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 s t d y of Sciences lying bet ween Chemistry Physics and Biology Volume 64 1968 Puges 1-1728 THE FARADAY SQCIETY LONDON @ The Faraday Society and Contributors 1968 PRINTED IN GREAT BRITAIN AT TEE UNIVERSITY PRESS ABERDEEN

ISSN:0014-7672    

DOI:10.1039/TF96864FP001

出版商:RSC    

年代:1968

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 Biology Volume 64 1968 THE FARADAY SOCIETY LQNDON @ The Faraday Society and Contributors 1968 PRINTED IN GREAT BRITAtN AT "HE UNWERSlTY PRESS ABEIRDEEN

ISSN:0014-7672    

DOI:10.1039/TF96864FP003

出版商:RSC    

年代:1968

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. E.S.R. Studies of Ion Association Part 4.-Mechanism and Rate of Sodium Ion Exchange Reaction in Solutions of m-Dinitrobenzene Sodium and Sodium Tetraphenyl Boron BY R. F. ADAMS AND N. M. ATHERTON Dept. of Chemistry The University Sheffield 10 Received 30th August 1967 Analysis of the electron spin resonance spectra of solutions of m-dinitrobenzene-sodium and of t-butyl-m-dinitrobenzene-sodium before and after the addition of sodium-tetraphenyl boron indi- cates that in the mixed systems the paramagnetic complex takes part in a cation exchange reaction in which the incoming cation goes to the uncornplexed nitro-group. Approximate rate constant data are presented for the reaction of the t-butyl-substituted compound.Analysis of line-breadth variations in electron spin resonance (e.s.r.) spectra can yield quantitative information about the dynamics of certain physico-chemical pro- cesses in a unique manner. Fraenkel has reviewed the theoretical methods available for analyzing line-breadth data but which have not been widely employed quantitatively. In this communication we report a novel though qualitative application of the theory. Line-breadth alternation 9 is observed when the paramagnetic species under- goes exchange between equivalent conformations or conformations in which the hyperfine coupling constants stand in special relation to one another. A situation which has been widely studied is where there is an intra-molecular cation exchange between two equivalent conformations of a complex of an alkali metal and an aromatic compound.Pyra~ene,~ and pyra~ine,~? durosemiquinone,6 and p-benzosemi- q ~ i n o n e ~ have been studied in some detail. Generally the rate of the intra-molecular cation exchange is slower the smaller the cation. This behaviour is also observed for m-dinitrobenzene (MDNB),** the subject of this paper. When our work was commenced it was known from Ward's work,1° that MDNB formed strong asym- metric complexes with sodium although the assignment of the ring proton coupling constants was not clear in particular there appeared to be two equivalent ring protons. Publication of OUT solution of this problem was pre-empted by Ling and Gendell,' and by S y ~ o n s ~ and we support their general conclusions.Our concern is the rate and mechanism of the cation exchange reaction between the MDNB-Na complex and another source of metal ions in the solution. In principle there are two possible mechanisms for this reaction ; (i) the incoming cation goes to the complexed nitro group or fii) the incoming cation goes to the uncomplexed nitro group; these (i) (ii) two mechanisms should be distinguishable by different line-breadth effects. For example at slow exchange rates on average three out of every four exchanges by (i) 7 8 E.S.R. STUDIES OF I O N ASSOCIATION will lead to equal broadening of all the lines whereas in (ii) some of the lines will be broadened by every exchange because of the additional modulation of the hyperfine coupling constants of some of the nuclei in the anion.Our observations near the fast exchange limit are consistent with mechanism (ii) operating in solutions in 1,2- dimethoxyethane (DME) of MDNB-Na or 1,3-dinitr0-5-t-butyl-benzene (TBMDNB)- Na when sodium tetraphenylboron (NaBPh,) sodium perchlorate or sodium iodide is added. EXPERIMENTAL MDNB was obtained from B.D.H. and zone-refined before use. TBMDNB was syn- thesized by the method of Bevan et aZ.,I1 and was recrystallized twice from ethanol. NaBPh (Koch-Light) and NaC104 and NaI (B.D.H.) were used without additional purification. Alkali metal reduction was carried out in the usual manner and small weighed portions of the required sodium salt added from behind break-seals. Spectra were recorded with a Varian V-4500 series spectrometer with 100 kc/sec field modulation and using a Honeywell recorder.The magnetic field sweep was calibrated with a Varian F-8 Fluxmeter in conjunction with an Advance TClA 1 Mc/sec frequency counter and a TCD 40 frequency divider. RESULTS AND DISCUSSION The TBMDNB was synthesized to facilitate the evaluation of the proton coupling constants for MDNB itself. The t-butyl group does not make a large perturbation to the n-electron system of MDNB and the unresolved t-butyl proton hyperfine structure I I I = %-= -___ TBMDNB -No-DME FIG. 1 .-Low-field half of the spectrum of TBMDNB-Na in DME -4°C. The assignments of al(N) and a,(N) and of a4 and a6 are chosen for convenience and are not determined. does not make an appreciable contribution to theline-breadth so the effect is essentially to remove a small proton splitting from the MDNB spectrum.Fig. 1 shows the spectrum of TBMDNB-Na in DME at -4°C ; there are three different ring proton R. F . ADAMS AND N. M . ATHERTON 9 hyperfine splittings. The analysis of the MDNB-Na spectrum was therefore consider- ably simplified and we were able to distinguish between the two proton hyperfine splittings which had not been resolved by Ward lo. Our coupling constants for both compounds are summarized in table 1 and for MDNB are in agreement with those of Ling and Gendell.8 We have also reduced both compounds with the other alkali metals and observed the same qualitative behaviour as described by Ling and Gendell,* and by S y m ~ n s . ~ TABLE HYPERFIN FINE COWLING CONSTANTS (GAUSS) IN DME system 011 a3(N) a2 u4 ub as CzNa MDNB-Na a 9-69 0.27 3-17 3-71 4-35 1.10 0.27 MDNB-Naf NaBPh 4.91 &0*3 3.25 f0.15 4-03 kO.15 1.09 20.07 - TBMDNB-Na 9.90 0.27 3-19 3.71 4-22 I 0-27 TBMDNB-Na+NaBPh4 5-06 f0.03 3.19 f0.06 3-89 30.03 - - a estimated accuracy & 2 % When small amounts (concentration ca.M) of NaBPh are added to MDNB- Na solutions the lines in the spectrum are broadened although because of the rela- tively poor resolution it is not possible to determine if some lines broaden more than others. Comparison of spectra computed for mechanisms (i) and (ii) using the modified Bloch equations in the slow exchange limit,12 confirms that for this parti- cular spectrum it is not feasible to distinguish between the two mechanisms in this limit. At higher concentrations of NaBPh the spectra become greatly broadened but at higher concentrations still they sharpen up again.Fig. 2 shows the spectrum of I a,+a -2(a,+ as) # c 2 b FIG. 2.-Spectra of MDNB-Na in DME (a) alone (b) after addition of NaBPh (0.4 M) 25°C. MDNB-Na in DME at 25°C both before (a) and after (b) the addition of NaBPh to a concentration of 0.4 M. Our interpretation of the spectrum at (6) is that there is hyperfine splitting from two protons a pair of protons with some line-breadth alterna- tion and a pair of nitrogens with very strong line-breadth alternation. This analysis is indicated in fig. 2(b) and a set of coupling constants is included in table 1. At the fast exchange limit 1* l2 the extra line-breadth contribution is of the form (1/T2)ex- ( A c o ) ~ ~ so that the pattern observed is that expected for mechanism (ii) if the exchange is still not sufficiently rapid to average out completely the differences in the hyperfine splittings.10 E.S.R. STUDIES OF ION ASSOCIATION Our use of the word " mechanism " is strictly a phenomenological convenience e.g. we can say nothing about the role of the solvent. Again we are not clear what is the nature of the incoming Na it is doubtful if there is a significant concentration of free sodium ions in the solutions and the work of Szwarc et aL.l3 indicates that in our systems the NaBPh is probably largely in the form of solvent-separated ion-pairs. There may be several associated Na+ and BPh species in the solution and the observed rate may be an average of the rates for various species exchanging Na+ with MDNB- Na. One feature of the reaction is clear however that it is not appropriate to describe the exchange as going through a transition state in which there is complete FIG.3.-Spectra of TBMDNB-Na in DME (a) alone 22"C (6) after addition of NaF3Ph4 (0.4 M) 22"C (c) as (b) at 52°C. dissociation. All the studies of MDNB-Na 8-10 indicate that it is astrong complex with little or no tendency to dissociate into the free ions and addition of NaBPh to the solution can hardly lead to enhanced dissociation. Fig. 3 shows the spectra of TBMDNB-Na before (a) and after (b) addition of NaBPh to a concentration of 0.4 M at 22°C. The interpretation of this spectrum is analogous to that for MDNB itself except that there is one proton splitting less. Table 1 includes a set of coupling constants. Because of this simplification we can confirm the analysis from the temperature dependence of the spectrum and obtain some quantitative information.Fig. 3(c) shows the spectrum at 52"C after the addition of NaBPh (0.4 M). The EMI = 0 lines of the triplets from the 4,6-protons have sharpened considerably as expected on our interpretation. Thus since we are close to the fast exchange limit with respect to the 4,6-protonsY we may determine the energy of activation from measurements of the relative amplitudes of the ZMI = 0 R . F . ADAMS A N D N. M . ATHERTON 11 lines of the 4,6-proton triplets. The procedure is analogous to that used for sodium- pyrazine. Fig. 4 shows a typical Arrhenius-type plot of data from a single run which lead to an energy of activation of 6.2 kcal M-' with a standard deviation of 0.5 kcal M-l. At about 70°C the 4,6-proton triplets approach the binomial inten- sities and we can make an estimate of the absolute rate constant.The absolute breadths of the I ZMI { = 1 components at the edges of the spectrum were measured directly and the breadths of the EM = 0 components of the same triplets obtained from the relative amplitudes. Under these conditions the limiting fast-exchange form of the line-shape expression I2 should hold well and since Ao is known we should get a good estimate of the lifetime. The important source of error in estimating the second-order rate constant is the uncertainty in the active concentration of NaBPh, + 0.1 - 0.0 - A 4 I -0-1 - 4 f l 3 -0.2- M 0 4 I I I I I 30 3.1 3-2 33 34 (I/TOK) x 103 FIG. 4.-Plot of line-amplitude data for determination of energy of activation. TBMDNB-Naf NaBPL.but if all reacts we obtain 1.3 x lof2 M-I sec-' for the pre-exponential factor using data corresponding to fig. 4. Our measurements are restricted to a narrow range of conditions but we are satisfied as to their reproducibility in this range. Subject to all the provisos we have made a realistic quotation of the second-order rate constant for the exchange between NaBPh and TBMDNB-Na in DME is (5 x lo1' -2 x 10l2) exp { -(6000+ 1000)/RT)M-' sec-'. The effects of adding NaClO and NaI to solutions of the anions have also been examined qualitatively. Mechanistically the interpretation of the observations is the same as for NaBPh, although the absolute rates are slower. For example at concentrations of 0-4 M for the added salts the spectra are still broad. Again this difference in rate probably reflects a different state of association of the additives.It is doubtful whether these experiments would have been carried out had not one of us (N. M. A.) been stimulated by working with Prof. S. I. Weissman and we also acknowledge subsequent discussions with him. We thank Mr. David Sykes for synthesizing the TBMDNB and for his general assistance the S.R.C. and the Royal Society for grants towards the purchase of equipment and the S.R.C. for the award of a research studentship to R. F. A. 12 E . S . R . STUDIES OF ION ASSOCIATION G. K. Fraenkel J. Physic. Chem. 1967,71 139. J. R. Bolton and A. Carrington MoZ. Physics 1962,5,161. 5 425. E. de Boer and E. L. Mackor J. Amer. Chem. SOC. 1964 86 1513. N. M. Atherton and A. E. Goggins Truns. Furuday SOC. 1965 61 1399. N. M. Atherton and A. E. Goggins Trans. Furuduy SOC. 1966 62 1702. T. E. Gough and M. C. R. Symons Trans. Furuduy SOC. 1966 62 269. A. Carrington Mol. Physics 1962 J. Freed and G. K. Fraenkel J. Chem. Physics 1963 39 326. ’ D. H. Chen E. Warhurst and A. M. Wild Truns. Faruduy SOC. 1967,63,2561. * C.-Y. Ling and J. Gendell J. Chem. Physics 1967 46,400. M. C. R. Symons J. Physic. Chem. 1967,71 172 ; T. A. Claxton W. M. Fox and M. C. R. Symons 1967 63 2570. C. W. L. Bevan T. 0. Fayiga and J. Hirst J. Chem. SOC. 1956 4284. Resonance (McGraw-Hill New York 1959). lo R. L. Ward J. Chem. Physics 1962 36 1405. l2 see e.g. J. A. Pople W. G. Schneider and H. J. Bernstein High Resolution Nuclear Magnetic l3 C. Carvajal K. J. Tolle J. Smid and M. Szwarc J. Amer. Chem. SOC. 1965 87 5548.

ISSN:0014-7672    

DOI:10.1039/TF9686400007

出版商:RSC    

年代:1968

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. Some Electronic Properties of the Molybdenum Bronzes BY P. G. DICKENS AND D. J. NEILD Inorganic Chemistry Laboratory South Parks Road Oxford Received 18th August 1967 Measurements of the e.s.r. and optical spectra of the potassium and sodium molybdenum bronzes have been made. It is concluded that the observed e.s.r. signals arise from Mo5+ donor levels situated < 1 eV below the conduction band of the host Mooa matrix. A model for the electronic structures of these compounds is proposed. The molybdenum bronzes of general formula M,MoO, where M is an alkali metal and 0 < x < 1 were first prepared by Wold et aZ.l Although the electronic and structural features of their tungsten analogues have been intensively studied so far only the crystal structures and electrical conductivities of the more complex molybdenum bronzes have been examined.In this paper measurements of the diffuse reflectance and e.s.r. spectra of the compounds K0.28M01.010J (blue) K o . ~ M O ~ . ~ O ~ (red) and Nao.l 8M~l.0803 are presented and interpreted in terms of a common model for their electronic structures. The compounds differ in analytical composition from those reported by Wold et al. but are identical in crystal structure. The crystal structures of these compounds have been determined by Wadsley and co-workers 2-4 and the results are summarised briefly. Both the blue and the red potassium bronze phases have layer structures the layers being composed of Moo6 octahedra sharing edges and corners.2* The potassium atoms are situated between the layers.The structures of the layers are different in the two cases; in the red bronze the basic unit comprises six octahedra in the blue compound ten. The co-ordination of the potassium atoms is also different. The purple sodium bronze has a structure similar to the corresponding sodium tungsten bronze i.e. a deficient perovskite in which the lattice symmetry is distorted from cubic to mono- clinic4 The constant common feature of these structures is that the local octahedral environment of the central molybdenum atom is maintained. The red potassium bronze is a semi-conductor whereas the blue phase is a metallic conductor above - 100°C. The sodium bronze is a metallic conductor.l EXPERIMENTAL PREPARATION Following Wold et al.the bronzes were prepared by electrolytic reduction. A.R. Moo3 and the appropriate molybdate were dried by heating at 120" for 24 h and mixtures of the following compositions made up 3-2 Moo3 1 K2M004 for the red bronze 3-5 1 for the blue bronze and 3.5 Moo3 1 Na2Mo04 for the sodium bronze. About 60 g of mixture was melted in an alumina crucible in a vertical furnace with the temperature accurately controlled at 2-3" above the melting point (in the range 540-560°C depending on the mixture composition). Two platinum electrodes were suspended in the melt and electrolysis was carried out for 5-7 days at a current density of -10mAcm-2. Crystals of the bronze grew on the cathode and on the bottom of the crucible. The melt was then poured off and the crystals washed successively in distilled water 2NHCl and N/lONaOH to remove superficial solidified melt.13 14 ELECTRONIC PROPERTIES OF MOLYBDENUM BRONZES CHARACTERIZATION The samples were analyzed for alkali metal content using a Unicam S.P.900 flame spectrophotometer. Analytical solutions were prepared by dissolving the samples in aqua regia and diluting with water. Solutions of the corresponding molybdates were used as standards. Analysis for molybdenum was performed in a similar manner using Unicam S.P.90 atomic absorption spectrometer. The compositions of the bronzes were found to be K0.33M01.0403 Ko.z&fol.olO3 and Na0.18M01.0803. The samples were further characterized by X-ray powder photography using a Debye-Scherrer camera with Cu Ka radiation.The photographs were indexed on the basis of Wadsley's analysis 2-4 and confirmed the identification of these compounds with those of Wold et al.' MEASUREMENT OF SPECTRA The ultra-violet and visible spectra of the bronzes were measured using a Unicam S.P.700 spectrometer with an S.P.735 diffuse reflectance attachment. The reference standard was A.R. KC1. Since the bronzes are strong absorbers the samples were diluted by grinding with three times their weight of KCl. Absolute extinction coefficients could not be deter- mined. The e.s.r. spectra were measured on a standard X-band instrument manufactured by J.E.O.L. The operating resonant frequency was 9.4 Mc/sec with a modulation frequency of 100Kc/sec. The temperature of measurement was varied between that of the room and - 170°C by means of a blast of cold nitrogen gas which circulated around the sample whilst in the cavity.The field sweep was calibrated using a sample of Mn2+ in MgO and g values were determined with reference to a sample of D.P.P.H. (g = 2.0036 line width 2.7 gauss) introduced into the cavity independently of the bronze sample. RESULTS AND DISCUSSION ULTRA-VIOLET AND VISIBLE SPECTRA The spectra of the three bronzes are shown in fig. 1. For comparison the spectra of two different preparations of MOO are shown in fig. 2. The one labelled (a) was a sample which had been heated in air at 700°C for 9 h to ensure that it was 4 12 2 0 28 36 44 frequency (lo3 cm-') FIG. 1 .-Diffuse reflectance spectra of (a) red potassium bronze (b) sodium bronze (c) blue potassium bronze. fully oxygenated. The one labelled (6) was a sample heated at 500°C in vacuo for 9 h in order to introduce oxygen vacancies.The absorption edge at - 3 eV (24,000cm-l) was common to all samples and is attributable to the charge-transfer process 02-,M06+.5 Below 3 eV '' MOO " does not absorb but all the bronzes and also " " have absorption peaks at around 1 eV. In order to explain this observation a model of the electronic structures of these compounds can be P. G. DICKENS AND D. J . NEILD 15 developed which is analogous to that used by Sienko and Goodenough in their discussions of the alkali metal tungsten bronzes and of certain transition metal oxides with the Re03 structure. The starting point is that the local octahedral co-ordination of a molybdenum atom by six oxygen atoms largely determines the frequency (lo3 cm-') FIG.2.-Diffuse reflectance spectra of (a) Moo3 (b) MOO^-^. common bonding pattern in the molybdenum bronzes and in the parent oxide MOO,. We consider first a discrete MOO unit; it is apparent that the 5p 5s and 4d (e,) orbitals of the central atom can combine with the six sp hybrid orbitals of the oxygen atoms (one per atom) to give a set of six bonding o and six anti-bonding o* molecular 5 P 5s t 1 4d 1 I \ SP Mo Bronze 0 FIG. 3.-Electronic energy level diagram for the molybdenum bronzes. - - - - - donor levels orbitals. In an extended lattice the discrete energy levels arising from this structure unit will broaden into bands. In addition the molybdenum 4d (t2g) orbitals can combine with three of the surrounding oxygen p n orbitals per octahedron to form bonding n and anti-bonding n* bands.This leaves three oxygen p n orbitals per in metallic conductors ; - - - donor levels in semi-conductor. 16 ELECTRONIC PROPERTIES OF MOLYBDENUM BRONZES octahedron which are of the wrong symmetry to combine with any of the molybdenum orbitals and which therefore remain as non-bonding levels (pn+). The band structure arising from this qualitative discussion is shown in fig. 3 . There are 24N valence electrons per mole of MOO (where N is Avogardro's number) and if these are allocated to the successive bands shown in fig. 3. they will occupy the 12 N levels of lowest energy ; i.e. the 0 and n bands and the oxygen p n f levels will be completely full. This combination constitutes the valence band. The n* and o* bands are empty and the former becomes the conduction band in MOO,.The absorption edge in the spectrum of MOO is thus associated with the onset of pronio- tion of electrons from the pn+ levels into the n* band and the energy gap between the valence and conduction bands is assigned a value of 2.96 eV as is shown in fig. 3. This value is decreased slightly (-0.2 eV) when MOO is oxygen deficient and a similar effect is also observed for the bronzes. This is understandable since the average charge on the molybdenum atoms decreases in these compounds relative to MOO,. In the peak at 1 eV can be assigned to excitation of electrons from Mo5+ donor levels (n/Mo5+) lying below the vacant conduction band into that band. A similar explanation can account for the presence of analogous peaks in the spectra of the molybdenum bronzes with reservations on account of their different crystal structures.It is suggested that electrons originating from the alkali metals are trapped at donor levels (M+/Mo5+) located between the valence and conduction bands of the MOO matrix. The large difference between the ioniza- tion potentials of the alkali metal M and Mo5+ supports this supposition. The low-energy peaks arise from excitation of electrons from the donor levels into the conduction band. This is substantiated by the observation that the peaks of the two metallic bronzes (potassium blue and sodium) extend to much lower energies than that of the semi-conducting red potassium bronze. Their donor levels must be much closer to the conduction band and may well overlap with it. This would be consistent with their metallic conductivities at room temperature and the observed change from metallic to semi-conductivity of the blue bronze at -100°C.In contrast the onset of absorption for the red potassium bronze shows its donor levels to be at least 0.75 eV below the bottom of the conduction band in accord with its observed semi-conductivity. Suggested positions for the respective donor levels are shown in fig. 3. E . S . R . SPECTRA The high electrical conductivities of the bronzes make the observation of their e.s.r. signals difficult since in powder form they strongly absorb microwave radiation in the absence of a magnetic field. This effect was overcome with the potassium compounds by the use of small single crystals. No signal could be observed however for the sodium bronze a metallic conductor.The signal obtained for the red potassium bronze g value 1.96 is shown in fig. 4. The effect of temperature on the signal in the range -162 to 20°C is shown in fig. 5. A similar signal was also observed for a sample of MOO,_ with g value 1.97 and line width of 40 gauss. It seems reasonable to associate both signals with the presence of Mo5+ donor levels. The signal shown in fig. 6 was observed for the blue potassium bronze at - 170°C the lowest obtainable temperature in this work. No signals could be obtained at higher temperatures. The g value was 1 a93 ; the line shape and width are comparable to those of the signal given by the red potassium bronze at - 50°C. This observation is again consistent with the proposal that the Mo5+ donor levels for the blue potassium bronze lie extremely close to the conduction band and at the more elevated tempera- tures considerable excitation of electrons into this delocalized band has taken place.P . G . DICKENS AND D. J . NEILD 17 Only at low temperatures where electrons are localized in isolated donor levels does a well-resolved e.s.r. signal appear and the compound behave as a semi- conductor. The increasing loss of resolution of the signal with increasing tempera- ture for the red potassium bronze shown in fig. 5 has the same origin but since in H H FIG. 4.-E.s.r. signal for red potassium bronze at - 150°C. FIG. 5.-E.s.r. spectra of red potassium bronzeat (a) 20"; (b) -40"; (c) -75"; (d) -110"; (e) - 150"; (f) - 162°C. 18 ELECTRONIC PROPERTIES OF MOLYBDENUM BRONZES this case the donor levels lie deeper than for the blue bronze a well-resolved signal can be observed at higher temperatures.It follows that if measurements were carried out at lower temperatures than were reached in this work it is possible that an e.s.r. signal could be found for the sodium bronze. H+ FIG. 6.E.s.r. signal for blue potassium bronze at - 170°C. The main conclusion from this work is that in the formation of alkali metal molybdenum bronzes an electron transfer process takes place M" + MoG++M+ + Mo5+ The Mo5+ (or M+/Mo5+ pairs) provide donor levels < 1 eV below the conduction band which give rise to observable e.s.r. signals and produce low-energy absorption peaks in the ultra-violet and visible spectra. The only other bronze system for which e.s.r. signals have been observed is Li,V2O5.' A. Wold W. Kunnmann R. J. Arnott and A. Ferretti Znorg. Chenz. 1964,3 545. N. C. Stephenson and A. D. Wadsley Acta. Cryst. 1965 19 241. J. Graham and A. D. Wadsley Acta. Cryst. 1966,20 93. N. C. Stephenson Acta Cryst. 1966,20 59. A. L. Companion and M. Mackin J. Chem. Physics. 1965,42,4219. M. J. Sienko Non-Stoichiometric Compounds ( h e r . Chem. SOC. Adv. in Chem. series no. 39) p. 224. J. Gendell R. M. Cotts and M. J. Sienko J. Chem. Physics 1962 37 220. ' J. B. Goodenough Bull. SOC. Chim. 1965,1200.

ISSN:0014-7672    

DOI:10.1039/TF9686400013

出版商:RSC    

年代:1968

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. Entropy of Volume Expansion of Gases Dissolved in Non-polar Solvents BY JOHN WALKLEY* AND W. IEUAN JENKINS? Received 22nd June 1961 The partial molaf volumes of six gases dissolved in four non-polar solvents have been measured.The values are compared to those of earlier workers. An attempt is made to assess the consistency of the data using the regular solution theory " entropy of volume expansion " concept. The thermodynamic solubility properties of gases dissolved in a wide range of solvents have been extensively studied. Empirical relationships have been established and some consistency of these data assessed.2 Even for the simplest systems i.e. with non-polar solvents no successful apriori theory has been developed. Regular solution theory which adequately relates the solubility properties of dilute solutions of both solid and liquid solutes in non-polar solvents apparently failed to interpret gas solubility data. However this apparent failure may be due to a lack of reliable data.3 The volume of expansion of the system incurred in dissolving a gas in a solvent is of fundamental importance both to the development of regular solution theory and to the further development of more rigorous theories.We here present data for a range of six gases in four common non-polar solvents. The volume change resulting from the dissolution of say 4 cm3 of gas (at s.t.p.) in 300 cm3 of solvent can be accurately determined by measuring either the volume expansion increment e.g. dilatometrically or the change in the density of the solvent. Horiuiti's basic design of the dilatometer has been used by all other workers. Kritchevsky and Illinskya have measured the volume changes incurred for a range of gases dissolved in methanol and water.studied CF4 and CH4 dissolved in various solvents ; and Hildebrand and Jolley and Hildebrand and Hiroaka * have investigated a wide range of gases in many non-polar organic solvents. Hildebrand and Walkley adapted this technique for the study of the partial molal volumes of H2 and D2 in a limited range of solvents. Schumm and Brown EXPERIMENTAL The dilatometer is essentially the " egg-timer " with two capillary side-arms design used by previous The bulk of the dilatometer was 300 cm3 in capacity and the two capillary side arms approximately 2-9x cm3 cm-' size. Both the dilatometer and the gas burette from which a known volume of gas was passed into the dilatometer were thermostatted at 25 -fO.o02"C by a method which minimized the short-time tempera- ture fluctuations and also retained a long-time temperature stability.The techniques are described in detail elsewhere. O The volume increase arising from the dissolution of a known volume of gas in the solvent constrained inthe dilatometer under mercury was measured using the method of Hildebrand and W a l k l e ~ . ~ This technique measures the volume of solution always at 1 atm external *Chemistry Dept. Simon Fraser University Burnaby 2 B.C. Canada. ?-Chemistry Dept. Imperial College of Science and Technology London England. 19 20 ENTROPY OF VOLUME EXPANSION pressure and so eliminates the uncertain " compressibility correction " present in other techniques. A single experiment covered the dissolution of 4-5 doses of gas into the initially well-degassed solvent. The partial molal volume (here defined as the expansion volume divided by the number of moles of gas dissolved) can be measured from the volume expansion increment resulting from every dose each dose being considered uniquely.It was most accurate however to retain the zero positions of measurement as those adopted by the mercury in the capillary side-arms prior to the addition of any gas to the solvent. The partial molal volume was then obtained from a plot of the measured (total) volume increase against the total number of moles of gas dissolved. Over the low concentration range (X2 < All solvents were of spectroscopic grade purity. The solvent degassing procedure was that of refluxing the solvent under low pressure. All gases were from the Matheson Co. Ltd. and quoted for % minimum purity as argon 99.998 ; methane 99 ; sulphur hexa- fluoride 98 ; carbon tetrafluoride 96 ; hydrogen 99.95 and deuterium 99-95.a strictly linear relationship was obtained. RESULTS All data pertain to a system at 25+0-002"C and 1 atm pressure. The partial molal volumes measured are considered accurate to r f l %. All data are presented in table 1 together with data from other sources. TABLE 1 .-PARTIAL MOLAL VOLUMES OF DISSOLVED GASES AT 25.00 f0-002"C solvent/gas Ar CH4 CF4 SF6 Hz D2 C6H6 44.6 53.3 82-3 97.1 35.4 32.7 ( 5 4 ~ 8 ) ~ (83-2)b (105.5)C (35~3)~ (32.7)d n-CGH12 47-6 5 87.4 101.4 41.0 39.4 C7H16 48.3 59 6 88.6 102.6 43.2 41.2 ( 55.4)b ( S6-5)b (1 05*8)c i-CgH18 49.6 56 6 86.7 103.3 46.2 43.1 ( 5 6. 6)b (85-4)b (1 04-2)C (a) Horiuti4 ; (b) Schumm and Brown ; (c) Hiroaka and Hildebrand ; ( d ) Hildebrand and Walkley ; ( e ) Jolley and Hildebrand.' DISCUSSION The overall pattern of our data follows that suggested by most of the datb obtained previous1y.l The partial molal volume increases with the increase in the molecular "size" of the gas molecules and decreases with the increase in the 6 value of the solvent (6 is the square root of the cohesive energy density of the solvent).Our data agree exactly with the value obtained by Jolley for argon in iso-octane and within experimental accuracy with the value of Horiuti for methane in benzene. Our data for SF6 show a marked disagreement with those of Hiroaka for both C6H6 and C7H16. We agree with Schumm and Brown's value for CF4 in benzene and disagree with their value for methane in n-heptane. In iso-octane solvent we agree exactly with their result for methane and almost within experimental accuracy for CF4.However these two values are contrary to the pattern of behaviour expected from the (uncertain) &value of this solvent. The data for hydrogen and deuterium agree well with earlier data and in all solvents the presumed " quanta1 difference " exists. J WALKLEY A N D W. I . JENKINS 21 We judge the merit of our measurements by extending an argument of Hildebrand.3 From accurate saturation solubility measurements Hildebrand finds that for given gas in the different solvents a plot of the experimentally measured entropy of solution - R(dhx2/d In T ) against the dilution entropy (- R In x2) gives a line of unit slope. For different gases in the same solvent a linear relationship is again observed but of slope greater than unity indicating a contribution arising through the volume change accompanying the disolution process.The volume and entropy of expansion are related (v - v~)(aSjau) = AS(expansion) and so making use of the calculated A S (expansion) the partial molar volume V,” and the isochore (dP/dT) for the solvent 1;’; may be determined. A S (expansion) may be calculated from the slope A of the experimental R(alnx,/dlnT) against - R ln x2 plot and is given as A S (expansion) = (A- l)R In x2. Using appropriate experimental data for the entropy of solution and the saturation mole fraction solubility at 25°C the values calculated for for Ar CH4 CF4 and SF6 are given in table 2. Calculations made using the V2 data of other workers TABLE 2.-v,” VALUES solvent gas i.CsH1a C-CsHiz C6H6 CC4 * Ar 9-6 14.5 14.1 (13-5) CH4 - 25.9 22.8 (24-4) (24.3) CF4 45.7 52.5 50 (47.6) SF6 74 74.9 71.4 (80) (75) (79.8) ( ) from data of other workers see table 1 ; * all data for CCI4 ref.(1). are quoted in brackets. For each gas one would expect a consistent value of z); and since the four different experimental values required are obtained from data of various previous workers a reasonable consistency does exist. However the signifi- cant difference in v2 values for SF6 in C6H6 is not well resolved since neither our value leading to a v; value of 71.4 nor that of Hiroaka giving a u;I value of 79.8 are in reasonable agreement with the values found in i-C8H18 or n-C6H12. The calculation of u; from the data of Hiroaka in C6H6 and cc1 solvents lead to con- sistent values. Our own data in i-CsH18 and c-C6HI2 again give consistent v; values.The comparison of the Z J ~ value possibly reflects the need for experimental data of greater accuracy. obtained 24.7 cm3 mole-1 for N2 in CC14 in good agreement with the 0°K solid-state molar volume of 24-6 cm3 mole-l. Our value for methane - 24.5 cm3 mole-l again agrees well with the solid-state molar volume. For argon the value of v; of approximately 14 cm3 mole-1 is not comparable to the solid-state molar volume of approximately 22.5 cm3 mole-l. We offer no explanation of this ; nevertheless the interpretation of the divergence from regular solution pattern of behaviour as a volume of expansion entropy term appears to lead to a reasonably consistent interpretation of both partial molal volume and saturation solubility data for the systems presently discussed although this explanation is far from satisfying even phenomenologically.For the magnitude of the calculated u; values Hildebrand 22 ENTROPY OF VOLUME EXPANSION J. H. Hildebrand and R. L. Scott Regular Solutions (Prentice-Hall Inc. 1962). R. Battino and H. L. Clever Chem. Rev. 1966 66 395. J. H. Hildebrand Proc. Nat. Acad. Sci. 1967 57 542. J. Horiuti Sci. Papers Inst. Physic. Chem. Res. Tokyo 1931 17 125. I. Kritchesvky and I. Illinskya Actaphysicochim. 1954 20 327. R. H. Schumm and 0. Brown J. Amer. Chem. Sac. 1953 75,2520. ’ J. H. Hildebrand and J. E. Jolley J. Amer. Chem. SOC. 1958 80 1050. * J. H. Hildebrand and H. Hiroaka J . Physic. Chem. 1963,67 1919. J. H. Hildebrand and J. Walkley J. Amer. Chem. SOC. 1959 81 4439. lo W. I. Jenkins Ph.D. Thesis (University of London). J. H. Dymond J . Physic. Chem. 1967,71 1830. l2 G. L. Pollack Rev. Mud. Physics 1964,36,748.

ISSN:0014-7672    

DOI:10.1039/TF9686400019

出版商:RSC    

年代:1968

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. Activity Coefficients in Binary Liquid Mixtures of 3-Methyl Butene- 1 and Sulphur Dioxide BY B. H. G. BRADY AND J. H. O'DONNELL Chemistry Dept. University of Queensland Brisbane Australia Received 19th May 1967 The total vapour pressures above binary liquid mixtures of 3-methyl butene-1 and sulphur dioxide have been measured at intervals of about 4°C in the range 14-40"C. Activity coefficients have been derived at 16 28 and 40°C by a Gibbs-Duhem mathematical analysis including corrections for non-ideal vapour behaviour of total vapour pressure against composition isotherms. Vapour phase compositions have also been calculated. The system shows positive deviations from Raoult's law with an azeotropic mole fraction of 3-methyl butene-1 of 0.15 at 16°C and 0.12 at 40°C.The excess free energy of mixing and the heat of mixing are slightly asymmetric functions of composition ; at 28°C the maxima are 197 and 568 cal mole-' respectively. An investigation of the thermodynamics of the formation of poly-(3-methyl butene-1 sulphone) from liquid mixtures of 3-methyl butene-1 and sulphur dioxide required a knowledge of the activity coefficients of the monomers in the mixtures over the temperature range 14-40°C. The activity coefficients were derived from total vapour pressure measurements by a Gibbs-Duhem analysis of total vapour pressure against liquid composition isotherms at selected temperatures. An alternative method is based-on experimental determination of the vapour composition as well as the total vapour pressure.2 In the present work the mathematical method was preferred due to the high pressures involved and the difficulty of obtaining vapour samples with the equilibrium composition.EXPERIMENTAL MATERIALS 3-Methyl butene-1 (Phillips Petroleum Co. pure grade > 99 %) was fractionally distilled under vacuum and stored over a sodium mirror for several weeks to remove peroxides. Sulphur dioxide (B.D.H.) was purified by fractional distillation under vacuum and several distillations over PzOs to remove traces of water. The final purity of the reagents was established by the absence of extraneous peaks in their mass s p e ~ t r a . ~ PREPARATION OF MIXTURES Liquid mixtures were prepared by condensing 3-methyl butene-1 and sulphur dioxide into a glass tube and sealing under vacuum.The quantity of each component was measured by its pressure in a 3-1. bulb at 25°C. The relationship between mass and pressure was determined separately for each monomer by condensing a measured pressure of the monomer from the bulb into a glass tube which was sealed under vacuum and weighed with and without its contents applying a buoyancy correction. MEASUREMENT OF TOTAL VAPOUR PRESSURE The apparatus used for the measurements of the total vapour pressures is shown in fig. 1. It consisted of a U-tube manometer A each arm of which was 110 cm in length 23 24 ACTIVITY COEFFICIENTS OF 3-METHYL BUTENE-1 + so and made of 4 mm int. diam. precision-bore glass tubing. Each arm contained 56 cm of mercury when the levels were equal and the closed arm B contained dry air above the mercury.The manometer was immersed in a tower C through which water was circulated at 25°C. A second smaller U-tube manometer F separated the trapped-air manometer from the mixture vessel D. This manometer was used as a null indicator and each arm consisted of 25cm of 2-mm bore capillary tubing containing 15cm of mercury. The mixture bulb and the space between it and the null manometer were connected to the vacuum line through E for the introduction of the monomers. The space between the null mano- meter and the trapped air manometer could be both evacuated (through G) and pressurized (through H) to about 7 atm. The mixture vessel and the null manometer could be immersed completely in a constant temperature bath I.The advantages of this apparatus were (i) the vapour space above the liquid mixture was minimized reducing problems of variation . I FIG. 1 .-Apparatus for measurement of total vapour pressures. in liquid composition with temperature due to differential evaporation and (ii) condensation problems i.e. distillation from the mixture bulb to cooler parts of the apparatus usually encountered above ambient temperature were avoided. The trapped-air manometer was calibrated by condensing sulphur dioxide into the mixture vessel and sealing at E. The mixture vessel and the null manometer were then immersed in a constant temperature bath and pressure applied through H from a cylinder of compressed nitrogen to balance the null manometer. The heights of mercury in the two arms of the trapped-air manometer were measured by a cathetometer at temperature intervals of 2-5°C in bath I from 5 to 40°C.The vapour pressure of sulphur dioxide at each temperature was interpolated from the results of Maass and Maass and of Kang Hirth Kobe and McKetta and these values used to calculate the relationship between pressure and the heights of the mercury columns. The total vapour pressure above each mixture at a series of temperatures was determined by distilling 3 ml of mixture of the required composition into vessel D and sealing at E. The same procedure was then followed as for pure sulphur dioxide. The mixture was B . H . G . BRADY AND J . H . O'DONNELL 25 stirred thoroughly by a magnetic stirrer J. At each temperature the mercury levels in the null manometer were equalized over a period of 20 min and 5 min further allowed to observe whether equilibrium had been attained.The temperature of the constant tempera- ture bath was measured with a calibrated mercury thermometer and was constant to +O-O2"C. RESULTS AND DISCUSSION VAPOUR PRESSURE OF 3-METHYL BUTENE-1 The measured vapour pressures of 3-methyl butene-1 over the temperature range 1546°C were plotted on a large scale and gave a smooth curve. The results of Scott and Waddington for 3-methyl butene-1 were similarly plotted and vapour pressures for the temperatures of the measurements in the present work obtained by interpolation. The trapped-air mano- meter was calibrated for the pressure range 1200-4900mm Hg. In this range the The comparison is shown in table 1. TABLE 1 .-COMPARISON OF VAPOUR PRESSURES OF 3-METHYL BUTENE-1 WITH LITERATURE VALUES 15.49 20-1 8 25.00 29.84 34.76 39.57 45-55 vapour pressure (mm H g at 0°C) present lit.654 646 775 767 914 906 1073 1067 1256 1247 1455 1446 1742 1733 agreement between reported and measured vapour pressures of 3-methyl butene-1 is satisfactory (better than 0.6 %). Pressures less than 1200 mm Hg were measured by extrapolation of the calibration of the trapped-air manometer. In this range agreement between reported and measured vapour pressure is not as good. However all vapour pressures measured above the mixtures were in the range 1200-4800 mm Hg. VAPOUR PRESSURES OF MIXTURE The total vapour pressures above a series of different mixtures at 4°C temperature intervals are shown in table 2. These values were obtained by interpolation in large-scale plots of the measurements at different temperatures.The values for sulphur dioxide have been interpolated from the results of Maass and Maass and of Kang Hirth Kobe and McKetta and those for 3-methyl butene-1 from the present work. The maximum change in composition of the liquid phase due to preferential evaporation was 0.2 % at the extreme compositions and the maximum temperature ; therefore this effect was neglected. ACTIVITY COEFFICIENTS Activity coefficients were calculated from the total vapour pressures using the method of Barker which is a Gibbs-Duhem analysis of the total vapour pressure against liquid mixture composition isotherms based on equations which relate activity coefficients and total vapour pressure with allowances for non-ideal vapour behaviour.Scatchard and Raymond * showed that the equation AG = X X ~ [ U + ~ ( X ~ - X ) + C ( X ~ - X ~ ) ~ + ] 26 ACTIVITY COEFFICIENTS OF 3-METHYL BUTENE-1 + so2 TABLE 2.VAPOUR PRESSURES OF BINARY MIXTURES OF 3-METHYL BUTENEi-1 AND SULPHUR DIOXIDE TCC) 16 20 24 28 P Xrn expt. calc. expt. expt. expt. calc. 0 0.050 0.101 0.204 0.305 0.396 0.502 0.647 0.794 0-899 1 2148 2220 2235 2281 2272 2281 2275 2253 2250 2208 2212 2140 2143 1971 1968 1630 1633 1245 1243 655 2479 2852 2550 2921 2619 2989 2620 2983 2581 2945 2532 2881 2430 2751 2242 2530 1841 2079 1412 1596 3240 3326 3346 3395 3390 3392 3383 3337 3332 3263 3260 3120 3131 2850 2844 2340 2342 1794 1794 1000 32 expt. 3688 3769 3842 3830 3760 3677 3507 3200 2626 2010 36 expt. 41 82 4261 4338 43 12 4230 41 33 3925 3570 2929 2245 40 expt.calc. 4730 4780 4800 4856 4861 4830 4828 4756 4735 4620 4610 4398 4406 3979 3979 3252 3259 2502 2498 1460 p vapour pressure in mm H g at 0°C ; xm mole fraction of 3-methyl butene-1 in liquid ; expt. values interpolated from smooth curve of experimentally determined vapour pressures calc. values calculated from Gibbs-Duhem mathematical analysis of vapour pressure against against temperature ; liquid composition isotherms. with sufficient terms can represent measured values of the excess free energy A G i of mixing of two components 1 and 2 to any desired accuracy. In the present work three empirical parameters a b and c were sufficient. where f is the mole fraction activity coefficient A = a/RT B = b/RT C = c/RT Zl = x; ml = -x~(l-4x1) n = x$(l-8x1+12xf) and similarly for fi except that m2 = xf(1 -4x2).The calculation offi andf involves successive computations of A B and C to give the best agreement between the calculated and experimental total vapour pressures. Barker's method requires values for the second virjal coefficients of the vapours and the molar volumes of the pure liquids. The second virial coefficient for sulphur dioxide was calculated from the Berthelot equation using the critical con~tants.~ The second virial coefficient for 3-methyl butene-1 was calculated from the experimentally measured relationship between pressure and quantity of gas in a 3-1. bulb and was - 1.076 1. mole-' at 25°C. This is com- parable with the literature values of the second virial coefficients at 25°C of the isomeric pentenes O viz. Since ' lnfl = AZ,+Bml+Cnl (2) pentene-1 - 1.143 1.mole-' - 1.163 1. mole-' - 1.276 1. mole-'. 2-methyl butene-1 2-methyl butene-2 The values of the second virial coefficient of 3-methyl butene-1 over the temperature range 1640°C were obtained by assuming the same temperature variation as for 2-methyl butene-1 .lo The molar volume of liquid sulphur dioxide was calculated from the liquid den~ity.~ The molar volume of liquid 3-methyl butene-1 was calculated similarly ; values of the liquid density at different temperatures were obtained by extrapolation of values in the range 15-25°C parallel to the temperature dependence of the density of liquid 2-methyl b~tene-2,'~ which is linear from 15 to 50°C. B . H . G . BRADY AND J . H . O'DONNELL 27 It was assumed that the mixed virial coefficient BIZ was the arithmetic mean of the individual virial coefficients B1 and B,; i.e.that the vapour behaves as an ideal mixture of the two imperfect gases a reasonable assumption for a system such as this one which shows positive deviations from Raoult's law.13 The corn- putation of the activity coefficients and simultaneously of the vapour compositions was performed on the University of Queensland GE225 digital computer. The third cycle of successive approximations produced changes of less than 0.003 % in the values of the activity coefficients. The results of the computations of the activity coefficients and vapour phase compositions at 16 28 and 40°C are given in table 3. Calculated total vapour pressures are compared with the experimental values in table 2. TABLE 3.-MOLE FRACTION ACTIVITY COEFFICIENTS IN BINARY LIQUID MIXTURES OF 3-METHYL BUTENE- 1 AND SULPHUR DIOXIDE AND EQUILIBRIUM VAPOUR PHASE COMPOSITIONS T("C) 16°C 28'C 40°C xi fm fs Ym fm fs .Vm f n fs Ym 0.050 0.101 0.204 0-305 0.396 0-502 0-647 0.794 0.899 4-88 1.01 3.83 1-03 2-58 1-10 1.93 1.22 1-58 1-35 1-34 1.55 1-15 1-90 1-05 2-41 1-01 2-93 0.080 0.1 24 0.169 0.191 0.207 0.228 0.27 1 0.358 0.498 4-20 1.01 3-36 1-02 2.35 1-09 1.80 1.19 1.51 1.31 1.30 1.48 1-13 1.78 1-04 2.21 1-01 2.64 0.073 0.1 17 0.1 64 0.191 0.21 6 0.239 0-289 0-386 0.532 3-43 1.00 2-88 1-02 2.14 1-07 1-71 1.16 1.46 1.26 1.27 1-41 1.12 1.68 1.04 2.04 1.01 2-38 0.063 0-106 0.160 0.193 0.2 19 0.251 0.307 0.410 0.562 xm mole fraction of 3-methyl butene-t in liquid phase ; ym mole fraction of 3-methyl butene-1 in vapour phase ; fm mole fraction activity coefficient of 3-methyl butene-1 ; fs mole fraction activity coefficient of sulphur dioxide.EXCESS THERMODYNAMIC QUANTITIES OF MIXING The excess free energy and heat of mixing at 28°C were calculated from the data in table 3 using the expressions AGE = 2*303RT(x log X + X log fs) (3) The variation of AG& and AHM with composition at 28°C are shown in fig. 2. The values for AG& lie on a smooth curve ; this results from the method of calculating the activity Coefficients which is essentiaIIy a smoothing of the excess free energy curve using a method of least squares. The values of AG$ at 28°C fit the expression The values of AHM do not lie on a smooth curve and this indicates the difficulty of obtaining values of 8 log f/aT with adequate accuracy. The curve of best fit shown in fig.2 was derived using the method of least squares and fits the expression AGZ = x,~,[786.6 - l51*O(xm - x,) +70*7(x - x~)']. ( 5 ) AH = ~,~,[2267*0- 375.1(~,-~,)]. (6) Our results can be compared with those obtained by Ayscough Ivin and O'Donnell ' for binary liquid mixtures of isobutene and sulphur dioxide. The temperature range in the isobutene system was lower (-20 to 10°C) hence in the 28 ACTIVITY COEFFICIENTS OF 3-METHYL BUTENE- 1 f SO present work the sulphur dioxide is the dominant component of the vapour and the maximum pressures are higher. The azeotropic composition is at a mole fraction of olefin x = 0.12-0-15 for 3-methyl butene-1 compared with x ~ = 0.40-0.45 600r 0 0.2 0.4 0.6 0’8 xm FIG. 2.-(a) Excess free energy AG& and (b) excess enthalpy AHM of mixing for the system 3-methyl butene-1 +sulphur dioxide at 28°C.for isobutene. The activity coefficients and their temperature dependence are of comparable magnitude. The values of AGL are similar but AH is considerably greater for 3-methyl butene-1. We thank Prof. L. E. Lyons for his encouragement and Prof. K. J. Ivin for helpful One of us (B. H. G. B.) is grateful to the University of Queensland for a advice. Demonstrat orship. B. H. G. Brady and J. H. O’Donnell Trans. Faraday Soc. 1968,64,29. P . B. Ayscough K. J. Ivin and J. H. O’Donnell Trans. Faraday SOC. 1965 61 1601. Amer. Petroleum Inst. Research project 44 Mass Spectral Data. C . E. Maass and 0. Maass J . Amer. Chem. Soc. 1928,50 1352. T. L. Kang L. J. Hirth K. A. Kobe and J. J. McKetta J. Chem. Eng. Data 1961 6 220. D. W. Scott and G. Waddington J. Amer. Chem. SOC. 1950,72,4310. J. A. Barker Austral. J. Chem. 1953 6 207. * G. Scatchard and C . L. Raymond J. Amer. Chem. SOC. 1938 60 1278. L. Gmelin Handbuch der Anorganischen Chemie (8 Adage System-Number 9 Schwefel Teil A Lieferung 2 1953) p. 219. lo D. W. Scott G. Waddington J. C . Smith and H. M. Huffman J . Amer. Chern. Soc. 1949 71 2767. A S . T.M. Card Index of Hydrocarbons. l2 G. Egloff Physical Contents of Hydrocarbons (Reinhold New York vol. 1 1939) p. 181. l 3 G. Scatchard Chem. Rev. 1949,44 7 .

ISSN:0014-7672    

DOI:10.1039/TF9686400023

出版商:RSC    

年代:1968

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. Thermodynamics of the Formation of Poly-(3-Methyl Butene- 1 Sulphone) from 3-Methyl Butene- 1 and Sulphur Dioxide Chemistry Dept. University of Queensland Brisbane Australia Receive 19th May 1967 Ceiling temperatures Tc for the copolymerization of 3-methyl butene-1 with sulphur dioxide have been measured for mixtures with mole fraction xm of 3-methyl butene-1 from 0.025 to 0.951. These Tc values have been combined with the corresponding monomer activity coefficients (fm andfs) to test the equation Tc = AHlc/(A&+ R In xmxsfmfs) where AHrc and ASIC are the enthalpy- and entropy changes for the conversion of 1 mole of each of the pure liquid monomers into 1 base- mole of condensed 1 1 copolymer.A substantial discrepancy between polymerization in olefin- rich and sulphur dioxide-rich mixtures has been found as was previously observed for isobuiene+ sulphur dioxide mixtures. The discrepancy is unaffected by the method of initiation and is not due to any variation from 1 1 composition of the copolymer. The explanation is believed to be a difference in the free energy of the polymer produced in different media resulting from a variation in conformation on precipitation. There is an equilibrium ceiling temperature T for all addition polymerizations which are accompanied by decreases in enthalpy and entropy where the free energy of formation of long-chain polymer from monomer is zer0.l Above this tempera- ture polymerization to long-chain polymer will not occur.A variety of olefins copolymerize with sulphur dioxide by a free radical mechanism to form alternating 1 1 copolymers i.e. the copolymerization reactivity ratios are zero. These polymerizations frequently have ceiling temperatures in the range - 80-70°C the value depending on the structure of the olefin and the activities of the two comonomers.2p showed that it was expected that for the copolymerization of binary liquid mixtures of an olefin (m) and sulphur dioxide (s) the variation of ceiling temperature with mixture composition when the copolymer was insoluble in the monomer mixture would be represented by Cook Ivin and O’Donnell where AHlc and ASlc are the enthalpy and entropy changes respectively for the conversion of 1 mole of pure liquid olefin and 1 mole of pure liquid sulphur dioxide to 1 base-mole of insoluble polymer; f, fs x,, x are the mole fraction activity coefficients and mole fractions of olefin and sulphur dioxide in the monomer mixture.However when this equation was tested for the copolymerization of isobutene and sulphur dioxide in binary liquid mixtures over the complete composition range the plot of log (fmfs x x,) against l/Tc was not linear as expected from eqn. (l) but consisted of two parts a lower linear arm corresponding to polymerization of sulphur dioxide-rich mixtures and an upper non-linear arm corresponding to polymerization of olefin-rich mixtures.The maximum separation of the arms of the plot corresponded to a difference in the free energy of polymerization between olefin-rich and sulphur dioxide-rich mixtures of 1 kcal mole-l. Cook Ivin and O’Donnell proposed that the most probable cause of the discrepancy was a difference 29 30 FORMATION OF POLY-(3-METHYL RUTENE- 1 SULPHONE) in crystallinity of the polymer arising from different trans/gauche ratios of the polymers formed in the different media. It was considered advisable to investigate a second system to determine whether this anomaly was peculiar to isobutene. There are few olefins which are completely miscible with sulphur dioxide over the entire composition range for the ceiling tempera- ture range and for which the polysulphone is insoluble in the reaction mixture for all comonomer compositions.3-Methyl butene-1 is one such monomer and has the added advantage that the ceiling temperatures are in an experimentally convenient range 15-40°C. The only respect in which the two copolymerizations differ is in the possibility of varying stereoregularity of poly-(3-methyl butene-1 sulphone) with mixture composition due to the introduction of an asymmetric centre C* CHp-CH + SO -CHZ-C*H-S02- I CH /\ CH CH I CH /\ CH CH3 EXPERIMENTAL Ceiling temperatures were measured using the dilatometric technique of Cook Dainton and Ivin, but a modified optical arrangement was used for photo-initiation. A Hanovia low-pressure mercury lamp was placed at the top of a thermostatted Perspex bath directed vertically downwards and the ultra-violet illumination reflected horizontally towards the dilatometer by a glass mirror.This is a convenient arrangement as Perspex almost com- pletely absorbs ultra-violet light below 3700 A. The 3660 line is mainly responsible for initiation of the copolymerization of olefins with sulphur dioxide by low-pressure mercury lamps.s Chemical initiation in the absence of light was carried out with silver nitrate at a mole fraction concentration of 2.0 x with the dilatometer wrapped in aluminium foil except for the required section of the capillary. Samples of poly-(3-methyl butene-1 sulphone) were prepared for chemical analysis by ultraviolet illumination of mixtures of 3-methyl butene-1 and sulphur dioxide at 2°C below their respective ceiling temperatures. The conversion of monomer to polymer was restricted to less than 5 % of the smaller component of the monomer mixture.Under these conditions the polymer was obtained in a finely divided form. There being no known solvent for poly-(3-methyl butene-1 sulphone) the polymer was purified by a series of four washings with filtered methanol and pumping in a vacuum oven at 25°C to constant weight. Analyses of the polymer samples for carbon hydrogen and sulphur were performed by the Australian Microanalytical Service Melbourne and for carbon and hydrogen by the University of Queensland Microanalytical Laboratory. RESULTS CEILING TEMPERATURE MEASUREMENTS The rates of contraction of the dilatometer contents for the photo-initiated copolymerization of 3-methyl butene-1 and sulphur dioxide were obtained from excellent linear plots of meniscus height against time within 2°C of the corresponding ceiling temperatures.The ceiling temperature of each mixture was obtained by linear extrapolation of plots of contraction rate against temperature to zero rate. The plots for the photo-initiated polymerization of 16 different mixture compositions are shown in fig. 1 and 2. There is some " tailing " near the ceiling temperatures caused by the increasing importance of initiation and termination compared with propagation. The ceiling temperatures are given in table 1. The variation of T with comonomer mixture composition is asymmetric with a maximum at about X = 0.30 T = 40°C. B . H. G . BRADY AND J . H O’DONNELL 31 Activity coefficients of 3-methyl butene-1 and sulphur dioxide in the various mixtures at their ceiling temperatures were obtained from the earlier measurements of activity coefficients by interpolation or short extrapolation from plots of activity coefficient against mixture composition and activity coefficient versus temperature.The appropriate activity coefficients are listed in table 1. temp. (“C) FIG. 1 .-Determination of ceiling temperatures for photo-initiated copolymerization of 3-methyl butene-1 and sulphur dioxide in binary liquid mixture. Mole fraction of 3-methyl butene-1 A 0.025 ; R,O-O52 ; D 0.101 ; F 0.250 ; H 0.352 ; I 0.404 ; J 0-498 ; K 0.606 ; L 0,749 ; M 0.805 ; N 0.850 ; 0 0.900 ; P 0.951. temp. (“C) FIG. 2.-Determination of ceiling temperatures for photo- and chemically initiated copolymerization of 3-methyl butene-1 and sulphur dioxide in binary liquid mixtures.Photo-initiation mole fraction of 3-methyl butene-1 C 0-098 ; E 0.201 ; G 0.303. Chemical initiation mole fraction of 3-methyl butene-1 Q 0-029 ; R 0.176 ; S 0-818 ; T 0.898. 32 FORMATION OF POLY-(3-METHYL BUTENE- 1 SULPHONE) TABLE 1 .-CEILING TEMPERATURES T AND CORRESPONDING MOLE FRACTION ACTIVITY COEFFICIENTS f FOR LIQUID MIXTURES OF 3-METHYL BUTENE-1 m AND SULPHUR DIOXIDE S X m 0.025 0.052 0.098 0-101 0.201 0.250 0.303 0-352 0.404 0.498 0-606 0.749 0.805 0.850 0-900 0-95 1 Tc. (4C> photo-initiation 30.4 10.1 34-0 rt 0.1 37.5 10.1 37.9 +0*1 39.5 &O.l 39.9 h0.l 40.0 f 0.1 39.9 f0.1 39.5 f0.1 38.3 h0.1 36.6 10.1 33.2 f0.1 31-2 f0.1 27.9 50-2 23.5 f0.2 16-0 f0-3 fm 4.87 3.80 3 *04 2.96 2.17 1.91 1 -72 1 a57 1 a44 1 a28 1-16 1.06 1 *04 1 *02 1.01 1 -00 fs 1-00 1 *01 1-02 1-02 1-08 1-12 1.16 1.21 1 *27 1-41 1-62 2-00 3.23 2-44 2.72 3.52 chemical initiation 0.029 3 1 -4 f0-2 4.65 1-00 0.176 39.0 f0.2 2.33 1 a08 0.8 18 30.4 f0-2 1 -03 2.27 0.898 23.6 f0.2 1.01 2.76 1 I I 1 3.15 3.25 3.3 5 3‘45 3.55 103/~ (“~-1) FIG.3.-Test of ceiling temperature eqn. (1) ; letters correspond to those in fig. 1 and 2. B. H. G. BRADY AND J . H. O’DONNELL 33 The plot of log (fmfsxmxs) against 1/T0 shown in fig. 3 is similar to that obtained for the copolymerization of liquid mixtures of isobutene and sulphur dioxide. It consists of two arms corresponding to olefin-rich and sulphur dioxide-rich mixtures instead of a single straight line as predicted by eqn. (1). However it differs from the isobutene system in that with the exception of the points G H I J the results lie approximately on two linear arms.The ceiling temperatures of four representa- tive mixtures were determined for chemical initiation by silver nitrate to test the effect of the method of initiation and these results are also shown in table 1 and in figs. 2 and 3. ANALYSIS OF THE POLYMERS The discrepancy between olefin-rich and sulphur dioxide-rich mixtures shown in fig. 3 results from a difference in the free energy of polymerization in these media. One explanation is a departure from exact 1 1 composition of the polymer. The carbon hydrogen and sulphur analyses for 12 polymer samples prepared in different comonomer mixtures are shown in table 2 as wt. %. TABLE 2.-&SLJLTS OF MICROANALYSIS OF POLYMERS AND QUANTITIES DERIVED FROM THE ANALYTICAL RESULTS mixture %C %H composition A.M.S.U.Q.M.L. A.M.S. U.Q.M.L. Xm 0.010 0-025 0.048 0.100 0.1 76 0-300 0.502 0.603 0.694 0-802 0.900 0-901 expected 43.86 44.61 7.53 7.50 43.38 44.65 7.49 7-51 44-14 44.45 7.48 7.47 44.70 44-75 7.76 7-53 44.17 44.51 7-67 7.45 43-29 44-96 7.32 7.56 43-92 44-20 7-66 7.41 44.63 44.37 7.56 7-50 44.38 44.89 7-38 7-62 44.70 44-47 7.53 7.43 45.00 44-48 7-58 7-66 44.37 44-42 7.39 7-48 44.75 7-51 regression a T C = a+bxm 44-24 /,S = a+bxm 23.39 [C]/[S] = a+bxm 5.004 TI = a+bx 98-13 %S A.M.S. - 22.97 23-63 23.39 23-62 23.63 23.36 24-05 23-84 23.71 23-61 23.68 23.89 b 0.36 0.44 0.007 1 -68 [Cl/[Sl [Hl/[Cl A.M.S. A.M.S. U.Q.M.L. TI A.M.S. - 5.042 4.987 5.1 02 4.992 4.891 5.019 4-954 4.970 5.033 5.088 5.002 5.000 2.065 2.057 2-019 2.068 2-069 2.01 5 2.078 2.018 1-981 2.007 2.007 1-985 2.000 2.005 - 2.005 96.76 2.002 98.83 2.005 99.19 1.992 99.03 2.004 97.82 1-998 98.25 2.014 100.24 2.023 99-39 1.991 99.60 2.004 99.75 2-006 99.07 100 standard correlation error coefficient 0-37 0.28 0-25 0.29 0-063 0.03 0.43 0.59 A.M.S.Australian Microanalytical Service ; U.Q.M.L. University of Queensland Microanalytical Laboratory ; TI = %C+ %H+64*07 %S/32-07 ; all percentages are wt. %. [C]/[S] = (%C X 32-066)/( %S x 12-01 1) ; [Hl/[C] = ( %H x 12-011)/( %C X 1.008) ; The [C]/[S] ratio is a useful quantity for evaluating changes in the polymer composition and the [H]/[C] ratio is a convenient measure of the consistency of the analytical results where [C]/[S] = (%C x 32.066)/( %S x 12-01 l) and [H]/[C] = (%H x 12.01 1)/( %C x 1.008). These values are also listed in table 2.The method of regression analysis was applied to the values of %C %H %S obtained by the Australian Microanalytical Service and the [C]/[S] ratios calculated from these results to show that there was no correlation between polymer composition and 2 34 FORMATION OF POLY-(3-hfETHYL BUTENE- 1 SULPHONE) monomer mixture composition i.e. deviations from a 1 1 ratio of the comonomers were purely random. The constants in the equation of regression assuming a linear relationship between polymer composition and monomer nixture composition calculated by the method of least squares and the standard error and correlation coefficient were calculated for each regression ; the results are shown in table 2. The total combustible material in each sample assuming that the sulphur is all in the form of SOz is also shown in table 2.DISCUSSION Cook Ivin and O’D~nnell,~ for the copolymerization of isobutene and sulphur dioxide considered that the discrepancy arose from one or more possibilities (i) departure from 1 1 composition of the polymer (ii) variation in the proportions of head-head and head-tail addition of successive olefin units (iii) adsorption or swelling effects (iv) an effect of polymerization medium on the conformation and hence on the free energy of the precipitated polymer (v) a variation in the degree of crystallinity of the polymer arising from the previous effect. These possibilities are all based on the assumption that the discrepancy arises from a difference in the free energies of the polymers precipitated in the different media. However an equally valid explanation could be (vi) that it is due to the involvement of “ activated monomer ” having a higher free energy than the pure liquid monomers this activated species making different contributions to the propagation reaction in olefin-rich and sulphur dioxide-rich media.The possibility of participation in the propagation reaction of a diradical or any other photo-excited species such as have been suggested for other polymeriza- tions,’~ was investigated by measuring ceiling temperatures of mixtures of 3- methyl butene-1 and sulphur dioxide using chemical initiation of the polymerization with exclusion of natural light from the polymerizing mixture. From fig. 3 the free energy discrepancy between polymerization in olefin-rich and sulphur dioxide- rich mixtures is not removed by the use of a chemical initiator.Therefore it is unlikely that the discrepancy is caused by the participation of ‘‘ activated monomer ” in the propagation reaction. The maximum separation between the two arms of the plot shown in fig. 3 for mixtures with the same ceiling temperature i.e. x = 0.025 and x = 0.815 corresponds to a difference in the free energy of polymerization in olefin-rich and sulphur dioxide-rich mixtures of 660 cal mole-l. In the isobutene + sulphur dioxide system the free energy difference for the copolymerization in mixtures of Composition Xm = 0.025 and x = 0.720 is 850 cal mole-‘. Exact correspondence of composi- tions cannot be obtained due to the differences in asymmetry of the ceiling tempera- ture against composition plots for the two copolymerizations but the discrepancy is smaller for 3-methyl butene-1 than for isobutene.We infer that there is no significant effect due to (vii) possible differences in stereoregularity of poly-(3-methyl butene-1 sulphone) prepared from olefin-rich and sulphur dioxide-rich mixtures. Therefore the discrepancy between copolymerization in olefin-rich and sulphur dioxide-rich mixtures for the 3-methyl butene-1 system are considered in terms of the explanations proposed by Cook Ivin and O’Donnell for the isobutene system. The first possibility deviation from 1 1 composition of the copolymer has been investigated here. The observed discrepancy could be explained by a decrease of 0.25 in the [C]/[S] ratio for the polymer from sulphur-dioxide rich to olefin-rich monomer mixtures. The results for the linear regression of [C]/[S] on x show that as x,+O [C]/[S]+5-004 and as x,+l [C]/[S]-+5.010.Since the correlation coefficient is so small (0*03) no correlation exists between [C]/[S] and x, i.e. the B . H. G . BRADY AND J . H . O’DONNELL 35 polymer composition is independent of the monomer mixture composition. How- ever the values of %C and %S show weak correlations with x, although the standard errors are large. The total amount T1 of carbon hydrogen sulphur and oxygen in each polymer sample was calculated from the analytical results of the Australian Microanalytical Service using the equation and the results are shown in table 2. The correlation coefficient standard error and parameters for a linear regression of TI on x are also given in table 2. There is a 95 % probability that a correlation exists between T1 and xm and T1 has the values 98-13 and 99.81 % for the polymers prepared from the limiting sulphur dioxide-rich mixture and the limiting olefin-rich mixture respectively.This variation probably indicates that the efficiency of combustion during analysis of the polymer depends on the composition of the monomer mixture from which it was prepared suggesting a significant difference in the physical properties of the polymers. This would explain the variation in %C and %S with x without any variation in the ratio ECI /PI. The second possibility is most unlikely for the reasons advanced by Cook Ivin and O’Donnell. The third adsorption or swelling effects has been rejected from the results of physical examination of the polymers. There were no obvious differences in the polymers when these were observed under a microscope in situ when freshly precipitated from olefin-rich and sulphur dioxide-rich mixtures of 3-methyl butene-1 and sulphur dioxide.The present results therefore support the conclusion that the discrepancy is probably caused by a combination of (iv) and (v). Finally the slope of the arm in fig. 3 corresponding to polymerization in sulphur dioxide-rich mixtures gives AHlc = - 22.0 kcal mole-I and ASzc = - 77.4 cal mole-I deg.-l These values compare favourably with those for the formation of other polysulphones from sulphur dioxide-rich mixtures of the liquid monomers but do not agree with the values for the copolymerization of isobutene and sulphur dioxide. Also the slope of the arm in fig. 3 corresponding to polymerization in olefin-rich mixtures of 3-methyl butene-1 and sulphur dioxide gives AHzc = -10.6 kcal mole-1 and ASl = -38.5 cal mole-I deg.-l TI = %C+ %H+64-07 xS132.07 (2) We thank Prof.L. E. Lyons for his encouragement and Prof. K. J. Ivin for helpful advice. One of us (B. H. G. B.) is grateful to the University of Queensland for a Demonstratorship. F. S. Dainton and K. J. Ivin Quart. Rev. 1958 12 61. R. E. Cook F. S. Dainton and K. J. Ivin J. Polymer Sci. 1957 26 351. R. E. Cook F. S Oainton and K. J. Ivin J. Polymer Sci. 1958,29 549. R. E. Cook K. J. Ivin and J. H. O’Donnell Trans. Farday SOC. 1965,61 1887. G. M. Bristow and F. S. Dainton Proc. Roy. Soc. A 1955 229 509. B. H. G. Brady and J. H. O’Donnell Trans. Faraday Soc. 1968 64 23. N. L. Zutty C. W. Wilson G. H. Potter D. C. Priest and C. J. Whitworth J. Polymer Sci. A 1965 3 2781. ’ S. Machi M. Hagiwara M. Gotoda and T. Kagiya Bull. Chem. SOC. Japan 1966,39,675.

ISSN:0014-7672    

DOI:10.1039/TF9686400029

出版商:RSC    

年代:1968

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. Relationships Between Measured and True Quenching Cross-Sections for Atoms with Doublet Excited States BY D. R. JENKINS “ Shell ” Research Limited Thornton Research Centre P.O. Box 1 Chester U.K. Received 23rd June 1967 The measurement of the intensity of fluorescence of metals in the vapour phase as a function of the partial pressure of other gases is the usual method used to determine the quenching cross- sections of metals by other atoms and by molecules. For atoms with two close-lying upper levels such as the alkali metal atoms the values deduced for the quenching cross-sections by the Stern- Volmer plot may not be equal to the cross-section for any specific process but only effective values which are functions of the actual ones.In this paper the relationships between the intensity of fluorescence the pressure of foreign gas and the actual quenching rates are derived and the experi- ments which would enable the true values to be deduced are identified. Most values of quenching cross-sections of metal atoms have been determined by one of three methods-by quenching of the fluorescence of metal vapours in glass bulbs by photodissociation of metal compounds and by flame fluorescence. The essential feature of each is the measurement of the fluorescence intensity of the metal in the presence of various partial pressures of the quenching gas the main differences between the methods being in the manner in which the excited atoms are produced.Except in the work of McGillis and Krause,l the measurements of fluorescence quenching have been interpreted assuming a singlet excited level even for the alkali metals. In investigations of the alkali metals the consequences of a transfer of excited atoms between the 2P1/2 and ‘P3/2 states in addition to the quenching of the excited atoms to the ground state do not appear to have been considered and as a result the values which have been deduced for the quenching cross-sections of the alkali metals do not refer to any specific process but are complex averages of the cross-sections for quenching of the two states and of the 2Pl/2tfzP3/2 transfer process.Only when certain assumptions concerning the relative magnitudes of these processes are valid are the values of the quenching cross-sections those of any specific process. The arguments presented here apply to all resonance quenching experiments but they are considered with particular reference to the flame fluorescence r n e t h ~ d . ~ . ~ In this method a flame containing trace amounts (about 1 part in log) of the element is irradiated with a modulated beam of resonance radiation. The ratio of the number A P of quanta/sec absorbed from the primary beam to the number Pf/sec emitted as fluorescence is measured and the effective quenching rate calculated from the fluorescence yield y and the singlet excited level expression (1) A y = - p.f - AP - ‘A+Zk[X]’ where a is a self-absorption factor which is determined by preliminary measurements 36 D.R. JENKINS 37 of the dependence of y on A P ; A is the spontaneous emission coefficient ; k is the effective quenching rate constant for the quenching gas X and the summation includes all quenching species present in the flame. By measuring the fluorescence yields of isothermal flames differing in composition the value of the effective quenching rate and hence the cross-section can be determined for each species. In resonance quenching experiments with metal vapours in glass bulbs and in the photodissociative methods the cross-sections are determined from an expression identical with (1) except that y is defined as the ratio of fluorescence intensity in the absence to that in the presence of the quenching gas and the self-adsorption term is generally neglected or the experimental conditions arranged so as to make it equal to unity.The commonest arrangement for sodium and the only possible one for lithium is to use both D-lines for excitation and for the fluorescence measurements. With increasing atomic number however it becomes less practicable to retain this arrange- ment and others are more convenient. Furthermore with increasing separation of the two 2P states the assumptions which make a simple interpretation of the data possible become increasingly less probable. Excited level I energy E l statistical weight g resonance frequency v i 2P % ['*Iz Excited level 2. energy E2 statistical weight g resonance frequent v2 I GROUND STATE FIG.1 .-Fluorescence of doublet excited level. Altogether there are nine different fluorescence experiments possible for each metal. These correspond to excitation by either one or both resonance frequencies combined with measurements of the fluorescence from either one or both levels. We derive the relationship between y and the pressure of the quenching gas for each of these cases. From these relationships the best experiments to deter- mine the cross-sections for the various processes and the conditions under which the simple " singlet excited level " interpretation of the measurements becomes valid can be identified. Fig. 1 shows the system of energy states and kinetic processes. The excitation process shown as dashed lines may be to either or both levels and occurs at a rate of AP sec-l.The radiative process occurs at a rate of A sec-l per unit excited atom concentration which is assumed to be the same for both levels. No large error is thereby incurred as the A values for the two levels differ only because of the dependence of A on v2. The maximum value for the ratio of the A values for the two levels is 1.1 for Cs and much less for the other elements. The quenching collisions to the ground state occur at rates of k,[X] and k,[X] sec-l for the two levels and the inter-level transfer process occurs at rates of k3[X] and k;[X] sec-l. By the principle of detailed balancing k3 and k; are related to each other by the expression. k3lG = (92191) exp [(El -Ez)IkTI (2) 38 QUENCHING CROSS-SECTIONS FOR ATOMS where g and E are the statistical weights and energies above the ground level respec- tively of the two excited states.For brevity the quenching by only one species X is considered and the summation over all species in flames is not included. As the incident beam of resonance radiation is a modulated one and the detectors respond only to modulated light it is necessary to consider only the rates of the processes induced by the incident radiation and the thermal processes occurring in the flame may be ignored. Self-absorption has been neglected (a = 1) and it is assumed that the radiative inter-level transfer process is forbidden. containing the metal is imagined to be irradiated by light of the resonance frequency v1 only and the fluorescence detector responds only to light of this same frequency. The number of quanta/sec absorbed by the flame is AP1 and the number emitted as fluorescence is Pf.When the flame is not irradiated both the excited levels may be regarded as empty since the detector does not measure thermal emission intensities. When the flame is exposed to the incident radiation the level 1 is populated and then by the inter-level transfer process level 2. The average values of the concentrations of excited atom M* in the two levels reach steady-state values in times which are much less than typical periods of modulation and are given by CASE 1 .-EXCITATION AND FLUORESCENCE OF UPPER LEVEL oNLY.-The flame The number of quanta emitted as fluorescence is and the fl uorescence yield is By substitution of eqn. (3) (4) and (5) in eqn. (6) pr = A[M*I, Y1 = PJIAP,. Y1 = (7) where R = k3k;[Xl21{A + (kl + k3)[XI){A + (k2 + k3CXl).(8) CASE 2.-EXCITATION AND FLUORESCENCE OF LOWER LEVEL omY.-The steady- state concentrations of M* are given by k;[M*I,CXI cM*ll =A+(k,+k3)[X]' AP2 + k3[M*I 1 [XI [M*] = _________ __ A+(k,+kj) [X] The fluorescence emission rate and yield are Pf = A[M*I, Y 2 =pflAp2. These expressions lead to (9) y2 =A+(k,+k;)[X] A (L). 1-R D. R . JENKINS 39 CASE 3.-EXCITATION OF UPPER LEVEL ; FLUORESCENCE OF LOWER LmEL.-The flame is irradiated with radiation of resonance frequency v 1 and the fluorescence detector responds only to light of resonance frequency v2. This is the type of experi- ment carried out by Lochte-Holtgre~en,~ Thangaraj,6 Siewert et aZ.7-9 and Krause et a2.l. lo in glass vessels to investigate the efficiency of the P312*P112 transfer process.Most of this work has been concerned with collisions between metal atoms or between metal atoms and inert gas atoms and there is little reliable quantitative work on the efficiency of molecular species in promoting an inter-level transfer. However from the work in ref. (1) and (9 such processes occur readily. The steady-state concentrations are the same as those for case 1 given by eqn. (3) and (4). Use of these and eqn. (11) leads to CASE 4.-EXCITATION OF LOWER LEVEL ; FLUORESCENCE OF UPPER LEVEL.-uSe of eqn. (9) (10) and ( 5 ) leads to CASE 5.-EXCITATION OF BOTH LEVELS ; FLUORESCENCE OF UPPER LEwL.-The expression for y depends on the ratio AP1/AP2 = y. It is intermediate between the expressions for y 1 and y4 and approaches these two limits as y3m and 0 respec- tively. The value of y depends on the ratio of the f-numbers for the two lines the concentration of metal in the flame and the intensity wavelength distribution of light from the source over the range of frequencies absorbed by the element in the flame.A calculation of y is not usually feasible because it requires detailed informa- tion about the characteristics of the light emitted by the source and in practice it is simpler and more accurate to determine y experimentally by direct measurement of AP1 and AP2. The expression for ys can be deduced from those already derived for y1 and y, since the intensity of fluorescence from the upper level in case 5 is the sum of the intensities in cases 1 and 4 i.e. Yl@l+Y4AP2 1 = -(YY1 +Y4). ''= AP,+AP2 1+y CASE 6.-EXCITATION OF BOTH LEVELS; FLUORESCENCE OF LOWER LEVEL.-Thh case is the complement to case 5.By the same arguments CASE i'.-EXCITATION AND FLUORESCENCE OF BOTH LEvELs.-Because O f the small separation of the two Ievels this is the only experiment which is possible with lithium and is the commonest one with sodium. The expression for y follows from case 5 and 6 since CASE EXCITATION OF LOWER LEVEL; FLUORESCENCE OF BOTH LEvELs.-The expression for y8 follows fromIthosezalready derived since TABLE 1 .-EXPRESSIONS FOR FLUORESCENCE YIELD experiment expressions for y under the following conditions L case cxcitation fluorescence Y kl = k2 k38 k l kZ and 8 A / [ X ] k3% kl = k2 and B A / [ X l A R upper lower - - k;[W 1-R Y2 Y2 A R A k m A + ki [XI A + + k3 + k%Xl lower upper - - k3[X] 1-R Y1 Y1 Y1 Y1 1 both lower l-$-y C Y ~ + Y Y ~ ) Y Z Y 2 both both Y 5 +Y6 A A+kl[XI lower both Y 2 +Y4 A A+klN Y7 upper both A Y7 D.R. JENKINS 41 CASE EXCITATION OF UPPER LEVEL; FLUORESCENCE OF BOTH LEVELS.-AS in case 8 y g follows from previous cases since The expressions obtained for y are summarized in column 4 of table 1. DISCUSSION From column 4 of table 1 the expressions for y are all more complex than the simple form given in eqn. (1). In all cases the Stern-Volmer plots of A(l/y- 1) against [XI are non-linear and no direct determination of any cross-section is possible from any one experiment. For example a Stern-Volmer plot for a case 1 experi- ment gives the expression which at low values of [XI where [X].gA/k2 and A/k; has a slope of (k,+k,) and at high values of [XI a slope of kl +k2k3/(k2 +k;). Similar plots for the other cases are no simpler and those for cases 5 6 and 7 are also functions of y.It is possible with accurate data to use a regression method to determine the value of the cross-sections which fit the plots but the method suggested later appears to be more satisfactory. Most experimental investigations of the quenching of the alkali metals have been concerned with sodium in case 7 experiments in which both resonance lines are used in excitation and measured in the fluorescence. Within the limits of experi- mental accuracy the data 2* l 1 appear to fit a straight-line Stern-Volmer plot. We conclude either that the range of vaues of p] used in the experiments was too small to reveal the non-linearity of the plot or that special conditions which render the Stern-Volmer plot linear apply.The expressions for y under various assumed conditions are shown in columns 5-7 of table 1. From these expressions A[(1/y7)- 11 is a linear function of [XI when kl = k2 and/or when k3sk1 and k2 and %.//[XI. If k = k2 then the slope of the Stern-Volmer plot gives the value of this rate constant ; if the other condition applies the slope gives the value (k;kl+k,k3)/(k3+kj). At present there are insufficient data available to decide if any of these assumed conditions apply. If the quenching of excited atoms by molecules is a resonance exchange process with vibrational and rotational levels of the quenching molecule then the two rates would not be expected to be equal particularly for the heavier alkali metals for which the energy difference between the 2P1/2 and 2P3/2 levels is appreciable (AE = 238 cm-l for Rb and 554 cm-l for Cs).However a determination of the cross- sections for caesium + hydrogen and caesium + nitrogen mixtures (which are the only systems involving molecular species to be fully analyzed) gave similar values for the two rate c0nstants.l More data on the relative values of the 2P1,24-+2P3/2 and the quenching processes are available however ; McGillis and Krause find that k3 k j are less than k l k2 for caesium +nitrogen collisions but of similar magnitude for caesium and hydrogen. Extensive results for k3 and k> for alkali metals and inert gas systems have been obtained by Krause and co-workers,1° Jordan l2 and S i e ~ e r t ~ and the values obtained range from 10-14-10-15 cm2 for potassium to 10-19-10-21 cm2 for caesium though there are fewer data of comparable precision for kl and k2 for the same gases.3 9 l 3 and results for the quenching of potassium by helium and argon (to be published) show that values of kl and k2 are over an order of magnitude smaller than the corresponding Results for the quenching of sodium by some inert 42 QUENCHING CROSS-SECTIONS FOR ATOMS values for k3 and k;. Because of the small values of AE/kT in flame fluorescence experiments (0.57 for caesium in a flame at 1400°K) the inter-level transfer process would be expected to occur more readily than the quenching process. Probably therefore the assumption k3$k1 and k2 and/or kl = k2 may apply for the data which have been obtained in the quenching of sodium and that the cross-sections obtained from the slopes of the Stern-Volmer plots are those corresponding to kl or to the average value (klk> + kZk3)/(k3 + k i ) .The expressions given in table 1 suggest several experimental processes which would give values for all the cross-sections. For example if y1 and y were measured as functions of [XI and the function (y1/y4)- 1 plotted against l/[X] the plot would give the values of k2 and k3 from the slopeand interceptsince[(y,/y,)- I] = A/k3[X] + k2/k3. A similar plot with [(y2/~3)-1] gives k l and k3. For lithium only the case 7 experiment is possible. However because of the closeness of the two levels the conditions of column 7 of table 1 will probably apply and a simple Stern-Volmer plot will give the quenching cross-section directly. D. A. McGillis and L. Krause Physic Rev. 1967,153,44. D. R. Jenkins Proc. Roy. SOC. A 1966,293,493. H. P. Hooymayers and C. Th. J. AUcenade J . Quant. Spectr. Radiative Transfer 1966 6 501. R. W. Wood Phil. Mag. 1914,27 1018. W. Lochte-Holtgreven 2. Physik 1928,47 362. M. Thangaraj Ph.D. Thesis (Univ. of Toronto 1948). R. Seiwert Ann. Physik 1954,18 54. K. Hoffmann and R. Seiwert Expt. Tech. Physik 1960,8,161. H. Bunke and R. Seiwert Optik und Spektroskopie aller Wellenlangen (Akademie Verlag Berlin 1962). lo G. D. Chapman and L. Krause Can. J. Physics 1966,44,753 and other references therein. R. G. W. Norrish and W. M. Smith Proc. Roy. SOC. A 1940,176,295. I2 J. A. Jordan Ph.D. Thesis (Univ. of Michigan Ann Arbor Mich. 1964). l 3 L. von Hamos 2. Physik 1932,74,379.

ISSN:0014-7672    

DOI:10.1039/TF9686400036

出版商:RSC    

年代:1968

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. Matrix Approach to the Kinetics of Open Systems BY G. M. SWINKELS * AND B. W. WOJCIECHOWSKI Received 8th May 1967 A matrix treatment of the kinetic behaviour of monomolecular open systems is developed. The coupled differential rate equations are transformed to the normal form. The resulting uncoupled differential equations are thereby rendered in a form convenient for computation and the study of system dynamics. The treatment offers an essentially time-free method for the experimental study of open system kinetics and presents powerful tools for the study of the morphology of open systems. Closed monomolecular systems have been extensively studied by Wei and Prater.In this presentation a similar treatment of open monomolecular systems is evolved. The method of approach is essentially analogous and the conclusions reached for the open system have many analogies in the closed system. The main difference between the two is in the lack of readily available transforms such as the orthogonality relations between the eigenvectors of the closed system. Despite this handicap the proposed method offers many advantages over the conventional treatment of open systems.3* Some of the features discussed in this paper were not described in previous conventional treatments due to the difficulty of achieving insight into the morphology of open systems without the geometric representation which is made possible by the matrix approach. An extensive con- ventional treatment of open systems is given by Denbigh whose main conclusions are reproduced here together with some new and unreported features.THE WCOMPONENT OPEN SYSTEM A characteristic feature of open systems is the unlimited availability of certain reagents at fixed concentrations. We consider the system of reactions shown in fig. 1. In the mechanism shown the reagents A! A; and A; are assumed to be avail- able in unlimited quantity at a constant concentration of a; a; and a! respectively. Assuming all reactions in the mechanism to be first order the set of linear differential equations describing the time course behaviour of all the components is da;/dt = daz/dt = das/dt = 0 daJdt = -(k01+k21+k31)al+k12a2+k13a3+kl,a~ da2/dt = k21al-(kO2 fk12+k32b2+k23a3 +k20&9 (1) da3Idt = k3lal + k3Za2- (k03 +k13 +k23)a3 + k30a03 where the a represent the concentrations corresponding to components of the same subscript in fig.1 ; the k are numbered in subscript such that the first subscript corresponds to the product and the second subscript to the reagent. Such a set of equations can be written in matrix form dA/dt = KA+GA" (2) * Dept. of Metallurgy Queen's University at Kingston Ontario Canada. t Dept. of Chemical Engineering Queen's University at Kingston Ontario Canada. 43 44 MATRIX APPROACH TO THE KINETICS OF OPEN SYSTEMS where ; A" is the vector k12 k13 - ( k 0 2 + k l 2 + k 2 3 ) k 2 3 k3 2 - (k03 + k l 3 f k 2 3 ) K is the matrix G is the diagonal matrix The differential vector dA/dt will approach zero as t approaches infinity. Thus for the steady state dA/dt = 0 and where KJ = -GA" A is the steady state composition vector A I (3) FIG.1. In open systems the matrix K is non-singular and hence the inverse K-l exists. In this the open systems differ from closed systems where the rate constant matrix is singular. Multiplying eqn. (3) from the left by K-l A = -K-lGA". (4) The vector 3 is merely a function of the rate constants and the external concentrations. The principle of equifinafity therefore emerges from the matrix treatment in the form of eqn. (4). The above treatment can be readily extended to an n-component system. G. M. SWINKELS AND B . W. WOJCIECHOWSKI 45 TRANSIENTS IN THE OPEN SYSTEM In order to obtain a convenient expression for the transient one must change from concentration terms used in eqn. (2) to terms involving useful potentials.Let where Y is a measure of concentration departure from steady state. Since A is a constant Y = A-A (5) dY/dt = dA/dt. (6) Substituting eqn. (4) (5) and (6) in eqn. (2) gives d Y/dt = KY. (7) The matrix K can be diagonalized by a similarity transform which when applied to the matrix K gives eqn. (8) where A is a diagonal matrix containing the negative of the eigenvalues of K a matrix consisting of unit eigenvectors of K written in sequence. length in the y system of co-ordinates by using eqn. (9) A = X-lKX (8) X is In constructing the operator X one can define an eigenvector xi to be of unit where Qi is an arbitrary vector in the direction of xi. Rearranging eqn. (8) and introducing into (7) gives dY/dt = XAX-l Y. Multiplying from the left by X - l We now define a new variable B as in eqn.(12) When eqn. (1 1) becomes X-ldY/dt = AX-' Y. B = X-l Y. dB/dt = AB. Eqn. (1 3) describes a set of uncoupled linear differential equations in B. The solution of eqn. (13) is given by where the parenthesis refer to the state at time t and the initial state respectively and (exp At) is a diagonal matrix of the form B(t) = (exp At)B(O) (14) e-Lit exp At = Eqn. (14) can also be written in terms of Y. Using eqn. (12) in (14) and rearranging By a proof analogous to one given by Wei and Prateryl the matrix K is negative Y(t) = X(exp At)X-l Y(0). (15) 46 MATRIX APPROACH TO THE KINETICS OF OPEN SYSTEMS definite. Thus all terms of (exp At) go to zero for t-+w and periodic solutions are excluded. We now compare one of the terms of eqn. (15) in the form yi = xilbl(0)e-’l‘+ ...+xinbn(0)e-’nr (16) (17) where yi is the ith term of the Y vector to the form of the conventional solution The A obtained in the conventional solution correspond to the eigenvalues and the C correspond to The comparison makes it clear why it is difficult to obtain rate constant values from a conventional solution of the open system. yi = Ci,e-’lr+ ... +Cine-’n‘. cij = Xijbj(0). (18) MORPHOLOGY OF THE OPEN SYSTEM Eqn. (1 5) describes the sequence of system compositions from an initial composi- tion to the steady state. This sequence of compositions can be plotted in a co-ordinate J PATH I .... Y2 N. -. RE ACT1 ON PATH 2 ...... .. .......... FIG. 2. system based on the potentials y l y .... Such a locus in y-space is referred to as a reaction path.The steady-state for the system is located at the origin. Eqn. (14) describes the same reaction path on the basis of another co-ordinate system the axes of which are directed along the eigenvectors xi. The elements bt of B can be interpreted as concentrations of a virtual component (see fig. 2). Thus the transform of eqn. (12) is interpreted as an ‘‘ alias ” transformation where the co-ordinate system not the composition itself is changed. In order to simplify the following considera- tions the reaction path can be expressed without reference to the time parameter. Rearranging eqn. (14) for the ith andjth eigenvector gives G. M. SWINKELS AND B . W. WOJCIECHOWSKI Eliminating t in (19) and rearranging where gtj is therefore a constant for any given set of initial conditions.We consider now an initial composition B(0) of the form bi(t) = gij(bj(t))“”’j gij = bi(0)/(bj(O)) ’i/’J i.e. the initial composition lies on one of the eigenvectors say xi. reduces to all other b(0) being equal to zero. The equivalent of eqn. (1 5) becomes Eqn. (21) and (22) represent a straight line reaction path. This straight line path coincides with the ith eigenvector. There is also a straight line reaction path for each of the remaining eigenvectors if suitable starting compositions are selected. With the help of eqn. (20) one can develop two limiting conditions for a general reaction path. First consider the limit of the vector Y which is expanded with the help of the inverse of eqn. (12) and the definition of X . Eqn. (14) now b,(t) = h ( O ) exp A d (21) yi(t) = b,(O) elitxi (22) lim Y = lim (blxl +b,x + ...bnxn) lirn Y = lirn (blxl + ... +gtjblaf’A1xi + ...) t- co Using eqn. (20) t- 00 By convention A1 is the smallest eigenvalue and &/Al> 1 for a l l j = 2,...,n. Therefore Thus the general reaction path is tangent to the xl eigenvector at the origin. A similar limit for t- - co shows all reaction paths to be tangent to the x eigenvector at a large distance from the origin. These limits are illustrated in fig. 2 for a two component system. It was once thought that open systems exhibited certain transient phenomena which do not have equivalents in the closed system. This is now known to be untrue. Specifically the phenomena of overshoot and false start have been previously identified in open systems and discussed by Denbigh and others. Overshoot in a variable y t occurs when the reaction path at some time 0 < t < co crosses the steady state value y,(co) = 0.The situation is illustrated in fig. 3. False start occurs when the variable yi initially moves away from its steady state reaches a maximum and then decays to its steady state value. In multicomponent systems oscillations about steady state can occur more than once. lim Y = blxl. (24) t-t co 48 MATRIX APPROACH TO THE KINETICS OF OPEN SYSTEMS We have also identified a novel response which we will call the initial excursion. This phenomenon illustrated in fig. 3 consists of the variable yi starting on its steady state value yi(oo) = 0 departing from that value and then returning to its steady state value. This behaviour has not been discussed in previous publications.All the above phenomena can and do occur in closed systems although Wei and Prater have only concerned themselves with the conditions which produce extremes.l Their method of approach in defining the loci of extremes called the isoclines is valid for the open system and can be summarized as follows. + Y 0 - Y FALSE START OVERSHOOT I N IT1 AL EXCURSION FIG. 3. An extreme value occurs where dyildt = 0. Using one of the set of eqn. (7) one may write where 2’ represents the sum of all terms with i # j . Eqn. (26) describes an n - 1 dimensional subspace in the n dimensional y-space. In this subspace reside all the extreme values of y in the system. The maximum number of such extremes in any given reaction path is rz - 1. dy;/dt = C’kijyj - (koi + 2’kji)yi = 0 (26) EXPERIMENTAL EVALUATION OF K In the usual experimental situation K X and A are unknown.Conventionally K is determined from initial rates or by non-linear curve fitting. However X and A (and thus K by the inverse of eqn. (8)) can be determined experimentally. The proposed treatment of data makes use of every available reaction path and only one experiment involving measurement of time is needed. The first step is the determination of X which is achieved by finding the eigen- vectors. This is equivalent to finding straight line reaction paths in y space. x1 and x, can be found using the limits developed in eqn. (24). A tangent to a reaction path at the origin is an approximation to the x1 eigenvector. Similarly initial com- positions on lines through the origin and parallel to the tangent at t = 0 approximate xpl.A general procedure for locating X~...X,-~ is based on ref. (6) which describes an iterative search for eigenvectors of a known matrix K. G . M. SWINKELS AND B . W . WOJCIECHOWSKI 49 Once the eigenvectors are determined the matrix X can be constructed. Using the newly found X matrix one can transform experimental data from Y to B co- ordinates using eqn. (12). From a given B vector various plots of In bi against In b for a l l j are constructed. According to eqn. (20) the slope of this plot is li/A,. Thus the ratios of all ;1J to one At are known and A is determined but for a constant multi- plier. 1 The plot of the one timed run In [bl(t)/bi(0)] against t will give the absolute value Ai which is needed fully to determine A Conversion of A to Kis done with the help of eqn.(8). A = ;liAred. (27) APPLICATION OF MATRIX METHODS TO A SIMPLE SYSTEM We turn now to a simple example of an open system in order to apply some of the above considerations. The open system considered by Denbigh is shown in fig. 4. FIG. 4. The system is open to source A; and sink A; by diffusional barriers and hence The K matrix for the system is klo = kol = k l ; k20 = koz = k2. k12 1. = [-(k1+k21) k2 1 - @2 +k12) A formula of Bodewig states that the two eigenvalues will lie in the regions where y is any arbitrary vector of unit length. A convenient vector to take is 21 > YTKY/YTY > A2 Y a = [;I giving and therefore Similarly for YTY* = 1 izl > - (k + k2 A2. one obtains 50 MATRIX APPROACH TO THE KINETICS OF OPEN SYSTEMS These conditions are sufficient but do not necessarily define the maximum and minimum values of ill and 1,.They do however reproduce the conclusions of Denbigh when eqn. (29) and (30) are rearranged The change in inequality arises because the ;I have been defined as being positive numbers whereas Bodewig deals with the real eigenvalues which are negative. The generalized statement of the above is that in an n component system the maximum and minimum eigenvalues bracket any and all the diagonal terms of the K matrix. 0 X w _t a t- f - A X E S ISOCLINES --- - *-*-- E I GENVECTORS * - * * REACTION PATH Fra. 5. The relation (31) allows one to determine the quadrant of the two dimensional y-space where the eigenvectors are located. The characteristic equations can be written for Al (A1 - (k 1 + K 2 m 1 1 + k12x12 = 09 kzlxll +(A - (kz +kl2))X12 = 0 9 (12-(k1 +kzl))xll+k12X12 = 0 ~ 2 1 ~ 1 1 + ( ~ 2 - ( ~ 2 + ~ 1 2 ) ) ~ 1 2 = 0 (33) (32) and for A2 where the xij are components of the eigenvectors xf.We consider the condition A1 <(k +kzl) in the first eqn. (32). The first term in that equation is negative and since the rate constants are by definition positive then xll and x12 have the same sign. The second equation gives the same result. Thus the eigenvector x1 corresponding to the smallest eigenvalue lies in the first and third G . M. SWINKELS AND B . W . WOJCIECHOWSKI 51 quadrants. Similar considerations taking A>(k,+k,,) in the eqn. (33) leads to the conclusion that the eigenvector x2 lies in the second and fourth quadrants. The situation is illustrated in fig. 5.The search for the isoclines proceeds in this manner. In the two component system eqn. (26) for the y1 isocline reduces to This is the equation of a straight line through the origin as shown in fig. 5. The slope G f the y1 isocline is given by (kl +k21)/k12 which when compared to the slope of the x1 eigewector taken from eqn. (32) -(A1-(kl+k21))/k12 and noting the condition A <(kl + k z l ) allows one to place the isocline as shown. It has been shown that all reaction paths will approach the x1 eigenvector asym- ptotically as t+O. Clearly then initial potentials corresponding to points in the shaded area will trace out trajectories which will cross the y isocline. In doing so they will pass through an extreme. In other words at the intersection of the reaction path and the isocline the tangent to the reaction path is parallel to the y axis.Further con- sideration of fig. 5 shows that points contained in the area between the x2 eigenvector and the yz axis will produce reaction paths showing overshoot. Points lying between the yz axis and the y1 isocline will show false start. An initial excursion in y1 will occur for all points starting on the y2 axis. The unshaded area contains all points which will result in monotonic functions in y. Similar considerations for y 2 will result in the overall picture of the morphology of this system shown in fig. 5 dy,/dt = - (k +k211Y1 +k12Y2 = 0. (34) METHODS OF EXPERIMENTATION An open system naturally tends to reside at its steady state not unlike the natural tendency of closed systems to reside at equilibrium. Just as it is necessary to know the equilibrium point in closed systems it is also necessary to ascertain a steady state in the open system One must then assure that the system under study will always return to the same steady state after tracing out its reaction path.This problem does not arise in closed systems at constant temperature when the equilibrium point is generally a function of the rate constants alone. In the open system the steady state is a function of external concentrations as well as of the various rate constants (see eqn. (3)). The eigenvectors are functions of the various rate constants and these too can be varied by techniques to be described. The experimental method that must be used is described as follows. A steady state is selected. The system is removed from that steady state by imposing a suitable change in conditions and allowed to come to some new steady state.The imposed perturbation is now removed and the trajectory of the system as it seeks its original steady state is plotted. In this way first x1 is found by a suitable interpolation of tangents to the reaction paths at the origin. x2 is found by the inverse procedure of seeking tangents at large values of -y and then drawing a line parallel to that tangent but passing through the origin. Clearly the above methods lend themselves to an iterative procedure which should eventually result in experiments which will trace each of the eigenvectors. For the purposes of achieving desired initial potentials the following methods of perturbing steady states are avail- able to the experimentalist.PERTURBING THE EXTERNAL CONCENTRATIONS The easiest and most commonly available approach to the perturbation of a steady state is a change in external source and/or sink concentrations a;. Let a'' be the perturbed external concentration and a' be the corresponding final external 52 MATRIX APPROACH TO THE KINETICS OF OPEN SYSTEMS concentration. Similarly 2' - is the perturbed steady state vector and A is the desired final steady state vector. Inserting these values in eqn. (3) gives KA+GA" = 0 (35) KA~+GAO~ = 0. (36) Subtracting (35) from (36) and noting that gives Simplifying eqn. (37) by the substitution gives Eqn. (38) for the two-dimensional system in fig. 4 may be written as ji'-A= y KY+G(A"'-A") = 0. AA" = A"'-A" KY+GAA" = 0. -(kl+k,l)Y,+~12Y2+klAa~ = 0 k 1Y 1 - (k2 + kl2)Y 2 + k2A4 = 0 where AaY = a:'-a;.When Aai = Aaz = 0 eqn. (39) and (40) reduce to the isocline form given in eqn. (26). We consider now the type of reaction path which will result when the steady state is perturbed by external concentration changes. First one cannot obtain an initial potential y which lies on the y r isocline by external concentration changes in a;. This makes little difference experimentally but is of interest in a subsequent discussion. Let any value on the y1 isocline be Assume a point above the isocline .=(Yp' y Y + A ) (37) Such points are shown on fig. 6. y1 isocline and rewriting (39) in terms of (41) with Aa" = 0 produces the y 1 isocline Subtracting (44) from (43) hence Substituting the values from eqn. (42) in eqn. (39) results in points above the (43) (44) kl,A+ k,Aa," = 0 (45) Aay = -(k12/k,)A<0.(46) -(k1 + k Z l ) y ~ + k l 2 ( y ~ + A ) + k,Aa," = 0 ; - ( k l + kzl)yt0+ kl2y? = 0. Thus points above the y1 isocline are produced by a decrease in a;. Similar considerations produce the other conditions noted in fig. 6. If Aa ; < 0 the area to the left of the y1 isocline can be reached experimentally. For Aa;<O the area to G . M. SWINKELS AND B . W. WOJCIECHOWSKI 53 the right of the y isocline is available. Similar arguments can be made for Aa; > 0 and Aaz > 0. When Aa,">O Aa,"<O or Aai>O Aag<O simultaneously only the area between the isoclines marked by lack of hatching is approachable and monotonic reaction paths result. On the other hand when the changes in ao have opposite signs only the hatched area on fig.6 is available and reaction paths containing extremes are generated. Moreover for a given Aai the initial potential will be on a line parallel to the y z isocline and at a vertical distance of k,Aa$/(k2+k12) away from it (fig. 6). The vertical distance is a linear function o f Ass. A similar argument obtains for Aai. Y. FIG. 6. One can obtain still stronger conditions concerning the nature of the extremes as follows. We consider e.g. the problem of false start in y z . On the y 2 isocline in the first quadrant Aaz = 0 and Aai>O. Inserting y 2 = 0 in (39) and (40) gives -(kl + kzl)yl + klAa;l= 0 (47) k2,y + k2Aai = 0. Eliminating y1 between (47) and (48) results in Aa,o = -(k1lk2@21l(k1 +k,l)lAa;. (48) (49) Since Aay > 0 one can write Eqn. (50) is the condition for false start in y2 from compositions starting in the first quadrant.A similar argument will produce the condition for false start in y 2 from the third quadrant. We call the phenomenon obtained when a starting composition lies on an axis an initial excursion. -klk2,Aa,01k2(kl fk,,)<Aai<O Aai>O. (50) 54 MATRIX APPROACH TO THE KINETICS OF OPEN SYSTEMS Overshoot occurs from the second quadrant when Aai < - k,k21Aay/k2(kl +IC2J Aa >O (51) A2Y1 = k A G (52) A2y2 = -k2Aai. (53) The other limit of the area for overshoot in y z lies on the x2 eigenvector. the equations given in (39) or (40) results in Introducing Eqn. (52) and (53) are the measure of departure of a given point in the y-plane from the x2 eigenvector. Substituting these equations in (53) gives which together with Aa; > 0 yields the conditions fm overshoot in y 2 shown in eqn.(75) and Aa; <O. Similar arguments can be made for points starting in the third quadrant. Perturbations in external concentrations make the whole y-space accessibls experi- mentally. PERTURBING THE INTERFACIAL RATE CONSTANTS In some systems it is possible to perturb the input-output interfacial rate constants kto and koi. One can then write eqn. (3) for the new steady state K'A'+ G'A" = 0 ; (56) Y2 lSOCLl NE FIG. 7. at this point the rate constant matrix K can be decomposed K i= -G+K (57) where the matrix G is the same as defined above as long as kio = kol. The matrix K is the rate constant matrix for the closed system which would result if input-output G. M. SWINKELS AND B. W. WOJCIECHOWSKI 55 are ignored.This matrix will remain unchanged by the perturbation under considera- tion. A similar procedure to that already outlined will lead to the conclusion illustrated in fig. 7. Considerations similar to those previously outlined also lead to the result that the whole y-space is experimentally accessible by this perturbation. Furthermore when changes in kl and k2 are in the same direction extreme values arise from the hatched area on fig. 7. When kl and k change in opposite directions only monotonic reaction paths result. Unlike the perturbation of external concentrations one cannot present conditions to produce false start in y2. Considerations similar to those outlined above lead to a;-ii,* kzl a - ii,. k l + k, -- Akl>Ak2>0 Ak,>O. Since the fraction ( a ~ - a l ~ ) / ( a ~ - a v ) is a dependent variable of Akl and Ak2 one can- not readily predict in what region of the hatched area on fig.7 a given perturbation system will settle down. Because of this deficiency the perturbation of input output rates is less useful than that of the external concentrations. PERTURBING THE INTERNAL EQUILIBRIA It is possible in some systems by the addition of catalysts or by step changes in temperature to design experiments where the internal rate constants are perturbed. FIG. 8. In such systems one arrives at the same conclusions as Denbigh.3 The region of y- space accessible by perturbation of the internal equilibrium lies in the second and fourth quadrants ; furthermore all systems which are studied in this way exhibit overshoot or an initial excursion.The eigenvector x cannot be located by this procedure except by taking tangents to the reaction paths at the origin. In this case one can also determine whether the overshoot occurs in y or yz. For overshoot in y the 56 MATRIX APPROACH TO THE KINETICS OF OPEN SYSTEMS necessary condition is kz < kl and for overshootin y2 kl < k2. The above are illust- rated in fig. 8 where the case of k2 = kl is also shown as giving rise to points on the eigenvector xz. PERTURBATION BY INJECTION Injecting the system with one or a number of the internal components at leads to initial compositions lying in the positive orthant. In the case under discussion one can therefore achieve conditions of false start in y1 or y 2 by injection. Overshoot cannot be achieved by this method and only the x1 eigenvector corresponding to the smallest A can be located.One may speculate whether false start conditions engendered by injection are of any significance in physiological systems undergoing therapy. SOME DEGENERATE CASES OF A TWO-COMPONENT SYSTEM The case where kl = k2 and klz = kzl leads to R1 = &. This can occur when all the rate constants are diffusion constants and eqn. (20) reduces to and all initial states decay in a straight line to the origin. The situation is shown in fig. (9) and from the figure extreme values cannot occur in this system. bi = gijbj (59) FIG. 9. The case where k12 = 0 leads to the matrix = [-(kl+kzl) k2 1 - " 1 k2 whose eigenvalues are given by eqn. (52) and (53) The corresponding eigenvectors obtained from eqn. (52) and (53) lie along the lines Two cases of this type can arise.If k2> (k +k2,) the situation shown in fig. 10 obtains. The eigenvector x1 corresponding to the smaller eigenvalue lies in quadrants izl = kl+kzl ; L2 = k2. ~21Y1+(k1+~21-k21Y2 = 0; Y1 = 0. (60) G . M. SWINKELS AND B . W. WOJCIECHOWSKI 57 one and three and overshoot can occur only in y2 and will be present in all paths starting from the second and fourth quadrants. Overshoot occurs from the hatched area again in yz only. If either or both of the input-output rates are If k2 < ( k +kJ the situation shown in fig. 11 obtains. INE FIG. 10. 0 . 0 y2 0 0 . ISOCL \ I FIG. 11. .INE irreversible the system behaves in the same way generally as the system shown in fig. 5 but corresponds in reality to a new class of systems which it is proposed to call throughput systems.58 MATRIX APPROACH TO THE KINETICS OF OPEN SYSTEMS CONCLUSIONS The treatment of open systems in terms of matrices and the associated geometric interpretation appears to facilitate the understanding of the morphology involved. The mathematical and experimental problems in the open system are more complex than those in the closed system. Nonetheless the approach presented above has much to recommend it for those who seek to understand the structure of rate processes as well as for the mathematically sophisticated experimentalist. The approach outlined here can also be applied to throughput systems where the input and output reactions are irreversible. Such systems have even greater generality ranging from control problems in industrial processes to linear systems in economic theory. The authors thank the National Research Council for support. J. Wei and C. D. Prater Adv. Catalysis 1962 13 204. N. R. Amundson Mathematical Methods in Chemical Engineering (Prentice Hall 1966) p. 146. K. G. Denbigh M. Hicks and F . M. Page Trans. Faraday Soc. 1948,44,479. E. Bodewig Matrix Calculus (Interscience 1956) p. 56. (a) L. Lapidus Digital Computation for Chemical Engineers (McGraw-Hill 1962) p. 237. (b) J. H. Wilkinson Proc. Cambr. Phil. Soc. 1954 50 536. 4A. C. Burton J. Cell. Comp. Physiology 1939 13 327.

ISSN:0014-7672    

DOI:10.1039/TF9686400043

出版商:RSC    

年代:1968

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. Kinetics of Combination of Oxygen Atoms with Oxygen Molecules BY M. F. R. MULCAHY and D. J. WILLIAMS Coal Research Laboratory CSIRO Division of Mineral Chemistry Chatswood N.S.W. Australia Received 10th July 1967 The kinetics of the reaction O+ 0 2 +M 4 3 + M where M = 02 He Ar or C02 have been determined at total pressures from 1 to 8 torr the oxygen atoms being generated by pyrolysis of ozone at 1300°K. The rate constants observed in the temperature range 213-386°K when M = Ar and M = C02 can be represented by k;4' = (1.7kO-2)x 1013 exp (+1680fIOO)/RT and kyo2 = (8.4+1.1)x 1013 exp (+1450f140)/RTcm6 molee2 sec-' or alternatively by kfr = (2*85&0*3)X 1014 (T/298)-"*0*0*2 and kyo' = (9-7f1.3)~ 1014 (T/298)-2*4*0-3 cm6 mole-2 sec-'.At 298°K the relative third-body efficiencies for equal molecular concentrations are O2 He Ar COz = 1.0 0-74 0.90 3.1. The values obtained for k p are greater than those calculated from previous investigations of the kinetics of pyrolysis of ozone even allowing for the accepted error in the equilibrium constant for reaction (1). Likewise the relative third-body efficiencies with the exception of O2 He differ from those derived from earlier work on the pyrolysis and photolysis of ozone. The combination reaction Of02 +M-+03 + M (1) has been investigated directly with non-equilibrium sources of atomic oxygen 1-3 and indirectly via studies of the thermal decomposition of o ~ o n e .~ ' ~ With the exception of Kaufman and Kelso,2 investigators using the direct method have generated the oxygen atoms by an electrical discharge and all have determined the kinetics by measuring the decay of the atoms in a flow tube. Results obtained before the importance of effects exerted by extraneous active species from the dis- charge was appreciated 2s lo* l1 are now superseded. Kaufman and Kelso elimi- nated these species-hydrogen atoms from impurities and electronically excited oxygen molecules-by generating the atoms by pyrolysis of ozone in a quartz tube at 1000°C. They obtained the value of 2.7 x 1014 cm6 mole-2 sec-l for k? (i.e.kl when M = 0,) at 298°K. Clyne McKenney and T h r ~ s h ~ on the other hand retained the discharge and relied upon rigorous purification of the gases and great 59 60 COMBINATION OF 0 ATOMS WITH 0 MOLECULES dilution with argon of the oxygen passing through the discharge to eliminate the unwanted species. They obtained (1) or otherwise expressed (14 for the temperature range 188-373°K. Their mean value for ktr at 290°K is 1.9 x 1014 cm6 mole-2 sec-l. If the value of ky2/ktr = 1.7 (determined from the photo- lysis of ozone 12) is accepted Kaufman and Kelso's work leads to the value 1.6 x lOI4 for kfr at 298°K. The agreement is satisfactory. Nevertheless it is desirable to have an independent determination of ktr over a range of temperatures which does not involve a discharge source of atomic oxygen.Secondly the relative third-body efficiencies of different molecules hitherto available are all derived from studies of the pyrolysis 4-9 or photolysis l2 of ozone. In general the values obtained by the different techniques agree well but they were mostly determined by involved analysis of manometric records and are based in part on the same assumptions regarding the mechanism of reaction. Hence it would be useful to determine k y directly for different inert gases in the same apparatus. These objects have been achieved in the present work k t r and kFo2 have been determined in the range 213-386"K and Icye and k y at 298"K by measuring rates of disappearance of oxygen atoms in a stirred-flow apparatus the atoms being generated by the pyrolytic method of Kaufman and Kelso.' ktr = 8.9 x 10l2 exp (+ 1800+400/RT) cm6 mole-2 sec-' ktr = 2.8 x 1014(T/273)-3'4*0*8 cm' mole-2 sec-l EXPERIMENTAL Oxygen or a mixture of oxygen and inert gas X containing a small concentration of oxygen atoms and a trace of nitric oxide was pumped through a stirred-flow reactor of volume Y (2234 cm3) at the rate of u cm3 sec-l measured at the reactor pressure p (1-8 torr).The relative concentrations of oxygen atoms at the inlet and outlet [O]i and [O],,t were determined photometrically from the intensities of the air afterglow at these points. Assuming that the atoms disappear from the reactor by reaction (l) recombination at the wall OE!+02 (w) and efflux only,* and that perfect mixing occurs the following relations apply whence (iii) Since in each experiment the mole fraction z of oxygen was constant the pseudo-&st order rate-constant kpfo becomes where K = (z2k~2++(1-z)k~) = constant.A plot of the values of kpfo derived from eqn. (iii) against p 2 for pure oxygen thus gave the value k y and this was used to obtain ky from similar plots with the gas mixtures. Since for the latter z was always (0.1 the contribution of .z2ky2 to K was small though not always negligible. a small concentration of ozone in the gas stream was totally decomposed in the quartz tube and a concentration of oxygen atoms of the order of 10-2-10-3 mole % emerged. If the gas did not contain NO (from the ozonizer) a trace was added before the stream passed Fig. 1 illustrates essential parts of the apparatus. Under appropriate conditions *The effect of the reaction O+O+ M +02+ M is negligible under the given experimental conditions.M. F. R . MULCAHY AND D. J. WILLIAMS 61 to the first of two similar optical cells. After traversing the spherical Pyrex reactor l3 the gas entered the second cell and passed thence to the pumps. The rotating slotted disk enabled the optical cells alternately to illuminate the same photo-multiplier tube with chopped light and the amplified outputs were read simultaneously on two meters. (Details of the optical and electronic assembly will be published e1~ewhere.l~) Since the same concentration of 0 atoms could not be caused to pass through both cells simultaneously the responses of the two optical-electronic systems were determined separately in situ by NOz titration. This required a higher concentration of atoms than was provided by the O3 pyrolysis and for this purpose (only) the 2450-Mc/sec discharge in the by-pass line was used.* For the chemiluminescence method to be valid the NO concentration must be sufficiently small for the consumption of 0 atoms in the reactor by reactions (2) and (3) to be negligible.O+NO+ M+N02+ M (2) NO~+O+NO+OZ (3) FLOWMETER hO INLET TO HcLEOO GAUGE + is5 NEEDLE VALVE FIG. 1 .-Apparatus (schematic). The condition for this was established by allowing a fixed amount of NO to diffuse into the flowing gas upstream of the first gas-cell and recording the two outputs from the photo-tube as the concentration of NO in the gas stream died away. During this period both luminescent intensities decreased continuously but their ratio eventually became constant-that is independent of NO concentration.This was then sufficiently low ([NO]<O.Ol[O]) for the value 2kz[O]mO] to be negligible (as was confirmed by calculation using the known value of kZ and the approximate absolute value of [O]). Care was taken to operate under this condition. The internal surfaces of the reactor and connecting tubing were coated with Teflon l5 to reduce heterogeneous recombination of the oxygen atoms. The coating was ineffective at 298°K but its effect became evident at higher temperatures. Since the homogeneous reaction becomes slower with increasing temperature whereas the heterogeneous reaction accelerates the effect of the latter may become inconveniently large at higher temperatures. For this reason the lower tcmperature coefficient recombination of Teflon proved to be a valuable property.Residence times were 1-5-6.5sec. Effectively perfect mixing occurs in this type of reactor when operated under conditions similar to the present.13 However for accurate determination of kpfo the measured values of [O]in/[O]out must be corrected for reaction occurring in the tubing between the measuring points and the reactor. This was done by the procedure outlined in the appendix. The corrections reduced the measured values of * Some kinetics experiments were carried out using discharged oxygen instead of pyrolysed ozone as source of 0 atoms. The results were similar to those obtained by previous workers' ; that is the values of kpfo obtained with purified oxygen were lower than the true values by a factor of about 40 (owing to the presence of excited O2 molecules in the discharged gas).It was observed in these circumstances that kpfo was linearly related to p2 up to p = 6 ton at 298°K. 62 COMBINATION OF O ATOMS WITH 0 2 MOLECULES [O]in/[O]out by 5-25 % (usually 10-15 %). The corresponding effect on K varied from about 8 % with measurements at 213°K to about 25 % at 346°K and 60 % at 386°K. Some preliminary experiments were carried out with pure oxygen using a smaller vessel (535 cm3) but were not continued because the corrections amounted to 30-40 % of the value of [O]i,/[O]o",. Values of kpfo derived at room temperature were in reasonable agreement with those obtained with the larger vessel. Gas mixtures and pure oxygen from commercial cylinders were purified by passage over quartz chips at 1 150"C platinized asbestos at 300°C and 5 A Linde molecular sieve (90 cm) at 25°C before passing at 1-5 atm pressure through a Siemens-type ozonizer to the low-pressure flow system.Their oxygen content was determined with a Servomex OA 137 paramagnetic analyzer calibrated with standard mixtures prepared by weighing. Impurity contents (p.p.m.) determined by gas chromatography and mass spectrometry before the gas mixtures passed through the purification train were Arlo mixtures H2 > 20 ; CH4 N C2H6 # 1 ; higher hydrocarbons + 4. Helo H2 # 100 ; CH4 = 2 ; higher h.c. >4. C 0 2 / 0 2 Hz + 20 ; CH4 = 0.5 ; higher h.c. > 1. In the presence of argon or helium a little NO (insufficient to affect the kinetics) was formed in the ozonizer. With C 0 2 up to 0.3 % CO was produced ; the effect of this on the kinetics was checked and found to be negligible.RESULTS Fig. 2 shows typical plots of kpfo against p 2 for pure oxygen and mixtures of helium argon and carbon dioxide with 5-7 % oxygen at 298°K. The values of kpfo reported are independent of the flow-rate u. If v was too great however high values of kpto were obtained. These were attributed to the escape of a little 5 10 15 20 2 5 311 p 2 (torr)2 FIG. 2.-TypicaI plots of pseudo first-order rate constant against (pr :ssure)2 at 298°K. Measure- ments with different flow-rates are indicated for the 02-COz mixfi!res viz. A 700-900 cm3 sec-l ; A 1000-1400 cm3 sec-l. undecomposed ozone from the tube furnace with the consequent occurrence of reaction (4) in the reactor. However as v was decreased kpfo fell to a limiting value and this limit was taken as the criterion of absence of ozone from the gases.(If v was too low no atomic oxygen reached the reactor but a sufficient range of v was available to 0 + 0 3 +202 (4) M. F. R. MULCAHY AND D . J . WILLIAMS 63 establish the limiting value of kpf,,.) The results conform well with eqn. (iv) and thus enable k y kye k t r and ky02 to be determined. In calculating ky from eqn. (iv) it is assumed that the concentration of ozone formed by reaction (1) in the reactor is sufficiently small for reaction (4) to be without effect on the stationary concentration of oxygen atoms. If this were not the case eqn. (iv) would have to be replaced by where kpfo = kv + (.l.>KO,l+ CX1I29 (v) a = (Vk4[01,,,+~)1(2~k4COI,"t+v)* It is necessary therefore for a to be close to 1.Values of k4 at the appropriate temperatures were calculated in retrospect from ky2 and mean values of the ratio k72/k4 derived 5 7 8 s l2 from the kinetics of pyrolysis and photolysis of ozone. These lead to the expression k4 = 6-5 x 10l2 exp (- 3900/RT) cm3 mole-1 sec-l.* TABLE VA VALUES OF (cm6 moW2 sec-l) FOR M = 02 He AK AND C02 AT 298°K mol % 0 2 in gas mixture 100 3.8 3-95 5-35 4-2 4-45 5-80 8.6 2.55 2.55 6-95 10-14ky 3-18 f0-13* 2-40 &O-22 2-19 f0.09 2.42 50.1 6 2-66 f0.13 2.49 f0.10 3-00 f0-13 3.24 f0-19 10-76 f0-45 10.10 f0.43 8.33 3~0.57 10-14ky mean 2.3 fO* 1 * I 2.85 f0.3 i *errors given as standard deviations. The maximum value of [OIout obtained in any experiment was about 10-5p/RT mole ~ m - ~ . The calculated values of a were all based on this value and except for two cases discussed later were >Om9 for all experimental results reported.If k4 were grossly underestimated the values of k y obtained would be too high by a factor of +2. Values of ky at 298°K are collected in table 1. The values of k for the same inert gas as third body show no trend with oxygen content of the mixture. The value of kpfo was linearly related to that of ([O,] + [X]j2 at several tempera- tures in the range 213-386°K when X = Ar or C 0 2 . In both cases K decreased with increasing temperature (whereas k increased). Assuming that the temperature- dependence of k y is not markedly different from that of k r or ky02 the Arrhenius *At 298°K this corresponds to k4 = 1 x 10'O cm3 mole-' sec-'. Mathias and Schiff have determined the ratio k4/ky2 by a mass-spectrometric investigation of the O3 concentration in dis- charged oxygen.When combined with the present value of k?' this yields k4 = 6.4 x lo9 cm3 mole-' sec-'. 64 COMBINATION OF O ATOMS WITH 0 2 MOLECULES plots of K shown in fig. 3 lead to the following expressions exp (+ 1680+ 100/RT) cm6 molee2 sec-l (VO k t r = 1013.11 Icyo2 = lo1 3.92 exp ( + 1450 f 140/RT) cm6 mole'2 sec- '. (vii) (via) (viia) 2 5 FIG. 3.-Arrhenius plots of slopes of kpfo against [MI2 plots. 0,4*45 % 0 in Ar; A 2-55 % 0 2 in CO,. Values of a calculated from the results obtained at 386"K(Ar) and 379"K(CO2) average at 0.75 and 0-85 respectively and therefore do not satisfy the relation a>0.9; nevertheless the values of ktr and ky02 at these temperatures fit well on the Arrhenius plots and their exclusion does not significantly alter the least-squares values of A and E.It seems therefore that the calculated values of ct are too low ; probably because the (overall maximum) value of [O],, inserted in eqn. (v) was too high. REACTION OF OXYGEN ATOMS WITH CARBON MONOXIDE The carbon dioxide used to determine kyo2 contained up to 0.3 % carbon monoxide. The reaction of carbon monoxide with oxygen atoms is slow and has a positive temperature coefficient but published rate data 18-20 are difficult to reconcile. The reaction was therefore briefly investigated. Partial pressures of carbon monoxide of 0.1-1.2 torr in excess oxygen at total pressures of 2-5-307 torr were used and oxygen atom concentrations were taken as proportional to the total chemiluminescence from the 0 + CO and 0 +NO reactions.Assuming that oxygen atoms were removed by the bimolecular 17-19 reaction o+co-+co2 ( 5 ) k5 was found to be (1 -0.5) x lo7 cm3 mole-l sec-l at 456°K. This value is such that the effect of the carbon monoxide on the results obtained with carbon dioxide was inappreciable. Likewise experiments with a Wratten 15 filter showed M. F. R . MULCAHY AND D. J . WILLIAMS 65 that any 0-CO chemiluminescence emitted in the experiments with carbon dioxide was too feeble to affect the results. The above value of k5 may be compared with values derived from previous work 1 x lo9 1 x lo8 and c5 x lo7 cm3 mole-1 sec-l from ref. (18) (19) and (20) respectively. The last value was derived on the (reasonable)20 assumption that the overall reaction has the same activation energy as the chemilurninescent reaction ; it alone is compatible with the present value.EFFICIENCY OF RECOMBINATION ON TEFLON For a spherical vessel of radius r the probability y that collision of an oxygen atom with the (geometric) surface leads to recombination is given by y+) 4rk 32n * An Arrhenius plot of values of y calculated from the intercepts k of the plots of k,, against p 2 is shown in fig. 4. It is described by the relation y NN 2 x exp (- 44OO/RT) (viii) for the temperature range 273-450°K. This result refers to the layer of Teflon used throughout the experiments with the large reaction vessel. Values of y obtained 3 RT at 298°K range from 7 x to 3 x The layer on the smaller vessel gave y = 4 x obtained previously l6 using a Teflon-coated flow tube and oxygen atoms from a discharge. Measurement of k became increasingly inaccurate as the temperature was decreased below 273°K.However results obtained in the range 207-253°K suggested that y is less temperature- dependent at these temperatures than is implied by eqn. (viii). Furthermore its value appeared to decrease with the nature of the ambient gas in the order He>Ar> COz indicating that recombination is retarded by physically adsorbed gas molecules. These values agree with that of 4 x 3 66 COMBINATION OF 0 ATOMS WITH 0 2 MOLECULES The " non-Arrhenius " temperature dependence between 207 and 273°K recalls that observed with an uncoated silica surface by Greaves and Linnett.21 150 n 8 145 L h N w 8 % I d 0 k- & 5 GI 0 0 135 4 DISCUSSION sec-l is in excellent agreement with that 2 . 7 ~ lof4 obtained by Kaufman and Kelsa2* The present results for kfr are probably best represented by combining the temperature-dependent terms of eqn.(vi) and (via) with the mean value of k p at 298°K (table 1). This leads to The value of ky2 at 298°K reported here (3.2+0-3) x 1014 cm6 kf' = (1.7 +0+2) x l O I 3 exp (+ 1680 100)/RT (ix) - - - ( M w 1 .-.A- - ( CMT ) ./ J D I 1 I I I I I 2 3 L 5 or The same procedure applied to the results for kyo2 gives kfr = (2*85+0.3) x 10'4(T/298)-3'0*0'2. (ixa) kyo2 = (8.4 1.1) x 1013 exp (+ 1450 + 140)/RT (4 or kyoz = (9.7 + 1.3) x 10'4(T/298)-2'4* O S 3 . Our results for k p are compared with those obtained by previous authors in fig. 5. The broken lines represent the limits assigned to the value of El in eqn. (i) and (vi) and are plotted assuming k p (Clyne McKenney and Thrush) at 273°K and k p (present authors) at 298°K to have the values given by eqn.(ia) and (via) respectively. The values KKa and KKb are calculated from Kaufman and Kelso's results using the present and Castellano and Schumacher's values of ktr/ky2 0-9 sec-' became available to the authors after this paper had been submitted for publication. The agreement is now less satisfactory. Their values of k f at 300°K for the four third-bodies studied by us are all lower than our values (table l) as also are their values for k p / k p and ky02/k?z (0.62 and 2.3 respectively; cf. table 2). We do not know the reason for the discrepancies. *Kaufman and Kelso's revised value,41 2.35 x l O I 4 cm6 M. F . R . MULCAHY A N D D. J . WILLIAMS 67 and 0.6 respectively. Our values are about 50 % higher than those of Clyne McKenney and Thrush the difference being greater than the combined standard deviations.Both investigations however yield substantially the same dependence of ky on temperature. Eqn. (vi) and (vii) show the apparent activation energy to be the same within experimental error whether the third body be Ar or COz and it seems reasonable to extend this conclusion to other simple molecules. This has not been demonstrated previously by direct measurements. However the negative activation energies associated with the recombinations of oxygen 22 and nitrogen 23 atoms and their cross-combination 22 have each been found to be the same within experimental error when M = either Ar or N2 ; and a similar result has been obtained 24 from reaction (6) when M = either Ar or SF6 (though not when M = C12) Cl + NO + M+ ClNO + M.The combinations of iodine and bromine atoms become more negatively temperature- dependent with increasing efficiency of M 25-28 but may be exceptional in this regard. Their behaviour has been explained 25-27 by assuming that a charge-transfer complex is formed between the halogen atom and M. The treatment of termolecular reactions based on RRK theory,29 on the other hand relates the negative temperature coefficient to the average energy of the collision complex formed by the two reactive species; the effect of temperature therefore should be non-specific to M except in so far as the temperature-dependence of the rate of deactivation of the complex depends on the nature of M. The present result is compatible with this mechanism.Returning to fig. 5 values of k p obtained from the pyrolysis of ozone in conven- tional apparatus (BA,5* and Z 9 and in the shock-tube (JD ’) are derived from k- via the equilibrium relation K1 = k,/k-,. Those of BA and CN originate from the same experimental data and all are based on the value l 2 0-25 for k t r / k p . The results of CMT can be reconciled with the pyrolytic results if in calculating K, the value of AH;! for ozone 30 is taken at the lower limit of the assigned error (k0-4 kcal mole-l). This is also the case with the value KKb 1* but is not so with the present values and KKa (which would require an error of 0-7 kcal mole-l in AH;). Increasing kfr/k:3 by 50 %-in line with the higher third-body efficiency of argon found in the present work-would bring Z’s CN’s and BA’s values up to all the direct values within the accepted limits of AH;.The shock-tube values however do not depend on this ratio ; nor does it appear that the discrepancy here is due to a serious error in extrapolating the direct results to the higher temperatures since the shock-tube results yield the same value for El (- 1700 kcal mole-l) as the present experiments. It seems therefore that a definite discrepancy exists between the present values of k t r and those obtained from the kinetics of pyrolysis of ozone. This conclusion is supported by the results obtained with different third bodies. Values of ky relative to ky are given in table 2. The present value for helium agrees well with those derived from the kinetics of decomposition of ozone but the values obtained for argon and carbon dioxide do not.The difference is particularly striking with argon which at equal pressures is a more efficient third body than helium accord- ing to the present results but less efficient according to the ozone experiments. Table 2 also shows that the relative efficiencies of oxygen helium and argon obtained in the present work are similar to those observed in direct studies of reaction (2) a reaction which is dynamically similar to reaction (1) and has the same tempera- ture coefficient ( - E = 1800+400 kcal The relative efficiencies of oxygen and argon in the reaction 0 + SO2 + M are also similar to the above. However the value of kyOz/ky~ obtained by Kaufman and Kelso 31 is closer to the pyrolytic than to the direct value of kyo2/ky‘. (6) CN 68 COMBINATION OF O ATOMS WITH 0 2 MOLECULES Whatever their cause the discrepancies found here between directly observed behaviour and that expected from the results of pyrolytic studies are not exceptional.Clark et aZ.24 have pointed out that their directly determined values of k are higher than those calculated from the results of conventional 33* 34 and shock-tube 35 measurements on the reverse reaction.* Relative third-body efficiencies are also probably different kg/kz' = 0-8+0*2 24 as against k?6/kN-'6 = 0-6+0*2 33. (Likewise different third-body efficiencies have been found for the forward and reverse direction of reaction (9) OH + OH + M+H,O + M (9) TABLE 2.-RELATIVE VALUES OF kS AT 298°K. M 0 2 He Ar c02 N2 ref. method reaction 1-0 0.74 0.90 3-1 - stirred-flow this work 1.0 0.77 0.60" 2.4 0.93 O3 pyrolysis 6 1.0 0.77 0.57 2.2 0.89 O3 photolysis 12 0 + 0 2 + M 1.0 0.67 1.0 1.1 flow-tube 20 { 1.0 0.82 1.0 2.1 1.5 flow-tube 31 - 0.9 - I stirred-flow 13 - 1.0 - - flow-tube 32 o+ soz-I- rvl l.O { 1.0 *calculated from kT2 via ratio @l/k?l = 1-54.from the flash-photolysis 36 and conventional pyrolysis 37 respcctively.) Again large discrepancies in the same direction as the above have been discovered 3 8 9 39s 43 between directly determined (rotating-sector) rate constants for combinations of alkyl radicals and the values obtained indirectly from conventional 38 and shock- tube 39 pyrolyses of hydrocarb0ns.t While allowance must be made for experi- mental error in a field where accuracy is difficult to achieve it seems that exceptions to the direct applicability of the equilibrium relation to atomic and radical combina- tions are more numerous than the rule.APPENDIX CORRECTION FOR REACTION I N CONNECTING TUBES OF STIRRED-FLOW REACTOR The value of k,f is obtained from eqn. (iii). However [O] and [O],,t are different from the measured concentrations ([Olf ,, [O]&,) because of reaction and pressure-drop in the tubing between the measuring points and the reactor. These effects were allowed for in the following way. Plug flow was assumed in calculating the reaction times z and *Indeed fig. 5 of their paper which shows Arrhenius plots of the collected values of ky is remarkably similar to fig. 5 of the present paper. ?Added in proof. Olschewski et ~ 2 1 . ~ ~ have noted that the directly determined value of the rate constant for H+OH+M -+H,O+M at 2,000"K is an order of magnitude greater than that derived from their shock-tube study of the reverse reaction.M. F. R. MULCAHY AND D. J . WILLIAMS 69 Poiseuille flow in calculating the pressure-drops and gas temperature~.~~ When reactor and tubing are at the same temperature [o]in/[o]in = Xi” exp (-nkz)in. (1) Xi is the corresponding pressure ratio (Pin/”fn) and k is the pseudo first-order rate constant for the decay of 0 atoms in the tubing where kwt is the heterogeneous rate constant for the tube of int. &am. 1-3 cni and [MI includes [O,] ; z is the residence time and where [MI refers to [MI at the measuring point (for the entrance tube). Combining eqn. (I) with the analogous expression for the exit tube gives A value of 1.7 sec-l was assigned to kWt and [MI, x and z for entrance and exit tubes were calculated from the reactor pressure and flow-rate.An estimated value of k was first inserted in eqn. (111) and eqn. (V) was solved to find [O]i,/[O],, and hence k,f via eqn. (iii). The procedure was repeated with the measure- ments made at various pressures with the same gas composition and the least-squares fit of k,f against [MI2 was found. This gave an improved value of k (from eqn. (iv)). The procedure was repeated until the value of K was stationary ( f 5 %). When the reactor was not at room temperature the wall temperature of the tubes was assumed to pass abruptly to the reactor temperature T at the entrance to the thermostat. The mean residence times 62 gas temperatures T and values of [MI in successive 1 cm axial segments of the entrance-tube inside the thermostat and of the exit-tube outside were calculated using the Graetz formula40 for the temperature.For each segment IC was calculated from the relation I C T ~ = ~ ~ ~ ~ ( 7 ’ ~ / 2 8 9 ) - ~ using an estimated value of N ; the decre- ment in [O] was obtained by the plug-flow formula. The decrements were summed for all segments and added to those from the gas reaction in the section of tube at constant temperature and from the wall reaction. For the entrance tube this gave to allow for pressure drop ; the effects of temperature on Xi* and n were only roughly taken into account since Xjn and n are both approximtely equal to 1. Combination of (VII) with the similar equation for the exit tube gave an expression closely analogous to V. Values of IC were then found as before and “ plotted ” against T to give a new value of N.The whole operation was iterated to yield a stationary value ( f 3 %) of N (and hence also of E). The above procedure is undoubtedly more elaborate than is strictly necessary and a more intuitive approach could be employed without much loss of accuracy; its adoption was facilitated by access to a CDC 3200 computer. The authors express their gratitude to Mr. H. R. Brown Chief of the former Division of Coal Research C.S.I.R.O. for his constant support and encouragement during the course of the work. Their thanks are also due to Mr. B. R. Carruthers for carrying out the glasswork. 70 COMBINATION OF O ATOMS WITH 0 2 MOLECULES F. Kaufman Progress in Reaction Kinetics ed. Porter (Pergamon Press Oxford) 1961,1 p.1. F. Kaufman and J. R. Kelso Disc. Furaday SOC. 1964 37,26. M. A. A. Clyne D. J. McKenney and R. A. Thrush Trans. Furuhy SOC. 1965 61,2701. A. Glissman and H. J. Schumacher 2. physik Chem. B 1933 21 323. S. W. Benson and A. E. Axworthy J. Chem. Physics 1957 26 1718. S. W. Benson and A. E. Axworthy J. Chem. Physics 1965,42,2614. W. M. Jones and N. Davidson J. Amer. Chem. Sac. 1962,84,2868. E. S. Campbell and C. Nudelman (U.S. Air Force Office of Scientific Research) Report J. A. Zaslowsky H. B. Urbach F. Leighton R. J. Wnuk and J. A. Wojtowicz J. Amer. Chem. SOC. 1960 82,2652. M. A. A. Clyne B. A. Thrush and R. P. Wayne Nature 1963,199,1057. TN-60-502 1960. I f A. Matthias and H. I. Schiff Disc. Faruday Soc. 1964,37 38. l2 E. Castellano and H. J. Schumacher 2. physik. Chem.1962,34 198. l3 M. F. R. Mulcahy J. R. Steven and J. C. Ward J. Physic. Chem. 1967,71,2124. l4 A. B. Ayling and D. J. Williams unpublished work. l5 H. C. Berg and D. Klepner Rev. Sci. Instr. 1962 33 248. l6 D. J. Williams and hf. F. R. Mulcahy Austral. J. Chern. 1966 19 2163. l7 V. N. Kondratiev 7th Int. Symp. Combustion (Butterworths 1959) p. 41. lS L. I. Avramenko and R. V. Kolesnikova quoted in ref. (17) p. 43. l9 B. H. Mahan and R. B. Solo J. Chem. Physics 1962 37 2669. 2o M. A. A. Clyne and B. A. Thrush Proc. Roy. SOC. A 1962,269,404. 21 J. C. Greaves and J. W. Linnett Trans. Faraday SOC. 1959,§§ 1355. 22 I. M. Campbell and B. A. Thrush Proc. Roy. Soc. A 1967,296,222. 23 I. M. Campbell and B. A. Thrush Proc. Roy. SOC. A 1967 296,201. 24 T. C. Clark M. A. A. Clyne and D. H. Stedman Trans.Faruday SOC. 1966 62 3354. 25 D. L. Bunker and N. J. Davidson J. Amer. Chern. SOC. 1958,80,5085. 26 G. Porter and J. A. Smith Proc. Roy. SOC. A 1961,266 28. *' G. Porter Disc. Faraduy SOC. 1962 33 198. 28 W. G. Givins and J. E. Willard J. Amer. Chem. Soc. 1959 81,4773. 29 S. W. Benson The Foundations of Chemical Kinetics (McGraw Hill New York 1960). 30 JANAF Interim Thermochemical Tables (The Dow Chemical Co. Midland Michigan 1963). 31 F. Kaufman and J. R. Kelso Symp. C~zemilL~minescence quoted by Campbell and Thrush 32 C. J. Halstead and B. A. Thrush Proc. Roy. SOC. A 1966 295,363. 33 P. G. Ashmore and M. G. Bumett Trans. Furaday Sac. 1962,58 1801. 34 P. G. Ashmore and M. S. Spencer Trcns. Furaday SOC. 1959 55 1868. 35 B. Deklau and H. B. Palmer 8th lizt. Symposium Combustion 1960 (The Williams and Wilkins 36 G. Black and G. Porter Proc. Roy. Soc. A 1962 266,185. 37 D. E. Hoare J. B. Protheroe and A. D. Walsh Trans. Farduy SOC. 1959 55 548. 38 M. C. Lin and M. H. Back Can. 1. Chem. 1966,# 2357. 39 W. Tsang J. Chem. Physics 1966,#,4283. 40 M. F R. Mulcahy and M. R. Pethard Austral. J. Chem. 1963 16 527. 41 F. Kaufman and J. R. Kelso J. Chem. Physics 1967,46,4541. 42 H. A. Olschewski J. Troe and H. G. Wagner 11th Int. Symp. Combustion (The Combustion 43 M. C. Lin and M. H. Back Can. J. Chern. 1967,4§ 2115. Ann. Reports 1965 62 17. Co. Baltimore 1962) p. 139. Inst. Pittsburgh 1967) p. 155.

ISSN:0014-7672    

DOI:10.1039/TF9686400059

出版商:RSC    

年代:1968

数据来源: RSC