摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. TRANSACTIONS OF THE FARADAY SOCIETY Founded in 1903 to promote the study of Sciences lying between Chemistry Physics and Biology Volume 67 1971 Pages 1-1858 THE FARADAY SOCIETY LONDON @ The Faraday Society and Contributors 1971

ISSN:0014-7672    

DOI:10.1039/TF97167FP001

出版商:RSC    

年代:1971

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. TRANSACTIONS OF THE FARADAY SOCIETY Founded in 1903 to promote the study of Sciences lying between Chemistry Physics and BioIogy Volume 67 1971 Pages I 859-36 I 8 THE FARADAY SOCIETY LONDON @ The Faraday Society and Contributors 1971 PRINTED IN GREAT BRITAIN AT THE UNIVERSITY PRESS ABERDEEN

ISSN:0014-7672    

DOI:10.1039/TF97167FP003

出版商:RSC    

年代:1971

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. N.M.R. Studies of Some Dimethylthallium Compounds BY A.G. LEE AND G. M. SHELDRICK University Chemical Laboratory Lensfield Road Cambridge Received 29th May 1970 The proton n.m.r. spectra of (Me2T1X)2 (X = OEt OBu-t OPh SMe S02Me CsHs and CCPh) have been observed. The methyl doublet in the dimethylthallium ethoxide spectra shows an unusual variation with temperature tentative explanations are discussed. The variation of 2 J ( H . . .T1) with mol ratio in mixtures of trimethylthallium and trimethylamine shows that this coupling constant has the same sign in Me3Tl and Me3T1.NMe3. The dimethylthallium derivatives Me,TlX (X = NMe, OEt OPh SMe SO,Me etc.) are 1*4 predominantly dimeric with bridging X groups On the other hand trimethylthallium is monomeric i-n ~olution,~ and infra-red and Raman studies suggest a monomeric planar TIC3 skeleton.6 The n.m.r.spectra of mixtures of trimethylthallium with dimethylthallium cyclopentadiene and with dimethylthallium ethoxide give no indication of the presence of mixed dimers with bridging methyl groups. The methyl proton resonances of the compounds Me,TlX take the form of a doublet; the couplings to the I = 3 nuclei z03Tl (30 %) and ,05Tl (70 % natural abundance) are not resolved because these nuclei have similar magnetogyric ratios. For several of these compounds the methyl doublets are unusually broad at room ternperat~re.~~ 4 9 '9 * We have extended these observations and have found an unusual variation with temperature for dimethylthallium ethoxide (fig. 1) which is difficult to reconcile with a simple exchange of methyl groups bonded to thallium.EXPERIMENTAL The dimethylthallium derivatives were prepared from trimethylthallium by published procedure^.^ All preparations were carried out on a vacuum line of standard design. The samples were prepared in situ in the n.m.r. tubes to minimize the possibility of the presence of any catalytic impurity. The solvents were dried by distillation through 4A molecular sieve which had been flamed out in uucuo. N.m.r. spectra were run on a Varian Associates HA 100 spectrometer operating at 100 MHz for protons fitted with the standard 5 mm variable-temperature probe (-60 to +120°C). The probe was precalibrated with respect to temperature by measurement of the peak separation in methyl alcohol. Spectra were scanned by use of the field-sweep mode using the respective solvent as lock.A frequency meter was used in determining chemical shifts from the solvent and in measuring coupling constants. 7 8 N.M.R. STUDIES OF DIMETHYLTHALLIUM COMPOUNDS + 39O A n I + roo MezTIOEt in toluene(2Hs) FIG. 1 .-N.m.r. spectra of a solution of dimethylthallium ethoxide in deuterotoluene (mol ratio MezTIOEt /CsD5CD = 0.60). Most of the dimethylthallium compounds studied were relatively insoluble in non-polar organic solvents such as toluene but dimethylthallium ethoxide a liquid at room temperature was completely miscible with toluene and so was an ideal compound for a variable tempera- ture study. RESULTS AND DISCUSSION Table 1 lists the coupling constants and methyl peak widths w at half-height measured at 39°C for a number of dimeric dimethylthallium compounds ; except for the ethoxide all the data refer to saturated solutions.The significantly larger values of 2J(T1.. . H) for X = CCPh and (especially) for X = S0,Me might imply appreciable ionic character in these compounds; for the dimethylthallium cation in pyridine a value of - 41 5 Hz has been reported.* When the n.m.r. spectrum of a solution of dimethylthallium ethoxide was recorded at successively lower temperatures each of the methyl doublet peaks became steadily TABLE 1 compound Me2T10Et Me2 TlOB u- t Me2T10Ph Me2TlSMe Me2TI SO2 Me Me2T1C5H MezTIC = CPh solvent toluene toluene toluene pyridine pyridine pyridine pyridine V(TI ... H)/Hz w/Hz 371 -50 (see text) 377 5 368 20 372 5 426 4 379 3 393 7.5 A . G . LEE AND G. M. SHELDRICK 9 broader until at about - 10°C the two had virtually coalesced.On further cooling however the two peaks gradually sharpened again leading to a doublet with the original limiting value of 2J(Tl.. . H). The peak widths at half-height were measured in the temperature range -60 to +39"C; the two values were always equal within experimental error ; the methyl spectrum remained symmetrical throughout the temperature range. The observations are illustrated in fig. 1 and 2 ; the lines were broader for the more dilute solution in deuterotoluene especially at low tempera- tures. Sharp 1 2 1 and 1 3 3 1 multiplets were observed for the ethoxide group throughout the temperature range. 250 ' 3QO 200' ' ' ' ' ' ' 50 (K) FIG. 2.-PIot of w against T(K) for dimethylthallium ethoxide at mol ratios Me2T10Et/C6D,CD A 0.60; B 0.25; C 0.22.The addition of trimethylthallium to a solution of dimethylthallium ethoxide in toluene had no effect on the dimethylthallium ethoxide spectrum although as the temperature of such a mixture was raised the trimethylthallium doublet broadened due to intermolecular exchange of methyl groups as observed for solutions of trimethylthallium alone. lo The addition of dimethylthallium iodide also had no marked effect on the dimethylthallium ethoxide spectrum. Since the line shapes are insensitive to the presence of the dimethylthallium cation they presumably do not arise from exchange involving ionic species. We have considered three other possible explanations. (a) EXCHANGE OF METHYL GROUPS BONDED TO THALLIUM.-~ the crystal structure of trimethylthallium monomer units are associated by unsymmetrical methyl bridges to give tetramers which are themselves associated by slightly longer unsymmetrical methyl bridges to form a network polymer.Thus it is possible that the presence of methyl bridged dimethylthallium ethoxide oligomers would provide a pathway for exchange of methyl groups from one thallium atom to another. It is difficult for this model to account for the temperature dependence of the observed spectra or for the lack of methyl group exchange between dimethylthallium ethoxide and t rimet hy 1 thallium . 10 N . M . R . STUDIES OF DIMETHYLTHALLIUM COMPOUNDS (b) EXCHANGE OF THE DIMERIC DIMETHYLTHALLIUM ETHOXIDE WITH A SMALL EQUILIBRIUM CONCENTRATION OF MONOMER.-T~~S is consistent with the observed spectra provided that the monomer and dimer have similar chemical shfts and that the coupling constant in the monomer is large (> 1000 Hz) and of opposite sign to that in the dinier.The high temperature spectra in fig. 1 then represent the " fast exchange " limit and the observed coupling constant is the weighted mean of the monomer and dimer values. The low temperature spectra are then due to the dimer in the " slow exchange " limit ; the weak lines due to the monomer are not observed possibly because they would be very broad. Since the apparent value of J is similar in the high and low temperature limits (371.4 and 371.2 Hz respectively) the dimer/ monomer ratio must be very large. In the intermediate temperature region the left-hand dimer line is partially coalescing with a weak monomer line far to the right of the spectrum and vice versa; it follows that J takes opposite signs in the monomer and dimer.The spectra are symmetrical so the two species must have similar chemical shifts. Although this model accounts for the observations it places severe constraints on the n.m.r. parameters required for the monomer; in particular it suggests that 2J(Tl.. . H) will have opposite signs for three and four coordinated thallium. This is not consistent with the experiment described below in which 2J(Tl.. . H) has the same sign in TlMe and Me,N. TIMe,. A difficulty in the analysis of the temperature dependence is that both the rate constant for the exchange and the monomer-dimer equilibrium constant would be expected to be temperature dependent. low temperature spectra give no indication of a coupling 4J(Tl...H) e.g.in Me2205T1(OEt)2203T1Me2 although coupling constants involving thallium are usually large. Thus monomer/dimer exchange may be rapid at all temperatures investigated. The observed spectra could be accounted for by relaxation of the thallium nuclei which would necessarily give symmetrical spectra. If the relaxation mechanism involves scalar Tl.. .TI coupling in the dimer there will be a particular " mean dimer lifetime " and hence temperature at which the relaxation is most effective. The very large value (2560 Hz) of 2J(Tl.. .TI) in the tetrameric thallous ethoxide l2 suggests that the scalar TI.. . T1 coupling in dimethylthallium ethoxide might be unusually large leading to effective relaxation. The problem is complicated by the presence of two thallium isotopes. It is difficult to reconcile the observed concentration dependence with any of the above hypotheses unless there is some specific interaction between dimethylthallium eihoxide and toluene.Trimethylthallium has an apparent dipole moment of 0.5 in benzene but of zero in heptane? (C) FAST MONOMER/DIMER EXCHANGE WITH TI.. . TI SCALAR RELAXATION.-The TRIMETHYLTHALLIUM-TRIMETHYLAMINE EXCHANGE In view of the question of the relative signs of 2J(T1...H) in three and four coordinated thallium compounds raised in (b) we have measured the apparent value of 2J(Tl.. . H) for mixtures of trimethylthallium and trimethylamine in dichloromethane at room temperature. This system undergoes rapid exchange of the type Me,Tl + Me,TI . NMe +Me,TI. NMe + Me,TI so we should expect to observe the weighted mean of the coupling in Me,TI and Me,Tl.NMe,. A plot of J against mol ratio should pass through zero if and only if 2J(T1.. . H) has opposite signs in Me,Tl and Me,TI. NMe,. The results presented in fig. 3 show that there is no change in the sign of J. The deviation from linearity A . G . LEE AND G. M. SHELDRICK 1 1 2 4 5 . 1 0 I.0 2.0 “Me,l/[TI Meal FIG. 3.-Plot of ’J(T1.. . H) for Me3Tl in CHzClz against mol ratio NMe3/TlMe3. probably arises because the adduct Me3Tl. NMe is partially dissociated ; it does not affect the above conclusion. The dimethylthallium cation also exhibits a larger value of 2J(Tl.. . H) in more basic solvents ; this was rationalized in terms of a d-s mixing scheme involving the 5d electrons on the thallium atom.14 Hypothesis (c) seems to be the most consistent with the indirect evidence available.One of us (A. G. L.) thanks King’s College and the Salters’ Company for Research Fellowships. G. E. Coates and R. A. Whitcombe J. Chem. SOC. 1956,3351. H. Kurosawa K. Yasuda and R. Okawara Bull. Chem. SOC. Japan 1967,40,861. A. G. Lee J. Chem. SOC. A 1970,467. H. Gilman and R. G. Jones J. Arner. Chem. Soc. 1946,68 517. A. J. Downs and A. G. Lee to be published. ’ A. G. Lee Znt. J. Mass Spectr. Ion. Phys. 1969,3,239. ’ A. G. Lee J. Chem. SOC. A 1970,2157. * J. V. Hatton J. Chem. Phys. 1964,40 933. A. G. Lee and G. M. Sheldrick J. Organometal. Chem. 1969 17 481. lo J. P. Maher and D. F. Evans J. Chem. SOC. 1963 5543. l 1 G. M. Sheldrick and W. S. Sheldrick J. Chem. SOC. A 1970,28. l 2 W. G. Schneider and A. D. Buckingham Disc. Faraday SOC. 1962 34 147. l 3 W. Strohmeier and K. Humpfner 2. Elektrochem. 1957 61,1010. l4 G. D. Shier and R. S. Drago J. Organometal. Chem. 1966 5 330.

ISSN:0014-7672    

DOI:10.1039/TF9716700007

出版商:RSC    

年代:1971

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Thermodynamic and Structural Properties of Liquid Ionic Salts Obtained by Monte Carlo Computation Part 1 .-Potassium Chloride BY L. V. WOODCOCK AND K. SINGER Dept. of Chemistry Royal Holloway College Englefield Green Surrey Received 2nd July 1970 The equilibrium properties of liquid potassium chloride are simulated by a Monte Carlo model consisting of 216 particles interacting according to pair potentials of the form +(r) = ar-l+b exp (-Br)-c~r-~+dr-* with constants derived from the properties of the solid at 298 K.l The internal energy pressure molar heat capacities temperature coefficients of pressure and volume compressibility and entropy as well as radial distribution functions are computed for 24 V,T points lying on one solid phase (1045 K) and four liquid phase (1045 1306 2090 2874 K) isotherms at pressures up to 5 kbar.The calculated quantities which include the normal melting point and some experimentally inaccessible data are in good agreement with the available experimental results.The resolution of the radial distribution function into contributions from different types of ion pairs provides new information about the structure of the liquid salt. Computer simulation by the Monte Carlo (MC) and the molecular dynamics methods is at present the most powerful tool for deriving the macroscopic and micro- scopic properties of assemblies of classical particles from realistic intermolecular potentials. The results of these calculations are used (i) to test the adequacy of different forms of pair potentials (ii) as quasi-experimental material which permits analytical theories to be tested unambiguously (iii) to provide experimentally inaccessible information about molecular arrangement and movement and about properties at extreme temperatures and pressures.A remarkable result of recent work of this type is the fact that the properties of a real liquid argon can be cal- culated with considerable accuracy from a model consisting of lo2 to lo3 particles interacting according to the Lennard-Jones (1 2-6) pair potential with constants derived from the second virial coefficient of the gas (at super-critical temperatures). The purpose of this investigation is to explore whether MC calculations can be successfully applied to neutral systems of classical charged particles ; more specifically whether the properties of the simplest liquids of this type the liquid alkali halides- which are of theoretical and practical interest in their own right-can be derived from suitable pair potentials. It is hoped that this work will pave the way towards the study of more complex systems.Potassium chloride is chosen for extensive computations chiefly because of the wealth of experimental data available for this salt ; but also because of the approxi- mately equal size of the Kf and the Cl- ions and the consequently relatively simple radial distribution function (r.d.f.) and because both ions are iso-electronic with argon the simplest and most extensively studied liquid. Pair potentials derived from the properties of the solid at ordinary temperatures are used in the computation of the thermodynamic and structural properties of the 12 L. V . WOODCOCK AND K . SINGER 13 liquid at temperatures ranging between 1045 and 2874 K. The experimentally inaccessible data which have been obtained include the contributions of the coulomb dispersion and short range repulsion energy to the total configurational energy ; the resolution of the short range repulsion into + + + - and - - contributions and the resolution of the r.d.f.into contributions from like and unlike ion pairs; the mean Madelung constant; the free volume of the positive and negative ions of the solid and the liquid at the melting temperature and thermodynamic and structural properties at temperatures outside the range of experimental techniques. A pre- liminary report has been published and further details can be found in ref. (4). MC calculations for neutral systems of charged particles have been reported by Barker and by Brush et al. ; although designed to simulate the properties of plasmas these papers are of great methodological importance because the coulomb energy is evaluated by the rigorous method due to Ewald.' MC calculations for a model of electrolyte solutions-i.e.hard sphere ions in a dielectric continuum-have been carried out recently.8- THE MODEL In spite of the undoubted presence of many-body forces in ionic salts it has been suggested that the interactions can be represented by a pair-wise additive effective potentials.lO* l1 have shown that the Born-Mayer-Huggins potential In an extensive analysis Tosi and Fumi in which the last two terms represent dipole-dipole and dipole-quadrupole dispersion energies but which does not contain a r-4 ion-dipole term is compatible wih the properties of the solid alkali halides. The exponential repulsion term leads to better agreement with experiment than an inverse power repulsion term.The constant b has the same value for all alkali halides; B has a common value for the three ion pairs in any salt ; oij is a sum of ionic radii ; the constants cij and dij are calculated from spectroscopic data. The values for KCl are ~i j cm- 8 b 10-12 erg R lo8 cm-1 iij 10-60 erg cm6 dij 10-76 erg cm8 + + 2.926 0.423 2.97 - 24.3 - 24.0 + - 3.048 0.338 2.97 - 48.0 - 73.0 - - 3.170 0.253 2.97 - 124.5 - 250.0 ( I SiQ I = 23.067 ergx lo-'' cm) The three pair potentials are plotted in fig. 1. The MC model consists of 108 positive and 108 negative ions represented by coordinate triplets within a cube of side L. According to the periodic boundary conditions this cube is surrounded by replicas generated by translations by &L parallel to its edges and the interactions are not confined to the parent cube.The evaluation of the potential energy is complicated by the presence of long- range forces. At first an attempt was made to use the method of Evjen l2 in this the coulomb sum for each ion is truncated outside a cube of side L centred on the ion and containing equal numbers of positive and negative ions. When this method is applied in a MC process starting from a stable lattice configuration the coulomb energy gradually decreases to a value which is by -25 % too low ; at the same time marked changes appear in the r.d.f. ; a similar behaviour is observed when the initial configuration is that of a liquid. A drift towards low potential energies is also shown in some exploratory MC calculations by Krogh-Moe et aZ.13 in which the 14 PROPERTIES OF LIQUID IONIC SALTS Evjen method is used.This phenomenon cannot be attributed to the truncation if the side of the cube over which the summation extends is trebled (from L to 3L) the coulomb sum remains unchanged.15 One is thus forced to conclude in agree- ment with Brush et aZ.,6 that the Evjen method though valid for perfect lattices and for dilute electrolyte^,'^ leads to erroneous results when applied to systems of high effective charge density. 15- $ Pi U ' 10- 8 2 I 1 1 2 3 4 5 6 Y x cm FIG. 1 .-Pair potentials for potassium chloride.' No difficulties are encountered when the coulomb energy is evaluated by the method of E ~ a l d . ~ This is a mathematical transformation which is equivalent to the addition of mutually cancelling charge distributions whereby the non-convergent coulomb sum is converted into two more complicated but rapidly convergent sums.into two more complicated but rapidly convergent sums. The given distribution of point charges dr) = x c k 6 ( r - Irk) k is replaced by pl(r) + pr,(r) where p,(r) = CCk6(r - rk) - a3z4 exp (- a2 I r - rk i2) pIl(r) = x c k [ a3n-4 exp (-a2 I r-rk 12)-L-3]. In pl(r) the second term is a normalized Gaussian charge distribution of half width a-l and of opposite sign centred on each ion. pII(r) consists of an identical Gaussian charge distribution of the same sign as the ion and of a uniform normalized charge distribution of opposite sign. The Gaussian distributions in pI(r) and prI(r) clearly cancel each other as do the uniform distributions corresponding to equal numbers of positive and negative ions.The potentials of pl(r) and pIr(r) howevcr converge k and k L . V . WOODCOCK AND K . SINGER 15 rapidly the former because the potentials of the point charge and the Gaussian cancel each other at large I r-rk I ; the latter because the integration of the Poisson equation for p,,(r) leads to a convergent Fourier series. The expression for the coulomb energy takes the form aj = q + q g where rkkI is the distance between ions k and k’ in a cube of side L centred on r,; n is a vector with integer components ; rkkn = I rk-rkp+Ln I ; the prime in the summa- tion of QI indicates that k = k’ is omitted when n = (O,O,O) ; in @ n = (O,O,O) is oinitted. TABLE 1.-COMPUTATIONAL DATA. A IS THE NUMBER OF TRIAL DISPLACEMENTS IN THE MC PROCESS ; A IS THE NUMBER OF ACCEPTED MOVES ; A@ AND Ap ARE THE ESTIMATED STATISTICAL ERRORS IN THE POTENTIAL ENERGY AND PRESSURE.17 I N ALL RUNS THE MAXIMUM DISPLACE- MENT IN MC MOVES IS (Ax Ay Az) = (f0.5 h0.5 f 0 .5 ) ~ lo-* cm. N = 216 Y run cm3 mol-1 T/K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 41.48 42.70 43.92 48.80 46.36 48.80 51.24 53.68 58.56 48.80 51.24 53.68 54.66 58.56 63.44 58.56 63.44 68.32 73.20 85.40 63.44 72.30 85.40 97.60 1045 1045 1045 1045 1045 1045 1045 1045 1045 1306 1306 1306 1306 1306 1306 2090 2090 2090 2090 2090 2874 2874 2874 2874 solid solid solid solid liquid liquid liquid liquid liquid liquid liquid lidqid liquid liquid liquid liquid liquid liquid liquid liquid liquid liquid liquid liquid A/N 741 1481 1296 1296 1296 1852 1667 1667 148 1 1852 1481 1667 2407 1667 1667 1296 1296 1667 1667 1481 926 1667 1667 1667 A@ AP 32.2 0.15 0.08 33.4 0.15 0.05 35.0 0.40 0.11 38.2 0.20 0.11 32.9 0.20 0.17 33.7 0.25 0.19 35.1 0.25 0.21 36.5 0.20 0.11 36.9 0.15 0.07 38.7 0.25 0.20 39.5 0.20 0.13 40.8 0.20 0.17 40.7 0.10 0.07 41 .O 0.35 0.18 43.4 0.30 0.10 50.8 0.55 0.22 51.8 0.25 0.19 53.7 0.20 0.15 54.2 0.35 0.16 54.6 0.40 0.14 57.9 0.20 0.1 3 60.1 0.25 0.15 60.9 0.45 0.15 61.7 0.40 0.12 lOOA/lz lo3 J mol-1 lo3 bar The magnitude of the parameter a has opposite effects on the convergence of @I and iDII.Computing labour is minimized if @I can be truncated at 1 rk - rkt 1 = L/2 and the Fourier series of This can be achieved with a = §.714/L. If full use is made of tabulation the replacenient of the Evjen method by the Ewald method adds about 30 % to the computing time.The sums arising froni the second at I n I = 1. 16 PROPERTIES OF LIQUID IONIC SALTS and third terms in (1) are truncated at 1 rk-rk? 1 = L/2. A long-range correction whereby the effect of distant particles is replaced by that of a medium of uniform density is added to the r6-sum. The contribution of the dipole-quadrupole (r8) term is evaluated at every 2000th step ; this term adds only about - 0.5 % to the potential energy and its omission from the Boltzmann-factor which controls the MC process is not likely to lead to a significant distortion of the distribution. This was checked by showing that the correlation between the r8 sum and the other terms in (1) is negligible.15 The heavy requirements in computing time precluded the use of a larger number of particles in the model.A check calculation with 64 particles yielded-within the limits of statistical error-the same internal energy and pressure as the 216 particle model ; it is therefore reasonable to assume that an increase of the sample size would have little effect on the results. Configurations are generated by the method of Metropolis et al.16 The basic MC data include ensemble averages (indicated by angular brackets) of (i) the potential energy (a) and its different component (CD,") (@; -) (aDD) (where the superscripts refer to electrostatic short-range repulsion dipole-dipole dipole-quadrupole dis- persion and the subscripts to the type of ion pair) ; (ii) the virial (Y) = (zrk.VkQ) ; N (iii) the second moments k' (iv) the potential energy distribution F(E)AE ; (v) the r.d.f.s. obtained by compiling pair distance histograms (with intervals of 0.02 cm-8) at every 2000th MC step.When a computation for a V,T point in the liquid range starts from the NaCl-type lattice configuration the first lo5 MC steps are rejected to allow for fusion and sub- sequent equilibration; when as is normally the case the initial configuration is that of another V,T point in the liquid range the first 4 x lo4 steps are rejected. Table 1 lists some computational details including the number of MC steps used for each V,T point (mostly 2-4x lo5) and the statistical errors in the calculated potential energies and pressures determined from the standard deviations of sub-averages of 40 000 MC steps.17 The computer programme generates 80 000 steps per hour on the Mark 1 Atlas computer of the University of London.THERMODYNAMIC PROPERTIES The calculations cover 24 V,Tpoints lying on one isotherm of the solid at T = Tf = 1045 K and four liquid phase isotherms at T = T' 1.25 T, 2.00 Tf and 2.75 T'. The results are given in table 2. THE INTERNAL ENERGY is obtained from the mean potential energy by means of UINkT = (@)/NkT++. Thermochemical internal energies for 1045 and 1306 K at zero pressure can be calculated from the crystal energy at 298 K (Tosi Is) and from the specific heats and the heat of fusion compiled by Kelley.lg These agree with the MC results within 0.5 % (table 3) which is probably within the experimental error. If the lattice energy is taken from other sources,20 the discrepancy may increase to between 1 and 2 %; this is to be expected because the pair potential (i) of Tosi and Fumi is adjusted to fit the data of Tosi.18 The calculated difference between the energy of the liquid and that of the solid at 1045 K agrees well with the observed values (table 4).V c1-113 mol-1 41.48 42.70 43.92 48.80 46.36 48.80 51.24 53.68 58.56 48.80 51.24 53.68 54.66 58.56 63.44 58.56 63.44 68.32 73.20 85.40 63.44 73.20 85.40 97.60 T K 1045 (4 1045 (0 1306 2090 2874 lOfbar 0.95 - 1.38 - 3.26 - 6.28 2.82 0.67 -0.58 - 1.41 - 3.29 3.71 1.44 - 0.03 - 0.46 - 1.17 - 2.20 3.43 2.09 0.42 - 0.01 - 0.77 5.67 2.90 1.52 0.59 U lo3 J mol-1 - 655.0 - 652.1 - 650.0 - 639.0 -631.6 - 629.4 - 627.1 - 624.4 - 620.0 - 615.8 - 614.1 - 612.0 -611.1 - 607.6 - 603.0 - 571.3 - 567.2 - 563.1 - 559.7 - 552.4 - 533.4 - 526.7 - 518.8 -511.9 Pi lo3 bar 21.2 19.4 17.9 16.5 12.6 10.4 9.05 7.99 6.46 9.45 8.38 8.23 7.85 7.74 11.3 12.9 10.1 8.32 6.88 4.18 13.0 9.63 7.56 6.09 K 10-6 b a r 1 7.14 15.1 22.5 37.1 19.2 30.6 40.9 51.8 74.8 4.04 30.2 52.5 57.9 74.9 88.4 19.6 58.3 90.7 124.0 230.0 20.8 86.3 139.0 188.0 10-4 ClP K-I 1.45 2.80 3.87 5.86 2.33 3.04 3.54 3.96 4.62 0.35 2.19 3.37 3.65 4.50 5.24 1.21 2.82 3.61 4.09 4.61 0.94 2.89 3.67 3.99 B" bar K-1 20.3 18.5 17.2 15.8 12.1 9.92 8.66 7.65 6.18 8.66 7.24 6.42 6.30 6.01 5.93 6.16 4.84 3.98 3.29 2.00 4.51 3.35 2.63 2.12 CV CP J K-1 mol-1 48.4 48.3 48.4 52.7 47.1 51.7 48.7 53.7 51.7 48 .O 45.3 46.1 46.7 49.5 52.3 47.8 44.8 42.0 45.7 45.9 43.3 41.5 41.6 39.6 61.3 71.7 79.3 100.0 60.9 67.3 65.3 70.9 69.4 50.7 56.0 61.5 63.3 70.4 78.4 57.0 63.1 62.8 66.5 62.6 51.1 62.1 65.6 63.6 C P I G 1.27 1.48 1.64 1.91 1.29 1.30 1.34 1.32 1.34 1.04 1.24 1.33 1.36 1.42 1.50 1.19 1.41 1.49 1.46 1.36 1.18 1.50 1.58 1.61 S J K-1 mol-1 149.5 151.8 154.0 161.8 169.1 174.0 176.3 178.3 181.3 186.3 187.2 189.9 190.6 192.9 195.7 213.1 215.8 218.0 219.7 222.8 227.0 230.8 234.4 273.2 Y -4 18 ;s* -600- - 620 PROPERTIES OF LIQUID IONIC SALTS TABLE 3.-cOMPARISON OF MC RESULTS WITH EXPERIMENTAL DATA - U lo3 J mol-1 Vcm3 mol-I ap K-l pu bar K-l C J K-l mol-I C J K-l mol-1 S J K-l mol-1 KT lop6 bar-' expt.- 625.5 49.9 36.5 3.58 9.81 46.9 66.9 177.8 T = 1045 K MC - 628.0 50.20 36.1 3.33 9.23 50.5 66.8 175.1 expt. - 608.3 54.7 58.5 3.92 6.70 45.2 66.9 192.7 T = 1306 K MC TABLE 4.-cHANGES ON FUSION T = 1045 K solid liquid *MC U lo3 J mol-1 - 654.3 - 628.0 26.3 (QE) lo3 J mol-1 -747.9 - 722.0 25.9 (aR) lo3 J mot1 97.9 94.8 - 3.1 (@YD+ODQ) lo3 Jmol-I - 30.4 - 25.9 4.5 V cm3 mol-1 41.75 50.20 8.45 ICT bar1 10.1 36.1 26.0 a 10-4 K-1 1.97 3.33 1.96 & bar K-l 19.4 9.23 - 10.2 C J K-l mol-1 48.4 50.5 2.1 C' J K-l mol-l 65.3 66.8 1.5 -611.8 53.91 52.7 3.37 6.40 48.0 63.4 190.0 Aexpt.25.5 lo 26.5 24 8.3 2 5 9.09 23 7.23 26 9.2 27 3.5 l9 / / / / / ref. 18,19 23 22 23 22,23 22 19 19 % change (MC) - 4.0 - 3.5 - 3.2 - 14.8 20.2 257 99.5 - 52.4 4.3 2.4 -640tdp' I I I I I 50 60 76 80 90 V cm3 mol-1 5,2874 K liquid ; -- p = 0. FIG. 2.-U V isotherms. 1 1045 K solid ; 2 1405 K liquid ; 3,1306 K liquid ; 4,2090 K liquid ; TABLE 5.-cONTRIBUTIONS OF DIFFERENT INTERACTIONS TO THE MEAN CONFIGURATIONAL ENERGY V cm3 mol-1 41.48 42.70 43.92 48.80 46.3 6 48.80 51.24 53.68 58.56 48.80 51.24 53.68 54.66 58.56 63.44 58.56 63.44 68.32 73.20 85.40 63.44 73.20 85.40 97.60 T K 1045 (4 1045 (0 1306 2090 2874 WE> - 749.7 - 743.5 - 738.2 - 720.8 - 730.2 - 724.4 - 720.2 - 714.5 - 706.8 - 721.4 - 715.7 -711.0 - 709.0 - 704.4 - 697.2 - 692.5 - 686.1 - 677.8 -673.1 - 663.4 - 674.8 - 662.5 - 651.2 - 641.2 <QDD> ~ 1.8 1.6 1.5 1.2 2.3 1.9 1.7 1.5 1.3 2.3 2.0 1.7 1.6 1.5 1.3 1.9 1.7 1.4 1.3 1 .o 2.2 1.6 1.3 1 .o 95.1 90.3 86.4 77.2 96.4 91.5 88.8 85.0 80.6 95.4 90.7 87.4 86.0 84.1 80.4 88.7 85.4 80.2 78.5 74.9 87.9 80.8 76.4 72.5 2.3 2.1 1.9 1.6 3.0 2.6 2.3 2.0 1.6 3 .O 2.6 2.3 2.2 1.9 1.6 2.6 2.2 1.9 1.7 1.4 2.8 2.1 1.7 1.3 - 26.5 - 25.4 - 24.4 - 21.5 - 25.6 - 23.7 - 22.6 -21.5 - 19.9 - 24.2 - 22.9 - 21.8 - 21.4 - 20.3 - 19.0 - 20.9 - 19.7 - 18.2 - 17.5 - 15.9 - 20.0 - 17.7 - 16.1 - 14.7 -4.1 - 3.4 - 3.3 - 2.8 - 3.6 - 3.4 - 3.2 -3.1 - 2.8 - 3.5 - 3.3 - 3.2 - 3.1 - 3.0 - 2.8 - 3.2 - 2.9 - 2.8 - 2.6 - 2.5 - 3.2 - 2.7 - 2.6 - 2.5 <@) -681.1 - 678.3 - 676.1 - 665.1 - 657.7 - 655.5 - 653.2 - 650.6 - 646.0 - 648.4 - 646.6 - 644.6 - 643.7 - 640.2 - 635.6 - 623.4 - 619.3 - 615.3 -611.7 - 604.5 - 605.1 - 598.4 - 590.5 - 583.6 M 1.755 1.758 1.762 1.782 1.774 1.790 1.810 g 1.823 0 1.859 1.798 0 1.814 ' 1.850 U 1.881 R 1.819 1.851 2 1.874 1.976 1.820 1.874 1.940 1.997 0 1.783 0 1.820 * 2 U Z 1.904 w @E electrostatic coulomb energy ; W short range repulsive energy ; <DDD dipole-dipole dispersion energy ; (DDQ dipole-quadrupole dispersion energy ; M mean Madelung constant.20 PROPERTIES OF LIQUID IONIC SALTS Fig. 2 shows that U varies almost linearly with Y at constant temperature and that (aU/aV) changes little between 1045 and 2874 K ; the value is by about 50 % smaller than that of the solid at 1045 K.The change of (aU/aY) on fusion of a simple non-polar liquid is only about 5 % 21 ; the difference between the two types of liquid must be ascribed to the effect of long-range forces. Table 5 shows the mean contributions of the various terms in (1) to the configura- tional energy. The magnitude of the coulomb short-range repulsion dipole-dipole and dipole-quadrupole dispersion energies are approximately in the ratio 100 12.5 3.0 0.5 throughout the range. The short-range repulsion is made up of 96-97 % repulsion between unlike and 3.4 % repulsion between like ions; the latter contribute about 0.6 "/o to the total potential energy. The electrostatic energy of a uni-univalent ionic salt can be thought of as determined by the volume and by the dimensionless (mean) MADELUNG CONSTANT For the sodium chloride lattice M = 1.747 56 and for a completely disordered system i.e.an electrolyte in the limit of infinite dilution M = 0. The value of M in the solid near the melting point and in the liquid is unknown. The MC results in table 5 show that M increases roughly linearly with volume on the solid and liquid isotherms at T = Tf and increases on fusion (by 3 %). M decreases with increasing temperature at constant volume ; this points to an increasing cancellation of positive and negative potentials as a result of an increase of thermal motion; the increase of M with volume by contrast indicates a less complete cancellation of potentials due to ion-pair formation.This interpretation is supported by the r.d.f.s (see below). I I 100 0 2000 3000 temperature (K) FIG. 3.-Variation of the internal energy at p = 0 with temperature. L. V. WOODCOCK A N D K . SINGER 21 THE MOLAR HEAT CAPACITY Ct is determined from the second moment of the potential energy the statistical error is about + 3 J K-l mol-l. As can be seen from table 2 C decreases with increasing temperature along isochores and changes little along isotherms. The values for 1045 and 1306 K and p = 0 (obtained by interpolation with least squares straight lines fitted to the isotherms) are in good agreement with experiment (table 3). The molar heat capacity at constant pressure is determined from the thermal expansivity and pressure coefficients (see below) Cp = C,+ VTa,p,.Cp decreases with increasing pressure at constant temperature and is within the statistical error independent of temperature. This is in agreement with the experi- mentally observed constancy of Cp between T = Tf and 1650 K (= Tb)l0 and con- sistent with the almost linear variation of U(p = 0,T) with T between 1045 and 2874K (fig. 3). The numerical agreement between the MC and the experimental values for Cp is satisfactory (table 3). The constancy of Cp(p = 0,T) over a wide temperature range may in view of the approximate validity of the principle of corresponding states for fused be a general property ; if so the determination of thermodynamic properties at high temperatures would be greatly facilitated. C,INk = ((<D2) - (@)2)I(NkT)2 THE PRESSURE is calculated from the mean virial pV/NkT=l -(Y)/3NkT.Least-squares parabolae fitted to the computed pressures (table 2) are plotted in fig. 4. No fluctuations indicative of a phase change are observed in the MC calcula- tions for the solid and liquid branches at T = T f though equilibration of the I I I 1 I I 50 60 70 80 90 Vcm3 mol-1 FIG. 4.-p V isotherms. 1 1045 K solid ; 2 1045 K liquid ; 3 1306 K liquid ; 4 2090 K liquid ; 5 2874 K liquid ; D expt. points p = 0. 22 PROPERTIES OF LIQUID IONIC SALTS " liquid " at this temperature is slow. There is no sign of instability in the computer model at (moderately) negative pressures. The statistical error in the pressure is 150 bar which corresponds to an error of k0.5 em3 in the VOLUME. Within this margin the MC results agree with the most recent measurements 23 (table 3 fig.4) ; earlier experimental data are by 2-3 % lower.2s The omission of the r-*-term from the pair potentials leads to volumes which are by about 5 % larger. The computed change of volume on fusion at p = 0 lies well within the range of rather widely scattered experimental results (table 4 ref. (27) p. 46). The THERMAL PRESSURE COEFFICIENT (ap/aT) = Pv can be calculated either from the covariance of the potential energy and the virial or from (dp/dT) = [(aU/aV),-p]/T i.e. from U,V,T and p,V,T data. The two methods are in approximate agreement but the second is preferred because statistical estimates of second moments are generally less accurate than those of first moments. Table 2 shows that pv decreases with increasing volume along isotherms and that the rate of decrease also decreases (in magnitude).Pv decreases slowly with increasing temperature along isochores and changes little along isobars. On crystallization pv increases by -100 %. Experimental estimates obtained from the ratio of expansivity to compressibility are in satisfactory agreement with the MC results (table 3). The THERMAL EXPANSIVITIES are obtained from where (dH/dp) is determined from the variation of U+pV with p along isotherms. up increases by about 100 % on fusion and it increases with increasing temperature along the isobar p = 0. The MC results at 1045 and 1036 K are respectively by 7 and 14 % lower than the experimental values (table 3). The ISOTHERMAL COMPRESSIBILITIES are calculated by means of -(av/aP)T/v = ICT = a p / P v ; the alternative methods i.e.numerical differentiation of curves fitted top- V-isotherms and from the r.d.f. g(r) through the relationship 0 1 = NkT L V [ 1 + r;)J-(g(r) - l)r2dr are less satisfactory ; the former because the gradients are not determined with sufficient accuracy the latter because small fluctuations of g(r) at large r cause large errors. As expected the compressibility increases rapidly with increasing volume along isotherms and decreases with increasing temperature along isochores. The agreement with experiment at 1045 K is fortuitously close ; at 1306 K there is a discrepancy of 10 %. ENTROPY A N D FUSION Entropy changes along isochores and isotherms are calculated by integration of least squares parabolae fitted respectively to Cv,T and p,V data. For one solid and one liquid phase point at T = 1045 K the free volume and the absolute entropy L .V . WOODCOCK AND K . SINGER 23 have been determined. The method has been discussed elsewhere,29 but is presented here somewhat differently. The range of attempted MC displacements defines a volume vD around each particles; for liquids near the melting point it is possible to choose a 0D<L3/N but so large that the chance of acceptance of moves to positions outside uD is negligibly small. The ratio number of accepted MC moves to the number of attempted MC moves is then a MC estimate of where W ( r k ) = eXp (-(@,-@Tin)/2kT) @k = c4( I I'kt-rk I ) and @Ti" = k'*k c+( I rkt-rFin I ) is the minimum of the potential well in the volume vD the " cell " k' of particle k. ( )N-l indicates the average over the positions of the particles k' =I= k and uf is the mean free volume.The configurational integral Q' = s...l exp (-@/kT)& l...drN (2) can be written in the form N Q' = [vD...s n w(rk) exp( - g ) d r k . OD k = l According to cell by the Nth power of the mean one-particIe configurational integral i.e. the N-particle configurational integral can be replaced Although this step cannot be rigorously justified some evidence for its validity has been obtained by showing that sequences of acceptances of MC moves follow the statistics of independent events.29 The configurational partition function Q equals CQ' where C = 1 for the solid and NN/N! for the liquid. These values of C imply that-in contrast to the findings of Hoover and Ree for hard-sphere fluids l t h e entire communal entropy 2R appears on fusion.This is supported by the following evidence (i) the changes of entropy of a Lennard-Jones (12-6) liquid calculated by the present method are consistent with the values obtained by integration of MC Cp- and p-V-data (ii) the absolute entropies calculated for the 12-6 liquid with parameters corresponding to argon are in satisfactory agreement with the experimental entropy of liquid argon between T = 1.16 Tf and 1.62 T 29 ; the discrepancies are <0.25 R and show no trend with temperature as would be expected if the communal entropy were to appear gradually ; (iii) for liquid potassium chloride the calculated entropies at T = Tf and T = 1.22 Tf differ from the experimental values by less than 0.2 R. The entropy of the ionic species i is therefore SJNik = ((@1)-(@';'"))/2kT+l.5 [l+log (2~m~kT/h~)]+Ni~ log C+lOg ~f(i).The acceptance ratio of MC moves for a suitably defined volume uD and the mean minimum one particle energies for fixed positions of the other particles are determined by separate computations. The statistical convergence is satisfactory ; less than lo5 steps are sufficient to estimate the free volume within 5 % and the entropy within + 1 %. 24 PROPERTIES OF LIQUID IONIC SALTS The agreement between the computed and experimental entropies is good (table 3). The calculated free volumes (in units of 1045 K V = 41.48 cm3 rnol-l solid vf' = 0.68 k0.03 uf = 0.73 k0.04 1045 K V = 51.24 cm3 mol-l liquid vf' = 1.14+0.06 v; = 1.13k0.06. The MELTING TEMPERATURE at p = 0 is obtained by determining the melting pressure p t at T' = 1045 K and then T,(p = 0) by means of the Clausius-Clapeyron equation.The first step can be carried out graphically by plotting the isotherms of the Gibbs free energies of the two phases (fig. 5) or by means of cm3 per ion) are \ Gcryst(P1,T) + 4(Vcryst(pl,T') + Vcryst(p',T'))(~'-~l) = Gliq(p2,Tt) + 4( Vl i q(P2 T') + Vl i q(Pt T'))(p' - P J . Taking the data corresponding to p 1 = 0.95 kbar (solid) and p2 = 0.67 kbar (liquid) one finds p' = - 0.05 kbar,and -730 The excellence of the agreement with the experimental value is undoubtedly fortuitous ; but the result remains satisfactory when ample allowance is made for margins of error ; this leads to Tf = 1043+20 K. Because of the agreement between the experimental and the calculated melting point the entries in table 4 originally obtained by assuming the experimental value of Tf = 1045 K can be regarded as applying to the melting point of the model.- i -840 / -6 -4 -2 0 2 4 6 P lo3 bar FIG. 5.-Isotherms of the Gibbs free energy of the solid and the liquid at T = 1045 K. m solid V-T points; 0 liquid V-T points. RADIAL DISTRIBUTION FUNCTIONS The pair separation histograms formed from the MC configurations are normalized to give r.d.f.s. corresponding to all pairs (gm(r)) unlike ion pairs (g,(r)) and like ion pairs (gl(r)). The similar size of the K+ and the Cl- ions makes the further resolution L. V. WOODCOCK AND K. SINGER 25 of g into g++ and g- unnecessary. Only gm(r) has been determined experimentally for potassium chloride 32-34; the unambiguous resolution of gm(r) by X-ray or neutron diffraction is in general difficult if not impossible.The r.d.f.s are characterized by the following quantities the distance of closest approach d the position rmax and height h of the main peak the position rmin of the minimum following the main peaks and the apparent coordination numbers n defined by ,min n = (N - 1)VW14nJ r2g,(r)dr nu = ~ N V - I ~ ~ J ' r2g,(r)dr nl = (fN-I)V-'4nl 0 ' r2g,(r)dr. 0 ,min 0 ,min These parameters are listed in table 6. R.d.f.s for one solid phase point near the triple point and for one high temperature phase and one liquid are plotted in fig. 6. - The r.d.f. of the solid near the melting point exhibit some unexpected features which appear to anticipate the changes on fusion r r and n are respectively by 0.18A and 0.5 smaller than the values for the perfect lattice.The last two columns of table 6 where n is resolved into contributions due to like (n,J and unlike (n,,,) ion pairs shows that there is even in the solid some penetration (- 4 %) by like ions into the apparent first coordination shell; and the number of ions in this shell n = 5.3 is well below the perfect lattice value of 6. These features are accentuated on fusion n decreases to 4 n,,l increases and rF decreases. Between 1045 and 2874K the percentage of like ions in the first coordination shell increases from 7 to 15. This is important because attempts to resolve r.d.f.s. (g,(r)) obtained from scattering experiments have been based on the assumption that there are no like ions in the first coordination shell i.e. n,,z = 0.32* 33 This implicit identification of the first peaks of g and gu also leads to erroneously low estimates of the apparent coordination number because of the rapid rise of g at r<rEin rZin is appreciably smaller than rFin and n is consequently smaller than nu.If the first coordination shell is taken to be defined by gu rather than by g, one obtains the perfect lattice value nu = 6 for the solid and 5.5 for the liquid at T = T' ; the corresponding values of n are 5.3 and 4.0. The position of the first peak of g, ryx is fairly insensitive to temperature but decreases with increasing volume in the liquid range. The height of this peak h decreases gradually with increasing temperature along isochores but increases with increasing volume along isotherms. The behaviour of rumax and h on expansion indicates the incipient forma- tion of ion pairs at a separation closer to that corresponding to the minimum of the + - potential energy curve (1) at 2.6 A (see fig.1). For non-polar simple liquids where rmax is very close to the minimum of the pair potential curve the height of the first peak decreases strongly on fusion and with increasing temperature in the liquid range while rmax remains constant or increases slightly. Other features are similar to those of non-polar liquids the distance d of closest approach decreases with increasing temperature while the first peak of g becomes lower and broader (table 6 and fig. 6). The liquid phase r.d.f.s. for like and unlike ion pairs are strikingly different from the mean r.d.f. (fig. 6); g is similar to the r.d.f. of a simple liquid e.g. argon near the critical temperature ; there is no indication of any order beyond the weak second peak i.e.beyond Y = 6 A. Both gu and g r , 26 r,A FIG. 6.-Radial distribution functions. (a) solid T = 1045 K V = 41.48 cm3 mol-I ; 1 g,(r) ; 2 gl(r); -- gm(r) ; (h) liquid T =1 1045 K V = 48.80 cm3 mol-1 ; 1 g,(r) ; 2 gi(r) ; -- gm(r) ; (c) liquid T = 2874 K Y 97.60 em3 mol-' ; 1 g&) ; 2 gi(r) ; -- gm(r). T (K) 1045 (4 1045 (0 1306 2090 2874 a. A 3.253 3.285 3.316 3.434 3.376 3.434 3.491 3.545 3.650 3.434 3.491 3.545 3.567 3.650 3 748 3.650 3.748 3.842 3.931 4.139 3.748 3.93 1 4.139 4.327 TABLE 6.-QUANTITATIVE CHARACTERISTICS OF THE RADIAL DISTRIBUTION FUNCTIONS rmax du U 2.34 3.07 3.10 3.13 3.04 2.33 2.97 2.96 2.94 2.93 2.90 2.26 2.97 2.95 2.94 2.93 2.91 2.86 2.15 2.94 2.92 2.89 2.88 2.85 2.11 2.97 2.94 2.91 2.89 ,min 4.45 3.90 4.50 3.78 4.60 3.67 4.70 3.45 4.55 3.74 4.55 3.77 4.55 3.82 4.55 3.87 4.60 3.96 4.55 3.49 4.60 3.52 4.65 3.55 4.65 3.56 4.65 3.59 4.65 3.64 4.70 3.06 4.75 3.13 4.86 3.28 4.85 3.46 4.90 3.74 4.85 2.82 4.95 3.11 5.05 3.33 5.15 3.56 U hU I’U 6.0 6.1 6.2 6.0 5.7 5.5 5.3 5.1 4.8 5.6 5.4 5.3 5.2 5.0 4.7 5.2 4.8 4.6 4.5 4.2 4.6 4.4 4.2 3.9 dr rmax 1 rmin 1 3.18 4.54 5.70 4.58 5.75 4.63 5.80 4.58 6.56 2.98 4.30 6.65 4.38 6.75 4.45 6.85 4.52 6.90 4.64 7.00 2.91 4.45 6.80 4.50 6.85 4.58 6.90 4.61 6.90 4.73 7.00 4.78 7.05 2.65 4.76 7.05 4.85 7.10 4.90 7.10 4.93 7.15 4.98 7.25 2.54 4.94 7.15 4.99 7.25 5.05 7.30 5.13 7.35 hl 3.12 12.2 2.96 12.2 2.87 12.2 2.46 14.4 1.79 15.7 1.77 15.6 1.75 15.4 1.72 15.2 1.68 14.5 1.68 15.1 1.67 15.0 1.65 14.9 1.64 14.8 162 14.2 1.63 13.5 1.44 14.6 1.45 13.8 1.46 12.7 1.45 12.1 1.45 11.0 1.27 13.6 1.34 12.4 1.39 11.1 1.41 10.1 ,min m 3.75 3.80 3.85 3.75 3.65 3.65 3.70 3.70 3.70 3.65 3.65 3.70 3.70 3.75 3.75 3.70 3.75 3.75 3.80 3.85 3.75 3.80 3.85 3.95 gm(r) nm,u m,l 5.3 0.2 5.3 0.2 5.2 0.2 4.4 0.1 4.1 0.3 4.0 0.3 3.9 0.3 3.8 0.3 3.7 0.2 4.0 0.4 3.9 0.3 3.7 0.3 3.7 0.3 3.6 0.3 3.5 0.3 3.5 0.4 3.4 0.4 3.3 0.4 3.1 0.4 3.0 0.3 3.1 0.6 3.0 0.5 2.8 0.4 2.7 0.4 a is the NaCI-type lattice constant corresponding to the given molar volume.The suffices 21 I m denote “ unlike ” ‘‘ like ” and ‘( mean ” ; g,(r) = +(gu(r)+gL(r)) ; d is the distance of closest approach ; rmax and h are the position and the height of the main peak ; rmin is the position of the minimum following the main peak ; n is the mean number of particles in the apparent first coordination shell.28 PROPERTIES OF LIQUID IONIC SALTS on the other hand display oscillations up to lOA. This alternation of spherical shells of predominantly positive and negative charge has been predicted on theoretical grounds. R.d.f.s. for liquid potassium chloride obtained by X-ray and neutron scattering 32-34 are in qualitative agreement with the MC results for g (table 7). There is a decrease of rmax on fusion but it is smaller than in the MC model; the difference (0.2 A) is perhaps not greater than the experimental ~ncertainty.~~ TABLE 7.-EXPERIMENTAL AND CALCULATED CHARACTERISTICS OF THE MEAN RADIAL DISTRIBUTION FUNCTION r y (A) nm Lark-Horowitz and Miller X-ray 32 3.14 5.8 Z a r ~ y c k i ~ ~ X-ray 3.14 5.2 Levy et c ~ Z . ~ ~ X-ray 3.08 3.7 Levy et aZ.,34 neutron diffr.3.10 3.5 Zarzycki /Levy * 3.20 4.5 M.C. 2.96 4.3 * recalculation by Levy et al. from the original data of Zarzycki. DISCUSSION The MC results are here related to some theories of fused salts. Stillinger Kirkwood and Wojtowicz 35 have obtained integral equations for the r.d.f.s of hard sphere ions. Although they have not solved these equations they predict the charge ordering of the type seen in fig. 6b and 6c. Successful calculations of thermodynamic properties have so far resulted mainly from semi-empirical theories based on simple models in particular cell 37 and cell- hole 38 theories and the theory of significant structures.39* 40 These theories do not derive macroscopic properties from pair potentials but from parameters adjusted to fit some bulk properties.The MC results can be used to test the physical reality of the models and to provide independent estimates of the theoretically important parameters. The MC calculations lead to the conclusion that the cell theory gives the correct configurational partition function if correct ensemble averages are used for the free volume and for the depth of the cell potential energy minimum. If this is done there is no need to postulate the existence of holes ; indeed the fact that the probability of acceptance of MC moves to positions outside a cell of volume u,<v/N is negligibly small shows that holes of a sufficient size to accomodate ions cannot be an important feature in the liquid near the melting temperature. For the same reason it is difficult to attribute physical reality to “ gas-like regions ” as postulated by the theory of significant structures.The latent heat of fusion is largely due to the increase of the coulomb energy (table 5); not as has been surmised because the Madelung constant M 39 but because a small increase of M(-3 %) on fusion does not com- pensate the effect of the increase of volume. The solid if expanded to the volume of the liquid at T = T’ is electrostatically unstable compared with a typical liquid structure. McQuarrie 37 has adapted the Lennard-Jones and Devonshire cell theory to fused salts; he assumes that the exsitence of the Madelung constant implies that ions can be regarded as moving within a uniformly charged sphere i.e. unaffected L. V. WOODCOCK AND K . SINGER 29 by electrostatic forces. This is at variance with the MC values for the root-mean- square fluctuation of the electrostatic potential acting on an ion; these amount to 9.2 % of the total potential energy for the solid and 11.2 % for the liquid at T = Tf.A cellular hole theory 38 has been applied with some success to the calculation of latent heats expansivities and compressibilities of fused salts. Good agreement with the experimental temperature changes of volume and entropy on fusion and Cv (though not Cp) has been obtained by means of the theory of significant struc- t u r e ~ . ~ ~ . 41 In view of the implications of the MC results referred to above the value of these theories lies in their predictive power rather in the reality of the under- lying models. Bockris and Richards 22 have estimated the mean free volume from the velocity of sound and from an equation of state ; the two methods give 0.85 and 0.51 cm3 mol-1 for KCl near the melting point and agree within the estimated error of +50 % with the MC value 0.68 k0.03.After correction "for the presence of holes" both experi- mental methods however give a much lower value (0.27). A corresponding states theory 42* 43 has been successfully used to correlate the thermodynamic properties of some liquid ionic salts and their mixtures. The basic assumption of this theory is that the effective pair potentials in a given class of molten salts differ only by a scaling factor ; this in turn implies that configurations in which the short-range repulsion between like ions comes into play do not contribute to the Configurational integral (2). The entries for (a",) (@!!-) (@+,) and (@) in table 5 show that for potassium chloride this assumption is reasonable the mean short-range repulsions between like ions contributes 3-4 % to (BR) and only -0.6 % to the total potential energy.CONCLUSIONS The present work shows that computer simulation by the Monte Carlo method of neutral ionic liquids of high effective charge density is practicable and can produce quantitatively significant results. The Born-Mayer-Huggins potential (1) with constants derived from the properties of the crystal at 298 K is an excellent effective pair potential for liquid potassium chloride. Comparison between computed and observed properties though limited by the scarcity of experimental data for T> 1.25 T, reveals no systematic discrepancy and the agreement is often within the experimental error.This being so the experimentally inaccessible data obtained by MC simula- tion e.g. the different contributions to the configurational energy the r.d.f.s for like and unlike ion pairs the ionic free volumes and the properties at high tempera- tures are likely to correspond to the physical reality and throw light on the nature of the liquid ionic salt. We thank I.B.M. for a research award (to L. V. W.) and the staff of the Institute of Computer Science (University of London) for helpful advice and for a generous allocation of computing time. M. P. Tosi and F. G. Fumi J. Phys. Chem. SoZids 1964 25 31. I. R. McDonald and K. Singer Quart. Reu. 1970,24,238. This review contains a bibliography of Monte Carlo and molecular dynamics calculations applied to simple liquids.L. V. Woodcock and K. Singer Proc. Culham Con$ Computational Phys. 1969 (H.M.S.O.) paper no. 25. L. V. Woodcock Thesis (University of London 1970). A. A. Barker Austral. J. Phys. 1965,18 119. S . G. Brush H. L. Sahlin and E. Teller J. Chem. Phys. 1966,45,2102. ' P. P. Ewald Ann. Phys. 1921 21 1087. 30 PROPERTIES OF LIQUID IONIC SALTS P. N. Vorontsov-Veliaminov A. M. Eliashevich and A. K. Kron Electrokhimaya 1966,2,708. P. N . Vorontsov-Veliaminov and A. M. Eliashevich Electrokhimaya 1968,4,1430. S. Card and J. P. Valleau J. Chem. Phys. 1970,52 6232. lo S . Rice and W. Klemperer J. Chem. Phys. 1957,27,573. l 1 E. C. Baughan Trans. Farday SOC. 1959,55,736. l3 J. Krogh-Moe T. Gbstvold and T. Farland Acta Chem. Scand. 1969 23 2421. l4 ref. (4)) chap. IV. l5 ref. (4) chap.111. l 6 N. Metropolis A. W. Rosenbluth M. N. Rosenbluth A. H. Teller and E. Teller J. Chcm. Phys. 1953,21,1087. l7 W. W. Wood in Physics of Simple Liquids ed. H . N. V. Temperley J. S. Rowlinson and G. S. Rushbrooke (North-Holland Amsterdam 1968) p. 153. l8 M. P. Tosi J. Phys. Chem. Solids 1963,24,965. l9 K. K. Kelley US. Bur. Mines 1960 Bull. 584. ’ O T. C. Waddington Adv. Inorg. Radio Chem. 1959,1 157. ” J. O’M. Bockris and N. E. Richards Proc. Roy. SOC. A 1957,241,44. 23 A. K. Kirshenbaum J. A. Cahill P. J. McGonigal and A. V. Crosse J. I/zary. Nuclear Chem. 24 A. S. Dworkin and M. A. Bredig J. Phys. Chem. 1960 64,269. 2 5 C. J. London and A. R. Ubbelohde Trans. Faraday SOC. 1956 52,647. 26 H. Schinke and F. Sauerwald 2. anorg. Chem. 1956,287,313. 27 G. J. Jam Molten Salts Handbook (Academic Press New York 1967).28 I. S. Yaffe and E. R. van Artsdalen J. Phys. Chem. 1956,60,1125. 29 E. M. Gosling and K. Singer Proc. Int. Con$ Thermodynamics (I.U.P.A.P. and I.U.P.A.C. 30 T. L. Hill Statistical Mechanics (McGraw-Hill Book Co. New York 1956) chap. 8. 31 W. G. Hoover and F. H. Ree J. Chem. Phys. 1968,49,3609. 32 K. Lark-Horowitz and E. P. Miller Phys. Rev. 1937,51 61. 33 P. J. Zarzycki J. Phys. Rad. suppl. 4 1958,19 13. 34 H. A. Levy P. A. Agron M. A. Bradig and M. D. Danford Ann. N. Y. Acad. Sci. 1960,79 35 F. H. Stillinger J. G. Kirkwood and P. J. Wojtowicz J. Chenz. Phys. 1960 32 1837. 36 K. Furukawa Disc. Faraday SOC. 1961,32 53. 37 D. A. McQuarrie J. Phys. Clzem. 1962 66 1508. j8 I. G. Murgulescu and G. H. Vasu Revue Roumaine Chem. 1966,11,681. 39 C. M. Carlson H. Eyring and T. Ree Proc. Nat. Acad. Sci. 1960 46 333. 40 G. E. Blomgren Ann. N. Y. Acad. Sci. 1960,79,781. 41 R. Vilcu and C. Misolea J. Chem. Phys. 1967,46 906. 42 H. Reiss S . W. Mayer and J. L. Katz J. Chem. Phys. 1961 35 820. 43 M. Blander Adv. Chem. Phys. 1967,11,83. H. M. Evjen Phys. Rev. 1932,39,675. I. R. McDonald and K. Singer Disc. Fmaday SOC. 1967,43,40. 1962,24,1287. Cardiff 1970). 762.

ISSN:0014-7672    

DOI:10.1039/TF9716700012

出版商:RSC    

年代:1971

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Solid-Liquid Phase Equilibrium in the Sodium-Caesiuni Alloy System BY J. BEVAN OTT J. REX GOATES AND DEE E. OYLER Dept. of Chemistry Brighain Young University Provo Utah Received 26th May 1970 Thermal methods werc used to determine with high precision the solid-liquid phase equilibria diagram for the sodium-caesium system.The results differ greatly from those of earlier workers especially near the eutectic composition where differences in melting points as large as 35 K occur. Identification of the phases involved in the peritectic halt was not conclusive but does support the proposal that the peritectic results from the formation of an Na2Cs intermetallic compound by a sluggish reaction. Two previous investigations have been made of the freezing points of sodium- caesium alloys in order to determine the solid-liquid phase diagram for the system.'* The measurements were made without the advantages of precision resistance thermo- metry high-purity metals and adequate inert atmosphere facilities.As might be expected the two sets of data are in poor agreement. Freezing point differences as large as 30°C and a difference in eutectic composition of 5 mol % exist between the two sets of data. Both Rinck and Goria observed an invariant point at about 265 K on the sodium-rich side of the diagram. This they attributed to the formation of a peritectically melting Na2Cs intermetallic compound. The reaction apparently is very sluggish since the eutectic halt was still observed in alloys with less than 10 mol % Cs. X-ray measurements failed to show the existence of the compound presumably because of the small amount of it which was formed in the sample that was studied. The techniques now available for making freezing point measurement are at least an order of magnitude better than was reported by any of the previous investigators.In addition improved techniques now available for annealing the sample for long periods of time improve the chances for forming intermetallic compounds. As part of our extensive study of alkali metal mixtures we thought it was worthwhile to re-examine the complete phase diagram for this system. EXPERIMENTAL CHEMICALS High purity (99.9 % minimum) caesium was obtained from the Kawecki Chemical Company. Batch analysis by Kawecki Chemical indicated 0.049 mol % Rb 0.010 mol % K 0.025 mol % Na with negligible amounts of other elements. Oxygen analysis was not available. However calculations of the change in melting point with fraction melted indicated less than 0.01 % oxygen. The caesium is considered to be better than 99.9 % pure.Reactor-grade sodium obtained from the U.S. Industrial Chemical Company was used in making the alloys. The sodium is the same as was used in previous work on the Na-Rb sy~tem,~ where it was shown that the impurities were limited to t0.05 mol % total. 31 32 SODIUM-CAESIUM ALLOY SYSTEM PREPARATION OF SAMPLES Samples were prepared in a Vacuum Atmospheres Corporation argon glove box. Oxygen and water vapour concentrations were kept at t l p.p.m. by circulating the argon through a purification train. Under these conditions the Na-Cs alloy sample showed no oxide formation after several hours in the box and showed only a slight oxide layer when left for several days. Samples were prepared in the box by weighing the sodium and caesium on a top-loading Mettler P-160 single pan balance (0.001 g accuracy).The metals were weighed into a nickel crucible and melted to form a homogeneous liquid mixture which was then transferred into the freezing point apparatus. To conserve caesium some samples were prepared in a similar manner by dilution of an alloy sample of known composition with sodium or caesium. APPARATUS Two different time-temperature devices were used in making the measurements. The general designs of both devices have been described previ~usly.~~ Briefly the apparatus in which the (time-temperature) cooling curves were obtained consists of a doubly-jacketed stainless steel sample tube. By controlling the temperature in the outer jacket and the vacuum in the inner jacket cooling and warming rates varying from a few degrees per minute to degrees per hour were obtained.The sample was stirred in this apparatus with a rotary stirrer. This entire apparatus was suspended inside the argon glove box so that all operations from preparation of the sample to freezing point measurement were made with minimal chance of contamination of the metals with oxide. Temperatures were measured with a Leeds and Northrup high precision recorder. The thermometer was calibrated by Leeds and Northrup Co. at the ice steam sulphur and oxygen points. The calibration was checked by us at the ice point (273.150 K) the mercury freezing point (234.29 K) and the sodium sulphate decahydrate transition temperature (305.534 K) before during and at the conclusion of the measurements. In all cases the values obtained agreed with the calibra- tion to within 0.01 K.We estimate our temperature scale to be accurate to within 0.02 K over the range of the experimental measurements. The second apparatus is essentially a cryogenic calorimeter. A stainless steel sample vessel (volume E75 ml) is suspended inside an evacuated chamber. Temperatures in the sample vessel are measured with a Leeds and Northrup low temperature (type 8164) platinum resistance thermometer. This thermometer (162 689 5) was calibrated by the National Bureau of Standards at sixteen temperatures over the range 10-400 K. In this apparatus the sample vessel is effectively insulated from the surroundings. As a result a wide range of cooling and warming rates can be obtained by controlling the tempera- ture of the surroundings and the rate at which electrical energy is fed into a heater wound around the sample vessel.Because of the precise temperature control that was possible this apparatus was used principally to cycle thermally very slowly and to anneal an alloy sample within narrow temperature ranges making possible optimum conditions for the formation of the intermetallic compound. RESULTS AND DISCUSSION MELTING POINTS Melting points were determined over the entire composition range from (time- temperature) cooling and warming curves. The results are summarized in table 1 and fig. 1. The data are considered accurate to within k0.2 K. The eutectic point occurs at 241.32k0.10 K and 0.791 mol fraction caesium. A peritectic halt was observed at 265.25 k 0.20 K and 0.704 mol fraction caesium. and those of Goria,2 shows that the data are all in reasonably good agreement at compositions below 0.3 mol fraction caesium.At this composition however the different sets of data diverge. A comparison of our results with those of Rinck J . B . OTT J . R. GOATES AND D. E. OYLER 33 Differences become large at compositions around the eutectic value. Compared with the present study Goria's values are as much as 27 K low to the left of the eutectic and 35 K high to the right of the eutectic (see fig. 1). The data of Rinck are more extensive and in better agreement with the present work. His,data on the caesium-rich side of the diagram are on the average within 2 K of our values. Excessive scatter in his experimental points in this region however make some of his data differ from ours by as much as 5 K. TABLE 1 .-MELTING POINTS Sodium-caesium system mol fraction caesium O.OO0 0.0506 0.1022 0.2001 0.2501 0.3327 0.4276 temperature K 371.05 357.86 352.88 349.08 347.51 344.13 334.66 mol fraction caesium 0.4989 0.5496 0.6018 0.6584 (0.704)a 0.7131 0.7447 temperature K 323.44 312.42 297.94 279.08 265.25 262.68 253.58 a peritectic point ; b eutectic point.mol fraction caesium 0.7789 (0.791)b 0.7985 0.8393 0.8959 0.9422 1 .oooo temperature K 243.78 241.32 243.00 253.59 269.35 283.27 301.59 At the eutectic composition the values of Goria and Rinck are 9 and 4 mol % lower respectively than the present study. The eutectic temperature determined by Goria is 4 K higher and the value by Rinck is 2 K higher than the present study. Agreement on the peritectic temperature is within 1 K. 380 I I I I 1 1 0'2 0'4 0 6 0 8 110 220; mol fraction caesium FIG.1 .-Solid-liquid phase diagram for the sodium-caesium system. 2 34 SODIUM-CAESIUM ALLOY SYSTEM PERITECTIC COMPOUND FORMATION Both Rinck and Goria attributed the peritectic halt to the formation of a Na@ intermetallic compound although no data were given to support the 2 1 composition of the compound. We found the formation of the peritectic as observed by the earlier investigators to be indeed a sluggish reaction. ' Considerable effort was expended in an attempt to get complete conversion of alloy mixture to inter- metallic compound. The temperature in the conventional freezing point apparatus could not be varied slowly enough to achieve equilibrium in the samples. In fact the halt was observed at all compositions to the left of the peritectic point.As a result we turned to the calorimetric apparatus where precise temperature control and slow annealing were possible. This procedure gave excellent highly reproducible peritectic halts. Three different samples with compositions corresponding to 0.25 (3 l) 0.33 (2 1) and 0.50 (1 1) mol fractions Cs were placed in the apparatus. The samples were cycled and annealed at temperatures between the peritectic and eutectic halts for periods of time as long as three weeks. In all three cases the results were similar. Initially a reaction occurred as evidenced by the shortening of the eutectic halt and lengthening of the peritectic halt. After about 100 h of annealing however the process slowed to the point that no further measurable change in the relative lengths of the halts was observed.In all three cases considerable eutectic remained even after the conversion had apparently ceased. Estimates based on the relative lengths of halts indicate that no more than 70 % conversion from the eutectic alloy to compound was achieved. In an attempt to overcomc the difficulties of obtaining equilibrium in bulk samples we next worked with a thin film system where the length of diffusion path of reacting components could be greatly reduced. A thin film of liquid alloy (2 1 composition) was smeared onto a piece of nickel foil. A thermocouple spot welded to the nickel foil measured the temperature of the sample. Time-temperature warming curves were obtained for the sample after annealing for periods of time ranging from 5 min to 6 h. We were again unsuccessful in getting complete conversion to compound as evidenced by the persistence of a eutectic halt.Our failure to anneal completely away the eutectic halt in either the calorimetric or thin film studies prevents us from establishing unequivocally the formula of the compound. However the peritectic halt in the calorimetric study extrapolated to the length it would have at zero eutectic halt (complete conversion to compound) and normalized to the same sample size is longest for the 2 1 composition. This gives support to the supposition by Rinck and Goria that the halt is a peritectic resulting from the formation of solid Na,Cs. We are convinced that an approach other than thermal measurements will be required to establish fully the composition of the compound. The authors acknowledge the support given this project by the United States Atomic Energy Commission under contract #AT (11-1)-1707. The help of H. T. Hall Jr. with some of the freezing point measurements is also appreciated. E. Rinck Compt. rend. 1934,199,1217. C. Goria Gazz. Chim. Ital. 1935 65 1226. B. Bohm and W. Klemm 2. anorg. Chem. 1939,243,69. J. R. Goates J. B. Ott and C. C. HSU Trans. Furaduy Soc. 1970 66 25. J. B. Ott J. R. Goates D. R. Anderson and H. T. Hall Jr. Trans. Fmuday Soc. 1969,65,2870.

ISSN:0014-7672    

DOI:10.1039/TF9716700031

出版商:RSC    

年代:1971

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Electric Permittivities and Dipole Moments of Solutes in Polar Solvents BY C. W. N. CUMPER AND P. G. LANGLEY Chemistry Dept. Woolwich Polytechnic London S.E. 18 Received 6th May 1970 Equations based upon the approaches of Debye Onsager Weaver and Parry and Buckingham are developed for calculating the electric dipole moments of polar solutes in polar solvents and employed for 21 solutes in benzene chlorobenzene and ethyl acetate solutions.Consistent results are obtainable from the measurements made in the non-polar and both polar solvents. Many electric dipole moments have been obtained from measurements made upon dilute solutions in non-polar solvents. This is because although Debye’s extension of the Clausius-Mosotti equation was derived for gases few compounds can con- veniently be studied in this phase and the approximations in applying the Debye equation to dilute solutions in non-polar solvents are not considered to be serious. In a polar liquid however the large electrostatic interactions between molecules modifies their rotational freedom and alters the reaction fields in the medium to such an extent that the Debye equation is no longer satisfactory even as an approxi- mation.The Onsager equation attempts to allow for the effect of the reaction field and has frequently been applied to pure liquids but does not take into consideration the geometrical and optical anisotropy of the polar molecules. Modifications for these effects have been introduced in several ways,3* depending upon the precise assump- tions made about the volume of the cavity occupied by the polar molecule and about its polarizabjlity. Buckingham has also amended Onsager’s relationship between polarization and the mean value of the component of the total electric moment of a molecule in the direction of the applied field.Many polar compounds are insufficiently volatile to be studied in the vapour phase and are too insoluble to be studied in non-polar solvents. In pure liquids the interactions between neighbouring molecules tend to be somewhat specific so there is much to recommend their investigation as solutes in dilute solutions in a polar solvent particularly if the results are extrapolated towards zero concentration to eliminate solute-solute interactions. Equations have been derived for the polariza- bility of solutes in polar solvents but they have been inadequately tested experi- mentally and are seldom expressed in a form which is convenient for extrapolation towards zero solute concentration. Four approaches are considered in this paper.One feature is common to all the equations. The mixture law for the specific polarization p of a solution with weight fraction w2 which emerges from the Clausius-Mosotti treatment,6 is P = WlPl +W2P2 = (1 -WJP1 +w2p2. The convention of employing subscripts 1 and 2 for solvent and solute respectively and an unsubscripted symbol for the solution is adopted. This law is not strictly 35 36 DIPOLE MOMENTS I N POLAR SOLVENTS valid for polar solutions since dipolar interactions between the molecules result in p 1 and p2 being concentration dependent. To obtain p free from solute-solute interactions it is customary to employ the limiting expression when w2 approaches zero viz. where p i is the specific polarization of the pure solvent and the last term expresses the variation of p1 with solute concentration.In a non-polar solvent this last term is negligible but Smith pointed out that it can be significant with a polar solvent. He suggested that 8pl/aw was approximately equal to F(84dw2) where 8 is the electric permittivity and the solvent factor F may be estimated from the variation of its specific polarization with the volume polarization of the solution. Experimentally it is found that in dilute solutions except when the solute associates P2 = Pi + ~ ~ P l ~ ~ 2 ~ W ~ ~ o - ~ a P l I ~ ~ 2 ~ ~ ~ ~ 0 ~ (1) E = E ~ + ~ W ; v = v l + p w 2 ; n2=n:+yw2 (2) where 0 is specific volume and n refractive index. The limiting gradients a p and y are employed in the following equations. CLAUSIUS-MOSOTTI-DEBYE EQUATION According to this equation the specific polarization of the solution is p = V(E- 1)/(&+2) that of the pure solvent being p i = vl(cl - 1)/(e1 + 2).Inserting these expressions into eqn (1) above and considering the limiting value of the solute polarization at infinite dilution The distortion polarization of the solute is frequently equated to its specific refraction r2 either determined upon the pure liquid solute (r = v2(ni - l)/(ni +2)) or from measurements upon dilute solutions when The specific orientation polarization 0p2 and dipole moment p2 of the solute at infinite dilution are consequently given by 0p2 = p 2 - r 2 = 4nN&/9kTM2 = where Nis the Avogadro number and M2 the solute molecular weight. ONSAGER EQUATION The Onsager equation is widely employed to allow for the reaction field in pure polar liquids.For a two-component system the relevant form of this equation is wIvl(&- n?) W,V,(E - nz) ~ ( 2 ~ + n ) + ~(2~+n;) Utilizing the Onsager relationship for the ratio p; / M l for the pure solvent and for convenience defining X = - n ; and Y = 2g1 +n we obtain by differentiating C. W. N. CUMPER AND P . G . LANGLEY 37 eqn (4) with respect to w2 and considering the limiting situation as w2 approaches zero It can be assumed that the effective specific volume v2 of the solute in solution is u + /? and its “ internal ” electric permittivity measured at high frequencies is eint = n4 +y. These values are close to 21 and n$ respectively and might be the more appropriate quantities in dilute solutions. Eqn ( 5 ) then becomes To incorporate the contributions from both electron and atom polarizations the refractive indices of the solute and solvent should be measured at infra-red frequencies but in practice the value for Na(D) light is often used.In a solvent of small polarity the value of X would be uncertain. WEAVER AND PARRY EQUATION One of the equations which makes some allowance for the shape of the molecules was derived in a form suitable for direct application to dilute solutions of polar molecules in polar solvents by Weaver and Parry. Their expression apparently contains printing errors and makes no allowance for the variation of solvent polariza- tion with composition. Solute molecules are considered to be ellipsoids of uniform internal electric permittivity e int = nz immersed in a medium of uniform electric permittivity 8,. The solute volume is taken to be the volume per molecule in the pure liquid and its point dipole moment is located near the centre of the ellipsoid and directed along one of its axes.For this model the differential form of the equation applicable as w2 tends to zero is where G1 is a function of the solvent alone and 3(v1 +/?)n+vl(el +2n:)y (u +p)(2e1 + H=( 3 ( U i +/?)n:Y-2U,Xy ) 3 % V l * In these equations PI depends upon the electric permittivity of the pure solvent (PI = (8 - 1)/(2e1 + l)) and C and D are defined in terms of the internal field function or shape factor A introduced by Ross and Sack :’ C = 3A - 1 and D = [2(n2 - 1 ) + C(2n2 + l)]/[(n2 + 2) + C(n2 - l)] where A = elm ds 2 [(a2 + s)3(b2 + s)(c2 + s)]% * a b and c are the semi-axes of the ellipsoid occupied by a solvent or solute molecule.38 DIPOLE MOMENTS IN POLAR SOLVENTS BUCKINGHAM EQUATION This equation was derived by Buckingham to take account of molecular shape and to modify the Onsager relationship between polarization and total electric moment. For two components his equation is 1 +(nf - l)Al l+(n:-1)A2 E ( ~ E ( E - + n2)v n2) = W1Pl( e + (nl-E)A1 )Z+W2P2( E + (n$-&)A2 ) Differentiating with respect to w2 applying the equation to the limiting situation at zero weight fraction and utilizing the reduced equation for the pure solvent we obtain h N p $ c1 + (n - g1)A2 2Xvi oP2 = - 9kTM2-( - 1+(ni-1)A2) When using any of the above expressions for the orientation polarization of the solute the greatest difficulty is in deciding how the specific orientation polarization of the solvent varies with its weight fraction in dilute solutions.Smith has given an approximate method of estimating d0p1/aw2 but it would seem desirable to deter- mine it experimentally. To do this 0p2 or p2 should be known for suitable solute molecules in the gas phase but in practice it is simpler to take the values obtained from dilute solutions in a non-polar solvent such as benzene. Each of the above equations can be used with non-polar solvents by putting X = c1 -nf equal to zero and making the normal assumption that aopl/aw2 is negligible. The investigation has been limited to equations which cover the main general approaches to the problem of calculating dipole moments in solution. The Guggen- heim-Smith * method gives identical results to the Debye equation when used in its complete form and the orientation polarizations in non-polar solvents differ by less than 1 % when the approximate expression is employed; the difference would be greater in polar solvents.The approach adopted in the Kirkwood-Frohlich treatment incorporating a correlation parameter g is not discussed because even in a one-component system our knowledge of liquid structure is normally insufficient to enable adequate values of g to be obtained by statistical mechanics. In systems with two polar components there would be three concentration-dependent g values so that in practice this approach would give an equation similar to (6) with the addition of empirical correction factors. EXPERIMENTAL AND RESULTS The purification of benzene has been described.'O Chlorobenzene was repeatedly shaken with concentrated HzS04 until the acid layer remained colourless washed with water dried over CaC12 and fractionated three times the middle fraction being used in each case.Ethyl acetate was dried over MgS04 and fractionated three times. TABLE NAL EXPERIMENTAL VALUE§ OF a p AND ')J AT 25.0"C FOR THE SOLUTIONS AND THE INTERNAL FIELD FUNCTION A OF THE SOLUTES solute A benzene naphthalene an thracene p henanthrene n-hexane cyclohexane dioxan diphenyl toluene anisole p henet ole chlorobenzene n-heptanol cyclohexanol ethyl acetate p-chlorotoluene 2-pentanone acetone methyl ethyl ketone benzophenone c yclohexanone nitrobenzene 0.21 1 0.243 0.269 0.135 0.118 0.275 0.282 0.160 0.190 0.156 0.144 0.185 0.082 0.246 0.165* 0.155 0.253 0.244 0.273 0.265 0.252 0.171 solvent benzene chlorobenzene 0 0. l O4 1.574 1.707 2.494 2.51 0 3.224 3.742 3.31s 9.243 14.01 1 1 .29 5.957 10.43 14.1 7 B Y a B Y - 4.691 0.232 -0.097 - 3.794 0.049 0.306 -2.975 - 0.024 0.636 - 2.93 1 - 0.022 0.555 - 6.681 0.559 -0.651 -5.623 0.387 -0.429 - 3.968 0.059 -0.320 0.208 -0.018 -4.542 0.248 -0.111 -0.128 0.054 -2.257 0.098 -0.026 -0.122 0.034 -1.653 0.129 -0.059 0.088 -0.286 -0.700 0.328 -0.432 - 0.070 - 0.168 l.189 0.184 -0.262 -0.027 -0.048 l.6& 0.198 -0.529 - 0.204 0.061 0.639 0.031 -0.019 0.096 -0.373 10.96 0.316 -0,531 0.116 -0.451 18.22 0.369 -0.550 0.117 -0.381 13-96 0.327 -0.572 -0.072 -0.126 E.19 0.142 -0,247 -3.598 0.067 0.293 - 0.235 0.059 - 0.286 0.352 6.281 -0.019 0.270 - 0.299 0.111 18.& - 0.089 0.079 * A for ethylacetate has been taken as 0.295 (see discussion).ethyl acetate U -3.633 -2.504 - 1.972 -2.318 - 6.350 - 5.075 -3.325 -3.872 -0.768 -1.158 0.489 0.393 - Z M 7 2.508 0.844 7.579 9.575 5.269 8.540 13-26 15.70 B -0.180 - 0.203 - 0.278 0.032 0.395 0.225 -0.148 -0.180 0.043 -0.122 - 0.086 - 0.221 0.123 - 0.049 -0.188 0.099 0.153 0.135 - 0.255 - 0.064 - 0.327 J 0.340 0.649 0.935 0.843 0.008 0.113 0.126 0.673 0.371 0.404 0.361 0.390 0.142 0.304 0.367 0.043 0.018 0.578 0.220 0.389 - 0.01 6 u W TABLE DIPOLE MOMENTS IN BENZENE AND CHLOROBENZENE SOLUTIONS AT 25.0"C dipole benzene solution chlorobenzene solution with c?pi/awz = 0 corrected for apllawz A m APD solute moment APB *PD APO Arcwp PD toluene 0.36 anisole 1.24 phenetole 1.38 chlorobenzene 1.59 n-hep t anol 1.74 cyclohexanol 1.74 ethyl acetate 1.84 p-chlototoluene 1.96 2-pentanone 2.77 acetone 2.78 methyl ethyl ketone 2.79 benzophenone 3.07 cyclohexanone 3.09 ni trobenzene 3.99 r.m.s.corresponding r.m.s. value for ethyl acetate solutions APO - 0.03 - 0.01 0.00 0.00 0.05 0.02 0.08 - 0.01 0.11 0.15 0.12 - 0.05 0.05 0.01 0.07 - 0.01 0.13 0.17 0.15 0.34 0.11 0.26 0.22 0.21 0.25 0.18 0.00 0.18 0.39 0.21 0.01 0.22 0.28 0.24 0.52 0.18 0.39 0.36 0.32 0.38 0.28 0.13 0.30 0.67 0.34 0.47 - 0.21 -0.17 - 0.23 -0.34 - 0.39 - 0.56 - 0.76 - 0.84 -0.81 - 0.91 - 0.98 - 1.43 0.72 0.04 - 0.22 - 0.08 0.15 0.07 0.12 - 0.24 0.24 0.20 0.23 - 0.19 - 0.04 - 0.34 0.19 oP = -1.33 OP = -3.59 - 0.05 0.04 0.19 0.34 0.61 0.23 0.42 0.16 0.46 0.45 0.38 0.12 0.51 0.58 0.94 0.35 0.67 0.37 0.71 0.74 0.61 0.28 0.30 1.05 0.40 0.61 0.39 - 0.20 0.02 (0.32) 0.16 0.10 - 0.24 0.09 - 0.04 0.02 - 0.04 -0.10 - 0.38 0.19 0.76 0.05 0.64 0.69 0.21 AmvP 0.00 0.08 0.10 (0.36) 0.09 0.01 0.00 0.09 0.01 0.01 -0.10 - 0.06 - 0.04 0.06 0.15 *PB - 0.02 - 0.08 0.10 (0.41) 0.08 0.03 0.02 0.10 0.01 0.00 -0.10 - 0.07 - 0.02 0.07 0.12 C.W. N . CUMPER AND P. G. LANGLEY 41 Each solute was extensively purified immediately before its solutions were prepared and the necessary measurements made at 25.0"C by the methods described previously.'' Seven dilute solutions were studied in each determiqation and the coefficients in eqn (2) are recorded in table 1. DISCUSSION BENZENE SOLUTIONS The dipole moments are designated as follows p, from the Debye eqn (3); po Onsager eqn (6); pwp Weaver and Parry eqn (7); pB Buckingham eqn (9). To obtain ,uwp and pB the internal field functions A were obtained from the graphs of Osborn,12 employing dimensions obtained from molecular models and are also listed in table 1.Table 2 contains the dipole moments in benzene solution evaluated from the Debye equation together with the increments above this value given by the TABLE 3 .-APPARENT ORIENTATION POLARIZATIONS OF NON-POLAR SOLUTES AT 25.0"C chlorobenzene solution - solute with apl/awz = 0 corrected for apl/awz OPD OPO OPWP OPB OPD opwp opB benzene napththalene anthracene phenanthrene n-hexane cyclohexane 1.4-dioxan dip hen yl 10.72 8.40 6.04 8.59 19.28 15.91 13.39 12.66 0.70 -3.85 -4.46 -10.34 -3.40 -10.25 -1.10 -10.66 8.93 -6.98 5.00 -3.04 -1.21 - 8.52 4.40 0.50 - 6.07 - 13.04 - 12.04 - 14.88 -12.51 -5.18 - 0.70 - 12.74 6.13 0.06 -15.21 -4.03 -28.72 -4.15 -25.16 -1.61 -29.96 -1.40 18.53 0.66 -3.14 5.15 9.80 -0.54 -0.06 -3.42 - 3.46 -0.77 -2.15 0.46 5.94 - 0.30 r.m.s.12.54 4.45 7.67 10.72 19.32 2.86 2.84 corresponding r.m.s. value for ethyl acetate solutions 16.12 9.47 8.01 10.46 24.09 5.80 5.16 other three named equations. Dipole moments given by the Debye equation agree reasonably well with those from Onsager's equation. Both the Weaver and Parry equation and that of Buckingham allow for the shape of the molecules and give significantly larger values particularly pB which are about 0.12 D greater than pwp. The average difference between pwp and pD is 0.18 D. POLAR SOLVENTS Table 3 lists the apparent orientation polarizations of eight non-polar solutes as dilute solutions in chlorobenzene ; they should be zero. Measurements in ethyl acetate solution give similar results. When no allowance is made for the variation of solvent polarization with concentration the results are not acceptable ; those from the Debye equation being particularly unsatisfactory.The Onsager equation is moderately successful but the remaining two equations frequently overcorrect and produce negative values for ,,P. The internal field function A for ethyl acetate depends on the average conformation of its molecules the value quoted in table 1 ( A = 0.165) refers to a planar molecule. Since its molecules are flexible its effective value would be greater and 0.295 is more consistent with the results for this solvent. Table 2 also lists the dipole moments of the polar solutes in chlorobenzene; the figures quoted are the increments above the dipole moments determined in benzene solution by the Debye method.With ap,/aw = 0 those derived from the Debye equation are significantly lower than the results obtained in benzene solution. The 42 DIPOLE MOMENTS IN POLAR SOLVENTS agreement between the results in non-polar and polar solvents obtained with the Onsager equation are much better but the expressions of Weaver and Parry and of Buckingham lead to values which are a little higher in the polar solvents Part of the difference resides in the omission of the term allowing for the variation of the polarization of the polar solvents with the solute concentration. We take the view that since most dipole moments have been measured in benzene solutions and cal- culated by the method of Debye it is expedient to obtain values for as dopl law which TABLE 4.-EMPIRICAL CONSTANTS FOR EQN (lo) AND (1 1) chlorobenzene D WP B ethyl acetate D WP B a -0.1609 0.0405 0.1366 - 0.1468 0.0943 - 0.1479 b -0.0609 0.0252 0.045 1 - 0.0932 0.0194 0.0333 c o.Ooo1 0.001 2 0.0010 - 0.W5 0.0016 0.0023 a' 0.3306 - 0.1779 - 0.3729 0.4140 - 0.1487 - 0.2873 CI 0.0409 - 0.2788 - 0.7817 0.0352 -0.5509 -0.8177 e' - 0.0203 - 0.0482 b' - 0.6788 0.4540 1.0948 - 0.7505 0.7072 1.2198 d' 0.1447 0.3589 0.1 259 0.1922 give the best agreement with the ,,PD and pD values in benzene solution.Except for the Onsager equation there is a moderate correlation (see fig. 1) between the values of i30pl/dw necessary to give this agreement with each solute and its total polarization or to a lesser extent its a value. The regression lines through the calculated points may be expressed by the power series 3opllaw = a + ba+ ca2 (10) (11) = a' + biP + ckP2 + dip3 + eiP4 with the coefficients in table 4.The corrected orientation polarizations and dipole moments in tables 2 and 3 were calculated employing eqn (10) and (1 I) by a process of successive refinement -0.4 I I I I 2 3 TP FIG. l.-lJpl/lJw2 values for 20 solutes in chlorobenzene solutions as a function of their total specific polarizations TP. C. W. N. CUMPER AND P . G . LANGLEY 43 to give results of the desired accuracy. This procedure could not be applied with the Onsager equation because it was not possible to obtain an empirical expression for aOp /a w2. The corrected apparent oP values for the non-polar solutes (table 3) are inferior to the uncorrected-values when the Debye equation is used but for the other two equations they are nearer to zero.Correction for the solvent effect also produces a considerable improvement in the dipole moments calculated in the polar solvents (table 2); the only solute for which a significant discrepancy remains is n-heptanol where errors arise through association of the solute and because of some uncertainty as to the correct A value for a flexible molecule. Although the coefficients of eqn (10) and (1 1) were chosen to give agreement between the results from measurements in the polar solvents and those obtained employing the Debye equation upon measurements made in benzene solutions with modified coefficients equally good agreement is obtainable with the results in benzene solution calculated from the Weaver and Parry or the Buckingham expressions. Our conclusions are that the orientation polarizations and dipole moments evaluated from measurements made on dilute solutions in a non-polar solvent (benzene) are nearly the same as from those made in the polar solvents chlorobenzene and ethyl acetate if the equations of Onsager Weaver and Parry or Buckingham are used.This is especially the case with the last two equations named if empirical corrections are made for the dependence of solvent polarization upon the concentra- tion of the solutions. Chlorobenzene is marginally superior to ethyl acetate as a polar solvent because of some uncertainty about the correct value to be employed for the internal field function A with a flexible solvent molecule. P. Debye Phys. Z. 1912,13,97. L. Onsager J. Amer. Chem. SOC. 1936,58,1486. Th. G. Scholte Physica 1949 15,437,450 ; Rec. Trav. Chim. 1951,70 50. J. A. Abbot and H. C. Bolton Trans. Faraduy SOC. 1952 48 422. F. Buckley and A. A. Maryott J. Res. Nut. Bur. Stand. 1954,53,229. R. J . W. Le F&re and D. A. A. S. N. Rao Austral. J. Chem. 1955,8 329. J. R. Weaver and R. W. Parry Inorg. Chem. 1966,5,703. A. D. Buckingham Austral. J. Chem. 1953,6 323. J . W. Smith Trans. Faraday SOC. 1952,48,802. ' I. G. Ross and R. A. Sack Proc. Phys. SOC. By 1950 63 893. * J. W. Smith Trans. Faraday Soc. 1950,46,394 ; C. W. N. Cumper A. I. Vogel and S. Walker J. Chem. SOC. 1956,3621. J. G. Kirkwood J. Chem. Phys. 1939,7,911 ; Trans. Faruday SOC. A 1946,42,7. H. Frohlich Trans. Faraday SOC. 1948,44,238. lo C. W. N. Cumper A. I. Vogel and S. Walker J . Chem. SOC. 1956,3621. l1 C. W. N. Cumper A. A. Foxton J. F. Read and A. I. Vogel J. Chem. Soc. 1964,430. l2 J. A. Osborn Phys. Rev. 1945z67 351.

ISSN:0014-7672    

DOI:10.1039/TF9716700035

出版商:RSC    

年代:1971

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Direct Measurement of Small Differences in Dipole Moment and Polarizability BY E. A. HALEVI E. N. HARAN AND B. RAVID Dept. of Chemistry Technion-Israel Institute of Technology Haifa Received 2nd April 1970 An instrument for the direct measurement of dielectric constant differences between gases of similar polarity is described. The method is based on the pressure dependence of the frequency ratio between two LC oscillators the capacitive cell of each of which contains one of the gases. A sequence of measurements at different temperatures yields the dipole moment and polarizability differences.A check of the method with a pair of known gases HC1 and HBr yielded [p(HCl)- p(HBr)] = 0.284 D ; [ct(HCl)-a(HBr) ] = -0.95 x [(PE +PA)(HC~) - (PE+PA)(HB~)] = - 2.40 Cm3/mOl ; cm3/molecule. The error in the distortion polarization difference is 0.05 cm3/mol and the dipole moment difference is precise to 0.002 D. Since our initial interest in isotopic polarity differences,l dipole moment deter- mination by microwave and molecular beam techniques have become so accurate as to allow many isotopic dipole moment differences to be firmly establi~hed.~'~ However the need for a differential method based on dielectric constant differences has not been obviated. One reason is that the various spectroscopic techniques measure the expectation value of the dipole moment in a given molecular level or a transition moment between two such levels; these are closely related to but not identical with the dipole moment suitably averaged over a large assembly of mole- cules which is the quantity obtained from dielectric constant measurements.Further- more the spectroscopic methods cannot always distinguish between the permanent and induced moments in nearly non-polar molecules and are subject to higher order perturbations from whxh the dielectric constant method is free. In the present paper we describe a differential instrument for the direct measure- ment of small dipole moment and polarizability differences between molecules of similar polarity. The capabilities of our instrument are illustrated with the two polar gases HCl and HBr.PRINCIPLE OF THE METHOD The method is based on the measurement of the ratio between the frequencies of two similar LC oscillators. In each oscillator the inductance is fixed and the capacitance which is mainly due to a gas capacitor varies with the nature of the gas its temperature and pressure. Provided certain instrumental conditions are met only the dependence of the frequency ratio on the equal pressure of the two gases has to be measured in order to obtain the ideal specific dielectric susceptibility difference Ae defined below. Repetition of the measurement of Ae at different temperatures then allows the calculation of the differences in dipole moment and polarizability by the classical Debye method or refinements of it 44 E.A. HALEVI E. N. HARAN AND B . RAVID 45 In any one circuit with the gas cell evacuated the total capacitance Co is Co = Ca+Cst (1) where C and C, represent the active capacitance and the total stray capacitance respectively. With gas in the cell the total capacitance will be c = EC,+ Cst. (2) At gas pressures p sufficiently low that ideal behaviour can be assumed the dielectric constant E varies linearily with pressure E = 1+ep. (3) The quantity e thus defined may be called the ideal specific dielectric susceptibility.* The value is determined by linear extrapolation of the measured values of E to a pressure p = 1 atm.7a Denoting the capacitance ratio Cst/Ca by q we rewrite eqn (2) C = ca(l +ep+y). (4) I f the ohmic losses in the circuit are negligible the Thomson-Kirchhoff formula 4n2f2LC = 1 relating frequency f capacitance C and inductance L can be applied to C and Co separately so that the squares of the frequencies are related by If the same gas at the same pressure (and temperature) were present in both cells and we would measure directly the frequency ratio p = fi/f2 between the two channels ; eqn ( 5 ) would hold separately for both and where po denotes the frequency ratio at p = 0.Clearly if ql and y2 were made equal by adjusting C, of one or both channels the frequency ratio would become indepen- dent of pressure. In the “ untrimmed ” instrument ep/(l + q ) will be a small fraction of unity at pressures below 1 atm even for the most polar gases. The denominator of (6) may thus be expanded as (1 +x)-’ yielding to second order The limiting slope of a plot of p2 against p which we call the “ trim correction ” btrim is Now suppose a gas of ideal specific susceptibility e is in cell 1 and another gas at the same pressure with a slightly different ideal dielectric susceptibility (e + Ae) is in cell 2.Then provided eqn (3) holds for each gas separately (9) 2 1 + ePK1 +Y2) + Aepl(l+ Y2) 1+epl(l+rl1) P2 =Po * Strictly speaking (E-1) is the susceptibility only in the rationaliied M.K.S. system. We use here the c.g.s. system so neglect the factor 4x. 46 DIRECT MEASUREMENT OF DIPOLE MOMENT Expansion of the denominator and algebraic manipulation yields If the instruinelit is in “ trim ” i.e. yll = q2 we obtain and the specific dielectric susceptibility difference Ae is directly obtainable from the limiting slope of a plot of p 2 as a function of pressure Otherwise the limiting slope includes the “trim correction ’7 so that l+rt d(P2) Ae = (e2-el) = 7 - P O [ ( dp ) p + o - The difference in total molar polarization (PT = [(E + l)/(& + 2)]v) between two ideal gases extrapolated to 1 atm is where ’i7 is the molar volume at 1 atm T is the absolute temperature and R is the gas constant expressed in cm3 atm K-l mol-l.APT may be written as the sum of two terms the distortion polarization difference (APE + PA) and the orientation polarization difference POR7 i.e. APT = A(PE+PA) +APoR. If the conventional Debye treatment is applied directly to the total molar polarization difference we obtain 4xN 1 APT = 4 z A ~ + - A ( P ~ ) ~ 3 9k in which k and N are Boltzmann’s and Avogradro’s constants and Aa and A(p2) are the respective differences between the molecular polarizabilities and the squares of the dipole moments.As recognized by Bell and Coop,* the precise evaluation of the dipole moments of polar diatomic hydrides requires the use of the Van Vleck eq~ation,~. 7b which takes account of rotational quantization. Applied directly to APT we obtain instead of eqn (15) where C = 4nNhA(Bp2)/27k2. The correction term quadratic in (l/T) thus includes (in addition to h Planck’s constant) the squares of the two dipole moments and the rotational constants B1 and Bz which are inversely proportional to the two moments of inertia Il and Z2. ( B = h/8x2Z). E. A . HALEVI E. N . HARAN AND B . RAVID 47 = (APT + C/T2) It is convenient to use eqn (16) in its linear form. Defining (16) can be rcwritten as the correction being applied to APT separately at each temperature.The rotational constantsaregenerally wellknown but since either p1 or p2 is regarded as an unknown eqn (16a) is solved by iteration. Whichever of the eqn (15) or (16a) is used the intercept of a plot of APT (or APFr) against 1/T thus directly yields Aa and the slope yields A(p2). If one of the com- pounds say that in cell (2) is not polar and the other is only slightly so the dipole moment of the gas in cell (1) is simply When both compounds are polar it is necessary to know the dipole moment of one of them from an independent measurement. In the comparison of molecules with similar dipole moments we can approximate A(,uz) with 2pAp and obtain Here the uncertainty in the absolute value of the known dipole moment introduces an additional error into Ap but this error is generally trivial.Ap ci A(p2)/2p. (19) EXPERIMENTAL DESCRIPTION OF THE APPARATUS The apparatus which is depicted schematically in fig. 1 is essentially a twin instrument with two test channels made as identical as possible. All components except the high vacuum pump are located in a room held at a constant temperature to within f0.3"C. The arrangement of components is shown in fig. 2. Both dielectric measuring cells are Sfwwe Flask CHANNEL I &'* CHANNEL 2 Vacuum Manifold I l l Sloro Flask I FIG. 1 .-Schematic layout of apparatus. w Mercury Float Vulvcs kept at the same temperature by immersion in a common vapour bath. These cells make up most of the total tuned-circuit capacitance of a transistorized 1 MHzLC oscillator.All the other components of the oscillator are in a thermally insulated box about 30cm above the bath. The exact frequency of oscillation is determined by the dielectric constant of the gas all other circuit parameters being held as constant as possible. The frequency ratio p of the two channels is measured directly with an electronic frequency and frequency- ratio counter (Elron Electronics hdustries Ltd. Israel model MFC-7B). 48 DIRECT MEASUREMENT OF DIPOLE MOMENT --GI regulated power supply hermal insulation ernpemture control circuit ermal insulation heavy concrete Slab t rubber cushions "U" shaped concrete base FIG. 2.-Arrangement of components. FIG. 3.-Measuring capacitor. E. A. HALEVf E. N. HARAN AND B . RAVID 49 GAS SYSTEM HANDLING All parts of the gas handling system are made of glass.(Secondary gas monitoring components such as auxillary cold fingers manometers etc. are not shown in fig. 1). In order to avoid the use of greased stopcocks specially designed magnetically released mercury float valves lo were used. Gas is admitted into the system via inlet B after thorough pumping to about Torr for 2 days. Cold fingers D and J are used to transfer condensible gases from one part of the system to the other. For example cell G is filled with gas as follows. Valves 1 3,5 are open while all the others are kept shut and the gas is transferred from the storage flask A by condensation in cold finger D. Valves 1 3,5 are then shut and 6 and 7 are opened. The pressure in the measuring cells is brought close to a predetermined value by gradual warming and recooling the condensed gas in the cold finger and shutting valve 6 at the right moment.Final precise adjustments are made by Toepler pumps I and E. During a normal test run only valve 6 need be used different pressures typically in the range 0.07-0.70atm being attained by suitably cooling or warming cold finger D. The same sample can be used repeatedly or taken out of the system without appreciable loss. Absolute pressures are measured and pressure equality is maintained with the same dual- purpose mercury manometer F. One branch is connected to each of the two gas cells and the third to the vacuum manifold. Pressure variations in the test channels change the height of the meniscus in the reference branch thereby eliminating errors due to level changes in the common mercury reservoir.All pressures are measured to within f0.02 Torr using a cathetometer. MEASURING CAPACITORS The measuring cells of nominally lOOOpF shown in fg. 3 are constructed with the utmost care to ensure maximal dimensional stability at all pressures and temperatures. All metal parts are made of stainless steel all surfaces and edges are smoothed to minimize adsorption which should not be a significant factor in differential experiments with per- manent gases. Enclosed volumes are eliminated for easy degassing by slotting bolts and spacers where necessary. Twenty-nine steel discs form two interleaving combs with a gap of 0.75 mm. The design ensures that only a small part of the space between the plates contains a dielectric other than the gas to be tested.Gas is admitted via tube (1) into the welded stainless steel cup (2) that encloses the measuring capacitor. Electrical connections from the capacitor leave the cup via glass-to-metal seals (3) and reach the electronics box by two rigid coaxial lines (4). VAPOUR THERMOSTAT The temperature of the measuring cells is held at a predetermined level by the vapour of a boiling liquid heated by a glass-sealed electric immersion heating elemnt. Six or seven different non-corrosive organic liquids were used in each sequence covering the temperature range from about 40°C (methylene chloride) to about 205°C (tetralin). The exact temperatures are measured during each test with a calibrated mercury thermometer set in a well extending into the vapour bath. Heater power is adjusted between 50 and 350 W by means of a Variac variable transformer.TEMPERATURE CONTROL OF OSCILLATOR ENCLOSURE No inherently stable oscillator configuration was found that could guarantee sufficiently stable frequencies without precise temperature control of all oscillator components. The two identical oscillators are enclosed in a box thermally insulated from a second outer receptable by polystyrene foam sheets. A stable thermal field is set up within the box the thick copper base plate of which is heated by the output stage of the transistorized tempera- ture controller shown in fig. 4. Thermistor Th senses the base plate temperature close to the transistor. The regulator is essentially a 3-stage direct-coupled amplifier. Emitter voltage of transistor Ql rises when the temperature falls. Collector current changes of transistor Q1 are amplified by Qz and Q3.The last stage Q3 saturates when the sensed 50 QI RS Th f * * DIRECT MEASUREMENT OF DIPOLE MOMENT I I I I 1 - temperature differs from the value preset by R1 by more than half a degree. This ensures quick initial heating with the power of about 10 W and subsequent proportional control at levels of 3-4 W. The final short term temperature stability in the box is better than -fO.O3"C. FURTHER THERMAL CONSIDERATIONS The air temperature around the electronics box is not constant even when the whole set-up is in a thermostatically controlled room. These changes due to imperfect insulation of the vapour bath enclosure are especially serious in the upper temperature range above -150°C. Thermal decoupling between the vapour bath enclosure and the electronics box was achieved after the upper lid of the former had been fitted with copper cooling coils.No direct indication of thermal stability more sensitive than the frequency is provided nor is one required. The whole system is ready for use after a long-term frequency ratio stability of better than 0.5 p.p.m./h has been reached. Temperature induced drifts decrease to this value in less than a day after the test temperature has been changed. OSCILLATOR The oscillator shown in fig. 5 which resembles that described by Sulzer,ll was chosen since this configuration showed initial promise of being very stable. Q1 is the oscillator stage proper the grounded base configuration of which allows a high oscillation frequency with a low cut off frequency transistor.To enhance the frequency stability at 1 MHz a HF transistor (BSX27) was selected. The output of transistor Q2 is rectified by D1 and Dz and superimposed on the quiescent bias voltage set up by the divider R9 Rlo RI1. Distortions due to transistor nonlinearities are small since the amplitude of oscillations is only about 0.8 V or so at the collector of Q1. CaWlAL LINE Ca -it-. TO CWUNTER Rs FIG. 5.-Oscillator. E. A. HALEVI E. N . HARAN AND B . RAVID 51 All components except the measuring capacitor CM (gas cell) and the inductor L1 are mounted on a printed circuit board for layout equality of both channels. In order that the capacitance and inductance of the connecting coaxial line remain as nearly fixed as possible its temperature is stabilized by maintaining good thermal contact with the cooling coil on the upper lid of the vapour bath enclosure.The oscillator coil L1 is a single layer 45 turn solenoid of 0.8 mm enamelled copper wire wound around a 20 mm fused silica tube and glued to it with epoxy cement and has a nominal inductance of 25 pHy. The oscillator frequency changed with the 12 V supply voltage at a rate of about 10 Hz/V. The high-frequency response limitations of the regulated power supply allow fast line fluctuations to be transmitted to the load producing occasional erratic ratio counts. The frequency ratio p does not change appreciably if the voltage depen- dence of both channels is equalized by the variable resistors Rll. OPERATION Two initial calibrations have to be carried out before measurements can be performed (a) determination of the value of the instrumental parameter q for one channel say channel (2) taken as the reference channel ; (b) trimming of the two channels to a common value of q by adjusting Cst of the other channel.EVALUATION OF ( 1 f- q ) The parameter q which appears in eqn (13) for the dielectric constant difference must be evaluated separately. In principle it could be calculated as the ratio of C, and Co after each had been measured by conventional electrical techniques. To obtain a value of 17 sufficiently precise for our purposes it is simpler to rely on eqn (5) which relates q to the dependence of the frequency on the pressure of a reference gas (N2 COz or dry air the dielectric constants of which are all accurately known) viz. Ten-second counts at our frequency of 1 MHz allow resolution to so that intercept f; 2 and the slopes d(f-2)/dp of eqn (5) can be determined to high precision.It is still more convenient experimentally to work with frequency ratios as follows cell (1) is evacuated and the reference gas is introduced into cell (2). Frequency ratio readings ( p = fi/f2) counted over 10 s are recorded at several pressures usually seven per set and the elapsed time t is also recorded for each reading. To separate the effect of thermal drift from that of the pressure the latter was varied in an arbitrary order within the range 0.07-0.70 atm the entire set requiring 1-2 h. Manipulation of eqn (5) leads to In practice long-term drift is allowed for by introducing an additional term linear in time p2 = pi+at+bp. The data are fitted to eqn (22) by least squares with a digital computer and (l+y2) is obtained from the calculated slope and intercept.With dry C02-free air for which Maryott and Buckleyf4 cite e = (5.364 f0.003) x loA4 at 20°C we obtained the following values of (1+q2) T("C) = 22.9 23.3 GO. 6 60.5 99.6 99.6 (1+~2) = 1.041 1.040 1 . 0 4 7 1.046 1.045 1.045 The average value of (1 +y2) is 1 .OM f0.003 with no significant temperature dependence over this range. TRIMMING If it were possible to obtain perfect trim p2 would be independent of pressure whenever the same gas is present in both cells. We were not able to eliminate the pressure dependence 52 DIRECT MEASUREMENT OF DIPOLE MOMENT completely. Over a period of several months the apparatus would go " out of trim " at any given temperature. Moreover initially perfect trim at one temperature did not ensure trim at the other temperatures.In practice trimming is carried out as follows. After the instrument has reached thermal equilibrium the same polar gas is introduced into both cells simultaneously and p is recorded several minutes later. The (same) pressure in both cells is then reduced and the new value of p is recorded. Capacitor C1 (fig. 5) of channel (1) is then adjusted so as to decrease the absolute magnitude of dpldp. The procedure is repeated until no change of the frequency ratio with pressure can be detected. To determine the trim correction btrjm at a given temperature the pressure dependence of the frequency ratio p is determined in essentially the same way as in the preceding section. The principal difference is that p is now the common gas pressure in both cells.The results are fitted by " least squares " to eqn (22). The time dependence coefficient a which is generally very small represents the long-term drift. No allowance need to be made for non-linearity of the pressure dependence arising from non-ideality of the gas or for the higher order terms in eqn (lo) so the slope b is simply the trim correction btrim required for eqn (13). A typical set of parameters for HCl at T = 99.6"C was h-l ; pg = 0.991 801 64&0.000 000 32; b = + (1.564 40.603) x loM6 atm-l. a = -(1.673f0.178)~ The value of p$ calculated with eqn (22) which differed slightly from the measured value of p2 at zero pressure was used throughout. Several values of btrjm for different temperatures which were used in the trim corrections for the subsequent HCI-HBr measurements along with corresponding values of (ql - yz) calculated with eqn (8) are in table 1.TABLE 1 lo6 x b (atm-l) 2.23 1.94 3.23 1.56 2.27 6.55 lo3 x e* 3.42 3.07 2.80 2.53 2.22 1.94 lo3 x ( y r y z ) 0.71 0.69 1.26 0.67 1.11 3.68 T ("C) 40 60 80 100 130 170 * e values were interpolated from standard values. ' The difference (ql-qz) is thus of the same order of magnitude as the uncertainty in the absolute value of y. However the statistically calculated errors in b ranged between 1 x lo-' and 1 x atm-l so the trim corrections while small are outside experimental error. CHECK WITH KNOWN GASES (HCl AGAINST HBr) To check our procedure we chose two polar gases HCl and HBr the polar properties of which are relatively well known and sufFiciently close for our differential method to be used.Two pairs of experiments were carried out; one pair with HCl and HBr in cells (1) and (2) respectively and the other with the gases interchanged. The procedure was essentially as described in the preceding section. The frequency ratio p was measured as a function of pressure as determined by least-squares analysis using eqn (22) ; the slope 6 and intercept pg were then introduced into eqn (13) to obtain Ae. (When HCI was in cell (l) btrim was taken directly from table 1 ; when HBr was in cell (l) btrim was multiplied by eHB,/eHcl taken from Zahn's dielectric constant values. A typical set of measurements (39.4"CY with HCl in cell (1)) yielded the following parameters p i = 0.992 087 50 ( fO.OOO OOO 19) ; b = -8.811 (f0.004)~ atm-l. a = - 1.061 ( f0.091) x h-' ; An attempt was made to allow for non-linearity with the pressure which might arise from differences in non-ideality or adsorption.The data were fit to p2 = p z + a t + b p + c p 2 (23) E. A. HALEVI E. N. HARAN AND B. RAVID 53 and yielded pg = 0.992 087 85 (fO.OO0 0022) ; b = -8.847 (f0.017)~ loB4 atm-l ; a = - 1.006 (f0.086) x lov6 h-l ; atm-2. c = 5.84 (f2.63)~ The values of Ae calculated in the two cases from the linear coefficient b were respectively -9.293 (f0.004) x Even at this our lowest test tempera- ture where non-ideality should be most pronounced the two values do not differ significantly ; moreover the added parameter merely increases the computed statistical error. Our use of the linear eqn (22) throughout would thus seem to be justified. The values of Ae calculated at each of six temperatures in the range 40-170°C with the linear value of 6 were converted to A P F with eqn (14) and (17).The values of A(PE+PA) and A(p2) were obtained by iterative least-squares solution of eqn (16a) on the computer. A characteristic experiment which included the set at 39.6"C cited above is summarized in table 2. Before considering the rest of our results we note that a calculation with the Debye-Van Vleck equation requires that the value of the dipole moment of one gas that in cell (2) be known. The " best values " of p(HBr) range from 0.82 to 0.83 D whereas those for HCl range from 1.08 to 1.12 D.13 In the experiment tabulated in table 2 the assumed value of p(HC1) enters only trivially through the rotational correction into the calculation of A(PE+PA) and A(p2) but much more weightily into that of Ap.Thus though the essentially random error of 0.004 in A(pz) is converted to one of 0.002 D in Ap for a molecule of p N 1 D (cf. eqn (19)) this neglects the uncertainty in p(HC1). and - 9.331 (f0.018) x TABLE 2.-TYPICAL EXPERIMENT HCl AGAINST HBr cell (1) cell (2) HCl HBr - - gas B - - 10.591 cm-l 8.473 cm-l p (assumed) = 1.080 D - lO3x T-1 APTrn (expt.) AP;Orr(calc.)* 2.266 - 5.01 3 - 5.039 2.471 - 5.758 - 5.724 2.682 - 6.427 - 6.429 2.837 - 6.945 - 6.948 2.998 - 7.482 - 7.485 3.199 -8.159 - 8.159 Number of iterations = 3 ; A(PE+PA) = 2.538 f0.071 cm3/mol ; (Act = (I .006&0.028) x cm3/molecule ; Ap2 = -0.5489f0.0041 D2 ; Ap = -0.2942rt0.0019 D. * calculated with eqn (16a) from final values of APE+PA and A@'). The values of Ap2 Ap and A(PE+PA) calculated with the Debye-Van Vleck eqn (16a) for the limiting " best values " of p(HC1) and p(HBr) are shown in table 3.The instrument shows no apparent bias the results being substantially the same whichever gas was used as reference. With each calculation given equal weight the following average quantities are obtained The error cited for each is the standard deviation of the mean which for four independent measurements is half the standard deviation. p2(HC1)-p2(HBr) = 0.546 f0.002 ; p(HC1)-p(HBr) = 0.284 f0.003 ; (PE+PA)(HCl)-((PE+PA)(HBr) = -2.40 f0.05 ; 1024x [a(HCl)-ct(HBr)J = -0.95 f0.02. The " best values " of p(HC1) (1.08- 1.12 D) and p(HBr) (0.82-0.83) differ from each other by between 0.25 and 0.30D so our value for the difference falling in this range, 54 DIRECT MEASUREMENT OF DIPOLE MOMENT must be regarded as the best available to date.* There are no reliable figures for the polariza- bility differences from non-optical measurements.If APA (the difference in atomic polariza- tion) can be assumed to be negligibly small because it depends directly on force constants and is independent of atomic masses 7c A(&+PA) can be equated to the difference in molar refraction the best value for which is cited by Maryott and Buckley l4 to be -2.36 in excellent agreement with our result. TABLE 3.-sUMMARY OF RESULTS 1 HBr 0.82 0.83 2 HBr 0.82 0.83 3 HCI 1.08 1.12 4 HCl 1.08 1.12 0.5469 0.2842 0.5470 0.28 17 0.5487 0.2851 0.5488 0.2825 - 0.5489 - 0.2942 - 0.5500 - 0.2807 - 0.5400 - 0.2885 - 0.5405 - 0.2751 -2.351 - 2.352 - 2.367 - 2.368 2.538 2.551 2.338 2.342 This research was performed under grant no.N.B.S. (G) 22 from the U.S. Dept. of Commerce National Bureau of Standards administered by the Technion Research and Development Foundation. We are grateful to Dr. K. Bar-Eli Dr. U. Feldman and Dr. A. Konstam for their contributions to this research in its early stages and to Prof. U. Garbatski for useful suggestions. The efforts of various members of the Technical Service of the Dept. of Chemistry in the construction and maintenance of the apparatus were of immense value. APPENDIX CONVERSION TO s.1. UNITS We have used the c.g.s. system of units. Conversion to the S.I. units would affect our results as follows. All volumes given in cm3 are converted to m3 by multiplication by Since the mol defined in S.I.units remains the g-mole (rather than the kg-mole) the same conversion factor applies to molar volume. Our standard pressure is 1 atm ( E 101.325 kN m-2) and our values for the pressure dependence in equations (13) (21) (22) etc. b 3 (d(p2)/dp),=o would have to be divided by this factor. However to obtain the dimensionless e or Ae which refers to 1 atm the pressure dependence would have to be multiplied by the same factor for use in eqn (8) (12) (13) etc. The Debye equation on which eqn (14) and (15) are based is E - 1 - - V = ? q + & ) E f 2 3 The quantity on the left the total molar polarization PL is the total molar polarizability and has the dimensions of a molar volume. In S.I. units or the rationalized MKS system the Debye equation takes the form E - 1 - in which E has been retained to represent the dimensionless relative dielectric constant common to both systems and go is the permittivity of free space ( E ~ = 8.854~ 10-l2 F m-l) * After the preparation of this manuscript was complete we learned that a precise value of the dipole moment of HC1 had been obtained by a molecular beam rnethod.16 For the non-rotating molecule in its lowest vibrational level i.e.poo = 1.10847rfi0.0004. If this figure had been used as our reference value in all four experiments cited in table 3 we would have obtained Ap = 0.2826 f0.0013. The absolute value of the dipole moment of HBr can thus now be set at 0.826f0.002. E. A . HALEVI E. N . HARAN AND B. RAVID 55 C m) and the The dipole moment is expressed in coulomb-metre (1 D = 3.334~ Boltzmann constant takes its S.I.value (1.380 54x J K-l). If eqn (25) is rewritten in a form comparable to (24) the left side PT in c.g.s. retains the dimensions of molar volume but not of molar polariza- bility. So does (PE+PA) which is Na/3ns0); the volume corresponding to the molecular polarizability appears as a14nnso. The simplest acceptable way of converting (&+PA) and a to S.I. units would be to cite these volumes in m3/mol and m3/molecule and specify that they represent (PE+PA)/E~ and a/(4nnso) respectively. Our results for the HCl-HBr difference would thus be Ap = 0.947 x C m ; A(PE+PA)/E~ = - 2.40 x m3/mol ; Aa/(4n&o) = -0.95 x lod3' m3/molecule. E. A. Halevi Trans. Faruday Soc. 1958,54,1441. D. R. Lide Jr. J. Chem. Phys. 1960,33,1519. J. S. Muenter and V. W. Laurie J. Chem. Phys. 1966,45,855.J. S. Muenter M. Kaufman and W. Klemperer J. Chem. Phys. 1968,48,3338. J. S. Muenter and V. M. Laurie J. Amer. Chem. Soc. 1964,86 3901. A. D. Buckingham and R. J. Stephens Mol. Phys. 1962,7,481. (6) p. 12;(c) p. 417. R. P. Bell and I. Coop Trans. Faraday Soc. 1938,34,1209. J. H. Van Vleck The Theory of Electric and Magnetic Susceptibilities (Oxford University Press London 1932) p. 198. P. G. Sulzer cited in S. Schwartz Selected Semiconductor Circuits Handbook (John Wiley New York 19,60) pp. 5-15. for Molecules in the Gas Phase (NSRDS-NBS 10 1967). Substances in the Gaseous State (N.B.S. circ. 537 1953). ' C. D. Smyth Dielectric Behaviour and Structure (McGraw-Hill N.Y. 1955) (a) p. 210 ; lo E. N. Haran Rev. Sci. Instr. 1966,37 523. l2 C. T. Zahn Phys. Rev. 1924,24,400. l 3 R. D. Nelson Jr. D. R. Lide Jr. and A. A. Maryott Selected Values of Electric Dipole Moments l4 A. A. Maryott and F. Buckley Table of Dielectric Constants and Electric Dipole Moments of l5 E. A. Halevi E. N. Haran and B. Ravid Chem. Phys. Letters 1967,1,475 l6 W. Kayser 23rd Symp. Mol. Structure and Spectra (Columbus Ohio Sept. 1968); cited by J. Muenter personal communication Oct. 1969.

ISSN:0014-7672    

DOI:10.1039/TF9716700044

出版商:RSC    

年代:1971

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Electron Spin Resonance Studies of Photo-Oxidation by Metal Ions in Rigid Media at Low Temperatures Part 1 .-Ce(1V) Photo-Oxidation of Alcohols BY D. GREATOREX AND T. J. KEMP School of Molecular Sciences? University of Warwick Coventry CV4 7AL Received 29th June 1970 Photolysis of deoxygenated solutions of ceric perchlorate and ceric ammonium nitrate in alcoholic aqueous alcoholic and water + alcohol + acetonitrile solutions at 77 K by light of wavelength > 300 nm leads to formation of radicals derived from the alcohol identified by electron spin resonance (em-.) spectroscopy. Primary alcohols RCH20H yield ReHOH. but secondary alcohols RzCHOH yield R e in addition to and sometimes to the exclusion of R2COH.Tertiary alcohols always give an alkyl fragment e.g. CzH5 from tert-amyl alcohol. Allylic alcohols produce the corresponding hydroxyallyl radical and 1 ,Zdiphenylethanol gives a spectrum of benzyl radical indicating C-C cleavage. The mode of photo-oxidation by Ce(IV) clearly parallels that of the corresponding thermal oxidation. Aqueous solutions of certain oxidizing inorganic ions particularly of the one- equivalent type are reduced by ambient light. The additional presence of ions such as C1- or of organic molecules such as alcohols aldehydes and carboxylic acids especially oxalate ions enhances the rate of photoreduction of the metal ion,l such a process forming the basis of the ferri-oxalate actinometer. The mechanism of these photo-oxidations is believed to be free radical in character following charge-transfer- to-metal (CTTM) transitions in the complexes formed by the metal ion,l the evidence including (i) the ability of photolyzed solutions to initiate radical polymerization,2 e.g.that of acrylonitrile by FeCl in dirnethylf~rmamide,~ (ii) the production of an optical spectrum attributable to NO3- on flash photolysis of aqueous acidic Ce(1V) in the presence of NO; (iii) the characterization by e.s.r. spectroscopy of radicals derived from the ligand following photolysis of frozen solutions of the oxidizing ion complexed with reducing ligands e.g. the oxalato complex of Fe(II1) and various carboxylic acid complexes of Pb(IV).6 The products of photolysis of carboxylic acids in the presence of Pb(1V) and Ce(1v) * have also been shown;-by Kochi and his collaborators to indicate radical pathways.We have reported that the primary processes in the photolysis of 1 1 complexes of Ce(1v) with tertiary alcohols lo and aliphatic carboxylic acids can be followed by e.s.r. at 77 K. The present paper sets out the results of a systematic investigation of Ce(1V) photo-oxidation of different types of alcohol by means of this technique. EXPERIMENTAL MATERIALS A.R. ceric ammonium nitrate was used. Solutions of Ce(1V) in HC104 were prepared as follows ; concentrated aqueous ceric ammonium nitrate was treated with 0.880 ammonia until precipitation of ceric oxide ceased ; the oxide was separated in a sintered-glass funnel 56 D. GREATOREX AND T . J . KEMP 57 and washed with much distilled water and finally dissolved in 60 HC104 (A.R.).Alcohols were of the best grade available commercially laboratory-grade materials being redistilled or recrystallized. CH3CN was of spectroscopic quality. IRRADIATION Photolyses were carried out in the cavity of a Decca X-band spectrometer equipped with a Newport Instruments 7in. magnet. The lamp was a Hanovia 1OOW xenon compact source fitted with a reflector and focusing lens and the output was filtered through a Corning C50.54 clear glass filter transmitting light of A> 300 nm. The temperature was maintained either by standing the sample tube in liquid nitrogen in a quartz dewar vessel of 4 mm i,d. or by passing cooled nitrogen gas through the low-temperature cavity supplied by Decca Radar Ltd. The cavity temperature was monitored with a thermocouple.The sample tube of Spectrosil (3.2mmo.d.) was joined to a quartz tube (lOmmo.d.) and thence via a graded seal pq to a Pyrex tube (fig. 1). 0.5 ml each of solutions of Ce(1V) and alcohol were placed separately in the bulbs b which were then placed in the sidearms s fitted with Teflon O-rings each backed by an O-ring of Viton A. The upper section was constructed from thick-walled Pyrex to enable the device to withstand considerable torque and a B10 cone provided the connection to a high-vacuum line. The vacuum was maintained B 9 FIG. 1.-Arrangement of sample tube (the B10 cone is normally at right-angles to the plane of the paper). by a greaseless stopcock g again based on a Teflon O-ring backed by a Viton A O-ring constructed initially by Mr. K. Holden of the departmental workshop but supplied latterly by J.Young Ltd. of Acton. The solutions were degassed by a series of freeze-pump-thaw cycles and the stopcock finally closed. Following melting of the solutions (often at -273 K) mixing was effected by vigorous shaking whereupon a red or orange colour usually developed and a portion of the mixed solution immediately shaken into the e.s.r. tube and frozen to 77 K being then ready for photolysis in the cavity. Solutions were prepared in several different ways of which the following are most generally typical. METHOD A.-ceric perchlorate (0.1 M) in aqueous 4 M HC104 and the organic substrate (0.1 or 1 .O M) in water. METHOD B (used when the substrate was insufficiently water-soluble to give a solution of 58 Ce(1V) PHOTO-OXIDATION OF ALCOHOLS concentration >0.05 M or if the substrate precipitated during the final cooling state) a quantity of acetonitrile was added as co-solvent.METHOD C ceric ammonium nitrate dissolved in neat organic liquid to ca. 0.1 M or to saturation (whichever the least concentrated). In this case the solution was placed rapidly in one bulb and degassed in the usual way. METHOD D ceric ammonium nitrate (0.1 M) and the organic substrate (1.0 M) in water. METHOD E as with method D but with acetonitrile-water (50 % v/v) as solvent for water-insoluble substrates. RESULTS NO ADDED SUBSTRATE Using filtered light (A> 300 nm) only weak absorptions appeared on photolysis. 0.1 M Ce(1v) in 4 M HC104 produced weak H-atom signals which were intensified on removal of the filter. Prolonged irradiation of 60 % HC104 also produced H- atoms when the full source was used.1 M aqueous ceric ammonium nitrate gave a very small singlet near g = 2 before photolysis a small signal assigned to NO2- with filtered light (see below) and a larger NO2- signal and some H-atom absorption on removal of the filter. PRIMARY ALIPHATIC ALCOHOLS METHANoL.-MethodS A C and D all yielded a distorted but reproducible basic 1 2 1 triplet of average separation 20+2 Oe (fig. 2@) (b)) ; methods C and D produced in addition two wing peaks of average separation 120+2 Oe the high field peak being of asymmetric character (fig. 2(b)). The wing peaks were a feature of all experiments involving ceric ammonium nitrate irrespective of substrate although in a number of cases e.g. the tertiary alcohols its intensity was only a few percent of that of the co-existing carbon radical.We attribute the additional spectrum to NO2- radical. The 1 2 1 triplet although distorted compared with spectra obtained with higher aliphatic alcohols is probably due to .CH20H which has been characterized in rigid solution by photolysis l1 and radiolysis l2 methods (a 19 Oe) and in solution by oxidation of methanol by the Ti3+/H202 couple in a continuous-flow system with a reported principal coupling constant of 17.2 Oe.' METHANOL-d3.-The spectrum obtained by method C and illustrated in fig. 2(c) is much narrower than that obtained from methanol and suggests formation of an incompletely-resolved CD20D spectrum. A broad singlet was obtained on radiolysis of solid CD30H. l2 ETmNoL.-Method A produced a basic five-line spectrum of average separation 22.3kO.l Oe with additional subsidiary peaks due to a minor species (fig.2(d)). Method C also produced this spectrum (a 22.1 Oe) together with the NO2- spectrum (width 116 Oe). The five-line spectrum closely resembles that obtained both on photolyzing ethanol + H20z mixtures at low temperatures and on radiolysis of ethanol at 77 K l2 (aH 22 Oe by both methods) and is assigned to CH,CHOH. PROPAN- 1-oL.-Method A produced a poorly-resolved quartet of basic pattern 1 3 3 1 (aH-24 Oe) with an additional central peak. Method C produced initially a spectrum identified as that of ethyl radical (azH2 19.8 26.4Oe) but an additional spectrum appeared on further photolysis. Method D yielded a mixture of three radicals shown in fig. 2(e) consisting of NO2- and C2HS- and a basic five- line spectrum (a 22 Oe) which is probably due to CH3CH2cHOH.On standing in the dark at 77 K for 10 rnin the C2H5- signal diminished appreciably ; on warming D . GREATOREX AND T. J . KEMP 59 the mixture to -175 K only the five-line spectrum remained (fig. 2 0 ) . The e.s.r. spectrum obtained on radiolysis of propan-1-01 also exhibits five lines (a 21 0e)l2* l4 and is assigned to CH,CH,cHOH and similar results are obtained on photolysis of a propan-1-01 glass containing H202.11 However the liquid phase spectrum produced by photolyzing propan-1-01 containing 0.4 % H202 using an intense source shows six lines with a&,H) 15.06 apH 21.40 0e.ls A FIG. 2.-E.s.r. spectra obtained during photo-oxidations of primary alcohols by Ce(IV). (a) methanol (method A); (b) methanol (method D); (c) methanol-d3 (method C); (d) ethanol (method A); ( e ) propan-1-01 (method D 77 K) ; (f) propan-1-01 (method D warmed to -175 K) ; (9) 2-methyl- propan-1-01 (method C) ; (h) butan-1-01 (method C) ; (i) pentan-1-01 (method C).2-METHYLPROPAN-1-OL (ISOBUTANOL). Method C gave a 1 2 1 triplet (a 20.2 Oe) together with an NO2* spectrum of width 120 Oe (fig. 2(g)). A similar spectrum was obtained by Alger Anderson and Webb on radiolysis of isobutanol l2 and Chacaty’s similar experiments also produced a basic triplet (a 21 & 1 Oe) with some weak satellite lines.14 Accordingly it appears that (CH,),CHt]HOH is formed a radical characterized in solution by both intense photolysis l5 and Ti3+/H202 oxidation flow l3 techniques with a&OH) 14.74 21.41 Oe.15 BUT AN-^ -or.,.-Method c gave a five-line spectrum of an approximate intensity distribution 1 2 2 2 1 (a 19 Oe) together with an NOz- spectrum of width 117 Oe (fig.2(h)) cf. pentan-1-01. Radiolysis at 77 K of butan-1-01 produces a seven-line spectrum with five central lines of Comparable intensity and two weaker outermost lines,12* l4 but Chacaty l4 noted that warming to 120 K results in a change to a five-line spectrum (a 21+1 Oe).14 The change is attributed to a conversion from CH3cHCH2CH20H-+CH3CH2CH2cHOH. Low-temperature H202 photo-oxidation experiments indicate six or seven lines in a poorly-resolved 60 Ce(IV) PHOTO-OXIDATION OF ALCOHOLS spectrum l1 with aH-20 Oe. Room temperature H202 photolysis produces a six-line spectrum of CH3CH2CH2cHOH with 15.3 20.0 Oe.15 It seem probable that we are observing the 120 K species of Chacaty i.e.CH3CH2CH2cHOH. PENTAN- 1 -0L.-Fig. 2(i) illustrates the spectrum obtained using method C which can be seen to be almost identical with that found for butan-1-01. Alger Anderson and Webb l2 also found a strong similarity between the e.s.r. spectra of butan-1-01 and pentan- 1-01 following radiolysis implying formation of structurally similar radicals RCH2CH2cHOH (R = Me or Et). SECONDARY ALCOHOLS PROPAN-~-OL.-M~~~O~ A ([substrate] - 0.1 M) yielded initially the relatively narrow-lined quartet characteristic of CH3- but a minor radical was also present which increased in size on further photolysis relative to that of CH3 until both species were in comparable concentration. The radical mixture illustrated in fig.3(a) was analyzed in terms of CH3. (a 23.0k0.2 Oe) and Me,cOH (a& 20.0k0.5 Oe) by means of a computer simulation (fig. 3(b)). (a) (b) (b) computer simulation. FIG. 3.-E.s.r. spectra obtained during photo-oxidation of propan-2-01 by Ce (IV). (a) experimental ; Using method C initial photolysis produced a radical mixture comprising Me2cQH CH3 and NOz but continued photolysis resulted in relative enhance- ment of Me,cOH and NO *. Method D yielded only CH3. and NO2 -. The averaged coupling constant in Me2cOH compares with values of 20Oe obtained by other low-temperature methods of generation. 11* D . GREATOREX AND T. J . KEMP 61 BUTAN-2-OL (sec-BuTANoL).-Method c yielded a mixture of CH3 (aH 22.7 f 0.5 Oe) and a 1 2 1 triplet (a 33.8 Oe). Method D produced a poor CH3* spectrum.Photolysis at 77 K of butan-2-01 containing H202 gave a six-line spect- rum l1 and clearly C-C fission has taken place during Ce(1V) photo-oxidation. PENTAN-~-oL.-M~~~o~ C yielded C2H5* ( a & ~ ~ 26.8 k 0.1 a& 20.5 k0.2 oe). CYCLoHExANoL.-Method C produced a mixture of NO2* and an eight-line spectrum. Gibson Symons and Townsend l1 obtained a six-line spectrum on low-temperature photolysis of an Hz02 solution (a 20 Oe) and we have been able to confirm this result. TERTIARY ALCOHOLS TERT-BUTANoL.-Photo~ysis at 77 K under different conditions led to the immediate production of a 1 3 3 1 quartet with a = 22.7k0.3 Oe identified as CH3* radical. Method C produced in addition a minor spectrum which intensified on continued photolysis e.g. for 15 min to yield a 1 2 1 triplet of overall width 42 Oe.Warming a photolyzed aqueous ceric ammonium nitrate sample to 180 K resulted in the disappearance of CH3- and production of a similar 1 2 1 triplet. Standing a sample prepared by method C and irradiated for only 4s (to give a " pure " CH3* spectrum) for a period of 27 h at 77 K also led to the same triplet at the expense of CH3- (fig. 4) which was again produced by photolysis of ceric ammonium nitrate in neat tert-butanol at 245 K. The triplet presumably originates from a *CH2X species the most likely candidate being .CH2CMe20H for which a coupling of 21.3 Oe has been reported l3 in water at 293 K. Photolysis of ceric perchlorate in a solution of tert-butanol in CH3CN produces in addition to CH3- a spectrum attributable to *CH2CN l6 which often appeared when this co-solvent was utilized.(a1 (b) &I (dl FIG. 4.-Decay in dark of e.s.r. spectrum of methyl radical in tert-butanol at 77 K following photo- oxidation by Ce(1V). (a) immediately after 4 s photolysis ; (b) 3 h later ; (c) 19 h later ; (d) 27 h later. ~ - E T H Y L P E N T A N - ~ - O L . - - I ~ V ~ S ~ ~ ~ ~ ~ ~ ~ ~ by methods A and c yielded the spectrum of C2H5* with a&3 26.5f0.3 Oe a& 21.0A0.3 Oe. 1,l -DIMETHYLPROPAN- 1 -OL (TERT-AMYL ALcoHoL).-Method C gave an ethyl radical shown in fig. 5(a) with uFH3 26.3k0.3 a& 20.8k0.3 Oe. Method A unexpectedly gave a 1 3 3 1 quartet with 23.3 Oe; this suggests CH3. 62 Ce(1V) PHOTO-OXIDATION OF ALCOHOLS is formed but the peaks were unusually broad and the outermost peaks were partially split into doublets.FIG. 5.-E.s.r. spectrum obtained during photo-oxidations of tertiary alcohols by Ce(IV). (a) 1,l- dimethylpropan-1-01 ; (b) 3-methylhexan-3-01 ; (c) 2,3-dirnethylbutan-2-01. 3-METHYLHEXAN-3-OL.-MethOd C gave a spectrum consisting of a mixture of C2H5* identified by the coupling constant of the two most intense peaks (a&3 27.0k0.3 Oe) and a 1 2 1 triplet (aH-24 Oe) (fig. 5(b)). 2,3-DIMETHYLBUTAN-2-OL.-whi1St method A gave only a poorly resolved spectrum method C gave a nine-line spectrum shown in fig. 5(c) of overall width 120 Oe. This is due to a mixture of radicals of which one displays a basic seven-line spectrum of binomial character (a 20 Oe) and which cannot therefore be Me2cH known to exhibit an eight-line spectrum with 26.4 Oe.17 ALLYLIC ALCOHOLS ALLYL ALcoHoL.-Methods A C and I) all resulted in production of a four-line spectrum of total width 44.3 Oe (fig.6(a)) and identical in appearance and width with that reported by Maas and Volman using H202 photo-oxidation at 125 K l8 FIG. 6.-E.s.r. spectra obtained during photo-oxidations of allylic alcohols by Ce(1V). (a) ally1 alcohol ; (b) but-2-en-1-01 (193 K) ; (c) but-3-en-2-01 (130 K). D . GREATOREX AND T. J . KEMP 63 and by other groups using a similar technique.l9* 2o It is assigned to the allyl-type radical CH,=CH-CHOH. BUT-~-EN-~-OL (CROTYL ALcoHoL).-Method A ([substrate] N 1 M) produced a broad spectrum at 77 K showing only traces of structure but subsequent warming to 193 K yielded a six-line spectrum shown in fig. 6(b) of total width 77+ 1 Oe (aH 15.4 Oe). This is identical with the spectrum obtained by photo-oxidation of crotyl alcohol by Hz02 and measured at 122 K l8 (total width 75 Oe) and is assigned to B U T - ~ - E N - ~ - O L .- M ~ ~ ~ ~ ~ C gave a partly-resolved six-line spectrum at 77 K but subsequent warming to 130 K resulted in improved resolution illustrated in fig. 6(c) and an overall width of 71 Oe was obtained i.e. aH(average) equals 14.3 Oe. Again an identical spectrum of 70 Oe width was obtained on low-temperature oxidation CH,-CH=CH-~HOH by *OH.18 BENZYLIC ALCOHOLS BENZYL ALcoHoL.-Method C produced only NOz. after 8 min of photolysis. However by shaking benzyl alcohol with ceric perchlorate solution removing the organic layer degassing and photolyzing that at 77 K a spectrum consisting of a large singlet of width 50 Oe and three smaller peaks on either side was obtained which could not be analyzed.It did not appear to be the spectrum expected of 1 ,~-DIPHENYLETHANOL.-M~~~~~ E produced the spectrum shown in fig. 7(a) which was analyzed by computer simulation as due to benzyl radical (fig. 7(b)) with the coupling constants acH2 16.5 aH(4) = aH(2.6) 5.5 Oe. These compared with values of aCHz 16.4 aH(4) 6.19 aH(2.6) 5.17 Oe reported for a solution spectrum 21 and with identical values obtained from a solid-state spectrum.22 C~H&HOH.~~ (0) (b) FIG. 7.-E.s.r. spectrum of benzyl radical obtained during photo-oxidation of 1 ,Zdiphenylethanol by Ce(IV). (a) experimental ; (b) computer simulation. 1,1 -DIPHENYLETHANOL.-Method E produced a spectrum of CH2CN. Photolysis of ceric ammonium nitrate in CH3CN for a comparable period gave no signal and we ascribe the appearance of .CH2CN to attack of phenyl radical upon CH3CN.DISCUSSION The photochemistry of complexes of one-equivalent oxidizing metal ions is dominated by CTTM processes especially with light of wavelength <400 nm and this must be particularly so for Ce(1V) which is strongly oxidizing in HC104 and HN03 media (E" being + 1.70 and + 1.61 V respectively for the Ce(IV)/Ce(III) couple) 23 and which has an inert-gas electronic configuration being free therefore of complicating photosubstitution processes induced by ligand field transitions. Photolysis of complexes with simple ligands such as NO; results in simple electron 64 Ce(1V) PHOTO-OXIDATION OF ALCOHOLS abstraction from the ligand to give a small inorganic free radical like NO3- identifiable by optical and e.s.r.spectroscopy in fluid4 or frozen solution.24 An alternative mode of formation of NO3* and also HS04- (or SO;.) has been suggested to be preliminary oxidation of ligand water 2 5 ; Ce4+ aq-+Ce3+ +H++ .OH h v followed by attack of .OH upon free anion ; .OH+NO +OH- +NO,* .OH + HS04+ OH- + HS04. This remains controversial however,24 and the intermediacy of *OH is ruled out in those of our experiments involving solutions of ceric ammonium nitrate in neat organic liquid. Addition of molecules such as alcohols to solutions of ceric per- chlorate and ceric ammonium nitrate shifts the absorption to the visible and increases the extinction respectively imparting a red or orange-red colour which corresponds to the CTTM band of the resulting complex usually of 1 1 stoichiometry with a formation constant in the range 0.5 to 10 1.By restricting the irradiation wavelength to I> 300 nm we are partially confining excitation to these CT transitions and the transitions within the normal aquo species CeOH3+ or its polymeric forms in HC104 are less involved. Ceric ammonium nitrate does show appreciable absorp- tion from a CT band (I,, 290 nm) in the region we are utilizing and the appearance of radicals derived from the nitrate ligand in the absence of organic substrate indicates some degree of photo-oxidation ; however the increased extinction of the alcohol- containing solutions implies preferential absorption of light by the organic complexes. The behaviour generally closely parallel of the Ce(1v) perchlorate and nitrate solutions containing alcohols is reasonable indication that the nitrate ligands do not greatly affect the photochemistry although the ubiquitous wing peaks of ca.117 Oe separa- tion in most if not all experiments involving the nitrate could be adduced as evidence for electron transfer to Ce(1V) from NO operating in parallel with that from organic ligand. The assignment of these wing peaks to NO2* rests on the following evidence (i) The particularly intense spectrum obtained from benzyl alcohol by method C could be analyzed by the method described by Kneubuhl 27 as follows g1 = 2.006 g2 = 2.002 g3 = 1.995 (all +O.OOl) a = 48.9 Oe a; = 64.5 Oe a = 43.2 Oe (all k0.5 Oe). These values are similar to those reported by Ayscough and Collins 28 for NO2 in an alkaline glass at 77 K following photolysis of Fe(CN)% - ions in the presence of 0.5 M NO ions.(ii) The spectrum of NO3- the principal alternative radical expected is much narrower having an axially symmetrical g tensor and no hyperfine splitting with = 2.0041 +0.0003 and gL = 2.0207+0.0003.24 This species was produced in a M ceric ammonium nitrate. Continued photolysis in this wavelength range did not result in any transformation of NO3- into NO2- indicating that NO2- produced in our experiments is not a product of secondary photolysis of NO3- (which is photolyzed by light of b 4 9 0 nm to give diamagnetic The origin of the NOz- signal is problematical. We obtained a strong signal from a solution of ceric ammonium nitrate in benzyl alcohol even when a filter transmitting only beyond 360 nm was employed conditions normally giving rise to only NO3* in acid glasses.24 It seems possible that a small fraction of the organic radicals produced are able to reduce neighbowing NO ions to NOz- and OH-.soft ” lattice of HN03 and HC104 at 88 K by 320-420 nm irradiation of D. GREATOREX AND T . J . KEMP 65 The photo-oxidation of the simplest primary alcohols RCH20H can be expressed by eqn (1) RCH20H hv RCHOH + H ~ I (1) + Ce( III) 3 .1 Ce(IV) the corresponding hydroxyalkyl radical being found with methanol ethanol propan- 1-01 2-methylpropan-1-01 butan-1-01 and pentan-1-01. This mode is also found with propan-2-01 but in additional some C-C cleavage takes place to give CH3-. Cleavage is also apparent with butan-2-01 and pentan-3-01 and is the normal mode of photo-oxidation of tertiary alcohols by Ce(1V).The extremely prompt appearance of CH3. from tert-butanol e.g. suggests a concerted mode of cleavage (2) 0- hv Ri-CR2R3-0H+R1 + CR2R3=O + Hs+Olv (2) 11 + Ce(II1) ke(IV) rather than intermediate formation of R1R2R3C-0- for which we find no e.s.r. signal. The primary production of alkyl radicals during photo-oxidation of tertiary alcohols and some secondary alcohols by Ce(1V) contrasts with the behaviour of OH- which oxidizes alcohols by hydrogen-abstraction 11* 13* l5 in both matrices and solution CH3-CMe2-OH + OH- + -CH2-CMe20H + H20. This rules out intermediacy of OH- in photo-oxidation in perchlorate matrices. analogous to (l) Allylic alcohols produce the corresponding hydroxyallyl radxal by a process h v R1CH=CR2-CHR30H-+R1CH=CR~-CR3OH + Hi-solv 3- W V ) + Ce(II1).Here a close similarity exists between oxidation by OH- and photo-oxidation by Ce(1V). The course of photo-oxidation of alcohols by Ce(1V) has much in common with that of thermal oxidation by the same oxidant. Both reactions proceed through a 1 1 complex between oxidant and substrate and involve either attack on the C-H bond of the CHOH- group (for primary and secondary alcohols) or fragmentation of an alkyl group to yield a ketone (for tertiary alcohols).29 C-C cleavage is also a feature of secondary alcohol photo-oxidation e.g. of pentan-3-01 and cleavage has been reported during the thermal oxidation of this substrate by the highly oxidizing CoOH2+ A further analogy between thermal and photochemical oxidation by Ce(1V) is instanced by 1,2-diphenylethanol which undergoes thermal oxidation according to a C6H5CH2CH(C6H5)OHjC6HscH~ + C6HsCH0 + H+ + Ce(II1).Fig. 7 illustrates the spectrum of benzyl radical produced by an identical fragmentation in the Ce(1V) photo-oxidation. 1,l-Diphenylethanol might be expected to break down on photo-oxidation to a phenyl radical which even at 77 K is sufficiently reactive to attack hydrogen-contain- ing molecules of the matrix 32 and accordingly we attribute our observed spectrum of *CH2CN to such a secondary reaction. Ce(1V) 3 66 Ce(lV) PHOTO-OXIDATION OP ALCOHOLS Secondary reactions are evident in other of our examples. The CH3- produced from tert-butanol slowly attacks the alcohol matrix to produce CH,CMe,OH as indicated in fig. 4. From these experimental results it is clear that the technique described affords a useful insight into the primary processes in photo-oxidation.Use of Ce(IV) as the perchlorate or nitrate enables a more comprehensive picture to be gained of the various mechanisms of oxidation than the similar experiments on oxidative de- carboxylation of carboxylic acid complexes of Pb(IV).6 The high reactivity of Ce(1V) towards certain polyfunctional organic ligands can be overcome by using the milder U(V1) species as oxidant. We thank Mr. J. M. Worthington who performed a number of preliminary experi- ments using ceric ammonium nitrate as part of his undergraduate research project in the School. Mr. K. Holden made the apparatus shown in fig. 1 devising a reliable high-vacuum greaseless tap. The S.R.C. is thanked for a grant to purchase the spectrometer and for support of D. G.A. W. Adamson W. L. Waltz E. Zinato D. W. Watts P . D. Fleischauer and R. D. Lindholm Chem. Rev. 1968,68,541. G. Oster and N. Young Chem. Reu. 1968,68,125. F. S . Dainton and R. G. Jones Trans. Faraday Soc. 1967,63,1512. T. W. Martin R. E. Rummel and R. C. Gross J. Amer. Chem. SOC. 1964,86,2595. D. J. Ingram W. E. Hodgson C. A. Parker and W. T. Rees Nature 1955,176,1227. K. Heusler and H. Loeliger Helv. chim. Ada 1969,52,1495. J. K. Kochi R. A. Sheldon and S. S. Lande Tetrahedron 1969 25 1197. R. A. Sheldon and J. K. Kochi J. Amer. Chem. Soc. 1968,90,6688. D. Greatorex and T. J. Kemp. Chem. Comm. 1969 383. L. B. Young and W. S. Trahanovsky J. Amer. Chem. SOC. 1969,91,5060. R. S. Alger T. H. Anderson and L. A. Webb J. Chem. Phys. 1959,30,695. W. T. Dixon and R. 0. C. Norman J. Chern.SOC. 1963,3119. l 1 J. F. Gibson M. C. R. Symons and M. G. Townsend J. Chem. SOC. 1959,269. 14C. Chacaty Compt. rend. 1964,259,2219. l 5 R. Livingston and H. Zeldes J. Chem. Phys. 1966,44 1245. I6 P. Svejda and D. H. Volman J. Phys. Chem. 1970,74 1872. I7 P. B. Ayscough and C. Thomson Trans. Faraday Sac. 1962,58,1477. K. A. Maas and D. H. Volman Trans. Faraday SOC. 1964,60 1202. I9 J. F. Gibson D. J. E. Ingram M. C. R. Symons and M. G. Townsend Trntu. Faraday SOC. 1957 53 914. 2o M. Fujimoto and D. J. E. Ingram Trans. Faraduy SOC. 1958,54,1304. 21 H. Fischer 2. Naturforsch. 1965,204 488. 22 V. A. Tolkachev I. I. Chkeidze and N. Ya. Buben Dokl. Akad. Nauk S.S.S.R. 1962 147 23 W. H. Latimer Oxidation Potentials 2nd ed. (Prentice-Hall Inc. N.Y. 1952). 24 T. W. Martin L. L. Swift and J. H. Venable Jr. J. Chem. Phys. 1970,52,2138. 25 L. Dogliotti and E. Hayon J. Phys. Chem. 1967,71,3802. 26 L. B. Young and W. S. Trahanovsky J. Amer. Chem. SOC. 1969,91 5060. 27 F. K. Kneubiihl J. Chem. Phys. 1960,33,1074. 28 P. B. Ayscough and R. G. Collins J. Phys. Chem. 1966 70 3128. 29 M. Rangaswamy and M. Santappa Indian J. Chem. 1969,7,473. 30D. G. Hoare and W. A. Waters J. Chem. SOC. 1964,2560. 31 P. M. Nave and W. S. Trahanovsky J. Amer. Chem. SOC. 1968 90 4755. 32 J. E. Bennett B. Mile and A. Thomas Proc. Roy. SOC. A 1966,293,246. 643.

ISSN:0014-7672    

DOI:10.1039/TF9716700056

出版商:RSC    

年代:1971

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Mercury-Sensitized Luminescence of Alcohols BY C.G. FREEMAN M. J. MCEWAN R. F. C. CLARIDGE AND L. F. PHILLIPS Chemistry Dept. University of Canterbury Christchurch New Zealand Received 20th July 1970 Rate constants for quenching 253.7 nm fluorescence and quantum efficiencies for emission of luminescence during mercury-sensitized photolysis have been measured for methanol ethanol propanol isopropanol n-butanol isobutanol sec-butanol tert-butanol and tert-amyl alcohol. From the variation of luminescent efficiency with the structure of the alcohol it is concluded that the main process competing with luminescence is normally the abstraction of an or-hydrogen by a metastable HS(~P~) atom formed during quenching of Hg(3P1). For tert-butanol and tert-amyl alcohol the rate constants for reaction with Hg(3Po) are (7.5k2.5) x 10-l2 and (2.2rt0.8) x 10-1' cm3 molecule-' s-l respectively ; lower limits are given for the rates of reaction of the other alcohols with Hg(3P0).Previous work on 253.7 nm mercury-sensitized photolysis of alcohols has been reviewed by Cvetanovic and by Calvert and Pitts2 The results of previous work have been interpreted entirely in terms of reactions initiated by Hg(3P1) although Kato and Cvetanovic have pointed out that the difference of a factor of 3.5 between the '' physical " and " chemical " quenching cross-sections of methanol and ethanol is a strong indication that the initial quenching process with these alcohols yields mainly Hg(3P0). Our studies of mercury-sensitized luminescence 5-8 have shown that electron-donor inolecules can be expected to react with Hg(3P0) to form excited charge-transfer complexes and that such complexes are highly unstable with respect to undergoing transitions to their repulsive ground states with the emission of continuum radiation.It was therefore of interest to endeavour to observe similar radiation during mercury- sensitized photolyses of alcohols in order to assess the importance of metastable atoms in these systems to measure the rates of reaction of alcohols with Hg(3P0) and to determine the effect of the structure of the alcohol on the quantum efficiency of luminescence and the shape and position of the emission band. Our main con- clusions from these studies are that metastable atoms are important in these systems and that the dependence of luminescence efficiency on structure provides an indication of the nature of the primary step in the chemical quenching of Hg(3P0).In addition to giving information about the rates of reaction of alcohols with Hg(3P0) the experiments have also yielded some new rate constants for quenching of Hg(3P1). EXPERIMENTAL All the measurements described here were made using a 3 cm diam. reaction cell with the mercury-containing side arm immersed in a dewax of melting ice. Under these conditions the measured quenching of 253.7 nm resonance fluorescence by NH3 corresponded to a radiation trapping time of 2.1 x lo-' s assuming the value of 8 . 4 ~ cm3 molecule-l s-I given by Cvetanovic l for the rate constant of quenching Hg(3P1) by ammonia. Spectroscopic-grade methanol ethanol and isopropanol were used. The other alcohols were either of analytical reagent quality or were redistilled or recrystallized.In addition The apparatus and procedures have been described previ~usly.~~ 67 68 M ER C U R Y - S EN S 1.1 I ZED L U MI N E S C E N C E 0 F A L C 0 H 0 L S it is likely that the procedure of repeated freezing and thawing under vacuum which was used to remove dissolved gases and which usually resulted in the loss of about half of the alcohol being degassed would have removed most of any volatile impurity. Quantum efficiencies of luminescence were detcrmined by comparison of the integrated emission intensity for the alcohol in question with that for ammonia in the same reaction cell using the prcviously determined figure of 0.70 for the NH quantum The estimated uncertainty of the intensity comparison is f10 % for methanol ethanol tert- butanol and tert-amyl alcohol and &15 % for the others.To this must be added the uncertainty of i ~ 2 0 "/o in the biH3 quantum efficiency in order to obtain limits of error in the absolute values of quantum efficiency that are quoted in table 1. As before the effect of pressure broadening on the amount of 253.7 nm radiation being absorbed in the cell was calculated from the deviation of the 253.7 nm quenching data at high pressures from the Stern-Volmer line. TABLE 1.-sUMMARY OF QUESCHISG AND LUMINESCENCE DATA. RATE CONSTANTS ARE IN UNITS OF cm3 reactant A peak bandwidth 1011 kl ko 4 s-l ; WAVELENGTHS AND BANDWIDTHS IN nm water 286 23.8 2.8 2 . 0 ~ 10-14 0.19 methanol 295 27.2 17.5 > 5 x 0.033 ethanol 300 32.4 37 >2x lo-" 0.013 n-pro pano 300 28.8 43 >2x lo-" 0.0069 iso-pro pano 302 30.4 34 >2x lo-" 0.0030 n-butanol 298 29.9 50 >2x lo-" 0.0076 isobutanol 297 30.9 45 >2x lo-" 0.0041 sec-butanol 301 31.4 45 >2x lo-" 0.0021 tert-bu tanol 30 1 28.7 26 (7.5 j 1 2 .5 ) ~ 0.26 tert-amyl alcohol 303 29.9 35 (2.2 Ay0.8) x lo-' 0.042 RESU L'TS In fig. 1 the emission baiids for methanol cthaiiol and isopropanol are shown together with the analogous band for water. The bands for the other alcohols studied have the same basic shape and practically coincide in wavelength with the bands for ethanol and isopropanol. The areas under the emission bands expressed as normalized bandwidths for unit intensity at the peak wavelength are listed in table 1 as arc the wavelengths of peak intensity. Secondary butanol gives a tri- angular band similar to that shown for ethanol ; the other bands are more bell-shaped like the one shown for isopropanol.In the fourth column of table 1 arc listed the values obtained for the rate constant kl of quenching Hg(3P,). These rate constants were calculated from the ratio of the slope of the Stern-Volmer line (at partial pressures of quencher gas below 1 Torr) to the slope of thc corresponding line with ammonia as the quencher using k = 8 . 4 ~ lo-" for NH3. The estimated error of the k values is 10 %. The values obtained for water methanol and cthanol agree to within 10 % with thc results of previous workers. * The fifth column of table 1 contains estimates of the rate constant ko for reaction with Hg(3P,). As b e f ~ r e ~ thesc estimates are based on the dependence of the intensity of modulated luminescence on the frequency of chopping the 253.7 nm radiation from the lamp.For most of the alcohols studicd the reaction with Hg(3Po) was so fast and the luminescent efficiency was so low that it was not possible to make reliable measurements at the low pressures at which the frequency dependence became apparent. For this reason we can only quote lower limits for these rates. However for the two tertiary alcohols the combination of higher quantum efficiency C . G . FREEMAN M. J . MCEWAN R . F . C . C L A R I D G E L . F . PHlLLIPS 69 and significantly slower reaction rate made quantitative measurements possible. A number of attempts were made to measure k for methanol by observing the effect of small amounts of niethanol on the frequencydependence of ammonia lumines- cence at 350 nm but the aniount of niethanol required was so sniall that the measure- ments were subject to severe errors due to adsorption of the alcohol on the cell walls.We plan to repeat these measurements with a flowing mixture of methanol and ammonia ; the method of studying a nlixture with NH3 should also be applicable to substances like NO and COz which themselves give no sensitized luminescence. n C 0 c a x -. v) c. W Y .- Y 3 0.5 c c .- .- v) .- E 3 .O 2 50 300 353 wavelength (nm) FIG. 1 .-Emission band contours for methanol (filled circles) ethanol (open circles) and isopropanol (half-filled circles). The curve for HzO given by the broken line is derived from ref. (7). The last column of table 1 contains the values obtained for 4 the quantum efficiency of luminescence.Most of the figures show the expected steady decline in quantum efficiency with increasing molecular complexity. However tert-butanol and tert- amyl alcohol which were found to have the remarkably high luminescent efficiencies of 26 and 4.2 % respectively do not follow this simple trend. DISCUSSION We first consider the effect of the structure of the alcohol on the position of the emission band as given in the second column of table I . On the basis of the discussion in ref. ( 6 ) it would be expected that the substitution of methyl groups for hydrogen atoms which would increase the electron-donating ability of the oxygen atom should cause the peak of the emission band to move further towards the red as is in fact observed. Most of the wavelength shift occurs on going from water to methanol further substitution having less effect.In preliminary experiments with diethyl ether we have been unable to detect an emission band so the effect of replacing both of the hydrogen atoms in water by alkyl groups remains an open question. Since for a given electron donor both the peak wavelength of the emission band 70 MERCURY-SENSITIZED LUMINESCENCE OF ALCOHOLS and the rate constant ko for reaction with Hg(3Po) are expected to depend on the strength of the charge-transfer interaction one would also expect to find a correlation between these two quantities. A plot of loglok0 against the peak wavelength of the emission band given in fig. 2 shows that such a correlation does exist for sub- stances for which the quantum yield of decomposition is very small or zero.In constructing this graph we have assumed that the mercury excimer band at 485 nm is essentially a charge-transfer band and also that the curve should be drawn to become parallel to the vertical axis at 266nm the wavelength of the forbidden 3P0-+ 'So transition. Reference to table 1 reveals however that the alcohols react with Hg(3Po) much more rapidly than would be predicted on the basis of fig. 2 and we therefore conclude that the correlation breaks down when reaction channels leading to decomposition are more important than that for luminescence. -10 - 12 cy" M 0 - - 14 -16 I I I I I I I 250 350 450 peak wavelength (nm) FIG. 2.-L0g~~k~ for xenon water,' ammonia,6 and mercury * plotted as a function of the peak wavelength of the charge-transfer emission band. The quantum efficiencies of luminescence given in the last column of table 1 provide an indication of the outcome of the competition between luminescence and decomposition in the reaction with Hg(3P0).Considering first the result for tert- butanol the high quantum efficiency for luminescence despite the competition from other reaction channels implies that for this molecule at least the main outcome of quenching Hg(3P1) is the production of metastable atoms. In this respect tert- butanol might be expected to be a special case because of the lack of an a-hydrogen. However the values given for kl in the table show no marked decrease on going from a secondary to a tertiary alcohol. The expected trend in kl with increasing molecular size is found for each of the three groups n-alcohols iso- or sec-alcohols and tert-alcohols and there is a steady decrease in kl between one group and the next but there is no indication that there might be a basic difference in quenching mechanism between the tertiary alcohols and the others.Hence we believe that we have confirmed the suggestion of Kato and Cvetanovic regarding the production of Hg(3Po) in these systems. Unlike the data for k, the values of luminescence efficiency given in table 1 show a marked change on going from secondary to tertiary alcohols Both the increased c . G. FREEMAN M . J . MCEWAN R . F . c. CLARIDGE L. F . PHILLIPS 71 quantum efficiency and the decreased value of ko indicate that reaction channels leading to decomposition are much less important in the absence of an a-hydrogen. Consequently it would appear that the abstraction of an a-hydrogen is normally the most important process in the chemical quenching of Hg(3P0).For methanol the work of Pottie Harrison and Lossing and of Knight and Gunning lo has shown conclusively that the removal of the hydroxyl hydrogen is the predominant process but for ethanol this is not necessarily the case.3 Our results do not indicate whether the hydrogen atom removed in the primary step is simply dislodged or is abstracted to form HgH ; the results of Callear and Hedges l1 are consistent with the possibility that HgH might be formed as a short-lived intermediate. We are grateful to Mr. R. P. Garland for performing gas chromatographic analyses of our alcohols. This work was supported by the New Zealand Universities Research Committee and by Grant AF-AFOSR-1265-67 from the Directorate of Chemical Sciences United States Air Force Office of Scientific Research.' R. J. Cvetanovic Progr. Reaction Kinetics G. Porter ed. (Pergamon Press) 1364,2 39. J. G. Calvert and J. N. Pitts Photochemistry (John Wiley & Sons New York 1966) p. 105. A. Kato and R. J. Cvetanovic Can. J. Chem. 1967,45 1845. A. J. Yarwood 0. P. Strausz and H. E. Gunning J . Chem. Phys. 1964,41,1705. C . G. Freeman M. J. McEwan R. F. C. Claridge and L. F. Phillips Chem. Phys. Letters 1970,5 555. R. H. Newman C. G. Freeman M. J. McEwan R. F. C. Claridge and L. F. Phillips Trans. Faraday SOC. 1970 66,2827. ' C. G. Freeman M. J. McEwan R. F. C. Claridge and L. F. Phillips Trans. Faraday SOC. in press. C. G. Freeman M. J. McEwan R. F. C. Claridge and L. F. Phillips Chem. Phys. Letters 1970 6,482. R. F. Pottie A. G. Harrison and F. P. Losing Can. J. Chem. 1961,39,102. lo A. R. Knight and H. E. Gunning Can. J. Chem. 1961,39,1231,2251,2466; 1962,40,1134. l' A. B. Callear and R. E. M. Hedges Trans. Faraduy SOC. 1970,66,615.

ISSN:0014-7672    

DOI:10.1039/TF9716700067

出版商:RSC    

年代:1971

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Single-Pulse Shock Tube Studies of Hydrocarbon Pyrolysis Part 1 .-Pyrolysis of Cyclopropane BY J. N. BRADLEY AND M. A. FREND Dept. of Chemistry Univcrsity of Essex Colchester Essex Received 24th March 1970 The pyrolysis of cyc1opropane.t argon mixtures has been studied in a single-pulse shock tube over the temperature rangc 1060-1870 K.At a total prcssute of 500 mmHg and temperatures below 1300 K an apparent first-order rate constant of exp (-230 kJ/RT) s-I was obtained. This is in agreement with extrapolations from low temperature data provided allowance is made for the deviation from limiting first-order behaviour with increasing temperature. Above 1300 K radical chain decomposition of the cyclopropane and/or the propylene product was observed but the overall loss of cyclopropane which is best fitted by the expression exp (-48.5 kJ/RT) s-l was much lower than predicted by current unimolecular rcaction rate theory. Various alternative mechanisms arc examined but no acceptable explanation can yet be offcred. The thermal decomposition of cyclopropane to propylene is a relatively straight- forward reaction uncomplicated by interference from competing side reactions and is extensively used as a test for theories of unimolecular reaction rates.For similar reasons it has also been used to test novel shock tube techniques although it would be expected that at high temperatures radical chain processes would participate leading to a higher rate of reaction and more complex products. Preliminary studies l * have demonstrated the change in product distribution but have also revealed that the rate of reaction is retarded and not accelerated at high temperatures. EXPERIMENTAL The single-pulse shock tube is basically the same as that originally developed by Glick Squire and H~rtzberg.~ It is constructed from stainless steel tubing of 2.8 cm int. diam. and 0.5 cni wall thickness. The tubing is divided into segments connected by O-ring unions so that the lengths of the driver and experimental sections may be varied in order to obtain different reaction times.In all the experiments described below the experimental section was 2.5 m long and the driver section 0.9 m long. The dump tank is constructed from mild steel and is of 3601. capacity. The experimental section can be evacuated to mmHg by a two-stage rotary pump. The diaphragms consist of aluminium foil 0.025 mm thick sandwiched between two gaskets of polythene 1.6 mm thick. The first diaphragm is ruptured by a spring-loaded needle. A narrow strip of aluminium foil placed ahead of the diaphragm and insulated from both it and the shock tube is used to provide an electrical signal when the diaphragm breaks. This signal triggers a variable delay circuit whose output is used to trigger a condenser discharge between a tungsten electrode and the second diaphragm.This technique for rupturing the second diaphragm has been described else~here.~ In a single-pulse shock tube the gas is heated by a shock wave reflected from the end- plate and is cooled by a rarefaction wavc centred at the entry to the dump tank. In con- sequence the gas at different positions along the tube is heated for different periods of time. 72 mmHg by an oil diffusion pump and the dump tank and driver sections to J . N. BRADLEY AND M. A . FREND 73 This loss of time resolution has been circumvented in the present system by confining the reactants at high dilution between two sliding-vane valves 30 and 44 cm from the end-plate which are opened immediately prior to firing the shock.Two Kistler 601A piezo-clectric gauges are situated 14 and 42.8 cm from the end-plate. Signals from the gauges are amplified by Kistler Charge amplifiers and displayed on a Tektronix type 555 Dual Beam oscilloscope. The delayed sweep facility permits the output from the gauge adjacent to the end plate to be displayed at a sweep speed of 1.0 ms/cm giving the pressure history of the reacting gas and the outputs from both gauges to be displayed at 0.1 ms/cm giving the incident shock velocity. Reaction times of ca. 1 ms can be measured to 510 % the uncertainty being in determining the precise arrival time of the expansion wave. The uncertainty in the velocity measurements is much lower and corresponds to an error of :!I 10 K in the temperature measurements.Tailored-interface conditions which are necessary to maintain uniform temperature and pressure during the reaction period are achieved by using an appropriate hydrogen+nitrogen mixture in the driver section. For the present experiments the driver pressure was 1.5 atm and the experi- mental pressure lay in the range 15-35 mmHg. After the shock has been fired a pressure of 300 mmHg of nitrogen is admitted to the driver section to sweep the reaction products through a sliding-vane valve in the end-plate and into a glass trap of 45 ml volume. The products are then transferred to a Pye 104 gas chromatograph. The analysis was carried out using Porapak Q and Porapak T columns with programmed temperature control and a flame ionization detector. A stream splitter permits effluent samples to be analyzed on an A.E.I.M.S. 1Oc2 mass spectrometer as a check on the identity of the chromatogram peaks. The recovery always retains 80-100 % of the total products and the accuracy of the analysis checked by introducing standard mixtures to the shock tube is better than 95 %. Reflected shock temperatures are obtained from the incident velocity measurements assuming one-dimensional behaviour. The calculations are carried out on the University of Essex I.C.T. 1909 computer using standard thermodynamic data.5 Reactant mixtures are prepared in an independent vacuum system fitted with Springham greaseless taps and allowed to mix for 24 h before use. Hydrocarbons (purity 99 %) were supplied by Cambrian Chemicals Ltd. Cyclopropane-d6 (purity 98 %) was supplied by Merck Sharpe and Dohme.These materials were further purified by bulb-to-bulb distillation. Hydrogen nitrogen and argon (99.995 %) were supplied by British Oxygen Company Ltd. and used without further purification. RESULTS The rate of removal of cyclopropane in 1 % mixtures of cyclopropane in argon has been measured over the temperature range 1060-1870 K. Although some devia- tion from high pressure limiting behaviour may bc expected the experimental pressure only varies from 500 to 700 mmHg over the complete temperatwe range and the data are conveniently analyzed in terms of apparent first-order rate constants. An Arrhenius plot of these rate constants is shown in fig. 1. There is a sharp transition in rate at about 1300 K and least squares analysis yields the following rate expressions (1060-1300 K) (1350-1800 K) exp (-230 kJ /RT) s-l exp (-48.5 kJ/RT) s-l.The results of a limited number of experiments using 2 % mixtures of cyclopropane in argon are also illustrated. A limited number of experiments was also carried out at a total pressure of ca. 150 mmHg. Because of the deviation from high pressure limiting behaviour the results are not usefully illustrated in fig. 1 but are included in fig. 4. The composition of the products as a function of temperature at a reaction time of 1 ms is shown in fig. 2. The reaction is exclusively isomerization to propylene 74 PYROLYSIS OF CYCLOPROPANE 3 c 3 0 0 0 /J I-_-_ 0.6 0-7 0.8 0.9 1 0 3 ~ 1 ~ FIG. 1.-Arrhenius plot of apparent first-order rate constants for pyrolysis of cyclopropane. 0 l % A in Ar ; 9 2 % A in At-.With added gases 0 C2H2 ; A C2H4 ; ~3 allene ; A H2. The results above 1650 K are subject to appreciable error and have not been taken into account in the least squares analysis). temperature (K) FIG. 2.-Variation of product distribution with temperature. 0 C3Hs ; A C2H4 ; 0 C2H2 ; -- HZ ; 0 CH4; 0 methyl acetylene; 9 CzH6; A allene; B 1,3-butadiene ; A 1-butene. J . N. BRADLEY AND M. A . FREND 75 below the transition temperature of 1300 K but above this temperature the products are composed of propylene ethylene acetylene methane allene 1-butene butadiene methylacetylene and hydrogen. The analytical technique did not permit the detection of hydrogen but its yield may be estimated from mass balance. The products observed are identical with those observed during the high-temperature pyrolysis of propylene and it is therefore impossible to determine whether isomerization of cyclopropane to propylene occurs prior to or simultaneously with the decomposition reaction.A series of kinetic measurements has been conducted with added hydrogen ethylene acetylene and allene the total reactant concentration being maintained at 1 %. The apparent first-order rate constants are also shown on fig. 1 and agree within experimental error with the results obtained without additives. The rate constants obtained for mixtures of 0.5 % cyclopropane 0.5 % cyclo- propane-d, 99 % argon agreed with those for cyclopropane and mass spectral analysis revealed negligible H/D exchange in the residual cyclopropane (less than 2 % at 1500 K). Exchange was observed in the products at 1520 K about 18 "/o of the propylene shows exchange of one atom and 10 % showed exchange of three atoms.No two-atom exchange was observed. A parallel investigation of the pyrolysis of lower molecular weight hydrocarbons revealed a similar transition with changes in both activation energy and product distribution at 1350K for ethane and 1400 K for n-butane. No transition was observed for propane isobutane propylene butene-1 or butadiene. DISCUSSION The kinetic measurements on the pyrolysis of cyclopropane reveal a striking discontinuity at about 1300 K and it is convenient to discuss the behaviour in the two temperature regions separately. The unimolecular isomerization of cyclopropane has been investigated in the temperature range 690-820 K by four independent groups '-lo and in the range 860-1670 K by Barnard and Seeb0hm.l Because unimolecular reaction theory predicts a fall-off from the high pressure limiting behaviour with increase in tempera- ture as well as with a reduction in pressure the Arrhenius parameters obtained for the rate constants cannot be compared directly.The rate constant expressions obtained at the higher temperatures have therefore been corrected to the high pressure limit by calculating an " effective pressure " at 718 K using the relation p2/p1 = (T,/T,)S where s is the effective number of oscillators. The pressure correction has then been obtained from the fall-off curve at 718 K given by Lin and Laidler.12 Since this refers to pure cyclopropane and the experiments were carried out in the presence of excess argon it has been assumed that the efficiency of argon in collisional activation is 0.07 times that of cyc10propane.l~ Fig.3 shows that both the present results and those of Barnard and Seebohm agree with the lower temperature data within experimental error. The more significant feature of the pyrolysis is the sharp transition in reaction rate which occurs at about 1300K. The measured rate provides only an upper limit to the rate of the isomerization reaction since radical chain decomposition is occurring simultaneously. In fact the magnitude of the H/D exchange in the propylene formed and the rate of radical attack on propylene determined indepen- dently both suggest that the chain decomposition may account for the whole of the loss of cyclopropane under these conditions. This transition has also been observed by Miyama and Takeyama,l by Quinn,2 and by Barnard and Seebohm.ll Although the experimental conditions differ in each investigation all the data were obtained 76 PYROLYSIS OF CYCLOPROPANE using shock tube methods and it is necessary first to ascertain whether the observation could be an artefact of thc technique employed.If such an artefact were to arise from a peculiarity in the aerodynamics of the system then it should be observed for other reactions in the same temperature range. Some hydrocarbon pyrolyses do display similar transitions although at quite different temperatures whilst others show no transition at all. Since the reactants are present typically at concentrations of 0.5-1.0 % the different specific heats could have only an insignificant effect on the aerodynamics.Errors in the analysis can similarly be excluded since the identity of the chromatogram peaks was checked by mass spectro- metry and the different investigators used quite different column packings to resolve the constituents. The transition was associated with a change in the nature of the products buGthe rates were determined throughout from the consumption of cyclo- propane. No errors can be found in the determination of the temperature or the reaction time of sufficient magnitude to explain the findings. \ \ \ 0 0 - 0.8 1.0 1-2 1.4 103 KIT FIG. 3.-Comparison of shock-tube rcsults corrected to the high pressure limit with low temperature data. Curve (2) represents the results of fig. I curve ( 1 ) the samc results after correction to the high pressure limit and curve (3) the results from ref.( I 1). The effective number of oscillators s is Current unimolecular reaction theory provides no explanation for such a transition and the predicted fall-off with temperature correlates well with the rates on the low temperature side of the transition. Since there is a simultaneous change in the nature of the products it seems possible that one of the additional species produced might provide a mechanism for deactivating some intermediate involved in the decompo- sition. However the addition of allene acetylene ethylene and hydrogen in cxperi- ments conducted below the transition had no effect on the rates observed. It is always possible that a trace quantity of some undetected product could be responsible taken as 13. 1-1. ref. (10); x-X ref. (9); .-.ref. (7); +-+,ref. (8). J . N. BRADLEY AND M. A . FREND 77 but it is difficult to conceive of a molecule which would be so specific in performing this role. Another possibility is that at high temperatures the cyclopropane tends to break a C-H bond rather than a C-C bond the resulting cyclopropyl radical abstracting hydrogen from the products to re-form the reactants. This appears unlikely on thermochemical grounds and can be eliminated by the absence of appreciable H/D exchange when mixtures of cyclopropane and cyclopropane-d were pyrolyzed. Exchange did occur in the products but this merely emphasizes the part played by radicals in the subsequent reactions. A reduction in the apparent activation energy with increasing temperature is unusual in homogeneous gas-phase reactions although the converse is commonplace.One way in which it can occur is when the chain length of a radical chain reaction is reduced e.g. by the participation of a temperature-dependent termination process but it is difficult to visualize how the isomerization of cyclopropane can occur via a chain process. The only feasible explanation would appear to be that the decomposition of cyclo- propane takes place not from the ground state but from an excited state up to 48 kJ/mol higher. At low temperatures the population of this state is in equilibrium with the ground state population and decomposition from it is kinetically indis- tinguishable from direct decomposition. At higher temperatures the subsequent steps become relatively faster and the population of the excited states becomes r ate-determining .The mechanism can be expressed formally by ki kz k3 k4 k5 A+Ar+A*+Ar A* +- Ar+A** i- Ar A**-+products where A and A* represent the ground and excited states of cyclopropane. The unimolecular decomposition of A* is expressed for simplicity by the Lindemann treatment using rate constants k3 k4 and k5 and the intermediate A**. A station- ary-state analysis then gives the overall rate expression - - d P 1 - klk3k5PILArl - dt k,k4[Ar] + k2k + k3k5' Three limiting cases are possible depending on the relative magnitudes of the three terms in the denominator. Subject to the constraint A,>A and E3>E5>E2 E4 these will occur as follows. High temperature; low pressure -d[A]/dt = k,[A][Ar]. Intermediate temperature intermediate pressure Low temperature low pressure - d[A] /dt = klk3[ A][Ar]/k,.Low temperature high pressure -d[A]/dt = klk3k5[A]/k2k4. 78 PYROLYSIS OF CYCLOPROPANE Fitting this expression to the present data (fig. 4) gives k3/k2 = kl = exp (-48.5 kJ/RT) 1. mol-l s-l exp (- 179.8 kJ/RT) exp (-44.4 kJ/RT) mol/l. A small uumber of experiments using the mixture of 1 % cyclopropane in argon was carried out at lower pressures. The rate constants were scaled to a total pressure of 500 mmHg assuming the linear dependence on pressure predicted by this mechanism and are illustrated in fig. 4. Corresponding rate constants obtained from the results of other workers are also included. Fall-off with pressure is also predicted by this mechanism but since the simple Lindemann formulation has been used no quantitative significance should be attached to the values of k3 and k5.However the value of kl provides an upper limit to the rate of population of the k5/k4 = excited state. I C a n " 6 X 2 4 3 a 0 $ 4 4 2 0 \ \ FIG. 4.-Coiiiparison of apparent first-order rate constants with behaviour predicted by the three-step mechanism for a 1 % mixture of cyclopropane in argon at a total pressure of 500 mmHg. 0 results from experiments at 150 mHg. If this mechanism is of any significance this state must be vibrationally excited since low-lying electronic states are ruled out by quantum-mechanical calculations. As the 48 kJ/mol is an upper limit to the energy suitable vibrational levels are certainly available but it is then difficult to see why the population of such levels should be so inefficient. No satisfactory explanation of the anomalous behaviour of the cyclopropane isonierization can yet be presented although the evidence does suggest a possible J .N. BRADLEY AND M . A . FREND 79 deficiency in current unimolecular reaction theory in that it takes full account of the de-population of high vibrational levels due to reaction but pays little attention to the rate of population of the low-lying levels. The authors thank the Institute of Petroleum (Hydrocarbon Research Panel) for their support during this investigation. H. Miyama and T. Takeyama Bull. Chem. SOC. Japan 1965,38,2189. J. G. Quinn Ph. D. Thesis (Liverpool 1967). H. S. Glick,W. Squire and A. Hertzberg 5th Symp. (Znt.) Combustion (Reinhold N.Y. 1955) p. 393. J. N. Bradley R. N. Butlin and J. G. Quinn J. Sci. Instr. 1965,42,901. R. E. Duff and S. H. Bauer J. Chem. Phys. 1962,36,1754. J. N. Bradley and M. A. Frend unpublished results. T. S. Chambers and G. B. Kistiakowsky J. Amer. Chem. Sac. 1934,56,399. E. S. Corner and R. N. Pease J. Amer. Chem. SOC. 1945,67,2067. B. R. Davis and D. S. Scott Znd. Eng. Chem. 1964,3,20. lo W. E. Falconer T. F. Hunter and A. F. Trotman-Dickenson J. Chem. SOC. 1961 609. l 1 J. A. Barnard and R. P. Seebohm Symp. Gas Kinetics (July 1969 Szeged Hungary). l2 M. C. Lin and K. J. Laidler Trans. Furaduy SOC. 1968,64,927. l3 H. 0. Pritchard R. G. Sowden and A. F. Trotman-Dickenson,Proc. Roy. SOC. A 1953,217,563. l4 R. D. Brown and V. G. Krishna J. Chem. Phys. 1966,45,1482.

ISSN:0014-7672    

DOI:10.1039/TF9716700072

出版商:RSC    

年代:1971

数据来源: RSC