ANNUAL REPORTSON THEPROGRESS OF CHEMISTRY.GENERAL AND PHYSICAL CHEMISTRY.1. CHEMTCAL REACTIONS INDUCED BY IONISING RADIATIONS.1. Chemical changes produced in a photographic emulsion by theabsorption of rays emitted by a compound of uranium were the means ofBecquerel’s discovery of radioactivity in 1896 and are still used as atool in modern research in nuclear physics.2 Chemical changes broughtabout in living cells by X-rays are closely connected with the ensuingbiological effects, and are therefore of great importance in tlhe study ofradio therapeutic^.^^ It is the more surprising, therefore, that the mechan-ism of radiochemical reactions has until recently been so imperfectly under-stood. The reason for this is that the most obvious result of the absorptionof radiations from radioactive substances is the formation of ions, and, forabout forty years after Becquerel’s discovery, it was customary to ascribeall the chemical effects solely to the ion-pairs initially formed. The recog-nition of atoms and radicals in electrical discharges, and the growing realis-ation of the fact that molecular fragments are often much more reactivechemically when they are uncharged than when they are charged, havecaused a considerable reorientation of views about the way in which radio-chemical reactions proceed.A coherent account of this subject is thereforetimely.For the purpose of this Report, the subject of “ Radiation Chemistry ”will be defined as the study of the chemical effects produced by absorptionof all types of rays emitted in radioactive transformations, of quanta ofmagnitude greater than about 50 ev., and of electrons or positive ions ofthis energy range.Ions are formed in all these instances, but we excludeall photochemical changes (from which radiochemical changes differ, seebelow) even when these latter occasionally lead to i~nisation.~ Purelyphysical effects, such as radioluminescence, will not be discussed.Several monographs which deal particularly with earlier investigationsSee J. Becquerel, “ La RadiomtivitB,” Chapt. I, Paris, 1924.See, e.g., F. C. Powell et al., Nature, 1949, 163, 47.B. &I. Duggar, “ Biological Effects of Radiation,” New York, 1936.4 D. E. Lea, “ Actions of Radiations on Living Cells,” Cambridge, 1946.6 E.g., G.Volmer and K. Riggert, 2. phykkal. Chem., 1922, 100, 6026 GENERAL AND PHYSICAL CHEMISTRY.from the purely ionic point of view have been published,6-11 and the recentchange of outlook is most clearly seen in the proceedings of two recentsymposia,l2? l3 and in the second chapter of the late Dr. D. E. Lea’s2. Experimental Methods.-Reactions in discharges of all types havebeen fully discussed by G. Glockler and S. C. Lind.’ With the exceptionof the so-called “ gas electrode ” 21 all such reactions are restricted to gases,often a t low pressures in either static or flowing systems.The radiation may be supplied frorp a sourcesituated either inside or outside the reaction vessel. The use af externalsources, which include all high-voltage machines, is a dettermining factorfor the shape and material of the reaction vessel.Internal sources wouldminimise this restriction, but there are very few cases of their employment.A possible reason for this is the former scarcity of radioactive soqrces whichemit substantially one type of radiation. For example, radium, thoughavailable, can be used as a y-ray source only when the a- and p-rays areabsorbed in a screening material and can never serve as a pure a-ray source.(a) The principal positively charged rays are beams of helium nuclei,protons, and deuterons, all of which can be obtained from particle-acceler-ating machines such as the cyclotron and van der Graaff generator, Fndalready some radiochemical studies have been made by this means.14, l5Usually, natural radio-elements have been employed, e.g., (a) polonium,which emits only a-rays of 5.3 Me.v.energy,l6 ( b ) radon and its decayproducts, Ra-A and Ra-C’ mixed with the reactants.l7, l8 It is importantto use the source in such a form that it is not a chemical catalyst for thedestruction of the products.lg Other positive ions have occasionally beenused, for instance, I. Motschan et aL20 have used singly-charged alkali-s. C. Lind, “The Chemical Effects of Alpha Particles and Electrons,” Chem.Catalog Co., Inc., 1928.“ The Electrochemistry of Gases and other Dielectrics,” London, 1939.Lind, Chem. Reviews, 1930, 7, 203.2 (i). Radiation sources.13 W. Mnd, “ L’action chimique des rayons Alpha, en phrtse gazeuse,” Hermannet Cie., Paris, 1935.lo A. Kailan, “ Uber die chemische Wirkung der durchdringenden Radiumstrah-lung,” Vienna,, 1938.l1 F.Wegmiiller, “ Wirkung der Roentgenstrahlen auf einige organische Verbin-dungen,2’ Schuler, 1942.Symposium on “ Radiation Chemistry and Photochemistry,” University ofNotre Dame, June 24th--27th, 1947; J . Phys. Colloid. Chern., 1948, 52, 437.l3 Second Session of the Conference on ‘ I Certain Aspects of the Action of Radiationon Living Cells,” London, May 13th-14thy 1946 ; Brit. J . Radiol., 1948 Suppl. No. 1,41.l4 I. A. Breger, J . Phys. Colloid. Chem., 1948, 52, 551.l5 C. W. Sheppard and R. E. Honig, J . Physicat Chem., 1946, 50, 144; C. W. Shep-paxd and V. L. Burton, J . Amer. Chem. SOC., 1946, 68, 1636.l6 H. Folmer, Proc.K . AEad. Wetensch. Amsterdam, 1932, 35, 636.l7 P. C. Capron, Ann. 80c. sci. Brux., B, 1936, 55, 222.l8 L. H. Gray and J. Read, Brit. J . RadioE., 1942, 16, 125; 1941, 15, 380.l9 E.g., P. Bonet-Maury and M. Lefort, Campt. rend., 1948, 226, 1445.2o I. Motschan, S. Roginsky, A. Schechter, and P. Theodorof, Acta Playsicochim.U.R.S.S., 1936, 4, 757DAINTON : CHEMICAL RBACTIONS INDUCED BY IOWISING RADIATIONS. 'Imetal cations to induce the ammonia synthesis, and some of the changesobtained in aqueous solutions by V. I. Pavlov,21 using the so-called '' gas-phase anode '' method, are to be attributed to penetration of the solutionby positive gas ions of energy -103 ev. A novel recent development,which may prove valuable, is to use an external source of slow neutronsto irradiate a medium which can yield the required positive ions by anuclear reaction, I n this way, the advantage of an internal source wouldbe combined with that of the easier control of dosage which is associatedwith external sources.The met,hod has been applied to tissue,22 but the onlychemical reaction initiated in this way is the polymerisatian of styrene byrecoil protons and bromine ions formed by the Szilard-Chalmers reaction.23(6) Fast anions have rarely been used, the most important negativelycharged rays being electrons in the form of cathode or f3-rays. Wheneverexternal sources are used, the material to be irradiated should be in thefarm of thin layers, and, when a wall of a containing vessel has to be inter-posed between the source and the target, it should be as thin as is com-patible with the mechanical strain which it will be required t a bear.Ifthe soume is a radioactive element which is also cc-aetive, the thickness ofthe wall must, of course, exceed the range of the highest-energy cc-particleemitted. A common external @-ray source comprises radon " seeds," i.e.,thin-walled glass tubes containing radon gas, largely converted into anactive deposit of Ra-B and Ra-C.24 Many reinforced windows 259 26 madeof thin glass, aluminium, or mica, backed by fine wire meshes, have beendesigned for use with accelerating machines which operate a t low pressures,e.g., discharge tubes, van der Graaff generators. The choice of a windowmaterial will, of course, be partly determined by the nature of the chemicalreaction to be investigated.Internal @-ray sources do not appear to have been used-a fact whichis probably due to the lack of suitable naturally-occurring, purely @-emittingradio-elements, e.g., meso-Th-2, in adequate quantities. Increased avail-ability of artificial radio-elements such as 32P, and 204Tl may remedythis deficiency,( c ) High-energy photons, i .e . , X - and y-rays, possess a high penetratingpower, which is an advantage in that large samples can be adequatelyirradiated even when external sources are used. Disadvantagcs are (i) thatso much of the energy output of the source is wasted, and (ii) that con-siderable screening is required for the protection of personnel. All thework on y-ray-induced reactions has hitherto been effected by radium, -21 Compt.rend. Acud. Sci. U.R.S.S., 1944, 43, 236, 383, 385.22 P. A. Zahl and F. S. Cooper, Radiology, 1941, 3'5, 673,23 I. Landler and RI. Magat, Compt. rend., 1948, 226, 1720.24 A. T. Cameron and (Sir) Wm. Ramsay, J., 1907, 931, 1593; 1908, 966, 992.For n modern method of preparing radon " seeds " see Spicer, J. Sci. Instr., 1946,23, 207.2 5 See Chapter IV of ref. 7.28 W. D. Coolidge, J . Frunklin Inst., 1926,202,693 ; C. M. Slack, J . Opt. Sac. Amer.,1929, 18, 1238 GENERAL AND PHYSIUAL CHEMISTRY.in equilibrium with its decay products, and in a container of wall thicknesssufficient to filter out all a- and @-rays. The radiation thus emitted isnot monochromatic, but consists of eight lines varying in energy from0.189 to 2.198 Me.v. In contrast with the case of visible and ultra-violetradiation, the use of combinations of filters cannot lead to monochromatism ;it merely excludes much radiation of the longer wave-lengths.For maximumutilisation of the y-rays, the system to be studied is usually contained in achamber which has a central cavity for the source.27' 28 Other y-raysources of high energy and long life could be used, e.g., C'", 24Na, Y, lMSb,Mn, 85Sr, and Co.X-Rays are formed as scattered radiation when fast electrons fall on aprepared target, and consequently all machines which give electron beamscan easily be converted for use as X-ray sources. The X-ray beam con-tains quanta of all energies from very low values almost to the accelerationvoltage of the electrons, and becomes self-collimated more and more in theforward direction as this voltage is increased above 500 kv.In all X-rayexperiments reported hitherto, the source has been either specially con-structed or one of the convenient industrial units designed for radiographyor deep therapy.27~ z8( d ) Neutrons also bring about ionisation in the material in which theyare absorbed and have been used to initiate polymerisation.29 The highestneutron fluxes are most readily available as pile radiation, but this alsocontains a large proportion of y-rays.30 Alternatively, d,n reactions couldbe employed.312 (ii). Reaction vessels and temperature control. With internal sourcesof particulate radiation (K, p, etc.) the reaction vessel can be of any shapeand the reaction temperature controlled in the usual way by liquid orvapour thermostats. External sources require the use of very thin, butmechanically strong, windows [see 2 (i) (b)], and, since the range of suchparticles in dense media is very short," it is preferable to use only thinfilms of material to be irradiated. Such a reaction vessel cannot be totallyimmersed in a thermostat and furthermore, a good deal of heating of thespecimen and the adjacent window will occur.Reaction vessels for X-and y-ray work can be of much larger dimensions, and normal methods oftemperature control are possible.In order to meitsure the efficiency of the radiationin bringing about chemical reactions, it is essential to find the rate of energyabsorption in the medium.Convenient units are electron-volts (ev.) per2 (iii). Dosimetry.27 F. S. Dainton, J . Phys. Colloid. Chem., 1948, 52, 490.28 N. Miller, Nature, 1948, 162, 448.2s F. L. Hopwood and J. T. Phillips, {bid., 1939,143, 640.30 A. 0. Allen, J . Phys. Colloid. Chem., 1948, 52, 479.31 Ref. 4, p. 20.33 R. K. Appleyard, private communication.* E.g., the range of the a-particle from Po (5-3 a1e.v.) is 3.84 em. in dry air at 15"and 760 mm., but probably only about 3.42 x loda cm. in water.3mmfroN : CHEMICAL REACTIONS INDUCED BY IONISING RADIATIONS. 9litre per second. For internal sources of particulate radiation in reactionvessels which are large compared with the range of the particle, this (‘ doserate ” is readily calculable from the concentration, half-life, and 01- or (3-rayenergy of the radio-element employed.33 When the range is long, as isthe case in gas reactions, the calculation is more tedious.= When externalbeams of positive ions or electrons are used and all the rays reaching thereaction chamber are absorbed therein, the energy input can be estimatedfrom the beam current, the energy of the ions, and the stopping power ofthe windows.Although the absorption ofmonochromatic X - or y-ray photons is exponential with a coefficient char-acteristic of the energy of the photon and the absorbing substance, suchcoefficients are not readily determined.The reason for this lies in the factthat the energy is dissipated in the medium by photo-electrons and Comptonrecoil electrons [see section 3 (i) below].In the latter mecha,nism, there istherefore a good deal of scattered radiation, only a proportion of whichmay be absorbed. Nevertheless, it is possible 35 to calculate the ratio ofthe absorption coefficients of any two media for a given wave-length, providedtlhat their chemical compositions are known.In practice, most estimates of the dose rate are based on measurementsof the amount of ionisation produced either in the reacting system itself,if this is gaseous, or in an air-filled ionisation chamber. The method islimited by the difficulty of obtaining saturation currents in certain media.It is known that the mean energy dissipated in air at N.T.P.by electronsin creating an ion pair is 32.5 ev.36 and hence the rate of ionisation gives ameasure of the number of ergs absorbed. It is customary to define thatquantity of radiation absorbed by 1 C.C. of dry air a t N.T.P. which produces1 E.S.U. of charge (2.1 x lo9 ion pairs) as 1 roentgen; 1 C.C. of any othermedium placed in the same position relative to the same source wouldabsorb more energy, in the ratio of its volume absorption coefficients relativeto that of air. The relative number of ion pairs formed will also be inthis ratio if the same energy is required to create the ion pairs in thetwo media. In practice, the us0 of air-filled ionisation chambers in y-raydosimetry is not a simple problem, because almost all the ions formedin the small air cavity of the chamber are produced by the secondaryelectrons ejected from the walls of the chamber by the quanta which areabsorbed or scattered therein.The implications of this for accuratedosimetry of aqueous solutions have been discussed by L. H. Gray36 andN. Miller.37I n principle, some of the difficulties of dosimetry could be avoided byusing a reaction which is easily measured and the amount of which bears aX- and y-Ray dosimetry is less certain.33 E.g., G. Glockler and G. B. Heisig, J . Physical Chem., 1932, 36, 769.34 E.g., G . Glockler and R. Livingston, ibid., 1934, 38, 655.35 Ref. 4, p. 345.36 Brit. J . Radiol., 1937, 10, 600, 721; Proc. Roy. SOC., 1936, A , 156, B T S .37 In the press10 GENERAL AND PHYSICAL CHEMISTICY.fixed relation to the dose, as an integral dosimeter.Several attempts toconstruct such dosimeters have been3. The General Features of the Primary Radiochemical Act.-It isunlikely that any radiochemical reaction proceeds in one act, in the sensethat the immediate consequence of absorption of some of the ene?gy of theincident radiation is the conversion of the absorbing reactant moleculeinto the product. It is therefore convenient,4l as in photochemical pro-cesses, to divide the reaction into two stages : the primary act of energyabsorption, and the secondary reactions which terminate in product form-ation. In accordance with U.S. practice the symbol -+ will be usedfor the primary process.3 (i). The mechanism of energs absorption.Positively charged ionspassing through matter lose most of their energy by elastic impacts withelectrons lying in their path. The gross disparity in mass of the collidingspecies means that the ion loses little velocity and is virtually undeflected,whilst the electrons may be ejected from the atoms to which they arebound, frequently with sufficiently high velocities to ionise other molecules.*Ion-pairs are thus formed along, or near, the track of the positively chargedions. Measurement of the total number of ion pairs per track and also ofthe number formed per element of length of the track (the specific ionisation)has established that (a) with x-rays, approximately 60% of the total numberof ions formed are due to the secondary electrons, ( b ) the mean energydissipated in a system per ion pair formed is about 30 ev., being independentof the velocity of the a-particle, but characteristic of the absorbing system,and (c) the specific ionisation is an inverse function of the velocity androughly proportional to the square root of the atomic weight of the sub-stance being ionised, when this substance is at some standard concentration.The theory of this process42 has been developed along classical lines byN.Bohr43 and quantum-mechanically by H. Bethe44 and F. B l o ~ h . ~ ~Unfortunately, no accurate numerical predictions can be made from thesetheories. Thus, that of Bethe requires knowledge of an “ average excit-ation potential,” which is difficult to obtain a priori and which is usuallyevaluated empirically.Moreover, the treatment is restricted to atoms,H. Fricke and S . Morse, Phil. Mag., 1929, ‘4, 129.W. Stenstrom and H. R. Street, PTOC. SOC. Exp. Biol. Med., 1935, 32, 1498.40 R. W. G . Wyckoff and L. E. Baker, Amer. J . Roentgenol., 1929, 22, 551.41 F. S. Dainton, Report C.R.C. 304 (1946), not classified. N.R.C. (Canada),Division of Atomic Energy. Also M. Burton, ref. 12, p. 568, and J. 0. Hirschfelder,ref. 12, p. 447.42 For a general account of the physics of this process see F. Rosetti, “ Elementsof Nuclear Physics,” London, 1937, and H. Bethe and M. 5. Livingston, Rev. Mod.Physics, 1937, 9, 246.43 Phil. Mag., 1913, 25, 10.44 H. Bethe, Handbuch derPhysik, 1933, 24 (i), 519.4 5 2. Physik, 1933, 81, 363; Ann. Physik, 1933, 16, 285.* When the ejected electron has a, very high velocity, say 1000 ev., i t is knownThe tracks of such rays may be seen m spurs on a-particle tracks in the as a S-ray.cloud chamberDMY'l'OY : CHEMICAL REACTIONS INDUCED BY IONISING RADIATIONS.11and hence tbe empirical Bragg additive law 46 must be used for problemsinvolving molecules.Electrons are of such low mass that, except when they possess extremelyhigh energies, they are frequently deflected. The associated tracks haveill-defined ranges and are curved, particularly at law velocities. Theexperimental results and the theory * concerning the specific ionisationare very similar to the a-ray case discussed above. The specifio ionisationis inversely proportional to the square of the velocity a t low velocities, andless dependent at higher velocities, passing through a shallow minimumbefore increasing slowly at energies >-1 Me.v. At low electron speeds,the specific ionistitian is proportional to the atomic number of the absorbingmaterial, but, due to the fact that the average excitation potential is alsopraportional to the atomic number, this proportionality does not holdamongst the higher elements.I n addition to the energy lost by elasticimpact, a, small proportion, which increases with the electron energy, islost by radiation as the electron is decelerated in passing through the fieldof the nucleus. This appears as a continuous X-ray spectrum (Bremstrah-lung), and loss of energy due to this cause may assume serious proportionsa t electron energies in excess of 1 Me.v., especially for systems containingelements of high atomic number.Whereas charged particles undergo a stepwise loss of energy, photonsare absorbed in a single elementary act and hence a beam of X - or y-raysof intensity I , will have fallen exponentially to a value I .. e-6d at a distanced, where E is an extinction coefficient characteristic of the wave-length andthe absorbing medium. A high-energy photon may be absorbed by one ofthree mechanisms,* each of which will make its cantribution to the totalValue of E . The first mechanism which is especially prominent for softradiation and absorbing media of high atomic number, is that of ejectionof a pboto-electron, which will have an energy equal to the magnitude ofthe quantum less the binding energy.Since the electrons most usuallyinvolved are those in the K shell, this binding energy may be considerable.Ultimately, this energy appears as a second electron, since one of the outer-shell electrons will fall into the vacant K orbit and a very soft X-ray maybe emitted or a second much slower photo-electron ejected (Auger effect).The sacond mechanism is Compton scattering, and in this the least-tightlybound electrons are the most likely to be ejected. The energy of theCompton-recoil electron depends on the angle of scatter, but it should benoted that the scattered photon may still have a very high energy andthat the chances of absorption of such quanta will not be large in systemsof small volume.Not all the energy of the incident quantum is dissipatedin the medium. The third mechanism is the creation of positron-electronpairs. This is only possible for photons of energy greater than 2moc2,where mo is the electronic rest mass and c the velocity of light, i.e., -1 Me.v.46 W. H. Bragg, " Studies in Radioactivity," p. 43, London, 1912. * Coherent scattering and nuclear interactian are here neglected12 GENERAL AND PHYSICAL CHEMISTRY.The photon is completely converted into an electron and a positron, betweenwhich the excess energy of the photon above 2rn,c2 is approximately equallydivided. The positron is quickly destroyed with another electron givingrise to a y-ray photon (so-called annihilation radiation) of much lowerenergy than the original photon, which is therefore absorbed by one ofthe two other mechanisms.The existence of these three possible types of y-ray absorption, each depend-ent on wave-length in a different way, makes determinat'ion of the extinctioncoefficient for each wave-length very complicated.The Compton scatteringcoefficients per electron, which are independent of atomic number, can becalculated from the Klein-Nishina formula.47 The total absorption co-efficient per g. can be measured and hence, if the chemical composition ofthe material is accurately known, the photoelectric absorption coefficientcan be evaluated by difference. The latter coefficients have been relatedempirically to wave-length and atomic number, and thus the total absorp-tion coefficient for a medium of such a nature that it cannot be measuredcan be calculated from the sum of the dculated Compton coefficient andthe empirical photo-electric ~oefficient.~~Whatever the magnitude of the y-ray wave-length, the energy of thephoton is converted, if only in part, into a fast electron, which will dissipatethis energy along its track by the mechanism already described.3 (ii).The mean energy to create an ion pair (W). The number ofion pairs formed per unit time in an ionisation chamber can be counted,provided that the system permits the attainment of a saturation current.If the rate of energy absorption is also known, the average amount ofenergy dissipated in the medium when an ion pair is formed ( W ) can bereadily calculated.Accurate values are known for a-particles in gases oflow dielectric constant and vary from 35 ev. in nitrogen to 20.8 ev. inxenon. The values for electrons 49 are of the same order of magnitude,but increase somewhat as the energy falls below 5 ke.v. The values forX- and y-rays should be those appropriate to the Compton-recoil electrons,or photo-electrons. These values have been critically discussed byL. H. Gray,36 who selected 32.5 ev. as the appropriate value for air.Itspractical significance lies in the fact that many systems, notably liquids,exist for which the rate of energy input can be determined, but in whichsaturation currents are unattainable. In order to find the rate of ion-pairformation and hence compute the ionic yield, a value of W must be assumed.This is usually taken to be the value for air, appropriate to the radiationemployed.I n the case of water, for example, the ratio of the volumeabsorption coefficients of air and water for X-rays can be calculated [seesection 3 (i)], and this will also be the ratio of the rates of ion-pair form-ation in the two media exposed to the same source under identical con-The value of W is of great practical and theoretical importance.4 7 0. Klein and Y. Nishina, 2. Physik, 1929, 52, 853.4 8 See Appendix t o ref. 4 for further details.49 W. Gerbes, Ann. Physik, 1935, 23, 648; 1937, 30, 169D..4TNTON : CHEMICAL REACTIONS INDUCED BY IONISINQ RADIATIONS. 1sditions, provided that WXH20 = WXair = 32-5 ev. On this basis, 1 roentgenof radiation corresponds to the formation of 2.1 x lo9 ion pairs c.c.-l inair and 1-8 x 10l2 ion pairs c.c.-1 in water. Unfortunately, the effect ofphase change on the value of W can be only conje~tured.~~Measured values of W for various gases vary only slightly from substanceto substance and are always considerably greater than, but apparently notsimply related to, the ionisation potential of the substance.The firstfact is not well understood. Attempts have been made to calculate valuesof W for nitrogen and neon,51 but the results are in poor agreement withexperiment. U. Fano 52 has attributed it to increased outer screening insystems which have high ionisation potentials.(a) Distribution.It has been remarked [section 3 (i)] that, for all types of radiation, ionisationtakes place along the track of some charged particle, that the ionisationdensity is larger the slower the particle and therefore increases along thetrack, and is larger for heavy particles than for lighter particles of thesame energy.The positive ions thus formed lie initially in the wake ofthe ionising agent. The ejected electrons will be scattered in all directions,and, if there are any molecular species present in the system, which haveelectron affinity, the scattered electrons will be captured after most of theirenergy has been dissipated. Such electrons may traverse considerabledistances before capture, and hence, very shortly after the ionising agenthas passed, its track will consist of a high concentration of positive ions,located in a narrow core, and a lower concentration of negative ions, spreadthroughout a larger volume.The steep concentration, and electrical poten-tial, gradients thus established will cause a general diffusion radially, andinterdiffusion leading to charge neutralisation (4.v.). The latter effect resultsultimately in the destruction of all the ions, unless the experimental arrange-ment is such that a clearing field is applied.62 The tracks of any fastsecondary electrons (&rays) will have much the same structure. Beforecharge neutralisation is complete, a finite interval elapses during whichboth types of ions may decompose, initiate chemical change, or act asnuclei for clustering of polarisable molecules. The elucidation of the natureof the primary act includes the identification of the ions first formed andtheir possible fates.(b) IdentiJication and stabiEity of positive ions.Depending on the bond-ing or antibonding character of the electron removed, ionisation may occuralone or may be accompanied by dissociation. The amount of energyThus G. W. Hutchinson(Nature, 1948, 162, 610) states that W for Ra-G y-rays in liquid argon is of the sameorder 8s the value for gaseous argon, Le., 25 ev. N. Davidson and A. E. Larsh (PhysicalReview, 1948, 74, 220) have observed the ionisation of liquid argon by Po a-rays.F. L. Mohler and L. S . Taylor ( J . Res. Nat. Bur. Stand., 1934, 13, 663) give W = 24 ev.for liquid CS, using 0.27-~. X-rays. Saturation currents have been measured in hexaneand light petroleum by W.Stahel (Strahlentherapie, 1929, 31, 582).3 (iii). The charged species formed in the primary act.50 Estimates of TY for liquid phases have been made.51 E. Bagge, Ann. Physik, 1937, 30, 72.52 Phpsical Review, 1946, 70, 44. 53 Ref. 7, p. 36314 GENERAL AND PHYSICAL UHEMISTRY.expended in the various cases will differ, and ionisation potential data aretherefore of great value. Since in many cases a conaiderable proportion ofthe ions formed are due to impact by electrons of moderate velocities, muchinformation is to be gained from conventional mass-spectroscopical studiesof the ions formed by electron impact at various energies and pressures.Glockler and Lind 53 have summarised much of the data up to 1938 andF.S. Dainton27 has discussed the special case of water vapour where themost important ions are H20+, H+, and OH+. As formed, such ions maybe metastable and will therefore decompose very rapidly. For instance,J. A. Hipple, E. U. Condon, and co-workers 54 have shown that many ofthe ions of saturated hydrocarbons dissociate unimolecularly with halflives of the order of 10-6 see. into free radicals and carbonium ions or intoa paraffin molecule and an olefin ion. Thus, C4HI0+ --+ CH, + C3H,+ or ---+ CH, + C,H,+, and the carbonium ions may spontaneously dehydro-genate, e.g., C3H7+ -+ C,H5+ + H,. Alternatively, the positive ion mayreact with a neutral molecule, either in an electron-transfer reaction whenthe ionisation potentials are suitable, e.g., N2+ (17 ev.) + NH, (11 ev.) ---+N2 + NH,+ + 6 e ~ ., ~ ~ or in a mass transfer, e.g., H20+ + H,O + H30+ +When fast nuclei are employed as the radiation, some of the ionisationis of a primary character [see 3 (i)] and the relevant information in thiscase will no doubt be forthcoming from mass spectrographs, now beingdeveloped, in which the ionisation occurs by impact of fast positive ionssuch as H f , H2+, He+.57 All mass-spectroscopical data refer to gaseoussystems at low pressures. There can be little doubt that, at higher pressuresor in condensed systems, aggregation of neutral molecules round ions willoccur. (see section 5) andshould be manifested in unusually small ionic mobilities. Such low mobilitieshave been observed,68 but could equally well be explained by ion-induceddipole forces established between the ion and the polarisable molecules inwhose vicinity they move.59(c) Negative iom60 Electron capture by neutral atoms and moleculesonly occurs with slow electrons and when the neutral entities have appreciableelectron affinity.Unfortunately, there are few mass-spectroacopical data,on negative ions, and most of the information is obtained from electron“ swarm ” experiments,Bl from which it appears that lC diatomic molecules54 J. A. Hipple, R. E. Fox, and E. U. Condon, Physicat Review, 1947, 69, 257,and earlier papers referred to therein.5 6 S. C. Lind, J . Amer. Chem. Soc., 1931, 53, 2423.66 H. D. Smyth and D. W. Mueller, Physical Review, 1933,43, 116.5 7 J.R. Keene, private communication.6 8 A. M. Tyndall, “ The Mobility of Positive Ions in Gases,” Cambridge, 1938.-0 ~ . 5 6In gases, these are known as “ clusters ’’ 6 ,AIso ref. 12, p. 456.L. B. Loeb, “ Fundamental Processes of Electrical Discharge in Cfmes,” NewH. S. W. Massey, “ Negative Ions,” London, 1938.York, 1939.61 A. M. Crovath, Physical Review, 1929, 33, 605; N. E. Bredbury, ibid., 1933,44, 883; F. Bloch and N. E. Bradbury, ibid., 1935,48, 689DAINTON : CHEMICAL REACTIONS INDUCED BY ION IS IN^ RADIATIONS. 15do not form negative ions. Even a l C molecule may capture an electron,provided that the electron has sufficient energy to dissociate the moleculeinto fragments, one of which is not in a state, and therefore becomesthe negative ion, e.g., C1, + e + C1+ C1-.A further possibility, which does not appear to have been investigatedexperimentally, is simultaneous formation of positive and negative ions.Such heterolysis would probably require more energy than homolyticfission of the same bond.I n general, less is known about negative ions and their formation, butthere is no reason why they should not undergo the same types of reactionas positive ions, namely, breakdown, ion-neutral molecule reaction, cluster-ing, and ultimately, charge neutralisation.3 (iv).The uncharged species formed in the primary act. (a) From theions. Uncharged entities - differing from the molecules of the absorbingmedium may be formed by breakdown or reaction of the ions in processeswhich have been discussed in 3 (ii).Charge-neutralisation processes are not well understood, but it is con-ceivable that these also may cause formation of atoms and radicals.Thenegative charge is unlikely to be a free electron, and we therefore restrictour discussion to ion-ion reactions. If the ions concerned are radical oratomic ions, their union could give a finished molecule, e.g., H+ + OH--+H,O, provided a third body is present. The energy released might bedegraded to heat energy or used to dissociate the third body. Alternatively,charge neutralisation may be achieved by ionic dismutation, e.g., C,H,- +H+ -+ C,H, + H,. Even in such cases there might be considerableenergy release. The net effect of any charge-neutralisation process will beto release, in a restricted locality, energy approximately equal to that putin when creating the ion pair.J. 0. Hirschfelder 41 has pointed out thatthis energy is likely t o be completely used in immediate dissociation of themolecule on which the energy is located, but, if the molecule has a largenumber of internal degrees of freedom, this energy may be slowly degradedto heat.72There are two powerful arguments for the view thatsome of the reaction is effected through uncharged intermediates. Thefirst is that W is always larger than the ionisation potential. The excessenergy, of the order 15 ev., must be dissipated in processes not leading toionisation. Such processes are likely to be electronic excitation of themolecules, and, in view of the magnitude of the energy involved, it is possiblethat some of the energy is used to excite the molecule to non-ionic repulsivelevels. Estimates of the effectiveness of this process are ~onjectural.~~The second line of evidence is that H.Essex and co-workers 62 have shownthat the rates of decomposition of nitrous oxide and ammonia induced bya-rays are only slightly reduced when electrical fields are applied whichmaterially reduce the number of ions undergoing charge neutralisation.C. Smith and H. Essex, J. Chem. Physics, 1938, 6, 188; A. D. Kolumban andB. Essex, ibid., 1940, 8, 450; N. T. Williams and H. Essex, ibid., 1948, 16, 1153..(b) Directly16 GENERAL AND PHYSICAL CHEMISTRY.(c) Identi$cation of radicals and atoms. Mass-spectroscopic measure-ments are not of great value in identifying atoms and radicals formed inthe primary act, unless the appearance potentials can be accurately measuredand used to discriminate between radical ions formed directly and thoseformed by ionisation of radicals in the spectrometer.On the other hand,ultra-violet absorption and emission spectra should afford a valuable meansof identification, not only of atoms and radicals, but also of moleculesand ions. It has already been used to identify hydrogen atoms, andhydroxyl radicals in discharges through water ~ a p o u r . ~ ~ The study oflight emission from beams of high specific ionisation would be particularlyfruitful in that it would serve to identify any electronically excited species.Surprisingly few spectroscopic observations have been made on ionisingradiations, although the luminosity of such beams in air is well known.H.Greinacher 64 has reviewed previous work and has shown that theintensity of radiation from polonium cc-rays in air, carbon dioxide, hydrogen,or oxygen is unaffected by complete discharge of the ions, and increases withpressure, and that, with hydrogen, much of the light emitted is in theultra-violet region. E. Kara-Michaelova 65 has established that total lightemission of wave-lengths >2000~. per element of length of the track ofPo a-particles in air, varies with the distance from the end of the range asdoes the variation of specific ionisation.W. E. Burcham and F. S. Dainton 66 have photographed the spectra ofthe light emitted from an -600-kv.proton beam. Preliminary resultsindicate that excited nitrogen molecules are formed in air, but no resultshave been obtained as yet with water vapour or other gases. Work hasalso been reported on the light emission of pencils of a-rays passing throughmercury or sodium vapour in an excess of nitrogen or Noluminescence associated with excited species has been observed in liquids,although the Cerenkov continuum, which is produced when electronstraverse a medium with a velocity exceeding that of light in the medium, hasbeen investigated in detaiLB8 Chemical tests for atoms and radicals canalso be applied. Usually the existence o f such reactive intermediates issuggested by features of the kinetics of the reaction, e.g., very large ionicyields, or polymerisation.Atoms and radicals formed by rapid decompositionof metastable ions or by efficient reaction with neutral molecules will havean initial distribution very simiIar to that of the parent ions [section 3 (iii) (a)].63 K.Bonhoeffer and T. G. Pearson, 2. physikal. Chem., 1931, B, 14, 1 ; G. I. Lavinand F. 3. Stewart, Nature, 1929,123,607; 0. Oldenburg et al., J. Chem. Physics, 1939,7, 485, and earlier papers.(d) Distribution.64 2. Physik, 1928,47, 344.66 Sitzungsber. Akad. Wiss. Wien, R h s e 2A, 1934, 143, 15.6 7 A. Luyckx and J. Bodart, Physica, 1943, 10, 79.68 L. Mallet, Compt. rend., 1926,183,274 ; 1929,188,445 ; P. A. Cerenkov, PhysicaEReview, 1937, 52, 378; G. B. Collins and V.E. Reiling, ibid., 1938, 54, 499; H. 0.Wyckoff and J. E. Henderson, ibid., 1943, 64, 1 ; P, B. Weisz and B. L. Anderson,ibid., 1947, 72, 431,66 UnpublishedDAINTON : OHEMICAL REAUTIONS INDUCED BY IONISINQ RADIATIONS. 17Thus, all the radicals derived from positive ions will be situated along theaxis of the track, whereas those derived from the negative ions will bemore widely distributed. Uncharged species which are formed by directexcitation [section 3 (iv) ( b ) ] may be widely spread or confined to the centreof the track, depending on whether the lifetime of the excited levels of theparent molecule is long or short. Radicals which have their origin incharge neutralisation reactions will almost certainly be widely spread. Itis important to remember that those formed from metastable ions will becommonly of the same chemical nature when derived from ions of thesame charge, whereas direct excitation and charge neutralisation produceseveral radicals, not necessarily identical, which could, under suitableconditions, recombine to form the original molecule.The total number of uncharged species formed when acertain amount of energy is absorbed is of great importance.It is also avery elusive quantity and, like the quantum yield of the primary photo-chemical act, has an upper limit. For example, if H and OH are the onlyproducts of the primary act in water vapour, it is certain that not morethan six of each of these radicals can be formed per 32.5 ev. of energyabsorbed. The fraction of these which ultimately cause the observedreaction is probably less, and will depend on the nature of the reaction.Once the identities of the products of the primary act have been revealed,it should be possible to estimate their number from the magnitude of thereaction which they cause with a reagent of known rea~tivity.~'3 (v). The effect of the state of aggregation on the primary act.69 Thegreat increase in density associated with liquefaction will have severalimportant consequences. First, the methods available to identify the inter-mediates are almost exclusively chemical tests.Secondly, the primaryact may be profoundly affected.27 The specific ionisation will be muchhigher, and the mean energy, W , and ionisation potentials may be altered,although there is no direct evidence on the latter point.5O Deactivationalpossibilities will be enhanced and the persistence of, excited species willtherefore be less. If the liquid is polar, the effects of solvation will modifythe stability of any ions formed and their probability of being transformedinto radicals. Exothermic recombination processes, of ions and radicalsalike, will be facilitated by the nearness of third bodies. Immediaterecombination by the Franck-Rabinowitch rne~hanisrn,~~ of fragmentsformed from the same molecule by direct dissociation [3 (iv) ( b ) ] will alsoplay a part. The overall effect may be that the number of species capableof effecting decomposition of a pure liquid or reacting with a solute is muchreduced and that the products of decomposition of a pure liquid ariseprincipally from the radicals formed from the ions [3 (iv) (a)].The latterdistinction has been drawn in a somewhat different form and emphasis byA. 0. Allen in the case of liquid ~ a t e r . 7 ~See &o M. Burton, ref. 12, p. 575.(e) Number.70 J. Franck and E. Rabinowitch, Trans. Paraday SOC., 1934, 'SO, 120.71 Ref. 12, p. 47918 GENERAL AND PHYSICAL UHEMISTRY.Aply energy which is not used in chemical change or light productionwill appear as heat which will be manifested as a temperature rise.I?. H. Krenz 72 has detected this dilatometrically in the case of liquid waterirradiated with y-rays. A feature of this effect is its persistence far abouta minute after the irradiation is stopped.This after-effect is attributedby the author to the slowness of the degradation of the internal energyinto heat, which would be expected if the internal energy was originallyexcitational energy of complex units. Krenz identifies these units withwater polymers. The same lag would be expected in all associated liquids,not only as an after-effect, but also as an induction period to the expansion.Moreover, as the author points out, such lags should not be observed inrelatively unassociated liquids, but might occur when polymeric COM-pounds are dissolved in them. This behaviour is exemplified by benzene,which alone shows no lag, whereas 1% solutions of polystyrene in benzeneshow a short lag. These observations are of great interest and, if extended,might yield interesting information concerning the structure of liquids.It is to be hoped that the influence of temperature will be investigated,since this should reduce the number and complexity of the water polymers,but not affect the polystyrene solute molecules, and would thus discriminatebetween the two systems.8 (ti).A similar division into primary and secondary processes is madein photochemistry. The two subjects are similar only in respect of secondaryprocesses. In all other respects they differ very widely.734. Secondm Proceaes, Ionic Yield, and the cc Cluster '' !Cheory.-Inthe preceding section, emphasis was laid on the view that, chemically,the most important products of the primary act are the uncharged atomsand radicals.An alternative hypothesis, formerly widely held, is the'' cluster theory " in which uncharged species are disregarded and the ionsregarded as the more important, The essence of the cluster theory, asproposed by 8. C. Lind,0, 7 is that one or both members of an ion pairact as nuclei, to which neutral molecules are drawn and held as clustersby polarisation forces. Reaction was conceived as occurring on chargeneutralisation, all the molecules of the complex undergoing chemical changeand the requisite energy of activation being provided by the heat of neutral-isation. For example, the oxidation of methane was written as (02CH,02)+ +(0,-CH,O,) --+ 2C0, + 4H,O. Such a theory is clearly bapable ofaccounting for ionic yields slightly in excess of unity, and for the usualkinds of variation of M / N with pressure, since the size of the cluster willbe related to the initial pressure.In its simple form, specific ion clusterswere assumed and de~ignated,'~ but later work by W. M ~ n d , ' ~ E. K. Rideal,76and R. S. Livingston77 has been concerned with the nature of the inter-72 F. H. Krenz, Canadian J . Res., 1948, 26, 647.73 F. S. Dainton, Research, 1948, 1, 488.74 See, e.g., ref. 6, table VIII, p. 100.76 Troisibme CoszseiiE c h h . Solvay, 1928, 1.7 7 Bull. SOC. chim. Belg., 1936, 45, 334.7 6 Bull. SOC. chdrn. Belg., 1934, 43, 100DAINTON : CHEMICAL RBIACTIONS INDUCED BY IONISING RADIATIONS. 18action of the central ion with its surrounding molecules. The main evidencefor clusters has been recently reviewed.'*Whilst values of ionic yields calculated on the cluster theory are claimedto be in quantitative agreement with e~periment,'~ and whilst the averagedistribution in the system will include some aggregation of molecules aroundcharges, there are several major objections to adopting the cluster theoryas a general mechanism for radiochemical reactions.Thus, (a) Essex andco-workers 62 have shown that, under conditions where ion neutralisationis eliminated or considerably reduced, the ionic yield is only slightly affected,and ( b ) excitational processes leading to, and experimental evidence for,uncharged atoms and radicals known to induce the chemical change observedhave no place in the theory.In the ensuing pages the " atom-radical " theory of the primary actwill be most frequently employed and it will be assumed that the secondaryprocesses are merely those reactions into which the uncharged products ofthe primary a c t would enter whatever their mode of formation-thermal,photochemical, or radiochemical.This " carry over " of information fromone investigation to the interpretation of another has been discussed byE. W. R. Stea~ie.'~The number of reactions which have been stimulated by radiation isvery large and the reactions mentioned in this Report have been choseneither because the primary act is well understood and exemplifies principlesalready mentioned, or because the observed kinetics have no parallel withother modes of initiation, or because the reaction is intrinsically importantand recent work has clarified a previously obscure mechanism.5. Single Inorganic Substances (excluding Water).-The deoornpogitionof solid and gaseous inorganic substances has been extensively investi-gated.6, 7p No coherent theory exists for the former, except where thesolids can be detonated by impact, e.g., nitrogen tri-iodide and bariumazide.81 Hydrogen iodide has been studied in all three phases.82 In thegaseous phase the oxygen-ozone system,83 the oxides of nitrogen,s4 andvarious hydrides, e.g., NH3,62 ND3,85 HI 82 and H,S 86 have been muchstudied.A feature of many of these reactions is that the ionic yield exceeds78 R. S. Livingston and S. C. Lind, J . Amer. Chern. SOC., 1936, 68, 612; S. C. Lind,ref.12, p. 437, and J . Chern. Physics, 1939, 7, 790.70 Ref. 12, p. 441.M. Haissinsky and R. J. Walen, Compt. rend., 1939, 208, 2067; E. Feenberg,W. E. Garner and C. H. Moon, J., 1933, 1398.Physical Review, 1939, 55, 980.82 P. Giinther et aZ., Bev., 1943, 75, B, 2064; Giinther and Leichter, 2. physikal.83 S. C. Lind, Monatsh., 1912, 32, 295; P. C. Caprim and R. Cloetens, Bull. SOC.84 G. R. Gedye, J., 1931, 3016; W. Mund and R. Gillerot, BulE. SOC. c h h . Belg.,85 J. C. Jungers, J . Physical Chem., 1936,40, 155.86 W. Mund et al., Bull. SOC. china. Belg., 1934, 43, 49, 100; 1937, 46, 129; P. Gal-Chem., 1936, B, 34, 443 ; K. G. Brattain, J . Physical Chem., 1938,42, 617.chim. Belg., 1935, 44, 441 ; B. Lewis, J . Physical Chern., 1933, 37, 533.1929, 38, 349.mont, {bid., 1932, 41, 43130 GENERAL AND PHYSICAL OHEMISTRY.unity and is several times larger than the quantum yield of the correspond-ing photochemical reaction, which is strongly suggestive of more than oneradical being formed per ion-pair. 87The spin isomerisation of hydrogen under the influence of a-rays has avery large ionic yield, 800-1000, too great to be accounted for by clusteringand strongly suggestive of a chain mechanism.P. C. Capron l7 found therate of destruction of para-hydrogen by a-particles from radon in a sphericalvessel to be given by-d@H,]/dt = ke-lt. [pH,] . . . . . . (1)where A is the decay constant of radon. The ionic yield is therefore inde-pendent * of the dose rate and any reaction chain cannot undergo mutualtermination, a result which is somewhat surprising since in the high-tem-perature thermal conversion it is certain that the chains are stopped inpairs by recombination of hydrogen atoms.ss Capron therefore consideredthe possibility of the chain carrier being a proton, but, since no reactionsoccurred at -187", he suggested that a hydrogen atom is the effectiveagent.Reprodueible results were obtained in the presence of mercuryvapour which Capron found to be a retarding agent. These kinetic resultscould be explained by assuming the reaction sequence, (i) H, -A+- 2H,(ii) H + pH2 a OH,+ H, (iii) H + Hg --+ HgH, but H. EyringJ. 0. Hirschfelder, and H. S. Taylor 89 have calculated the equilibrium,constant of reaction (iii) and find that, at the partial pressures of mercuryconcerned, this reaction cannot be regarded as an efficient process forremoval of atomic hydrogen.They therefore conclude that the majortermination reaction is removal of atomic hydrogen a t the vessel walls.If a perfectly efficient wall removal was assumed and since the dimensionsof the reaction vessel and source, the velocity constant of the propagationreaction (ii),88 and the diffusion constant of atomic hydrogen throughmolecular hydrogen were known, a rate of formation of hydrogen atomscould be calculated which accounted for the observed reaction rates , pro-vided that six hydrogen atoms were formed per 33 ev. of w a y energyabsorbed.The most important feature of these authors' work is that it containsthe fist close theoretical analysis of a primary act.Equilibrium dis-tribution of doublet (H, H,+) and triplet (H, H,+H,) clusters are calculatedon reasonable assumptions, and the values indicate that larger clusters areimprobable. The ion H,+ is regarded as constituting upwards of 90% ofthe primary ionisation. The velocity constant of the reaction (iv), H2+ +H2-+ H,+ + H, is calculated to be 1.25 x 1015 C.C. mole-l sec.-l, andthis reaction therefore predominates at reasonable pressures. The neutral-s' Ref. 4, table XX; ref. 27, table I.8 s A. Farkas, 2. physikal. Chem., 1930,10, B, 419.89 J. Chem. Physics, 1936, 4, 479.? Note that Eyring et al. (ref. 4, p. 491) mistakenly remark that " the M / N yieldwas dependent on the radon intensity, etc.DAINTON : CHEMICAL REACTIONS INDUCED BY IONISINQ RADIATIONS.21isation reaction of H,+ with an electron is considered to yield between 2and 3 hydrogen atoms. Hence the total net yield of hydrogen atoms fromthe ion pair H,+ + electron is between 3 and 4 [cf. section 3 (iv) (a)]. Thepart of W (= 33 ev.) not used in ionisation is regarded as causing excitationof hydrogen molecules (lC + Q ) , a process which requires 12 ev., andresults in dissociation of the hydrogen into two hydrogen atoms.6. Binary Inorganic Mixtures.-When one component, the solvent, is ingreat excess, the products of the primary act will be derived largely fromthat component. When the chemical change observed is due solely toreaction of these products with the solute, it is referred to as "indirectaction" of the radiation [cf. section 3 (v)].Few examples are known ofindirect action on systems in which both components areHydrazine, a t concentrations of 0.05 to 0.1% in hydrogen, is reduced toammonia by the action of a-rays from radon, with an ionic yield of 3.91The mechanism suggested includes : H, --+ 2H ; N,H, + H + NH, +NH,; ZNH, + M + N,H, + M. Decomposition of hydrazine andhydrogen sulphide by indirect action is also possible in excess of nitrogen,but in this case the mechanism is less well understood. P. Gunther andL. Holzapfelg2 have studied the decomposition of ammonia, and thesynthesis of water, by indirect action of X-rays in an excess of xenon. Aradical mechanism is here difficult to formulate.Some of the reaction isdoubtless due to collisions of excited xenon atoms with the reactants andmay result in the dissociation of the latter. The point has also been madeby H. Eyring 93 that the xenon ion is electronically merely a very reactiveform of an iodine atom. Part of the reaction in this case might thereforebe represented as Xe+ + NH, -+ (XeH)+ + NH,.Most radiochemical reactions in inorganic mixtures are systems in whichboth reactants make their contributions to the primary act, which is there-fore rather complex. The reactions investigated include addition reactions,H, + C1, + 2HCl,94 H, + Br, =+ ~HBI-,'~, 95 H, + I, + 2HI,s2 CO 4-C1, ;." COCl,,96 CO + 0.50, CO,; 97 isotopic exchange reactions,e.g., H, + D, T+ 2HD; 98 and many oxidations, e.g., CnHzIl + , + 02,99N, +- O2.lo0 Many of these, particularly those involving halogens, haveThe first investigators to achieve indirect action through hydrogen were W.Duaneand G. L. Wendt (Physical Review, 1917, 10, 116).91 A. van Tiggelen, Bull. SOC. chim. Belg., 1938, 4'9, 577.98 2. physikal. Chem., 1937, 38, By 211.93 J . Chem. Physics, 1939, '4, 792.94 F. Porter, D. C. Bardwell, and S. C . Lind, J . Amer. Chem. SOC., 1926, 48, 2603;S. C. Lind and R. S. Livingston, ibid., 1930, 52, 593; S. Gotzky and P. Giinther, 2.physikal. Chem., 1934, 26, B, 373.95 E. F. Ogg, J. Physical Chem., 1939, 43, 399.O 6 H. N. Alyea and S. C . Lind, J . Arner. Chem. SOC., 1930, 52, 1853.9 7 8. C. Lind and C. Rosenblum, Proc. Nut. Acad. Sci., 1932, 18, 374.98 W.M u d , L. Kwrtkemeycr, M. Vanpee, and A. van Tiggelen, Bull. SOC. chim.99 Lind and Bardwell, J . Amer. Chern. SOC., 1926, 48, 2336.Belg., 1940, 49, 187.loo R. Cloetens, Bull. SOC. chim. Belg., 1936, 45, 9722 GENERAL AND PHYSICAL UHEMISTRY.photochemical counterparts which itre chain reactions, and the aimilarityof kinetics suggests the participation of halogen atoms as chain centres.In several cases, detailed analysis of the primary act has shown that thaatoms are formed at this stage, of a kind and number t o enable quantitativeinterpretation of the experimental results.lol7. Single Organic Substances.-Much qualitative work OQ the stabilityof organic oompounds to rays from radium was carried out by A. Kaila,n.loMany of his experimepts were conducted with access to air and with wetmaterials.Nevertheless, the essential features of the radiolysis weradeteoted and have been contirmed by later work. Saturated compoundatend to break at a weak bond and to lose some easily eliminated group.If the remaining fragment is a radical, it may dimerise, and, if it ia &Punsaturated molecule, it will be polymerised. Thus the paraffins aredehydrogenated and the residue consists of liquid hydrocarbans, whethera-particles 99 or high-speed electrons lo2 are used. Similarly, alcohols yieldhydrogen and polymerised aldehydes lo3 amongst the products. Irradiationof chloroform by y- or X-rays causes evolution af chlorine in the initialstages of reaction.lO4 Reabsorption of some of the chloride with formatianof hydrochloric acid and hexachloroethane may occur subsequently.Unsaturated compounds, e.g., olefh~,~O~ cyanogen,lo6 carbonyl Io3 andvinyl compounds 29 polymerise as freely under irradiation as by any atharinitiating action.The polymerisation of acetylene has been very closelystudied because it appeared to be a clear example of it reaction proceedingby the ion-cluster mechanism.107 The evidence for this view as against thenormal radical-type chain polymerisation was principally the apparentconstancy of the ionic yield = 20 over a wide variety of conditions, includ-ing the presence of non-reaetive diluents such as the inert gases or nitrogen.The mechanism, suggested by Lind, was that 19-20 acetylene moleculesclustered about either a C,H,+ ion or an inert-gas ion.On neutralisationthe whole complex was supposed to liberate, as the only product, a solidyellow polymer of formula (C2H2)20. Substantially the same results wereobtained and the same mechanism proposed for dideuteroacetylene, C2D2. lo8The insolubility of the product prevented determination of its molecularIo1 H. Eyring, J. 0. Hirschfelder, and H. S. Taylor, J. Chem. Physics, 1936, 4, 590;loa C. S. Schoepfle and C. H. Fellows, Ind. Eng. Chem., 1931, 23, 1398.lo3 J. C. McLennan and W. L. Patrick, Canadian J . Re., 1931, 5, 470.lo4 W. B. S. Bishop, J . Proc. Sgdney Tech. Coll. %kern. SOC., 1933, 5, 66, quotedlo5 G. B. Heisig, J . Amer. Chem. Soc., 1931, 53, 3245; J . Physical Chem., 1936,lo6 D.C. Bardwell, J. M. Perry, and S. C . Lind, J . Amer. Chem. SOC., 1926, 48, 1556.lo' Ref. 6, G. Glockler and F. W. Martin, Trans. EZectTochem. Sou., 1938, 74, 67;J. C. McLennan, M. W. Perrin, and H. J. C, Ireton, Proc. Roy. SOC., A , 1929,135, 246;W. Mund, C . Velghe, C . Devos, and M. Vanpee, Bull. SOC. chim. Belg., 1939, 48, 269.lo8 S. C. Lind, J. C. Jungers, and C. H. Schifflett, J . Amer. Chem. SOC., 1935, 5'9,1032.1938, 6, 783.in Chem. Abs., 1934,28, 2212; G. Harker, Nature, 1934, 133, 378.39, 1067; 1939, 43, 1207DAlNTON : CBEMICAL REACTIONS 1NDUCED BY IONISING RADIATIONS. 23weight. Recently, it has been shown that the electron micro-photographsof this material are not those expected of a substance C40H40,'09 More-over, this is not the only product of reaction.Benzene is also formed, andunder suitable conditions it may represent as much as 20% of the product.l1°Although these facts render the original cluster hypothesis for this reactionuntenable, they do not necessarily exclude an ionic rnechanism,lll whichappears to be the preferred method when unsaturated hydrocarbons arepo1ymerised.ll28. Binary Organic Mixtures.-Very little systematic work has beenpublished in this field. Direct action has been observed,l13 and indirectaction with an organic compound as solute 114 or s01vent.l~~9. Water and Dilute Aqueous Solutions.-The action of radiations onwater is of great importance, for both its intrinsic interest and its relevanceto the study of the biological action of radiation^.^ All the peculiar featuresof radiochemical reactions, e.g., radiochemical equilibrium, indirect action,influence of track density, etc., are here displayed, Several reviews areavailable.116(i) Experimental results. (a) Ice, Water, and Steam. X-Rays haveno action on ice, unless it contains oxygen, when hydrogeri peroxide isformed. The yield decreases with temperature, becoming zero at - 116°.117On the other hand, a-rays decompose ice even in the absence of oxygen,with an ionic yield of about 0.05 to 0-1 molecule of water destroyed per35 ev. absorbed. This reaction does not appear to be temperature dependent,but, whereas P. Bonet-Maury 117 claims that the product is H,O,, W. Duaneand 0. Scheuer 118 stated that this is exclusively hydrogen and oxygen.Water uapour appears to be even less affected by a-rays, Duane and Scheuerfinding an ionic yield of about 0.01.However, electrons appear to bringabout speedy decomposition. Thus the xenon-sensitised X-radiolysis 119results in formation of much hydrogen in unit yield in amounts strictlyproportional to the dose. Likewise, cathode rays rapidly set up the equi-librium, 2H,O In addition, there is much spectro- H,O, + H,.l2olog J. H. L. Watson, ref. 12, p. 470.l10 C. Rosenblum, ref. 12, p. 474.ll1 W. M. Garrison, J. Chem. Physics, 1947, 15, 78.112 See, e.g., C. E. H. Bawn, " The Chemistry of High Polymers," London,113 E.g., Halogenation of CO- and C,H, : ref. 6 and H. N. Alyea, J. Amer. Chem.114 P. Giinther and H. Theobald, 2.physikal. Chem., 1938, 40, B, 1.116 L. Baumeister and R. Glocker, ibid., 1921, 9'4, 368; E. Broda, Nature, 1943,116 C. 33. Allsopp, Trans. Paraday SOC., 1944, 40, 79; 0. Risse, Ergebn. Physiol.,11' P. Giinther and L. Holzapfel, 2. physikal. Chem., 1939, 44, B, 374; P. Bonet-118 Radium, 1913, 10, 33; Compt. rend., 1913, 156, 466.llV P. Giinther and L. Holzapfel, 2. physikal. Chem., 1939, 48, B, 346.lZo M. Kernbaum, Radium, 1910, 7, 242.1948.SOC., 1930, 52, 2743.151, 448.1930, 30, 242; H. Fricke, Cold Spring Harbor Symp., 1936, 3, 65.Maury and M. Lefort, Nature, 1948, 162, 38124 GENERAL AND PHYSICAL CHEMISTRY.scopical and mass-spectroscopical data on the break up of water by slow-electron bombardment and in discharges.121Many of the thirty-five or so papers which have been published on waterappear to contain contradictory results.The reasons for this are the pro-found effect exerted by dissolved air, the existence of a radiation-sensitisedback reaction, and the inherent instability of one of the reaction products.Despite such diiliculties the following facts have been established. (a) Watercontaining dissolved oxygen is converted into hydrogen peroxide, whatevertype of radiation is used,122 and there is evidence that the amount of H202so formed is proportional to the dose and increases with the concentrationof oxygen present initially and with temperature. (b) The extent of reac-tion is less in ice than in water, and there is thus a discontinuity in theyield a t 0°.1175 118 (c) By use of carefully de-aerated water and massive radi-ation, i.e., a-rays, the products of reaction are hydrogen peroxide andsometimes oxygen, in amounts which together are equivalent to the hydrogenevolved.71, 123 The yield does not appear to depend on temperature butdecreases abruptly on freezing.117 ( d ) When X- or y-rays or fast electronsare the radiation employed, the hydrogen peroxide concentration formed isvery low, and in some cases undetectably (e) Certain compoundswithin a very wide range of chemical substances, when added to water,raise the H202 concentration enormously, without necessarily being affectedthemselves.89~ 125 (f) Hydrogen and hydrogen peroxide are the primaryproducts, and oxygen is formed, not initially, but as the result of somesecondary processes.71Irradiation of solutions containing reduc-ing agents leads to liberation of hydrogen and oxidation of the solute,e.g., Fe++ salts --+ Fef++ salts; 126 nitrites --+ nitrates.127 The presenceof dissolved oxygen increases the rate of oxidation and prevents evolutionof hydrogen; but, as soon as the oxygen is exhausted, the rate falls to thevalue appropriate to de-agrated water and the evolution of hydrogen com-men~es.3~9 128 If the solute is an oxidising agent, e.g., ceric sulphate,potassium dichromate, it is reduced and oxygen is evolved; or, if the soluteis organic, e.g., formic acid, carbon dioxide may be produced.Whenneither oxygen nor hydrogen are detected, it is usually because the solute(b) Dilute Aqueous Solutions.121 For references see Dainton, ref.12, p. 517.lZ2 F. L. Usher, Jahrb. Rad. Elekt., 1911, 8, 323; 0. Risse, 2. physilc’al. Chem.,1929, 140, 133; H. Fricke, J. Chem. Physics, 1934, 2, 556; J. Loiseleur, R. Latarjet,and T. Caillot, Compt. rend., 1941, 213, 730; Bonet-Maury and Lefort, ref. 117.123 C. E. Numbergar, J . Physical Chem., 1937, 41, 431.124 0. Risse ; 122 H. Fricke and F. R. Brownscombe, Physical Review, 1933, 44, 240 ;H. Fricke ; 122 Piffadt, Compt. rend. Soc. B i d , 1939,130,43 ; Giinther and Holzapfel ;Loiseleur et al.; 122 Bonet-Maury; 117 A. 0. Allen.71126 H. Fricke and E. J. Hart, J . Chem. Physics, 1935, 3, 596.lZ6 H. Fricke and S . Morse, Phil. Mag., 1929, 7, 129; H. Fricke and E. J. Hsrt,lZ7 H. Fricke and E.J. Hart, ibid., 1938, 3, 366.lZ8 N. A. Shishakov, Phil. Mag., 1932, 14, 198.J . Chem. Physics, 1935, 3, 60DAINTON : CHEMICAL REAUTIONS INDUUED RY IONISINB RADIATIONS. 25undergoes neither reduction nor oxidation, e.g., it may be polymerised orhydrolysed. The magnitude of the chemical change is often proportionalto the dose and independent of solute concentration over wide 12'For example, this is true of the enzyme carboxy-peptidase, even when it ispresent to the extent of 14% by weight. This constancy of ionic yield isproof that under these conditions the change in the solute is due to therate of energy absorption in the solvent, i.e., that the action is indirect(cf. section 6). However, there is also evidence that a critical concen-tration exists, below which the ionic yield decreases with falling solutecon~entratioii.~~~~ l30 It also seems likely that (a) in the concentrationrange where M / N is constant, different types of radiation may be associatedwith different ionic yields,131 and ( b ) the value of the critical concentrationis determined partly by the nature of the solute and partly by the nature ofthe radiation.Certain solutes, notably large organic molecules of biologicalimportance, subject to indirect action a t concentrations above any real orhypothetical critical value decay exponentially ( i e . , according to a first-order law) throughout a r ~ n . l 3 ~ This suggests the interpretation, nowaccepted, that only that part of the effect of the radiation on the waterwhich is proportional to the percentage of solute remaining is transmittedto the solute.The remainder of the energy is therefore assumed to betransmitted to the soluble product into which the reactant is ~0nverted.l~~When two or more solutes of comparable concentration and reactivity arepresent, there is competition between them; when they are of differentreactivity, the more reactive is transformed preferentially, thereby pro-tecting the less rea~tive.l3~ Pew data are available concerning the effectof temperature 135 and dose rate.37Most of the data summarised above can be inter-preted on a non-cluster mechanism.It was first suggested by 0. Risse in 1929 136that the assumption that X-rays dissociate water into hydrogen atoms andhydroxyl radicals and that these species then dimerise, would account forthe formation of hydrogen peroxide and hydrogen and for the doubling ofthe ionic yield in the X-ray oxidation of ferrous sulphate solution by dis-solved oxygen.I n the same year the capacity of water vapour containinghydrogen atoms and hydroxyl radicals to behave in the dual role of bothan oxidising and a reducing agent was recognised by G. I. Lavin andF. B. Stewart.63 During the following decade the investigations of J. Weiss(ii) -Interpretation.(a) The Primary Act.lz9 H. Fricke, 3.3. J. Hart, and H. P. Smith, J. Chem. Physics, 1938, 6, 228.130 W. Stenstrom and A. Lohmann, J. Biol. Chem., 1928, 79, 673.131 L. H. Gray, W. M. Dale, and W. J. Meredith, private communication.lS2 H.Fricke a d B. W. Peterson, Amer. J. Roentgenol., 1927, 17, 611.133 W. M. Dale, W. J. Meredith, and M. C. K. Tweedie, Nature, 1943, 151, 281.134 W. M. Dale, Biochem. J., 1942, 36, 80.136 T. Alper, Nature, 1948, 162, 616 ; W. Minder and A. Liechti, Ezperientia, 1946,lSe Strahhntherapie, 1929, 34, 6.81.2, 41026 GENERAL AND PEYSICAL CHEMISTRY.and others 137 demonstrated the existence of ready electron-transfer pra-cesses involving hydrogen atoms or hydroxyl radictds in aqueous media,and in 1944 Weiss 13* proposed that the hydrogen atoms and hydroxylradicals present in water subjected to irradiation were formed by loss ofan electron from an OH- into a neighbouring H+ ion, thus : (H0)-H+ +radiation -+ HO + H. He further pointed out that the recombinationreaction, H + OH ---+ H,O, would proceed very easily by the Franck-Rabinowitch mechanism, and that the tendency of the hydrogen atom todonate an electron to, and of the hydroxyl radical to accept an electronfrom, a solute accounted for the oxidising and reducing properties ofirradiated water ; e.g.:Reduction .- He + Ce4+ --+ Ce3+ + H+ ; the excess of OH ultimatelyOxidation : HO- + Fe2+ + Fe3+ + OH-; the excess of H ultimatelyIt is now realised that these simple ideas require considersLble modific-ation, and the picture of the primary act which is in best accord with thedata may be summarised as follows. Transfer of energy from the fastcharged particles to the water molecules which they encounter will producethe following effects.The principal ions so formedare likely to be H20+ (which rapidly reacts to form H+ aq.+ OH withconsiderable energy release), H+ (and the associated OH radical), OH+(and the associated H atom). These will he distributed along the trackwith a concentration proportional to the specific ionisation. Since theradical ion will probably react rapidly with neighbouring water moleculesaccording to HO+ + (H,O), + H+aq. + ZOH, the net instantaneous effectwill be of a column of small cross-section containing predominantly OHradicals with a few H atoms. Some of the hydroxyl radicals may beelectronically excited (,C) and both species may have excess of translationalor internal energy. Such translationally non-average entities will bereferred to as “hot,” because their effective temperatures will be abovenormal. The ejected secondary electrons may have Considerable energywhich will be lost in ionisation and other processes.On the average, suchelectrons will travel considerable distances before their speeds are reducedto a value which permits capture by the only species present in quantitywith appreciable electron affinity, namely, water molecules. H,O- ionswill thus be formed over a much wider area and in lower concentrationthan are the positive ions. This difference in concentration will be themore marked the heavier the ionising partiole, Since H,O- ions break downon hydration, H20- -+- OH- aq. + H, the total effective action of theionisation processes is formation of H + OH in somewhat uneven con-centration, but both entities will occur in increasing concentratios as theend of the track is appr0a~hed.l~~forming H202 via molecular oxygen.forming H,.(1) Ionisation of the water molecules.lS7 See Ann.Reports, 1947, 44, 60. Is@ Nature, 1944, 153, 748DAINTON : CHEMICAL RBACTIQNS INDUCED BY IONISING RADIATIONS. 27( 2 ) Excitation. Both the primary particle and secondary electronsexcite some of the water molecules with which they collide. If 33 ev. isthe total energy required to create an ion-pair, possibly 12-14 ev. may beused in excitation only. Part may be used to excite vibrations in the(‘ micro-icebergs.” The slowness of the degradation of this internal energyto heat is manifested in the (( lag ” in contraction after the radiation sourceis removed from pure water.72 Much of the 12-14 ev.may be employedin direct dissociation of water molecules, Le., H20 + H(W) + OH(2X or ,II).Tho overall effect is thus H2Q --+ H + OH, but it is improbable thatany appreciable amount is formed by direct electron transfer,(b) Secondary Processes. (1) Decomposition of water. Diffusion ofradicals and atoms will occur within the tracks, and also from the tracks.The latter process will lead to intermingling of radicals and atoms origin-ating from different tracks. It is important to know whether such adiffusion pracess follows the normal mechanism in liquids, and thereforewhether the diffusion coefficient can be regarded as of the same order ofmagnitude as that of known molecules of comparable size through water,or whether it occurs by a more rapid process, The possibility of a Grotthuss-type transport of H or OH through a water polymer unit, i.e., HO +H(H,O),OH --+ (H,O),+ + OH, cannot be overlooked.Experiments onthe degree of enrichment of oxygen gas evolved from a dilute solution ofhydrogen peroxide in water which is several-fold enriched in H2180 indicatethat the exchange reaction, H160 + H2180 + H2160 + HlsO, is notunduly fast.139 It would therefore appear that in respect of the OH radical,a t least, diffusion from the tracks occurs by normal processes. Competingwith the diffusion are the ‘( combination ” and (‘ recombination ” reactions.The latter is the reactian, H + OH --+= H,O, and may concern a hydrogenatom and a hydroxyl radical formed from different water molecules situatedsome distance from the point of recombination.It is unlikely to requirean energy of activation and probably occurs a t every collision. On theother hand, the recombining radicals may be derived from the same watermolecule, recombination occurring within the solvent “ cage ” in whichthey were formed.70 Both types of recombination are exothermic and willprovide the means by which much of the energy of the radiation is con-verted into heat. The important difference between the two is that theradicals recombining by the former mechanism will have appreciable separateexistences between formation and destruction and may therefore be regardedas more available for reaction with any solute added or produced.By(‘ combination ” reactions we denote reaction between like species, namely,2H or 20Hy the products of which are H, and H,O,, re~pectively.~~ Suchproducts will accumulate most rapidly where the local concentration of theappropriate radicals is highest and the concentration of the other specieslowest. Thus, H,O, will be formed in the centre of the track and H,over a wider area, both products appearing in larger amounts as the13e E. Collinson and F. 8. Dainton, unpublished28 GENERAL AND PHYSICAL CHEMISTRY.end of the track is approached, and both probably derived from the“ ionisational ” rather than from the “ activational ” hydrogen atomsand hydroxyl radicals, since the latter type is better placed for recom-bination.Furthermore, the lower the energy and the higher the massof the particulate radiation, the more favourable are the conditions forformation of hydrogen peroxide and hydrogen, a result which has beenwell established.71 It has been argued that dipole repulsion forces causereactions between hydroxyl radicals to require an energy of activation,140and some experimental support exists for this.141 The fact that the yieldof hydrogen peroxide in de-&rated water decomposed by a-rays is inde-pendent of temperature 117 shows either that this is not true, or that theradicals are in possession of the necessary energy of activation. Thelatter suggestion is in keeping with the notion that the radicals are “ hot.”71The sharp decrease of ionic yield on freezing could be due to the polymolecularstructure of ice which might increase the temporary “ trapping,” followedby delayed unproductive release, of a greater proportion of energy than inliquid water .The presence of dissolved oxygen enhances the yield of hydrogen per-oxide owing to the fact that some of the hydrogen atoms react readily accord-ing to H + 0, + HO,, the hydroperoxide radical so formed being sub-sequently converted into hydrogen peroxide.This mechanism is respon-sible for most of the yield of hydrogen peroxide in X-irradiated aeratedwater, and, since this yield increases with rise of temperature, one of thesesteps must require appreciable energy of activation. This might be thedismutation, 2H0, -+ H,O, + 0,.As the concentrations of dissolved products build up during an irradi-ation, they will diffuse from the tracks and become increasingly liable toattack by those hydrogen atoms and hydroxyl radicals which have appreci-able lifetimes before recombination.Possible reactions which are known tooccur with great facility at room temperature are (i) OH + H, ---+ H,O + H,(ii) OH + H,O, --+ HO, + H,O, and (iii) H + H,O, --+- H,O + OH ;together with (iv) HO, + H,O, -+ H,O + OH + 0, and (v) H +0, + HO,, these provide for a net back reaction, H, + H,02 + 2H20,which will be a chain process. If a solute is present which reacts withone or both of the radicals with great facility? but which, owing to thevery high local concentration of “ ionisation ” radicals formed with massiveradiation, cannot gain access to these before combination? then, as Allen~uggested,~~ the back reaction will be inhibited and the equilibrium dis-placed towards the products.This author has argued that such a dis-placement effect is to be expected from all solutes, not only from thosewhich react with both radicals, e.g., vinyl compounds and hydrolysablesolutes, but also from those which react with either the H or OH only.The reason is that prolonged irradiation will establish a balance betweenoxidised and reduced forms of the solute, the position of the equilibriumlP0 J. Weias, Tram. Paraday Soc., 1940,30, 866. D. E. Lea, ibid., 1949,45, 81DAINTON : CHEMlUAL RICAOTIONB INDUOED BY IONISING RADIATIONS. 29being determined by the standard redox potential.Thereafter, both Hand OH will be equally destroyed, and the back reaction suppressed. Onthe other hand, if high-energy y-rays are used, very few radicals will beformed in the immediate neighbourhood of similar radicals and a veryreactive solute present in sufficient concentration might destroy practicallyall the radicals, ionisational as well as activational, before combinationoccurred. The forward reaction would then also be suppressed and nohydrogen peroxide or hydrogen be detected. Much more work requiresto be done on this aspect and the more puzzling “gas phase volume ”effect described by Allen.Solutes may undergochemical transformation by one, or a combination, of the following mechan-isms: (i) photochemical change due to absorption by the solute of partof the cerenkov radiation; (ii) excitation of the solute when it deactivatesexcited water polymers ; (iii) reaction with hydrogen peroxide or hydrogen ;and (iv) reaction with hydrogen atoms or hydroxyl radicals formed in theprimary act.These mechanisms are arranged in order of increasing im-portance. Although process (i) must occur, the fraction of the total reactioneffected in this manner is probably very slight. The second mechanismmay be operative, since it is known that even low concentrations of ferroussulphate destroy the ‘‘ lag ” in energy dissipation, but the magnitude of theeffect is The hydroxyl radical and the hydrogen atom may beregarded as very reactive forms of hydrogen peroxide and hydrogen,respectively, and it is therefore surprising that it is necessary to includemechanism (iii) in addition to (iv).The most direct experimental evidenceas to the mode of reaction in any particular system is obtained from studiesof the reactivity of the solute to hydrogen) hydrogen peroxide, hydrogenatoms, and hydroxyl radicals separately in the absence of any ionisingradiation.For this purpose reliable methods of generating hydroxyl radicals andhydrogen atoms in water are required. Hydroxyl radicals can be pro-duced (i) by the action of light of wave-length less than 3700 A. ondilute aqueous solution of hydrogen peroxide, H202 + hv + 20H(2x),(ii) by spontaneous or photochemical electron transfer from a powerfuloxidising ion to a water molecule of its solvation sheath, e.g., CO+++ aq.--+CO*+ aq. + H+ + OH, Fe+++ aq. + hv + Fe++ aq. + H+ + OH,(iii) electron transfer to hydrogen peroxide, e.g., Fe++ aq. + H20, -+Fe+++ aq. + OH- + OH, or (iv) oxidation of a strongly reducing ion bydissolved oxygen, e.g., V++ aq. + 02+ VO+ I- aq. + 20H. Methods whichemploy hydrogen peroxide have the marked advantage that, in the absenceof a solute, the hydroxyl radical initiates a chain decomposition of theperoxide and much oxygen is evolved. Inhibition, by a solute, of thisoxygen evolution is easily detected and can be used as a criterion of reactionof the substrate with the hydroxyl radical. Method (ii) involves cations ofhigh valency, and the presence of strong acid is often necessary to preventhydrolysis. Method (iv) is particularly valuable for effecting polymeria-(2) The chemical nature of indirect action in water.o30 QENBIRAL AND PHYSIUAL GHHMISTRY.ation of water-soluble vinyl compounds, since the oxygen whioh ig normallyan embarrassment owing to its capacity to cause induction periods is, in thiscase, effectively removed in the initiating reaction and can never exert itsretarding action.142In principle, hydrogen atoms could be generated by any prooess leadihgto acceptance of an electron by water.This requires a powerful electrondonor. A uniform concentration of hydrogen atoms might conceivably beachieved by using a highly reducing ion, aqueous solutiona of which spon-taneously evolve hydrogen, e.g., U3+. * Alternatively, photochemical stimul-ation of the electron transfer can be effected, and this method possessesthq advantage that the rate is not markedly temperature-dependent andhigh local concentrations of hydrogen atoms can be produced.Suchadvantages may be offset if the electron-aflnity spectrum of the conjugateoxidising ion falls in the same spectral region or if the solute forms a com-plex with the ion.l*g Moreover, the solutes which may be used are restrictedto those which are either transparent in the appropriate wave-length regionor are unaffected chemically by light in this region.Molecular hydrogen is rarely an effective reducing agent for aqueoussolutes, and most oxidising solutes are therefore considered to react tviththe hydrogen atoms. This may be a simple electron transfer, e.g.,I&+++ aq.+ H + Fe++ aq. + H+ aq,, or addition, e.g., reduction ofoxygen or methylene blue,143 or opening double bonds,27 or a combinationof the two, e.g., S2O8- + H --+ HS0,- + SO4-. It hag been demon-strated that acrylonitrile is polymerised and gas evolution prevented whenaqueous solutions of slightly acidified ferrous sulphate containing this sub-stance are illuminated with ultra-violet light.144 Part of the y- and X-ray-induced polymerisation of this monomer in aqueous solation may thereforebe attributed to the hydrogen atoms. Another chain reaction which isprobably partly initiated by hydrogen atoms is the radiolysis of hydrogehperoxide s01utions.l~~Most reducing solutes which react with hydrogen peroxide will alsoreact with hydroxyl radicals, but the converse does not necessarily hold.Radiochemical reactions in which hydroxyl radicals are presumed to play apart include single-electron-transfer oxidation of reducing ions, e.g.,Fe++ aq.+ OH + Fe+++ aq. + OH- aq., hydrogen-atom extraction,e.g., H,S + 20H __$. 2H20 + S,146 and C,H, aq. + OH -4- H20 +o.5Ph2,147 hydroxylation of aromatic nuclei, e.g., C,H6 _3 C,H,*OH,147and initiation of polymeri~ation.~7 In the la& two examples, the hydroxyl148 D. (3. I;. James and F. S. Dainton, unpublished.143 Colwell, Lancet, 1932, I, 932.144 F. S. Dainton, unpublished; M. G. Evans, private communication,145 H. Fricke, J . Chm. Physics, 1936, 3, 364.laQ J. Loiseleur, Compt. rend., 1942, 215, 536.14' J.Weiss and U. Stein, Nature, 1947, 161, 650.* Added in proof, March 27th, 1049. A wide range of these ions has bow been in-vestigated.142 None appeara to fulfil this r6quirementDAINTON : CHEMICAL REACITIONS INDUGHD BY IONISINQ RADIATIONS. 31group is readily detected in the reaction products. Most of these reactionswould be expected to require little energy of activation; and in keepingwith this it is found that temperature has no effect on the rate of oxidationof ferrous sulphate solutions by X- and y - r a y ~ , ~ ~ ~Solutes which are of biological importance present certain interestingohemical features. The chemical changes undergone are often not under-stood, but are associated with a drastic alteration of biological activitywhich is made the basis of assay.The methods available for identifyingthe active agent are thus reduced. Two examples must suffice. Theenzyme ribonuclease is inactivated by X-rays in dilute aqueous solution.Protection against such inactivation may be achieved by addition of organicreducing agents, e.g., thiol-containing compounds, an observation whichsuggests that hydroxyl radicals or hydrogen peroxide rather than hydrogenatoms or molecules are responsible. The enzyme is, however, fairly stableto O.O~N-H,O,, and it is concluded that hydroxyl radicals must cause theinactivation. E. Collinson, P. 8. Dainton, and (Mrs.) B. Holmes 14* haveconfirmed this directly by demonstrating that ribonuclease is inactivated,and inhibits the evolution of oxygen, when dilute hydrogen peroxide isilluminated by ultra-violet light.By contrast with this behaviour T. A l ~ e r l ~ ~has shown that hydrogen peroxide and not the hydroxyl radical is the activeagent in the X-ray inactivation of bacteriophage S.13, since (a) hydrogenperoxide is detected, (b) phage is inactivated by hydrogen peroxide, (c) theamount inactivated, plotted against time, shows a lag to be expected of aseries of consecutive steps, and (d) the reaction has a considerable tem-perature coefficient.Several independent attempts havebeen made which agree in general outlook, but differ in detail, to predictthe dependence of ionic yield on such variables as concentration, specificionisation, e t ~ . ~ * ~ All these treatments omit any consideration of the backreaction, an omission which is of less importance when solutes are presentwhich react easily with both hydrogen atoms and hydroxyl radicals.Thefollowing over-simplified treatment enables the important features to beemphasised. Let I be the dose rate (ev./W absorbed per unit volume perunit time), and 1%/2 be the net number of water molecules dissociated perWev. absorbed after allowance has been made for the almost instantaneousrecombination of radicals by the Franck-Rabinowitch mechanism. Denotethe concentration of any solutes by sI, slI, etc., and let kl’, kl”, etc., be therate constants for removal of the radicals by the appropriate solutes. Thus(3) The kinetics of indirect action.dnldt = 0.5kI - X k l t ~ ’ f i - (1%3 + E,)n2 .. . . . (2)where n represents the concentration of radicals, and is initially non-uniformthroughout the system, Tc, is the velocity constant for recombination ofunlike radicals which have been formed from different molecules, and k,D. E. Lea, ref. 4, Chapter 11; Weiss, Trans. Faraday Xoc., 1947, 43, 314;Dainton and N, Miller, X?th Indstw&. CoszgTeda, 1947 ; F. S , Dninton.’814* Unpublished32 GENERAL AND PHYSWAL CHEMISTRY.is the velocity constant for combination of like radicals in pairs to formhydrogen or hydrogen peroxide. Actually, the extent of mutual interactionof the radicals (the last term) will depend upon the specific ionisation of thetracks, the distribution of hydrogen atoms and hydroxyl radicals within thetracks, and their diffusion constants.The alternative , more quantitativeapproach * is concerned much more with the fractional number of radicalswhich have recombined at any instant in a track of given specific ionisation.If pl', p(', etc., are the probabilities that in the radical-solute collisionthe solute is destroyed, the rate of reaction = - Zds'/dt = Xpl'El's'n,When only a single solute is and the ionic yield M / N =present, two extreme cases are possible :Cpl'kl's' . n . I(a) E1'd > (k3 + E,)n, whence M / N = p1'k/2(b) El's' < (k3 + E,)n, whence MIN = pl'k,'s'[k/21(k3 + E4]*Thus a t high concentrations the ionic yield is independent of solute con-centration and dose rate, whereas at low concentrations the ionic yielddecreases with decreasing solute concentration and increasing dose rate.The value of s' a t which the dependence of ionic yield on s' commenceswill be determined by the relative values of El', and (k3 + E4).Very reactivesolutes will show type-(a) behaviour to lower concentrations than do lessreactive solutes, and use of "heavy " radiations which give large specificionisations will lead to change from type (a) to type (b) at higher concen-trations than " light " radiation. Several experiments have been reportedfor which the dependence of ionic yield on s' and type of radiation can beexplained in this way,73' l31 and N. Miller 37 has shown that change of doserate has no effect on M / N in region (a) for the oxidation of ferrous sulphatesolution.When the product of the reaction removes the radicals as efficientlyas the reactant, it is easily shown that, if no combination of radicals isoccurring [type (a)], then s = s0exp.( --- I t ) . Such exponentialdecrease of solute concentration with dose (It) has often been 0b~erved.l~~Protection of one solute sI by a second (&I) is easily seen from equa-tion (2), since the ionic yield with respect to sI is given byApplication of this equation enables the relative protection efficiencies ofvarious agents with reference to a given substrate to be assessed.lSThe above discussion relates to solutes which react with hydrogenatoms or hydroxyl radicals. For those rare cases in which the solute maybe inert thereto but reactive to hydrogen peroxide, we have three simul-taneous equations :290(MIN)' = pl'kE,'~/2(kl's' + kl"~'')dn/dt = 0.57~1 - (b + k4)n2d(H,O,)/dt = kpn2 - X:k,'(H202)s'- dd/dt = pl'kG'S'(HaOaHARTLEY : AQUEOUS SOLUTIONS OF SOAP-LIEE SUBSTANCES.33There will therefore be a lag phase before the hydrogen peroxide concen-tration reaches a stationary value, when the rate will be given byds’ - p,‘k,’s‘E,kIdtUnder appropriate conditions, protective action and exponential dependenceon dose would be observed, but in no case would the steady state ionic yielddepend on dose rate. The velocity constant k, refers to reaction betweenthe solute and hydrogen peroxide and is likely to have a much larger energyof activation than any rate constant hitherto mentioned. Greater tem-perature dependence is therefore to be expected for reaction via hydrogenperoxide than via hydrogen atoms or hydroxyl radi~a1s.l~~- - _2(k3 + k4) .Ck5”’1 am grateful to Messrs. E. Collinson and Y. Smith for unstinted helpin searching the literature.F. 8. D.2. STRUCTURE OF AQUEOUS SOLUTIONS OF SOAP-LIKE SUBSTANCES.A soap is an alkali-metal salt of a straight-chain fatty acid or mixtureof fatty acids having upwards of about 10 carbon atoms. On grounds ofrelative hvailability from natural sources and solubility in the desiredtemperature range, the most frequent mean numbers of carbon atoms are12, 16, and 18 in the saturated series and 18 (oleic acid is the cis-form) inthe series with one double bond in the chain.Numerous compounds of similar physical properties have becomeindustrially available in recent years, differing in the nature of the ionicgroup. Many of these have been the subject of extensive academic investig-ations, and, where the ionic group has been derived from a strong acid orbase and is not bulky or coinplex in structure, these compounds are similarin their behaviour and.better suited to exact enquiry, the complicationsintroduced by the hydrolysis of the salts of the weak carboxylic acids beingavoided.These compounds, too, have been placed by same authors under thegeneric title of “ soaps ”, while in other quarters and largely influenced bytrade policy, the extension of this title beyond its original meaning hasbeen vigorously opposed. The general title “ paraffin-chain salts ” proposedby the Reporter has been very widely used, but suffers from a potentiallyexcessive generality which is becoming increasingly important.With thedevelopment of synthetic compounds in this field, particularly products ofthe petroleum industry, the simple pattern of an unbranched aliphaticchain with a simple terminal ionic group is frequently discarded, sometimesthrough accident of easier synthesis, more often deliberately in order toobtain certain desirable physical properties. Compounds with more thanone chain, or branched chains, or containing mixed aliphatic and aromaticelements form solutions of markedly different structure.REP.-VOL. XLV. 34 GENERAL AND PHYSIUAL CHEMIBTRY.We shell therefore distinguish in this Report between normal parafin-chain salts, including soaps, where the parafin chain is unbranched andthe ionic group terminal (Le., normal in the sense in which normal primaryamyl alcohol is distinguished from secondary and iso-alcohols) , and complexparaffin-chain salts of various types.The deviation from the simple typeis, of course, frequently so small as to leave the most important physicalproperties largely unaltered.The industrial development of these compounds as emulsifying, wetting,and suspending agents has sought amongst other objects that of avoidingthe limitations of the true soaps due to the very low solubility of theircalcium and magnesium salts. This is not simply avoided by replacementof the carboxylic by the sulphonic group, as is sometimes loosely stated,since many of the sulphonates form equally insoluble salts with thesemetals.It is unfortunate that the alkaline-earth metals are the mostintractable in this respect. Soluble paraffin-chain salts of zinc, copper,and even iron are more numerous (even the fatty acids have solublecuprammonium salts).More generally resistant to hard water are the " reversed " salts, Le.,those with a surface-active cation. These do not appear to have a corre-sponding tendency to form insoluble salts with bivalent anions. Mostresistant of all are the numerous compounds where the ionic group hasbeen replaced by a non-ionic water-attractive group such as lightly poly-merised glycerol or ethylene oxide. These neutral amphipathic agents havenow a very considerable field of technical application. They have, how-ever, been the least studied of the whole group by academic research workers,mainly on account of the great difficulty of obtaining them in a pure state.Academic work on this group of compounds is still primarily concernedwith the nature of their aqueous solutions, and in this report we shall dealwith this subject almost exclusively.It is desirable to note, however,that some of the most important technical applications of the compoundshave very little relation to the more peculiar features of solution structuresince these appear in concentrations well above the range of most technicalinterest. It is a matter of regret that academic research has seemed hereunduly slow to discover a field of a t least equal intellectual interest andmore technical importance.One may note also that few of the morecomplex types of salt have found their way into academic literature. Wherethey have done so, technical preparations have most often been used andtoo little help seems to have been given by the preparative chemist to hisphysical colleague-a state of affairs which could be remedied by morepreparative activity on the part of the latter.andagain in 1940.2 The Reporter published a summarising article dealing withhis own theory of the structure of aqueous solutions of the normal saltsin 1939.3 I n this article we shall therefore consider fully only the workThe present subject came under review in these Reports in 10361 N.K. Adam, Ann. Reports, 1936, 33, 103.8 A. S. C. Lawrence, im., 1940, 87, 90. G. S . Hartby, K o l M - Z . , 1930, 88, 22HAR-TLEY : AQUEOUS SOLUTIONS OF SOAP-LIKE SUBSTANCES. 35which ha& appeared since these dates, except where reference to specificearlier papers is necessary for an understanding of the more recent develop-ments. There have been developments along three main branches of thesubject : (1) examination, mainly by already established methods, of themore complex salts, (2) study of the solvent power of aqueous solutions,and (3) application of X-ray diffraction technique to the problem.1. The Behaviour of the More Complex Salts.It was inevitable that the development of synthetic imitations of soapwould lead to that of amphipathic substances of more complex type which,while retaining the essential combination of a non-polar part of the moleculewith a strongly water-attracting part, altered substantially the geometricaldistribution.Leaving aside the mixed aryl alkyl salts developed technicallyas wetting agents and the complicated and impure sulphation products ofunsaturated glycerides (e.g., Turkey-red oil), the earliest reference to workon compounds of defined structure differing essentially geometrically fromthe normal paraffin-chain salts appears to be one * in which salts withbranched paraffin chains were noted to have remarkable powers of killingacid-fast bacteria. Unfortunately, in this work numerous salts and acidswere compared under conditions of undefined differences of physical form,some being undoubtedly in solution and others equally certainly existingas suspensions of more or less crystalline solids.Reference to aliphatic compounds where the chain is branched fromthe carbon atom adjacent to the ionic group was first made in the patentliterature in describing the compounds now known as Tergitols, the emulsi-fying properties of which were later described in the technical literature.6These are sulphates of secondary alcohols where the ionic group is nearerthe middle than the end of the chain and where the chain itself may bebranched.Later,' the Aerosols were announced. These are sulphonatesof dialkyl esters of succinic acid, the sulphur being attached to one of themiddle carbon atoms of the acid.Here, too, the ionic group is near themiddle of the chain, but, since the ester groups also will contribute insmaller measure to the water attraction, they are perhaps better regardedas compounds where two chains of moderate length are attached to oneionic head in place of the traditional single long chain of the soaps andearlier synthetic detergents. A convenient series of compounds of thistype was made by the Reporter by sulphonation of various dialkyl ethersof dihydric phenols.It was expected that these compounds would be able less easily to formthe normal type of dilute solution micelle than compounds containing thesame number of aliphatic carbon atoms in a single chain. The ReporterW. M. Stanley, G. H. Colman, C. M. Greer, J. Sacks, and R.Adams, J . Pharm.Exp. Ther., 1932, 45, 121.ti B.P. 440,539.B. G. Wilkes and J. N. Wickert, I d . Eng. Chem., 1937, 29, 1234.B.P. 446,668. G. S. Haxtley, J., 1939, 182836 GENERAL AND PHYSICAL UHEMISTRY.has advanced in a number of papers9 the view that the micelles whichform in dilute solutions of the normal paraffin-chain salts are essentiallyliquid and approximately spherical, their radius being determined by thedepth to which the end of a paraffin chain can reach when its ionic endgroup is anchored approximately in the surface. Replacement of one longby two short chains must reduce the maximum radius of this type of micelleand therefore very greatly reduce the number of ions in each micelle. Asa result, the surface of the micelle will be much less completely hydrophilic,and surface energy considerations would lead us to the conclusion thatthe micelle will be much less readily formed.On the other hand, an ion with two short chains will not be adsorbedon a macroscopic oil surface in water with much less energy advantagethan an ion with a single chain of the same total length.At a concen-tration where no aggregates exist in either solution we might expect thesingle-chain salt to be more surface active than the double-chain salt. Athigher concentrations, however, where micelles have formed in the aqueoussolution of the single-chain salt, the concentration of separate ions will bemuch higher in the double-chain salts. The surface activity of the latterwill therefore become greater, In a study of the interfacial tensions betweencarbon tetrachloride and cycbhexane and solutions of various compoundsof the ether series above rnentioned,lO it was indeed found that the double-chain salts, while less active than a single-chain salt in very dilute solutions,cause the interfacial tensions to fall much lower in higher concentrations.At a concentration of 0.08% the monosulphonate of the dioctyl ether ofresorcinol was found to have an interfacial tension against a mixture ofthe above non-polar liquids of only 0.04 dyne/cm.Only experimentaldifficulties of measurement prevented lower interfacial tensions beingrecorded. Normal paraffin-chain salts do not reduce interfacial tension toless than 1 dynelcm. in any concentration.It was noted in the above work that these salts are not so effectivewith aromatic oils, and a drift of interfacial tension with time was evidentowing presumably to slow transfer of salt to the oil phase.These salts areall much more soluble in organic liquids than comparable normal salts.Copper and nickel salts of Aerosol O.T., for example (O.T. is the sulphonateof the dioctyl ester of succinic acid), are obtained by evaporation as clearglasses which are indefinitely soluble in most organic liquids.11 Thepotassium salt of 1 : 3-dioctyloxybenzene-4-sulphonic acid is freely solublein benzene and chloroform, moderately in petrol, but almost insoluble indry acetone. That of 1 : 4-dioctyloxybenzene-3-sulphonic acid is verysoluble in all solvents with the exception of paraffins a t one extreme andwater a t the other.8’ 11 It is to be expected that these salts would, ongeometrical grounds, form less stable crystals and so be universally moresoluble, but this does not seem a fully satisfactory explanation.Onemight also expect a greater facility in the formation in organic solvents* Summarised in ref. 3.l1 I&m, unpublished observations.l o G. S. Hartley, Trum. Pura&ay SOC., 1941, 37, 130HARTLEP : AQUEOUS SOLUTIONS OF SOAP-LIKE SUBSTANCES. 37of the reversed type of micelle, considered to be present in solutions ofalkali and alkali-earth soaps in non-polar oils. This would lead to theexpectation of greater solubility in paraffis than in more polar solvents,which is not found to be general.More work on these almost absurdsolubilities would be desirable.It is well known that the soaps give rise successively to three new liquidphases as the concentration is increased.12 No phase-rule studies on theinore complex salts seem to have been made, but it is evident to anyonewho has worked with these substances that here too new phases can ariseand in much lower total concentrations. At ordinary temperatures thesulphonates of near-symmetrical dialkyl ethers of resorcinol have a limitedrange of concentration in which clear homogeneous solutions are obtained.Above this concentration a very fine emulsion is formed which can becoagulated by siniple salts to give a macroscopic second liquid phase. TheReporter has noted that crystals of potassium 1 : 3-dioctyloxybenzene-4-sulphonate, formed by slow evaporation of an aqueous glycerol solution,disperse spontaneously to the emulsion form if transferred to water.The crystals mentioned above are massive rhombohedra, obviously offundamentally different structure from the very thin plates formed by thenormal salts.Yet another unexpected property of these double-chainsalts is their ability to form stable thin films in aqueous and glycerol solu-tions. These surpass in length of life the standard ammonium oleatesolution,s but have evidently lower viscosity as they thin down by drainagethrough the coloured interference bands to the very thin black film muchmore rapidly than do soap solutions and remain almost indefinitely in theblack state when protected from evaporation and dust.P. A. Winsor lRhas observed that this thinning gives a characteristic ghost-like appearanceto a " head " of froth in these solutions (he worked with near-symmetricalsecondary sulphate esters) and that the normal salts are antagonistic tothis type of film. Addition of a small concentration of a normal salt pro-duces a solution with very transient frothing power. Further additionreplaces the stable ghost froth by a stable opaque froth similar to thatformed by soap solutions.A. W. Ralston and his collaborators l4 have applied the establishedconductivity technique to study the aggregation of solutions of these double-chain salts. They examined a series of dimethyldialkylammonium salts.They found here, too, the rather abrupt fall of equivalent conductivity a ta critical concentration, known to indicate the sudden formation of aggregatesin the normal salts.The fall was, however, not so great and the criticalconcentration not so low as in a solution of a normal salt with the samel2 See, e.g., J. W. McBain and M. C. Field, J . Physical Chem., 1926, 30, 1545;J. W. McBain, L. H. Lazarus, and A. V. Pitter, 2. physikal. ClLem., 1930, A , 147, 87;J. W. McBain and E. Gonick, 3. Amer. Chem SOC., 1946, 68, 683.l 3 Nature, 1946, 157, 660.l4 A. W. Ralston, D. N. Eggenberger, and P. L. du Brow, J . Arner. Chenz. Xoc.,1948, 70, 97738 GENERAL AND PHYSICIAL CHEMISTRY.number of aliphatic carbon atoms. For example, the critical concentrationsfor C8C,CC and C,oCloCC compounds are about 0 .0 3 ~ and 0.0025~ ascompared with interpolated values of about 0.002~ and 0.0004~ for theisomeric Cl,CCC and C,,CCC compounds. It is noteworthy that the dis-crepancy is much greater between the salts of lower molecular weight.No great difference was found between the C,C12CC and CloCloCC compounds.Extensive solubility work recently published by P. A. Winsor, whichwill be referred to in other connections below, includes measurements ofthe critical concentration l5 in a series of sodium sulphates of n-tetradecane,differing in the position of the carbon atom to which the sulphate groupis attached. The indicator method of M. L. Corrin, H. B. Klevens, andW. D. Harkins l6 was employed. It was found that the critical concen-tration rose throughout the series from that of the normal compound,1.7 x lOP3~, to that of the most symmetrical (7-sulphate), 16 x l O V 3 ~ .Consistently with H.V. Tartar’s observations, however, the relative changefor a displacement of one carbon atom is least when the compound is nearsymmetrical.J. W. McBain l7 and his collaborators have measured the freezing pointsin low concentrations of aqueous solutions of some of the double- andbranched-chain salts. They find a less abrupt fall of osmotic coefficienta t a less well-defined critical concentration than in normal salts, that forAerosol O.T., O - O O ~ N , being some ten times greater than for a normal saltwith 18 aliphatic carbon atoms. For Aerosol I.B. (diisobutyl) the criticalconcentration is about 0 .3 ~ . The ratio is consistent with the findings ofA. W. Ralston and his collaborators l4 for the dimethyldialkylamines.H. V. Tartar and his collaborators have reported some very preciseconductivity data on aqueous solutions cf alkylbenzenesulphonates l8 andalkyltrimethylammonium bromides l9 over a range of temperatures. Theextreme sharpness of the break in the curves relating equivalent conductivityto the square root of the concentration is very clearly demonstrated in thiswork. In the sulphonates the sulphonic group was para to the alkyl and,in this arrangement, it was concluded that the benzene ring was the equiv-alent of one and a half aliphatic carbon atoms in its effect on the criticalconcentration.From the same laboratory was published an interestingstudy 2o of conductivity in another type of double-chain salt, where bothcation and anion have one short paraffin chain, in this case trimethyloctyl-ammonium octylsulphonate. The critical concentration was much lowerand the fall much greater than in the case where one ion is simple.Another development in conductivity studies may conveniently bereported here. E. C. Evers and C. A. Kraus 21 noted that octadecylpyrid-l7 J. W. McBain and 0. E. A. Bolman, J . PhysicaE Chem., 1943,47,94; J. W. McBainand A. P. Brady, J. Amer. Chem. SOC., 1943, 65, 2072.l 8 A. B. Scott and H. V. Tartar, ibid.Jp. 692.2o A. B. Scott, H. V. Tartar, and E. C. Lingafelter, ibid., p. 698.21 Ibid., 1948, 70, 3049.Trans.B’araday SOC., 1948, 44, 467. l6 J . Chem. Physics, 1946, 14, 480.R. G. Paquette, E. C. Lingafelter, and H. V. Tartar, ibid., p. 686HARTLEY : AQUEOUS SOLUTIONS OF SOAP-LIKE SUBSTANCES. 39inium iodate behaves unusually in that the equivalent conductivity fistrises abruptly over a short range with increase of concentration above thecritical, before going through a maximum and then falling steeply in thenormal manner. The nitrate and bromide showed normal behaviourthroughout. One may note that the mobility of the paraffin-chain ionconstituent always rises a t the critical concentration,22 as would be expectedfrom the reduced resistance of the combined ions. The fall of total con-ductivity is due to the predominant effect of the secondary association ofions of opposite sign when the charge density is increased by the primaryaggregation.Could homo-ionic aggregation occur in an infinitely dilutesolution, a rise of total equivalent conductivity would always be expected.The more dilute the solution in which primary aggregation can occur andthe smaller the conductivity of the counter icns, the more likely is thisphenomenon to occur. It is not therefore surprising that it is not evidentuntil a t least 18 carbon atoms are introduced into the single chain andthen only with less mobile counter ions. A conductivity rising with aggreg-ation was, of course, first foretold by J. W. McBain, although, in thecase of very much higher concentrations where a rising conductivity wasfirst found, we now know that the explanation must be sought on differentlines.23 It was first found experimentally by C.Robinson and H. E. Garrett 24in the case of certain dyes. At high field strengths the same type of curvewas found 25 in cetylpyridinium chloride, the effect of secondary aggregationbeing reduced a t high relative velocities of the ions.In a later paper, P. F. Grieger and C. A. Kraus26 first confirm earlierresults of A. F. H. Ward 27 that addition of lower alcohols blyrs the criticalphenomenon and, in sufficient concentration, eliminates it, but they findadditionally that, with some salts, the presence of 10-35% of methylalcohol in the aqueous solvent calls into being, a t the critical concentration,a transient rise of equivalent conductivity, which is not evident in wateralone. This is found with octadecylpyridinium chloride, bromate, andformate but not with bromide, nitrate, and oxalate.This peculiar behaviourremains obscure.The transient rise of equivalent conductivity a t the critical concen-tration in water alone and in normal field strengths was also found byA. W. Ralston et aZ.15 in the double-chain quaternary salts when two12-carbon-atom chains were present. In this cam we have altogether 26a-liphatic carbon atoms, probably a higher number than in any compoundpreviously known to be soluble a t ordinary temperatures. The criticalconcentration is about ~ O * N and the micelle will presumably contain fewerions than a normal salt aggregating a t this concentration, so that the con-ditions are very favourable to an abnormally small effect of secondaryionic association.22 C.S. Samis and G. S. Hartley, Trans. Paraday SOC., 1938,34, 1288.23 Ref. 3, p. 36.25 J. Malsch and G. S. Httrtley, 2. physikal. Chern., 1934, A , 170, 321.28 J . Amer, Chem. SOC., 1948, 70, 3803.24 Tram. Paraday SOC., 1939, 35, 771.27 Proc. Roy. SOC., 1940, A , 51240 GENERAL AND PHYSICAL CHEMISTRY.Solubility measurements in solutions of more complex salts will bereported in the next section.2. Solubility Phenomena.Many organic substances of limited solubility in water are renderedcompletely miscible by addition of paraffin-chain salts. Others, of verylow solubility in water, are much more soluble in solutions of paraffin-chain salts.This phenomenon is concerned with a reversible, equilibriumprocess and is quite distinct from that of emulsification. Benzene, forexample, can be added slowly to a 10% solution of cetylpyridiniuni chloridein water and is taken up entirely therein to give an optically empty solution,provided the benzene concentration does not exceed about 7 yo, dependingon temperature. Further added benzene forms a visible emulsion con-taining droplets of varying size where average size depends on the historyof the mixture. Several careful researches 28 have established the reversibleequilibrium in the true solutions. For hexane in sodium oleate solution,J. W. McBain and J. J . O’Connor 29 have measured the equilibrium vapourpressure in solutions below saturation and find a normal type of pressure-composition curve.There has been a general usage of a new word to describe this phenomenon,namely, “ solubilisation ”.The Reporter considers that this is unneces-sarily confusing. It appears to imply that an essentially new process isunder investigation and it is often held, in consequence, that the resultingsolutions are not in equilibrium. We are not dealing with an entirely newprocess when we dissolve benzene in an aqueous paraffin-chain salt solution.The peculiarity is that the solvent is unusual in structure rather than t.hatthe solute is brought into an unusual state. Phenomenologically, thedifference between a system where alcohol or acetone is the co-solvent andone where a paraffin-chain salt is the co-solvent is quantitative only.A much smaller amount of a paraffin-chain salt than of acetone isnecessary to bring amyl alcohol and water into complete miscibility.Amuch larger amount of naphthalene is dissolved by a given concentrationof paraffin-chain salt in water than by the same concentration of acetonein water. There is, associated with this difference, an even more dis-tinctive one, but still essentially quantitative. A rapidly increasing addi-tional amount of naphthalene is brought into solution by each successiveequal increment of acetone. With paraffin-chain salts, over a considerablerange of concentration, the additional concentration of saturant is pro-portional to the additional concentration of co-solvent. The solvent powerof the paraffin-chain salt, unlike that of the acetone, is not appreciablylost by dilution with water.Below the concentration known from othermeasurements to be the critical one for formation of micelles, the solventpower is, however, very rapidly lost.2 8 R. S. Steams, H. Oppenheimer, E. Simon, and W. D. Harkins, J . Chem. Physics,1947, 15, 496; J. TV. McBsin and A. A. Green, J. Amer. Chem. SOC., 1946, 68, 1731.Ibid., 1940, 62, 2855HARTLEY : AQUEOUS SOLUTIONS OF SOAP-LIKE SUBSTANCES. 41The fundamental explanation of this difference is now generally agreedby all workers in this field. The unusually high solvent power of theparaffin-chain salts, but little affected by dilution, is due to the salt beingpresent in the form of relatively large aggregates.Amicroscopically, theco-solvent is not diluted by the water and thus retains its solvent power.The solvent power of ordinary co-solvents is also due to aggregates, butthese are relatively smaller and therefore less effective and widely dis-tributed in size and therefore the mean size is much dependent on con-centration. The less ideally miscible with water is the co-solvent, the lesscompletely does it lose its solvent power, as is well illustrated in the datafor naphthalene and the three lowest alcohols obtained by J. Christiansen 30and previously commented on in the present connection by the Reporter.31It is noteworthy that there are observations, somewhat neglected inthis connection, of the solubility of several organic substances of low watersolubility in solutions of simpler organic electrolytes, such as sodiumbenzoate and ~alicylate.~~ The normal salting-out effect of the electrolyteis reversed a t quite low concentrations and in high concentrations the‘( organic ” effect predominates.There is, of course, no sharply definedcritical concentration, and the solvent power, presumably due to smallclusters as in solutions of alcohol in water, is great only in concentratedsolutions.The Reporter31 found that the solubility of azobenzene in aqueoussolutions of cetylpyridinium chloride is approximately the same as in anequivalent amount of hexadecane. His argument that the micelle is there-fore essentially liquid in its paraffinic interior has received adverse comment 33when taken out of its context.Simple paraffinic solvent properties areonly to be expected and are only found when the solute is non-polar. Polar,and especially amphipathic, molecules are likely to be oriented in thesurface of the aggregate. Since the diameter of the latter is only of moleculardimensions, it is to be expected that orientation will have a very greateffect on solubility. Many simple dyes are much more soluble33 inparaffin-chain salt solutions than would be expected on simple addition ofthe water and paraffin solvents. J. W. McBain and H. McHan34 haveshown that dimethyl phthalate, which has practically zero solubility inwater and a low solubility in higher paraffins, is much more soluble inparaffin-chain salt micelles.Recently, W.D. Harkins and H. Oppenheimer 35 have proposed a dis-tinction between ‘( solubilisation ” when the solute is dissolved in theinterior of the micelle and “ penetration ” when it is oriented in its structure.30 Medd. K . Vetenskapsakad. Nobel-Inst., 1918, 4, No. 2.31 G. S. Hartley, J., 1938, 1968.32 J. Traube, I. Schoning, and L. J. Weber, Ber., 1927, 60, 1808; E. Lersson, 2.physikal. Chent., 1930, A , 148, 304; 1931, A , 153, 299, 466; H. Freundlich andG. V. Slottman, Biochem. Z., 1927, 188, 101.3s J. W. McBain, article on “ Solubilisation ” in Advances in Colloid Science (Inter-science, 1942), Vol. 1,34 J . Amer. Chem. Soc., 1948, 70, 3838. J . Chem. Physics, 1948, 16, 100042 UENERAL AND PHYSICAL CHEMISTRY.There can bs no doubt that molecules themselves amphipathic will beincorporated in the micelle with similar orientation.A. F. H. Wardz7considers that the lower alcohols are held predominantly in the micellesurface. E. Angelescu and T. Manolescu 36 consider phenols t o be similarlydisposed or even oriented outside the micelles.I. M. Kolthoff and W. F. Johnson 37 have made use of the solvent powerof micelles for dimethylaminoazobenzene to determine the critical concen-trations in several soaps. They found the critical concentration veryindefinite with rosinate. J. W. McBain, R. C. Merrill, and J. R. Vino-grad 38 find that the solubility of phenylazo-9-naphthylamine in soapsolutions is considerably less than in solutions of salts of paraffin-chaincations and of many more complex salts.R. C. Merril133 finds a lessmarked disadvantage of the soaps as solvents for o-tolylazo- @naphthol,and A. M. Soldate’s results33 put potassium oleate as much less effectivethan Aerosol O.T. as a solvent for propylene vapour.I n the studies just referred to, Turkey-red oil, which is, of course, largelysulphated unhydrolysed glycerides, stands out as having solvent powerfor the dyes examined comparable with that of the higher alkyl quaternaryammonium salts. The bile salts have no very outstanding solvent powerin solution, the extraordinary adsorption properties of deoxycholic acid inthe solid state evidently being due to an abnormal crystal structure. I nsolutions of Aerosol O.T. and sodium deoxycholate the critical transitionfrom the ultimately dissolved state to the aggregated state is shown bythe solubility measurements to be less abrupt than with normal paraffin-chain salts, consistently with the other evidence quoted above on theformer compound and related dialkyl salts.The phenomenon of indicator equilibrium displacement, noted in 1934 39and later applied to quantitative titration of paraffin-chain cations byparaffin-chain anions 40 and to investigation of the ratio of surface to bulkpH,4l has been the subject of further research and experimental refinement.It is, of course, an example of the “ solubilisation ” phenomenon.M. L.Corrin and W. D. Harkins 42 have found indicators particularly suitable tothe determination of the critical concentration without interference with it.Other less direct applications of solvent power have been made in analyticalprocedure.43 The influence of the solvent properties of the paraffin-chainsalt micelle on the bactericidal effect of dissolved phenols has been thesubject of a recent research.44Phenols and alcohols of medium molecular weight have long been used36 Kolloid-Z., 1941, 94, 319.38 J.Amer. Chem., 1941, 63, 670.39 G. S. Hartley, Trans. Faraday Xoc., 1934, 30, 444.40 G. S. Hartley and D. F. Runnicles, Proc. Roy. SOC., 1938, A , 168, 420.41 C. S. Hartley and J. W. Roe, Tram. Farday Xoc., 1940, 36, 101.42 J . Amer. Chem. SOC., 1947, 69, 679.4a T. U. Marron and J. Schifferli, I d . Eng. Chem. Anal., 1946, 18, 49.44 A. E. Alexander and A. J. H. Tomlinson, Faraday Society Discussion, “Reoent37 J.Physical Chem., 1946, 50, 440.Advances in Surface Chemistry ” (in the press)HARTLEY : AQUEOUS SOLUTIONS OF SOAP-LIKE SUBSTANCES. 43technically in the formulation of special soap solutions and studies of soap-water-phenol systems were among the first made in this field.45 Renewedinterest has recently been taken in similar systems. J. H. Schulman andT. S. McRoberts 46 have examined the consolution of water and benzene orparaffin by sodium oleate in the presence of various alcohols, by titratingmixtures to the end-point of fluid transparency. Accepting a t that timethe lamellar view of the micelle in aqueous solutions, they consider thatthe penetration into it of the oil phase first liquefies it and that the swollenmicelle is then capable of growth to spherical droplets of the order of 200 A.diameter.Whether an oil-continuous or water-continuous system resultsthey explain in terms of the relative wettability by water or oil of theinterfacial layer consisting of alcohol and soap molecules. Distinctionbetween these two types of system is made experimentally by conductivityobservations. They find that, over certain ranges of composition, thesystems are, with regard to this inversion, extremely sensitive to themolecular size of the alcohol and the nature of the hydrocarbon.R. C. Pink*' has examined the equilibrium adsorption of water vapourby benzene solutions of ethanolamine oleate and finds that the adsorptionincreases very rapidly with further rise of temperature above about 45".This he attributes to a fusion of 8 previously crystalline aggregate-in thiscase, of course, of the " reversed " structure, with the paraffin tails arrangedexteriorily .A very extensive study has been made by P.A. Winsor of oil, alcoholor amine, water, paraffin-chain salt systems. Various types of system canbe reslised,48 isotropic solutions from oil-continuous to water-continuous,such solutions in equilibrium with excess oil or water, and anisotropic gelsystems a t intermediate compositions between the two extreme types.He interprets the behaviour in terms of a somewhat ill-defined ratio of theinteraction between the amphipathic substance and oil to that betweenthe amphipathic substance and water.This somewhat obscures thegeometrical factor in the amphipathic or, as this author prefers, " amphi-philic ", property. This is brought out in the section dealing with allseven n-tetradecane sodium sulphates,16 where, as previously mentioned,it is shown that the critical concentration for micelles in aqueous solutionincreases as the ionic group moves towards the centre of the chain, whichwould indicate on this author's view an increasing water attraction, andyet' the compounds behave as though more oil-attractive as far as solubilis-ation is concerned. The author apparently goes to an opposite extreme tothat visited by explorers with the X-ray diffraction camera, in that heminimises the importance of organised structure, although accepting theanistropic gel phase as a lamellar intermediate between the amicro-emulsionsof oil-in-water and water-in-oil forms envisaged by J.H. S ~ h u l m a n . ~ ~I n the other papers in this series, P. A. Winsor notes that the addition45 E. Angelescu and M. Popescu, Kolloid-Z., 1930, 51, 336.*13 Trans. Paraday SOC., 1946, 42, B, 165.47 Ibid., p. 170. 4 8 Ibid., 1948, 44, 37644 GENERAL AND PHYSICAL CHEMISTRY.of simple salts 49 can in part replace the addition of intermediate alcoholsby increasing the ratio of oil-phase attraction to water-phase attractionof the amphipathic substance. The effects of the nature of the oil phase 50and of that of the amphipathic substance 51 are examined, the latter supple-menting earlier work by R. Durand 52 on sodium soaps from C, to Cll.Solubilisation in glycol in place of water is also examined 53 and is dis-tinguished by absence of the anisotropic gel phases.The author considersthat the hydrogen-bonded pseudo-ice structure in water is necessary forthe adhesion between the units of dispersed phase without which gel structurecannot be evident.3. Organisation in Concentrated Solutions.of the production by clear solutions of soapsof an X-ray diffraction pattern of a much more definite nature than thatproduced by normal liquid systems threw new light on the problem of thestructure of these solutions. Unfortunately, the X-ray diffraction cameraas a precision tool is held in rather uncritical respect by many physicalchemists unfamiliar with the complications of the subject, and specialistsin the subject have been perhaps insufficiently familiar with other workon solutions of soap-like substances to have appreciated that there mightbe some doubt about apparently obvious conclusions from the measure-ments. The result has been that the advance following on this discoveryhas been much more rapid measured as a scalar than as a vector quantity.The diffraction patterns indicate the presence of a single characteristicshort spacing of about 4-6 A.and a long spacing, greater than twice thelength of the extended paraffin-chain ion, which increases with dilution.The diffraction ring due to the long spacing is not detectable at concen-trations of salt much under loyo, but that due to the short spacing is stillevident at less than 5y0.552 56J.Stauff examined the sodium salt of the C,, primary sulphate esterin parallel experiments at temperatures of 20°, where the salt exists as asuspension of microscopic curd fibres, and a t 75", where it is in clear solution.In the curd condition, two rings due to short spacings are evident and onedue to a long spacing which in this condition of the salt is, as expected,independent of concentration. Insolution the first two fuse together to a single constant value of 4-60 andthe second ranges from about 6 2 ~ . at 20% concentration of salt to 4 2 ~ .a t 80%.Following K. Hess and J. Gundermann 54 and H. Kiessig and W. Philip-The discovery in 1937The values are 4.55, 4.00, and 38.2 A.49 Trans. Faraday Soc., 1946, 42, By 382.51 Ibid., p.390.53 P. A. Winsor, Trans. Paraday SOC., 1948, 44, 451.54 K. Hess and J. Gundermann, Ber., 1937, .70, 1800.56 W. D. Harkins, R. W. Mattoon, and M. L. Corrin, J. Amer. O h . SOC., 1946,50 Ibid.? p. 387.52 Cornpt. rend., 1946, 225, 898.55 J. Stauff, Kolloid-Z., 1939, 89, 224.68, 220HARTLEY : AQUEOUS SOLUTIONS OF SOAP-LIKE SUBSTANCES. 45p ~ f f , ~ ~ Stauff interprets the short spacing as that between adjacent parallelplanes in which the chains lie parallel to one another, and the replacementof the two corresponding identity periods in the crystalline phase by asingle period as indicating that, during the transition of the curd suspen-sion to clear solution, partial fusion of the crystal occurs similar to thatin transition from a normal crystal to a smectic melt.In the crystal, allthe zigag C-C links of a chain are in the same plane and these planes areregularly disposed with respect to one another. In the smectic state thesechain planes, by virtue of freedom to rotate, have effectively becomecylinders. It will be noted that this process involves a lateral expansionamounting to some 15% on the original area, only some 5% of which isattributable to thermal expansion alone.All these and other 58’ 59 investigators have, until very recently, acceptedthe interpretation of the long spacing by Hess, Kiessig, and their collab-o r a t o r ~ . ~ ~ , 57 It is considered to have a similar origin to the constantlong spacing in the true crystal, which represents, of course, the distancebetween planes containing the terminal ionic groups, which planes arenearly perpendicular to the chains, The expansion of this spacing withdilution of the salt is considered to be due to the increasing separation ofthe pairs of ionic planes by a more or less organised layer of water.Thegeneral picture is that of an assembly of smectic-crystalline leaflets, theso-called laminar micelles, separated by layers of water of thicknesscharacteristic of the dilution.This concept may perhaps have been suggested by analogy with thequalitatively similar behaviour of montmorillonite clays onIn this well-established case, however, a water layer thickness of morethan 4 molecules has never been observed, whereas the laminar soap micellesmust be separated by up to a maximum of a t least 8 water molecules.Moreover, the clays remain insoluble.Any excess water produces a sus-pension of macroscopic particles of size determined by the origin and treat-ment of the clay and separated to distances determined by sedimentationconditions.This picture of regularly separated lamin8 has frequently been describedand equally frequently drawn. It has the merit of being easily drawn.The difficulty is to stop drawing it, and one may fairly ask whether Naturewould not find a corresponding difficulty. There is no doubt a t all thatthe clear solutions of paraffin-chain salts are equilibrium systems in thestrict sense, and no hysteresis of any exactly measurable property has yetbeen detected.Addition of further paraffin-chain ions to any one of thesepictures of the laminar micelle would seem to involve no difference from67 Naturwiss., 1939, 27, 593; see also K. Hess, W. Philippoff, and H. Kiessig,6 8 P. Krishnamurti, Indian J. Physics, 1929, 3, 307.6o See E. A. Hauser and L. S. Le Beau in Alexander’s “ CoIloid Chemistry ” (Rein-Kolloid-Z., 1939, 88, 40.D. Dervichian and F. Lschampt, Bull. SOC. chim., 1945, 12, 189.hold, 1946)’ Vol. 6, p. 19146 GENERAL AND PHYSICAL CHEMISTRY.the last additions in any way which could distinguish the chosen size asbeing energetically or statistically preferable. Only when clusters ofmolecules are very small will there be any optimum size in an equilibriumsystem unless some special factors operate to give the optimum size astrongly marked maximum potential energy loss for each molecule enteringthe cluster.Criticism along these lines has already been made in advance byK.H. Meyer and A. van der Wyk 6 1 directed against the Reporter’s hypo-thesis of an optimum size of micelle on thc mistaken assumption thatthe micelle considered had a parallel alignment of ions. It has been answeredby the Reporter elsewhere *033 for the case of the spherical micelle, butremains a very valid objection to the laminar micelle. I n developing atheory of a reversible aggregation colloid it is just as important to find amechanism for the limitation of aggregation as it is to find a primary causeof aggregation. The argument is therefore of some importance and it hasbeen so consistently overlooked that it is desirably briefly to repeat it.Aggregation of paraffin-chain ions is due to the very strong mutual attrac-tion of water molecules which tend to eliminate as far as possible theintrusion of indifferent paraffin between them, The strong attractionbetween water and the ionic end groups is responsible for limiting thisprocess of extrusion of the separate chains into clusters presenting a muchsmaller area of paraffin to the water.If the arrangement is laminar, how-ever, this would explain only a limitation of the thickness of the micellesand leave their area indeterminate. If the greater entropy of the liquidarrangement of the paraffin chains causes this state to be preferred (andwhere it does not do so we have in fact indefinite laminq i.e., our salt isinsoluble), then a spherical cluster will result, the single linear dimensionof which is now controlled by the balance of forces referred to.If thespherical micelle were much smaller than necessary to enable a fullyextended chain to penetrate from its surface to the centre, a greater areaof paraffin than necessary would be exposed to the water. If it weremuch larger, then ionic groups would have to leave the water against thestrong attraction of the latter, or the assembly would have to deviate fromspherical form and so the entropy would be reduced. It is perhaps desir-able to recall that a strongly marked optimum size of micelle, varying butlittle with concentration of paraffin chain or added salts, is an experimentalfa~t.~OA similar difficulty about the laminar micelle theory was raised byJ.D. Bernal in the Faraday Society Discussion on Swelling and Shrinkingin comment on the contribution by D. G. Dervichian.62 He pointed outthat a simple calculation showed that the increase of spacing betweenalternate ionic planes, if assumed to be due to entry of water betweenneighbouring planes, could account only for a fraction of the total waterpresent. To take an example from J. Stauff’s data 55 on the C,, sodiumHdv. Chim. Acta, 1937, 20, 1321. 62 Trans. Paraday SOC., 1946,42, B, 180HARTLEY : AQUEOUS SOLUTIONS OF SOAP-LIRE SUBSTANCES. 47sulphate, in a system containing 40% of water, the long spacing has increasedfrom its “ dry ” value of 38 A.to 48 A. This will account for 16% only ofthe water. The remaining 24% must separate the indefinite lamellaelaterally, where it will be in contact with the exposed sides of the parallelbundles of paraffin chains.Before considering the latest developments in this subject, mentionmust be made of a further quantitative difficulty in the lamellar hypo-thesis, pointed out by W. D. Harkins, R. W. Mattoon, and M. L. Corrin @after following up, in a more extensive investigation, Kiessig and Philippoff’sobservation 57 that the long spacing is increased by dissolving (“ solubilising ”)oils in the soap solution. They consider that the oil is located as anotherlayer, this time between the planes defined by the terminal methyl groups.The difficulty here is the reverse of that found in accounting for the watervolume, in that oil increases the spacing by niuch more than would beexpected from its inclusion in this location without other changes in thesystem.The authors are therefore forced to the view that the introduc-tion of the oil layer has a secondary effect, by some unknown mechanism,on the water layer.I n a later paper, Harkins et aZ.64 report the results of more thoroughinvestigation of the X-ray diffraction photographs which reveal a new,less well-defined, long spacing attributed to the individual thickness ofthe micelle. At this stage they favour a cylindrical micelle with theparaffin chains parallel to the cylinder axis. They envisage the inter-pretation of the original long spacing on a point lattice system in which“ no special shape for the micelle is necessary ’,.In this paper the diffusion-measurement evidence*O for the size of the micelle is for the first timeconsidered in relation to the X-ray studies. The cylindrical model hasbeen further considered byM. L. Corrin has recently briefly reviewed the X-ray diffraction evidencefrom the point of view of the spherical micelle hypothesis, and finds thetwo not inconsistent. He considers that “ the observed patterns can arisefrom a system of spherical micelles and that the Bragg law ‘spacings’may be meaningless ”. The communication is too brief to permit thederivation of the distance distribution functions which he proposes, and afuller treatment by this author will be awaited with interest.The Reporter had already suggested 66 that a distortion of the sphericalmicelles might occur, owing to packing effects operating in the concentratedsolutions examined by the X-ray technique.Such effects were not con-sidered in the development of the theory of spherical micelles from evidencebased only on measurements in dilute solution. It now appears unnecessaryto envisage such distortion. It would presumably give rise to a morerather than a less complex diffraction picture. Once the principle is admitted63 J . Colloid Sci., 1940, 1, 105.64 R. W. Mattoon, R. S. Steams, and W. D. Harkins, J . Chem. Physics, 1947,15, 209.6 5 Idem, ibid., 1948, 16, 156.6 6 G. S. Haxtley, Trans. Faraday SOC., 1946, 42, B, 648 GENERAL AND PHYSICAL CHEMLISTRY.that the corresponding, regularly spaced assemblies of atoms responsible forthe diffraction need not be planes, the spherical micelle offers much thesimplest explanation of the diffraction phenomena.In a recent con-tribution 67 the Reporter has suggested that the strong electrostatic repul-sion between the micelles will, in concentrated solution, cause them to bemore or less regularly disposed and in such a way that each is the maximumdistance from the maximuin number of neighbours. This condition issatisfied by the three dimensional " honey-comb " or close-packed assembly,the geometry of which leads directly to the simple relationshipI = (3+/22/2x)*rwhere I is the distance between centres of ncighbouring spheres, r theirradius, and + the fraction of the total volume occupied by the spheres.It is shown, not only that this equation leads to a good approximation tothe observed variation of I (the " long spacing ") with 4 on the assumptionof constant r, but that the calculated values of r are, as expected and as foundby diffusion measurements, slightly greater than the length of a fullyextended chain.Not only is the water thus accounted for, but this view of the structureexplains also the anomaly of a disproportionately great increase of I onaddition of oils, A non-polar oil will be contained mainly in the interiorof the micelle and tend to be concentrated near its centre, so that a maximumincrease of radius results from the addition of a small amount of oil.Inthe extreme case, let the oil be located exclusively a t the centre, occupyinga sphere of radius 6. The whole micelle now has radius r + 6, and theparaffin chains occupy the volume $ x [ ( r + 6)3 - s3]. The volume ratio ofadded oil to paraffin chains is thus, in the limit of 6 -+ 0, equal to a2/3r2.The relative increment of T resulting from addition of an amount of oilcorresponding to a small fraction f of the paraffin-chain volume will thusbe dv, whereas the relative increment of spacing in the simple laminarmodel will be equal to f. A disproportionate increase of I follows directlyfrom that of r .J. H. Schulman and D. P. Riley 68 have published an investigation byX-ray diffraction technique of the transparent emulsion systems previouslydescribed by the former.46 They interpret their results in terms of thelattice point distances of the emulsion droplets, and the investigation showshow far this simple view is applicable. They find evidence of the distortionwhich must occur when the ratio of dispersed phase exceeds the 74% corre-sponding to close packing of equal spheres. These authors issue a cautionagainst the full acceptance of their model for the case of solutions of theparaffin-chain salts alone on the ground that an ideally liquid sphericalmicelle would not show the characteristic short spacing found in photo-graphs of these solutions.It is to meet this difEculty that Harkins et al.propose a micelle with a cylindrical, parallel-packed core rounded off a t67 Nature, in the press.68 J. Colloid Sci., 1948, 3, 383HARTLEY : AQUEOUS SOLUTIONS OF SOAP-LIKE SUBSTANCES. 49the sides with more randomly-packed chains presenting their ionic groupsto the water.The short spacing cannot be due to regular disposition of ionic groupson the outside of the micelle. Diffusion measurements4() indicate aneffective radius for the cetylpyridinium micelle of about 25 A. This willcontain between 70 and 100 para&-chain ions. The mean distance apartof the ionic groups will therefore be not less than 8.5 A. The outer diffrac-tion band probably arises from a regular spacing between paraffin chains.No exact compiwison seems to have been made with the pattern producedby a liquid paraffin of comparable chain length, to see whether the trueliquid in bulk has sufficient regions of ordered arrays to make any furtherexplanation necessary.It has been mentioned above that the soaps, and perhaps other salts ofyaraffin-chain anions, have less solvent power than those of paraffin-chaincations.The long spacings also appear to be greater in the latter, indicatinga larger m i ~ e l l e . ~ ~ It is a question worthy of further study, by all methodsavailable, whether there may be more internal order in the anionic micelles.That the spherical liquid micelle is not a complete explanation of allthe properties of paraffin-chain salt solutions has always been appreciatedby the Reporter. Although many solutions, even when concentrated, haveviscosities little in excess of that of water, yet others may be very viscousor gelatinous over a limited range of temperatures or even show a permanentelasticity persisting to very low concentration^.^^ The latter effect is veryspecifically influenced even by the nature of the small ions.The occurrenceof pronounced elasticity in very dilute solutions indicates that, in thesecases, very stable filamentous particles must be present. One may imaginethat an indefinitely long cylindrical form of the paraffin micelle is pre-ferred in these cases, with the paraffin chains parallel to the axis, as inHarkins’s but adhering together by the ionic lattices, which wouldaccount at once for a specific ion effect. On the other hand, the chainsmight be as chaotically disposed as is geometrically possible, with the ionicgroups on the cylindrical surface, an arrangement which we should expectto be more probable in view of the factors causing limited aggregation ofamphipathic ions.A filamentous arrangement is suggestively similar tothe “ myelinic figures ” described by D. G. Dervichian.62 The very highdegree of elasticity shown suggests that the filaments must be elasticallycontractile. The liquid cylinder would have this property, since it wouldbe extensible without disruption and its surface would tend to contract tothe smallest area consistent with the radius not exceeding the effectivestretched length of the chain ion.Optical anisotropy has been a much neglected method of enquiry intothis subject. Its occurrence in streaming suspensions of soap curd is, ofcourse, well known, as also the strong birefringence of the gelatinous phasesformed in many systems where organic liquids are present within certainO9 G.S . Hartley, Nature, 1938, 142, 16150 GENERAL AND PHYSICAL CH1MISTRY,concentration limits 48 and at sufficiently high concentrations of the puresalts. ' 0 The ordinary solutions should also show streaming birefringenceif the micelle were indeed of laminar form.In the course of pioneer studies of the aggregation of lower fatty acidsand soaps which revealed the existence of the critical transition fromultimately dissolved to aggregated solution, J. Grindley and C. R. Bury 71studied the changes in a number of physical properties, including that ofdensity.They found that aggregation resulted in a decrease of the partialvolume of water and an increase in that of the solute. The importance ofthis fact has not been generally recognised. The Reporter 66 has drawnattention to the fact that the expansion of the salt may be so great as togive rise to an increase in the volume of the whole system, water pluscrystalline salt, when solution occurs. Since the partial volume of a simpleelectrolyte is always smaller than its volume in the solid state, the expan-sion of the paraffin-chain salt must be due to increase of volume of theparaffinic portion, which would, of course, be expected on transition of theorganised crystal lattice to a liquid arrangement.Density measurements on solutions of the higher paraffin-chain saltsare not sufficiently exact and comprehensive to enable a precise estimateof the density of the paraffinic portion of the micelle to be made.Takingthe data at 25" for potassium we find that the differences of partialmolal volumes between the octoate and propionate are 79.2 C.C. a t 0 . 3 ~ whereno aggregation is evident and 88.9 C.C. a t 1 . 0 ~ where it is effectively corn-plete. Correspondingvalues derived from the difference between octoate and acetate are 13-1and 14.5 C.C. per g.-mol. CH,. The volumes per g.-mol. CH, in liquidparaffins obtained from densities of hexane, octane, decane,and hexadecaneare fairly constant a t about 16.3 C.C.tri-methylammonium bromides from the differences between which we maysimilarly deduce volumes per g.-mol.CH, (average between 0.1 and 0 . 4 ~ )to be 16.5 c.c.*The partial volumes even in simple electrolytes, such as potassiumacetate, vary considerably with concentration and the significance of densitymeasurements, as well as the provision of more accurate data, is a matterwhich merits further consideration. There is a prima facie case that theinterior micelle density in the higher paraffin-chain salts is a t least as lowas that of the liquid hydrocarbon.Harkins and his collaborators 63 report density measurements onThe volumes per CH, group are 13.2 and 14.8 C.C.Scott and Tartar l8 record densities a t 25" of the C,,, CI2, and70 J. W. McBain and E. Gonick, J. Amer. Chem. SOC., 1946, 68, 683.71 J., 1929, 679.* Professor E.C. Lingafelter has kindly communicated to the Reporter the follow-ing density figures atl 25". For the C, compound at O . O ~ N , 1.00046; for C, and CBcompounds at 0 . 2 ~ , 1.00321 and 1.00160. From these data we obtain the followingvalues for the volumes per g.-mol. of CH,. From the difference C,,-C8 at O . ~ N , 16.25.From the difference C1,-C, at O - ~ N , 16.0.7 2 D. G. Davies and C. R. Bury, J., 1930, 2263.From the difference Cl,-C, at O*~N, 16.5WILLIAMS AND SINGER : CHEMICAL KINETICS. 51potassium laurate solutions in which n-heptane and 1 : 2 : 3-trimethyl-butane and2* ethylbenzene were dissolved. The first and the last liquidhave, in the solutions near saturation, apparent densities nearly equal tothose in the bulk liquids, but, in very dilute solution of the added liquid,the apparent densities are considerably higher.This might be expected if weconsider the micelle, straining to be as large a s possible, to be not com-pletely filled in the centre until non-polar molecules are added. 1 : 2 : 3-Trimethylbutane, on the other hand, has an apparent density in dilutesolution approximately equal to tha.t in bulk and a higher density nearsaturation. Its bulk density is considerably higher than that of n-heptaneand any volume change occurring on solution in bulk in normal paraffinswould need to be known before speculation on this remarkable result wouldbe profitable.G. S. H.3. CHEMICAL KINETICS : HOMOGENEOUS THERMAL GAS REACTION&I n his Presidential Address to the Chemical Society, Sir Cyril Hinshel-wood has discussed, in terms of general principle, the present position ofchemical kinetics. It has become evident that the overall “reactionorder” has not now the theoretical significance which it may once haveappeared to possess, however important the concept may still be as apractical tool of the experimenter. Most reactions take place in a seriesof stages, either as chain processes, involving interactions between freeatoms and radicals, or as non-chain reactions, in which, again, each individualstep may be of great siniplicity.Correspondingly, there has been, in recent years, great interest in theindividual reactions of free atoms and radicals and progress in thisdirection has been reviewed in Annual R e p ~ r t s .~ However, these Reportshave not, for many years: reviewed the overall kinetics of gas reactions;and this is the subject of the present Report. In so large a field it is im-possible to be exhaustive, so we have deliberately selected reactions (payingsome attention to examples which have been important in the history ofreaction kinetics) 5, 6, 7 to illustrate the kind of progress which has beenmade. In order to concentrate upon overall kinetics, we have had toleave without mention much important work upon elementary reactions,such as that of Steacie with hydrogen atoms.J . , 1947, 694.E.g., cf. E. W. R. Steacie, “Atomic and Free Radical Reactions,” New York,1946 ; and Faraday Society Discussion, 1947, 2, on the “ Labile Molecule.”Cf.M. Ritchie, Ann. Reports, 1940, 37, 79; C. E. H. Bawn, ibid., 1943, 40, 36;D. H. Hey, ibid., 1944, 41, 181; W. A. Waters, ibid., 1945, 42, 130; J. Weiss, ibid.,1947, 44, 60.Cf. ibid., 1934,31, 46; 1935, 32, 89; 1936,33, 86; 1937, 34, 43.Hinshelwood, “ Kinetics of Chemical Change in Gaseous Systems,” 3rd edn.,H. J. Schumacher, “ Chemische Gssreaktionen,” Dresden and Leipzig, 1938. ’ R. N. Pease, “ Equilibrium and Kinetics of Gas Reactions,” Princeton, 1942.Oxford, 1934; “ The Kinetics of Chemical Change,” Oxford, 194052 GENERAL AND PHYSICAL CHEMISTRY.Overall Order of Reaction.Second-order Reactions.-The formation and decomposition of hydrogeniodide stand out in exhibiting a second order which bears a direct relationto the molecular events which determine reaction.(For newer work onthese and the corresponding reactions of deuterium compounds, cf. A. H.Taylor and R. H. Crist.8) The fate of other reactions which have, a t onetime or another, been formally classified as second-order reactions may beillustrated by the example of the thermal decomposition of acetaldehyde.The earlier work upon thisreaction has been critically reviewed by Pease ; and the conflicting evidenceas to whether the decomposition occurs by a chain mechanism or not hasbeen summarised by J. R. E. Smith and C. N. Hinshelwood? who havereinvestigated the reaction. Points in favour of a chain mechanism are :(1) Very careful work by M. Letort lo showed that the order was 1.5, inagreement with the Rice-Herzfeld theory 31 of chain reactions.(2) Thereaction appeared to follow a mechanism similar to that of the photo-chemical decomposition which was known to involve free radicals.ll (3)The rate was reduced by propylene.12 (4) Theoretical arguments based onspectroscopy had been advanced to show that internal rearrangementpreceding dissociation was ~n1ikely.l~ (5) The presence of free radicalshad been e~tab1ished.l~ On the other hand, there was some evidence againsta chain mechanism. (1) Nitric oxide seemed normally not to inhibit the reac-tion.15 (3) The reactionappeared to be similar to that of the " fully inhibited " decomposition ofbenza1dehyde.l' The reaction had been found to exhibit 8 variable orderand the simultaneous occurrence of more than one mechanism had beenpostulated.l 8find that increasing additions of propylenereduce the rate of decomposition a t 550" until a limiting value is reached;further additions of propylene have a slight catalytic effect. They also findthat nitric oxide does reduce the reaction rate only at low acetaldehydepressures ; a t moderate pressures inhibition is masked by a strong catalyticeffect. The reaction proceeding with the limiting rate attained by " fullinhibition " with propylene is of approximately second order ; and a velocitycoefficient calculated for a bimolecular collisional activation involving twosquare terms agrees well with the observed value (as it does also for form-aldehyde). By subtracting the '' fully inhibited " from the normal rate,T h e thermal decomposition of acetaldehyde.(2) Too few free radicals appeared to be present.16Smith and HinshelwoodJ .Amer. Chem. SOC., 1941, 63, 1377.A. 0. Allen and D. V. Sickman, J. Amer. Chem. SOC., 1934, 56, 2031.Proc. Roy. SOC., 1942, A , 180, 237.lo J . Chim. physique, 1937, 34, 206, 265, 355, 428.l2 F. 0. Rice and 0. L. Polly, J . Chena. Physics, 1938, 6, 273.l3 T. W. Davis and M. Burton, ibid., 1939, 7, 1075.l 4 M. Burton, J. E. Ricci, and T. W. Davis, J. Amer. Chem. SOC., 1940, 62, 265.l5 L. A. K. Staweley and C. N. Hinshelwood, J., 1936, 812.l6 F. Patat and H. Srachsse, 2. physikal. Chem., 1936, B, 31, 105.l7 R. E. Smith and C. N. Hinshelwood, Proc. Roy. Soc., 1940, A, 1'95, 131.la C. J. M. Fletcher and C.N. Hinshelwood, ibid., 1933, A, 141, 41WILLIAMS AND SINGER : CHEMICAL KINETICS. 53it is possible to investigate the part of the reaction which may be assumedto be due to a chain mechanism; it appears to be of the first order.The simultaneous occurrence of a molecular and a chain reaction hasbeen proved in a very satisfactory manner by J. C. Morris,lg who decom-posed mixtures of fully deuterated and ordinary acetaldehyde at 542".Great pains were taken to purify the materials, and in particular to removeall traces of oxygen, and to reduce the polymerisation of the aldehyde toa minimum. When this careful pretreatment is applied, the decompositionproducts contain mainly CH,, CD,, and CO, and only small amounts ofmixed methanes (CH3D, etc.).The reaction can therefore proceed neitherby a chain mechanism (involving CH, radicals) nor by a bimolecular processsuch as\ * \ CH3 D ,,'\ / \ ,,' oc"'\ . \ I, + :, CO=CH,D+ CD3H+2C0'\ /Moreover, the reaction rates observed for the highly purified materialapproach those of Smith and Hinshelwood's " fully inhibited " reactionand are lower than the rates observed by all other investigators.On the other hand, when "untreated" mixtures of CH3*CH0 andCD3*CD0, or mixtures of " pretreated " materials to which small amountsof oxygen had been added, were decomposed, the products contained largeamounts of CH3D, CHD,, and-surprisingly-CH,D,.Neither prolonged heating of mixtures of CH,, CD,, CO, and traces ofO,, nor the decomposition of pure CH,*CHO in the presence of CD, andCO gives rise to the formation of appreciable amounts of mixed methanes.These results appear to prove (though this is not fully accepted bySteacie2) that the decomposition of pure acetaldehyde proceeds by aunimolecular mechanism, and that the presence of minute amounts ofimpurities-in particular of oxygen-gives rise to a chain reaction.Morrisestimates that " untreated " aldehyde decomposes to the extent of 50%by a chain mechanism. Smith and Hinshelwood's work indicates 60-70% of chain mechanism. The discrepancies between the rates reportedfor this reaction can be readily understood. Not even Morris's carefultreatment succeeded in reducing the chain reaction to below 10-20~0 ofthe overall rate.Although this work explains much that has baffled previous investigators,it raises some new problems.The order of the moEecuEar reaction remainsin doubt. The appearance of appreciable amounts of CH,D, among theproducts of the chain decomposition does not lend support to the chainmechanisms that have been suggested. One may also wonder whethersmall amounts of oxygen or other impurities are not responsible for thechain mechanism in other reactions where this has not been suspected.The effect, of oxygen on the decomposition of acetaldehyde has beenThe order of the reaction is still between 1 and 2.l9 J. Amer. Chem. SOC., 1944, 66, 58454 GENERAL AND PHYSICAL CHEMISTRY.further investigated by M. Letort and N. M. LetorL20 Pure acetaldehydeis thermally stable below 400", but in the presence of oxygen the rate ofdecomposition is still measurable at 150".I n mixtures of acetaldehyde(237 mm.) and 0.1-20 mm. of oxygen only definite fractions of aldehydeare decomposed. It is thus possible to calculate the number of molttculesdecomposed by one molecule of oxygen. This number varies with thetemperature in a surprising manner, giving rise to an N-shaped curve.There is a maximum of 200 at 200", followed by a minimum (65) a t 315",after which the curve rises steeply. The curve obtained by plotting thelogarithm of the initial velocity against 1/T shows a bend at 190". Itappears that the activation energy is 13 kcals. below 180" but 24 kcals.a t 200-290".Experiments of E. Leifer and H. C. Urey,21 who followed the decompos-ition of acetaldehyde by means of an interesting, though as yet inaccurate,new mass-spectrographic technique, indicate a second-order reaction.Free radicals obtained by the pyrolysis of diacetyl strongly catalysethe decomposition of acetaldehyde and other compounds.22 This catalysisis not reduced by the presence of nitric oxide, although in the case of di-methyl ether, the diacetyl-promoted pyrolysis is strongly inhibited bynitric 0xide.~3The decomposition of acetaldehyde is also catalysed by hydrogensulphide. W.L. Roth and G. K. Rollefson2* found the reaction to behomogeneous. No hydrogen sulphide is consumed by the reaction, and theproducts are methane and carbon monoxide as for pure acetaldehyde.The overall activation energy is 36 kcals.(the value found by Smith andHinshelwood in the absence of catalysts is 47 kcals.).Third-order Reactions.-Interactions of nitric oxide with oxygen andwith halogens are the classical third-order 6~ 73 3* although thesehave not always been held to demand a termolecular process as the vitalstep. However, the reaction of nitric oxide with chlorine is subject toheterogeneous complications; 25 and it is not certain that the oxidation ofnitric oxide is free from them. I n new work on the vexed question of" intensive drying," E. M. Stoddart 26 reported non-interaction betweenoxygen and nitric oxide, intensively dried in separate vessels, but onlywhen mixing of the gases took place in the oxygen-containing bulb. Heinferred that heterogeneous processes, influenced by adsorbed moisture,were essential to the oxidation of nitric oxide, contrary to M.Bodenstein'soriginal view. F. B. Brown and R. H. C r i ~ t , ~ ~ using very carefully purifiedgases, find the oxidation of nitric oxide to be of third order, at 25", for 3-and &fold variations of reactant concentrations, with pressures of nitric2o Compt. rend., 1948, 226, 77.22 F. 0. Rice and W. D. Walters, ibid., 1941, 63, 1701.23 C. I€. Klute and W. D. Walters, ibid., 1945, 67, 550.24 Ibid., 1942, 64, 1707,2s E. M. Stoddart, J., 1940, 823; 1944, 388.26 J., 1939, 5.21 J . Amer. Chem. SOC., 1942, 64, 994.27 J . Chem. Physics, 1941, 9, 840WILLIAMS AND SINGER : CHEMICAL KINETICS. 65oxide between 0.01 and 0.1 rnm. and of oxygen between 8 and 22 mm.The rates observed differ from those of Bodenstein (obtained with about10 mm.pressure of each reactant) by 5*5y0. Brown and Crist 27 have alsoexamined the reaction NO, + CO = CO, + NO (found to be of secondorder) a t 225-290'; and they have investigated the products and ratesof reaction occurring in mixtures of nitric oxide, oxygen, and carbon mon-oxide a t 25-265". In the ternary mixtures they observe the formationof carbon dioxide a t temperatures which are too low for it to be ascribedto the above reaction between carbon monoxide and nitrogen dioxide.Moreover, experiments a t higher temperatures,28 with the ternary mixturesof NO, 0,, and CO, gave reaction rates proportional to the first power ofthe nitric oxide concentration.These two facts are inconsistent with themechanism2N0 + 0, = 2N0,and Brown and Crist propose the reactionsto account for a t least part of the third-order oxidation of nitric oxide,together with NO, + CO = NO, + CO, for the ternary mixtures containingcarbon monoxide.Heterogeneous reactions occur in the mixtures containing carbon mon-oxide ; but the above niechanisrn applies to homogeneous reaction studiedin Pyrex glass vessels rinsed with potassium chloride solution.The oxidation of nitric oxide by nitric acid vapour has been studied.29The reaction has " some termolecular characteristics " but surface effectsoare prominent.At onetime it was argued that unimolecular processes in gases could not resultfrom collisional activation.Then the Lindemann-Hinshelwood theory (sub-sequently elaborated) showed that they could ; and first-order gas reactionswere discovered experimentally. A little later these were interpreted bysome as chain reacti0ns.3~ Still more recently, it has been held (cf. R. N.Pease 7 9 32) that many of the apparently first-order decompositions, whichfurnish the subject matter for the whole discussion, are, in fact, betterrepresented experimentaZZy as reactions of order 1.5.One reaction, whose first order has never beendenied, is the thermal decomposition of dinitrogen pentoxide vap0ur,3~which, indeed, retains its speed and first order down to embarrassingly low28 G. M. Calhoun and R. H. Grist, J . Chem. Physics, 1937, 5, 301 ; R. H. Grist andJ.E. Wertz, ibid., 1939, 7, 719.29 J. H. Smith, J . Amer. Chem. SOC., 1947, 69, 1741.30 Cf. H. C. Ramsperger, Chem. Reviews, 1932, 10, 27.31 E.g., F. 0. Rice and K. F. Herzfeld, J . Amer. Chem. SOC., 1934, 56, 284; J . Chem.Physics, 1939, '7, 671; cf. F. 0. Rice and E. Teller, ibid., 1938, 6, 489; A. Kossiakoffand F. 0. Rice, J . Amer. Chem. SOC., 1943, 65, 590.NO, + CO = NO + CO,NO, + NO = 2N0, NO + 0, + NO,First-order Reactions.-The history of these is a curious one.Dinitrogen pentoxide.32 J . Chem. Physics, 1939, 7, 749.' 'E.g., cf. F . Daniels, " Chemical Kinetics," Ithatea, New York, 193856 UENERAL AND PHYSICAL CHEMISTRY.pressures (of the order 0.05 mm.). An abnormally large collision diameterwas proposed to account for this.= Doubt has been expressed whetherthe diminution of speed a t even this low pressure is due to the expectedtheoretical insufficiency of the rate of activation.F. Daniels and P. L.Veltman 35 suggested, as a chemical explanation, that the interaction ofnitric oxide and dinitrogen pentoxide, assumed to be a rapid step, in boththe old and the new mechanism (see below) for the dinitrogen pentoxidedecomposition, might, a t very low pressures, have a speed comparablewith that of the dissociation of N205 molecules. J. H. Smith and F. Daniels 36find the reaction between dinitrogen pentoxide and nitric oxide, a t 0-25",with reactant pressures from a few hundredths of a mm. up to 20 mm.,to be susceptible to catalysis by moisture and surface. The rate of anessentially homogeneous reaction in vessels coated with paraffin is approxini-ately proportional to the pentoxide concentration and nearly independentof nitric oxide concentration, particularly a t low pressures of the latter.The overall reaction is proved to beN205 NO = 3N02and the mechanism suggested tentatively isN,05 -+ NO, + NO, (slow) NO, + NO = 2N0, (fast)A new interpretation for the dinitrogen pentoxide decomposition has beensuggested by R.A. Ogg?' who proposes the mechanism(1) N,O5 ---+ NO, + NO, (4)(2) NO, + NO, = N,O, (k2)(3) NO, + NO, = NO, + 0, + NO (k3)(4) NO + N,O, = 3N02 (rapid)There being reason to suppose that k, << E,- d",O51/dt = 2dTr\JOI/dt = 2k,k",O,I/(h + k3) - (2~1/k#,[N,O5]The apparent first-order constant is thus a product of an equilibrium con-stant E1/k, and a bimolecular constant k,.The theoretical grounds foranticipating a diminution of order and rate a t low pressures thereforevanish.The theory of unimolecular decompositions wasfounded upon three main groups of reactions. These were the decompos-itions of ethers and of azo-compounds 30 and certain isomerisation pro-cesses. As already mentioned, both the experimental and the theoreticalinterpretation have been questioned.Whatever be the theoretical interpretation, it can scarcely be deniedthat there exist homogeneous gas reactions which are empirically of the34 L. S. Kassel, " The Kinetics of Homogeneous Gas Reactions," New York, 1932;cf. R. H. Fowler and E. A. Guggenheim, " Statistical Thermodynamics," Cambridge,1939, p.525.PyroZyses of vupours.3 5 J . Chem. Physics, 1939, 7 , 764.37 J . Chem. Physics, 1947, 15, 3.37; cf. 0. K. Rice, ibid., p. 689.36 J . Amer. Chem. Soc., 1947, 69, 1735WILLIAMS AND SINGER : CHEMICAL KINETICS. 57first order over a limited range of conditions. For example, the decompos-ition of benzylideneazine 38 at 335" gives first-order velocity coefficients,independent of the initial pressure, in individual experiments ; and the timefor a, given fractional decomposition is constant for initial pressures rangingfrom 5 mrn. (tt = 4.6 mins.) to 378 mm. (t - 4.2 mins.). The discussionturns, however, on reactions observed over mder pressure ranges. Accord-ing to the theory of unimolecular decompositions, the first-order behaviourprevailing a t high pressures may be expected to change over and approachsecond-order kinetics a t sufficiently low pressures.R. N. Pease 7 7 32 hasput forward the view that many of the reactions which have been inter-preted as unimolecular decompositions are better represented, experi-mentally, over the whole range of pressures as reactions of order 1.5. Thebest example is the decomposition of diethyl ether. The supposedly first-order velocity coefficients attained a t 0.5 atm. pressure have been foundto rise further when pressures up to 20 atm. (and later up to 3.00 atm.)are used (for refs., see Pease '). Pease represents the reaction over thewhole pressure range as one of order 1.5, with a velocity coefficient con-stant within a factor of 2.This would correspond to a mechanism of thetype : Et,O+R ; R + Et,O+products + R ; 2R+X.Questioning also the " unimolecular " interpretation of the azomethanedecomposition, on the ground that this reaction is chemically far morecomplex 39 than had been supposed, so that pressure measurements are nota safe guide in measuring the reaction velocity, Pease concluded that theisomerisation of cyclopropane to propylene was the only reaction to whichthe theory of unimolecular reactions could properly be applied. In a newinvestigation of this reaction, E. S. Carner and R. N. Pease 40 have observed,a t 500°, first-order velocity coefficients which do not appear to fall by morcthan some 8% for initial pressures of 910--150 nim.; but then fall sub-stantially as the initial pressure is reduced to 10 mm.A velocity coefficientderived from a radical mechanism is very satisfactorily constant over thewhole initial pressure range. The effects of added gases fail to decidebetween the " unimolecular decomposition " and '' free radical " mechan-isms. Nitric oxide, propylene, ethylene, and hydrogen are practicallywithout influence upon the rate of reaction. In the presence of decom-posing n-butane, the isomerisation is accelerated.(1) As pointed out byHinshelwood,4l a chain mechanism, of the type quoted above for ether,itself involves a unimolecular decomposition as one step. (2) The repre-sentation of vapour decompositions as processes of order 1-5 is based onthe data for reactions whose chain components have not been inhibitedby nitric oxide.Even if the experimental order is accepted as unity, it had earlier been38 G.Williams and A. S. C. Lawrence, Proc. Roy. SOC., 1936, A , 156, 444.38 E. W. Riblett and L. C. Rubin, J . Amer. Chem. Soc., 1937,59, 1537 ; H. A. Taylorand F. P. Jahn, J . Chem. Physic.s, 1939, 7 , 470.4u J . Anzer. Chem. SOC., 1945, 67, 2067.*rThe whole discussion calls for two remarks.4 1 J . , 1948, 53158 GENERAL AND PHYSICAL CHEMISTRY.argued,31 with supporting experimental evidence, that the reactions werenot unimolecular decompositions, but chain reactions, proceeding bymechanisms which happened to give an experimental first order. ThiBquestion was resolved by the discovery 59 42 that chain components in thesedecompositions could be inhibited by small additions of nitric oxide, whichreduced the rate of decomposition to a fraction of its original value, inde-pendent of further additions of nitric oxide over a certain range.Theresidual reaction was taken to be a genuine unimolecular decomposition.Certain reactions appeared to defy retardation by nitric oxide ; amongthem were the decompositions of acetophenone43 (in contrast to that ofbenzaldehydel') and of acetone (and also of ethyl vinyl ether43a). How-ever, J. R. E. Smith and C. N. Hinshelwood44 have found the decom-position of acetone to be partially inhibited by propylene l2 and also bynitric oxide, which must be applied in rather larger amounts than usual,indicating a low mean chain length.Both the uninhibited and the residualreactions are of first order at pressures >lo0 mm. a t 570". (For otherrecent work on acetone, see Steacie ; also G . M. Harris and Steacie 45 andV. B. Falkovsky and M. Ya. Kagan.46) Rather similar results have beenobtained for methyl ethyl k e t ~ n e . ~ ~ a Much nitric oxide is needed toproduce a small retardation in the initial stages; and the decomposition isthought to be unimolecular. The activation energy of 67.2 kcals. is ascribedto rupture of the methyl-carbonyl bond (cf. E = 68 kcals. for the uninhibiteddecomposition of acetone).It could still be held, however, that the residual reaction was a chainreaction and that nitric oxide could start, as well as stop chains; l2 andidentity of reaction products in the decomposition of n-butane a t 525":'in absence and in presence of nitric oxide, has been considered to supportthis view.It has been countered, however, by J. R. E. Smith and C. N.Hinshelwood: who find that nitric oxide and propylene reduce the rate ofreaction to the same residual value in the decomposition of diethyl etherand also in that of propaldehyde. Moreover, the decomposition of prop-aldehyde, maximally inhibited by nitric oxide, is not further retarded bypropylene. This is strong evidence that the residual reactions are freefrom chains. With diethyl the residual reaction is of first order.The products are essentially the same for the normal reaction and for thereaction inhibited by nitric oxide.With propaldehyde and benzaldehydeit is approximately of second order.gAmong other instances of inhibitory action by nitric oxide, it has been42 L. A. K. Staveley and C. N. Hinshelwood, J . , 1937, 1568.43 R. E. Smith and C. N. Hinshelwood, Proc. Roy. SOC., 1940, A , 176, 468.43a S. N. Wang and C. A. Winkler, Canadian J . Res., 1943, B, 21, 97.44 Proc. Roy. SOC., 1945, A , 183, 33.4% J . Physical Chem. Russia, 1948, 22, 445.460 C. E. Waring and W. E. Mutter, J . Amer. Chem. SOC., 1948, 70, 4073.47 E. W. R. Stemie and H. 0. Folkins, Canadian J . Res., 1940, B , 18, 1.48 J. G. Davoud and C. N. Hinshelwood, Pmc. Roy. Xoc., 1939, A , 171, 39; 1940,46 J . Chem. Physics, 1944, 12, 554.A, 174, 50WILLIAMS AND SINGER : UHEMICAL KINETICS.58noted that 1% of this causes an extreme lengthening of the inductionperiod preceding the homogeneous dimerisation of acetylene at 400-700°.49 Transient inhibitory action by nitric oxide has been observed inthe decomposition of n-butane 50 and of methyl n-butyl ether.51 With thelatter, cyanide was detected in the reaction products, as in some otherreactions inhibited by nitric oxide. It has been suggested 52 that, in com-bining with methyl radicals, nitric oxide forms CH,*NO, which isomerisesto formaldoxime CH,:NOH. Formaldoxime 52 decomposes at 350-415" ina first-order reaction (up to half-life above 400"), primarily to hydrogencyanide and water. The activation energy of 39 kcals. is close to the N-0bond energy (37.7 kcals.) in alkyl nitrites.53 With hydrogen atoms, nitricoxide may form HNO.@ Formaldoxime has actually been isolated in theproducts of interaction of nitric oxide with free radicals from decomposingdi-tert.-butyl peroxide.58 The value 6.5 kcals.has been estimated for theactivation energy of interaction of nitric oxide with methyl radi~als.5~ The" inhibition curves " describing the influence of inhibitor concentration uponthe extent of inhibition (which are, for example, independent of diethylether pressure for nitric oxide, but. not for propylene) provide informationabout the action of inhibitor^.^, 447 50 It is inferred that propylene, whencompared with nitric oxide, combines more readily with CH, than withlarger radicals, such as CH2*O*C,H5 or CH,*CO*CH,.Recent work upon thermal decompositions, not mentioned in the pub-lications of SchumacherThe decomposition of di-tert.-alkyl peroxides 57 in the vapour phasefollows the mechanismand of SteacieY2 includes the following.CMe,*O*O*CMe, --+ 2COMe,COMe, -+ COMe, + CH,CH, + CH, = C2H6The kinetics have been investigated .58 At 140-160", the decompositionof di-tert.-butyl peroxide is a first-order homogeneous reaction. The rateof decomposition is not reduced (as judged from flow experiments) bypropylene or nitric oxide, although, as mentioned above, the latter combineswith methyl radicals formed in the second stage of the reaction. There isno chain reaction. The energy of activation is 39-1 kcals. The 0-0 bond49 D. A. Frank-Kamenetsky, Acta Physicochem.U.R.X.S., 1943, 18, 148; E. A.Blumberg and D. A. Frank-Kamenetsky, J. Physical Chem. Russia, 1948, 22, 171.50 L. S. Echols and R. N. Pease, J. Amer. Chem. SOC., 1939, 01, 1024.51 S. J. Magram and H. A. Taylor, J. Ghem. Physics, 1941, 9, 755.Ga H. A. Taylor and H. Bender, ibid., p. 761.53 E. W. R. Steacie and G. T. Shaw, ibid., 1935, 3, 344.64 H. A. Taylor and C: Tanford, ibid., 1944, 12, 47.5 5 J. S. A. Forsyth, Trans. Faraday SOC., 1941, 37, 312.56 J. E. Hobbs, Proc. Roy. SOC., 1938, A, 167, 456.5 7 Cf. N. A. Milas and D. M. Surgenor, J. Amer. Chem. SOC., 1946, 68, 205, 643;68 R. H. Raley, F. F. Rust, and W. E. Vaughan, J. Amer. Chem. SOC., 1948, 70, 88,P. George and A. D. Walsh, Trans. Faraday Xoc., 1946, 42, 94.2767; F.F. Rust, F. H. Seubold, and W. E. Vaughan, ibid., p. 9560 GENERAL AND PHYSICAL CHEMISTRY.energy in the peroxide is calculated to be 39 kcals. so the rate-determiningstep is taken to be unimolecular fission a t the 0-0 bond. The frequencyfactor of the Arrhenius equation has the high value of 3.2 x 1016.58a Thepyrolysis of di-tert. -amyl peroxide is approximately first order, the activ-ation energy for the initial step being 3 7 4 1 kcals. The inclusion of addedcompounds (e.g., hydrocarbons) with the decomposing peroxides is a valu-able means of studying the interactions of free radicals with those com-pounds. For instance, the vapour-phase addition of hydrogen chloride toethylene, by a free-radical mechanism, may be induced by di-tert.-butylperoxide.First order has been assigned to the decompositions of glyoxal tetra-acetate,59 isopropyl formate,60 tert.-butyl acetate and propionate,60" iso-propyl chlorocarbonateY6l digermane,62 and tetramethyltin (no inhibitionof primary process by nitric oxide).63 The dehydrochlorinations of 1 : 2-dichloroethane, ethyl chloride, and 1 : l-dichloroethane 63a are of first order.The first of these (retarded by propene and by n-hexane) has a free-radicalchain mechanism; the two latter appear to be genuine unimoleculardecompositions.Order 1.5 is ascribed to the decompositions of trimethylaluminium 64and tetrahydrofuran (nitric oxide does not inhibit,, but catalyses when inlarge amount ; so does propylene) .G5Morerecent work includes the following : (1) the decomposition of n-heptane 66by a flow method (first order, using kinetic equations of H.M. H u l b ~ r t ) , ~ ~giving products in agreement with the theories of F. 0. Rice; and of iso-butane 67a (some retardation by propylene) ; (2) the decomposition ofcyclohexene, cyclohexane, methylcyclopentane, and cyclopentane 68 (alluninfluenced by nitric oxide; rate-determining steps, first order), and ofcyclopentene 68a (no inhibition by nitric oxide) ; (3) the demonstration 419 6958n For a suggestion about high-frequency factors, see M. Szwarc, J. Chem. Physics,1949, 17, 107.59 J. C. Arnell, J. R. Dacey, and C. C. C o f i , Canadian J . Res., 1940, B, 18, 410.6O R. B. Anderson and H. H. Rowley, J . Physical Chem., 1943, 4'7, 454.6 1 A.R. Choppin and E. L. Compere, J . Amer. Chem. Soc., 1948, 70, 3797.62 H. J. Emelbus and H. H. G. Jellinek, Trans. Faraday Soc., 1944, 40, 93.63 C. E. Waring and W. S. Horton, J . Amer. Chem. SOC., 1945, 67, 540.630 D. H. R. Barton, J., 1949,148; D. H. R. BartonandK. E. Howlett, ibid., 155, 165.64 L. M. Yeddanapalli and C. C. Schubert, J . Chem. Physics, 1946, 14, 1.6 5 C. H. Klute and W. D. Walters, J . Amer. Chem. SOC., 1946, 68, 506.66 W. G. Appleby, W. H. Avery, and W. K. Meerbott, J . Amer. Chem. SOC., 1947,6 7 Id. Eng. Chem., 1944, 36, 1012.67a A. D. Stepukhovich, J . @en. Chem. Russia, 1945, 15, 341.68 L. Kuchler, Trans. Faraday SOC., 1939, 35, 874; 2. physikal. Chem., 1943, B, 63,307 ; G. R. Schultze and G. Wassermann, 2. Elektrochem., 1941,47, 774.6 8 0 D.W. Vanas and W. D. Waiters, J . Amer. Ckem. SOC., 1948, '70, 4035.69 C. N. Hinshelwood, Faraday Society Discussion, 1947, 2, 1 1 1 ; R. G. Partington,The pyrolysis of hydrocarbons is dealt with, in detail, by Steacie.2.E. Warrick and P. Fugassi, ibid., 1948, 52, 357, 1314.69, 2279.ibid., p. 114WILLIAMS AND SINGER: CHEMICAL KINETIOS. 61that the rates of the chain-inhibited decompositions of saturated paraffinsare almost independent of molecular size and shape for molecules largerthan propane (in contrast to oxidation rates); (5) the unimolecular fissionof toluene to form a hydrogen atom and a benzyl radical, and correspondingreactions for xylenes and the picolines, yielding information about bondstrengths and resonance energies of radicals; 70 (6) the application of theniass-spectrometer 7l to the study of intermediates formed in the decom-position of hydrocarbons.Theory of unirnoZecuZar processes. .A uninioleculnr reaction may beconsidered to consist of the following three steps :A = A * A * + - $ A f - + B + C(1.) (11.) (111.)Step (I) represents the acquisition of (at least) a critical amount of energyby the molecule (sometimes referred to as ( ( energisation ”), (11) the localis-ation of the critical energy in a particular bond (activation), and (111) theactual dissociation.Some attempts have been made in the period under review to obtaina better understanding of these individual steps.Either step (11) (case 1)or step (111) (case 2) may be rate-determining; and in step (11) the prob-ability of activation of an “energised ” molecule may have a constantvalue, independent of the excess of energy over the critical amount, or itmay be equal to the (statistical) probability that (at least) the criticalamount of energy is concentrated in one oscillator, while the remainder ofthe energy is shared among the other oscillators of the molecule (0.K. Riceand H. C. Ramsperger ; 72 L. 8. Kassel 73). If. G. Evans and G. S. Rush-brooke 74 have shown that both for case 1 and for case 2-the validity ofthe second hypothesis being assumed-the rate constant can be expectedto be of the order of e- Eo/kT; the distinction between case 1 and case 2is thus not a useful one. On the other hand, D. D. Eley 75 has suggestedthat such a distinction could be made by determining whether the temper-ature coefficient of the activation energy is positive or negative.Comparing Kassel’s treatment with the transition state method, Evansand Rushbrooke ascribe the discrepancy between the two to the fact thata dissociating bond does not vibrate harmonically (as assumed by Kassel)and that, consequently, the entropy of activation for this model is too low ;the two methods are equivalent if allowance is made for this factor.R.M. Barrer 76 has investigated the mechanism of step (11) for anidealised model : the molecule is considered to consist of a number ofharmonic oscillators of equal frequency, which can exchange energy quantaby “ vibrational collisions.” Making special assumptions concerning theprobability for the transfer of quanta between oscillators, it is possible to70 M.Szwarc, Faraday Society Discussion, 1947, 2, 39 ; J . Chena. Physics, 1948, 16,128 ; J. S. Roberts and M. Szwarc, ibid., p. 981.G. C. Eltenton, ibid., 1947, 15, 455. 72 J . Amer. Chem. SOC., 1927, 49, 1617.74 Trans. Faraday Soc., 1945, 41, 621.76 Ibid., 1948, 44, 399.73 J . Phy8icccZ Chem., 1928, 32, 225.7 K Ibid., 1943, 89, 16862 QBNERAL AND PHYSIOAL CHEMISTRY.calculate how much time will elapse before a given initial energy distributioiiis replaced by one in which a critical number of quanta is accumulated inthe “ breakable ) ) oscillator. The rather cumbersome calculations lead tothe result that the relatively greatest contribution to the reaction ratecomes from molecules whose energy considerably exceeds the critical amount.A more powerful method has been applied to the calculation of thefirst-order rate constant by N. €3.Slater.” If dissociation occurs when theextension of a bond is greater than qo, the absolute rate can be calculatedby finding the frequency with which the normal vibrations of the moleculewill combine in such a way as to make the extension of the bond (a,) greaterthan qo.According to the theory of small vibrationsQ, 5 F(t) = CcxSdg cos 2x (vst + #,)Swhere v, is the 8th normal frequency and t,hs the corresponding phase angle.The activation energy E, is the smallest value of the sum ’CE~ = E for whichthe condition Xlaslss = qo can be fulfilled.This turns out to be E, =B/2B1, . qo2, where B is the determinant llbrsll and B,, the cofactor of bllformed from the coefficients of the expression for the potential energy in9Sterms of “ internal )’ (e.g., stretching and bending) co-ordinates, V =tc %sq,qs.r . sTo obtain the rate constant? i t is necessary to calculate the averagefrequency of attainment of the critical extension for any particular dis-tribution of energy ( E ~ , E ~ , . . ., E ~ ) over the n modes of the molecule andthen to average over all possible values of E ~ , c2, . . ., E, (assuming thermo-dynamic equilibrium). The result for the rate constant is k = v . e-Eb/RT;v is of the order of 1013 sec.-l and can be expressed explicitly as v =1 ~ 2 / A , , B / A B , , , where B,, and B have the same meaning as above, andA,, and A are defined in an analogous manner by means of the coefficientsa,, of the expression for the kinetic energy &CZa,,q,q,.An alternativeformula for v is (v1v2 . . . vn)/(v2’v3’ . . . v n ’ ) ; v,, v2 are the normal fre-quencies, v2’, etc., the normal frequencies of the system when q1 has thefixed value qo.A particularly simple case arises when the potential energy of the dis-sociating bond is independent of the potential energy of the rest of themolecule : V becomes &(b,,qI2 $- XgZb,q,q,), E, = bl,qo2 and v = 1/2x . dbll/m(m is the reduced mass of the two atoms sharing the breaking bond) : themolecule behaves like a diatomic one (with respect to decomposition).This result was also obtained some time ago by H.Pel~er,’~ who used asimilar but less general method.7 7 Proc. Camb. Phil. SOC., 1939, 35, 56; Nature, 1947, 159, 264; 160, 576; PTOC.Roy. Soc., 1948, A , 194, 112.78 2. Electrochem., 1933, 89, 608; Nature, 1947, 160, 676.7 WILLIAMS AND SINGER : CHEMICAL KINBTICS. 63Slater’s treatment can be translated into the formalism of the transition-state theory by writing k = v/dpo . F*’/F, where F is the partition functionof the molecule, F*’ the partition function of the molecule with the co-ordinate q1 between qo - dq, and qo, and 21 the average velocity along ql.Although accurate predictions can perhaps not be expected from amolecular model based on the approximation of classical harmonic oscil-lators, i t is a satisfactory feature of this theory that the frequency factor vis expressed in terms of experimentally accessible parameters (i.e., thecoefficients, ufs, b, which can be obtained from spectroscopic data).An interesting empirical correlation between the activation energy ofuniinolecular decomposition and the vibration frequency of the dissociatingbond has been found by P. Fugassi and E.Warri~k,’~ The formulaEaCt. = 2.858V(35-5 - 900.45. <IDe) (i is the observed wave-number of thebreaking bond, D, its’ dissociation energy obtained by adding the zero-point vibrational energy to the therinochemical bond energy) has beenapplied in all cases where the necessary data for the weakest bond of themolecule were available; as well as in other cases, where only tenbativeassignments of observed frequencies could be made.The agreementbetween calculated and observed activation energies is, on the whole, sur-prisingly good. The authors do not give a theoretical explanation for thevalidity of the formula, but they point out that the expression bears aclose resemblance to the Morse energy of an anharmonic oscillator :EL.ibr. = Nhv(n + 8 ) - (Nhv)2(n + 4)2/4D, with n = 35.The validity of this correlation would seem to lend support to Pelzer’s(and Slater’s) result that the activation energy depends on the force eon-stant of the breaking bond only-provided its potential energy be notcoupled with that of the rest of the molecule. It is, of course, only in thiscase that an observed frequency can be assigned to the particular bond.The established theories of chemical kinetics contain the hypothesisthat the activated molecules are in thermodynamic equilibrium with t,henormal molecules (in the absence of chain processes).Some attemptshave recently been made to provide a theory not dependent on this assump-tion. A chemical reaction can be considered as the passage of a repre-sentative point in phase space over a pcjtential barrier ; the analysis of thisproblem is analogous to that of a system of Brownian particles escapingby diffusion over an energy barrier (e.g., a repulsive potential) in a viscousmedium. H. A. Kramers,80 who has developed this argument by classicalmethods, has shown that for a wide range of conditions, though not for all,the equilibrium hypothesis for the transition state will yield approximatelycorrect results. B.J. Zwolinski and H. Eyring 81 have considered a chemicalreaction to be represented by the transitions between a number of quantumstates which may be divided into “ initial ’’ and “ final ’’ states. Thekinetic equations applicable to this system are the same as those of a set79 J . Physical Chem., 1942, 46, 630. 80 Physica, 1940, 7, 284.J . Arnw. Chem. SOC., 1947, 69, 270264 GENERAL AND PHYSICAL CHEMISTRY.of simultaneous reactions. Calculations made for an idealised model,numerical values being assumed for the transition probabilities, lead to theconclusion that the results of the transition-state theory are not veryinaccurate.J.0. Hirschfelder 82 considers that the activated state of a unimolecularreaction must be approached by a number of steps involving the acquisitionof not more than one energy quantum at a time. The discrepancy betweenthe concentration of activated molecules calculated for this case and theequilibrium concentration of activated molecules is not negligible (the ratiois 0.385), but the difference between the expected reaction rates is notvery great.Although this ( ( non-equilibrium '' treatment of chemical reactionswould appear to be superior to the '' equilibrium " theory from a logicalpoint of view, it cannot yet rival the latter in usefulfiess.Chain Reactions.G. B. Kistiakowsky and E. R. van Artsdalena3 have found that thethermal and photochemical brominations of methane proceed by the samemechanism as the bromination of hydrogen.The initial rate of the thermalreaction a t 570" K. is almost the same for both reactions.(4( I ) Br, --+ 2Br(2) Br + CH, -!&+ CH, +HBr(B.)(1) Br + CH, = CH,Br + HBr(2) CH,Br + Br, = CH,Br, + Brx-3 (3) cH3 + Br, + CH,Br + Br (3) CHzBr + HBr = CH,Br + Br(4) CH, + HBr(5) 2Br + M --% Br, + MCH, + ErThe mechanism (A) gives the rate law (first approximation for methylbromide as sole bromination product) :[ K = equilibrium constant for (l)] which is in agreement with observation.Oxygen inhibits the reaction. The activation energy for the photochemicalreaction (determined from the rates at 423", 453", and 483" K.) is 17.8 kcals. ;this is ascribed to reaction (2).The coefficient k,/k, is not independent oftemperature as in the hydrogen-bromine reaction. From the temperaturecoefficient of the hydrogen bromide inhibition, E, - E , - 2 kcals. (E,, E3are the activation energies for E , and k3, respectively).The bromination of methyl bromide 83 is 7-5-10 times faster than thatof methane; it is not inhibited by hydrogen bromide. The observedactivation energy of 15-6 kcals. is attributed to step (1) of the scheme (23).82 J . Chenz. Physics, 1948, 16, 22. Ibid., 1944, 12, 469WILLIAMS AND SMOEB : CHEMICAL KINETICS. 65Calculations carried out by means of a reasonable model for the transitionstate of (1) give a rate which is in excellent agreement with the observedone.Although only the photochemical bromination of ethane has beeninvestigated,s* it is probable-by analogy with methane-that, in this casetoo, the thermal reaction would follow the same mechanism.Here, how-ever, the constants of the Bodenstein-Lind expression show trends.The data obtained from the kinetic analysis of the bromination ofmethane 83 and ethane 84 have been used to calculate the bond strengthsof the C-H bonds as 102 and 98 kcals., respectively.Another reaction following this type of rate law is H, + (CN), = 2HCN 8 5a t 550-675". There is no trouble due to polperisation of (CN),, but thereaction is a t least partly heterogeneous below 650". Apart from an induc-tion period and failure a t low pressures, the equationdlHCpU'1- w 3 2 I [(CpU'),IP a ' dt - 1 + 0.25[HCN]/Z[(CN),]is obeyed approximately, while the constants for 1-5 order fall sharplywith time when the ratio [H,]/[(CN),] is high.The activation energy is73 kcals. The mechanism is exactly the same as for the hydrogen-brominereaction, if Br, is replaced by (CN),.The nitrogen-oxygen reaction. The oxidation of nitrogen introducedinto explosive mixtures has been investigated by J. Zeldovich.86 Theresults reported and the ingenious kinetic analysis relate to the interactionof nitrogen and oxygen in a system whose temperature is falling.From the yields of nitric oxide in the reaction products of differentexplosive mixtures of nitrogen, oxygen and some gaseous " fuel " thefollowing facts are established : (1) The yield of nitric oxide is stronglycorrelated with the concentration of nitrogen and the concentration ofoxygen remaining after the combustion of the fuel.(2) The nature of thefuel used (e.g., H,, CO, CH,, etc.) does not influence the amount of nitricoxide produced, except in so far as the reaction temperature is affected.(3) I n independent flow experiments analysis of samples taken at differentpoints in a rapid stream of burning gas shows that the exothermal combus-tion is virtually completed in see., before measurable amounts of nitricoxide are formed (the oxidation of nitrogen ceases after see.). (4) Theyield of nitric oxide is always smaller than the equilibrium concentrationa t the (calculated) highest temperature attained during the explosion.The nitrogen-oxygen reaction is reversible ; and the rate of decompos-ition of nitric oxide was determined by measuring the yield of NO in mixturesto which nitrogen dioxide had been added initially.Extrapolation of thedata on the rate of decomposition of nitrogen dioxide 87 into nitric oxide84 H. C. Andersen and E. R. Van Artsdalen, J . Chem. Phylsics, 1948, 16, 479.*' N. C. Robertson and R. N. Pease, J . Amer. Chem. Soc., 1942, 64, 1880.Acta Physicochim. U.R.S.S., 1946, 21, 577; cf. M. V. Polyakov, L. A. Kostyu-chenko, and D. S. Nosenko, J. Physical Chem. Russia, 1944,18, 115. *' M. Bodenstein and H. Ramstetter, 2. physilca2. Chem., 1922,100, 106.REP.-VOL. XLV. 66 QDINBRAL AND PHYSICAL CHEMISTRY.and oxygen shows that decomposition will be complete in less than 10-8 8ec.in the relevant; temperature range ; consequent'ly, the final concentrationof nitric oxide is greater or less than its initial concentration depending anthe amount of nitrogen dioxide added initially.The " critical " concen-tration of nitric oxide, defined as that which is not changed by the reaction,depends on the maximum temperature (TTrl) reached; if this is below2500" K. the '( critical " concentration is comparable to the equilibriumconcentration at T,; it is relatively much smaller a t higher temperatures.The approximate activation energy for the decomposition of nitric oxideis obtained as follows : if the reaction is reversible and bimaleculard[NO]/dt k'[N2][02] - k[NOJ2 . . . . . (1)At the '' critical " concentration of nitric oxide (denoted by { 11, k'[N,][O,] =k(N012, since d[NO]/dt = 6 (approximately). Making the simplifyingassumption that the reaction proceeds for r seconds a t T, and then stops,( 1 ) can be integrated : this gives kz as a function of the " critical " con-centration and of the final conoentration of nitric oxide.If kr is plottedagainst l/Tm a, fairly straight line is obtained (2O0O--29QOo K.), The activ-ation energy ( A ) determined in this manner is 82 f '10 kcals./mole. Theactivation energy for the formation of nitric oxide ( A ' ) equals A $- 2E,where E is the known heat of the reaction : A' = 82 f 10 + 2 x 21-4 =125 f 10 kcals.The remainder of the analysis is carried out with the aid of these resultsand some ingenious dimensional considerations.Let [NO],.denote the equilibrium concentration and k the rate constant€or decomposition a t the instantaneous temperature, and [NO], the equili-brium concentration and k, the rate constant a t Tm. The rate equationcan be writtend[NO]/dt = k[NO]i'- lc[N0I2 . . . . .It is supposed that k/km and [NO];/[NO], depend on the dimensionless timevariable t / ~ only (7 is as yet unspecified) ; k/k, = f1(t/.) ; and [NOIa/[NO], - f 2 ( t / r ) for all reactiod mixtures. Thus (2) becomesIt can be shown that (3) would hold €or all reactions of this type (carriedout in the same system) provided the cooling lawdT/dt = - aT2 or 1/T = l/Tm + at . . ' (4)is valid. This cooling law has in fact been verified by independent experi-ments. Substituting De- A for the rate constant k and Re- EIRT for thoequilibrium constant K = [NO]~/([N2][O2])+, one can eliminate fi and f2from (3), using (4) WILLIAMS AND SINGER : CHEMIOAL KINETICS.67where z can now be identified with &/(A Jr 2E)a - R/6Ea (since A - 4E).Equation (5) can be integrated by means of approximate methods. Thecurve thus obtained for the variation of [NO]/[NO], with T, is very similarto the observed one ; the deviation of 12-13% for large yields is attributedto the inhomogeneity of the temperature distribution.Calculation of the cross-sectional area for the bimolecular reaction ofnitrogen and oxygen, however, gives a value about 1000 times too large( L e . , 3 x 10-13 The following chain mechanism has therefore beensuggested to the author by Semenov :k* .h.,kd k,(1) 0 + N, + 0, + N - 47 kcals.; (2) N + 0, + NO $- 0 + 4 kcals.k, /Ic3 and k,/k, may be calculated by statistical mechanics. Introducingthe calculated values for these, assuming equilibrium with respect to thedissociation of oxygen, and neglecting a term Tc,[NO] in a sum Ic,[NO] +E,[O,] (since [NO]<[O,]), the stationary state method gives :d[NO]/dt = 5 x 1011[02]-*. e-86>000/RT ([O,][N,] .2J . e- 439000/RT -- "012)1.-l mol. sec.-l . . . (6)This rate law differs from the bimolecular equation first assumed only bythe factor [O,]-*. Experiments designed to investigate the effect of theoxygen predsure over a wide range gave results in fair agreement with (6).The chain mechanism is compatible with reasonable cross-sectional areas forthe collisions.Branching-chain Reactions.The Hydrogen-Oxygen Reaction.-The general features of the thermalreaction between hydrogen and oxygen ar0 well known.88 At temperahresbetween 500" and 600" c., a very slow reaction at low pressures gives placeto an explosion a t the " first explosion limit " (pressure of a few mm.).At the '( second explosion limit " (about 100 mm.in a silica vessel a t 550"),explosion gives way to a reaction of measurable speed. The numericalvhlues of both limits vary with temperature ; and, on a pressure-temperaturegraph, the curves for the first and the second limit meet, forming a con-tinuous curve, bounded on the low-temperature side, which enclose8 aregion-referred to by some writers as the '' explosion peninsula "-inwhich explosion ocours.It is well established that the first limit occurswhere the concentrations of radicals formed in branching chains are nolonger kept stationary by surface deactivation, and that the second limitoccurs where a reaction in the gas phase prevents further effective branch-es C. N. Hinshelwood and A. T. Williamson, "The Reaction between Hydrogenand Oxygen," Oxford, 1934; N. Semenov, " Chemical Kinetics and Chain Reactions,"Oxford, 1935; B. Lewis and G. von Elbe, " Combustion, Flames and Explosions ofGases," Cambridge, 1938 ; W. Jost, " Exploaione und Verbrennungsvorgange in Gasen,"Berlin, 1939; L. 5. Kseeel, Ohem. Reviews, 1987, 21, 33168 QEENERAL AND PHYSICAL CHEMlSTR17'.ing of the chains.Above the second limit, the reaction is again controlledby deactivation of chain carriers a t the vessel wall. At still higher pres-sures, explosion again occurs. This can be due.to breakdown of isothermalconditions; but, even if isothermal conditions are maintained, a " thirdexplosion limit " is to be expected, on theoretical grounds, at which branch-ing of chains gets out of control. Evidence for a third limit has now beenobtained; and it appears that it is controlled by the extent to which chaincarriers are deactivated a t the surface.Recent work has made use of the observationby R. N. Pease 89 (in flow experiments) that the thermal combination ofhydrogen and oxygen is greatly retarded (up to 2000-fold) if the reactionvessel is rinsed, before use, with potassium chloride solution. I n Pease'sexperiments the rinsing also eliminated the formation of hydrogen peroxide,which otherwise appeared at 530-550" in the region of slow reaction.A. A.Frost and H. N. Al~ea,~O working with a Pyrex-glass vessel previouslyrinsed with a 10% potassium chloride solution, observed an increase in thefirst explosion limit of about 5-fold compared with earlier values in silicavessels. I n more recent. work, visible, coherent salt deposits have beenused; and their effect upon the first limit has been confirmed by A. H.Willbourn and C. N. Hinshelwood.loO Using various salts a t 500°, theseauthors have found increases in the first limit up to 18-f01d, as comparedwith an uncoated silica vessel.They find relative efficiencies to be Cs+,Kf > Ba++, Ca++ and I- > F-, Br-, SO,--, C1-, the effect of iodide beingparticularly marked. Clearly, the effects are due to much enhanced efficiencyof chain-breaking at the salt surfaces. Correspondingly, Willbourn andHinshelwood find the effect of the salts KCI, KI, CsCl, and CsI upon thesecond explosion limit to be very small, there being a slight depression, themore noticeable the higher the temperature. However, G. von Elbe andB. Lewisg9 find that the explosion region is diminished a t both its boun-daries by salt coatings, the second limit being appreciably lowered a t 500-530" by coating quartz or Pyrex vessels with the salts KC1, BaCL, Na2W04,and K,B,04. The same workers found that the salts KCl, BnCl,, Na2W04,and K2B40, reduced the rates of combination of hydrogen and oxygen, a tpressures above the second limit, to identical values; K2B,04 was lesseffective, except under conditions of rapid reaction; but K2B,0, + KOHbehaved like the other salts.A boric acid surface behaved like clean silicaor Pyrex. Von Elbe and Lewis drew the theoretically important con-clusion that limiting conditions had been reached where the chain-breakingefficiency of the surfaces had reached a constant maximum efficiency, so thatthe rate of chain destruction was governed by the rate of diffusion of chain-carriers to the wall. Willbourn and Hinshelwood made a similar assumptionin interpreting their own experiments in potassium chloride-coated vessels ;but they have pointed out that their assumption cannot be made withoutreserve, because caesium chloride (rate a t 550" = 0.28 mm./min.) retards@* A.A. Frost and H. N. Alyea, ibid., 1933, 55, 3227.Coated reaction vessels.J. Amer. Chem. SOC., 1930, 52, 5106WILLIAMS AND SINGER : CHEMICAL KINETICS. 69the reaction more eficiently than potassium chloride (rate = 0-60). Cullisand Hinshelwood loo find that iodide-coating completely alters the characterof the reaction, probably because of the liberation of minute amounts ofiodine, which is known to be an inhibitor of the hydrogen-oxygen reaction(cf. A. B. Nalbandyan 107). The efficient retarding salts have cationswhich can form hydrides; 100 and hydrogen atoms may be removed byreactions of the type KX + H = K + HX, ICX + H = KH + X.TheHO, radical might form H202 + H, the 'H being taken up as hydride andthe peroxide being decomposed on the salt surface (cf. Pease s9). On theother hand, von Elbe and Lewis99 have suggested that the chain-breakingefficiency of salt surfaces is due to strong adsorptive forces exerted bythem.The rupture of chains at surfaces has been treated mathematically byN. N. Semenovg2 and experimentally by A. B. Nalbandyan, in silver (ex-plosions observed, contrary to earlier work) and iron vessels 93 and on wiresof various material^,^^ and by W. V. Smith.95 Surfaces of ZnO,Cr,O, andgraphite are particularly effective in raising the first limit. In a vesselcoated with potassium tetraborate, containing a graphite rod, the energyof activation for H + 0, = OH + 0 is estimated to be 17.8 k ~ a l s .~ ~The practical importance of salt-coated vessels is that they make thereactions both slower and much more reproducible. The theoreticallyanticipated effects of vessel diameter and gas pressures upon the firstand the second explosion limits have been clearly observed in suchvessels.(In connection with surface effects, it is noteworthy that S. von Bogdandyand M. Polanyi 96 found an increased chain length in the hydrogen-chlorinereaction, induced by sodium atoms, when the vessel surface was coveredwith sodium chloride.)New investigations withsalt-coated vessels 97-100 have led to firm conclusions about the mechanismof reaction, with a substantial measure of agreement. The present positionof the reaction has been reviewed by C.N. Hinshelwood; lol and the estab-Mechanism of the hydrogen-oxygen reaction.92 Acta Physicochim. U.R.S.S., 1943, 18, 93.93 Compt. rend. Acad. Sci. U.R.S.S., 1941, 32, 196; 1944, 44, 328.94 Ibid., 1945, 47, 202; A. B. Nalbandyan and S. Shubina, J Physical Chem.Russia, 1946, 20, 1249; cf. V. V. Voevodsky, ibid., p. 779.9 5 J . Chem. Physics, 1943, 11, 110.9G 2. Electrochem., 1927, 33, 554.9 7 M. Prettre, J . Chim. physique, 1936, 33, 189.9 8 0. Oldenberg and H. S. Sommers, J . Chenz. Physics, 1939, 7, 279 ; 1940, 8, 468 ;1941, 9, 114, 573; 1942,10, 193; cf. F. S. Dainton, ibid., 1941, 9, 826; Trans. ParadaySoc., 1942, 38, 227.9B G. von Elbe and B. Lewis, J . Chem.Physics, 1939, 7, 710; H. R. HeiPle andB. Lewis, ibid., 1941, 9, 584; von Elbe and Lewis, ibid., 1942, 10, 366.A. H. Willbourn and C. N. Hinshelwood, Proc. Roy. SOC., 1946, A , 185, 353,369, 376; C. F. Cullis and C. N. Hinshelwood, ibid., 186, 462, 469.lol C. N. Hinshelwood, ibid., 188, 170 GENERAL AND PHYSIUAL UEBMISTRY.lishment of a plausible mechanism has, in turn, given riae to new discussionsof the explosive reaction.lQ5 The mechanisms proposed are :Scheme I Scheme II(von Elbe and Lewis). (Willbourn and Hinshelwood).(Authors' numbering of reactions.)(i) H,O, + M = 20H + M Initiation -+ H or OH(1) OH + H2 = H20 + H(2) H + 0, = OH + 0(3) 0 + H2 = OH + H(6) H + 0, + M = HO, + M(1) OH + H2 = K20 + H( 2 ) H + 0, = OH + 0(3) 0 + H, = OH + H(4) H + 0, + M = HO, + M(6) HO, + H, = H20 + OH(11) H02 + H2 = H202 + H ( 5 ) HO, -+ *H20 (walls)or (7) HO, + H, = H,O, + HSurface3 H,O, + 0 (12) 2H02 --(5) -I- O, + H2°2 = H2° + '2 -I- OH and (8) H,O, = H20 + QO, (7) HO, + H202 = H20 + 0, + OHSurface (13) H20, ---+ H2O + +OzSurface(14) H, + 0, --+ H,O,Surface Surface H, 0, OH ----+- Destruction H, 0, OH -----+ DestructionAgreement is reached on the following points : (a) The principal potentialchain-propagating processes are the reactions numbered (l), (2), and (3)in both schemes. They would give rise to branching chains.( b ) At pres-sures up to the first limit, branching is controlled by surface deactivationof H, 0, and OH. (c) Control of branching is re-established at the secondlimit by the reaction labelled (I, 6) and (11, 4).Gaseous recombinationssuch as 2H + M = H, + M are inadmis~ible.~~ (d) The radical HO, isdestroyed at the wall [reactions (I, 12) or (11, S)], but it may also reactwith H, by reactions (I, 11) and (11, 6) [or I1 (7)], and one of these processesbecomes the principal chain carrier in the reaction a t measurable speedabove the second explosion limit. Competition between (11, 6) or (I, 11)and surface deactivation of HO, accounts for the influence of surface uponthe reaction above the second limit. Von Elbe and Lewis argue that, withuncoated surfaces of low chain-breaking efficiency, the lifetime of HO,should become large and reaction (I, 11) should become noticeable at pres-sures around the second limit.Consequently, the value of the secondlimit should be higher in uncoated than in salt-coated vessels, as, indeed,these authors find experimentally (compare previous section).In scheme (I), the condition for explosiona t the second limit reducea toThe second explosion limit.Ic,[M] = 2k2in which [M] = [Ha] + [O,] + [XI, X being an inert molecule.second limit : lo2At the[H,I+ kO,[O,l+ kCXI= K ' (1WILLIAMR68 AND SINGER : CHEMICAL KINETICS. 71In this equation Ice, = &z/Z~,; Ex = &/&, and &,, goa, BX are oon-stants proportional, with the simpler gases, to the collision numbers ofthe respective molecules with the " reaction complex," H-0,; ko, andbx(kH2 = 1) can be calculated from the kinetic theory of Theyhave also been determined experimentally, from measurements of thesecond explosion limit pressure, by von Elbe and Lewis (I), in potassiumchloride-coated Pyrex vessels, for different proportions of hydrogen andoxygen in the reaction mixture, with and without addition of inart gases,a t temperatures of 480-570"; and also by Willbourn and Hinshelwood (11)a t 550-580", for uncoated silica and €or potassium chloride-coated vessels.The results of the two investigations are compared in the following table :kx, c~c., = Zx/ZH, kx, obs.kx, obs.Gas, X. I. 11. I. 11. - 1.80 - He ......................... 1.600, ........................ 0.42 0.4 0.35 0.4" -0.325N, ........................ 0.46 0.45 0.43 0.39*-0.35HSO 0162 14.3 l l * O * -8.1 ........................0.6-0.9CO, ........................ 0.43 0.51 1.47 0.90* Uncoated silioa vessel at 550".The agreement in the quantitative interpretation of the second explosionlimit appears to be excellent, and it supports the postulated mechanism.Nevertheless, this mechanism is not a unique solution, though much themost plausible one.99The two sets of experiments concur in furnishing a value for kco, higherthan the theoretical one, and also a particularly high value for kEzO (cf.Nalbandyan,lo7 who finds 7cRn0 = 5-5 a t 450"). The latter is important,because steam is the reaction product. Even a small amount of watervapour markedly lowers the second limit pressure; 91 and von Elbe andLewis consider that this fact explains a number of earlier observationsupon the hydrogen-oxygen reaction.The formation of OH or H irl.the processes[(I, 6) and (I, 11) ; (11,4) and (II,6) or (II,7)] which continue the (stationary)chain reaction, a t pressures above the second limit, implies that, a t highenough pressures, increased concentrations of H and OH may again causea branchiiig-chaii explosion at third limit. In uncoated reaction vesselswith surfaces o f low chain-breaking efficiency, the branching-chain explosiona t the third limit is masked by thermal explosions; but, with the slowerreactions in potassium chloride-coated vessels, the third limit has beendetected and cliaracterisecl. It occurs a t pressures between 400 and1600 mm. a t temperatures between 550" and 610". Since the principalchain-breaking process, above the second limit, is the surface deactivationof KO, [(I, 12); (11, 5 ) ] , it may be predicted that explosion a t the thirdlimit should be favoured and the third limit pressure should be lowered,by increasing diameter of the reaction vessel.This effect has been veri-fied.989 99 Quantitatively, the influences of the proportions of hydrogenThe third explosion limit.lo2 G. H. Grant and C. N. Hinshelwood, Proc. Roy. SOC., 1933, A , 141, 2972 GENERAL AND PHYSICAL CHEMISTRY.and oxygen in the reaction mixture, and of added inert gases, upon thevalue of the third limit pressure, resolve themselves into the influence ofgas composition upon the rate of formation of the HO, radical in the gasphase (as they do a t the second explosion limit), together with the influenceof gas composition upon the rate of diffusion of HO, to the wall, and withthe effect of hydrogen proportion in reaction (11, 6).For the influence ofgas composition upon the rate of (11, 4), the constants derived to accountfor the effects of changing gas composition a t the second limit can also beused at the third limit. This procedure has been employed both by vonElbe and Lewis and by Willbourn and Hinshelwood. It involves theassumption, made in both investigations, that the chain-breaking efficiencyof the salt surface is so high that the rate of diffusion determines the rateof destruction of the chain carrier. The validity of this assumption hasalready been commented on.Taking the reaction mechanism to be composed of the steps (11, 1)-(11, 6), the rate of formation of steam is given by equation (3), below.loOThe condition for explosion is that the denominator in the expression onthe right-hand side of this equation should be zero ; i.e.,in which2E,/Ch,[lMl = E,/(E,[H,I + 4CE,[MI = k41([H21 + ~0,[0,1 + hXlXl>*Using relative diffusion coefficients Dx' -- DHz/DX, which can be derivedfrom the kinetic theory of gases, the condit-ion for explosion, a t a giventemperature, reduces toin which px = [X]/[H,], K is identical with the constant K in equation (l),and C is a constant which must be found from experiments on the thirdlimit itself.Willbourn and Hinshclwood have applied equation (2) to theirresults for the effects of hydrogen-oxygen proportion and of admixednitrogen, carbon dioxide, and water vapour upon the value of the thirdlimit pressure a t 586".They find that the constants which must be insertedin equation (2) to give the best fit between the theoretical and the experi-mental curves are not far removed from the theoretical constants and thosedetermined from measurements a.t the second limit, It is noteworthy thatthe experimental curve for the influence of 100 mm. of carbon dioxide uponthe third limit a t varying proportions of hydrogen to oxygen is quite differentin form from the corresponding curve for 100 mm. of nitrogen (nitrogenlowers the third limit pressure) ; and that the general theoretical equation (2)reproduces this difference in form when suitable constants are inserted.The form is governed by the value of Ex.More elaborate equations--corresponding to the more elaborate scheine(1)-have been successfully applied to the third limit by von Elbe andLewis.Por these, reference must be made to the original paper. ThesWlLLIAMS AND SINGER : CHEMICAL KINETICS. 73authors point out that values of the third limit pressure may be distortedby two contradictory factors, namely, a thermal influence in the very rapidreactions (just below the explosion limit, rates as high as 80-100 mm. ofwater per min. were observed), tending to displace the third limit to lowerpressures; and the formation of steam, which should raise the third limitfor the same reason that it depresses the second limit (high kH-,o).How-ever, in the experiments of Willbourn and Hinshelwood water vapour loweredthe third limit pressure. This result, accompanied by a reduction of theconstant C of equation (2), was ascribed to an effect of water upon thepotassium chloride-coated surface, reducing its chain-breaking efficiency.Von Elbe and Lewis state that the third limit pressure is independentof the nature of the surface, if it is heavily coated with any of the saltsused by them. They find that the third limit explosion is preceded by aninduction period, during which a rapid reaction occurs. The inductionperiod (up to 70 seconds) is small near the junction of the second and thethird limits and increases towards lower temperatures.Nothing has so far been said about howthe chains are started.Von Elbe and Lewis reject the dissociation ofhydrogen into atoms as chain initiator, on the ground that the temperaturecoefficient of the reaction, in a range uninfluenced by explosion limits, givesan overall activation energy of the order of only 100 kcals., which theyhold to be insufficient to include the activation energies both of chain con-tinuation and of chain initiation, if the latter is the dissociation of hydrogenmolecules. Instead, they suggest that a spontaneous reaction (hetero-geneous or gaseous) in the first brief stage preceding the establishment ofstationary concentrations supplies atoms which react by the processes(I, S), (I, 12), and (I, 11) to form hydrogen peroxide. They summarisethis stage by the equationThe chain-initiation process.(11, 14) H, + 0, = H,O, (possibly a t surface)and they consider that the steady-state initiation reaction is(i) H,O, + M = M + H,O + 0 or 20Hmanner. Their reaction scheme (11) leads to the equationWillbourn and Hinshelwood 100 treat the initiation reaction in a novelin whichfi is the rate of the initiation reaction.A function R* is definedsuch that d[H,O] I dt = 2f1R*. With the expressions for Xk,[M] and for k,used in treating the experiments a t the third explosion limit, R* is givenby an expression involving the gas composition and the constants kx, Dx’,K , and C of equations (1) and (2)) already evaluated at the third limit. Thefunction R* can thus be calcubted, without reference to experiments on th74 GENERAL AND PHYSICJAL CHEMISTRY.rate of reaction.The rate of reaction is proportional to (f,R*), so thevariation of reaction rate with the pressures of hydrogen, oxygen, and inertgases can be calculated for different possible forms of the functionf,. Com-parison with the observed influence of these variables upon the rate shouldindicate the correct form off,.At the temperature of the experiments (>560") chain initiation in thegas phase is thought to be possible. Four processes are considered :( a ) H2 + 0, = 20H (c) H2 + 0 2 + H20, -++ 20H(b) H2 + M = 2H + M (d) H2-(Walls) -+ 2HOf these, reaction ( b ) , as chain initiator, gives much the best agreementbetween experiment and calculation. For this case, the function fl takesthe formf1 = E[H21(ZH~[H21 + z0~[021 +where ZHz, Zo2, and Zx are the relative collision numbers for hydrogenmolecules, respectively, with hydrogen, oxygen, and an inert gas X.TheZ values are calculated from kinetic theory.Cullis and Hinshelwood loo have measured rates of reaction a t differenttemperatures (560-596") and have calculated R* a t each temperature fromthird-limit data. They have thus obtained the temperature coefficient offl and are able to calculate, directly, the activation energy for the initiationreaction. They find this t80 be 100 kcals. for potassium chloride-coatedvessels and 92 kcals. for cEsium chloride-coated vessels. They regard theformer value as the more reliable and consider that the result supports theview that the dissociation of hydrogen into atoms is the initiation stepunder the conditions of their experiments.(Third-limit pressures arehigher for cesium than for potassium chloride.) P. G. Ashmore and F. S.Dainton lo2a support this conclusion. They find 134 and 123 kcals. forthe activation energy of initiation at two different gas pressures.The measurable reaction between the second and the third explosion limits.The schemes (I) and (11) concur in attributing the major part in the con-tinuing reaction above the second limit to the steps (I, 6), (I, ll), and(I, 12) or (11, 4) with (11, 5) and (11, 6) or (11, 7). To preserve a steadyconcentration of hydrogen peroxide, von Elbe and Lewis introduce the steps(I, 7) and (I, 5), together with (I, 13) (because hydrogen peroxide is knownto decompose heterogeneously) .lo3 They have formulated equations forthe reaction velocity to correspond with scheme (I) and have tested themexperimentally with generally satisfactory results.In uncoated silica or Pyrex vessels, the reaction above the second limitshows auto-acceleration in its early stages, and is often not easily repro-ducible in speed.I n salt-coated vessels, the reactions are, as a rule, notauto-accelerated, but proceed a t a constant rate for an appreciable time.The rates are reproducible.102a Nature, 1946, 158, 416.lo3 Cf. R. C. Mackenzie and M. Ritchie, PTOC. Roy. Xoc., 1646, A, 185, 207WILLIAMS AND SINGER : CHEMICAL XINETICS. 75To account for the auto-acceleration, V. V. Voevodsky104 adds thereactian NO, + H,O = H,O, + OH to the scheme (I), with the suppositionthat it is an easier reaction than (I, 11).In uncoated vessels, the difficulty ofstep (I, 11) leads to an accumulation of HQ, radicals (calculated to attain apartial pressure of nearly 3 mm. near the beginning of the reaction) andcombination is slow. The small amounts of water formed enter easilyinto reaction with HO,, forming OH. The reaction accelerates and theconcentration of HO, falls.The reactionin this region has been discussed by N. N, Semenov.lo5 Explosion is pre-ceded by it period of auto-acceleration, during which, according to Semenov,Ap = Ce4t. The experiments of A. Kovalsky,lo6 at pressures near thefirst limit, confirmed this and gave values for $ a t different temperaturesand initial pressures.Adopting, for the reaction mechanism, the stepsH, + 0, = 20H, followed by (I, 1, 2, 3, 6), with wall deactivation of Hand HO,, Semenov 1°5 derives equations for the reaction rate, a t pressuresnot greatly exceeding the first limit pressure. On introducing experimentalresults for +, p l , and p , (the first and the second limit pressures), the equa-tions lead to quantitative deductions, which are in approximate agreementwith experiment. Approximate agreement is also obtained a t higher pres-sures (still between the first and second limits), though experiments are verydifficult here, because of thermal effects. Experiments of A. €3. Nal-bandyan lo7 (made with a sensitive membrane manometer, furnishing photo-graphic reoords) give induction periods of <0.1 to 0.4 see.(decreasingtowards the middle of the explosion region and increasing near the ex-plosion limits), whose values are in acoord with theoretical calculation.Neither the nature of the wall (in potassium chloride-coated and stainless-steel vessels), nor the presence of water vapour, influences the temper-ature dependence of the induction period inside the explosion peninsula,and of 4. Water therefore does not react chemically with the activecentres.Semenov's equations lo7a also furnish rates for individual steps in themechanism (see below), and an estimate cjf the concentration of hydrogenatoms present a t various stages of the explosive reaction. The remarkableconclusion is reached that for stoicheiometric mixtures a t initial pressurepo = 1*43p1, 2p1, and 4p1, 5, 15, and 40%, respectively, of the initialhydrogen is present as hydrogen atoms (cf.von33lbe and Lewis's 99 estimatesfor the partial pressure of hydrogen atoms during the slow reaction ; e.g.,a t 560", pR = 9-7 xExperimental support is put forward for the prevalence of high con-Io4 J . Physical Chem. Russia, 1946, 20, 1285.Io6 N. N. Semenov, Bull. Acad. Sci. U.R.S.S., C1. Soi. Chim., 1945, 210; Compt.rend. Acad. Sci. U.R.S.S., 1944,43, 342 ; 44, 62, 241.Io6 Physikal. 2. Sovietunion, 1932, 1, 595; 1933, 4, 723.Io7 Acta Physicochim. U.R.S.S., 1944, 19, 483, 497 ; 1945, 20, 31 ; cf. Kondratev,Compt. rend, Amd. Sci. U.R.S.S., 1945, 49, 116.Acta Physicochim.U.R.S.S., 1945, 20, 291.The expllosive reaction between the first and the second limits.mm. a t total pressure 170 mm.)76 GENERAL AND PHYSICAL CHEMISTRY.centrations of hydrogen atoms in mixtures reacting within the explosionpeninsula. In the first place, this rests on the estimation of OH-radicalconcentration by absorption spectroscopy.lo8 Estimates by L. I. Avramenkoand V. N. Kondratev 109 were shown by 0. Oldenberg and F. F. Rieketo need re-interpretation. Taking this into account, later work by Avra-menko 111 leads to the conclusion that in a hydrogen-oxygen flame, a ttotal pressure about 40 mm. (flame temperatures 900-1370"~.), the OH-radical concentration exceeds lo4 times the thermodynamic equilibriumvalue and is thus brought into being by the chemical reaction. On thesupposition that the partial pressure of OH radicals (pOH) may amount to0.1% of the initial oxygen pressure,lo52 112 it is deduced from the relativerates of the reactions ( b ) and (c), below, that (PH should be 40-200 timesp O H , which means that pH is 6 2 0 % of the initial hydrogen pressure, inapproximate agreement with the above theoretical estimate.(In mixturesundergoing slow reaction at about 1 atm. pressure and 550", 0. Oldenberg,E. G . Schneider, and H. S. Sommers 113 detected no OH radicals by absorp-tion spectroscopy and concluded that their concentration was less than oneradical in 300,000 molecules.)Kondratev 114 furnishes experimental evidence of a different kind. Athermocouple inside a thin quartz tube, coated with ZnO,Cr,O,, is exposedto the reaction mixture.The heak of recombination of hydrogen atomsupon this particularly efficient catalytic surface 943 95 is registered as atemperature difference AT between this thermocouple and a second, un-coated, thermocouple. (On a third, potassium chloride-coated thermo-couple AT = 0, showing that the temperature rise on ZnO,Cr,O, is notcaused by recombination of OH radicals; cf. Smith.95) A temperaturerise AT is observed only for mixtures a t pressures within the explosionpeninsula; and it is not due to surface interaction of molecular hydrogenand oxygen. Total pressures up to 5 mm. were used, a t temperatures of476-693". The maximum observed value for AT was 284", with totalpressure, p = 3.83 mm.From a consideration of the heat balance, theexpression AT = 1000pH/p is deduced theoretically, which would givepE = 1 mm. It is found experimentally that pHjpcxAT, when pH/p iscalculated from the kinetic expressions, with the proportionality constant3000, so that the theoretical expression gives the correct order of magnitudefor the hydrogen-atom concentration.lo* Cf. A. G. Gaydon, " Spectroscopy and Combustion Theory," 2nd edn., London,lo9 Acta Physicochim. U.R.S.S., 1937, 7, 567.110 J . Chem. Physics, 1938, 6, 439, 779; 1939, 7, 485.ll1 Acta Physicochirn. U.R.S.S., 1942, 17, 197.112 V. N. Kondratev, J . Physical Chem. Russia, 1946, 20, 1231 ; Cornpt. rend. Acad.113 Physical Rev., 1940, 58, 1121.114 V. N. Kondretev and E.I. Kondrateva, ibid., 1946, 51, 607 ; J . Physical Chent.Russia, 1946, 20, 1239; H. Kondrateva and V. N. Kondratev, Acta Physicochim.U.R.S.S., 1946, 21, 1, 629.1948, p. 115.Sci. U.R.S.S., 1944, 44, 20WILLIAMS AND SINGER : CHEMICAL KINETICS. 77Sir A. C. Egerton and G. J. Minkoff have detected considerableamounts of hydrogen peroxide in hydrogen-oxygen flames (at 30-40 mm.)directed against c?, surface held a t -180". Part of tho hydrogen peroxide isformed in the gas phase, and the mechanism H + 0, -+ H02* ; HO,* +H, = H,O, + H is suggested for its formation, an excited HO, radicalbeing produced in binary collision between H and 0,.The evidence for the existence of the HO, radical in the gas phase hasbeen reviewed by Minkoff,l16 who applies the " semi-empirical " transition-state method to the reaction H + 0, = HO + 0.The following estimates are derived bySemenov and his collaborators (units : 1.sec.-l) :Rates of elementary reactions.( a ) H, + 0, = 20H ;( b ) OH + H, = H,O + H ; k = 7 x 10-12T4e-10,0oo/I~~'(c) H + 0, = OH + 0 ; k = 6.4 x 10-12T)e- l*$OO/RT(d) 117 0 + H, = OH + H ; k: < 3 x 10-11Tbe- fh00"/RT= 2-46 x 10-12THe- 45,oooiR7'For (c), Nalbandyan and Shubina 94 find E = 17,800 cals. from observ-ations on the first limit, in agreement with observations on the secondlimit. Von Elbe and Lewis 99 give E = 45.5 and 17.0 kcals., respectively,for reactions ( a ) and (c).For recent work on the influence of nitrogen dioxide upon the hydrogen-oxygen reaction, see F.s. Dainton and R. G. W. Norrish 11* and A. R.Nalbandyan. 119The Hydrogen Sulphide-Oxygen Reaction.-The oxidation of hydrogensulphide 120 takes place according to the equation 2H,S + 30, = 2S0, + 2H,O.The kinetics of the reaction have been comprehensively investigated byN. M. Emanuel.121 Over a wide range of pressure and temperature oxidationproceeds a t a measurable speed. At sufficiently high pressures and tempera-tures thermal explosions occur. At low pressures and high temperatures,explosions occur between pressure limits. The reaction clearly shows thecharacteristics of branching chains.The phenomenon of the induction period has been ingeniously investi-gated.122 The experimental arrangement included three interconnected115 Proc.Roy. Xoc., 1947, A, 191, 145; cf. W. 13. Rodebush, C. R. Keizer, F. S.McKee, and J. V. Quaglino, J. Amer. Chem. Soc., 1947, 69, 538; E. J. Badin, ibid.,1948, 70, 3651.116 Faraday SOC. Discussion, 1947, 2, 151.11' P. Harteck and U. Kopsch, 2. physikal. Chem., 1931, B, 12, 327.Proc. Roy. SOC., 1940, A, 177, 445.llS J . Physical Chem. Russia, 1946, 20, 1283.120 Cf. L. Farkas, 2. Elektrochem., 1931,37, 670 ; H. W. Thompson and N. S. Kelland,J., 1931,1809; B. YakovlevandP. Shantsrovich, Acta Physicochim. U.R.S.S., 1937,6,71.121 J . Physical Chem. Russia, 1940, 14, 863; Acta Physicochim. U.R.S.S., 1944, 19,360.lZ2 N. M. Emanuel, J. Physical Chem. Russia, 1945, 19, 15; cf. Semenov, J. Chern.Physics, 1939, 7, 683; Semenov and Emanuel, Compt.rend. Acad. Sci. U.R.S.S., 1940,28, 21978 GENERAL AND PHYSICAL CHEMISTRY.cylindrical vessels, the " preparatory " vessel (l), the " intermediary "vessel ( R ) , and the " indicator " vessel (2). Mixtures of hydrogen sulphideand oxygen, generally a t an initial pressure (Po) of 100 mm. were assembledin vessel (1) (kept generally a t 270"). After a known time (t,) in vessel (l),the reaction mixture was transferred to vessel (2) (kept generally a t ahigher temperature, e.g., 300"), either directly or after a sojourn (t') in (a).Let rl" be the normal induction period for a reaction mixture with theinitial conditions prevailing in vessel (11, and T~~ that for the temperatureof vessel (2) and for a freshly prepared reaction mixture a t an initial pres-sure equal to that taken up by the experimental mixture when transferredto vessel (2).Then, forexample, with (1) a t 270" and with Po = 100 mm., T ~ " - 27 secs. Afterdirect transfer of reaction mixture from vessel (1) to vessel (2) (which wasat 300") the pressure (P) in (2) was 83 mm. In a series of experiments,it was then found that when t, = 7,' - 27 secs., 72 = 0, i.e., reaction in (2)proceeded immediately with kinetics corresponding to the new temperatureand pressure. Thus, active centres formed during the induction periodin (1) survive the transfer to (2). With t, < 7," then 22 < T ~ " and T~ issmaller the nearer t, is to 7," ; r2 approaches 720 as t, _L, 0, corresponding tothe immediate transfer from (1) to (2) of an " unprepared " reaction mixture.The behaviour of the active centre was examined quantitatively bymaking use of the intermediary vessel (R).After a preparatory period oft, < T ~ " in vessel (l), the mixture was kept for time t' in R, a t room tem-perature. On connection with the indicator vessel (Z), the pressure in thelatter was approx. 50 mm., corresponding to - 60 secs. I n these cir-cumstanoes the observed induction period 22 in vessel (2) was a linearfunction of t,. This result is in accord with Semenov's theory; for (withq = fractional pressure change) in (1) q = Ale+ltl and, after transfer to (2)at time t,, q = A2e+*tz. Assuming no change during transfer, Aleditl =Let the observed induction period in (2) be T~.A2e+pt3 and T~ = 41t1/42 + ( 1 / ~ $ ~ ) In A,/A2.With t, = r,", and with vessel R a t different temperatures (always lessthan that requiied to bring about the oxidation of hydrogen sulphide), thelife of the active centre was found to be about 8 hours at room temperatureand about 8 mins. a t 135", as indicated by the observation r2 -+ rc20. At alltemperatures of R, r2 was a linear function oft', the period of sojourn in R.Defining the " relative concentration," c, of the active centre by puttingc = 1 for t, = T,O, the relation between T~ and c was determined, by trans-ferring a " prepared '' mixture to R after a time t, spent in (l), and thenreplacing a known fraction of the mixture in R by an " unprepared " onefrom (l), and measuring T ~ . The relation found is log c proportional to 72,which is itself linear with t,. This exponential growth of the active centrewith time is one of the first direct experimental proofs of Semenov's theory.The destruction of the active centre (SO, see below) in R is of firstorder, with an activation energy of 8-5 kcals./mole. Water vapour (andalso adjacent tap grease) accelerates its destruction. After a series ofexperiments a deposit of sulphur was found on the walls of RWILLIAMS AND SINGER : CHEMICAL KINETICS. 79Sulphur monoxide. The active centre has been identified as sulphurmonoxide, SO, pfeviously suggested by Semenov as an intermediate inthe oxidatiod of carbon disulphide and of carbon o ~ y s u l p h i d e , ~ ~ ~ anddetected spectroscopically 124 (along with CS) in a carbon disulphide flame.Sulphur monoxide was investigated particularly by P. W. S ~ h e n k , l ~ ~ whoprepared it by the action of an electric discharge upon a mixture of sulphurand sulphur dioxide vapours, and assigned to it bands in the spectral regionA 2490-3400~. Schenk found sulphur monoxide to be stable for a con-siderable time a t low pressure, then the characteristic bands vanished after48 hours, giving place to bands of sulphur dioxide. The decompositionwas written : 2SO f= SO, + S. In the gas phase, sulphur monoxide islargely present as the dimer S202.125, 126The spectrum of sulphur monoxide has been identified in a reactingmixture of hydi-ogen sulphide and 0 ~ y g e n . l ~ ~ In further experiments byN. M. Emanuel,122 the indicator vessel (2), of the previous apparatus, wasreplaced by an absorption tube for the spectroscopic observations. Thepartial pressure of sulphur monoxide, Pso, was estimated from the relativeintensities of the absorption bands, calibrated by measurement of thepressure of sulphur dioxide formed by decomposition of sulphur monoxide.The concentration of sulphur monoxide was found to grow during theinduction period. With a stoicheiometric mixture, Po = 100 mm. a t 270°,the maximum value of Pso was approx. 7-5 mm. a t an extent of conversion(as indicated by pressure change) of 3 = 0-18. The maximum rate ofreaction occurred a t 3 = 0.13. Thus, in the initial stage of the oxidationof hydrogen sulphide, up to 20% of the latter was converted into sulphurmonoxide. The spectroscopic measurements of Pso fell on the kineticcurve for increase in the concentration of the active centre.The decomposition of sulphur monoxide was followed spectroscopicallyin the intermediary vessel R a t various temperatures. The spectroscopicresults agreed with the previous kinetic results for the decay of the activecentre and gave an activation energy of 8 kcals. (cf. kinetic value). Theinteraction of sulphur monoxide (formed in the preparatory vessel) withwater, in the intermediary vessel, a t O---40°, was also examined spectro-scopically. The rate of reaction decreased with rising temperature andwas given by - dc/dt = kc3I2y, in which c and y are (dimensionless) relativeconcentrations of sulphur monoxide and water vapour respectively. Thereaction SO + S,02 + H,O = H2S + 2S0, was proposed in interpretationof the result.The identification of sulphur monoxide as the active centre was finally123 Cf. V. N. Kondratev, Acta Physicochim. U.R.S.X., 1942, 16, 272.12* Idem, 2. Physik, 1930, 63, 322.125 2. anorg. Chem., 1933, 211, 150; P. W. Schenk and H. Platz, ibid., 1935, 222,126 E. I. Kondrateva, and V. N. Kondratev, J. Physical Chern. Russia, 1940, 14,12’ N. M. Emanuel, D. S. Pavlov, and N. N. Semenov, Compt. rend. Acad. Sci.177.1528; V. G. Markovich and N. M. Emanuel, ibid., 1947, 21, 1251.U.R.S.S., 1940, 28, 618; Bull. Acad. Sci. U.R.S.S., C1. Sci. Chim., 1942, 9880 GENERAL AND PHYSICAL CHEMISTRY.confirmed by the introduction of synthetic sulphur monoxide 12* (made bythe method of Schenk) into stoicheiometric mixtures of hydrogen sulphideand oxygen. With various proportions of added sulphur monoxide (estim-ated spectroscopicalIy), the induction period was reduced to an extentwhich was in accord with the reduction caused by similar proportions ofthe active centre, formed in the preparatory vessel, as deduced from thekinetic experiments. The influence of synthetic sulphur monoxide uponthe induction period of the explosive reaction (see below) and upon thevalues of the explosion limits was also in satisfactory quantitative agree-ment with that deduced for the active centre formed in the preparatoryvessel. Synthetic sulphur monoxide enters into an explosive reaction with0 ~ y g e n . l ~ ~This has been studied 130 by arranging for thetransferred gas in the “ indicator ” vessel (e.g., a t 347”) to be a t pressures(e.g., 14 mm.) lying within the explosion peninsula, after sojourn in the“preparatory” vessel a t 270”, with Po = 100 mm. An induction periodnormally precedes explosion. It is again found that for t l < ~ l I , 7, forexplosion is a linear function of t,, approaching zero as t, + T~ . Witht, > explosion occurs in the “ indicator ” vessel without an inductionperiod, and will now take place a t pressures which lie outside the normalexplosion peninsula. For the increment AP, of the second limit pressurein the “ indicator ” vessel, it is ‘found that AP, = xPs0 and that Pso = @Po,where a and @ are constant a t a given temperature. These relations arenot observed a t the third (thermal) explosion limit.B’or the mechanism of the reaction, the following scheme is put forward(author’s numbering of equations) :A lower pressure limit has been observed.The explosive reaction.(0) H,S + 0, = H,O + SO + 44.4 kcals.(1) S + 0, = SO + 0 - 0-8 kcal.(2) 0 + H,S = H,O + S + 45-4 kcals.(3) SO + 0, = SO, + 0 + 20.4 kcals.(4) SO + SO + 0, = 2S0, + 158.4 kcals.S and 0 deactivated at wall.The step (4) is introduced because the maximum velocity occurs at anearly stage (at 18-20% conversion) of the reaction.lo5Emanuel l3l has studied the “ intermediates ” formed in chain reactionsby a novel “ contraction ” method. The reaction is arrested by expandingthe reaction mixture from the hot reaction vessel into a cold evacuatedvessel (or by removing the heat source, with subsequent rapid or slow128 N. M. Emanuel, Compt. rend. Acad. Sci. U.R.S.S., 1942,36, 145.129 H. Kondrateva and V. N. Kondratev, ibid., 1941, 31,. 128; E. Kondrateva andV. Kondratev, J. Physical Chem. Russia, 1941, 15, 731 ; 1944,18, 102.130 Emanuel, Compt. rend. Acad. Sci. U.R.S.S., 1942, 35, 250.131 Ibid., 1945, 48, 488; 1948, 59, 1137; V. G, Markovich and N, &I. Emanuel,J . Physical Chem. Russia, 1947, 21, 1259WILLIAMS AND SINGER : CHEMICAL KINETlCS. 81cooling). The contraction A (due to recombination of radical " inter-mediates " or sometimes to association of end products) is determined asthe difference between the pressure exerted in the cold vessel by the cooledreaction mixture and that exerted by dry air under the same conditions.Contractions have been observed during the oxidation of hydrogen sulphide,acetaldehyde, propylene, and acetylene. For hydrogen sulphide, A changesregularly as the reaction proceeds, going through a maximum a t 20% con-version. It is found that Acc[SO]; and that the dependence of A ontemperature of the reaction mixture agrees with the temperature effect of[SO], calculated from the influence of [SO] on the ignition limit.Additional papers on the mathematical theory of chain reactions arethose of N. N. S e r n e n ~ v , ~ ~ ~ A. A. Frank-Karnenetsk~,~~~ N. S. .Ak~lov,~~*and L. von MUffli11g.l3~K. S.G. W.F. S. DAINTON.G. S. HARTLEE-.K. SINGER.G. WILLIAMS.132 J . Physical Chenz. Russia, 1943,17, 187 ; Acta Physicochim.. U.R.S.S., 1943,18,93.133 Ibid., 1942, 16, 357.134 E.g., Compt. rend. Acad. Sci. U.R.S.S., 1945, 48, 644.13G 2. Physik, 1944, 122, 787