seeking a better model let us again consider an “ elastic ” collision between aparticle and a bubble, but unlike in section 3, we shall now assume that a three phasewetting perimeter is formed at the time of the impact. Assuming that the impactenergy U 9 A,, we can ignore the barrier A , for large particles.The position of aparticle will again be defined by the central angle a. The successive stages in themovement of a particle to the interface ( ) and in the opposite direction ( 4 ) areshown in fig. 4.FIG. 4.-The sequence of movement of an attachable particle to (t) and from (4) a liquid surface.Position 3’, detachment of the particle in the upper phase. Position 5’, detachment in the lowerphase.In position 1 the particle touches the surface and forms a wetting perimeter, whichdraws it into the surface and increases the kinetic energy from U in position 1 toU+Foe in position 2. This increase, which is due to the decrease in the free surfaceenergy on transition from 1 to 2 is equal toF~~ = F ~ - F ~ = n ~ 2 q -cos ey (4.6)where Fo is the free surface energy for a = 0, and Fe for a = 6.Eqn (4.6) is obtainedfrom elementary geometrical considerations by summation of the products of thesurfaces and the corresponding tension oi j , using eqn (1,l’). This same result can beobtained as the work of displacement of the particle for 0 = const, as will be shownlater, or as the work of displacement of the wetting perimeter over the surfacc of theparticle for 8 = a under the influence of the tangential force 2nra(cos a - CQS 0) in therange from CI = 0 to a = 0 [see eqn (1.8)].Under the influence of U+F,, the particle passes through position 2 and proceedsfurther into the upper phase, and it now expends its energy in the deformation of theliquid surface. If it loses its kinetic energy at a < a,?, the limiting immersion willbe reached (position 3) ; the particle will come to rest and start to move in the oppositedirection (if U+Foe is very large, the particle may pass on through position 3 andbreak away into the upper phase to position 3’).On the way back to position 4, theparticle recovers the kinetic energy of position 2, but with its direction reversed ; thekinetic energy then starts to decrease, and the particle reaches either position 5 (witha > a, c> or the detachment position 5’ (a < a Im). The “ kinetic ” limit of flotationwill obviously satisfy the conditionU+F0(?+F(jgm; = 0. (4.7A . SCHELUDKO, B . V . TOSHEV AND D. T. BOJADJIEV 2823It is easy to see that for 8 < 90', the breakaway into the upper phase calls for moreenergy than the breakaway into the lower phase.If' we limit ourselves to 8 < go",therefore, we shall not observe the case corresponding to position 3', and instead ofa, we shall now simply write a,. The opposite case (8 > 90') is easily obtained byinterchange of the upper and lower phases.A closed circle requires Foe + Foam+ Famo = 0, SO that Foe +Foam = - Farno = Aa,0where Aa,o is the work of reversible isothermal displacement of the particle in rela-tion to the surface of the undisturbed liquid between the positions a = a, and a = 0.Eqn (4.7) can thus be written in the form(4.7')Ammo is calculated by integration of dA =fdZ, where Z is the distance between thecentre of the particle and the planar liquid surface.In this case according to fig. 3Z = Rcos a+h. (4.8)For h we use the complete Derjaguin formula l9where y is the Euler constant 0.577. . . .Expressing p and Y in terms of a, we obtainforh = RB sin a sin(0- a)sina[l+cos(0-a)](4.10)(4.11)The formula (4.9) is taken from a later work,20 where it is shown to be sufficientlyaccurate for cylinders having radii and wetting angles typical of flotation. Thisformula is given incorrectly in Derjaguin's pub1i~ation.l~ Integration of dA = f d Zwith this equation and with eqn (1.4) (which has also been shown lo to be sufficientlyaccurate for flotation) givesdZda2nRo sin a sin (8-a) - da (4.12)where dZ/da is obtained by differentiation of eqn (4.8), taking eqn (4.10) and (4.1 1)into account, i.e.sin a sin2 (e-a) .(4.13)1 dZ --- = sin a-B sin (8-2a)+sin (&a) cos a+ R da I +cos (e-a)The integral in eqn (4.12) becomes 0 for a = 0, for a = 8, and for dZ/da = 0.This last condition occurs for 0 < a, < 8 and corresponds to the transition to in-stability (detachment). Now a, is calculated from eqn (4.13) for dZ/da = 0 as afunction of 8 and a = (R/4))Jpg/o. For cr w 50 dyncm-l, the factor of t,,/pg/achanges from 1 to 2.5 as p changes from 1 to 5 g ~ m - ~ , so that in the estimation ofthe results it may be assumed that a = R. The angle a, is close to 8/2, though thetwo do not coincide.Eqn (4.12) can be written in the formA,, = ~ E R ~ ~ T I , ~ (4.142824 CAPILLARY THEORY OF FLOTATIONwith1 dZ SE R da Iam0 = sin a sin (8 - a)- - da.(4.15)This integral was calculated with the aid of a computer, and solutions were obtainedfor 0 = 5-90" at intervals of 1" and for a = and cm. Theresults can be supplied by the authors to anyone wishing to use them. The range ofparameters chosen covers all those required for an interpretation of flotation. At theupper limit of a = cm the approximations adopted above begin to break downand at the lower limit, a = cm, the model used loses its physical significancesince the wetting perimeter approaches molecular dimensions even for fairly largevalues of 8. The latter is also true for 8 + 0.It will be convenient in future to use the relationC = Aamo/Foo = 21am0/(l -COS 8)' (4.16)whence eqn (4.14) assumes the form(4.14')Table 1 shows the values of C calculated for various wetting angles from 8 = 5-90"and for various values of a.It can be seen that C shows only a slight dependence onthese parameters, so that interpolation is safe within the limits of this table.' a m 0 = C(,,RpR2a(l - cos O)2.TABLE 1.-vALUES OF c, THE RATIO OF THE WORK OF LIiiITING IMMERSiON TO THE WORK OFDISPLACEMENT OF THE WETTING PERIMETERa/cmoldeg51015203040506070809010-21.25441.09050.99560.92910.83110.77360.72610.68870.65850.63370.61 3 110-31.81051.64211.54501.47621.38021.31341.26291.22291.19031.16321.140410-42.37452.205 12.10612.03631.93'871 A7071.81911.77821.74471.71671.693210-52.94232.77212.67252.60222.50392.43532.38322.341 82.30792.27962.255510-63.51223.34183.24183.17123.07253.00362.95 122.90932.87542.84702.8229C = 21GImo/(1 -cos 8)2 from eqn (4.16) and a = ( R i 4 ) d Z .With the aid of these data and eqn (4.7') it is possible to estimate the upper limitof fiotability for the case in which removal is determined not by the weight ofthe particle but by the kinetic energy of its impact with the bubble.Assuming as insection 2 that this kinetic energy has a mean value of U = nzv2/4 and once again thatin = 4nR3p/3, we find with the aid of eqn (4.16) that(4.17)5. DISCUSSIONThe theory that we have proposed is quite simple compared with the real situationobtaining in foam flotation. This is not only because we use as a model a singlA .SCHELUDKO, B . V . TOSHEV AND D. T. BOJADJIEV 2825sphere that wets without wetting angle hysteresis but also because we have neglectedhydrodynamic factors and conventional surface forces. We should be able to judgeto what extent this theory reflects the basic features of the flotation process by a com-parison with some data from flotation practice but unfortunately we have not foundany work that deals simultaneously with the influence of particle size, wetting angleand the ascent velocity of bubbles on the flotability of one material only. To obtainthese data from investigations on different materials under a wide variety of conditionsis very delicate and a choice of measurements would be so arbitrary that there wouldbe little confidence in a detailed comparison with theory.Instead we examine themore general conclusions from a broad range of flotation data found in the classicbook by Klassen and Mokrousov 22 (and published again more recently in the bookby Glembotski and Klassen 2 3 ) and compare them with theory using only representa-tive values of the major parameters.Although the adsorption of the various surfactants used to modify the surface ofthe particles is considered in detail in these books it should be noted that there ishardly any information about the wetting angles. As a consequence in the applicationof our theory we have chosen rather a wide range for these angles, the limits of which(20 and 40") describe approximately the range we and others have noted for theeffective flotation of quartz.The choice of a value for the mean velocity, V, of thebubbles is also subject to some uncertainty because of its dependence on the size ofthe bubbles and the variations in size distribution among the machines. A typicalsize analysis from a conventional mechanical flotation machine gives an average dia-meter of -0.9 rnm with 80 % of the bubbles within 0.5 and 1.2 mm diameter,22although sizes well outside this range are often encountered (from 0.05 to 1.2 mm).If we assume a representative size of about 1 mm, then an ascent velocity a little> 10 cm s-l is computed from an experimental plot of V against diameter given inref, (22). This contrasts with the value of 40 cm s-l quoted for a similar machine.22In view of this divergence the value of 20 cm s-l used in the calculations to be dis-cussed below seems a reasonable approximation.It would appear that Y dependsonly very slightly on the solids content of the flotation medium in the range 0-50 %,22and that for bubbles certainly <0.25 mm diameter the presence of surfactant has noeffect on the velocity of ascent.22The considerable dispersion of V about our probatory value makes it pointlessseeking great precision in other parameters of less influence, such as surface tensionwhere a value of 50dyncm-l is quite acceptable. The relative density is quitestraightforward to assess for each system and a typical value of 3 g ~ r n - ~ has beenselected.According to ref.(22) and (23) there is both an upper and lower limit to the sizeof particles which can be floated and special sections were devoted to these limits andmeans of overcoming them. It was stated in ref. (22) that effective flotation takesp!ace with particles with sizes between 0.1 and 0.01 mm although later in the sametext these limits are defined more accurately and extended. The experimental upperlimit is estimated between 0.15 and 0.30 mm for heavier materials and between 0.5 and2 mm for lighter ones (e.g. coal and sulphur). On these grounds we assume tenta-tively for the upper limit a size of 0.2 mm for a relative density of 3 g ~ m - ~ . Thelower limit of flotability is indicated by poorly floated fine grained slimes. In ref. (23)it is reckoned that their particle size is < 10-3 pm whereas a limit of 10-5 pm is quotedin ref.(22). Our assumption of a size of several microns, i.e. Rmin w cm for thelower limit thus seems a reasonable one.In practice, extraction of particles with dimensions beyond the limits we have justoutlined can take place, firstly because of dispersion of many of the parameters abou2826 CAPILLARY THEORY OF FLOTATIONtheir average values (particularly V ) and secondly because the scraped-off foam oftencontains a considerable quantity of pulp with unattached particles. The limits wehave chosen should therefore not be seen as absolute but rather as quite diffuseboundaries.As stated in section 4, eqn (4.5) which follows from previous work 1' gives aconsiderably higher flotability limit than that observed in foam flotation.Forexample, with CT = 50 dyn cm-l and p = 3 g ~ m - ~ , eqn (4.5) gives Rmax,g values of2.7 x cm for 6 = 20 to 40", whereas flotation is normally no longereffective for R > 1 x cm. Moreover, according to eqn (4.5) flotation of particleshaving the optimum size of R = 20 pm should proceed successfully at very low wettingangles, 8 = lo, whereas this is again not observed. In contrast, eqn (4.17) for Rmax,vgives figures closer to the values found in flotation practice. For example, again withCT = 50 dyn cm-l, p = 3 g ~ r n - ~ , V = 20 cm s-l and 8 E 30" we obtain Rmax,v =2.6 xas functions of 8 for Q = 50 dyn cm-l and p = 3 g~ m - ~ . The curve for Rmax,g was calculated from eqn (4.5) and the curve for Rmax,vfrom eqn (4.17) for an interpolated selection of C in table 1.These curves are givenup to 6 = 50°, since above this angle we pass outside the range in which it is safe toapply eqn (4.9). As can be seen lies below Rmax,, and the former determinesthe upper limit of flotability. limits flotation much more stronglythan at low values of 6, and makes flotation impossible for 8 < 20"; as wasnoted earlier, this corresponds more closely to flotation data. Finally, since the limitof flotation by Rmax,v is near that actually observed, it is unlikely that inertia forcesof removal due to agitation which were not taken into account here, play any significantrole.to 5.5 xcm, for the value C = 1.15 computed from table 1.Fig.5 shows R,,,,, andMoreover,contact angle B/degFIG. 5.-Dependence of the radius (RmaJ of the biggest particles which can be floated on the wettingangle 0 ; Rmm,g for a particle detached by gravity ; Iimax,V for detachment by the kinetic energy of acollision. Calculations are for parameters typical for flotation, namely 0 = 50 dyn cm-l, p = 3 g~ m - ~ , V = 20 cm s-l.The results of the above simplified analysis of flotation are shown in fig. 6 for theparameters taken earlier as more or less typical of flotation. The curve ofwhich constitutes the upper limit of flotation, corresponds to the curve from fig. 5A . SCHELUDKO, B. V . TOSHEV AND D . T. BOJADJIEV 2827The curve of Rmi,, the lower limit of flotation, was calculated with the aid of eqn.(2.3)for an average IC value of 4 x dyn. The shaded area corresponds to the dimen-sions and wetting angles of flotable particles. By comparison of with Rmin,it can be seen that flotability disappears at wetting angles < - 10" not only becauseof the sharp decrease in Rmax,v but also because Rmin rises above Rmax,v. It can alsobe seen that Rmin decreases slightly with increasing wetting angle, so that there is noprospect of overcoming this limit by increasing 8. It is worth noting that in ref, (22)and (23) the influence of density on the lower limit of flotability is not mentioned.I I10 20 3(3 4 00 /degFIG. 6.--Region of flotation (hatched) limited by the maximum (Rmax,v) and minimum (Rmin) size ofthe particle for different wetting angles: D = 50dyncm-', p = 3 V = 20crns-l andx = 5 x dyn.If this is because there is only a weak dependence of this limit on p then this is ingood agreement with our interpretation ; according to eqn (4.17) - l/p2,while according to eqn (2.3) Rmin N (l/p)*. A further point to note is that the limitof flotability with respect to small wetting angles is almost independent of the disper-sion in V . This is also followed by theory. The solution of eqn (4.17) and (2.3) givesthis limit, i.e. 8 = 8, and for C constant, 1 -cos 8, - V4/' and hence the sharpdecrease of flotability below 8 - 10" is preserved for the various V.C. W. Nutt, Chem. Eng. Sci., 1960, 12, 133.A. Scheludko, B. Radoev and A. Fabrikant, A1z.v. Unit.. Sofia, 1968169, 63, 43.L. Evans, Ind. Eng. Chem.: 1954, 46, 2420.B. V. Derjaguin and S . Dukhin, Izzcest. Akad. Nauk, S.S.S.R., 1959, 1, 82.A. Scheludko, S1. Tschaljowska and A. Fabrikant, Faradcly Special Disc., 1970, 1. 112.H. 1. Schulze, Colloid and Polymer Sci., 1975, in press.A. Scheludko, Kolloid-Z., 1963, 191, 52.M. V. Smoluchowski, Phys. Z., 1916, 17, 557, 585.B. V. Toshev, Ann. Uniu. Sofia, Fac. Chimie, in press.lo A. Scheludko and A, Nikolov, Colloid and Polymer Sci., 1975, 253, 396.l 1 D. Reay and G. A. Ratcliff, Canad. J. Cliem. Eng., 1973, 51, 178.i 2 L. R. Flint and W. J. Howarth, Chem. Eng. Sci., 1971, 26, 1155.l 3 I. Langmuir, J. Chem. Phys., 1933, 1,756.l4 W. D. Harkins, J. Chem. Phys., 1937, 5, 135.l 5 F. P. Buff and H. T. Saltsburg, J. Chem. Phys., 1957, 26. 23.l6 B. A. Pethica, Progr. Appl. Chem., 1961, 46, 14.S. Torza and S. G. Mason, Ko!loid-Z., 1971, 246, 5932828 CAPILLARY THEORY OF FLOTATIONl 8 J. Mingins and A. Sheludko, J.C.S. Faraday I, submitted.l 9 B. V. Derjaguin, Dokl. Akad. Nauk S.S.S.R., 1946, 57, 517.2o D. F. James, J. Fhid Mech., 1974, 63, 657.21 R. Warbanow, Ann. liniu. Sofa, Fm. Chirnie. 1970/71, 65, 49.22 V. I. Klassen and V. A. Mokrousov, Vuedenie u teoriju floratzii (GNTIGD, Mosltwa, 1359).23 V. A. Glembotzki and V. T. Kiassen, Flotatzija (Nedra, Moskwa, 1973).(PAPER 511149

ISSN:0300-9599    

DOI:10.1039/F19767202815

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Laser-Raman Study of the Isomerization of Olefins overAluminaBY IRVINE D. M. TURNER, SILVIA 0. PAUL, EUAN REID AND PATRICK J. HENDRA"Department of Chemistry, The University, Southampton SO9 5NHReceived 18th August, 1975Raman spectra are given for hexenes and pentadienes adsorbed onto alumina over wide ranges ofcoverage. The spectra are interpreted in terms of the mechanism of adsorption and subsequentisomerization.Molecular vibrations are an excellent diagnostic characteristic of molecular com-position and structure. However, not all modes of vibration are equally active in thetwo major detecting techniques (infrared absorption and Raman scattering). Thus,some structural groups are more readily found in one technique than the other and innormal circumstances the combined spectral data are always considered to comple-ment one another.However, in surface chemical studies, infrared spectroscopy iswell established,"For some years, it has been feasible lo record good vibrational Raman spectra ofefficiently scattering species sorbed to white, high area catalysts. Reports are avail-able on a number of well understood trial systems and on technique but to date therehas been a paucity of applications of the method to problems where infrared spectro-scopy has not already been applied. This comment is not relevant to the study ofelectrochemically active surfaces where Raman spectroscopy gives unique data.The whole field, although a small one, has been repeatedly re~iewed.~-~The apparent lack of enthusiasm for the Raman method arises from poor sensiii-vity compared with infrared absorption and probleins arising from persistent fluore-scence often associated with activated absorbents.Fortunately, sensitivity is nowmuch improved," and the fluorescence problem is now at least partially understoodand methods exist for its contr01.~' '* It remains, however, that adequate sensiti-vity in the Raman experiment is obtainable only if the adsorbate is an intense Rainaiiscatterer, the surface white or pale in colour and of high specific area and fluorescencecan be controlled.For some years, there has been considerable interest in the isornerization of olefinsover acidic oxide surfaces. A number of mechanisms have been proposed based ona wide variety of experimental data.lg 9-12 It seems, however, that the more recentanalyses of the olefin + alumina system favour sorption of the olefin to a pair of dumi-nium ions lying in the surface followed by isomerization on desorp:ion.ll*Much of the contemporary work in this field has involved the use of infraredabsorption spectroscopy on the butene +alumina system.''.l2 In this paprr weapply Ranian methods and use the hexenes as adsorbates. The Raman technique isindicated in this case because the hexenes are strong scatterers (hence lilading to highsensitivity in the Raman experiment) and the isomers of hexene are readily distinguish-able from one another by their Raman spectra.but Raman far less so due to experimental difficulties.28 22830 ISOMERIZATION OF OLEFINSEXPERIMENTALy Alumina (Peter Spence, Grade H) with a B.E.T.surface area of 125 m2 g-' was usedas supplied. The alumina was studied as a powder in a cell which has been describedpreviously.4* Torr and at 1220 K inorder to minimise fluorescence. In all cases the standing pressure in the cell after pre-treatment was < Torr.Hex-1-ene, pent-1-ene and penta-l,4-diene were vacuum distilled and adsorbed onto thealumina at room temperature. Raman spectra were recorded at room temperature at variouscoverages as the cell was subsequently evacuated.The Raman spectra were recorded on a Cary 82 triple monochromator spectrometerusing an argon ion laser source (- 100 mW at 514.5 nm at the sample). High sensitivitymeasurements were made using a specially constructed instrument based on a Coderg T800triple monochromator, an argon ion laser source (-50 mW at 4880 nrn), multiple scanningand computer averaging of data.The design of Raman spectrometers for maximumsensitivity and suitability for the study of surfaces will be described e1~ewhere.l~The absorbate was pretreated at a pressure <RESULTSOLEFINSHex-1-ene was adsorbed onto y alumina pre-treated at 1220 K, the spectrumrecorded, the sample tube evacuated to reduce coverage and a new spectrum obtained.This process was repeated several times ; the resultant family of spectra are presentedin fig. 1. Comparison of these data with the Raman spectra of pure hexene isomers(see table 1) confirms that isomerization has occurred.If it is assumed that the inten-sities of Raman spectral features are not severely altered from those characteristic of3100 3000 2900C ' . . * . ' L ' ~ ~ '1700 1600 1500 1400 1300 1200AGlcrn-lFIG. 1.-Raman spectra of hex-1-ene adsorbed to y alumina. Adsorbents pretreated at 1220 Kunder vacuum. Quantities of hex-1-ene adsorbed (mg g-I aIumina) (a) 450, (b) 90, (c) 40, (d) 30.the liquid when the material becomes physisorbed to a surface, one can then make anestimate of the molar proportion of isomers on the oxide surface after isomerization.General experience in the field suggests that this assumption can be made. It there-fore appears from the bands in the 3000, 1650 and 1380 cm-1 regions that the isomerspresent vary with coverage.At approximately monolayer coverage ( - 30 mg g-1 absorbate) trans-hex-2-enepredominates.However on removal of sorbates to a coverage of 9 mg g-I the cis-isomer predominates. At high coverage the molar ratios of isomers derived from thI . D. M. TURNER, S. 0. PAUL, E. REID AND P. J . HENDRA 2831TABLE RAMAN AN BANDS FOR LIQUID HEXENEShex- 1 -ene cis-hex-Zene trans-hex-2-eneshiftAv/cm-131336140263 18228788959221058110812241290130014221445164528682882292029422968298630043086relativeintensity2828169092835621017520519518080751 6040shift relative shift relativeAv/cm-1 intensity Avlcrn- 1 intensity86097110511250 461456 551662 1822876 1702925 2052942 1823022 12578086089610261048109212201294131213821436145816752850287029252944300820262820487234587420078126236230641 1 * * ' a & J 1 1 1 1 b 1 * 1 I I l I i3100 3000 2900 2800 1700 1600 1500 1400 1300 1200A71cm-lFIG. 2.-Raman spectra of penta-1,4-diene adsorbed to y alumina.Adsorbents pretreated at 1220 Kunder vacuum. Quantities of penta-1,4-diene adsorbed (mgg-l alumina) (a) 48, (b) 14, (c) 7-82832 ISOMERIZATION OF OLEFINSRaman data are close to thsse predicted from free energy computations, uiz. hex-1-ene3.5 %, cis-hex-Zene 19.3 % and trans-hex-Zene 77.2 %.Sorption of cis-hex-2-ene and trans-hex-Zene onto alumina produced very similarRaman spectra at low coverages as shown in fig.I, i.e., some hex-1-ene is formed andcis-hex-Zene predominates at very low coverage. As the coverage was reduced to< 8 mg 8-l the bands attributed to hexene isomers could no longer be detected. Atthese coverages, however, the Raman spectrum contains a band at 1450 cm-l and aTABLE 2.-FREQUENCIES AND INTENSITIES OF THE RAMAN BANDS FROM LIQUID PENTADIENESfrutzs- I ,3-pentadiene 2-methyl- 1,3-butadieneshiftAv/cm-l21 235939048561 5890905958I045116512501295135613821434144615931642256528962927299330153091relativeintensity6416442354628271775330150255177747911302931914012721shiftAv/cm-12074534828 1990310301070118012651294138014531605166328502888292029993092relativeintensity171031217788215832447648 14058147301 633shiftAv/cm-l19041 749287890091 89951065821233129613181416143516452857290329361503087relativeintensity654339232371226150602637820547315037shiftAv/cm-128742552978090095399410701293139214171425164128632908293029873011309 Irelativeintensity593632123216471322258873 80145255471 7028broad diffuse band centred near 1575 cm-'.Attempts to pump off the remainingorganic matter failed in that a residue of N 5 mg g-1 appeared to be inseparable fromthe surface, at least at rooin temperature.However, if the alumina was pretreatedsimply by prolonged evacuation at room temperature, all the hexene could be removedwithout isomerisation. In this case, a band at 1646 cm-l could be recorded atcoverages as low as 3 rng g-I.Very similar results to those described above were observed when pentenes wereused as absorbents. The spectrum obtained when pent-l,4-diene waq absorbed ontI . D. M. TURNER, S . 0. PAUL, E. REID A N D P. J . HENDRA 2833alumina is shown in fig. 2. The change in relative Raman band intensities near1650 cm-I with coverage indicate that isomerization to the cis- and tra~ls-1~3-isornersoccurred with the former persisting at low coverage (see tables 2 and 3). At equili-brium in the vapour phase, free energy calculations give the molar proportions cis-penta-173-diene 44 %, trans-penta-l,3-diene 55 %, all remaining isomers small.Sorp-tion of either cis- or trans-penta-l,3-dienes onto activated alumina again resulted inTABLE 3.-FREQUENCIES AND ISOMER ASSIGNMENTS OF BANDS OBSERVED IN THE RAMAN SPEC-TRUM OF 1,4-PENTADIENE ADSORBED TO ALUMINA PRETREATED AT 1 2 2 0 Krtarnan band/cm- 1 pentadiene isomer2042523 9 06087888 2 489810411 1 8 612511295 :Eq1 4 5 21 4 4 2 shoulder1 6 0 216542 8 5 02890292229702999301 5 shoulder3091trans-1,3-~ i s - 1 ~ 3 -cis-l,3 -trans-1,3-cis-1,3-cis-trans-l,3-trans-1,3-cis-l,3-all--trans-l,3-cis-1,3-cis/trans-l,3-cisltrans-l.3-allallc i s l t r n s - l , 3 -trans- 1 , 3 -cis-1,3-Total coverage on surface 54.5 mg 6-l aluminaisomerization to approximately equimolar cis- and trans-isomers and again the cis-isomer persisted at low coverage.DISCUSSIONIt is apparent from these results that hexene and pentene are more stronglyabsorbed to alumina when in their cis-2-isomeric forms.In the case of the dienes,the cis-l,3-isomers are preferentially adsorbed. These results are in agreement withPeri's data on oxide catalysed butene isomerisation where again the cis-isomer wasshown from infrared evidence to persist at low coverages.1o The alumina used hasbeen repeatedly characterised by its adsorption of pyridine, BC13, nitriles, acetylenesand many other sorbates from which it is apparent that it has negligible Lewis acidityif evacuated at room temperature but a very high degree of Lewis acidity if activatedat 1220 I(.'* ** l4 Bronsted acidity has never been shown by Raman methods to beimportant and it is clear from pyridine absorption experiments that the vapour pres-sure over Lewis coordinated pyridine is much lower than that over any other sites2834 ISOMERIZATION OF OLEFINSWe therefore conclude that the highly efficient isomerisation reactivity characteristicof Spence H alumina must lie in its Lewis acidity.Taken in collaboration with thepreferential absorption referred to above this conclusion favours an isomerizationmechanism similar to that originally proposed by Ha11.12 Hall has suggested that inalumina the key feature of the isomerization mechanism is the sorption of the olefinto an adjacent pair of aluminium ions on the oxide surface.This " double site "is capable of retaining a cis-disubstituted olefin (specifically butene in Hall's work)through its terminal atoms. Isomerization then proceeds intra-molecularly and theproducts are desorbed. Turning now to measurements made at low coverage, spectracan readily be recorded of hex-1-ene absorbed onto alumina at coverages below 10 mgsorbate g-l Al,03. This represents specific coverages below 20 % monolayer. If thealumina was activated by prolonged evacuation at room temperature all the hex-1-enecould be removed without isomerization. In this case a band at Av = 1646 cm-lcould be recorded at coverages as low as 3 mg g-1 A1203.Thus, we conclude thatwith the sensitivity available we would expect to record spectra of normal olefinicspecies down to a coverage of < 3 mg g-l A1203. As hexene is desorbed fromalumina activated at high temperatures, the band at Av = 1661 assigned to cis-hex-2ene predominates but cannot be detected when the coverage falls below 8 mg 8-lA1203. Furthermore, a residue of - 5 mg g-1 Alz03 appears to be inseparable fromthe surface after prolonged evacuation. This residue is characterized by a broadRaman band at 1575 cm-l and a band at 1450 cm-l. This latter band can be assignedto CH deformation vibrations but an assignment of the feature at 1575 cm-' is notSO obvious. It is interesting to note that a recent study of the infrared spectra of avery similar system has indicated the strong absorption of material at low coveragewhich has infrared bands at Av = 1570 cm-l and Av = 1440 cm-'.15 In the infraredstudy these bands are assigned to adsorbed carboxy compounds which are stronglyheld at the surface, presumably incorporating oxygen from the alumina surface.These spectra are recorded when the alumina was pretreated at temperatures > 600 K,i.e., very similar conditions to those used in this study.Unfortunately it is impossibleto predict with any certainty the relative intensities of infrared and Raman bands dueto vibrations of adsorbed carboxy species. Therefore we can only conclude that theRaman spectra confirm the results obtained by infrared. In conclusion thereforethese results indicate that the application of Raman techniques to the study of surfacescan produce data complementary to that obtained by infrared techniques and, pro-vided an experiment is well designed, that the sensitivity of the two techniques arecomparable.The authors thank the S.R.C.and the U.S. Office of Naval Research for generoussupport.' L. H. Little, Infrared Spectra of Adsorbed Species (Academic Press, New York, 1966).M. L. Hair, Infrared Spectroscopy in Surface Chemistry (Marcel Dekker, New York, 1967).P. J. Hendra, M. Fleischmann, A. J. McQuillan, R. L. Paul and E. Reid, J. Raman Spectr.,1976, 4,269.P. J. Hendra, Spex Speaker, 1974, 19, 1.R. P. Cooney, G. Curthoys and N. T. Tam, Adu. Catalysis, 1975, 24, 293.T. A. Egerton and A. H. Hardin, Catalysis Rev. Sci. Eng., 1975, 11, 1.J. Catalysis, 1974, 32, 343.P. J. Hendra and E. J. Loader, Trans. Faraday SOC., 1971, 67, 828.W. W. McCarthy and J. Turkevitch, J. Chem. Phys., 1944,12,405.' T. A. Egerton, A. H. Hardin, Y . Kozirovski and N. Sheppard, Chem. Comm., 1971, 887;lo J. B. Peri, Proc. 2nd Int. Cungr. Catalysis, Paris, 1960 (Technips, 1961), p. 1333I . D . M. TURNER, S . 0. PAUL, E. REID AND P . J . HENDRA 2835l 1 G. Gati and H. Knozinger in Catalysis, ed. J. W. Hightower (North Holland, Amsterdam,l 2 H. R. Gerberich and W. K. Hall, J. Catalysis, 1966, 5, 99.l3 P. J. Hendra and E. S. Reid, to be published.l4 I. D. M. Turner, P h B . Thesis (Southampton, 1974).l 5 A. Corado, A. Kiss, H. Knozinger and H. D. Muller, J. Catalysis, 1975, 37, 68.1973), p. 819.(PAPER 5/1632

ISSN:0300-9599    

DOI:10.1039/F19767202829

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Theory of Tracer Diffusion Measurements in Liquid SystemsBY S r ~ o L~UKKONEN, * PENTTI PASSINIEMI, ZOLTAN NOSZTICZIUS~AND JUSSI RASTASHelsinki University of Technology, Department of Chemistry,SF-01250 Espoo 15, FinlandReceived 20th October, 1975The differential equation of non-steady state tracer diffusion has been solved for liquid s) stemswith general initial and boundary conditions. On the basis of the solution the measurement of thetracer diffusion coefficient can be reduced, regardless of the geometry of the cell, to the determina-tion of the eigenvalues. of which the first one only is necessary after a certain time. An obviousdistinction can be made between relative and absclute measuring methods. The planning of newexperiments is possible if the roles of the initial condition and the counting efficiency are appreciated.As a special example of a three dimensional dipision cell, a slightly conical open-ended capillaryhas been analysed.To obtain 0.1 % accuracy with the 0.8 mm diameter capillary, a variation ofonly 0.001 mm in the diameter can be allowed.The space dependent tracer diffusion coefficient has also been treated. The tracer diffusioncurrent density and the corresponding differential equation of continuity, which take into accountthe unequal equilibrium distribution of the tracer concentration in the system, have been derived.The solution of the differential equation for this continuous multiphase system has been obtained inan analogous manner to that of the single phase. Here again after a certain time the first eiger,valuecan be determined experimentally. However, the eigenvalue may include only a certain part of thetracer diffusion coefficient which is independent on the positional coordinates.In this case theform D = Dof(r) is used for the tracer diffuqion coefficient with the constant Do.In the last fifteen years continuous monitoring methods have been developed formeasuring radioactive tracer diffusion in isothermal systems, among them the open-ended capillary method with and without stirring,1-6 a modification of this methodapplying a permeable membrane on the open end of the capillary,' and the continuousmeasurement of the radioactive tracer diffusion in a diaphragm In both theopen-ended capillary and diaphragm cell methods calibrations are required for theflow rate of the outer solution and for the cell constant.In this paper we solve the partial differential equation of tracer diffusion by usinggeneral initial and boundary conditions in order to find a uniform basis for the analysisof different measuring arrangements. To effect this solution, the properties of theeigenfunctions in the Sturm-Liouville differential equation are applied.'' We areparticularly interested in obtaining a relation between the tracer diffusion cocEcientand the cell geometry, since we can thus give a clear meaning to the calibration pro-cedure. Also in this paper we examine tracer diffusion in a heterogeneous system,which is here considered as a continuous multiphase system because of the assumptionsof continuity made for both the thermodynamic and transfort quantities over thesystem.An overall tracer diffusion equation will be derived for the system. Thecorresponding partial differential equztion will then be solved and possibilities ofdetermining the space dependent tracer diffusion coefficients will be discussed.t present address : Technical University of Budapest, Institut of Pnysics, Budapest, Hungary.283s. LIUKKONEN, P . PASSINIEMI, z. NOSZTICZIUS AND 3 . RASTAS 2837SOLUTION OF TRACER DIFFUSION EQUATIONIn tracer diffusion experiments a very small amount of radioactive tracer is usuallyadded to part of the liquid system, which was in equilibrium prior to the addition.The system may be composed both of electrolytes and nonelectrolytes, of which oneis considered as the tracer component.During diffLision the current density of thetracer is given at isothermal and isobaric conditions byEqn (1) is Fick’s first law in which C is the concentration of the tracer and D the tracerdiffusion coefficients depending on the concentrations of the nontracer componentsin the system. For the determination of the diffusion coefficient Fick’s second lawis applied in the formJ = -DVC. (1)acat- = DV2C-11.,C,where A, is the radioactive decay constant of the tracer.we must solve eqn (2) with very general initial and boundary conditionsTo discuss the possible measuring arrangements in tracer diffusion experimentsc = C(r, 0) t = 0, (3)ac aC +p- = o t > 0 .Is an/, (4)According to the conditions of eqn (4) the system or the diffusion cell may haveopen and/or closed parts on its surface S. The partial differential in eqn (4) is takenin the direction of the outer normal and a and p are space dependent functions.By applying the method for the separation of variables, i.e. by writing C =R(r)T(t), we can solve the differential eqn (2) with the result lo00 c(r, t ) = bo + C b , ~ , ( r ) exp [-(A$ +A$) ( 5 )i = 1where Ai is the eigenvalue corresponding to the eigenfunction Ri. The coefficientsb, are determined from the equationQ)by using the orthogonal properties of the eigenfunctions.coefficient (i = 0) isSpecifically, the firstbo = Y - l 1 C(r,O)dV = C, ( 7 4bo = 0. (76)VorFor eqn (7a) the diffusion cell is sealed and C , is the equilibrium concentrationof the tracer.For eqn (7b) the cell is open somewhere on its surface and thus C , = 0.During an experiment the diffusion cell is connected to the nuclear detector system,which is assumed to have a time independent counting efficiency denoted by h(r).The instabilities of the measuring devices and the dependence of the counting efficiencyon the intensity can be taken into account, if necessary. The intensity I; of the cellat time t is derived from eqn (5) asr coI ; = N,A, exp ( - A r t > (h(r)bo + h(r)b,R,(r) exp (-)$t)) dV (8)V i = 1where NA is the Avogadro constant2838 THEORY OF TRACER DIFFUSION MEASUREMENTSDefiningI , = I: exp (Art),I, = N,l,bo 1 h(r) dV,Veqn (8) becomesIi = N , i , b , / h(r)R,(r)dV,Voc)I , = I , + C I , exp (-Aiot).i = 1The eigenvalues Ai increase rapidly for any region Vwith the index i.Thereforeafter a certain time, which depends on the geometry of the cell, the first term in thesum of eqn (10) predominates and taking logarithms we find(1 1)for theopen-ended capillary method. On the basis of eqn (11) we can use one-, two- orthree-dimensional cells, in which the initial concentration distribution may be quitearbitrary. In all cases, after an appropriate time the product A,D may be determinedfrom the slope of the plot of In[ It - I , 1 against t . Hereafter we have two possibilities :(i) If the dimensions of the cell are known accurately enough, i.e. the part A, ofthe product, we can calculate the tracer diffusion coefficient directly.This methodis absolute.(ii) If we are unable to measure the dimensions accurately or if we use a cell ofarbitrary geometry, a calibration measurement is required. To effect this calibration,a tracer is required whose diffusion coefficient is known from other, possibly absolute,measurements. From the slope we now calculate %, and use it for the cell in otherexperiments. In the open-ended capillary method, e.g., the determination of the cor-rect flow rate of the outside solution l 1 can be regarded as part of the calibrationprocedure. A completely closed diffusion cell may also be used, since in this case thereare no problems such as the A1-effect in the open-ended capillary,12 and thus we havean absolute measuring method for the tracer diffusion coefficients.This is verydesirable as independent measurements are required e.g. for the calculation of thephenomenological coefficients in self-diffusion systems. l4 As mentioned else-where,15 we can also apply the optimal initial condition and the optimal countingefficiency function in connection with eqn (10). In this way, the time required foreqn (1 1) to become valid may be shortened.ln~It-Zm~ = -L,Dt+ln Il.Eqn (1 1) is a general form of the result derived by Rastas and KivaloOPEN-ENDED CONICAL CAPILLARYTo compare the first eigenvalue of the cylindrical open-ended capillary with theweakly conical one, we replace the top and bottom planes of the conical capillary bysphere surfaces.This is a good approximation sincee = (rg/2)f(m+L)is very small (cf. fig. 1). We may have e.g. r2 = 0.2and e N 10nm.The diffusion equation for spherical symmetry is(12)mm,L = 20mm,m+L = 2ms. LIUKKONEN, P . PASSINIEMI, z. NOSZTICZIUS AND J . RASTAS 2839(14)(154The eigenfunctions for eqn (13) arethe boundary conditions beingui(x) = A ~ x - ~ cos[Jl,(x-k,)], i = 1,2, . .v,(m +L) = 0 (open end)= 0 (closed end). $1 x = mFIG. 1 ,-The conical capillary.From eqn (14) and (1 5a) the first eigenvalue is obtained in the formJC = (nP)J(L-z) (1 6)tg(zdn,> = (&m)-l N zdn, when z + 0. (17)where the notation z = k , -rn has been used. Correspondingly from eqn (14) and(15b)By applying the first eigenvalue of the cylindrical open-ended capillary (7c2/4L2)for the A1 in the approximation of eqn (1 7) and by substituting z into eqn (1 6)A1 N (7c2/4L2)(1 8Ar/n2r,)-1in whichAr/rl = (r2-rl)/rl = L/m.(1 9)The minus sign in eqn (18) corresponds to the conical capillary open at its larger endand the plus to that open at its smaller end.From eqn (18) it can be deduced that if Ar in the conical capillary is - 1.2 % ofrl, the eigenvalue differs from the cylindrical one by - 1 %. Thus to measure thetracer diffusion coefficient by the open-ended capillary method, the diameter of thecapillary being 0.8 mm, to an accuracy of 0.1 %, the diameter must not vary by> mm. In practice the capillary is never as accurately conical as in the aboveexample. Along the length of the capillary the diameter can vary both ways fromthe mean and thus the conicity may be cancelled.The treatment still indicates howa small error in dimensions of the capillary can cause a considerable systematic errorin the value of the tracer diffusion coefficient. This is important when the Onsagerlimiting law is being tested.TRACER DIFFUSION I N CONTINUOUS MULTIPHASE SYSTEMIn tracer diffusion a heterogeneous system can be transformed to a continuoussystem by applying certain conditions ; the eigenvalue for the entire system can alsobe determined. Thus, here, a tracer equation corresponding to eqn (1) in a simplephase is derived and the partial differential equation analogous to eqn (2) solved2840 THEORY OF TRACER DIFFUSION MEASUREMENTSThe isothermal and isobaric system is composed of a limited number of solutionor partially miscible solution phases, gel and neutral membrane phases.Each phasecontains a solvent, nonelectrolytes (sub-index k) and electrolytes (sub-index q). Thetracer component (sub-index 1) may be a non-electrolyte (k = 1) or an electrolyte(q = I). For the phases, super-indexf(= a, /3, y, . . .) is used. The chemical poten-tial of a nonelectrolyte in the phase f i s given by,f.fkf = p P f + R T In (ykCk/Ce)f k = (I), 2,. . ., M - 1 (20)and that of an electrolyte byq = (l), M , M+1,. . ., N . (21)y,, yQ and C,, C, are, respectively, the activity coefficient and the concentration of thekth non-electrolyte or of the qth electrolyte. p e f ( i = k, q) is the standard value ofthe chemical potential in the phasefand C* ,= 1 mol dm-3.Eqn (21) is for the casewhen the electrolyte has a common anion with the other electrolytes of the phase.v,+, vQ-, and v, = v,-+v,- are the stoichiometric numbers for the qth electrolyteand vim is that of the common anion in the mth electrolyte, In the following deriva-tion eqn (21) is shortened making the substitutionsThe system is in equilibrium before addition of the tracer, and we assume thatafter addition the system reaches a new equilibrium position. Then the chemicalpotential of each component has the same value everywhere in the system. We can,therefore, define the distribution coefficients Kaf(f = p, y , , . . ; Kaa = 1) as followsusing eqn (20), (21) and (22)(23a)During the tracer diffusion we assume that in the system the diffusion curren-tdensities are continuous across the interfaces and that the components are in chemicalequilibrium, or that there are conditions of the form p: = p f ( i = k , q ) at the inter-faces of the neighbouring phases.Using eqn (23) we can now express the chemicalpotentials in eqn (20) and (21) with reference to the standard values @. If we assumethe Kff values to be continuous functions of the space coordinates and leave out thesuper-indexes for the phases, we obtain the continuous chemical potentials for theentire systemThe phenomenological equations in the continuous system are written as ISNJi = LijXj i = 1, 2,. . ., Nj = s. LIUKKONEN, P. PASSINIEMI, z .NOSZTICZIUS AND J . RASTAS 2841where .Ii is the diffusion current density or diffusion flow in the solvent fixed frame ofreference, Lij is the phenomenological coefficient and X j the negative gradient of thechemical potential. In the case of the tracer diffusion process we are chiefly interestedin the flow J1 (k = 1 or q = 1) although the other flows do not disappear in “ pure ”tracer diffusion. The phenomenological coefficients depend on temperature, pressureand on the concentration of the components. In systems where dissociation is pos-sible the phenomenological coefficients of the species can also be used. These co-efficients are expressed as a power series in conczntration.l’* l8 Since the pheno-menological coefficients of the species can always be coupled to the coefficients of thecomponents, the corresponding series expansions for the L i j values may be applied.We also assume the L i j values to be continuous over the systemLii = LfiCi[l +Ai(C1, C,, .. .)] ; i = k, q (26d(26b) Lij = L;jC,Cj[l +gij(C,, Cz, . . .)] ; i, j = k, 4, i # j .In eqn (26) Lri and L;’ are independent of concentration andLi and g i j are power seriesin concentrations having positive powers. As in the Onsager reciprocal relationLij = Ljl(i # . j ) in eqn (25), Lrj = L$.The concentration of the tracer (C,) is very small through the entire system i.e.C1 + Ci (i = 2, 3, . . . N ) . When the logarithms of the activity coefficients, lny,,and their derivatives with respect to the concentrations are assumed continuous andfinite over the system we find the following limitsFrom eqn (24), (25), (26a) and (27), and with C, 6 Ci (i # 1) the following expressionmay be derived for a nonelectrolyte as a tracerV(C1K1) -D,V(CIK1) (284 RTLl1 lim LIlX1 = -~c1+0 ClKland for a tracer electrolytein which D1 and D1+ are the tracer diffusion coefficients of the component inquestion in the continuous multiphase system.The above derivation does notexclude the possibility of there being a cation common to the tracer electrolyte andthe other electrolytes, or even the case of no common ion. These alternatives canbe treated analogously. For the cross-phenomenological part of the sum in eqii (25)and eqn (24), (25), (26b) and (27), and with C1 -+ Ci (i # 1) we obtainlim L I j X j = 0 j = 2 , 3 , .. ., N .c1+0Eqn (29) means that the tracer flow is not coupled pheno~nenologically to the flowsof the other components.On the basis of eqn (28) the tracer flow may be written in the formJ = -DV(CK) (30)in which D and K depend on the space coordinates. The continuity eqn (31) isderivable from eqn (30)- = V [DV(CK)] -&C.aCat(312842 THEORY OF TRACER DIFFUSION MEASUREMENTSThis differential equation is solved by the method of separation of variables lo aseqn (2) by using the general boundary conditiona vav + p - = o Is an Iswhere v(r) = K(r)R(r) is the substitution made for the space dependent part afterseparation of the variables. The solution of eqn (31) isa,C(r, 0 = exp(- A,t)Cbop + c b,P, exp( - &Ol (33)i= 1where p = K-l and Al is the eigenvalue corresponding to the eigenfunction ui.Thecoefficients bi are determined in accordance with the initial concentration distributionwhich now hasCorrespondingorbo = 0depending on whether the cell is entirely closed or open somewhere at its surface.The measured intensity I( of the system at time t is obtained by integration usingC(r, t ) from eqn (33) and the integral in eqn (8). Further, if the terms It, Iao and Iiare defmed analogously to eqn (9a)-(c)Again after an appropriate time the first term in the sum of eqn (36) is predominantand thenFrom eqn (37) it is possible to determine experimentally the slope which is characteris-tic of the system in question. We cannot now, as with a simple phase in eqn ( l l ) ,divide the exponent by the product of a tracer diffusion coefficient and a geometricfactor.If the space dependence of the tracer diffusion coefficient can be estimatedwith D = Dof(r), then by using certain explicit functions for f(r) both Do and someparameters in f(r) may be obtained.lg* 2o The concept of a space dependentdiffusion coefficient was also applied by Mulholland 21 to a study of self-diffusionthrough a liquidfvapour interface.ln~It-Iw~ = -A,t+ln I t . (37)CONCLUSIONHowever, theimportant relation between the tracer diffusion coefficient and the cell geometry andThe mathematics used in the above derivations is well knownS . LIUKKONEN, P. PASSINIEMI, Z . NOSZTICZIUS AND J . RASTAS 2843the influence of the counting efficiency h(u) on the term (It - I,) have not been inter-preted broadly enough elsewhere in connection with measurements. The theoreticalbackground outlined here for continuous measurements can be applied both in tracer-and self-diffusion experiments.We gratefully acknowledge a scholarship to Z .N. for his stay in Finland on thebasis of the cultural agreement between Hungary and Finland.' R. Mills and E. W. Godbole, Austral. J. Chem., 1958, 11, 1.R. Mills and E. W. Godbole, Austral. J. Chem., 1959, 12, 102.E. Berne and J. Berggren, Acta Chern. Scand., 1960, 14, 428.A. Gosman, Chem. listy, 1962,56,1435.J. Rastas and P. Kivalo, Acta Pol-vtech. Scand. (Chem.), 1964, SO, 4.A. Gosman, Coll. Czech. Chem. Comm., 1968, 33, 1480.1.R. Mills, L. A. Woolf and R. 0. Watts, Amer. Inst. Chem. Engineers J., 1968, 14, 671.R. Mills and R. J. Boland, J. Sci. Instr. Ser. 2, 1969, 1,483.vol. I, p. 324, 370.R. Mills, J. Amer. Chem. SOC., 1955, 77, 6116.' S. Liukkonen, J. Rastas, R. Hassinen and P. Kivalo, Acta Polytech. Scand. (Chem.), 1966, 55,l o R. Courant and D. Hilbert, Mefhocls of Mathematical Physics (Jnterscience, New York, 19-53)]l2 P. L. Spedding and R. Mills, J. Electrochem. SOC., 1966, 113, 599.l3 S. Liukkonen, Acta Polytech. Scand. (Chem.), 1973, 113, 1.l4 J. Anderson and R. Paterson, J.C.S. Faraa'ay I, 1975, 71, 1335.lJ Z . Noszticzius, S. Liukkonen, P. Passiniemi, and J. Rastas, J.C.S. Faradav I, 72, 2537.f7 €3. Schonert, J. Phys. Chem., 1969,73,62.l8 J. Rastas, Acta Polytech. Scand. (Chem.), 1966, 50, 1.l9 R. M. Barrer in Diflusion in Polymers, ed. J. Crank and G. S. Park (Academic Press, London,2o R. Ash and R. M. Barrer, J. Bhys. D, 1971, 4, 888.21 G. W. Mulholland, J. Chem. Phys., 1976, 64, 862.R. Haase, Thermodynamics of Irreuersible Processes (Addison-Wesley, London, 19691, chap. 4.1968), pp. 197-199.(PAPER 5/2040

ISSN:0300-9599    

DOI:10.1039/F19767202836

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Electrical Double Layer Interactions under Regulationby Surface Ionization Equilibria--DissimilarAmphoterk SurfacesBY DEREK CHANTSUnilever Research, Port Sunlight, Wirral, Merseyside L62 4XNANDTHOMAS w. HEALY* AND LEE R. WHITE?Dept. of Physical Chemistry, University of Melbourne,Parkville, Victoria, AustraliaReceived 1st January, 1976The electrostatic interaction between similar and dissimilar double layers under regulated approachis considered. During the interaction the surface potentials and charges are regulated by theassociation and dissociation of ionizable groups at each surface. A new method, similar to themethod of isodynamic curves, is developed to study this problem. This method can provide aqualitative description of the salient features of the surface charge, the surface potential and thepressure between the surfaces as a function of separation without first having to obtain an exactsolution of the problem.This qualitative and the accompanying exact solution are presented interms of the Gouy-Chapman approximation as an illustration of the role of surface regulationduring interaction. -1. INTRODUCTIONIn a variety of situations that involve particles of colloidal dimensions, forinstance, in fibrous bed filtration of emulsions mineral fl~tation,~ it is necessaryto understand the interaction between dissimilarly charged particles.In the classical Gouy-Chapman theory of electrical double layers, it has beenusual to assume, as boundary conditions for the electrostatic problem, that constantcharge or constant potential is maintained on either or both surfaces throughout theinteraction.For certain surfaces, where the charge is due, for example, to strongacid sites, the constant charge assumption may indeed be correct at pH % pK,.However, there are as yet no criteria for determining the extent to which such anassumption is valid, nor are there criteria for selecting a priori whether interactionunder constant charge or constant potential is more appropriate for many otherimportant colloidal systems. The problem of interacting dissimilar double layershas been considered by a number of a u t h o r ~ . ~ - l ~ In all instances, the constant chargeor constant potential boundary condition was employed. It has been recognisedfor some time that these boundary conditions lead to infinitely large surface potentialor surface charge, as the case may be, at small interparticle separations.Thisdifficulty can, of course, be avoided by invoking some minimum cut-off in the7 CSIRO Port-doctoral fellow.Part of this work was performed at the Department of Applied Mathematics, Australian NationalUniversity and Part at the Department of Physical Chemistry, University of Bristol.3 Present address: Departiiient of Physical Chemistry, University of Bristol, Bristol BS8 ITS.284D . CHAN, T. W . HEALY AND L . R . WHITE 2845separation," or, perhaps more satisfactorily, by a proper consideration of thechemical potential of adsorbed ionic species at the surface.' 8-20In a previous paper,24 (I), we have considered in detail the electrical double layerinteraction between two identically charged planar surfaces where the surfacepotential is regulated by those equilibria at the surface that are responsible for thedevelopment of the surface ~ h a r g e .~ At each interparticle separation, the surfacecharge density which determines the potential distribution in the diffuse layer is itselfgiven as a self-consistent function of the surface potential.Using the notions developed in (I), we consider the double layer interaction be-tween two dissimilar amphoteric planar surfaces. Although we are dealing specificallywith amphoteric surfaces, the analysis which follows also applies to surfaces whichbear only acidic or basic groups. In the next section, by a consideration of the dis-sociation of surface groups, we shall briefly recapitulate the relation which governsthe regulation of surface charge and potential. The formulation of the potentialdistribution, assumed to be given by the Poisson-Boltzmann (PB) equation, and alsothe pressure, as a function of distance will be derived.From the first integral ofthe PB equation and the boundary conditions, we can predict qualitatively thebehaviour of the repulsive pressure, surface potential and surface charge as a functionof the separation. Our analysis is analogous to the method of isodynamic curvesdue to Deryag~in.~ The interaction between surfaces having like signs at infinity(but different magnitudes in charge and potential) is described in Section 3 ; thatbetween unlike surfaces in Section 4.The method of quantitative solution of theinteraction for all cases is considered in Section 5.2. FORMULATIONAs in (I), we adopt the concept that each surface develops a surface charge viadissociation equilibria of amphoteric surface groups. The reactions may be writtenas :AH; +AH+H+ (2.1)AH + A-+H+. (2.2)Although the discussion is independent of the type of PDI, we shall assume they arehydrogen ions as, for example, in hydrous metal oxides, and that for each reaction,the ratios of the concentration of surface species are given by surface dissociationconstants, viz.,The dissociation constants K+,K- are assumed to be functions only of temperatureand pressure. The validity of eqn (2.3) and (2.4) has been discussed in detail in (I).For N, surface groups per unit area, the net surface charge density is (e - protoniccharge)= eNsa.[AH,+] - [A-I= eNs [AH] + [AH,+] + [A-]The fraction, a, defined by eqn (2.5), can assume any value between plus and minusone.1-92846 ELECTRICAL DOUBLE LAYER INTERACTIONSIn the Gouy-Chapman approximation, which we shall adopt, the concentrationof ionic species at any point is related to the bulk value by the Boltzmann factorexp( - e$/kT). The electrostatic potential $ is measured with respect to the valueat the reservoir (taken to be zero). In particular, the surface concentration of PDI is :[H+], = H exp( - elC/JkT) (2.6)where H is the bulk concentration of PDI and $s is the surface potential.Combiningeqn (2.3), (2.4) and (2.6) the surface charge can be written as :(2.7)Given the dissociation constants, K+ and K-, which characterize the surface, andthe bulk concentration of PDI, eqn (2.7) represents a canonical relationship betweenthe values of the surface charge and the surface potential. It is used in place of theconstant charge or potential boundary condition for solving the Poisson-Boltzmann(PB) equation that governs the distribution of the diffuse layer. If during the inter-action the surface potential changes from $, to &, the surface charge will changefrom d, where ($s,a) and ($:,a') must satisfy eqn (2.7) which is thus an " equationof state " of the surface. It specifies all possible values of the '' coordinate " ($s,a).It is instructive to rewrite eqn (2.7) in the form :where6 = 2 x 10-ApK'2 = 2[K-/K+]$andApK = pK--pK+.(2.10)We shall call the potential :(2.1 1)the Nernst potential since it is related to the point-of-zero-charge (pzc)by the Nernst eqn (2.11). We note from eqn (2.8) that a >< 0 if @, 5 $N and 0 = 0when $, = $N. When the surface potential is far away from the Nernst value, thesurface charge attains the saturation values keN,. In view of eqn (2.10) to (2.12),the surface equation of state can be completely specified by the pzc (pH,) and ApKtogether with the bulk pH, or equivalently the Nernst potential. A detailed study ofthe non-Nernstian behaviour of amphoteric oxides, based on eqn (2.8), is given else-where.26 We can now proceed to study the potential distribution and the pressurebetween two amphoteric surfaces.Consider the general Poisson-Boltzmann (PB) equation that governs the electro-static potential $ in an electrolyte :PHo = $(PK++PK-) (2.12)4ne V2$ = - - nivi exp (- ev,$/kT).E i(2.13)In eqn (2.13) n, is the bulk number density of ion types having valence vi and E isthe dielectric constant of the solvent.For the onc-dimensional problem of twD . C H A N , T . W . HEALY A N D L. R . WHITE 2847charged flat surfaces at z = 0 (hereafter referred to as surface 1) and at z = L (surface2) interacting across the electrolyte, eqn (2.13) can be written as :d2$ 4ne - - - - - nivi exp (- evi$/kT).dz2 E iThis has to be solved with the usual boundary conditions(2.14)(2.15)(2.16)According to eqn (2.7) the surface charges ol, o2 are functions of the surface potentials11/1, $2 when we have dissociation equilibrium at the surface.The exact forms ofthe functions are determined by the dissociation constants of each surface and thebulk concentration of PDI.A first integral of (2.14) yields :8nkT C ni [exp (- ev,$/kT) + C ] . (2.17)Applying the boundary conditions, we get two equations for the surface potentials11/2 and the constant of integration C :(2.18)(2.19)We observe that if electrical neutrality were to be preserved in the limit of smallseparations we must either have o1 = -cZ or o1 = 0 = o2 as L-0. In either case,both surface potentials must become the same in this limit. Further if both o1 02+0as L-+O both surface potentials must approach their own Nernst values [eqn (2.8)],and this is only possible when both surfaces have the same pzc (pH,) but differentApK's (to remain as dissimilar surfaces at infinity).The repulsive pressure between the plates (P > 0 implies repulsion) can be writtenin the physically perspicuous form :zWe can now use eqn (2.17) giving :whereP = -2nkT(C+ 1)n = 5 C ni.1(2.20)(2.2 1)(2.22)It is well known* that the second integration of the PB equation requires a know-(i) C < - 1 (i.e., P > 0 repulsive) (2.23)(ii) ICl < 1 (i.e., P < 0 attractive) (2.24)or (iii) C > 1 (i.e., P < 0 attractive) (2.25)'* see for example ref.(4), (9, (lo), (12) and (15).ledge of whethe2848 ELECTRICAL DOUBLE LAYER INTERACTIONSbecause the integration procedure is different for each case.Therefore, a thirdrelation between $2 and C can be obtained. This, together with eqn (2.18) and(2.19) would enable us to obtain a complete solution of the problem.Before proceeding further, we shall make one simplifying assumption by con-sidering only the case of a 1 : 1 electrolyte. The PB eqn (2.14) now takes on thesimpler form :8nne 3- - sinh (et+blkT).dz2 E(2.26)A moment’s reflection will reveal that only the three types of solution illustrated intable 1 are allowed. These results will be useful in later discussions.TABLE EXAMPLES SHOWING THE THREE TYPES OF SOLUTIONS ALLOWED BY THE POISSON-BOLTZMANN EQUATION TOGETHER WITH SOME GENERAL RELATIONS BETWEEN d AND $I.Like charges and like potentials11. Unlike charges and like potentials111. Unlike charges and unlike potentialsd2$ At $ = -2 = 0.dxFor notational convenience, we introduce the reduced potentialy = e$/kTthe Debye screening parameter= (!!Tthe dimensionless constanti = 1,2 K N s i yi = -4n ’(2.27)(2.28)(2.29D . CHAN, T. W. HEALY AND L . R. WHITE 2849withNI1000n = -where I is the ionic strength in mol dm-l and Nis Avogadro’s number. The subscripts1,2 will refer, as before, to surface 1 and 2. Eqn (2.18) and (2.19) can now be writtenin the form :ql(yl)= -+(C+ 1) = t(cosh y1 - l)-yia;(yi) = sinh2(y1/2)-y~cc~(y,) (2.30)q2(y2) = - +(C+ 1) = sinh2(y2/2) -y2a$(y2) (2.3 1)where [cf.eqn (2.5) and (2.8)](2.32)Since the pressure must be the same on both surfaces, the relationYl(Yl> = qz(y2) (2.33)must hold for the functions yl, y2 defined by the above equations.The key to solving the problem of interacting dissimilar amphoteric surfaces liesin understanding the interplay between the curve sinh2(y/2) and the charge curvesy2a2(y), of each surface. Therefore, it is important that we systematically characterizethe manner in which these curves intersect each other. To begin with, let us plotsinh2(y/2) and y2a2(y) as a function of the surface potential y. [Subscripts 1 and 2will be suppressed when we are considering a general surface. The surface potential yunder consideration should not be confused with the potential at some generalposition y = y(z).] This is shown schematically in fig.1. We have shown, withoutFIG. 1.-A schematic plot of the functions sinh2(y/2) (broken curve) and y2a2(y) (solid curve)showing the points of interaction between these curves, and the regions where the function ~ ( y ) andthe surface charge CT is positive or negative.loss of generality, values of the concentration of PDI such that the Nernst potential,yN, is positive and we observe that the quantity ApK [eqn (2.10)] is a measure of thewidth of the charge curve. For ease of later discussions, it is useful to adopt thefollowing nomenclature. Since q(y) and hence the pressure is the (vertical) differencebetween the two curves, we can delineate regions where y > 0,O > y > - 1, y < - 1corresponding to cases (i), (ii) and (iii) in eqn (2.33) to (2.25).We label the point2850 ELECTRICAL DOUBLE LAYER INTERACTIONSof intersection between the two curves (where q = 0) as a, b, c and d with thecorresponding potentials ya, y b , yc and yd. The point a is defined as the intersectionwhere ya falls between the origin and the Nernst potential yN. Points b and c arethe intersections where Yb and y , have the same sign as yN. Under some circum-stances there may be no intersections b and c or the points b and c may coincide.The point of intersection on the opposite side of the origin to yN is labelled d.For a single surface in equilibrium with a bulk solution containing a givenconcentration of PDI, there is no net force exerted on the surface.Therefore thepressure P is identically zero, that is, q = -$(C+ 1) = 0. Of the four points whereq = 0, only point a, where the surface charge and the surface potential have the samesign, satisfies the PB equation. [This multiplicity of solution does not arise if werealize that since (C+ 1) = 0, we can take the appropriate square root of eqn (2.30),say, and the resultant expression then only has one root.] Thus we obtain the generalresult that the surface potential of an isolated amphoteric surface always lies betweenzero and the Nernst potential. The only occasion when ya equals zero is when theNernst potential is zero. That is, the concentration of PDI is at the point-of-zero-charge, pH = pHo and a = 0.To study the electrostatic interaction between two dissimilar amphoteric surfaces,we need to examine the functions ql(yl) and q2(y2) given in eqn (2.30) and (2.31).This is best accomplished by plotting (schematically) the two charge curves r;al(y),yiaz(y) and the function sinh2(y/2) on the same graph.See for example fig. 2 (a) and (b).We define y* to be the potential corresponding to that point of intersection of thetwo charge curves which falls in between the Nernst potentials y,, and yN2.FIG. 2.-Typical arrangements of charge curves for like (a) and unlike (b) surfaces.The state of surface i (i = 1,2) can be identified with the coordinate (yi, a,).However, the values of the surface potential t,hi = kTyi/e and the surface charge aicannot vary independently as they are related by eqn (1.7) or (1.8).In other words,the state of each surface must correspond to some point (y, a) on its own chargecurve y2a2(y). As the surfaces approach each other, changes in the charge andpotential at each surface due to the interaction can be envisaged as movements ofthese points along their own charge curves. Since the surfaces are interacting, theloci of these two points must be correlated. Firstly, the movement of these pointsmust ensure that eqn (2.33) [cf. eqn (2.30) and (2.31)] is satisfied. Secondly, thevalues of y , and y 2 must satisfy the PB equation. That is, the relationship betweeD . CHAN, T. W. HEALY AND L. R . WHITE 285 1the charge and potential at each surface and between surfaces must fall within oneof the three types listed in table 1.Thus it is possible to obtain a description of thebehaviour of the repulsive pressure, surface potential and charges as a function ofseparation by considering the charge curves y;al(y), $a;(y) and the function sinh2(y/2).Most of the results we are about to describe can be deduced from the fact thatsinh2(y/2) increases monotonically as I y I increases and that the charge curves y2a2(y)have an absolute minimum at y = yN.Before proceeding to an analysis of the interaction between like and unlikesurfaces it is important to note that the preceding formulation makes no comment onthe rate at which surfaces can regulate when H+ and OH- or any other ions areinvolved in surface equilibria. It is, however, directly applicable to increasingnumbers of direct measurements of interaction where the surfaces are brought togethervery slowly and/or where assemblages of particles are forced together slowly incompression experiments.As to whether H+/OH- equilibria can readjust in thetime of Brownian collision awaits more experimental testing.3 . THE INTERACTION BETWEEN LIKE SURFACESWe have already shown in Section 2 that the surface potential of a single surfacein isolation falls between zero and the Nernst value. Here we consider only thosevalues of the bulk concentration of PDI where the Nernst potentials of each surfacehave the same signs. That is, both surfaces have the same sign of the charge atinfinite separation. For the purpose of this analysis, we can assume without lossof generality that the surfaces are both positive and that surface 1 has a lower Nernstpotential, i.e., yNi < yN2.(In fact, by reversing the sign of the Nernst potentials,negative surfaces can be " transformed " into positive ones and the following analysiswill be applicable.)For the interaction of surfaces having like signs of infinity, there are three distinctcases classified by the number of times that the repulsive pressure curve changes sign.Each is in turn determined by the position of y* as follows (with L designating likesurfaces) :case L1 : y* < Yblcase L2 : Ybl < y* < y c ,case L3 : ycl < y*.We shall consider each of these separately.3a. CASE L1chtoisThe appropriate charge curves for this case are given in fig.3 (a) and (b). The.aracteristic feature of these sets of curves is that y* (the potential correspondingthe intersection of the two charge curves that falls in between the Nernst potentials)< Ybl. This case also includes the situation where surface 1 (defined to bethe one with the lower Nernst potential) does not have the intersection points bl andC1.Since the arguments involved in deducing the behaviour of the surfaces are rathertedious, we shall first summarize the results. The (schematic) variations withseparation for the repulsive pressure P, surface charge and potential of each surfaceare given in fig. 4 (a) and (b).(i) In case L1, the interaction is always repulsive, P > 02852 ELECTRICAL DOUBLE LAYER INTERACTIONSFIG.3.--(u), (b) Arrangements of charge curves between like surfaces [surface 1-solid curve, surface2-dotted curve, and sinh2 (y/2)-dashed curve] that correspond to Case L1.(ii) If the function I(yl) has a maximum in the range yal < y1 < y*, then the pressurehas a maximum (Pmax) at y1 = j1 say, where J1 2 yNI [fig. 4 (a)] ; otherwise thepressure increases monotonically from zero at infinite separation to the finalvalue P* at zero separation [fig. 4 (b)].(iii) At zero separation, the surface potentials are equal and the surface charges areequal in magnitude but opposite in sign (cf. discussion in Section 2).The results summarized in fig. 4 can be deduced from fig. 3 if we bear in mindthe discussion in Section 2 regarding the charge curves.We shall briefly summarizethe main points :(A) The surface charge and potential of each surface is related to each other by eqn(2.7) or (2.8). A state of the surface, i.e., (y, a), can be represented by a pointon the charge curve y2a2(y).(B) Changes in the surface charge and potential due to interaction are described bythe movement of this point along the charge curve.(C) The loci of the points for each surface must together satisfy eqn (2.33) and thePB equation (cf. table 1).(D) The function sinh2(y/2) increases monotonically as I y I increases and similarlyy2a2(y) is a monotonic increasing function of 1 yN -7 I.Using (A)-(D) above we now demonstrate how the results from fig. 4 (a) can bededuced from fig. 3 (a) and (b). When the surfaces are far apart, we have already shownin Section 2 the potentials of surface 1 and 2 are yal and ya2 respectively.Referringto the charge curves, we say surface 1 is at the point a, and surface 2 is at a2. Wefirst consider the case shown in fig. 3 (a) where yaz > yal. We defineand observe that the surface charges at infinite separation cl(yal), 02(ya2), obey therelationsbut ol(ya,) can be > or <a*.As the surfaces approach each other and just begin to interact, we know, by theoverlap approximation that the surface potentials must increase and the interactiona" = o,(y*) = -o,(y*) (3.1)o Z ( ~ a 2 ) > a", ol(YaJ (3.2D . CHAN, T. W. HEALY AND L. R. WHITE 2853is repulsive. That is P > 0, yl(yl) = q2(y,) > 0 [cf. eqn (2.21), (2.30)-(2.33)].Therefore, each surface would move along its own charge curve towards its respectiveNernst potential.While the surface potentials increase, the surface charges decrease.This minimizes the interaction energy. As the surfaces approach the rate of changeof the charge and potential of each surface with separation (i-e., the velocities alongthe charge curves) must of necessity be different since the equality yl(yl) = y2(y2)must be maintained at all times.v) E n E! nPY - Y -N2 f\ N20 0(u) (b)FIG. 4.-(u), (b) Schematic results showing the different possible variations of the repulsive pressure,surface potentials and surface charges with plate separation for Case L1 (surface 1-solid curves,surface 2-dashed curves).We assume that the function ql(yl) has a maximum between y,, and y*(ya, <y , < y*) ; at J I say.It is clear from point (D) above that jjl is between yN1 and y*(yNI < j? < y*). Now, as the separation between the surfaces decreases, both sur-faces would move closer to their Nernst potentials. When surface 1, which has thelower Nernst potential, reaches yN1 where its charge has decreased to zero, surface2 is still below its Nernst value with a finite and positive surface charge.As the separation further decreases, the potential of surface 1 continues to increasebeyond yNl, but with a surface charge of opposite sign to that at infinity (cf. fig. 1).When surface 1 reaches jjl where ql(yl) has a maximum, surface 2 is at jj2 whereyl(jjl) = y2(jj2). Again from point (D) we can deduce thaty* 72 yN22854 ELECTRICAL DOUBLE LAYER INTERACTIONSAs surface 1 proceeds beyond J1 towards y*, ql(yl) can only decrease.Hencesurface 2 must retrace its path along the charge curve from j 2 and approach y* fromabove. Therefore surface 2, which has the higher Nernst potential, never reachesyN2 and so its surface charge always retain the same sign as that at infinite separation.Now both surfaces must reach y* at the same time because ql(y*) = qz(y*).Here we have rfa?(y*) = yga$(y*) and the potentials are equal but the charges areequal and opposite. The surfaces cannot proceed beyond y* as this would violatethe PB equation (cf. type 11, table 1). Clearly, the boundary conditions y1 = y2,o1 = -02 can only be attained when the separation between the surfaces is zero.The above results are summarized in fig.4 (a). The variations with separationof the charge and potential of surface 1 are given in solid lines, and those of surface 2in dashed lines.(iv) for interactions between surfaces having like signs at infinity, the surface withthe lower Nernst potential would always reach its Nernst potential and reversesthe sign of its surface charge while the other surface never changes sign.Obviously, this excludes the degenerate case where both surfaces have the sameNernst potential. In this instance, neither surface charge changes sign.Now it is possible for surface 2, which by definition has the higher Nernst potential,to have a lower surface potential than surface 1 when they are far apart [see fig.3 (b)].It is clear from the figure that the surface charges at infinity obey the inequalitiesIt will be shown that :ol(Ya,> > a,(ya2) >If ql(yl) has a maximum in y,, < y1 < y*, the results for surface 2 are given in dottedlines in fig. 4 (a). These can be derived using the arguments given above. The onlynoticeable differences between this case (yaz < y,,) and the previous case (ya2 > yal)are the cross-over points between the charge and potential curves. These must occurwhen both o1 and 0, are greater than o*. The behaviour of the repulsive pressureand the properties of surface 1 remain essentially the same for both cases.If ql(yl) does not have a maximum in the range yal < y1 < y*, the interaction isstill repulsive but there are no turning points in the pressure, potential and chargecurve [fig.4 (b)]. The arguments needed to deduce these results follow along the lineof those given above. The results pertaining to surface 1 are given in solid curves.If y,, > y,, (yNI > yNi) the charges at infinite separation satisfy02(yaJ > u*, ol(yaJbut al(y,,) can be greater or less than o*. The charge and potential for surface 2 forthis case are given in dashed lines.Here~l(ya,) > 0 2 ( ~ , , ) > o* and the cross-over points in the potential and charge mustoccur when the charges of surfaces 1 and 2 are > cr*.When the Nernst potentials are very far apart [fig. 3 (a)], the pressure may exhibita local minimum after the maximum.However, the pressure still remains positivefor all separation. The charges and potentials will have corresponding maxima andminima.In the degenerate case where the surfaces have the same Nernst potential (i.e.,the same pzc), e.g., identical surfaces, then y* = yN, = yN2 and neither surface changessign. The surface potentials start off at y,, and y,,, and increases monotonicallytowards their Nernst values. The surface charges decrease monotonically to zero.At zero separation, both potentials are equal and surface charges are reduced to zero.If JJa, < yal (yNz < yN1) the results for surface 2 are given in dotted linesD . CHAN, T . W. HEALY AND L . R . WHITE 2855ItwhenThis important to note that significant changes in the pressure etc.only occurthe separation is within the Debye screening length l / ~ .is completes the discussion on the various possible types of behaviour undercase L1.3b. CASE L2The appropriate charge curves for this case are shown in fig. 5 (a). The character-istic feature of this set of curves is that :Ybi Y* < YCI.The variations with separation of the repulsive pressure P, surface potentials andcharge of each surface are given in fig. 5 (b), (c).Io r 0-(b) (c)FIG. 5-(a) The arrangement of the charge curves for like surfaces Case L2 (surface 1-solid curve,surface 2-dotted curve, sinh2(y/2)--dashed curve) ; (b), (c) schematic results showing the possibleways which the repulsive pressure, surface potentials and charges can vary with separation (surface 1-solid curves, surface 24ashed curves)2856 ELECTRICAL DOUBLE LAYER INTERACTIONSIn case L2 the interaction is initially repulsive (P > 0) but becomes attractive(P < 0) at smaller separations. If rl(yl) has a minimum between y b l and y* thenthe pressure has a local minimum Pin < 0 at y1 = F1 and y 2 = F2 say, whereLet us now deduce the results from the charge curves in fig.5. As with case L1,surfaces 1 and 2 start at a, and a2 respectively, and move along their charge curvestowards their Nernst potentials as the surfaces approach. Clearly ql(yl) has amaximum at some yl where yNI < J 1 < ybr' This maximum corresponds to themaximum in the repulsive pressure. Thus as the potential of surface 1 increasesfrom yal to yN1 and then onto jjl, its surface charge decreases to zero at yI = yN1 andchanges sign between yN1 and pl.Meanwhile the potential of surface 2 increasessteadily from ya2 to 7, where q2(jj2) = ql(jjl) while the charge decreases from a2(ya2)to 0,(jj2). Since jj2 < yN2, the sign of the charge on surface 2 does not change.As surface 1 now moves from j j , to y b l , rl(yl) can only decrease; thereforesurface 2 must return along its charge curve towards ya, increasing the charge anddecreasing the potential. When surface 1 reaches the point b,, surface 2 reaches a2whereby rl(Ybl) = 0 = q2(yar) and the pressure is zero at this point.Between Yb, and y*, q1 = q2 is negative which corresponds to attraction. Now-Y z Y*.IVIseparationFIG.6.-(a) The arrangement of the charge curves for surfaces having like signs at infinity, Case L3(surface 1-solid curve, surface 2-dotted curve, sinh2(y/2)--dashed curve) ; (6) schematic resultsof the variation of pressure surface potentials and charges with separation (surface 1-solid curves,surface 2-dashed curves)D . CHAN, T . W . HEALY A N D L . R . WHITE 2857ql(yl) may have a minimum (i.e., Iql(yl)l a maximum) for yb, < y1 < y*. If this isindeed the case, the pressure will have a minimum turning point [see fig. 5 (b)].Corresponding to this, the potential of surface 2 will decrease below y* and finallyapproaches y* from below. There will be a similar turning point for the charge onsurface 2.If ql(yl) does not have a minimum in Ybl < y 1 < y* the pressure just decreasesmonotonically after turning attractive [see fig. 5 (c)].Similarly the extra turningpoints in y2 and cr2 would not occur.From fig. 5 we obtain the following inequalities which hold for all separations :Y2 > Y19 0 2 > 61and when the surfaces are far apart :Ya2 > Y* > Yalg* > o z ( ~ a 2 ) > 01(~al)*3C. CASE L3The charge curves pertaining to this case are given in fig. 6. They are characterizedby the inequality y* > ycl. The variations with separation of the repulsive pressure,surface potential and charge of each surface are given the same in fig. 6 (b). Theseresults can be derived from the charge curves by a similar consideration to that givenin the previous two cases.In case L3 the interaction is initially repulsive (P > 0), then it turns attractive(P < 0) and finally becomes repulsive again as the separation decreases from infinityto zero.We note that if Pax < P* then the potential (charge) curve of surface 2 wouldnot extend above (below) y* (o*) at the corresponding turning point.4. THE INTERACTION BETWEEN UNLIKE SURFACESIn this section we consider those values of the bulk concentration of PDI wherethe signs of the Nernst potentials are different.This means that when the surfacesare far apart, the surfaces have different signs. Given two unlike surfaces, we canalways make a transformation (e.g., reversing the signs of the potentials) so thatsurface 1 (yal) is initially negative, surface 2 (Ya2) is positive and that y* is also positiveas well.[See for example fig. 2 (b)].First let us define the nomenclature useful in describing how the charge curveof surface 1 (the negative surface) intersects with the curve of sinh2(y/2). This isdone in fig. 7. Depending on the value of yN1 and ApK of surface 1 it is possiblethat onIy one of the points dl, el and fl exists. In this case we label this one pointas dl.In general there are four distinct cases where the interactions are different. Againthese are classified by the number of times the repulsive pressure changes sign whenthe separation varies from zero to infinity. These cases are determined by the positionof y* and hence by the relative position and shape of the charge curve of surface 2(the positive surface).Each case is defined as follows (with U designating unlikesurfaces) :Case U1. 0 < y* < YdtCase U2. yd, d y* < yelCase U3. yel < y* < yflCase U4. yfl d y*2858 ELECTRICAL DOUBLE LAYER INTERACTIONSY q YdlFIG. 7.-Showing the relative positions between the functions sinhZ (y/2)-dashed curve, the chargecurve of surface 1-solid curve, and of surface 2 4 o t t e d curves, for surfaces having different signsat infinite separation. The Cases U1 to U4 are indicated.I.."\&,/--'---a*5 '* \pmaxi separation i&=-FIG. 8.-(a)-(d) Schematic results for the variation of the pressure, surface potentials and charges forcurves U1 to U4 respectively (surface 1-solid curves, surface 2-dashed curves)D.CHAN, T . W. HEALY AND L . R. WHITE 28 59We shall only outline how the given results can be deduced from the charge curvefor cases U1 and U2. The results of the other cases should be self-evident.4Q. CASE u1In case U1, where 0 < y* < y d l , the interaction is always attractive (P < 0).The behaviour of the repulsive pressure, the surface potential and charge aresummarized in fig. 8 (a). The results for surface 1 are given in solid lines, and forsurface 2 in dashed and dotted lines. Referring to the curves for case Ul in fig, 7we can deduce these results.When the surfaces are far apart, surface 1 is at a l and surface 2 is at a2. Asthey approach each other, we know (e.g., by the overlap approximation) that theinteraction is attractive, i.e., P < 0, ql = q2 < 0, and the surface potentials mustdecrease in magnitude.These conditions can be satisfied if both surfaces movealong their charge curves towards y = 0. This way the interaction energy is mini-mized (i.e., maximize attraction) by making the positive surface (2) more positiveand the negative surface (1) more negative.We observe that if ql(yl) has a minimum (Iql(yl)l a maximum) for some y1(0 < J1 < y*) then there would be a minimum in the pressure and correspondingturning points in the potential and charge of surface 2-see dashed lines in fig. 8 (a).Otherwise, all quantities are monotonic in the separation (dotted lines).We note that since j j 2 , where ql(yl) = q2(jj2), is always positive, the potentialof surface 2 never changes sign.(This is in fact true in all cases of interactionbetween unlike surfaces.) On the other hand, the potential of surface 1 alwayschanges sign. It is worthwhile noting here for cases U2-U4 that y 2 cannot riseabove yN2 ; therefore, the charge of surface 2 also retains the same sign (positive).At zero separation, the potentials are equalY1 = Y* = Y2and the charges are equal and opposite6 2 = 6" = - 6 1 > 0.4b. CASE U2In case u 2 (ydi < y* < yel) the interaction is initially attractive (P c 0) but wouldeventually turn repulsive.Initially the surfaces start at yal and y,, and move towards y = 0 (cJ: case Ul)and the interaction is attractive. Since ql(yl) has a minimum for 0 < y 1 < ydt therewill be a minimum in the pressure and a corresponding turning in the potential ofsurface 2.When surface 1 changes sign and reaches ydl from below, yz returns toy,,. Here the pressure is zero [ql(ydl) = 0 = q2(ya2)].When surface 1 now moves from ydl to y* the interaction becomes repulsive.If ql(yl) has a maximum between y d l and y* the potential of surface 2 will increasepast y" and then return to approach y* from above. There will also be a similarmaximum in the pressure curve (see dashed curves). If ql(yl) does not have thismaximum there would not be a final turning point for y 2 and P (see dotted curves).The results are summarized in fig. 8 (b).Again at zero separationY2 ' 0 y1 = y* =6 2 = Q* = -61 > 0.an2860 ELECTRICAL DOUBLE LAYER INTERACTIONS4C. CASE u3In case U3 (yel < y* < yf,), the interaction is at first attractive, then turnsrepulsive and finally becomes attractive again.The variations with separation of the potential and charge of surface 1 are givenin solid lines in fig.8 (c). If q1(y1) has a minimum (Iql(yl)l a maximum) for y1between yel and y* the behaviour of the pressure and the surface potential and chargeof surface 2 are given the dashed lines; otherwise the results in the dotted portionswould hold.We note that if Pmin is less than P* then the potential (charge) of surface 2 wouldextend below (above) y* (a*) at the corresponding turning point.4d. CASE U4Case U4 is characterized by the condition that yfi < y*.The behaviour of the pressure, surface charges and potentials are illustrated infig.8 (d)-solid lines for surface 1, dashed lines for surface 2.~~ ~ ~~case like charge & potentio I unlike charge&potentiolI II I II2repulsive-attractivePatt roc tive -repulsiverepulsive attractiveIn the degenerateFIG. 9.-A summary of the possible variations of the pressure with separation under the differentpossible cases consideredD. CHAN, T. W. HEALY AND L . R. WHITE 286 1case where points el and fl do not exist, the portions of the curves indicated by dottedlines should hold for the various quantities.If Pax > P* the corresponding turning points for y 2 and o2 will extend beyondy* and Q*.This completes the discussion of all possible types of double layer interactionsbetween dissimilar amphoteric surfaces under regulated interaction.Although theabove discussion cannot yet give the actual values of the pressure and potentials, etc.,relative magnitudes of the surface potentials and charges and all the interestingfeatures of the pressure curve can be elucidated.Before we proceed, it is worthwhile to summarize the results discussed so far.This is accomplished in fig. 9 where all possible variations of the pressure as a functionseparation is given schematically for the various cases of like and unlike surfaces atinfinity. Here positive pressure represents repulsion.To obtain numerical results, we need to solve the PB equation. We show howthis can be done in the next section. It is important to stress, however, that thegraphical techniques that we have summarized give directly the form of the pressure-distance curve and key points on the curve (e.g., zero, minimum or maximum pressurepoints) can also be located directly.5 .METHOD OF SOLUTIONFor a 1 : 1 electrolyte, the first integral of the PB eqn (2.17) has the form '("'r 2 dz = rc2(cosh y + C).To obtain a second integral, we need to know the value of the constant of integrationC. The solutions, in terms of Jacobi elliptic functions or elliptical integral^,^'^ 28 aredifferent, depending on whether(i) C < - 1, (ii) 1 Cl < 1, or (iii) C > 1. These solutions are well known and theycan be written in terms of the reduced variablewhere 4, = 4(zo) and at z = zoHere zo can be inside or outside the range z = 0 to L.(ii) [Cl < 1 Attractive1-+"4 - (';">" sd ( KIZ-Z& (1;c)+) - , 1+) -where at z = zo, the potential $(zo) = 0, that is &, = (z,) = 1 .(iii) C > 1 Attractive(5.52862 ELECTRICAL DOUBLE LAYER INTERACTIONSHere K(k) is the complete elliptic integral of the first kind of modulus k.The constantC is given byc = +(#);+402) (5.7)and at z = zo, $(z0) = 0.0 to L, it is convenient to write the solution in the formEqn (5.7) is suitable for 0 < zo < L. For zQ outsidewhere 41 = #)(z = 0). In eqn (5.3), (5.9, (5.6), (5.8) and (5.9) cd(x;k), sd(x;k)and sc(x;k) are Jacobi elliptic functions of argument x and modulus k, sc-l is theinverse function of sc with the same modulus. These solutions match up at thetransition points C = f 1, as expected.From eqn (2.30)-(2.32) we can solve for values of the surface potentials at C = - 1,I , i.e., at y1 = y12 = 0, - 1.Putting the appropriate values of the reduced potentialsand $2 at C = - 1 (ql = y2 = 0) into eqn (5.3) we can eliminate zo to give(5.10)The length (I,),= - is the value of the separation where the transition from C c - 1to ICl < 1 takes place, that is, where the pressure changes from positive to negativeor vice versa.Further from eqn (2.30)-(2.32) we can obtain the potential of surfaces 1 and 2at C = 1 that is where q1 = -1 = y2. Using these values in eqn (5.5) and settingC = 1, we can eliminate zo to get(5.1 1) F2 = f [( I - F:)+ sin(lcL) p1 COS(KL)] for L 5 z,where(5.12)This gives us the separation where the transition from ICl < 1 to C > 1 occurs.Hence, given the dissociation constants for each surface, the bulk concentrationof PDI and the ionic strength, we know which of the types of solutions (i), (ii) or (iii)to use for a given value of the separation L.This then gives us a complete solutionof the problem. The qualitative descriptions given in the previous sections willenable us to keep track of the signs and relative magnitudes of the potentials andcharges. Further it also helps in determining the position of zo, that is, whetherzo < 0, 0 < zo < L or zo > L, and choose the appropriate solutions for the casesICl < 1 and C > 1.6 . DISCUSSIONIn practical situations, the dissociation constants of the surfaces arc fixed, onlythe concentration of PDI can be varied (provided the particles do not dissolve atextreme concentrations of PDI!).In terms of the charge curves, this means that therelative positions of the two Nernst potentials are fixed. Any variations in theconcentration of PDT merely shift both charge curves relative to sinh2(y/2) by thD . CHAN, T. W . HEALY AND L . R. WHITE 2863From the definition of the Nernst potential (assuming H+ are the same amount.PDI)YN = 2.303 ('Ho-pH) = 2.303 ApH, (6.1)we see that yN is proportional to the change in pH. Therefore, for like (positive, say)surfaces the effect of decreasing pH can be described by the curves in fig. 10 (a), (b).PH2 case L2repulsioncase L1 PH1 case L1(c) (4FIG.10.-Showing the effects of bulk pH on determining the case which interaction should take placefor two arrangements of the charge curves (surface 1-solid curve, surface 2-dotted curve). Theeffects of changes in pH is indicated as a relative displacement of the curve sinh2(y/2) (dashed curves)with respect to the two charge curves. (See text).In fig. 10 (a), y,, and yN2 are close together. As pH increases we pass from case LZ(pH,) to case L2 (pH,). However, wheny,, and y,, are sufficiently far apart, fig. 10 (b),we pass from case L1 (pH,) to case L3 (pH,) to case L2 (pH,) as pH increases.Clearly we can only consider pH values smaller than the pzc of surface 1 (thesurface with the lower pzc) otherwise we would not have like positive surfaces ! Thuson a plot of pH against separation, we can construct regions where the interaction isattractive or repulsive.In fig. 10 (c), (d) we have constructed such diagrams COT-responding to the situation in fig. 10 (a), (b). The lines delineating the attractive andrepulsive regions can be obtained from eqn (5.10) for various pH values. Noticethat when we are at the pzc of surface 1, the interaction is always attractive.We have developed a method whereby we can analyse the main features of theforce curve due to double layer interaction between two dissimilar amphotericsurfaces under dissociation equilibrium. The resultant free energy of interactionmust of necessity be the lowest possible, since equilibrium is assumed to be maintainedthroughout the approach of the particles.Depending on the characteristics of eachsurface, it is possible to obtain force barriers and minima in the repulsive pressurefrom just the electrostatics alone. When combined with the contributions from vander Waals interactions (which in itself may be repulsive and/or attractive) to form th2864 ELECTRICAL DOUBLE LAYER INTERACTIONStotal force curve needed in DVLO theory of colloid stability, very interesting interplaybetween these two contributions may be observed.We have only used the Gouy-Chapman model for the double layer so we do notexpect the present theory to be a good description of real systems. Several successfulmodels have been proposed to describe the inner region of the double layer at ampho-teric surface^.^^'^^ These models also use the concepts of surface dissociationgiving rise to the surface charge.In addition, new effects such as the binding of inertions or the existence of a gel layer have been included. These new features are inthemselves charge and potential regulating. Thus by using the Gouy-Chapmanmodel, we have embraced all the basic physical principles behind regulated interaction.The main features predicted here are essentially correct.When the collision time is too fast for the surfaces to regulate, the constant chargeapproximation then becomes valid. Here the charge curves are horizontal (constantcharge for all potentials). At constant charge, we expect the interaction betweensurfaces with(i) like charges to be always repulsive(ii) unlike charges to be attractive at large separations and repulsive at smallseparations-except when the surfaces have equal and opposite charges wherethe interaction is then always attractive.The pressure will always diverge at small separations except for the “equal andopposite situation ” where it remains finite.When the regulation of potential is perfect, i.e., constant potential, the chargecurve is essentially an infinitely narrow “ V ’’ centred at the Nernst potential.Thereare no saturation plateaux when the potential is far from the Nernst value. Underconstant potential interaction, surfaces (at infinity) with(i) unlike potentials will always attract(ii) like (but not identical) potentials will repel at large separations and attract atsmall separations.Identical surfaces however will always repel.Of the various cases given for interaction between like and unlike surfaces underregulation, case L3 for like surfaces and cases U3 and U4 for unlike surfaces [fig. 6,8 (c), (d)] cannot be predicted by the constant potential of constant charge approxima-tion. If the equilibrium interaction is possible these cases may be observable.Two of us (D. C. and L. R. W.) acknowledge the award of postgraduate scholarshipsWe also acknowledge financial support at the Australian National University.from the Australian Research Grants Committee for part of the work.See for example, C. Y. Chen, Chem. Rev., 1955, 55, 595, for a review on the experimental andtheoretical aspects of fibrous beds.K. W. Sarkes, Ph.D. Thesis (Australian National University, Canberra, Australia, 1972).B. A. Pethica, Exp. Cell Res. Suppl., 1961, 8, 123.4B. V. Deryaguin, Disc. Farad. SOC., 1954, 18, 85. ’ 0. F. Devereaux and P. L. deBruyn, Interaction of Plane Parallel Double Layers (M.I.T. Press,Cambridge, Mass., 1963).R. Hogg, T. W. Healy and D. W. Fuerstenau, Trans. Faruday Soc., 1966, 62, 1638.K. J. Ives and J. Gregory, Proc. Soc. Water Treat. Exam., 1966, 15,93.G. M, Bell, S. Levine and L. N. McCartney, J. Colloid Interface Sci., 1970, 33, 335.a G. R. Weise and T. W. Healy, Trans. Faraday Soc., 1970, 66,470.lo G. M. Bell and G. C. Peterson, J. Colloid Interface Sci., 1972, 41, 542.l 1 V. A, Parsegian and D. Gingell, Biophys. J., 1972, 12, 1192.l 2 U. Wsui, Recent Prog. Surface Memb. Sci., 1972, 5, 223D . CHAN, T. W. HEALY AND L . R. WHITE 2865l3 U. Usui, J. Colloid Interface Sci,, 1973, 44, 107.l4 G. Kar, S. Chander and T. S. Mika, J. Colloid Interface Sci., 1973, 44, 347.l5 H. Ohshima, Colloid Polymer Sci., 1974, 252,257.l6 N. E. Hoskin and S. Levine, Phil. Trans. A., 1956, 248,449.l7 G. Frens and J. Th. G. Overbeek, J. Colloid Interface Sci., 1972, 38, 376.'* A. Bierman, J. Colloid Sci., 1955, 10, 231.l 9 S. Levine and G. M. Bell, J. Colloid Sci., 1962, 17, 838.2o S. Levine and G. M. Bell, J. Phys. Chem., 1963, 67, 1408.21 S. L. Brenner and D. A. McQuarrie, J. Colloid Interface Sci., 1973, 44, 298.22 S. L. Brenner and D. A. McQuarrie, J. Theor. Biol., 1973, 39, 343.23 S. L. Brenner and D. A. McQuarrie, Biophys. J., 1973, 13, 301.24 D. Chan, T. W. Healy, J. W. Perram and L. R. White, J.C.S. Faraday I, 1975, 71, 1046.25 B. W. Ninham and V. A. Parsegian, J. Theor. Biol., 1971, 31,405.26 D. Chan, T. W. Healy, L. R. White and D. E. Yates, J. Electroanalyt. & Interfacial Electro-27 M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, N.Y., 1965).28 E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge U.P., London,29 J. W. Perram, R. J. Hunter and H. J. L. Wright, Austral. J. Chem., 1974, 27, 461.30 D. E. Yates, S. Levine and T. W. Healy, J.C.S. Faraday I, 1974, 70, 1807.31 S. Levine and A. L. Smith, Disc. Furday SOC., 1971, 52,290.chem., 1976, in press.1969).(PAPER 6/004

ISSN:0300-9599    

DOI:10.1039/F19767202844

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Acidic Dissociation Constants of Malonic Acid in 50 MassPercent Ethylene Carbonate+ Water from 20 to 55°CBY J. C. HALLET and ROGER G. BATES*Department of Chemistry, University of Florida,Gainesville, Florida, U.S.A.Receiced 1st March, 1976The first and second acidic dissociation constants of malonic acid in 50 mass % ethylene carbonate+water solvent have been determined at eight temperatures from 20 to 55°C by e.m.f. measurementsof cells without transference. The results have been used to derive the standard changes of enthalpy,entropy and heat capacity for the two dissociation processes in the mixed solvent. It was foundthat K l / R z is -2700 in the mixed solvent, compared with -700 in water. There is evidence thatthe addition of the aprotic component to the solvent stabilizes the internal hydrogen bond in theprimary anion.In continuing studies of the effect of dipolar aprotic constituents in binary solventmixtures on specific ion-solvent interactions, we have examined the thermodynamicbehaviour of hydrochloric acid and acetic acid in the 50 mass % mixture of ethylenecarbonate (EC) and water.These studies covered the temperature range 20 to 55°C.This solvent mixture has a dielectric constant similar to that of water, ranging from83.5 at 20°C to 76.5 at 55"C.l The activity coefficient of HCl in the EC+H20 sol-vent was found to be nearly the same as in the pure aqueous solution, but the pKforacetic acid is higher by -0.9 unit. The latter finding suggests that the addition of theaprotic constituent to the solvent brings about a reduction of the solvation stabiliza-tion of the hydrogen and acetate ions.Following these studies, it appeared to be ofinterest to ascertain the influence of this change in solvent composition on the ratioKJK2 for a diprotic acid and on the possible internal hydrogen bonding in the acidanion.3 Malonic acid was chosen for the study; its dissociation constants and therelated thermodynamic quantities have already been determined in water. 3*The first and second dissociation constants of malonic acid (H,Mal) in EC + H20mixed solvent were determined from e.m.f. measurements of cells without liquidjunction by standard procedures. The first dissociation step was investigated bymeasurements of the cell(A) Pt ; H,(g, 1 atm)lH,Mal(m), NaHMal(m), NaCl(m) in EC + H,OIAgCl; Agand the second by measurements of the cellPt ; H2(g, 1 atm)lNaHMal(m), Na,Mal(m), NaCl(m) in EC + H201AgC1 ; Ag (B)where m represents molality.Because the solvent mixture has a freezing point> 15"C, the measurements were confined to the temperature range 20 to 55°C. Thestandard e.m.f. (E") of cells A and B from 20 to 55°C in this solvent mixture has beenreported earlier.'f NSF-CNRS Exchange Scientist 1974, on leave from the University of Paris, Paris, France.286J . c . HALLB AND R. G . BATES 2867EXPERIMENTALEthylene carbonate was subjected to four or five fractional freezings. Malonic acid wascrystallized twice from 95 % ethanol. Assay by titration with a carbonate-free standardsolution of sodium hydroxide gave 99.56 % with a standard deviation of 0.05.In preparingthe solutions, it was assumed that the residual impurity was water. Recrystallized sodiumchloride was tested and found to be substantially free of bromide.Stock buffer solutions with added sodium chloride were prepared from weighed amountsof malonic acid, standard NaOH solution, NaCl, ethylene carbonate and water. These werein turn diluted with 50 mass % EC+ H20 solvent to form the remainder of the cell solutions.The modified cell vessels were used, and once again the stability of the e.m.f. was foundto be satisfactory. In general, results at 25°C at the conclusion of the run agreed within0.1 mV with the initial data at 25°C. Other experimental details followed the proceduresalready described.RESULTSThe e.m.f.data for cells A and B, corrected to a partial pressure of hydrogen of1 atm (101.325 kPa) in the manner already described,l are listed in tables 1 and 2,TABLE 1 .-ELECTROMOTIVE FORCE (IN V) OF THE CELL : Pt ; H2(g, 1 atm)lH2Mal(m), NaHMal(m), NaCl(m) IN EC+H20 (50 % w/w)lAgCl ; Ag FROM 20 TO 55°Ctemperaturel'cmlmol kg-1 20 25 30 35 40 45 50 550.020 230.030 610.040 930.050 320.051 230.061 520.070 940.080 500.091 310.101 350,111 960.502 690.491 750.484 090.478 570.478 090.473 280.469 450.465 970.462 540.459 710.456 840.502 850,491 710.483 930.478 330.477 810.472 910.469 030.465 490.462 010.459 120.456 190.502 890.491 590.483 660.477 960.477 510.472 500.468 540.464 930.461 390.458 460.455 550.502 920,491 440.483 370.477 580.472 030.468 020.464 350.460 750.457 780.454 85-0.502 930.491 260.483 050.477 160.471 530.467 440.463 730.460 070.457 050.454 11-0.502 880.491 030.482 680.476 700.470 990.466 820.463 070.459 340.456 280.453 48-0.502 780.490 750.482 260.476 190.470 400.466 170.462 360.458 570.455 470.452 57-0.502 670.490 460.481 830.475 660.469 790.465 480.461 620.457 780.454 630.451 70-TABLE 2.-ELECTROMOTIVE FORCE (1N V) OF THE CELL : Pt ; Hz(g, 1 atm)lNaHMal(rn),Na2Mal(m), NaCl(rn) in EC+H20 (50 % w/w)lAgCl; Ag FROM 20 TO 55°Ctemperaturel'crnlrnol kg-1 20 25 30 35 40 45 5 0 550.005 9820.007 9660.008 9010.009 9020.009 9910.014 9430.01 9 6780.025 100.029 810.029 950.034 870.039 790.044 810.049 830.055 030.059 970.721 960.713 290.709 700.706 140.706 450.693 430.684 950.676 780.671 020.670 980.665 470.661 070.656 730.653 030.649 050.645 970.727 300.718 580.714 890.711 250.711 680.698 480.689 830.681 540.675 680.675 630.670 060.665 600.661 260.657 530.653 390.650 360.732 610.723 750.719 950.716 200.716 680.703 200.694 520.686 100.680 210.680 160.674 470.669 990.665 580.661 820.657 560.654 470.737 890.728 900.725 040.721 700.708 020.699 210.690 680.684 700.684 650.678 880.674 3 10.669 870.666 040.661 700.658 58-0.743 120.733 960.730 060.726 640.712 790.703 840.695 180.689 120.689 070.683 180.678 560.674 070.670 190.665 760.662 63-0.748 290.738 960.734 980.731 480.717 550.708 450.699 650.693 520.693 460.687 460.682 740.678 240.674 280.669 820.666 66-0.753 010.743 840.739 840.736 110.722 180.713 030.704 020.697 830.697 510.691 640.686 600.682 300.678 370.673 890.670 45-0.757 770.748 740.744 570.740 450.726 700.717 420.708 320.702 120.695 740.690 520.686 320.682 320.677 840.674 15-2868 ACID DISSOCIATION CONSTANTSrespectively.In all instances, the stoichiometric molalities (m) of the acid, its sodiumsalt and sodium chloride were equal.FIRST DISSOCIATION STEPThe e.m.f.EA of cell A is related to the " apparent " first dissociation constant,K;, of malonic acid by the equation(EA - E ")F m(m - m,) pK; = + logRT In 10 m+m,The activity coefficient term, omitted from eqn (I), is expected to vary linearly withthe ionic strength, I, whereand consequently pK,, the thermodynamic value, is obtained by a linear extrapolationof pK; to I = 0. Values of mH, of an accuracy sufficient for the purpose, were ob-tained from the e.m.f. and estimated values of ya(HCl) in the solutions byI = 2m+mH (2)( E A - E ")F-logm, = + log m + 2 log y ,(HCl).RT In 10 (3)The activity coefficients were taken equal to y*(HCl) in solutions of HCl in 50 mass %EC+H,O at the appropriate ionic strength.l The expected linear variation of pK;with I was realized.The values of pK,, together with the standard errors of the esti-mates, are listed in table 3.TABLE 3.-FIRST ( K , ) AND SECOND ( K z ) DISSOCIATION CONSTANTS OF MALONIC ACID IN 50 MASS% ETHYLENE CARBONATE+ WATER SOLVENT FROM 20 TO 55°Ct/"C PK1 s.d. a pK2 s.d. 520253035404550553.5383.5333.5283.5273.5263.5273.5293.5330.00060.00070.00060.00060.00050.00070.00060.00076.9456.9646.9837.0067.0267.0487.0687.0870.00240.00260.00290.00290.00300.00280.00270.0037* Standard deviation of the intercept.SECOND DISSOCIATION STEPThe e.m.f. EB of cell B is related to the " apparent " second dissociation constant,K;, of malonic acid by the equationSince solvolysis of the malonate ion is negligible, the true buffer ratio is equal to theratio of stoichiometric molalities (zk, is unity) and does not appear in eqn (4).Furthermore, in formulating this equation, it was assumed that the activity coefficientterm yHMalyCI/yMal can be expressed by an equation of the Huckel form,5 where A andB are constants of the Debye-Huckel theory, listed in an earlier contribution,l a" isthe ion-size parameter in A, and j? is an adjustable linear slope.The ionic strengthI = 5mJ . c. HALLB AND R . G . BATES 2869Plots of pKi were linear in Iwhen a was taken to be 3A at each temperature. Theintercepts, pK,, are listed in the fourth column of table 3, and the correspondingstandard errors are found in the fifth column.THERMODYNAMIC QUANTITIESBy the method of least squares, pK, and pK2 were fitted to the equations925.75T - 2.4037 + 0.0094952T ( 5 ) pK, = -and20.042TpK, = ~ f5.6127 +0.0043092Twhere T i s the thermodynamic temperature in K.The standard deviations for thefit of the data were respectively 0.0005 and 0.0012. Values of the standard enthalpy,entropy and heat capacity changes in the two dissociation processes were derivedfrom these relationships by the customary thermodynamic formulae and are listed intable 4.TABLE $.-THERMODYNAMIC QUANTITIES FOR THE DISSOCIATION OF MALONIC ACID IN 50 MAS S% ETHYLENE CARBONATE+ WATER AT 20,25 AND 40°Ctl"C AH"/cal mol-1 AS"/cal K-1 mol-1 AC- lcal K- 1 mol- 1first dissociation step202540202540502374- 25- 14.5- 14.9- 16.2second dissociation step- 1603- 1661- 1842- 37.2- 37.4- 38.0- 25- 26- 27- 12- 12- 12DISCUSSIONThe intramolecular hydrogen bond in the acid anion HA- of many dibasic carb-oxylic acids H,A in aqueous solutions was first revealed through abnormal variationsin Gibbs energies of strengthened the evidencethrough the analysis of enthalpies and entropies of ionization.We now examine theeffect of changing solvent on these thermodynamic functions in order to determinehow they may reflect the solvent effect on the strength of the hydrogen bond.The stabilization of the internal hydrogen bond increases the dissociation constantKl of the uncharged acid and decreases that, K2, of the acid anion, so that the ratioK1/K2 increases.Unfortunately, even large changes in K,/K2 can lead only to quali-tative conclusions concerning bond stabilization unless normal medium effects onthe acidity (from changes of dielectric constant, solvation patterns, and the like) areknown or can be estimated.In water, Kl/K2 for malonic acid is -700, and there seems little doubt that thevery large values for this acid in dimethylformamide and acetonitrile, namely 1013and 1.6 x l O l 5 , l o respectively, reflect a definite strengthening of the intramolecularLater, Das and Ive2870 ACID DISSOCIATION CONSTANTShydrogen bond by the solvent. Unfortunately, the situation is less clear in water +organic solvent mixtures, even though the ratio K1/K2 in 50 mass % EC+H,O(2700) exceeds that in water by a considerable margin.Following the reasoning of Das and I v ~ s , ~ we have nonetheless compared thethermodynamic functions for the first dissociation of malonic acid with those forother substituted acetic acids.To reveal substituent effects, these functions have beenreferred to those for acetic acid itself. Thus, for a substituent group X, differencessuch as AAG" have been defined byand similar quantities were calculated from AH;, ASZ and AC;? for substituted aceticacids with reference to the same quantity for the parent acetic acid (X = H) in water.llThese differences, namely AAG", etc., thus represent the thermodynamic functionsfor the processFor malonic acid (X = COOH), these quantities can now be obtained for the 50 mass% EC + H20 solvent as well as for water ; for this purpose, the data for acetic acidwere taken from our earlier papera2 These functions are summarized in table 5.AAG" = AGh-AGg (7)CH3COOH + X-CH2COO- % CHsCOO-+ X-CH,COOH.(8)TABLE 5 .-STANDARD THERMODYNAMIC FUNCTIONS FOR THE EQUILIBRIUM PROCESS CHsCOOH+X-CH,COO- + CHjCOO-+X-CH,COOH IN WATER AND IN 50 MASS %EC+HzO A T25°C ax AAGo AAH' A AS" AACpDwaterI 2.158 1.32 - 2.7 -4Br 2.530 1.14 - 4.6 1c1 2.577 1.03 -5.1 9COOH 2.605 - 0.1 1 - 9.0 24CN 3.120 0.79 - 7.7 - 150 mass % EC+HzOCOOH 2.881 - 0.90 - 12.7 9a U G 0 and AAH" in kcal 11101-' ; AASo and AAC; in cal K-' niol-'. 1 cal = 4.184 J.Das and Ives have pointed out that AH" calculated from Kl for malonic acid issome 1000 cal mol-l more positive than those for the other substituted acetic acidsand that the negative values of AS" and AC; are respectively lower and higher thanone would expect from comparison with the other acids of the series.They concludethat internal hydrogen bonding between the carboxyl hydrogen and the carboxylateoxygen, with delocalization of charge, is responsible for the anomaly.For AHo and AS", the abnormalities observed in water become more pronouncedwhen ethylene carbonate is added to the aqueous solvent. This trend suggests thatethylene carbonate imparts greater stability to the internally bonded anion structure.Parker l2 has expressed the view that anion solvation by dipolar aprotic solvents,though generally not extensive, is linked closely with delocalization of the negativecharge. The internally hydrogen bonded structure, where the charge is shared bytwo oxygen atoms, should therefore be stabilized to some extent by solvation withethylene carbonate.This work was supported in part by the National Science FoundationJ . C . HALLE AND R. G. BATES 287 1J. C. Halle and R. G. Bates, J. Chem. Thermodynamics, 1975, 7, 999.J. C. Hall6 and R. G. Rates, J. Solution Chem., 1975, 4, 1033.S. N. Das and D. J. G. Ives, Proc. Chem. Soc., 1961, 373.W. J. Hamer, J. 0. Burton, and S. F. Acree, J. Res. h'at. Bur. Stand., 1940, 24, 269.E. Hiickel, Physik. 2.. 1925, 26, 93.L. Hunter, Chem. Ind., 1953, 155. ' D. €3. McDaniel and H. C. Brown, Science, 1953, 118, 370. * R. E. Dodd, R. E. Miller and W. F. K. Wynne-Jones, J. Chern. SOC., 1961,2790.E. Roletto and J. Juillard, J. Solution Chem., 1974, 3, 127.lo I. M. Kolthoff and M. K, Chantooni, Jr., J. Amer. Chem. Sac., 1971, 93, 3843.l 1 R. A. Robinson and R. H. Stokes, EZectrolyfe Solutions (Butterworths, London, 2nd revisedl2 A. J. Parker, Chem. Rev., 1969, 69, 1.edn., 1970), appendix 12.1.(PAPER 6/41 3

ISSN:0300-9599    

DOI:10.1039/F19767202866

出版商:RSC    

年代:1976

数据来源: RSC

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Dislocations in Pyrene CrystalsBY ROBERT M. HOOPER AND JOHN N. SH.ERWOOD*Department of Pure and Applied Chemistry,University of Strathclyde, Glasgow G1 lXL, ScotlandReceived 3rd March, 1976A study has been made of the geometry of common dislocation slip systems in solution-grownpyrene single crystals using surface etching and X-ray transmission topography. Good agreementis found between the results of the two examinations. The slip systems which readily contribute toplastic deformation are (001) [1101 and [ITO], (110) [liO], (110) [110], (110) [OOl] and (110) [Ool].There is little agreement between the dislocation counts obtained from surface and bulk examinationunless care is taken to avoid surface damage arising from etching and mechanical handling.Some recent examinations of organic and inorganic solids have indicated thatlattice defects and in particular dislocations play a significant role in determining thephysical and chemical properties of the so1id.l For the most part these studies haveused surface etching to provide an indication of the geometry, nature and concentra-tion of the defects.2 This information has then been correlated with the results ofthe subsequent physical and chemical e~amination.~ The surface of the solid maybe significantly different in its defect structure to the bulk.Confirmation of theetching experiments by bulk methods of examination is desirable. Of the two mostsuitable available methods, electron microscopy and X-ray topography, the formerpresents the better resolution. It has the disadvantage however that it can be usedonly with thin samples which readily suffer mechanical and radiation damageand which may not reflect the properties of dislocations in the bulk lattice.X-raytransmission topography, although of more limited resolution permits the assess-ment of the defect structure in the bulk of large (cm3) crystals. Such samples aremore suitable for the further physical and chemical examination of the influence oflattice defects on bulk properties. The X-ray technique has been used to examinedislocation distributions in several molecular solid^.^-^ In this paper we describe itsapplication to the monoclinic aromatic crystal pyrene and compare the results withthose of an etching examination.EXPERIMENTALLarge, colourless (10 cm3) crystals of pyrene (max.impurity content 100 p.p.m.) weregrown on previously prepared seeds by slow cooling of a saturated toluene solution.i0 Thetabular crystals (fig. 1) exhibited well-developed (110), (lTO), (001) and 107) faces andcleaved readily in the (001) plane. Some of the more defective crystals also exhibited a lessPYRENEFIG. 1 .-External habit of solution grown pyrene crystals.257R . M. HOOPER AND J . N. SHERWOOD 2873well-defined (110) and (110) cleavage. This is believed to result from solvent inclusion inthe defective (110) and (110) planes.ETCHING STUDIES“As grown” or cleavage surfaces were etched at room temperature with con-centrated sulphuric acid to which had been added a trace of pyrene to inhibit attack.Initial light etching yielded random patterns of etch-pits [fig.2(a)]. These comprisedareas of high superficial density usually localised at the damaged edges of the crystalor in regions where cleavage stresses had developed, together with areas where fewetch-pits had formed. The damaged area could be removed by solvent polishingto produce a clear surface which on further etching yielded a diminished number ofrandomly distributed etch-pits. The usual tests for dislocation etching, i.e., com-parison of cleavage halves, persistence on continued etching and reproducible align-ments following straining, indicated that etching was occurring preferentially atemergent dislocation sites. Interference contrast micrographs of some of the resultingpatterns on the three principal surfaces are shown in fig.2.Vigorous repeated etching of the (001) faces gave rise to numerous alignments ofangled pits in the [I 101 and [lrO] directions [e.g. the bands of pits in fig. 2(b)] and to alesser extent the [OlO] directions [fig. 2(c)]. We attribute the former to the readymultiplication of an easily provoked slip system in relieving the thermo-mechanicalstrains produced by chemical attack. Similar alignments resulted following mechani-cal deformation.(110) and (1TO) faces were highly defective and etched rapidly suggesting that amajor slip system emerges on this face. Etching yielded centre-bottomed etch-pitsaligned in the [110] (or [liO]) and [OOl] directions. Note for example the patternclose to the indentation mark in fig.2(d) and the alignments in fig. 2(e).Initial attempts to etch the (1Oi) faces were unsuccessful. This was believed tobe due to the fact that the dislocation configurations most likely to produce thepatterns observed on the other faces would intersect this face at too high an anglefor etch-pits to be observed. During acid etching a fine layer of decomposed materialformed on the crystal surface. Attempts to remove this by careful wiping resultedin its collection in etched depressions thus revealing even the most shallow etch-pits[fig. 2071. The triangular etch-pits thus decorated were in some cases aligned in the[OlO], [ 1111 and [Tli] directions consistent with the original speculation.Consideration of the geometry of the pits and their relative alignment on differentfaces suggest the following principal slip planes : (110), (lTO), (001) and to a lesserextent (100).X-RAY TOPOGRAPHYTabular samples 1-2 mm thick (A, B and C, fig.1) were cut from and ‘‘ as grown ”crystals using a solvent saw and a 3 : 1 (v/v) toluene +ethanol mixture as the workingfluid. The cut samples were washed in pure toluene to remove residual surfacedamage and were fixed to aluminium annuli with a non-straining cement for mountingon the topographic camera.All topographs were taken in the transmission mode on a conventional Langcamera using Mo Kal radiation and recorded on Ilford L4 nuclear plates. Satis-factory topographs could only be obtained using second order reflections on (1 10) or(1TO) and (001) planes.Fig. 3(a) shows a 220 topograph of a (001) slice (A, fig.1). The sample planecontains the seed crystal which is visible as the mass of deformed material at thecentre of the lower edge (X). This damage results from the initial drilling of the see2874 DISLOCATIONS IN PYRENE CRYSTALSprior to mounting in the crystallizer. As the crystal has grown, the intersection of thcrapidly growing (1 10) and (110) faces has led to instability and solvent incorporationalong the [loo] direction (Y). Other than in the region of the seed, the dislocationstructure consists almost entirely of two large fans of dislocations radiating to the[I 101 and [IT01 directions from the seed. These dislocations lie in planes parallel tothe plane of the slice.Confirmation of this geometry is given by fig. 3(b), a 220topograph of slice B (fig. l), which does not contain the seed and which shows noneof these images. Apart from damage emanating in the [OOl] direction from the seedand from the instability noted above, the slice contains few dislocations. The highcrystallographic perfection of the outermost parts of the sample is demonstrated bythe occurrence of Pendellosing fringes (e.g. at Q). This restriction of the maindislocation bundles indicates that the Burgers vector of the dislocations lies in the(001) plane. Crystallographic considerations (see below) and the linearity of thedislocation images suggest that they are likely to be predominantly of the types (OOI),[110] or [110] but no definite assignment can be given.We note the occurrence of a small group of dislocations at P [fig.4(6)]. Theseare probably high energy dislocations generated from the strain induced in the latticeby the inclusions at their head. No assignment of their geometry can be given on thepresent evidence. It is doubtful if this type of dislocation will contribute significantlyto normal plastic deformation of the solid.A 220 topograph of a (110) slice (C, fig. 1) is shown in fig. 4(a). Again, the por-tion of the crystal nearest to the seed (X) is highly defective compared with the latterlygrown region. A 002 topograph of the same slice is shown in fig. 4(b). A largenumber of well contrasted dislocation images lying along the [OOl] direction, not visiblein fig.4(u) can now be seen. This difference permits a definite assignment of thedirection of the Burgers vector, b, of these dislocations. Image contrast becomes aminimum when the strain vector, u, of the dislocation has no component in thedirection of the diffraction vector, g, i.e., u.g = 0. Since the dislocations fully crossthe slice it is likely that they have a predominantly screw component. For purescrew dislocations u and b are parallel and in the present case b must lie in the [OOI]direction. Other than the white, out of contrast, areas which are indicative of a localtwisting of the lattice around the [110] directions and which confirms the defectivenature of the (110) planes, these dislocation images are the dominant features ofthis topograph.We conclude that the dislocations involved i.e., (1 10) or (lIO),[OOl] are a common and ready slip system.In the 220 topograph [fig. 4(u)], other than the small number of straight disloca-tions (M) which cross the plane of the slice and which do not lie in a simple crystallo-graphic direction, (and hence are probably growth dislocations) the remaining imagesrepresent dense interpenetrating tangles of dislocation loops. Detail of a selectedarea (N) which shows typical arrangements is shown in the enlargement, fig. 5.Fig. 5 shows two types of loops. The first, penetrating into the surface regionsfrom the top surface, are loops punched in by surface damage during handling. Theseare the residue of the dislocations responsible for the dense alignments of etch-pitsnoted on (001) faces after light etching; most having been removed by dissolutionduring preparation.The loops in the bulk arise from the mild strain resulting from the white, out ofcontrast area of fig.4(a) and thus must represent an easy slip system. From theirsize and geometry it is reasonable to suggest that they lie in the (110) plane andrepresent the dominant slip system noted from etching the (001) surfaces. Loops inl(10) and (010) planes would yield a more acute projection. The loops will be ofmixed character and hence no absolute assignment of Burgers vector can be mad(el (.f 1FIG. 2.-Characteristic etch-pit distributions on cleaved and habit faces of pyrene crystals grown fromsolution (X250).(a) (001) face-random distributions on " as grown " crystals ; (b) and (c) (001) face-following straining by the etchant ; ( d ) and (e) (1 10) face-after indentation and compressionrespectively ; ( f ) (mi) face.[To face page 287FIG. 3.-(a) 220 Topograph of a (001) slice (A in fig. 1). (6) 220 Topograph of a (001) slice (B infig. 1)FIG. 4.-(a) 220 Topograph of a (1 10) slice (C in fig. 1).plane of the paper). (b) 002 Topograph of the same (110) slice.(n.b. the diffraction vector points into theFIG. 5.-Enlargement of area N of fig. 4(a)R. M. HOOPER AND J . N. SHERWOOD 2875from diffraction contrast. We note however that these images are relatively muchless well contrasted in the original topograph of fig. 4(b). This is in keeping with apredominant (110) Burgers vector.Thus an assignment of (110) [110] is not un-reasonable. The complementary (1 10) [ 1 TO] system must also exist.Pyrene crystallises in the monoclinic system with the space group P2,/a. Theunit cell parameters are a = 1.36 nm, b = 0.924 nm, c = 0.837 nm, /3 = 100.2°.12The molecules are planar and lie in parallel pairs at approximately 40" to the abplane.Consideration of the structure and the application of an empirical close-packing,wide-spacing criterion for slip indicates that, in accord with the experimental evidence,the slip should occur most readily on (OOl), (110) and (110) planes. On the basal(001) plane the shortest molecular translations are +[110], = +[lTO] c [OlO] < [loo].Thus slip should be predominantly restricted to the [l lo] and [lTO] directions withBurgers vectors of +[110] and +[liO] (b = 0.822 nm).In the case of the (1 10) and(110) planes the packing is favourable to slip along [lTO], [I 101 and [OOl] directionswith resultant Burgers vectors of 3[1iO], $[110] and [OOl] (b = 0.837 nm).Thus in contrast to some other monoclinic organic solids [Ool] slip on the non-basalplane in pyrene is energetically, approximately equivalent to [OlO] basal slip andeasy slip is not restricted to the basal plane.This equivalence of basal and non-basal slip is reflected in the morphology of thecrystal. It has been noted previously lo that the development of crystal morphologyis dependent in part on the ease of slip of the dislocations emergent on the varioushabit faces.Dislocations generated by thermomechanical stresses during growth actas growth centres for the development of the face. In the present case the equi-valence between the three basic slip systems results in a similar ease of multiplicationand formation of dislocations emergent on the (110), (1x0) and (001) faces. This inturn allows a similar rate of growth of these faces and leads to a tabular habit insteadof the " platy " habit more characteristic of P2Ja monoclinic crystals e.g. anthracene,where basal slip is more readily activated than non-basal slip.From the above etching and topographic information we conclude that there arethree principal defective planes in pyrene : (1 lo), (110) and (001) and that dislocationsglide on these planes with Burgers vectors in the [l lo], [lTO] and [OOl] directions.Wealso note that the bulk of the crystals is much more highly perfect than is suggested bynormal surface etching. This difference will be common to most organic crystals.We gratefully acknowledge the support of the S.R.C. in the provision of anapparatus grant (J. N. S.) and a fellowship (R. M. H.).J. M. Thomas, Adv. Catalysis, 1969, 19,293.J. N. Sherwood, Mol. Cryst. Liq. Cryst., 1969, 9, 37.J. M. Thomas and J. 0. Williams, Progr. Solid-State Chem., 1971, 6, 121.W. Jones, J. M. Thomas and J. 0. Williams, J.C.S. Faraday 11, 1975, 71, 138.A. R. Lang in Modern Dirraction and Imaging Techniques in Material Science, ed. S. Amelinckx,R. Gevers, R. Renaut and J. Van Landuyt (North Holland, 1970).D. Mitchell, P. M. Robinson and A. 0. Smith, Phys. Stat. Sol., 1968, 26, K93.H. Klapper, J. Crystal Growth, 1971, 10, 13.E. M. Hampton, R. M. Hooper, B. S. Shah, J. N. Sherwood, J. Di Persio and B. Escaig, Phil.Mag., 1974, 29, 743.J. Di Persio and B. Escaig, Cryst. Lattice Defects, 1972, 3, 55.A. R. Lang, Modern Diffraction and Imaging Techniques in Material Science, ed. S . Amelinckx,R. Gevers, R. Renaut and J. Van Landuyt (North Holland, 1970), p. 450.R. W. G. Wykoff, Crystar Structures (Interscience, 2nd edn, 1963), vol. 6.lo E. M. Hampton, B. S. Shah and J. N. Sherwood, J. Crystal Growth, 1974, 22, 22.(PAPER 6/439

ISSN:0300-9599    

DOI:10.1039/F19767202872

出版商:RSC    

年代:1976

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Solvation SpectraPart 5 1.l-Di-t-butyl Nitroxide as a Probe for Studying Water and Aqueous SolutionsBY YAN Y. LIM, EDWARD A. SMITH AND MARTYN C. R. SYMONS*Department of Chemistry, The University, Leicester LEI 7RHReceived 25th March, 1976Dilute aqueous solutions of di-t-butyl nitroxide have been studied by e.s.r. spectroscopy, andchanges in the I4N hyperfine coupling and the line-widths have been monitored as a function of thetemperature and of the concentrations of a wide range of added solutes.The 14N hyperfine coupling is strongly dependent upon hydrogen-bonding, reaching a maximumin cold water, and low values in aprotic media, The alcohols give intermediate values, because ofthe presence of hydrogen bonded and non-hydrogen bonded radicals. Trends in A(14N) as basicsolvents are added to aqueous solutions show a preference for the non-hydrogen bonded form,especially for strong bases such as hexamethylphosphoramide. These changes are interpretedin terms of a competition for water molecules, rather than preferential solvation of the nitroxide bythe aprotic media.At 25°C or above, the widths of all three components increase equally as non-aqueous solvent is added. We conclude that spin-rotational relaxation and changes in A(lH) arethe width-controlling phenomena. Estimates of the latter were obtained using the perdeuteratednitroxide and computer simulations. The width increases correlate linearly with the changes inA(14N) which suggests that it is mainly the " free " nitroxide that contributes to the width enhance-ments.Values of TJ, the spin-rotational correlation time have been calculated in selected cases.Differential line-broadening is observed for dilute aqueous solutions at low temperatures. Thiseffect is greatly enhanced by certain additives such as t-butyl alcohol and triethylenediamine, whichare thought to be water structure enhancers. Two possible causes are a reduced tumbling rate, witha consequent broadening resulting from the anisotropy of the 8- and A-tensors, and a slowing downof the equilibrium between hydrogen-bonded and " free " nitroxide. The control exerted by viscosityis shown by the very large asymmetric broadening caused by added glycerol at 0°C.Added methanol causes a slow fall in A(14N) to the value in pure methanol, with a concomitantline-width enhancement, again linear with A(14N).This is interpreted in terms of an increase in theconcentration of " free " nitroxide, which results primarily because non-hydrogen bonded lone-pairelectrons of methanol compete effectively with the nitroxide for hydrogen bonds. At low tempera-tures, added t-butyl alcohol initially has no effect on A(I4N), but beyond about 0.05 M.F. (molefraction), A(14N) falls very rapidly to the value for nitroxide in the pure alcohol. However, at 70"C,this initial plateau in the 0 to 0.05 M.F. region is absent. Again, the widths of the lines follow exactlythe complex pattern of changes in A(14N).These results are compared with those recently obtained by Jolicoeur and Friedman for similarsystems.Since the application of stable nitroxide radicals to the study of biological macro-molecule systems by McConnell and co-workers,2 widespread attention has beengiven to their use as " spin-labels ".This has been largely focused upon line-widthmeasurements, and detailed theories have recently been developed to explain theresults, especially in the slow-tumbling region 3 v and under anisotropic rotationalreorientative conditions.In our previous studies of solvation phenomena we have frequently used para-magnetic probes to utilise the power of e.s.r. spectr~scopy,~-~~ but we have notpreviously utilised nitroxides. However, whilst this work was underway, Jolicoeurand Friedman published two reports of their similar studies of aqueous solutions287Y .Y . LIM, E . A . SMITH AND M . C. R. SYMONS 2877of various nitroxides.' 6 p '' They utilised mainly 2,2,6,6-tetramethyl-4-piperidone-N-oxide (OTEMPO) and 2,2,6,6-tetramethyl-piperidine-N-oxide (TEMPO) as probes.Di-t-butyl nitroxide (DTBN) was also studied cursorily, but changes were found tobe " more subtle for DTBN than for OTEMPO or, especially, TEMPO ".17These authors focused their attention upon line-width measurements, and calcu-lated values for the rotational correlation time (7,) and the spin-rotational correlationtime (7,) as a function of changes in viscosity for a range of aqueous solutions. 6*We have been more concerned with changes in A(14N), and have found DTBNsatisfactory for such studies.EXPERIMENTALDi-t-butyl nitroxide was prepared by the method of Hoffman.'' TEMPO, OTEMPOand TEMPOH were prepared by the method of Bribre et aZ.19 The perdeuterated nitroxidewas prepared by photolysis of d9 t-nitrosobutane in d4 methanol.(A small sample of d9t-nitrosobutane was kindly donated by Professor M. J. Perkins.) The solutions were degassedto remove oxygen and nitric oxide. Water was twice distilled from alkaline permanganate.Other solvents of the best available grades were dried over molecular sieves and fractionated.All solutions were carefully deoxygenated. Concentrations of nitroxide were in the regionof 5 xE.s.r. spectra were measured with a Varian E3 spectrometer, sample temperatures beingmaintained to ,l"C. N.m.r. spectra were measured with a Jeol PSlOO lOOMHz specto-meter, using t-butylamine as a shift reference.to prevent any contribution from spin-spin broadening.RESULTS AND DISCUSSIONIdeally, all our linewidth studies should have been undertaken using the d'*nitroxide.Unfortunately, there was only sufficient to carry out a few checks, asindicated below. For studies of differential line-broadening, we have used the directlymeasured difference between the widths of the MI = 0 and MI = - 1 lines to demon-strate trends, since changes in A('H) thereby cancel out. However, when consideringoverall broadening effects we have resorted to a computer simulation method similarto that used by Poggi and Johnson.20 In order to do this, good values of the protonhyperfine coupling, A('H) are needed. These vary with the spin-density on nitrogen,decreasing in magnitude as A(14N) increases.Values of A(14N) for DTBN inaprotic solvents are known,lg* 21-23 and we have used the n.m.r. method to obtainvalues for concentrated solutions of DTBN in methanol. (Unfortunately, the solu-bility in water was too low to enable us to get n.m.r. spectra from aqueous solutions.)The widths of the proton features (W,) were extracted from a FORTRAN computerprogram, which calculated an envelope width from the given value of the protonhyperfine splitting A('H) and a given proton width W,. Nineteen lines of binominaldistribution separated by a distance A(lH) were fitted to a Lorentzian lineshape;each component having width WH. The envelope was scanned over 200 points infrequency steps of 5 x lo5 rad s-l from 59.9250 x lo9 rad s-l to 60.0250 x lo9 rads-l.A(lH) values were selected from the point of resolution given by fig.l(b).There is a significant discrepancy between the A('H) value for DTBN in methanolobtained from concentrated solutions in methanol and that obtained from computersimulation (0.09 and 0.08 G respectively). Discrepancies of similar sign andmagnitude have been observed in other cases. However, the difference in the resultingW' values [fig. l(b)] are not very great.The final results are plotted against A(14N) in fig. l(a) and AH values for othersolvent systems have been estimated froin fig. 1 (a). A series of curves connecting the1-9DTBNI 1 1 t I15.0 15.5 16.0 16.5' 17.0A('4N)IG"* IWHIGFIG.1.-(a) Correlation between A(I4N) and A('H) for DTBN in various solvents. (b) Correlationbetween the overall line-widths, AH, and computed individual widths for the separate components( WH) for DTBN for a range of A('H) values.DTBN : (1) HzO (simulation), (2) ethylene glycol [simulation, ref. (20)], (3) MeOH (n.m.r.),(4) MeOH (simulation), ( 5 ) n-butanol [simulation, ref. (20)], (6) CH2Cl2 (n.m.r. R. W. Krielick,J. Chem. Phys., 1966,45,1922), (7) C6H6 (n.m.r. K. H. Hauser and J. C. Jochams, Mol. Phy~., 1966,10, 253).TEMPO : (a) CCL, (b) C6H6, (c) Me2C0, (d) DMSO, (el HCCI,, (f') Me011 [all from ref. (19)]Y . Y . LIM, E . A . SMITH AND M. C. R . SYMONS 2879computed envelope width, AH, with the widths of the individual lines (W,) for aseries of A(I4N) values [fig.l(b)] were then used to give reasonable values for W,.The computed values of AH at which the first sign of resolution should appear areindicated in fig. l(b).*Despite the fact that the smallest widths were obtained for aqueous solutions,incipient resolution was never obtained. This supports the value for A(lH) between0.05 and 0.06 obtained from fig. l(a). Thus we suggest that the value of -0.094 Gused by Atherton and Strach 24 is in error. One disadvantage of OTEMPO andTEMPO is the presence of three different types of protons so that good simulation isdependent on an accurate knowledge of all three A('H) values.When presenting results for nitroxide probes it is usual to utilise calculated z, orzJ values. We prefer to show trends in measured parameters since, in our view,absolute values of z, and zJ estimated therefrom are often untrustworthy and errorstend to become hidden.Also, their precise magnitudes are not our real concern.However, we have calculated a selected set of zc and zJ values (see table 1 and 2) forcomparative purposes. Our calculations, based on the theory of Kivelson 2 5 as usedby Poggi and Johnson,20 are briefly outlined in the Appendix.TABLE 1 .-VALUES OF Zc FOR DTBN IN WATER + f-BUTANOL MIXTURES AT 3.3"cmole fraction oft-butanol0.0000.01 10.0210.03 10.0430.0640.0730.0870.109T~ (s) calculated from y9.74x1 . 2 7 ~2 . 1 4 ~2 . 1 5 ~ 10-l'2.43 x 10-l13.48 x 10-l'3 . 1 8 ~ 10-l13 . 4 0 ~3.63 x lo-"T~ (s) calculated from /?6 .4 0 ~ 10-l29 . 6 9 ~ 10-l28 . 1 6 ~ lo-''1.22x 10-l11.95 x 10-12.33 x 10-l'2.22x lo-ll3.05 x2.71 xTABLE 2.-TJ VALUES FOR DTBN IN DMSO AT VARIOUS TEMPERATURESTIK301305.2310.03 16.0320.0325.6330.5335.5341.5A HPPOi G0.5680.5880.5970.6040.5970.6280.6570.6490.703WHIG0.1800.2000.2250.2500.2250.3020.3580.3250.450a"o/G0.1750.1950.2240.2450.2330.2990.3530.3230.448G = 1 0 - 4 ~1.22x 10-l21 . 1 3 ~ 10-l23 . 2 0 ~ 10-131.1ox 10-l24.61 x 10-136 . 4 0 ~ 10-135.0 ~10-134 . 5 4 ~ 10-131 . 1 5 ~ 10-l26.71 x 10-147 . 4 0 ~ 10-148.35 x 10-148 . 9 8 ~ 10-148 . 0 7 ~ 10-141 . 0 6 ~ 10-131 . 2 4 ~ 10-131.11 x 10-131 . 5 2 ~ 10-13TRENDS I N THE 14N HYPERFINE COUPLING CONSTANTSThe effects of added co-solvents upon A(14N) for aqueous DTBN are summarisedin fig.2 as a function of the mole-fraction (M.F.) of the added solvent. The contrastbetween added methanol and t-butyl alcohol is marked, there being a small, steady* Approximate points at which resolution should become observable2880 SOLVATION SPECTRAr5 .mole fraction of cosolventFIG. 2.-Hyperfine coupling constants (14N) for DTBN in aqueous solutions as a function of themolc-fraction (M.F.) of added cosolvents. (0 MeOH = methanol, + t-BuOH = t-butyl alcohol,0 McCN = methylcyanide, A DMSO = dimethylsulphoxide, 0 Me2CO = acetone, x HMPA =hexamethylphosphorarnide and V DMF = dimethylformamide.)16.0[ , , , ,0.05 0.10 0.IS 0.20mole fraction of cosolventFIG. 3.-Hyperfine coupling constants (14N) for DTBN in aqueous soIutions containing t-butylalcohol at +, 3.3; 0 , 2 5 ; and x ,70°CY . Y . LIM, E . A . SMITH AND M. C . R. SYMONS 288 1fall in A(I4N) for methanol, whilst for t-butyl alcohol an initial period of insensitivity(shown in fig. 3) is followed by a rapid fall in A(I4N) such that the final value isalmost reached by 0.3 M.F. This behaviour was most marked at O"C, the initialplateau being absent at 70°C.For methyl cyanide and acetone the fall was greater than linear initially, becomingmore gradual in the high M.F. regions. However, this curvature was much moremarked for hexamethylphosphoramide, the initial fall being extremely rapid.TRENDS I N AH(M1 = 0)Except at temperatures well below ambient, when asymmetric broadening effectswere apparent, all three lines broadened at the same rate, trends for the central linebeing depicted in fig.4. The most notable aspect of these trends is their marked0.31 I I I I I 0 0.2 0.4 0 . 6 0.8 I .omole fraction cosolventFIG. 4.-Line-widths for DTBN in aqueous solutions as a function of the M.F. of added co-colvents.0 MeOH, + t-BuOH, CI MeCN, A DMSO, 0 MeKO, x HMPA, v DMF.similarity to those shown in fig. 2 for A(I4N). This is illustrated by the plots ofA(14N) against AH(0) in fig. 5, which are all close to linear over the whole M.F. range.In particular, the involved changes observed for t-butyl alcohol in the M.F. plotsare completely lost in the line for this solvent in fig.52882 SOLVATION SPECTRAClearly this behaviour would be observed if AH were controlled by changes inA(lH). We have therefore included our estimated values for W, in fig. 5. Thisshows that although the proton hyperfine coupling contributes to AH, the observedlinear trends are still present for W,.TRENDS I N AH(-1)-AH(0)Although the MI = - 1 line was usually marginally broader than the MI = 0 line,significant differences in width only appeared at temperatures well below 25°C.0 -70.60 0 . 5% s5 5 0.4." 2--- ni?30 . 30 . 2T 8 A (70" C) L A \ +I I I I15.5 16.0 16.5 17.0A(' 4N)/GFIG. 5.-Correlation between line-widths (AH and WH) and hyperfine coupling constants (14N)for DTBN in various aqueous solutions at 25°C.MeCN, A DMSO, 0 MeOH, 0 t-BuOH (TBA),0 Me2C0, x HMPA, V DMF, + TBA at 70°C.These have been monitored in the region of 0°C. Trends with M.F. of added co-solvents are depicted in fig. 6, and with temperature for various solutions in fig. 7(a).The way in which the line-widths are controlled at low temperatures by z, and athigher temperatures by 2, is indicated in fig. 7(b)Y . Y . LIM, E . A . SMITH A N D M. C . R . SYMONS 2883THE HYDROGEN-BONDING EQUILIBRIUMThe main reason for the fall in A(14N) on going from water to other solvents is,in our view, the loss of hydrogen-bonding to the oxygen atom of the nitroxide. Theeffect of hydrogen-bonding is to induce a partial negative charge on oxygen and henceto constrain the unpaired electron onto nitrogen with a consequent increase inA(14N).There is also a concomitant fall in gay since the major g-shift stems fromspin on oxygen. This is important when considering 7, values.R\/R& - (I) 6+ N6- 0 c d +1 111IMeThe results suggest that the extent of hydrogen-bonding is almost complete forwater, reduced for methanol, and small for t-butyl alcohol. There remain small, butsignificant differences between the A(I4N) values for the various aprotic solvents.06-%<IQ3-.0.04v A MeCN f I\Jle,CO++HMPA (25OC)OLOID-0 . 2 0.4 0.6 0.8 1.0 0mole fractionIcosolventFIG. 6.-Line-width difference (AN-l-AHO) for aqueous DTBN as a function of the M.F. ofadded cosolvents at 4 ° C . Glycerol (at 1.5"C), + HMPA(2.0), x t-BuOH (3.0), v Me2C0,0 Me CN, A DMSO (O.O), HMPA (at 25°C).We suggest that these differences reflect a form of dipolar solvation such as thatindicated in (I) for methyl cyanide.This will have the effect of inducing a smalldipole which will tend to increase A(14N) over the value for completely non-interactingsolvents such as heptane. The extent to which this occurs will depend partly upo28 84 SOLVATION SPECTRAT/KFIG. 7.-(a) (AH-' -AHo) and (b) line-width (AH and WH) as a function of temperature for DTBIJand DTBN (dI8) in water, 0.073 M.F. aqueous t-butyl alcohol, heptane and MeOH. (a) A DTBN/H20, 0 DTBN/MeOH, O d l s DTBN/CD,OD, x DTBN/H20 + t-BuOH, + DTBN/heptane.(6) A DTBN/H,O (AH), V DTBN/H20 ( WH), 0 dl8 DTBN/CD30D (AH), + DTBN/heptane,x DTBN/H20 + t-BuOH, 0 DTBN/MeOH (AH), 0 DTBN/MeOH ( WH)Y .Y. LIM, E. A . SMITH AND M. C . R. SYMONS 2885the local dipole of the aprotic solvent and partly on steric factors. Thus, for example,the relatively low value for hexamethylphosphoramide probably arises for stericreasons. These changes are, relatively, very small.The trends when basic, aprotic solvents are added to water can be represented interms of direct competition for hydrogen bonds :1 1R2NO-----HOH----- + B + R2NO + -----HOH-----B. (1)I I1 i(The relative strengths of the hydrogen bonds involved vary with the amount of addedco-solvent. Thus, for example, the hydrogen bond formed by an 0-H group of awater molecule bonded to three other water molecules in a water “polymer” isstronger than that formed by the 0-H group of the unit B - - - HOH.)26 The initialslopes for the curves in fig.2 can therefore be taken as a measure of the effectivebase-strength of the co-solvents. The order is :HMPA > DMSO N Me,CO - DMF 2 MeCN.Hexamethylphosphoramide is certainly the most basic, but the lack of differentiationfor the other aprotic solvents is surprising. (We stress that whenever this view ofsolvation effects is correct, quantitative treatments based upon the concept of prefer-ential solvation are not directly appli~able.)~~.-.- $ I 0.2T BN/ H,O (AH)IT/T/(degrees cp-’)FIG. 8.-Line-widths (AHand WH) for DTBN and TEMPO in various solvents as a function of T/71.[Data for TEMPO from ref. (17)].+ DTBN/DMSO, 0 DTBN/heptane, 0 DTBN/MeOH,0 TEMPOlDMSO.An extension of this concept explains the results for methanolic solutions. Thefall in A(14N) arises, not because methanol forms relatively weak hydrogen bondsto the nitroxide, which is not the case in the liquid phase, but because bulk methano2886 SOLVATION SPECTRAhas a large excess of basic lone-pairs of electrons not involved in hydrogen bonding.In contrast, bulk water utilises almost all its protons and lone-pairs of electrons in athree-dimensional network of hydrogen-bonds, and there is a relatively low residualconcentration of (OH),,, groups and an equal concentration of (lone-pair),,,,“groups”. When methanol is added to water there is a marked fall in the con-centration of groups, and this is thought to arise because each methanolmolecule provides two active lone-pairs, but only one OH group.26 Bulk methanol,because of the large excess of (lone-pair),,,, groups, contains no detectable (0H)frCegroups at ambient temperatures.Thus, when low concentrations of DTBN areadded to bulk water, there is a sufficient excess of (OH)fr,, groups to form hydrogenbonds to the weak nitroxide base, but as methanol is added, these groupsare scavenged, and the nitroxide has to compete with an increasing number ofmethanol (lone-pair),,, groups, so the percentage of (R2NO)fr,, molecules increases.The correlations between W, and A(14N) of fig. 5 can be understood if we postulatethat only (R2NO)free molecules contribute significantly to the line-broadening processgoverned by 7,.The extent of broadening is proportional to the length of time thesemolecules are free to execute their natural mode of rotation, and this is close to zerofor molecules that are hydrogen bonded into a network of water molecules. Foraprotic solvents the temperature dependence follows T/q reasonably well but, as thisfigure shows, this is not the case for protic solvents, the results for water being almostindependent of T/q. This result agrees with our postulate that zJ values are governedby [R2NOIfre,. Jolicoeur and Friedman also noticed this contrast, but offered acompletely different explanation. If our explanation is correct, then the line-widthtrends of fig. 3 are explained by the same arguments used to explain the trends of fig.2.REASONS FOR ASYMMETRIC BROADENINGImplicit in our discussion above and our derivation of z, values is the conceptthat the asymmetric broadening observed at low temperatures stems from anisotropyaP 1a aIFIG. 9.-Simulation of art exchange broadened spectrum for DTBN in water + HMPA mixturecontaining equal concentrations of hydrogen-bonded (a) and “ free ” (f3) DTBNY . Y. LIM, E. A . SMITH AND M. C. R, SYMONS 2887in the g- and A- tensors. This is the usual assumption, but there could well be analternative explanation for the present data, especially for systems with low viscosity.Lf eqn (1) represents the major cause for variation in A(14N) for a particular systemthen, as shown schematically in fig. 9, for sufficiently slow jumps, there could be anasymmetric line broadening of just the form observed, since the width is proportionalto ( ~ 5 ~ ) ~ in the fast exchange region.02 \ mX40 12 5OCn & 4II I I I I I f0.02 0.04 0.06mole fraction TEDFIG. 10.-Changes in e.s.r.parameters for DTBN on the addition of triethylenediamine (TED).(a) changes in A(I4N), (b) changes in AH, (c) changes in (AH-' -AHo). x at 25°C ; + at 5°C.There seems to be no easy method for distinguishing between these two possibilities,but we stress that computed values for z, (such as those in table 1) could be mostmisleading if the hydrogen bonding equilibrium makes a significant contribution tothe asymmetric broadening. The results are considered in terms of both possibilities.Broadening by this equilibrium process (fig.9) should be less significant for systemsin which the concentration of one component is small compared with that of the othe2888 SOLVATION SPECTRAThus for the glycerol+water solvents at low temperature, for which [AH(-l)-AH(O)] is large and the change in A(14N) small, it seems reasonable to assign thebroadening entirely to an increase in 2,. Added methyl cyanide or acetone inducelittle change in the extent of asymmetric broadening even at 0°C (fig. 6) but hexa-methylphosphoramide and dimethylsulphoxide cause an increase which reaches amaximum in the region in which A(14N) has fallen to its mid-value. Since this isjust the composition for which broadening by the equilibrium process (1) would bemost marked, it may well be that it plays a part.The viscosity of these solutions isrelatively high and this would have the effect of increasing the contribution from bothprocesses.t-BUTYL ALCOHOLThese considerations cannot explain the complex pattern of changes in A(14N)displayed by solutions in aqueous t-butyl alcohol (fig. 3 and 5). The temperatureeffect in the low M.F. region parallels that found for the hydroxyl proton resonancefor these solvent mixtures.28* 29 This was interpreted in terms of a low-temperatureenclathration of the alcohol molecules, the marked temperature effect arising becauseof strong thermal interference with the considerable organisation required to buildclathrate cages. We therefore postulate that both DTBN and t-butyl alcohol aresolvated in an elaborate manner by water at low temperatures, with hydrogen bondslinking the guests to at least partial clathrate cages.Initially, therefore, the alcoholmolecules encourage the structure building process, and there is a marked increase in[AH(-1)-AH(O)]. As the M.F. of alcohol increases, there is insufficient water toenclathrate all the guest molecules, and a cage-sharing process is thought to comeinto play.30 This will have the effect of removing the weakly hydrogen-bondedwater molecules from DTBN, thus causing the dramatic fall in A(14N) seen in fig. 2.In pure t-butyl alcohol, hydrogen bonding is an inefficient process, largely for stericreasons. Differential line-broadening increases in the initial " plateau '' region inwhich A(14N) is constant, which suggests z, control.However, it increases furtherin the region of rapid fall in A(14N) which suggests that the equilibrium (1) maymake a contribution in this region.It has previously been found 28* 29 that large, nearly spherical, molecules such astriethylenediamine are particularly effective in encouraging cage formation in waterat low temperature, so the effect of this solute on aqueous DTBN was also investigated.The results are summarised in fig. 10. The initial insensitivity of A(14N) found fort-butyl alcohol is not so marked in this case. This is because triethylenediamine hastwo basic functions and thus will compete strongly for (OH),,, groups. However,there is a large initial increase in asymmetric broadening at low temperature and thereis a small effect even at 25°C.METHANOL + T-BUTYL ALCOHOLTo check that the complex behaviour of DTBN in water+t-butyl alcohol is afunction of water structural effects rather than being due to a particular interactionbetween DTBN and t-butyl alcohol, we studied the e.s.r.spectra for solutions ofDTBN in methanol + t-butyl alcohol throughout the M.F. range. All propertiesshowed a smooth change with M.F. and none of the peculiarities of the aqueoussystems were observed.OTHER NITROXIDE PROBESIn our preliminary studies,15 we compared the behaviour of OTEMPO andQualitatively similar results were obtained. Thus, TEMPO with that of DTBNY . Y . LIM, E . A . SMITH AND M . C . R . SYMONS 2889for example, for the water + t-butyl alcohol solutions the A(14N) against M.F.plotshad the same form as those in fig. 2. However, in our view, DTBN was the mostsuitable because of the narrow lines and the absence of any tendency for the protonstructure to become resolved.CONCLUSIONSPrevious measurements 16, l7 leading to z, [ze in ref. (16) and (17)] were madeat 25°C. In our experience solvation effects on the extent of asymmetric broadeningare small and close to experimental errors at this temperature. Thus all the built-inerrors involved in extracting the widths of individual proton components and incalculating absolute correlation times combine to make the final results uncertain(except for aqueous glycerol solutions). However, at temperatures close to 0°Casymmetric broadening is a major effect for some systems, and the results are morereliable.We agree with Jolicoeur and Friedman that, with a large experimentalerror, it is impossible to differentiate between the effects of different additives at 25°Cbut this is only because the induced changes are extremely small at this temperature :differentiation is possible at - 0°C.Our major conclusion is that, for aqueous solutions of small nitroxide molecules,changes in A(14N) are relatively large and are a most informative part of the e.s.r.data. This is in direct contrast to previous conclusions.l69 l7 At -0°C asymmetricbroadening is often important for aqueous solutions, and is greatly enhanced by certainadditives. At this temperature 7, effects are small, but at elevated temperatures theyare dominant.The anomalously low dependence of the line-width for water andmethancl on T/q is explained in terms of hydrogen bonding.temperature/‘CFIG. 11.-Change in A(I4N) with temperature for aqueous solutions of DTBN.The most important conclusion drawn by Jolicoeur and Friedman l7 seems tobe that on cooling towards O’C, 7, actually increases instead of falling, for TEMPOin aqueous solution. This was interpreted to mean that TEMPO rotates morefreely near the freezing point than at ambient temperature. This, in turn, was claimedto be “the strongest and most direct evidence to date which tends to support theclathrate model of the hydration of hydrophobic solutes in liquid water ”. Whils2890 SOLVATION SPECTRAconsidering that n.m.r.results for aqueous solutions provide more direct evidencefor this effect,28* 29 we nevertheless feel that this e.s.r. evidence is open to question.It is true that acetone, whilst normally hydrogen bonded by liquid water is not sobonded when in solid clathrate cages,31 so an increase in T~ could indeed indicatethe onset of such enclathration for R2N0 molecules. However, this would requirethe loss of hydrogen-bonding with a consequent fall in A(14N). No such decreaseis observed (fig. 11). We have also observed an increase in line-width for DTBNin the low-temperature region, but as is indicated in fig. 7 this is due to the onset ofasymmetric broadening and should be ascribed to z, not zJ. Thus the anomaly isnot one of unusual rotational freedom but, apparently, of unusual lack of freedom.One possible explanatioii again involves enclathration but, since the nitroxide ishydrogen-bonded to the cage wall, we consider that this can lead to an enhancedlocal viscosity, rather than enhanced freedom.This is supported by the large increasein z, induced by added t-butyl alcohol at low temperature. In forming clathratecages about itself, this alcohol can stabilise cages around the nitroxide.However, when the enhancement of asymmetric broadening is accompanied by arapid fall in A(14N), we believe that a two-state model may be appropriate, involvingan equilibrium between “ free ” and hydrogen bonded nitroxide molecules. Jolicoeurand Friedman also invoked a two-state model, but theirs involved no change in thee.s.r.c0nstants.lAfter this work was submitted for publication, a paper on DTBN in supercooledwater appeared,32 in which it is claimed that at - - 15°C partial resolution of the protonhyperfine coupling was observed, from which a proton coupling of 0.091 k0.005 Gwas derived. Since this is completely different from our deduced value of -0.06 G,we have repeated these experiments. Our line-widths were consistently less than thoserep~rted,~’ being in the region of 0.36 G compared with minimum widths of 0.47 G.32At no stage between 0 and -24°C could any resolution be detected. Had a protoncoupling of 0.091 G been present then our lines would inevitably have been wellresolved. We suspect that the extra width found by Ahn was caused by dissolvedoxygen which was not removed, but we are at a loss to explain the reported partialresolution.The trends in parameters obtained from supercooled water have beenincluded in fig. 7. No extra factor is needed to explain these results.We thank the University of Malaya for leave of absence to (Y.Y.L.), Dr. D. Jonesfor preliminary studies, Professor M. J. Perkins for a gift of d9 t-nitrosobutane andDr. N. Hill for helpful discussions.Part 50 ; T. J. V. Findlay and M. C. R. Symons, J.C.S. Faraday 11, 1976,72,820.T. J. Stone, T. Buckman, P. L. Nordio and H. M. McConnell, Proc. Nat. Acad. Sci. U.S.A.,1965,54,1010.R. P. Mason and J. H. Freed, J. Phys. Chem., 1974,78,1321.R. P. Mason, C. F. Polnaszek and J.H. Freed, J. Phys. Chem., 1974, 78, 1324.J. M. Gross and M. C. R. Symons, Mol. Phys., 1965, 9,287.T. E. Gough and M. C. R. Symons, Trans, Faraday SOC., 1966, 62,269. ’ M, J. Blandamer, J. A. Brivati, M. F. Fox, M. C. R. Symons and G. S. P. Verma, Trans.Faraday Soc., 1967, 63, 1850.* J. M. Gross and M. C. R. Symons, Trans Faraday SOC., 1967, 63,2117.T. A. Claxton, J. Oakes and M. C, R. Symons, Trans Faraday SOC., 1967, 63,2125.J. Oakes and M. C. R. Symons, Trans Faraday SOC., 1968,64,2579.l 1 J. Oakes and M. C. R. Symons, Trans. Faraday Suc., 1970, 6 6 , l .l2 J. Oakes, J. Slater and M. C. R. Symons, Trans. Faraday Soc., 1970, 66, 546.l 3 L. C. Dickinson and M. C. R. Symons, Trans. Faruday Suc., 1970, 66, 1334289 1 Y. Y. LIM, E . A . SMITH AND M.C . R. SYMONSl4 D. Jones and M. C. R. Symons, Trans Faruduy Soc., 1971, 67, 961.l 5 D. Jones, Ph.D. Thesis (Leicester University, 1972).l 6 C. Jolicoeur and H. L. Friedman, Ber. Bunsenges. Phys. Chem., 1971, 75, 248.l7 C. Jolicoeur and H. L. Friedman, J. Solution Chem., 1974, 3, 15.l8 A. K. Hoffman, J. Amer. Chem. Soc., 1964, 86,641.l 9 R. Brikre, H. Lemiere, A. Rossat, P. Ray and A. Ruisseau, BuZf. Soc. chim. France, 1965, 32,'O G. Poggi and C. S. Johnson, J. Mag. Res., 1970,3,436.21 R. W. Kreilick, J. Chem. Phys., 1966, 45, 1922.22 K. H. Hausser, H. Brumner and J. C. Jochims, Mol. Phys., 1966, 10,253.23 R. W. Kreilick, J. Chem. Phys., 1967, 46,4260.24 N. M. Atherton and S. J. Strach, J.C.S. Furuduy II., 1972, 68, 374.25 D. Kivelson, J. Chem. Phys., 1960,33, 1094; P. W. Atkins and D. Kivelson, J. Chem. Phys.,26 M. C. R. Symons, Phil. Trans., 1975, B272, 13.27 A. K. Covington and J. M. Thain, J.C.S. Furuduy I, 1974, 70, 1879.28 B. Kingston and M. C. R. Symons, J.C.S. Faruduy 11, 1973, 69,978.29 W. Y. Wen and H. G. Hertz, J. Solution Chem., 1972, 1, 17.30 M. C. R. Symons and M. J. Blandamer, Hydrogen Bonded Soluent Systems, ed. A. K. Covington31 D. W. Davidson, Water : A Comprehensive Treatise, ed. F. Franks (Plenum Press, London,32 M-K. A h , J. Chem. Phys., 1976, 64, 134.3272 ; 1967,34,4479.1966,44,169.and P. Jones (Taylor & Francis, London, 1968).1973), vol. 2.(PAPER 61565)APPENDIX AThe overall width of each proton hyperfine component is given by :w, = a'+a''+P M,+y MI2where a', a", /3 and y are units of gauss (I G = 10-4T) and are given by :I [ ( g 11 - 2.0023)2 + 2(g, - 2.0023)2]And u = 1 /(I + W22,2)b is now in units of angular frequency. a', P and y are contributions to the linewidtharising from the averaging of the anisotropic g and A tensors by the moleculartumbling of the spin probe : a" is the spin rotational contribution to the linewidth2892 SOLVATION SPECTRAThe above equations can be put in the convenient form used by Poggi and1 and 0 lines ; expressing z, in terms of y and p Johnson l 9 by using the MI =respectivel

ISSN:0300-9599    

DOI:10.1039/F19767202876

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年代:1976

数据来源: RSC

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Adsorption Characteristics and the Thermal Stabilityof (TP, Na)-A ZeoliteBY MASAHIRO NITTA,* IYOSHI OGAWA AND KAZUO AOMURAFaculty of Engineering, Mokkaido University, Sapporo 060 JapanReceived 29th March, 1976Na-A zeolite was ion-exchanged with T1+ ions, and the molecular sieving ability of (Tlex, Na)-Ameasured as a function of the degree of exchange. An abrupt change in the amount of ethaneabsorbed occurred at 30 % exchange, as has been previously observed in (Kex, Na)-A. This wasattributed to site selectivity of the T1+ ion, and so the ion-exchange scheme was determined in orderto establish the cation distribution among the sites in the crystal. The stability of (Tlex, Na)-A asa desiccant was much better than that of the Linde Sieve 3A used in industry, as checked by measuringthe rate and amount of sorption of water vapour. The thermal stability was discussed on the basisof d.t.a.and X-ray pattern observations.The ideal composition of Na-A zeolite, contained in a unit cell, is given byNa12(A102)12(Si02)12 .nH20.' The 12 sodium ions are easily exchanged with mono-and divalent cations such as K+ and Ca2+. According to recent studies on the X-raystructural analysis of T1",oo-A,2* three kinds of sites in the crystal are available to12 TI+ ions. Two of these sites are similar to those of dehydrated Na1.00-A,4 onebeing near the centre of the six-membered oxygen ring (site I) and the other near thecentre of the eight-membered oxygen ring (site 11). The third is in the sodalite cageand is named site 111', while the corresponding site of Na-A is in the central cavityand is named site 111, for bre~ity.~ The eight sites I in a unit cell are occupied by8 TI+ ions and the three sites I1 are occupied by 3 Tl+ ions.The twelfth Ti+ ion occu-pies one of the four sites 111'. However, the positions of cations in partially exchangedzeolites, i.e., the distribution of Tl+ and Na+ ions, are not clear.Recently, Takaishi et aL6 and Nitta et aZ.' studied molecular sieving properties oftype A zeolites exchanged with several cations such as Ca'f, Zn2+, K+ and Ag+, andconcluded that they do not enter the three kinds of sites in the same order of exchange.On the other hand, no reports on the sorptive properties and structural stability ofT1-exchanged A zeolite have been found in the literature.8 Investigations of theseproperties have made it clear that the site selectivity of the Tl+ ion will have usefulpractical applications. We have published a brief account of the sorptive and thermalproper tie^,^ and a more detailed discussion is given here.EXPERIMENTALMATERIALThe starting material was Linde molecular sieve 4A in powder form.The compositionof a real crystal of Nal.oo-A is Na12(A102)12(Si02)12(NaA102)~ with 0 < 6 < 1.l0 In oursample, 6 - 0. Ion-exchange was carried out a t 358f 1 K for 12 h in a thermostat, andthe ion-exchanged zeolite sample filtered, thoroughly washed and dried in air a t 393 K for10 h. The sample was then stored over saturated NH4C1 solution for at least 2 weeks atroom temperature to ensure a constant moisture content.The degree of ion-exchange wasdetermined by flame photometry, EDTA titration and gravimeiric analysis.2892894and was subjected to two freeze-pump-thaw cycles before use.AD SORPTION CHARACTERISTICS OF TleX-A ZEOLITEAll chemicals were of a guaranteed grade ; adsorbate ethane had nominal purity > 99.5 %ADSORPTION MEASUREMENTEthane adsorption measurements were made in a volumetric apparatus. Prior to adsorp-tion at 273 K, the sorbent was baked at 573 K for 4 h under a vacuum pressure < 1.33 xN m-2.Water adsorption measurements were carried out by a dynamical method, i.e., in a flowsystem. The sorbent was exposed to air containing 2.33 x lo3 N m-2 water vapour at 323 K,in a flow rate of 100 cm3 min-'.When the weight of the sorbent ceased increasing appreci-ably, the sorbed water was desorbed by heating at given temperatures for 4 h, and thissorption-desorption cycle was repeated to test the durability of sorbent.D.T.A. AND X-RAY MEASUREMENTSDifferential thermal analysis of the zeolites was carried out in air using a Rigaku-Denki8001 DTA unit, the temperature being raised at 10 K min-l up to 1473 K. a-Alumina wasused as the reference material. X-Ray powder diffraction patterns were obtained on ascintillation counter spectrometer (Rigaku-Denki D-9C unit) using filtered Cu Ka radiation.Overall visual comparisons of the peak intensities were made to estimate the crystallinity ofthe zeolites.RESULTS AND INTERPRETATIONSORPTION CHARACTERISTICS FOR ETHANENo structural changes could be observed from the X-ray patterns on exchangingNa+ by T1+ ions and heating at 573 K, in agreement with the result of Barrer andMeier." The sorptive ability of (TleX, Na)-A for ethane was investigated. The rateof sorption was not studied in detail, and only the levels of sorption at equilibriumare discussed here.Equilibrium was taken to be established when no measurablechange in the degree of sorption was detected over a 2 h period. A plot of the amountsorbed against composition of the zeolite is shown by the solid line in fig. 1.The curve shows an abrupt fall at 30 % exchange in a manner similar to the(Kex, Na)-A system.l The window size of (TleX, Na)-A with a composition of 30 %3 0.06.4 *-- .*-I' 0.2 0.4 0.6 0.8 1.0Tl/(Na + T1)line is the coulombic potential at a position in the &oxygen ring.FIG.1.-Adsorption of ethane on (Tlex, Na)-A zeolites at 2.67 x lo4 N m-2 and 273 K. The dotteM. NITTA, K . OGAWA A N D K . AOMURA 2895T1 becomes smaller than that (4 A) of Na,.,,-A, since ethane (kinetic diameter 3.8 A)is not sorbed. 30 % exchangebecomes like Linde sieve 3A, which adsorbs only small molecules such as H20(2.65 A).The sorption level increased appreciably with the degree of thallium exchangebetween 0-20 % and 50-100 % exchange. This was not experimental error, being dueto an increase of attractive potential on the surface, induced by ion-exchange. Thisproblem will be discussed later.Hence, it may be concluded that (TlexNa)-ADURABILITY AS DESICCANTCommercial molecular sieve 3A [(K"", Na)-A] is used widely as a desiccant forHowever, it is thermally unstable, losing its dehydrating organic vapours and oils.t-- 6735 10 15 20number of regenerationsFIG.2.-Adsorption of water by 3A-type zeolites at 323 K. 0 molecular sieve 3A ; e improved3A ; A (T1E:46Na~.&A. The numbers on the curves are the regeneration temperatures.__l tFIG. 3,-The rate of sorption of water by 3A-type zeolites. 0,. molecular sieve 3A reactivated at573-673 K ; A,A (T18?,,Nao.&A reactivated at 673-823 K. The numbers on the curves are thenumbers of regenerations2896 ADSORPTION CHARACTERTSTICS OF TleX-A ZEOLITEsorptive ability easily in the regeneration process at higher temperatures ( - 623 K).Recently, Takaishi et dl' found that the thermal stability of (Kex, Na)-A wasmarkedly improved if the Na+ ions in sites I were replaced by Ca2+ ions; we shallcall this (Kex, Caex)-A zeolite "improved 3A".The test of the durability as adessicant of (TleX, Na)-A having 2 30 % exchange is very interesting, since its sievingcharacter is 3A type, and only water vapour is sorbed.The durabilities of these three 3A type zeolites for water vapour sorption areshown in fig. 2.Surprisingly, even after repeated water sorption-desorption cycles at the reactiva-tion temperature of 823 K, the sorptive ability of (Tl&6-Na0.54)-A remained almostthe same as that of the fresh sample, while the sorptive ability of molecular sieve 3Aand improved 3A fell rapidly.The rate of sorption on those zeolites also confirmedthat (TI'", Na)-A is the best desiccant, as shown in fig. 3. Thus, the order of thedurability is (TIex, Na)-A > (Kex, Caex)-A > (Kex, Na)-A.D . T . A . AND X-RAY PATTERNSAs a further indication of the stability of (TP, Na)-A, its differential thermalanalysis pattern was compared with others. The patterns of molecular sieve 3A aretemperature / Kvated 3A means the sample after 13 water sorption-desorption cycles (fig. 2).FIG. 4.-D.t.a. curves of molecular sieve 3A. Upper curve, fresh hydrated 3A ; lower curve, deacti-shown in fig. 4. The fresh sample showed endotherms in the temperature range 350-440 K and exotherms above 1100 K. The endotherms represent a dehydration stepand the exotherm a phase transition including loss of crystal structure.These resultsare summarized in table 1. The endothermic peaks of deactivated 3A became smallerand broader and the first exothermic peak shifted to lower temperature.(Tl'", Na)-A is thermally the most unstable of the three zeolites, as shown by itsfirst exothermic peak which appeared at the lowest temperature (1123 M). Furthermeasurements revealed that the dehydration of (TI"", Na)-A occurred most easily, asshown in fig. 5 and table 1. This was confirmed by the thermogravimetric curves.The X-ray powder diffraction patterns of hydrated molecular sieve 3A, improved3A and (TleX, Na)-A revealed that all the saniples were crystalline and that no changewas introduced by ion-exchange, compared with that of the original 4A.In the courseof heat treatment at the rate of 10 K min-', the X-ray patterns were measured aftercooling from the treatment temperature to room temperature. For all samples treateM. NITTA, K. OGAWA AND K . AOMURA 2897at temperatures below the first exothermic peak in the d.t.a. [(Q) in fig. 41, the patternswere the same as that of each hydrated sample, except that the diffractions fromseveral lattice planes were enhanced. After the first exothermic peak [(b) in fig. 41,the X-ray patterns of 3A, improved 3A and (TI", Na)-A showed a-phase, a-phase andamorphous phase, respectively. a-Phase is a new structure elucidated by Kokotailoand Lawton,12 in which the lattice is considerably strained. After the second exo-thermic peak [(c) in fig.41, the X-ray patterns showed only nepheline.3m ACQ 520 61iO 7temperature/KFIG. 5.-Endotherms in the d.t.a. of 3A-type zeolites. (a) (K;7,:5Nao.25)-A ; (b) (K$l(39Ca$:6kl)-A ;(c) (Tl:~46Nao.53)-A.From the above results, the thermal stability of the zeolites is in the order molecularsieve 3A > improved 3A > (Tl'", Na)-A, this being different from their stabilities asdesiccants.TABLE 1 .-RESULTS OF DTA MEASUREMENTS FOR 3A-TYPE ZEOLITESzeoliteendothermic peaksT/Kexothermic peaksT/Ka 348 443 1180 1265b 353 573 1140 1265a 348 443 493 1153 1273b (395) (550) 1123 1273(K:[75NaO.&A(KE6 iCa"03 9)-A(Tl:LNao. &A i} 413 1123 1243 1283a Fresh hydrated ; b after water adsorption-desorption treatments.Figures in parentheses smalland broad.The sample that had been deactivated by water sorption-desorption cycles showedHowever, the sharpness of the lines was the same X-ray pattern as the original.considerably diminished, indicating partial breakdown of structure2898 AD SORP TI o N c HA R A c T E RI s T I c s OF Tlex-A z E OL I TEDISCUSSIONSITE SELECTIVITY OF THE TIf IONAs stated above, the cation sites of Na1.00-A4 and Tl",*,-A2 zeolites were deter-mined by single crystal X-ray diffraction analysis. Also, the exchangeable cationshave their own intrinsic site preference^.^^ 7 9 9 9 l 1 Which of the three kinds of sitesis occupied preferentially by a cation, i.e., the site selectivity of a cation, can bededuced by sorption characteristics of partially exchanged forms, without a singlecrystal X-ray analysis.Molecular sieve properties of zeolite A are a function of thecation size and the level of occupancy of that cation in site 11, as indicated by a changein the size of the 8-oxygen window.0 2 4 6 8 10 12number of Na+ exchangedFIG. 6.-Scheme of ion-exchange and distribution of cations in (Tlex, Na)-A.As shown in fig. 1, the sorption of ethane decreases suddenly when the degree ofexchange of Na+ ions (ionic radius 0.98 .$) with Tl+ ions (1.40 A) exceeds -30 %.This sieving effect indicates that 3 Ti+ ions occupied sites II(3/12 = 25 %). Furtherexchange introduces Tlf ions into sites I, but this has no effect on sieving characteris-tics. The siting of the Tlf ion in site 111' cannot be proved from the sieving effect,but neither can it be excluded. The Na+ ion at site I11 seems to be energetically themost unstable of the 12Na+ ions, so exchange must occur there first and the intro-duced T1+ ion may sit in site 111'.Consequently, the ion distribution diagram for(Tl"", Na)-A may be as shown in fig. 6.It may be due to the ionic radii being much larger than the Na+ ion, that the siteselectivity of the TI+ ion is the same as that of K+ ion.'. On the other hand, theamount of ethane sorbed on (TIex, Na)-A increased appreciably in the ranges 0 to-20 % and -50 to 100 %. This cannot be explained on the basis of the change inapparent window size. Such a change in the sorption amount may be explained interms of an overlap of attractive effect due to electric field and molecular sievingeffects.An electric field could result from an uneven distribution of cations, andcould induce deformations of adsorbing molecules. The electrostatic potential fora point near the window was estimated. The potential for thejth point can be calcuM. NITTA, K . OGAWA AND K . AOMURA 2899lated using the X-ray structural data 2, of Na,.oo-A and Tl;:oo-A and the equationnwhere Qi is the charge on atom i of the framework and r t j is the distance betweenatom i and point j . Adsorbate molecules must pass through the 8-oxygen window tobe sorbed on the zeolite internal surface. Therefore, the potential on a point nearthe centre of the window was computed ; the coordinate of the j position is (0,0.602,0.500) on (TI"", Na)-A with <25 % exchange and (0, 0.627, 0.500) on those with2 33 % exchange.The result is shown by the dotted line in fig. 1. In the calculation,the sum was taken over the 112 framework atoms and the 12 cations surroundingpoint j . The coulombic potential increases with increasing degree of ion-exchange.This becomes an attractive force and gives rise to a small increase in the amount ofethane sorbed, overcoming the molecular sieving effect.STABILITYIn order to improve durability, Takaishi et 02. introduced a large number of Ca2+ions in place of K+ ions occupying sites I and 111', since they thought that molecularsieve 3A is thermally less stable than 4A because of the K+ ion on site 111' and theweak interaction of the K+ ions on sites I with the 6-oxygen rings.According to themthe (Kz3,Ca",l)-A prepared here retains its sieving character as 3A and should bethe most stable thermally of (Kex, Ca)-A series. If their quoted stability correspondsto the stability as a desiccant found here, this is partly verified (fig. 2). However, theimprovement was not sufficiently marked to increase substantially the lifetime of thesample as a desiccant, and it never increased the thermal stability.There are two possible interpretations for (TI"", Na)-A being the best desiccant(fig. 2). One is that the higher stability of the TI-exchanged zeolite is a result of thelower volatility of thallium compared with potassium. Another is the easy desorptionof sorbed water on the surface, as shown by d.t.a.results. When the d.t.a. curves ofNalSoo-A, Tl";f.,,-A and Ca";lo-A were recorded elsewhere, each showed two endo-thermic peaks : one peak appears at - 350 K for all the zeolites and another at 428,373 and 453 K for Na,.,,-A, Tl",o,-A and Ca",,,-A, respectively. According toDyer l 3 and Gal, l4 zeolite A has two kinds of adsorbed water ; free water and struc-tured water. The former aquates cations in the large cavity and is released easily asbulk water, while the latter is bound to cations linked to the oxygen-rings. The endo-thermic peak at the lowest temperature (350 K) therefore indicates the desorption offree water, being common to all the samples. The second endothermic peaks at highertemperatures (428,373,453 K) must correspond to the desorption of structured watercoordinated to Na+, TI+ and K+ ions, respectively.As can be seen from fig.5, the introduction of the divalent cation Ca2+ into thestructure causes the endotherm to shift to a higher temperature range. This agreeswith the results of Dyer and Wi1son,l5 who have investigated water loss in (Srex, Na)-Aseries with more detailed thermal analysis. Although their results show that theprocess is not as simple as the one described here, the differences in d.t.a. conditionsand cation type should be considered before rejecting our explanation.The results of endotherms for 3A, improved 3A and (Tl"", Na)-A are summarizedin table 1 and fig. 5. The endotherms of 3A and improved 3A, after several watersorption-desorption treatments, shifted to a higher temperature range (> 500 K),whereas that of (TleX, Na)-A did not change.These results show that the dehydra-tion of (TIex, Na)-A occurs most easily, as was also confirmed by the TGA curves2900 ADSORPTION CHARACTERISTICS OF TleX-A ZEOLITEThe easy dehydration may be a result of the hydration energy of the T1+ ion l6 beingmuch less than that of the Ca2+ ion in improved 3A.The authors thank Prof. Jiro Ishii of Tokai University for performing X-raydiffraction measurements and Prof. Kozo Tanabe of Hokkaido University for d.t.a.measurements.D. W. Breck, W. G. Eversole, R. M. Milton and T. B. Reed, J. Amer. Chem. SOC., 1956, 78,5963.P. E. Riley, K. Seff and D. P. Shoemaker, J. Phys. Chem., 1972,76,2593.A discussion of zeolite nomenclature is available : R. M. Barrer, suggestions presented at the3rd Int. Con$ Molecular Sieves (Zurich, 1973).R. Y. Yanagida, A. A. Amaro and K. Seff, J. Phys. Chem., 1973,77,805.M. Nitta, K. Ogawa and K. Aomura, Bull. Chem. SOC. Japan, 1975,48, 1939.T. Takaishi, A. Yusa and Y. Yatsurugi, Proc. 3rd Int. Conf. Molecular Sieves (Leuven Univ.Press, 1973), p. 246.M. Nitta, S. Matsumoto and K. Aomura, J. Catalysis, 1974, 35, 317.D. W. Breck, Zeolite Molecular Sieves (Wiley, New York, 1974), p. 593.K. Ogawa, M. Nitta and K. Aomura, J.C.S. Chem. Comm., 1975, 88 ; in this communicationthe amount of ethane sorbed on Tlex-A must be multiplied by 0.685.l o R. M. Barrer and W. H. Meier, Trans. Faraday Suc., 1958, 54, 1074; 1959, 55, 130.T. Takaishi, Y. Yatsurugi, A. Yusa and T. Kuratomi, J.C.S. Faraday I, 1975, 71,97.l 2 G. T. Kokotailo and S. L. Lawton, Recent Prop. Report, 3rd Int. Conf. Molecular Sieves(Leuven Univ. Press, 1973), p. 144.I 3 A. Dyer and R. B. Gettins, J. Inorg. Nuclear Chem., 1970,32,319.l4 I. J. Gal, 0. JankoviC, S. MalCiC, P. Radovanov and M. TodoraviC, Trans. Faradoy Soc., 1971,67,999.A. Dyer and M. J. Wilson, Thermochim. Acta, 1974, 10,299.I6 J. D. Bernall and R. H. Fowler, J. Chem. Phys., 1933, 1, 515.(PAPER 6/604

ISSN:0300-9599    

DOI:10.1039/F19767202893

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

hPart 1 .-Equilibrium and ThermochemistryBY ALAN M. DONCASTER AND ROBIN WALSH*Department of Chemistry, The University of Reading,Whiteknights, Reading RG6 2ADReceived 22nd April, 1976The title reaction has been investigated in the temperature range 609-649 K. The principalproducts were trimethylsilylniethyl iodide and hydrogen iodide formed in equal quantities at equili-brium, uiz.,I2 + MesSi + Me3SiCH21 + HI.Equilibrium constants were obtained over a limited range of reactant concentrations and in thepresence of added HI. The temperature dependence of the equilibrium constants was investigatedand thermodynamic parameters derived. At the mid temperature of the range, AGO (629.4 K) =+27.8 kJ mol-'. This result compares favourably with a group additivity estimate of +26.7 kJmol-' as well as the experimental value for AGO for the analogous equilibrium reaction involvingneopentane as reactant.There is no significant effect of Si for C substitution on the equilibriuminvestigated.There is considerable current interest in the gas phase kinetics and mechanismsof reactions of silicon containing compounds.l To understand the role of freeradical intermediates in such reactions a reliable free radical thermochemistry isrequired. This depends to a large extent on bond dissociation energy measurementsand we have recently undertaken a programme of such measurements beginning withD(Me3Si-H)2 and D(C13Si-H).3 The technique is that based on the kinetics ofiodination reactions developed by Golden and Ben~on,~ and we extend it here to astudy of the reaction between I, and tetramethylsilane. The measurement of thebond dissociation energy, D(Me3SiCH2-H) is described in part 2;5 in this paper wedescribe the study of the equilibrium reached in this reaction.Interest here centres on the question of whether tetramethylsilane acts typicallyas a silane or merely as a substituted hydrocarbon in its reaction with iodine.Inthe first case one might expect, by analogy with the reaction between I, and hexa-methyldisilane,6 the products Me3SiI and CH31. In the second case the productsanticipated are Me3SiCH21 and HI. Moreover, in this case the reaction would beexpected to reach equilibrium at very small extents of rea~tion.~EXPERIMENTALAPPARATUSThis was as previouslyMATERIALSTetramethylsilane (Fluka) as supplied for the n.m.r.reference, was 99.8 % pure. Smallamounts of a reactive but involatile impurity (probably Si,Me,) were removed by low7 The authors regret that no reprints are available.2902902 GAS PHASE REACTION OF 12+Me4Sitemperature distillation using a Podbielniack column. The SiMe4 was >99.95 % pure(by g.1.c.) after this treatment. It was degassed before use.Trimethylsilylmethyl iodide, Me3SiCH21, was prepared by reaction of sodium iodidewith Me3SiCH2Cl in dry a~etone.~ After removal of NaCl (water extraction) and distilla-tion to remove acetone, the product was identified by n.m.r. ['€I absorptions observed atT = 9.94 (9 protons) and 8.12 (2 protons)].Neopentane (K. and K.) was 99.9 % pure as supplied and was not further purified.Iodine (Koch Light, 99.998 % pure) and hydrogen iodide, prepared as before 2 .(fromFisons Analar solution), were degassed before use.PROCEDUREThis was as previously described.2* Equilibrium measurements were based on steadyst ate iodine spectropho t ometric absorbances .PRODUCT IDENTIFICATIONThis was in general made difficult by the low conversions resulting from the unfavourableequilibrium. Typically only - 0.5-3.0 Torr of products were formed which correspondedto conversions of -20-60 % (based on 12) or 0.5-2 % (based on SiMe4).HI was readily identified by evaporation from the frozen reaction products at 195 K andcomparison of its U.V. spectrum with that of an authentic sample in the reaction vessel.Me3SiCH21 could not be separated from the reaction mixture but was identified in twoways.First, by comparison of U.V. spectral differences obtained by subtraction of HI andI2 U.V. absorbances from those of equilibrium mixtures, with an authentic spectrum. Boththe Me3SiCH21 and unknown showed a broad maximum at A = 263 nm, Emax - 300 dm3mol-1 cm-l. Secondly, reaction of authentic Me3SiCH21 with HI rapidly resulted in fonna-tion of Me4Si and I2 (i.e. the equilibrium approached from the reverse direction).The reaction products were completely condensible at 77 K. Gas chromatographicanalysis of the gaseous fraction not condensible at -255 K (i.e. after removal of I2 andprobably Me3SiCH21) revealed complete absence of CH4 and other hydrocarbons but thepresence of small quantities of CH31 (corresponding to < 1 Torr in the reaction vessel.)The yields of CH31 were small and erratic but since they corresponded to -20-30 % of theHI formed, were not negligible.Blank experiments showed that when Me4Si and HI weremixed both inside and outside the reaction vessel methyl iodide was not formed. Howeverwhen such mixtures were passed through a 255 K trap containing condensed I2 (ix. a blankexperiment simulating extraction of product mixtures) methyl iodide was forrned in yieldscomparable to those formed in the experiments. This indicates that methyl iodide is almostcertainly formed during sampling and not reaction. U.V. and g.1.c. evidence also ruled outMe3SiI as a reaction product.RESULTSPRELIMINARY EXPERIMENTSThe qualitative product identification points to the occurrence solely of thereactionI2 + Me,Si * Me,SiCH21 +HI.This was supported by pressure measurements which indicated no pressure change (towithin k0.3 Torr* or better) during reaction.Me& was stable by itself, and didnot react with HI under reaction conditions. The best evidence for quantitativeequality between products was the fact that product U.V. absorbances summed togive the total reaction product absorbance. Fig. 1 shows an example of this at 641 K.The small discrepancy at ;1 = 240 nm was not regarded as serious in view of the goodagreement at other wavelengths.* 1 Tom-133.3 N m-2A . M. DONCASTER AND R . WALSH 2903At the end of a run the steady state iodine absorbance remained apparently con-stant for many tens of half lives (in the temperature range 609-649 K).At tempera-tures in excess of 680 K where this equilibrium is established in a few seconds, aslower further consumption of iodine was observed. Although this process was notinvestigated in detail, it was at least 250 times slower than the lower temperatureequilibration process.A/nmFIG. 1.-Comparison of the U.V. spectrum of reaction products (corrected for Iz) at 641 K with thesum of U.V. spectra of HI and Me3SiCH21. I, reaction product spectrum ; --.--- , HI spectrum ;_ - - , Me3SiCH21 spectrum ; - , sum of spectra.The reaction between neopentane and iodine reached a similar steady state atlow conversions and although products were not in this case specifically identified,past experience and the present observations with Me4% and I2 point to the reactionI2 + Me4C + Me,CCH,T + HI.EQUILIBRIUM MEASUREMENTSThese were made in the temperature range 609-649 K and equilibrium was judgedto have been reached when the iodine absorbance (at A = 484 nm) had been constantfor three or four half lives.In order to obtain sufficiently large changes in absorbancesit was necessary to use large excesses of Me4% This limited the possible range ofTABLE EQUILIBRIUM DATA AT 638 K[IzlolTorr5.365.285.135.334.8513.502.46[Me 4 s i] 0 f Torr61.1102.2122.9181.2243.2181.5118.0[I~le/Torr4.163.783.443.392.8710.011.421 0 3 ~5.8+ 1.45.9+ 1.06.8+ 1.76.2+ 1.25.7k0.96 .8 k 1.16.5k 1.2[Me3SiCH2IIL[HI],K = - where the subscript e refers to equilibrium value.[Me4SiJe[I2l2904 GAS PHASE REACTION OF I,+Me,Sistarting pressures considerably but in practice both reactants could be varied by afactor of from 5 to 10 in starting pressure and the ratio [Me4Si],/[I,]o was varied be-tween l l and 150. A selection of results obtained at 638 K is shown in table 1.Equilibrium pressures of the products were assumed equal to the decrease in iodinepressure.TABLE 2.-THE EFFECT OF ADDED HI ON EQUILIBRIUM AT 639 KtI210lTorr [Me&] o/Torr [HI] 0 ITorr tT21e/Torr6.69 305 0 3.916.71 31 1 1.14 4.356.20 308 4.19 4.556.66 300 8.32 5.392.74 302 0 1.202.48 23 3 3.70 1.812.65 29 1 4.67 1.911 0 3 ~6.6+ 1.16.2f 1 .O6.9k 1.07.6& 1.46.6+ 1 .O7.1f1.87.1f1.6The precision of measurement of this latter was limited to - & 5-10 % and the result-ing equilibrium constants were therefore uncertain to - f20 % in general.Theerror limits shown in the table represent a maximum based on uncertainty in experi-mental absorbances.In order further to substantiate that true equilibrium is reached in this system aseries of experiments was carried out at 639 K in which HI was added initially toattempt to suppress the consumption of iodine. In this case equilibrium constantswere calculated on the assumption that the HI product pressure was the initial valueincreased by an amount equal to iodine consumed. The results are shown in table 2where it can be seen that the equilibrium constants are, within experimental error,independent of the amount of HI added.Only limited variation of HI is possible andhigh pressures of Me& have to be used in order to ensure adequate conversion inthese experiments.Table 3 lists a summary of the equilibrium constants averaged at each temperature(although for consistency the HI " suppression " runs are omitted) together with thecalculated resulting reaction free energy changes. A Van't Hoff Isochore plot (seefig. 2) of the equilibrium constants yieldedlog,& = (0.13kO.67)-(29.Of8.1 kJ mol-l)/RTln 10from which, for the temperature range in question, (609-649 K), AH" = 29.0k8.1kJ mol-1 and AS" = 2.5+ 12.8 J k-l mol-1 are derived.A similar but more restricted investigation of the iodine/neopentane equilibriumled to K = (6.1 f0.5) x at 643.6 K (average of 6 experiments) and hence AGO(643.6 K) = (27.3 3.0.4) kJ mol-l.TABLE 3 .-SUMMARY OF EQUILIBRIUM CONSTANTS AND FREE ENERGY CHANGESTIK 1 0 3 ~ AGo/kJ mol-1650.1f0.3 6.05k0.53 27.6+ 0.5639.5k0.1 6.25f0.21 27.0f 0.2629.4+ 0.2 4.92f 0.34 27.8k0.4619.5 f 0.3 5.02f 0.39 27.3 k 0.4610.0fI 0.2 4.45 & 0.62 27.5 0.7ESTIMATED THERMODYNAMICS OF REACTIONThe thermodynamic properties of tetramethylsilane are incompletely known whilethose of trimethylsilyl methyl iodide are not known at all and so it is not possible tA .M . DONCASTER AND R. WALSH 2905make a direct independent check on the results obtained here. However, this systemis ideally suited for estimation of thermodynamic changes by the method of groupadditivity.** In the standard notation of the method for the reactions under con-sideration the change in a thermodynamic property X is represented by :AX = X(HI)+ X[C-(M)(H),(I)]-X(I,)-X[C-(M)(H),]where M is either C or Si.This expressior, represents the properties of M(CH3)4and (CH3)3MCH21 by the groups C-(M)(H)3 and C-(M)(H)2(I) respectively sinceall other groups in both molecules are the same and therefore differences in theirproperties cancel. A further assumption, which is known to work in practice,8 isthat changes in the associated atoms in a group have no effect. Thus C-(M)(H),is well represented by, say, C-(C)(H), and that differences such as,XEC--(M)(W2(I)I - xlC-(M)(H),Iare independent of nature of M.The implication of this is that the free energy changefor reaction at a given temperature should be the same for the reactions of bothtetramethylsilane and neopentane. This is well borne out by the data for the twosystems which are in agreement within experimental error.The appropriate thermodynamic properties of the C containing groups are listedin table 4 along with those of I, and HI. From these data the following may becalculatedAH" (298 K) = +39.7 kJ rno1-IAS" (298 K) = + 19.0 J IS-' mo1-I"TABLE 4.--SOME THERMOCHEMICAL QUANTlTlES OF INTEHESIC,/J K-1 mol IAS"/ ___--compound or group AH;'/kJ mol-1 J K- I inol 1 298 K 400K 500 K 600 1C12 a 62.43 260.58 36.88 37.24 37.44 37.57HI 26.36 206.48 29.16 29.3 3 29.74 30.35C-(C)(H), -42.17 127.24 25.90 32.80 39.33 45.15c-(c)(H)2(:) 33.64 179.70 40.08 48.33 54.31 60.84a Ref.(11). b Ref. (9). C Ref. (10).-Correction of these 8 *7.5 J K-I mol-1 givesto a mean reaction ternperaturc ( T ) , of 629 K using ACp" =AHo (629 K) = f42.2 kJ mol-'AS" (629 K) = +24.6 J K-' mol-'AGO (629 K) = +26.7 kJ mol-I is calculated. from whichIn general, the group additivity method 8* estimates AH: and AS" for compoundsto an uncertainty of +_4 kJ molkl and +4 J K-I mo1-I respectively. However, arecent review of the thermodynamic properties of iodides suggests uncertaintiesof about half this magnitude in this case. Carried through to AGO (629 K) an un-certainty of + 3 kJ mol-1 is reasonable for the method.Thus the agreement in AGOvalues between experiment and additivity is excellent. However, the agreement ispoorer between the corresponding pairs of AHo and AS" values. This is a common* This estimate includes allowance for symnietry differences between (CH&M and (CH,)3-MCHJ, amounting to +R In 122906 GAS PHASE REACTION OF I,+Me,Sioccurrence, and arises from experimental error causing a distortion of the tempera-ture dependence of the equilibrium constant. That this is not an especially seriousproblem is illustrated by the Van't Hoff plot shown in fig. 2 where both experimentaland additivity estimated lines are compared.0.8k2 0.7Me4-m0.60.500I I1.56 1.60 1.64103 KITFIG. 2.-Comparison of equilibrium constants with group additivity predictions (Me4Si system).0, experimental values ; - - -, least squares linear experimental fit ; ---.- groupIadditivity ; ------¶group additivity with adjusted AH".The best reconciliation between additivity and the data is obtained if the experi-mentally determined AG"(T) values are combined with the additivity estimates for ASoand Ei (which are more reliable than AH"). This leads to the third line shown onfig.2 which is in acceptable agreement with the data and from which is obtained at298 K, AHP[C-(M)(H),(I)]-AH?[C-(M)(H),] = 76.6 kJ mol-1 and for M = C,AH,"[C-(C)(H),(I)] = 34.4 kJ mol-l. This figure agrees well with the range32.0-34.4 kJ mol-1 within which previous values lie. OThus, in summary, despite the distortion in the Van't Hoff plot, these equilibriumconstants are in good agreement with thermodynamic estimates.DISCUSSIONThe results obtained in this study demonstrate conclusively that tetramethylsilanebehaves as a substituted hydrocarbon rather than a silane, not only by virtue of theobserved reaction products but also because of the small conversions and the magni-tude of the equilibrium constants obtained. The virtually identical magnitudes ofequilibrium constants and free energies for reaction of iodine with both neopentaneand tetramethylsilane demonstrate in particular that no special interaction existsbetween non-bonded iodine and silicon atoms in trimethylsilyl methyl iodide.The authors thank the S.R.C.for the provision of a grant in support of this work,and also Professor C. Eaborn for samples of Me,SiCH,Cl and Me,SiCH,BrA . M. DONCASTER AND R. WALSH 2907I. M. T. Davidson, Chem. SOC. Spec. Period. Report on Reaction Kinetics, 1975, 1, 212.R. Walsh and J. M. Wells, J.C.S. Faraday I, 1976, 72, 100.R. Walsh and J. M. Wells, J.C.S. Faraday I, 1976, 72, 1212.D. M. Golden and S. W. Benson, Chem. Rev., 1969, 69, 125.A. M. Doncaster and R. Walsh, J.C.S. Faraday I, 1976, 72, 2908.S. J. Band and I. M. T. Davidson, Trans. Faraday Soc., 1970, 66,406.S. W. Benson, Thermochemical Kinetics (Wiley, New York, 1968).S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O’Neal, A. S. Rodgers,R. Shaw and R. Walsh, Chem. Rev., 1969, 69, 279.J.A.N.A.F. Thermochemical Tables, 2nd edn., ed. D. R. Stull and H. Prophet (NSRDS-NBS37, Nat. Bur. Stand., 1971).’ C. Eaborn and J. C. Jeffrey, J. Chem. Soc., 1954,4266.l o S. Furuyama, D. M. Golden and S. W. Benson, J. Chem. Thermodynamics, 1969, 1, 363.(PAPER 6/787

ISSN:0300-9599    

DOI:10.1039/F19767202901

出版商:RSC    

年代:1976

数据来源: RSC