GENERAL AND PHYSICAL CHEMISTRY.INTRODUCTION.IN this year’s Report the policy, outlined last year, of having com-plete reports on certain aspects of physical chemistry has beencontinued. For a number of years there have been articles on infra-red and Raman spectra written from the point of view of applicationt o problems in molecular structure. This year the report on thattopic treats of electronic spectra in the Schumann ultra-violet andthe information such spectra give about the electronic structure ofsimple molecules. The Report for 1937 described the revival ininterest in the structure of liquids ; the continued interest justifiesanother article reviewing the more recent work on this subject.The chemical kinetics section this year is divided into two parts.The first deals with polymerisation reactions.Within the pastfour or five years a new branch of kinetics has thereby arisen, andalthough the growth continues, the subject is now sufficiently stableto merit some discussion in a co-ordinated manner. The secondpart deals with a problem of long-standing interest, namely, theeffect of the solvent on reactions in solution. This is restricted tobiinolecular reactions in order to simplify the discussion of theresults. In the realm of surface chemistry this year the propertiesand reactions of monolayers on aqueous substrates are discussed,but the biological implications of the work are omitted. An accountis also given of work on multilayers.H. W. M.1. STRUCTURE AND MOLECULAR FORCES IN LIQUIDS.Intermolecuhr Forces and the Properties of Solutions.In the Annual Reports1 for 1937 “Intermolecular forces and theproperties of liquids” were reviewed by J.A. V. Butler. Theadvances made in recent years in our understanding of the liquidstate have had great influence on the theories of solution and ofchemical reactions in solution. These problems are being ap-proached from the standpoint of the theories of the liquid state. Theimportance of reactions in solution and of the influence of solventon the velocity and the equilibrium constants of such reactions is sogreat and widespread that the need for an understanding of thenature of solutions and of solution processes in terms of inter-molecular forces and the behaviour of molecules requires no emphasis.1 P.76.REP.-VOL. XXXVI. 34 GENERAL AND PHYSICAL CHEMISTRY.Intermolecular Forces and the ‘Heats of Solution.-One of theinteresting points about the calculation of the heats of solution ofmolecules from our knowledge of intermolecular forces is that verysimple considerations can lead to quantitatively exact results for theenergies of solution.The general model which has been adopted for these considerationsis one in which the solution process is divided into two steps : (i)the formation of a cavity in the solvent large enough to accommo-date the solute molecule, and (ii) introduction of the solute moleculeinto the cavity.2 The energy change accompanying the solution ofa molecule from the gas phase will be made up of two terms, E =E, - E,, where E, and E, represent the two respective energychanges, the former being an expenditure of energy, and the latterbeing made up of the energies of interaction between the solutemolecule and the solvent molecules.The main differences in theattempts to calculate the energies of solution processes arise fromthe different methods employed for the calculation of the two termsE, and E,. We will review here several attempts which have beenmade with different types of system.H. H. Uhlig3 determined the energy (or rather the ftee energy)of cavity formation from the surface tension of the solvent. I nforming a cavity of radius r the free energy change is 4xr2y, where yis the surface tension of the solvent. If then the solute moleculehas a radius r, Uhlig writes the free energy change as 4w2y - E,.The Ostwald solubility coefficient ct is then related to the free energychange byIf E, is small compared with the energy of forming the cavity, or ifE, is constant from one solvent to another and from one solute toanother, then the greater the radius of the solute molecule and thegreater the surface tension of the solvent the smaller will be thesolubility.Uhlig finds that J.Horiuti’s4 data for the solubility of gases inorganic solvents do obey equation (l), and that the molecular andatomic radii resulting from this expression agree fairly well withvalues obtained from other methods. In view of the simplicity ofthe model and of the fact that the entropy changes accompanyingsolution are neglected, the correspondence is remarkable.D.D. Eley5 has considered other methods of determining theenergy change of cavity formation.- k T I n a = 4 x T v - E s . . . * (1)B. Sisskind and I. Kasarnowsky, 2. anorg. Chem., 1933, 214, 385.J . Physical Chem., 1937,41, 1215.Sci. Papers Inst. Phys. Chern. Res. Tokyo, 1931, 17, 126, 222.Trans. Faraday SOC., 1939, 35, 1421EVANS : STRUCT~JRE AND MOLECULAR FORCES IN LIQUIDS. 35(a) When 1 mol. of gas dissolves in an infinite volume of solutionThe at a concentration of 1 mol./l. an expansion of V C.C. occurs.energy change accompanying this expansion is given by( W a V T = P + ~(ax/aV),and if p is negligible AE, = TaAV/P, where a and p are respectivelythe thermal expansion coefficient and the compressibility of thesolvent.In forming a cavity in a liquid one is expanding the free volumefrom vf’ to vj, and hence the change in E, accompanying this changein free volume is given approximately by E, = TaV/p if the changein free volume is identified with the actual volume change of thesolution.(b) The second method is identical with that of Uhlig exceptthat the energy (y - T2y/aT)4xr2 is used.(c) The third method is that of E.Lange and W. whohave suggested E, = Evap.(r/rr)2 for the energy of forming a cavityof radius r in a solvent of molecular radius r,. The term E, isrelated to the latent heat of vaporisation L by Evap = L - RT.The values obtained by these three methods do not agree verywell-those given by ( b ) and (c) correspond most closely.The verywide disparity which Eley finds between the values given by thethree methods in the case of water is attributed to the specialstructure of liquid water.Rather striking success has been obtained from this model ofcavity formation followed by introduction of the solute molecule inthe case of solution of organic molecules in water by J. A. V. Butlerand of gases in water by D. D. Eley.8 Butler expresses the energyrequired to bring a solute molecule from the gas phase into solutionin terms of the energy &, required to separate water molecules inorder to make a cavity of the necessary size, and w, the energy ofinteraction of the solute molecule with the water molecules a t thesurface of the cavity.Hence= x#bV, W - x$A, WConsidering only those forces acting between adjacent molecules,we haveE = *n+w,w - q L , wwhere n is the total number of water molecules at the surface of thecavity ; i.e., in making a cavity +n water-water contacts are broken.If A is an organic molecule made up of different units a, and ba, is6 8. physikal. Chem., 1937, A , 180, 238.Trans. Faraday SOC., 1937, 33, 229.* Ibid., 1939, 35, 128136 GENERAL AND PHYSICAL CHEMISTRY.the interaction energy of group a of the molecule A with an adjacentwater moleculewhere a is the number of water molecules adjacent to the group a.If the quasi-crystalline structure of water is taken as a basis, then,e.g., a methane molecule, being approximately the same size as awater molecule, will occupy a ‘‘ lattice point,” i.e., a position equi-valent to a water molecule, in the water structure.This will involvethe breaking of two water-water contacts (four are broken and twoare re-made) and the forming of four water-methane contacts.HenceTo form a cavity to accommodate an ethane molecule, it will benecessary to replace two water molecules at ‘‘ lattice points ” by themethyl groups of the ethane, thus leaving a cavity with 6 watermolecules in its surface. HenceE = &y&v - C a $ , , wECH‘ = 2$W, W - Q$CH4. W= 3&7,m - 6$CHs.WButler extends this method to include hydroxyl, ketonic and alde-hydic and amino-groups, as well as the hydrocarbon unit CH,.Having obtained a value for &, from the latent heat of vaporisationof water and the characteristic values (e.g., &, w) from experimentaldata, it is then possible to calculate with remarkable accuracy theheats of solution of a large number of organic compounds by buildingreasonable models of the cavities required.There is a difference in viewpoint between Eley and Butler on thequestion of the energy change of cavity formation.Using method(a) for calculating the energy, Eley concludes that for inert gasesin water at ordinary temperatures there is no need for a cavity tobe formed by the breaking of water-water contacts; i.e., he doesnot consider it necessary for an inert-gas molecule to take up aposition by displacing a water molecule from a lattice point, butrather that the solute molecule can be accommodated in the largefree spaces in the water lattice which can be expanded if needbe by a small expenditure of energy.At ordinary temperatures, E, being negligibly small, the heats ofsolution are given by E = nE,, where n is the number of watermolecules adjacent to the inert-gas solute molecule; and E A , theenergy of interaction between a water molecule and the inert-gasmolecule, is given bywhere the subscripts 1 and 2 refer to the inert-gas and the wateEVANS : STRUCTURE AND MOLECULAR FORCES IN LIQUIDS.37molecules respectively, a is the polarisability, p the dipole moment,r the radius, and i the ionisation potential. To obtain agreementbetween the calculated and the observed heats of solution, n isrequired to be 10 for all inert gases except helium, where 4 is foundto be the best value.Heats of Solution of Ions.--If water were an ideal insulator ofdielectric constant -q, then for an ion of charge Ze and radius r theheat change accompanying the solution of the ion from the gasphase would beThe field set up by an ion is greater than the saturation field for thedielectric and, as pointed out by P.Debye,g equation (2) will nothold under these conditions.J. D. Bernal and R. H. Fowler lo have calculated the heats ofhydration of ions by splitting up the energy into the followingterms :(a) The energy of the water molecules in the co-ordination shell ofthe ion. This is approximately given by nP, where n is the numberof water molecules co-ordinated round the ion, and P is the inter-action energy between the ion and a water molecule.( b ) The energy of the main bulk of the water outside the spherein which the field is greater than the saturation field of the dielectric.(c) The mutual energy of the water molecules which have in thefield of the ion changed their normal orientations.The heat of solution of an ion is given by[(q - 1)/2q][Z2e2/r] .. . . . (2)q - 1 Z2e22-q ' R u, = ___ - + nP - u(w)where R is the radius of the saturation sphere and u(w) is the energyof re-orientating the water molecules in the field of the ion.M. G. Evans and D. D. Eley l1 have made very similar calculationsof the heat of hydration of ions by considering the energy changesinvolved in the following steps.(a) A tetrahedral group of five water molecules is removed fromthe liquid into the gas phase. The expenditure of energy involvedin this step arises from the interactions between the tetrahedralgrouping and the neighbouring water molecules.( b ) In the gas phase the tetrahedral group is dissociated intofive separate water molecules.This expenditure of energy arisesfrom the mutual interaction of the water molecules in the tetra-hedral group.9 " Polare Molekeln," Chap. V, 1929.10 J . Chem. Physics, 1933,1,511.11 Trans. Faraday SOC., 1938, 34, 109338 GENERAL AND PHYSICAL CHEMISTRY.( c ) In the gas phase four water molecules are co-ordinated roundthe particular ion to be dissolved. This energy will be 4P, where Pis the interaction energy between the ion and a single water molecule.( d ) The new tetrahedral structure including the ion is returnedto the cavity in the liquid.The energy terms involved in thisstep will include the reorientation energy of the water molecules,because the water molecules round an ion have a different orientationfrom that round a central water molecule, and the energy of intro-ducing a charged sphere of radius ri + 2r, into a dielectric medium.(e) Finally, the fifth water molecule is returned to the liquid, astep which involves the latent heat of condensation of water. Thetotal energy change involved in these steps amounts to an expressionwhich is practically identical with that given by Bernal and Fowler.Both these methods lead to calculated heats of hydration of ionswhich agree with those determined from the heats of solution of ionpairs on the assumption that potassium and fluorine ions have thesame heats of solution.The method first given by Bernal andFowler is the basis of all the recent attempts to calculate heats ofsolution whether of ions or of non-electrolytes when special attentionis being given to the structure of the solvent and the individualbehaviour of the solvent and solute molecules.The Partition Fwnctions for Solutions.-Since the thermodynamicproperties of a, system can be calculated from the explicit partitionfunctions for that system, it is a matter of great interest and im-portance to construct such functions for liquids and solutions.The partition function for a liquid of N molecules can be written l2as f N = JNB(T).Here J is the partition function for the internalelectronic, vibrational, and rotational states of the molecule whichare independent of the position of the molecule in the liquid; B(T)is then the partition function for the translational motion of themolecule and can be writtenB(T) = 1. . . lexp (- $) dxl.. . d z ~ . dpzl. . .where W is the potential energy of the system for a particularconfiguration in phase space.The problem of obtaining a partition function for a liquid becomesthat of obtaining an explicit form for B(T).J. E. Mayer, in a series of papers,13 has attempted an evaluation ofla R. H. Fowler, “ Statistical Mechanics,” 2nd Edition, Cambridge Univ.Press, 1937; R. H.Fowler and E. A. Guggenheim, “Statistical Thermo-dynamics,” Cambridge Univ. Press, 1939.l3 J. E. Mayer, J . Chem. Phy8/sics, 1937,5,67; J. E. Mayer and P. F. Acker-mann, ibid., p. 74; J. E. Mayer and S. F. Harrison, ibid., 1938, 6, 87;J. E. Mayer, J . Phy&ul Chem., 1939,43, 71EVANS : STRUCTURE AND MOLECULAR FORCES IN LIQUIDS. 39B(T), but in most cases the problem has been approached either bydealing with those systems for which B(T) can be obtained withsome certainty or by making approximations to a general form ofB(T). Thus, for example, H. Eyring l4 expresses the translationalpartition function for a liquid as312 NB(T) = [,(’*) ] exP(-j$)Here W , which is a function of the configuration, has been replacedby its average value E, averaged over all accessible configurations,and the whole uncertainty is now contained in the volume Vf;this is termed the free volume, and is the volume which is accessibleto the centre of the molecule. Eyring and his collaborators haveconsidered several models for determining the free volume.On the assumption that the whole of the free volume of the liquidis available to each molecule (which distinguishes the liquid statefrom the solid, in which each molecule is confined to its particularcompartment of free volume), the partition function of a liquid canbe writtenA large amount of work has been carried out on the thermodynamicproperties of the liquid state, using this expression.The approximation used by Eyring, of each molecule moving ina uniform average potential field E , was first made by E. A.Guggen-heim,l5 who points out that in this approximation no account istaken of the change in interaction energy as the molecule movesabout its average position. The behaviour of the molecule willprobably be better represented on the basis of the quasi-crystallinemodel of a liquid.16 Each molecule will be moving about a ‘‘ latticepoint ” of minimum potential energy E,, and will behave as an iso-tropic three-dimensional harmonic oscillator with a characteristicfrequency v. 17 The partition function for the liquid will be given byfN = (z) kT 3N JNexp { - Eo &kT}l4 H. Eyring and J. Hirschfelder, ibid., 1937, 41, 249; J. 0. Hirschfelder,I>. Stevenson, and H. Eyring, J. Chem. Physics, 1937, 5, 896; J.F. Kincaidand H. Eyring, ibid., p. 587; ibid., 1938, 6, 620; J . Physical Chem., 1939, 43,37 ; H. Eyring and R. F. Newton, Trans. Farachy SOC., 1937,33,73.l5 Proc. Roy. Soc., 1932, A, 135, 181.The model of a liquid as an assembly of harmonic oscillators is essentiallydue to G. Mie (Ann. Physik, 1903,11,657).l7 A more general model of a liquid has been used by J. E. Lennard-Jonesand A. F. Devonshire, Proc. Roy. SOC., 1937, A, 163, G l ; 1938, A, 165, 1.It is a model of a molecule moving in the available volume in a field of forceset up by the interactions between the molecule and its neighbours40 GENERAL AND PHYSICAL CHEMISTRY.Applying the same methods to binary mixtures of non-electrolytes,we can write the partition function for a mixture of ‘N, and N2molecules of species 1 and 2 asj”1+ 3 2 = J1N1 J2NaB( T)where J , and J, are the partition functions for the internal states ofthe molecules 1 and 2 which can be separated from the configurationaldegrees of freedom, andB( T) = I.. . / exp (- $) dxl . . . dzNl .dx,’ . . . dzns’. dpZ1. . . dpz,, . dpZ1,. . . dpxN,As in the case of a liquid, Eyring replaces W by an average value E,and introduces the free volume of the mixtureHere wf is the free volume of the solution and the term Wl + N2) !NI! N , !arises from the physically different permutations of the two-specieswhich are possible.To obtain the thermodynamic properties from this partitionfunction, we can write the free energyThermodynamic Properties of Regular and Ideal 8olutwns.lgE.A. Guggenheim l 9 has discussed the thermodynamic propertiesof systems with especially simple forms for B(T). He defines aperfect solution as one satisfying the following conditions : (1) Themolecular types A and B pack in the same way. (2) The molecularvolumes are sufficiently alike so that mixtures of the two species ofmolecule can pack in the same way as each of the pure liquids. (3)The ratio of the free volumes, vj, of the pure liquids does not differfrom unity by more than 30%. (4) When the two liquids are mixedthe molecular volumes Va and VB and the free volumes vfA and v p bothremain unaltered. ( 5 ) The average potential energy of a pair ofmolecules AB is zero.18 See R. H. Fowier, op cit. ; R.H. Fowler and E. A. Guggenheim, op. cit.Is Proc. Roy. SOC., 1935, A , 150, 552; Trans. Paraday SOC., 1937, 33, 151EVANS : STRUCTURE AND MOLECULAR FORCES IN LIQUIDS. 41For such a solutionwhere a is the average potential energy of molecule A in the pureliquid A, and a similar definition obtains for xB.This expression for the partition function leads to a valuefree energy P, vix.,NB { - xB - kT In +Bug - kT + kT Inwhere $ = (2~rnkTjh~)~'~Jwhich is approximately equal to the Gibbs function G.for the+SincexA, XB, vA, and vB are independent of ATA and NB, the partial potentials,which leads to Raoult's law.The extension of these ideas to strictly regular solutions, approxi-mate methods being used, has been made by A. W. Porter,20 J. H.Hildebrand,21 and G.Scatchard22 in an attempt to evaluate thedeviation of actual solutions from perfect solutions. The physicalsignificance of the approximation, that the change of entropy onmixing is the same as for an ideal solution, is complete randommixing. By random distribution one means that the neighboursof each molecule are on the average distributed among the variousmolecular species of the mixture in the proportions of their molefractions, the average local composition in the vicinity of a moleculebeing identical with the bulk composition of the solution.In real solutions with non-vanishing heats of mixing, randomdistribution is no more than an approximation to the actual state of2o Trans. Paraday SOC., 1920, 16, 336.21 J. Amer.Chem. SOC., 1929, 51, 69.z2 Chem. Reviews, 1932, 8, 32142 GENERAL AND PHYSICAL CHEMISTRY.affairs. The problem thus resolves itself into a study of the in-fluence of deviation from random distribution on the thermodynamicfunction of the system. The average distribution of the neighboursof a molecule in solution among the various species present is deter-mined by two opposing influences-the disordering effect of thermalmotion and the ordering effect of intermolecular forces. Forexample, if in a binary mixture of A and B the intermolecularattraction between A and B is greater than between like molecules,each molecule will exert an ordering effect in its vicinity resulting ina local composition richer in molecules of the opposite species thanthe solution in bulk. An extreme case of such an ordering influenceis to be found in the case of ions dissolved in water, where thestrong ion-dipole interaction causes a (‘ freezing ” or ordering of thewater molecules in the vicinity of the ion.The extent to whichsuch local segregation of species can be established will depend uponthe thermal motion and will be greater the lower the temperature.In recent years the problem of order and disorder has become ofgreat importance in discussions of solid solutions and alloys.23This case of order in solutions differs from that in solids in that thereis no long-range order in liquid solutions and we need only dealwith local order. Recent treatments of order-disorder in liquidsolutions have been made by R.H. Fowler and G. S. Ru~hbrooke,~*using the method worked out by Bethe 23 for solid solutions, and byJ. G. Kirkw00d,2~ who shows that the local order established by amolecule among its neighbours opposes the tendency of the solutiont o separate out into two phases. This process may be considereda macroscopic mechanism for establishing order, satisfying a ten-dency for a molecule to make its environment rich in its own species.This tendency may be partly satisfied without separation into twophases through the microscopic ordering mechanism by which amolecule establishes a local composition richer in its own speciesthan in the solution in bulk.Relations between the Energy and the Entropy of Solution.The transfer of a molecule from the gas phase to a solution ischaracterised by the change of any two of the three partial molalquantities : heat content H , free energy B, and entropy X :- - -- - -A F = AH - TASA complete molecular model of the solution process would give a93 H.A. Bethe, Proc. Roy. SOC., 1935, A , 150, 552.24 Trans. Faraday Soc., 1937, 33, 1272; G. S. Rushbrooke, Proc. Roy. SOC.,P 6 J. PhycwhE Chem., 1939, 43 107. 1918, A, 166, 296EVANS : STRUCTURE AND MOLECULAR FORCES IN LIQUIDS. 43priori values for these quantities, and we have seen in the precedingparagraphs that attempts are being made in simple cases to calculatethese terms.If we consider a series of solutions in which the forces acting arequalitatively similar, it might be possible to obtain a relationbetween AF, AH, and A s which would be valid for any system inthe series.Such a relation might be valid either for ( a ) a givensolute in a series of different solvents, or for ( b ) a series of differentsolutes in the same solvent. M. G. Evans and M. Polanyi 26 sug-gested the existence of such relations by considering a continuouschange in the solvent (particular solvents being points along acontinuously changing variable). If the continuously varyingsolvent can be represented by a parameter x thena(AH)/ax = y2 - y1 and Ta(AX)/& = 8, - 8,If yl, y2, a,, and 8, are constants with respect to x , the integratedforms areAH = (y, - yl) + const.TAS = (8, - 8,) + const.---If AH:, AH;, AH; . . . AH; are the heats of solution of substanceA in a series of solvents 1,2, 3 .. . j, and AS:, As: . . . AS; arethe corresponding entropy changes, then the above equations lead to- - -- *l)" and i = 1, 2, 3, . . . j ASA AHA 2 = a 2 + const.; a =R RT (Y2 - Yl)*-Similarly, if Akf, AH:, AH: . . . are the heat changes for a seriesof solutes A, B, C . . . in the same solvent i, then(', - 81){ and P = A, B, C . . . ASP A E- = a 2 + const. ; a =R RT (Y2 - Y l hEvans and Polanyi found that such a relationship was given for thesame solute in a series of solvents, but that the relationship for thesame solvent and a series of solutes was limited in the cases theyexamined to solutes which belong to the same chemical group. Thesolutes which Evans and Polanyi considered were, in general, fairlycomplex organic substances of high molecular weight.J. A. V.Butler 27 has shown that a linear relationship between AH and A 8- -2 6 Trans. Faraday SOC., 1936, 32, 1333.2 7 Ibid., 1937, 33, 168; J. A. V. Butler and W. S. Reid, J., 1936, 117141 GENERAL AND PHYSICAL CIIEMISTRY.for the same solute in a series of solvents is given by simpler systemssuch as methyl alcohol in solvents such as benzene, hexane, carbontetrachloride, and chloroform, and moreover, that as far as dataare available there are indications of a similar relationship for othersolutes such as nitrogen, argon, and helium. R. P. Bell28 hasanalysed the data for the solubility of gases in various solvents, andfinds that for a given solvent there is a linear relation between A Sand A H for the different solutes considered. I.M. Barclay andJ. A. V. Butler 29 have extended the linear relationship between theheats and entropies of solution for a series of solutes in a given sol-vent by measuring the heats and entropies of vaporisation fromdilute solutions of several solutes in acetone and in ethyl alcohol.The theory of such relationships has not yet been worked out inany detail. We have seen that the energy of a, solution is a verycomplicated function of the molecular configuration, but indicationsof how such linear relationships do arise can be seen fairly easily.Bell 28 has shown that if the configuration of the solvent moleculesis not appreciably disturbed by the presence of the solute molecules,or at least disturbed in the same way by different solute molecules,then A H and A S both depend upon the same parameter characteris-ing the interaction between solute and solvent molecules anddepending on the solute but not the solvent.This leads to afunctional relationship between A H and A S for a series of solutesin the same solvent, but not to one for variations in the solvent.If the rotational and vibrational states of the solute moleculesare the same in solution as they are in the gas phase, and if thebehaviour of the solvent molecules is not fundamentally affectedin the neighbourhood of the solute molecules, then the most impor-tant term in the entropy change accompanying the solution processwill be A S = R In v&, where vf is the free volume available to thesolute molecules in solution, and vg the volume in the gas phase.The former is not characteristic of the solvent alone and independentof the nature of the solute molecules.Lennard-Jones and Devon-shire,l7 in discussing the entropy changes accompanying the vaporisa-tion of pure liquids, have defined the available free volume for aparticular molecule in terms of the potential-energy field set up bythe interaction between the molecule and its neighbours :vf =/e-*r)PT d7In this expression #(r) is the potential energy of the molecule as azB Ibid., 1938, 34, 1445.-28 Trans. Paraday Soc., 1937, 33, 496EVANS: STRUCTURE AND MOLECULAR FORCES IN LIQUIDS. 45function of its distance from the centre of its cavity.This sameargument can be extended to the case of a solute molecule in thepresence of its neighbouring solvent molecules, and thus there is aclear indication of a connection between the free volume and thepotential energy of the solute molecule, i.e., the heat of solution.This functional connection seems to be in the sense that the largerthe heat of solution the smaller will be the free volume available tothe solute molecule, and consequently, the smaller the entropychange accompanying the solution process.W. M. Latimer 30 has pointed out a connection between the heatsof solution of ions and the entropy of ions in solution ; this relation-ship is in the sense that the greater the exothermicity of the solutionprocess the more negative is the corresponding entropy change.If the field set up by the ion is sufficiently strong, it will cause alocal freezing out of the water molecules in the co-ordination sphereof the ions.The water molecules in the neighbourhood of the ionwill vibrate and rotate less freely than in the water itself. The lossof entropy due to the restriction of the motion of the solvent mole-cules has been estimated by Evans and Eley : l1 using the modelof the water structure given by Bernal and Fowler and a model ofthe orientation of water molecules in the co-ordination sphere ofthe ion consistent with the heats of solvation, they obtain valuesfor the entropies of ions in solutions which are in fair agreementwith the experimental values.It is outside the scope of this review to deal with the applicationof some of the ideas discussed in detail here to velocity constantsand equilibrium constants of reactions in solution, but we canindicate some of the problems which are being dealt with.R. W.GurneyY3l in discussing the variation of the dissociation constants oforganic acids with temperature, and the wide adherence to theempirical relationship of H. S. Harned and N. D. Embree,32 hassuggested that the energy of electrolytic dissociation of an acid ismade up of two terms, one of which is non-electrical and the otheran electrical term which can be expressed in terms of the Borncharging energy. It is this second term, which includes the di-electric constant of water, which leads to the parabolic form for thetemperature variation of the logarithm of the dissociation constant.The ideas put forward by Gurney have been given a more quantita-tive form by E.C. B a ~ g h a n , ~ ~ who has shown that the ionic radii30 W. M. Lather and R. M. Buffington, J . Amer. Chem. SOC., 1926,48,2297 ;31 J . Chem. Physics, 1938, 6, 499.32 J . Amer. Chem. SOC., 1934, 56, 1050; H. S. Harned and B. B. Owen,Chem Reviews, 1939, 25, 31. 33 J . Chem. Physics, 1939, '7, 951.W. M. Lather, Chem. Reviews, 1936, 18, 34846 GENERAL AND PHYSICAL CHEMISTRY.resulting from an analysis of the Harned and Embree relationshipin terms of the Born charging energy are of reasonable magnitude.They are, however, uniformly small as compared with the radii onewould expect from molecular dimensions.W. F. K. Wynne-Jones and D. H. Everett 34 have given an expressionAHR1 R In K = - _iP + gp In T + (AS: -which they claim represents the experimental results better thanHarned and Embree’s expressionIn K - In K, = p(t - f3)2Prom that expression they are able to compute the specific-heatchanges accompanying the electrolytic dissociation process, andthey point out that the specific-heat change cannot be accountedfor by the temperature variation of the dielectric constant, whichleads to magnitudes much smaller than those obtained by Wynne-Jones and Everett. They postulate, therefore, a “ freezing-out ” ofthe water molecules in the co-ordination shell of the ions. This‘‘ freezing ” process leads to the disappearance of translational degrees3 of freedom and a loss of energy of -RT per water molecule co-ordin- 2ated by an ion.This leads to changes in the specific heat accom-panying dissociation which are in agreement with their calculatedvalues. At present there seems to be some divergence between thetwo points of view : on the one hand, that the Born-charging energyis insufficient to account for the energy, entropy, and specific-heatchanges accompanying ionic processes and, on the other hand, thatthese simple electrostatic methods cannot be used when saturationeffects of the dielectric enter in. The success of J. G. Kirkwoodand F. H. We~theimer,~~ however, in calculating the ratio of the twodissociation constants of dicarboxylic acids would seem to indicatethat saturation effects in the dielectric can be neglected. Theseauthors have shown that if a correction is applied to Bjerrum’streatment to take into account the electrical effects inside the cavityin the solvent caused by a molecule, then the lengths of hydrocarbonchains predicted are in excellent agreement with those to beexpected if the chains have free rotation.The division of the energetics of ions in solution into two terms,one arising from the Born charging energy and the other from theco-ordination of solvent molecules around the ion, is quite anarbitrary one, and indicates our incomplete knowledge of the34 Proc.Roy. SOC., 1938, A, 169, 190;3 5 J. Chem. Physics, 1938, 6, 506, 513.Trans. Paraday SOC., 1939, 35, 1380PRICE : ELECTRONIC SPECTRA OF POLYATOMIC MOLECULES.47electrical behaviour of polar liquids in electrical fields of high in-tensity. A complete theory of the dielectric behaviour of polarliquids would remove this arbitrary division, and the recent work ofKirkwood36 and Onsager 37 is moving towards a more completepicture of the dielectric behaviour of polar liquids.M. G. E.2. THE ELECTRONIC SPECTRA OF POLYATOMIC MOLECULES.During the last ten years the study of infra-red and Ramanspectra has been yielding results of considerable theoretical import-ance to the chemist. Although many data on the electronic spectraof polyatomic molecules have been available for a much longer time,the difficulties in their interpretation have until recently provedinsuperable. With the solving of the major problems connectedwith the electronic spectra of diatomic molecules, more attentionhas been focused on the spectra of polyatomic molecules, and theresults indicate that much information of chemical interest may besoon forthcoming.The spectroscopic investigation of polyatomicmolecules is restricted to absorption, since electrical dischargeswith one or two exceptions disrupt the molecule into diatomicfragments. This factor has very seriously limited the field fromwhich spectroscopic information can be obtained. However theextension of the absorption measurements into the vacuum ultra-violet, which has recently been accomplished, has improved thissituation considerably. The object to be aimed at in the study ofmolecular spectra is a complete description of the electronic structuresof polyntomic molecules in both their normal and excited states,similar to that now available for atoms.It appears that even in thecase of diatomic molecules this object will only be accomplished to asmall degree, and in the case of polyatomic molecules the expectationis still less. Some of the more fundamental facts can, however,certainly be derived from the available data. Although the morecomplicated organic molecules can never be subjected to rigorousmathematical treatment, considerable progress towards under-standing their spectra and thus towards obtaining a theory of colour,can be achieved by making certain broad assumptions and byutilising the more general results of quantum theory.Severalattempts in this direction have been made in recent years.1 How-ever, in this year’s Report it has been decided to confine the materialto an ‘introduction to the spectroscopic conception of the electronic36 J . Chem. Physics, 1939, 7 , 911.37 L. Onsager, J. Amer. Chern. SOC., 1936, 58, 1486.G. N. Lewis and M. Calvin, Chem. Reviews, 1939, 25, 273; R. S. Mulliken,J . Chem. Physics, 1939, 7 , 1448 GENERAL AND PHYSICAL CHEMISTRY.structure of some of the simpler polyatomic molecules, and to adescription of the spectra associated with them.The most elementary attempt to express the electronic structureof EL molecule is that embodied in the ordinary valency bond formula.When supplemented by resonance to other structures, these formuhhelp to correlate a wide variety of chemical data.However, theygive us very little detailed information about the electrons in themolecule. Facts such as what are the types of orbits the differentelectrons are in and what are their relative energy values are theimportant ones in the interpretation of molecular spectra, and anotation indicating these characteristics is clearly to be desired.The spectroscopic notation for the electronic configuration of sodiumin its ground state is ls22s22p63s, 2X. The groups of equivalentelectrons which are most strongly bound (i.e., with the greatestionisation potentials) are written first, and are followed by thegroups having successively lower energies. The type and energyvalues of the various groups are known from spectroscopic observa-tions.Groups of equivalent electrons occur in the electronicstructure of 'molecules just as they do in atoms but they are of aslightly different type because their character (i.e., number of electronsthey can hold, etc.) is determined by the positive nuclear framework(which is no longer a point as in atoms). On the '' molecular orbital "theory of Hund, Mulliken, and Lennard-Jones, there can be ascribedto every group of equivalent electrons an independent wave functionwith symmetry properties with respect to the symmetry operationswhich the nuclear framework permits (each group has a wave func-tion which has the character of a particular representation of thesymmetry group of the molecule).Mulliken has introduced system-atic classification symbols to express the symmetry character-istics of particular electron types (small letters) and the totalelectron configuration of the molecule (large letters). These aresimply an extension of the well known m X I I notation for diatomicmolecules (which is itself, of course, an extension of the notationfor atomic spectra). He gives expressions for the electronic con-figurations of a large number of simpler polyatomic molecules interms of these symbols in a series of articles in the Journal of ChemicalPhysics from 1935 onwards. It is not intended to use this nomen-clature here more than is absolutely necessary, as the mass of sym-bols may lead to some confusion and obscure important generalresults which can be obtained without their aid.They would,however, be necessary for more detailed discussion of the spectrathan is possible within the scope of this Report.The Single Bond.-The simplest single bond is that occurringin the hydrogen molecule. Here two atomic 1s orbitals overlaPRICE : ELECTRONIC SPECTRA OF POLYATOMIC MOLECULES. 49in such a manner as to give rise to a high electron density betweenthe two nuclei, so leading to the formation of the valency bond(see Fig. la). The abbreviated notation for the molecular orbitalwhich the two electrons can now be considered as occupying is(s + S, o ~ ) ~ . The plus sign indicates that the two atomic orbitalsoverlap so as to give bonding (negative sign means antibonding),the Greek letters indicate the magnitude of the component of theorbital angular momentum resolved along the bond axis (0, x .. . =0 , l . . . .) , and the superscript means that two electrons are occupyingthis orbital.2 This a type of orbital is clearly axially symmetricaland gives a bond about which there can be free rotation if no stericfactors are involved. A single bond is always of this type, sincethe CJ orbital is the orbital of lowest energy (analogous to the 1sshell in atoms) and therefore the first two electrons must go into it.In the formation of a single bond between an s electron of one atomand a p valency electron of another, e.g., in the formation of theHB ( l b ) , HC (lc), HN ( I d ) , HO ( l e ) , and HF (If) bonds, it is necessarythat the s electron should approach along the axis of the orbitalThe symbol g means that the wave €unction does not change sign withrespect t o inversion a t the centre of gravity50 GENERAL AND PHYSICAL CHEMISTRY.of the p electron in order to give magmum overlapping of the atomicorbitals.Thus the molecular orbital formed is symmetrical aboutthe bond axis and is o in type. One important fact to whichattention should be directed is that, for an electron to enter into amolecular orbital, all restriction on its spin must be removed.This means that the atom must be excited to its valency state,,and the coupling of the spins characteristic of the normal state ofthe isolated atom broken down. In the CH, radical, for instance,it is necessary that the two valency p electrons should be in mutuallyperpendicular orbitals (the electronic configuration of bivalentcarbon is ls22s22p2). In NH, the three NH bonds have to bemutually perpendicular.Because the hydrogens are slightlypositive in NH,, their mutual electrostatic repulsion makes theHNH angle somewhat greater than 90" (actually log").* In PH,and ASH,, where the positive charge on the hydrogens is less andthe distance between them greater, the tendency for this angleto approach 90" is more marked. Recently, Sutherland, Lee, andWu have found that HPH = 99" and HASH = 97".6Although atomic oxygen ( ls2Zs22p4) has four p electrons it cannotorient all these so that their spins are independent. The best thatcan be done is to make the orbitals of two p electrons mutuallyperpendicular and then to accommodate the other two in a singleorbital perpendicular to the plane of the first two.Because of thepairing of the spins of the second two they cannot enter into chemicalcombination (Fig. le). In fluorine the necessity of putting twoelectrons into a single orbital arises twice, and thus four of its fivep electrons cannot ordinarily take part in the chemical activity ofthe atom. These electrons are the so-called '' lone pair " electrons.It will be seen later that they play a very important part in theabsorption spectra of the molecules in which they occur. Theyare of the type known as non-bonding p x electrons ( p to signifythat they belong to a p atomic orbital and 71: because the axis of thisorbital is perpendicular to the valency bond).In order to com-plete the schematic representation of Fig. 1 we should put roundthe central atom two concentric circles to represent the Is and 2sshells. They have been omitted from the diagram for the sake ofclarity.In the ordinary electronic theory of Lewis and Langmuir nodistinction is made between the lone pair of 2s electrons and theA AR. S. Mulliken, J . Chem. Physics, 1934, 2, 782.Trans. Faraday SOC., 1939, 35, 1373.The apex angle in amines and also in alcohols and ethers is probably* A similar effect would of course be expected in CH,.about 120" owing to larger repulsions arising from the alkyl groupsPRICE : ELECTRONIC SPECTRA OF POLYATOMIC MOLECULES. 51lone pair of 2p electrons.However, the former are much morestrongly bound than the latter (i.e., have considerably higherionisation potentials) and differ in other respects also. For example,Mulliken estimates that in water the 2s electrons have ionisationpotentials of about 32 v., and the electrons in OH bonds about17 v., whereas the lone pair of p x electrons only require energiesof about 13 ev. for their removal. It will be noted that the pelectrons which go into the bonds automatically acquire a higherionisation potential than the px electrons which remain non-bonding,i.e., atomic in character. This is because in ionising them additionalenergy equal to their bonding energy must be supplied. Theionisation potential of the non-bonding electrons does not differmuch from that in the free atom (13-55 v.for atomic 0,").The maximum valency which we have obtained so far is three.This was obtained in the case of nitrogen by resolving three pelectrons along three mutually perpendicular directions. Anadditional valency can be obtained by breaking the pairing of theelectrons in the s2 shell and promoting one to the p shell. Thusquadrivalent carbon with the configuration sip3 has four unpairedelectron spins and four independent orbitals can be constructed fromsuch a configuration. The s shell has a maximum valency of one,and it has just been shown that the p shell has a maximum valencyof three; hence with s and p electrons we have the well-knownmaximum covalency of four. A configuration of the type sp* (apossible configuration of N) could only be tervalent, since two ofthe p electrons would have to combine to form a lone pair.Similarly, sp5 and sp6, which are possible configurations for 0and F respectively, could only be bi- and uni-valent.Although it is fairly simple to see the main determining directionalfactors in atoms involving only p valency electrons, it is not so easyto see why the sp3 configuration of quadrivalent carbon should givein the case of saturated hydrocarbons four valencies directed towardsthe corners of a regular tetrahedron, or in the case of unsaturatedhydrocarbons three coplanar valencies at 120°, one of which is double.However, it can be shown that it is possible to construct fourequivalent independent orbits from the aggregate configuration sp3by suitable hybridisation of the s and p functions. That by mixinga certain amount of an s with a p orbital we can enhance thedirectional properties of the p function is seen from Fig.2.The p wave function has different signs on opposite sides of thecentral plane perpendicular to its axis of symmetry; the s wavefunction is, of course, spherically symmetrical. By adding the two,the positive side of the p function will be enhanced and the negative' J . Chem. Physics, 1035, 3, 50652 GENERa AND PEYSICAL CHEMISTRY.side diminished. Thus the charge distribution is directed in onedirection, and as a valency bond is formed where there can be themaximum overlapping of the wave functions, it is clear that a directedvalency bond has been produced.Up to the present we have dealt with single bonds and haveseen that their molecular orbitals are of a B type axially symmetricalabout the bond.Althoughit may seem that the foregoing discussion of electronic structures isa digression from the main subject of this Report, it must be pointedout that a background of this character is necessary for the satis-factory understanding of molecular electronic spectra.The Double and Triple Bonds.-The next bonding molecularorbital into which electrons can go after two have filled the bondingp orbital is an orbital which is known as a x orbital. It is lesssymmetrical than the a type and has a plane of symmetry passingthrough the bond instead of an axis of symmetry.Because of theWe shall now discuss the double bond.I IFIG. 2.possibility of two mutually perpendicular planes of symmetrythere are two such orbitals each of which can contain two electrons.The simple double bond is formed by the presence of two electronsin the basic a orbital and two electrons in one of these x orbitals.The triple bond has the basic o and both the x orbitals flled. Theabove statements are only good approximations since it is not alwayspossible completely to localise the electrons in a molecule withseveral bonds. The new properties of the x molecular wave func-tions give rise to the important characteristics of the double bond,such as the rigidity of the C=C bond and the optical activity ofof the C=O bond in certain ketones.The configuration sp3 of carbon can give rise to another set ofdirected valencies apart from the four axially symmetrical tetra-hedral ones.These consist of the equal coplanar type valenciesa t angles of 120" to each other, together with a fourth valencyperpendicular to the plane of the other three. In the directedvalency theory this fourth valency is represented as a pure 2pwave function. Fig. 3 indicates schematically the wave functions8 There is an antibonding a orbital (8-8, a,) but this is higher than the Rbonding orbitalsPRICE ELECTRONIC SPECTRA OF POLYATOMIC MOLECULES. 53of two carbon and four hydrogen atoms just before they cometogether to form ethylene.It can be seen that the molecular orbital corresponding to the bondformed by the overlapping of the two p electrons is not axiallysymmetrical but has a plane of symmetry which is the plane of themolecule.These p electrons have the property of confining theother bonds all to one plane. If a valency bond is formed with anytype of electron other than the adjacent p electron (as in bromina-tion or hydrogenation), then the carbon atom reverts to its morestable tetrahedral valency state. Because the amount of overlapof two adjacent p x electrons is less than that with electrons whoseorbitals are symmetrical about the bond, the strength of the xbond is slightly less than that of the basic Q bond. This, and alsothe fact that it is not mixed with strongly bound s orbitals, resultsin its ionisation potential being considerably lower than the otherelectrons in the molecule.It will be shown later that this is ofFIG. 3.considerable importance in connexion with the spectra of unsaturatedorganic molecules. The foregoing brief introduction to the spectro-scopic conception of the electronic structure of some polyatomicmolecules will facilitate the following discussion of their absorptionspectra.One of the most important advances in the subject in recentyears is the extension of observations into the short wave-lengthregion of the spectrum known as the vacuum ultra-violet. Thisregion lies below 1800 A., where air and quartz absorb. It has longbeen known that the formulae which have been found to representthe ordinary refractive dispersion and natural and magnetic rotatorydispersion of substances contained in them terms which predictabsorption bands of extraordinarily great intensity (log E - 4) lyingat very short wave-lengths below 2000 A.That it is reasonable toexpect such strong bands in this spectral region can be seen from thefollowing discussion. The ionisation potentials of most moleculeslie between 10 and 15 v., which corresponds to phto-ioni8ution b54 GENERAL AND PHYSICAL CHEMISTRY.light of wave-lengths between 1300 and 800 A. Just as in theabsorption spectra of an atom a series of strong reasonance linescan be observed converging to a photo-ionisation limit at a definitewave-length (cf. Na), so in the absorption spectrum of a moleculestrong resonance bands might be expected to appear leading up toany ionisation potential characteristic of the molecule.The firststrong resonance line of sodium is the yellow D line. That it shouldoccur at such long wave-lengths as to lie in the visible part of thespectrum is only because of the abnormally low ionisation potentialof the alkali atoms. I n most other atoms (and molecules) thefirst resonance bands do not start until about 2 0 0 0 ~ . or less, andthe other Rydberg series members corresponding to increases of theprinciple quantum number by successive units to infinity at thephoto-ionisation limit, lie a t still shorter wave-lengths in the vacuumultra-violet. As a simple illustration let us attempt to predictwhat might be expected to result from the illumination of hydrogeniodide with a continuous background of light extending into thevery short wave-length region.The four non-bonding p x electrons( i e . , the lone pairs) of the iodine atom are not greatly affected bythe combination and thus probably have about the same ionisationpotential as in the free atom [- 10 v. or 1200 a.-known from theanalysis of the spectrum of I(l)]. Thus strong resonance bandscorresponding to these electrons might be expected to start below2000 A. (6 v.) and to converge to a photo-ionisation continuumaround 1200 A. (10 v.). Because the electrons do not participatein the bond, it is to be expected that little vibration will be causedby their excitation and removal. Absorption spectra agreeingvery closely with these expectations have been ob~erved.~ Electronsgoing into the molecular orbital forming the single bond might beexpected to have an ionisation potential somewhat greater than themean of the ionisation potentials of hydrogen and iodine [ i e .,> (13 + 10)/2 = 111, i.e., probably about 12-13 v. It might beguessed that strong resonance bands of these electrons would start.about 1400 A. and culminate in a photo-ionisation continuum near1000 A. (12.3 v.). A great deal of vibration would accompany theremoval of such a bonding electron. Unfortunately, all that canbe observed of these absorption bands is some diffuse bands lyingin the region 1209-800 A. That the estimate of the ionisationpotential of the bonding electrons is correct is known from theemission spectra of the halogen acids.1° The other electrons of themolecule (Le., the inner shells of the iodine atom) ionise at stillhigher potentials and shorter wave-lengths. Experimental diffi-W.C. Price, PTOC. Roy. SOC., 1938, A , 167, 216.10 F. Norling, 2. Physik, 1935, 95, 179; 1937, 104, 638PRICE : ELECTRONIC SPECTRA OF POLYATOMIC MOLECULES. 55culties prevent their observation. It appears to be a fairly generalrule that the outer electrons of a molecule with the lowest ionisa-tion potentials (usually the non-bonding electrons in lone pairs orthe x electrons of an unsaturated molecule) give rise to the strongestand most well-defined bands in the vacuum ultra-violet. It appearsthat these electrons are also responsible for most of the near ultra-violet absorption spectra of molecules, though there are notableexceptions, such as the salts of the rare earths, where the colour isdue t o electrons in the inner f shell of the rare-earth ion.The general features of the spectra of the alkyl halides may bededuced as for the halogen acids.The photo-ionisation of the lonepairs on, e.g., the iodine atom in methyl iodide has been observedexperimentally.ll The photograph of this spectrum11 is a very goodexample of the convergence of bands to a photo-ionisation limit.For the more highly excited electronic states when the orbit of theelectron is very large compared with the dimensions of the molecule,the electron may be regarded as escaping in an approximatelycentral field. Thus these higher electronic states should fit roughlyinto a Rydberg formula.This is found to be the case, and anextrapolation of the higher members to the convergence limit bymeans of the formula gives a very accurate ‘‘ spectroscopic ” valueof the ionisation potential of the molecule. It is found that theionisation potentials of the halogen electrons in the alkyl halides are1 volt or more lower than those in the halogen acids. This is inter-preted as being evidence of a greater transfer of negative charge onto the halogen in the former molecule, and is supported by theirdipole moments [p(HI) = 0.38 D., p(CH,I) = 1.59 D.]. It will bediscussed more fully later. Two photo-ionisation limits fairlyclose together are observed for these halogen compounds, L e . ,the molecular ion is a doublet. The magnitude of the doubletseparation indicates that the ionisation limit observed is definitelythat of the p x halogen electrons and that these are of a non-bondingcharacter.The ionisation potentials of the alkyl halides diminishto a limiting value as we ascend the homologous series, the greatestdrop occurring in going from the methyl to the ethyl compound,subsequent diminutions being very much smaller. In this sense thehalogen acid may be regarded as the first member of the series.The diminutions then are : HI - CH31 = 0.88 v., CH31 - C2H51 =0.19 v., C2H51 - n-C3H,I z a few hundredths of a volt.The spectra of ammonia- and water-type molecules have beentreated by R. S. Mulliken.12 The discussion of their electronicstructure given in a previous paragraph shows that the outermost11 W.C . Price, J . Chem. Physics, 1936, 4, 539.12 J . Chem. Physics, 1935, 3, 50656 GENERAL AND PHYSICAL CHEMISTRY.electrons (Le., those with the lowest ionisation potentials) should bethe lone pair p x electrons and that the ionisation potentials ofelectrons in single bonds should be 2 or 3 volts higher than these.The experimental evidence l3 indicates that this is the case, and hereagain the lone pairs seem to dominate the absorption. Bands,which by their rotational structure indicate the excitation of a non-bonding electron, appear at very low pressures and converge to theminimum ionisation potentials of the molecules. Only in the caseof water has it been possible to obtain spectra corresponding tothe excitation of electrons in single bonds.l* It should be stressedthat the simple picture we have drawn is not quite adequate.Forinstance, Mulliken's treatment indicates the existence of twoionisation potentials fairly close together for the OH bonding elec-trons where on simple theory only one is expected. A similar state-ment is true for the bonding CH electrons in methane or the xelectrons in benzene.The most prominent bands of the alkyl-substituted compoundsof water, hydrogen sulphide, and. ammonia (ie., the alcohols andethers, thiols and sulphides, and amines) require an interpretationsimilar to that given for the parent molecule. They are displacedto longer wave-lengths with successive alkyl substitution.15 This isinterpreted as an accumulation of negative charge on the oxygen,sulphur, or nitrogen atom with increasing alkyl substitution.Although the increase in the dipoles in going from H,S throughR*SH to SR, (R being an alkyl group) supports this idea of increasein negative charge, the diminution in the similar series for theoxygen and nitrogen compounds seems to discount it.However,this diminution in dipole moment can be explained by the opposinginduced dipoles in the alkyl groups of the oxygen and the nitrogencompounds. For these light atoms the induced dipoles play amuch larger part than in the heavier atoms. Because of t'he some-what wider apex angles, they tend to diminish the main dipolerather than increase it, as they do in the thiols and sulphides.The electronic structures of aldehydes, ketones, carboxylic acids,and related molecules have been discussed by R.S. Mulliken.lGIn this class of molecule an especially large charge transfer due tothe.large dipole associated with the C=O bond (-2.7 D.) causes aconsiderable excess negative charge to accumulate on the oxygenatom. This reduces the ionisation potential of the lone pair [O]la A. B. F. Duncan, Physical Rev., 1935, 47, 822; W. C. Price, J. Chern.Physics, 1936, 4, 137.l4 G. Rathenau, 2. Physik, 1933, 87, 32.l5 H. Ley and B. Arends, 2. physikal. Chem., 1932, B, 15, 311 ; G. Herz-berg and G. Schiebe, ibid., 1930, €3, 7, 390; W. C. Price, J . Chem. Physics,1935, 3, 256. lo Ibid., p. 564PRICE : ELECTRONIC SPECTRA OF POLYATOWC MOLECULES.57electrons by more than 2 volts relative to what it might otherwisebe expected to be. In formaldehyde, for example, it might bethought, without allowance for charge transfer, that the ionisationpotential of the oxygen lone pairs should be some 13-14 volts[cf. ionisation potential of O( 1) = 13.55 v.1.l’ That of the electronsin the double bond would be expected to be greater than 1 4 ~ .by several volts, and that of the electrons in the C-HI bonds not farfrom the ionisation potential of methane (i.e., 14 v.). The spectro-scopic and the electron-impact method agree in putting the minimumionisation potential of formaldehyde a t about 11 volts, and thespectra indicate that an electron in the carbonyl part of the moleculeis being excited.18 These facts can only be reconciled with thetheoretical expectations by the assumption that the accumulationof negative charge on the oxygen atom arising from the large dipoleknown to be associated with the C=O bond causes a lowering inionisation potential of the lone-pair electrons.This is supportedby the fact that the ionisation potential of acetone was fouBd to havethe still lower value of 10.1 v.19 Additional charge transfer from thetwo methyl groups is presumed to be responsible for this furtherlowering.The spectrum of formic acid shows great similarity in the regionbelow 1600 A. to the spectrum of formaldehyde, and the bandsconverge to ionisation potentials which are fairly close together-10.83 v. and 11.3 v.respectively.20 It is clear that in the acid, as informaldehyde, this ionisation potential corresponds to the lone pairon the carbonyl oxygen. The resonance between the two CObonds is not grmt in the monomer, and it does not greatly affect thelone pair electrons.The spectrum of formaldehyde in the near ultra-violet is particu-larly important, since the rotational structure of many of thebands has been analysed by G. H. Dieke and G. B. Kistiakowski.21They deduce that the electric moment of the transition vibratesperpendicularly to the axis of symmetry and in the plane of thomolecule. This fact, together with the determined ionisation offormaldehyde, enabled Mulliken to show that the transition mostprobably corresponded to the jump of an electron from the lone pairinto an antibonding orbital of the double bond [2p,b,+l7 Actually the ionisation potential of the lone pairs when the oxygenThis is predicted byl8 T.N. Jewitt, Physical Rev., 1934, 46,616 ; W. C. Price, J . Chern. Physics,Is W. A. Noyes, A. B. F. Duncan, and W. M. Manning, ibid., 1934,2, 717.2o W. C. Price and W. M. Evans, Proc. Roy. SOC., 1937, A, 162, 110.21 Physical Rev., 1934, 45, 4.atom is in its appropriate velency state should be used.Mulliken to be 14.73 v., J . Chem. Physics, 1934, 2, 782.1935, 3, 25658 GENERAL AND PHYSICAL CHEMISTRY.(zDH, - xo, a,)]. The optical activity of certain ketones is thusinterpreted as being due to the upper state of this transition and isnot due to the excitation of electrons originally in the double bondas is usually supposed.The absence or extreme weakness of ketonicbands at 3000 A. and 2000 A. in the carboxyl compound is probablydue to the transition becoming forbidden as a result of the excitedorbital being affected by the proximity of the hydroxyl group.The absorption bands of the alkyl derivatives of formic acid areshifted to longer wave-lengths with alkyl substitution. This is sowhichever of the two hydrogen atoms is replaced by alky1,22 and itmay be taken to indicate an increase in the amount of negativecharge transferred to the carbonyl oxygen. For instance, the shiftof certain bands of methyl acetate relative to the correspondingones of formic acid is about 0.9 v., and this may be comparedwith the difference in the ionisation potentials of acetone andformaldehyde, vix., 10.83 - 10.1 = 0.7 V.The Spectra of Methane, Ethane, Ethylene, and Acetylene.-Nearly all single-bonded compounds are transparent in the visibleand near ultra-violet and absorb only in the vacuum ultra-violet.This important fact seems to support the interpretations of nearultra-violet spectra as being the excitation of an electron to an anti-bonding orbital.Only in double-bonded compounds can an upperstate involving such an orbital be stable, i.e., the antibonding powerof the excited electron is then more than compensated by the bondingpower of the remaining three or more bonding electrons. In excitedRydberg orbitals the bonding or antibonding power of an electronis very small.Methane does not absorb strongly until about1250 A. (- 10 v . ) . ~ This absorption must be regarded as thefirst strong resonance (Rydberg) absorption, since the electron-impact value for the ionisation potential of methane is about 14.5 v.The electronic configuration is obtained by pairing off the electronsof the 5p3 configuration of quadrivalent carbon. It is given inMulliken’s notation as [$all2 bt2]6, the ionisation potential of thefirst electron group being estimated as about 22 v., and that of thesecond being identified with the minimum ionisation potential at14.5 v. The diffuseness of the methane absorption is attributed tostrong predissociation. It unfortunately prevents the identificationof consecutive electronic states which might be fitted into a Rydbergformula.The spectrum of ethane is very similar to that of methaneexcept that absorption begins at slightly longer wave-lengths(- 1350 A . ) . ~ This is in agreement with the slightly lower ionisation22 G. Scheibe, F. Povenz, and C. F. Lindstrom, 2. physikal. Chem., 1933,B, 20, 283.23 A. B. F. Duncan and J. P. Howe, J . Chem. Physics, 1934, 2, 851.24 W. C. Price, Phymkal Rev., 1935, 47, 444PRICE : ELECTRONIC SPECTRA OF POLYATOMIC MOLECULES. 59potential of ethane (- 12 v.) as compared with methane. Theexcitation and ionisation really corresponds to the electrons in theC-C bond. Propane starts absorbing at slightly longer wave-lengths than ethane. It is doubtful whether any pure saturatedhydrocarbon has strong absorption above 1500 A., which is wherecyclohexane starts to absorb.25A description of the spectrum of light and heavy ethylene (C,H4and C,D4) has been given by W.C. Price and W. T. Tutte.26 Theanalysis of the spectrum, which was greatly facilitated by theuse of the deuterium-substituted compound, shows clearly thatthe strong absorption bands occurring in the region 2000-1150 A.are due to the excitation and photo-ionisation of the x electronsin the double bond. The ionisation potential to which they corre-spond is 10.43 v. The bands of ethylene are very similar to bands ofacetylene also due to the excitation of a x electron in.this case fromthe ( x ) ~ group. For acetylene, certain features of the rotationalstructure of the bands point very definitely to the x electrons as theoriginators of the spectrum.The same features are present inethylene, only they cannot be observed so easily because of a slightdiffuseness of the bands. The slightly higher ionisation potentialof acetylene (11.35 v.) relative to that of ethylene can be regardedas due partly to the greater stability of the ( x ) ~ group and partlyto a smaller charge transfer (acetylene has only half as manyhydrogen atoms from which to draw negative charge as ethylenehas, and twice as many x electrons amongst which to share it).Both ethylene and acetylene have near ultra-violet spectra of anon-Rydberg character, i.e., probably transitions of electronsfrom bonding to anti-bonding orbitals associated with an electronicconfiguration not differing from that of the ground state by a changeof principal quantum number.The discussion of these and morecomplicated spectra will be continued in a future Report.Vibrational Structure and Selection Rules.-The vibrationalpattern of bands representing an electronic transition often givesconsiderable information about where the excitation is located.Electrons excited from bonds usually give rise to vibration in thesebonds, while little vibration usually accompafries the excitationof a non-bonding electron unless it be excited to an orbital of a bond-ing or an anti-bonding character. (As will be shown in later Reports,little vibration also accompanies the Rydberg jumps of an electronwhich is shared between several bonds by the process of resonance.)As most polyatomic molecules have a large number of differentmodes of vibration, it might be thought that their spectra would bevery complex.However, it is seldom that more than two Werent2 5 G. Scheibe end H. Grieneisen, 2. phy8ika.l. Chem., 1934, B, 25, 52.2 6 Proc. Roy. SOC., in the press60 GENERAL AND PHYSICAL CHEMISTRY.types of vibration are present in one electronic band system. Amost useful criterion for identifying modes of vibration in a spec-trum is the selection rules deduced by G. Herzberg and E. Teller 27by an extension to polyatomic molecules of the Franck-Condonprinciple. This principle expresses the fact that the electronictransition occurs so quickly relative to any change occurring in thepositions or velocities of the much heavier nuclei that these can beconsidered the same the instant after the transition as they were justbefore it.Thus the nuclear symmetry is preserved. It follows thatthe electronic and therefore the total molecular symmetry of theequilibrium position is the same in both the ground and the excitedstates. From this it can be shown that in the case of an allowedelectronic transition the quantum numbers of the totally sym-metrical vibrations 28 are the only ones for which changes may occur.In forbidden. transitions (Le., corresponding to upper and lowerelectronic wave functions of different symmetry) there must occur achange of the quanta of a non-totally symmetric vibration by atleast one unit-though it may be accompanied by any change in thetotally symmetric quantum number.The reason for this is that achange in the symmetry of the vibrational part of the wave-functionis necessary in order to correct for the altered symmetry of theelectronic part. By virtue of the coupling between the electronicand the vibrational parts, the total wave function can be made toretain its symmetry during the transition. However, because thecoupling is weak, transitions of this second kind are much less intensethan those in which the symmetry of the electronic wave functiondoes not change. The 2500 A. system in benzene is an example ofthe compensating of the symmetry of the electronic wave functionby a suitable vibrationalAbsorption in a cold gas occurs mainly from the vibrationlessground state because the fraction of molecules initially vibratingis very small at normal temperatures.In absorption-band systemswhich are strong a t normal temperatures, such as those occurringin the vacuum ultra-violet, only vibrations of a totally symmetriccharacter can be expected to appear. This is true in general, and acollection of the available data on this point has been made byA. B. F. Duncan.30 More recently, M. Wehrli 31 has shown that thevibrational structure of the ultra-violet spectra of the mercuric27 2. physikal. Chem., 1933, B, 21, 410.a * Invariant with respect t o all the symmetry operations.29 A. L. Sklar, J . Chem. Physics, 1937, 5, 669; H. Sponer, G. Nordheim,30 Ibid., 1935, 3, 384.31 Naturwiss., 1937, 25, 734; Helv.Physica Acta, 1938, 11, 330; see alsoA. L. Sklar, and E. Teller, ibid., 1939,7,207.H. Sponer and E. Teller, J . Chem. Physics, 1939, 7 , 382MELVILLE : CHEMICAL KINETICS. 61halides conforms to the rules of Herzberg and Teller. A. Henriciand H. Grieneisen 32 have done the same for the 2000 A. systems ofthe alkyl iodides.It has not been possible even to touch upon the absorption spectraof conjugated hydrocarbons and many other important classes ofcompounds in this brief Report. It is hoped to deal with them infuture Reports. w. c. P.3. CHEMICAL KINETICS.During the past four or five years slow but steady progress hasbeen made in attempting to deal with the mechanism of polymeris-ation reactions by kinetic methods.The reasons for this growthof interest are due to several factors. From our present point ofview probably the most important is that chemical kinetics hadbeen developed to such a stage that it was looking for new fieldsto conquer and this field was practically untouched. Moreover,the amount of work which had been done on the structure andreactions of naturally occurring substances of high molecularweight forced upon chemists the necessity of trying to make similarmolecules synthetically and also understanding how simple mole-cules aggregate to larger entities. The industrial development,too, has played a part for, though much of it is essentially empiricalin character, it has brought to light reactions and systems which aresufficiently simple to merit their detailed academic study.In broad outline two types of process are involved in the produc-tion of big molecules.The first consists in the interaction of suitablemonomeric molecules with the simultaneous elimination of a rela-tively simple molecule such as water, ammonia, etc. Typical of thisreaction is the polymerisation of hydroxy-acids :HO*P*CO,H + HO*P*CO,H j HO*P*CO*O*P*CO,H + H20Further molecules of monomer then add on to the dimer, eachprocess being accompanied by the elimination of one molecule ofwater.The second type concerns the interaction of compounds contain-ing a double bond. Here the essential characteristic is that, insteadof the elimination of a simple molecule each time the monomerreacts, a double bond is converted into a single bond.Ethylene beingtaken as the simplest system, the reaction may be represented thus :CH2=CH, + CH,=CH, + CH,-CH,-CH-CH,or -CH2-CH2- + CH,=CH, ----+ -CH,-CH2-CH2-CH2-33 2. physikal. Chem., 1935, B, 30, 162 GENERAL AND PHYSICAL CHEMISTRY.There are, of course, some reactions in which both types of processoccur, leading to molecules of great complexity. In kinetics,however, the mechanism of the first type, which is esterification,is not yet fully understood, and therefore there is little hope a tpresent of dealing a t all satisfactorily with the kinetics of condens-ation polymerisation. The second type of polymerisation isamenable to kinetic study, for a great deal of help is afforded bythe existing knowledge relating to the reactivity of double bondsand also to the behaviour of free radicals, which may be producedwhen the double bond is opened.The most elementary kind ofpolymerisation consists in the association of two molecules eachcontaining a double bond.Association Reactions.-By a study of dimerisation reactions itshould thus become possible to obtain some information aboutthe conditions for the activation of the double bond preliminaryto further polymerisation of the monomer to long-chain compounds.The unfortunate fact is that those molecules, such as styrene,vinyl acetate, chloroprene, vinylacetylene, and met hylacetylene,which under suitable conditions do form linear polymers, do noteven dimerise, far less polymerise thermally in the vapour state.lAs a preliminary, it is of course advisable to conduct the reactionsin this phase, for which the utmost aid is available from ordinarykinetics.None the less, dimerisation has been found to occurwith the following molecules : ethylene, butadiene, isoprene,and cyclopentadiene. In addition, a number of Diels-Alder reactionsmay be induced to proceed in the gas phase.The rate (R) of a bimolecular reaction between two molecules1 and 2 is defined byR = k,[N,][N,] = PZ . exp( - E/RT)where Ic, is the velocity coefficient, N , and N , are the molecularconcentrations, PZ is a factor, and E the energy of activation ofthe reaction; Z is the number of collisions between the moleculescomputed by using " kinetic theory " diameters; P is furtherdefined as a steric factor.A reactionis considered to be normal ifP is of the order of magnitude of unity. In point of fact, however,no precise significance can be attached 60 the value of P becausethe calculation of 2 is uncertain for the particular collision involved.Consequently another quantity A is defined by the equationk = A . exp(-III/RT)1 J. B. Harkness, G. B. Kistiakowski, and W. H. Mears, J. Chem. Physics,C. N. Hinshelwood, " Kinetics," 3rd Edn., Chap. 2, Oxford; L. Kassel,1937, 5, 682." Kinetics," Chap. 3, Amer. Chem. SOC. MonographMELVILLE : CHEMICAL KINETICS. 63If P = 1, then A = Z/[N1][N2], and for molecular diameters of theorder of If there-fore a reaction has an A factor of less than this value (in order ofmagnitude), then it is presumed that although the energy of activ-ation is available during collision some further criterion must befulfilled before reaction will occur.One possible interpretationis that the criterion is purely geometrical in that the moleculeshave to be orientated in a precise configuration; but, as will beseen later, there may be other explanations.For convenience in subsequent discussion, all the reactions whichhave been thoroughly investigated are given in Table I. Indirectcm. it has the value 1014 C.C. mol.-l sec.-l.TABLE I.Reaction.EthyleneButadiene H2 + C P 4 -+ C P ,3 -VinylcycZohexene + butadieneIsopreneAaY-Pentadiene&-Dimethyl- AaY-butadienecycZoPentadieneAaY-Butadiene + acraldehydeIsoprene + acraldehydeAaY-Butadiene + crotonaldehydecycZoPentadiene + acraldehydeDecomposition.endoMethylenetetrahydrobenzaldc-DicyclopentadienehydeVelocity coefficient,C.C.mol.-l sec.-l.1.8 x 1013 ~ X P ( -43150/RT)1.95 X 10" exp( -35000/RT)6 x lo1' exp(-24600/RT)4.7 X 10" e~p(-35300/RT)1.0 X lo1' e~p(-23690/RZ')5.3 X 10l1 exp( -23900/RT)4.7 X lo1' e~p(-25900/RT)3.5 X lo1' exp( -26000IRT)1.5 X 10" exp( -25300/RT)1-3 x lo1' exp(-38000/RT)8.5 X lo7 exp(-I4900/RT)1.2 X lo9 e~p(-16700/RT)1.46 x lo9 e~p(-19700/RT)0.90 x lo9 exp(-22000/RT)1-02 X lo9 exp(-l5200/RT)Velocity coefficient, sec.-l.1.02 X 10' exp(-18700/RT)2.2 X 1012 e ~ p ( -33600/RT)1.0 X 1013 exp( -33700/RT)1.0 X exp( -34200/RT)Ref.4561, 5887577101, 71, 71, 71, 7Ref.1, 71, 78, 910estimates have also been made of a number of simple bimolecularassociation^.^ The reverse unimolecular decomposition beingassumed to be normal, then the unimolecular constant kud is givenby the equation, k d = 1013exp(-E,,i/RT) sec.-l, where Euni isC.E. H. Bawn, Trans. Faraday SOC., 1936, 32, 178.R. N. Pease, J . Amer. Chem. Soc., 1931, 53, 613.Idem, ibid., 1932, 54, 1876.W. E. Vaughan, ibid., p. 3863.G. B. Kistiakowski and J. R. Lacher, ibid., 1936, 58, 123.G. B. Kistiakowski and W. W. Ransom, J . Chem. Physics, 1939, 7 , 725.W. E. Vaughan, J . Amer. Chem. SOC., 1933, 55, 4109.lo C. A. Benford and A. Wassermann, J., 1939, 362, 367; B. S. Khambataand A. Wassermann, ibid., pp.371, 375; G. A. Benford, H. Kaufmann,B. S. Khambata, and A. Wassermann, ibid., p. 38164 GENERAL AND PHYSICAL CHEMISTRY.the energy of activation. Also k = PZ . exp(-Ebi/RT), and K ,the equilibrium constant, is given by the equationK = k,,&,i = (1013/PZ)eAH’nTwhere AH is the heat of reaction. Thus if K is known, P may becomputed. The value of P for the reaction NO2 + NO, + N,O,is 2 x for C,H, + H,O --+ C,H,*OH, P = 1.4 x lo4. SinceK may be calculated from the entropy of the molecules taking partin the reaction, the steric factor for many reactions may be cal-culated.. The obvious assumption which it is somewhat difficult tojustify in any particular case is that concerning the magnitude of theunimolecular velocity coefficient.Although the reactions are simply classified above, there aresome complications and controversy about the nature of the products.For example, in the polymerisation of ethylene, H.H. Storch l1has found that oxygen strongly accelerates the reaction, whichwould imply the intervention of some chain mechanism. Theproducts of the reaction are, however, low-molecular-weight sub-stances and it is not unlikely that the nature of the reaction dependsto a very large extent upon the manner in which it is carried out.The addition of hydrogen to ethylene is apparently a normal reaction.As will be observed from Table I, conjugated double-bond com-pounds dimerise very much more readily, as is best shown by thefact that the energy of activation for association is lower than thatfor ethylene.The butadiene reaction has been particularly wellstudied, the product being 3-vinylcycZohexene. Complicationsarise, however, since there is further reaction of this product withbutadiene to give A3‘ 3’-octahydrodiphenyl.12 Although this re-action has been less completely investigated, its energy of activationis relatively high, and the A factor, curiously enough, is quite normal.Apparently there is no appreciable polymerisati~n to products ofhigher molecular weight. Since 3-vinylcyclohexene is the product ofthe dimerisation of butadiene, the mechanism of the reaction must be2 CH2// YH g H 2\\ \/CH2 CH2+ GH (P CH CH-CH=CH, CH CH-CHXCH,i.e., 1 : 4, 1 : 2 addition. This is precisely analogous to theDiels-Alder reaction between dissimilar molecules.13 It is fortunate11 J .Amer. Chem. SOC., 1934, 56, 374.l a K. Alder and H. F. Richert, Ber., 1938, 71, 373.13 0. Diels and K. Alder, Annalen, 1928, 460, 119; 1929, 470, 370MELVILLE : CHEMICAL KINETICS. 65that the latter reaction can be induced to occur in the gas phase,because it extends the number of systems for accurate study so thata more exact picture of association reactions may be formed. Evencyclopentadiene will react with acraldehyde to give endomethylene-tetrahydrobenzaldehyde. It is noteworthy that crotonaldehyde willreact as readily as acraldehyde. * The association of cyclopentadienehas been extensively studied, not only from the point of view of thegas reaction, but with the view of establishing a correlation betweengas- and liquid-phase polymerisations.l*> l4 The product of thereaction at temperatures below 150" is undoubtedly the troughform of endodicyclopentadiene shown in Fig.1. It is importantthat the velocity coefficients for the reaction are practically thesame in the gas and in the liquid phase (solution in paraffin). 4-XC - /fF I G . 1.With the exception of perhaps ethylene the experiments on di-merisation give some indication of the energy required for inducingreactivity in the double bond and demonstrate that this is notunduly large. Whether a similar degree of activation is necessaryfor the production of molecules of high molecular weight is, how-ever, a point upon which it is difficult to decide with the data a tpresent available. As will be seen later, the over-all energy ofactivation for many liquid-phase polymerisations lies within therange 20,000--30,000 cals., which would seem to indicate that theenergies required for the two processes do not at any rate differwidely.In production of long-chain molecules the energies of thepropagation and termination reactions must of course be taken into14 B. S . Khambata and A. Wassermann, Nature, 1937, 139, 699.* Crotonaldehyde, acids and esters cannot however be polymerised to long-chain compounds.REP.-VOL. XXXVI. 66 GENERAL AND PHYSICAL CHEMISTRY.consideration, with the result that such an apparent agreementmay be vitiated.Although there is some variation in the A factors of these di-merisations there is no doubt that they are all much smaller thanthe values of a normal bimolecular reaction. The simple geometricalpicture mentioned above is probably too crude to account completelyfor these observations, and an appeal has therefore been made tothe transition-state method of calculating velocity coefficients tosee what sort of an explanation it affords of the process.16According to this theory the bimolecular coefficient is given bywhere Fc' and F, are the partition functions for the transitionand the initial state of the system and p is the reduced mass ofthe whole system.From this it may be shown that the P factordefined previously is given bywhere f v is the vibrational partition function (all assumed to beidentical) and A , B, and C are the principal moments of inertiaof the molecules.Now the value of the denominator is of the order103-106; fv = (1 - exp(- hv/kT)>-l and since hv>kT, the vi-brational partition function may be taken as unity. The valueof P will thus be small and therefore in accordance with experi-ment.3 Qualitatively this may be stated by saying that in such abimolecular process three degrees of freedom of rotational energymust be converted in the complex into vibrational degrees of free-dom, and it is the difficulty of this transformation which is re-sponsible for the tardiness of the reaction. Recently, Kistiakowskiand his co-workers1s8 have boldly utilised the theory in rather adifferent way in order to find out something about the precisestructure of the transition complex of butadiene.The other way ofexplaining the smallness of the P factor consists in supposing thathv >kT and that therefore the vibration partition function mayhave a value very much less than unity. This naturally complicatesmatters considerably for then not only is it necessary to compute theexact magnitude of the partition function for each mode of vibra-tion of the initial state of the system, but it is also necessary toknow the modes of vibration of the transition complex. More-over, there may be several possible configurations of the latter,and this still further complicates the solution of tho problem.See, e.g., H. Eyring, Trans. FaracZay Soc., 1936, 34, 3 ; dso, in particular,M. G.Evans, ibid., 1939, 35, 824MXLVIIJLE : CHEMICAL KINETICS. 67None the less if, by postulating a given configuration for the complexand carrying through the calculations to the stage of computing theA factor, agreement is obtained with experiment, then there is goodreason to suppose that the correct transition complex has been chosen.This is an important piece of information in so far as the associationof molecules containing conjugated double bonds is concerned.Here the prime essential is to try to discover whether the electronsof the double bonds are merely excited or whether a di-radical isformed. The agreement for butadiene between theory and experi-ment is good enough to support the conclusion that the transitioncomplex is indeed a free radical.Although the energy of activationof the reaction is only 23,690 cals., diradical formation thus :CH,=CH-CHXCH, CH2=CH--C1H=CH2CH;=CH=CH-CH2-CH2-CH=CH=CH2 III I Ican also be justified from energetic considerations, for then2(B - A) + A + 23, - R, - 24 < 0where B is the energy required to open the double bond to a singlebond, and A is the energy of a single bond in the middle of a hydro-carbon chain; R, and R, are the resonance energies of butadieneand the di-radical, estimated as 15,000 and 5000 cals. respectivelyfrom C. A. Coulson’a calculations.16 Thermochemical data giveB - A = 24.5 kg.-cals., and therefore A must be less than 95kg.-cals. The energy of the -C-C- bond is certainly in some doubt,but in a hydrocarbon it probably does not exceed 95 kg.-cals.andhence di-radical formation is energetically possible on thesepremises. This does not mean, of course, that opening of a doublebond is invariably the mechanism in all other molecules, but theessential demonstration is that owing to resonance it need not bean unduly energetically expensive process.The Formation of Long-chain Molecules.-The study of the ki-netics of the thermal polymerisation of vinyl derivatives in the gasphase is out of the question, but the reactions proceed smoothlyin the pure liquid or in solution. The reason for this behaviourwill become apparent in what follows. In this way styrene, methylmethacrylate, vinyl acetate, and similar molecules have beenpolymerised under a variety of conditions.I n the gas phase onlythe photochemical method of starting polymerisation can beconveniently employed. Before dealing with either of thesedevelopments we may anticipate a little along the following lines.In these reactions it has been established beyond all doubtl6 Proc. Roy. SOC., 1938, A , 164, 38368 GENERAL AND PHYSICAL CHEMISTRY.that the mechanism is of the chain type, in that when one moleculeis brought into a reactive state by light or by a catalyst a largenumber of additional molecules may react with the active polymermuch more readily than they would with a normal molecule ofmonomer. Eventually the activity is destroyed in some manner.Hence, kinetically the problems to be solved are these : How is themolecule brought into the reactive state, and what is the natureof this state? Is it possible for one molecule to possess more thanone such state ? When subsequent addition of monomer occurs,what is the efficiency of the process and how does it vary, if at all,with molecular size? Finally, by what type of reaction is theactivity destroyed ‘1 Two further problems of especial interestare whether branched reaction chains can occur with the pro-duction of either branched or three-dimensional molecules, andwhether it is practicable to cross polymerisation chains, i.e., t o formtrue interpolymers.Another problem concerns the distributionof the sizes of the various molecules produced.First, we deal with gas-phase polymerisations, and in view ofthe early state of development it will be convenient to deal with eachreaction separately before attempting any correlation.As in theliquid phase, only those monovinyl compounds having the basicgroup CH,=C < undergo polymerisation, the exception beingacetylene. Unlike the vinyl derivatives, acetylene polymerisesthermally at high temperatures, but the reaction is too complicatedto be of much use kinetical1y.l7,1*,19 If, however, acetylene isirradiated with light of wave-length ca. 2000 A., it polymerises to ityellow solid-cuprene-of the same composition as acetylene at20°.20- 21 At higher temperatures isolable amounts of benzene areformed.22y23 S. C. Lind and R. S. Livingston24 found from itsystematic investigation of the kinetics that the chain length wasabout 10 a t 20°, and the rate of polymerisation was simply pro-portional to the intensity if absorption of light was incomplete ;i.e., -d[C,H,]/dt = const.Iiin.[C2H2]e-4000’fiT, where Ii,. is theincident light intensity. Nothing is known about the constitutionof the polymer, or of its molecular weight if it is a straight-chaincompound. If the primary efficiency were unity, the molecularl7 R. N. Pease, J. Amer. Chem. SOC., 1930, 52, 1158.18 H. A. Taylor and A. van Hook, J. Physical Chem., 1935, 39, 811.P. Schliipfer and M. Brunner, Nelv. Chim. Acta, 1930, 13, 1125.20 J. R. Bates and H. S. Taylor, J. Amer. Chem. Soc., 1927, 49, 2438.21 F. Reinicke, 2. angew. Chcm., 1928, 41, 1144.22 S. Kato, BULL Inst. Phys. Chem. Res. Tokyo, 1931,10, 343; W.Kemulaand St. Mrazek, 2. physikal. Chem., 1933, B, 23, 358.23 R. S. Livingston and C. H. Schifflett, J . Physical Chem., 1934, 38, 377.24 J . Amer. Chem. SOC., 1932, 54, 103MELVILLE : CHEMICAL KINETICS. 69weight would be ten times that of acetylene. If the molecularweight was found to be appreciably higher than this figure, then theefficiency must be less than unity. Similarly, in the mercury-sensitised polymerisation the rate is given by an equation almostidentical with that for the direct reaction, vix.,- d[C,H,] /dt = const. {li,.k[C,H,]/(k[C,H2] + T ) ) ~ - ~ ~ ~ / R ~where z is the lifetime of the excited atom.25 It may be mentionedthat the apparent energy of activation decreases with increasingtemperature, finally becoming zero.In this reaction the excitedmercury atom collides with and combines with the acetylene mole-cule, further molecules of acetylene adding to the initial complex.The variation in rate with pressure in both the direct and the sensit-ised reaction is simply connected with the starting process andhas therefore nothing to do with the polymerisation itself.At this point it is desirable to indicate how some mechanismfor the reaction may be constructed from these data in order toshow how the kinetics of polymerisation may be dealt with. Themechanism involves the photoactivation of the acetylene to somereactive state which need not be specified for the moment. Mole-cules of acetylene add on, but the process comes to a stop since thequantum yield is finite.It is now generally agreed that, exclusiveof inhibitors, there are only three ways in which termination ofgrowth may occur.25 26 The first consists in the spontaneous lossof activity of the growing polymer, as for example by isomerisationand at a rate k,[P], where [PI is the total concentration of activepolymer; the second consists in the destruction of reactivity bycollision with a molecule of monomer * a t a rate k,[P][M]; thethird consists in the interaction of two active polymers in such away as to lead to mutual removal of their activity. A polymerchain reaction is in a way simpler than the usual type of chain inthat only one reactive molecule instead of two is concerned. Hencewe may write the equation defining its concentration in the stationarystate thus :d[P]/dt = I + kp[P][M] - kp[P][M] - k,[P][M] 0where I is the rate of starting and monomer termination occurs;[PI may therefore be obtained, and since the rate of polymerisationis kp[P][M] = Ikp[M]kt-l, the whole problem would appear to besolved. Naturally much complication may arise in the initiation25 H.W. Melville, Trans. Faraday SOC., 1936, 32, 258.26 J. W. Breitenbach, Monatsh., 1938, 71, 275.* The collision must of course be of a different kind compared with that inwhich the polymer grows70 GENERAL AND PHYSICAL CHEMISTRY.and termination factors but the kinetics may be worked out in ananalogous manner. There is one simplification which may not bevalid. This is that the magnitude of the propagation coefficientkp is independent of molecular size-at any rate at the beginningof the reaction.Another difficulty of this simplified treatment is that it is notpossible to calculate the distribution of molecular sizes in the productsfor the simple reason that all active polymer molecules are consideredto be kinetically identical.It is evident therefore that some con-venient method of dealing with all possible polymer molecules,alive as well as dead, must be devised. This is done in the followingway. Suppose again there is monomer termination, then for eachpolymer molecule there is a corresponding equation defining itsconcentration, that concentration being assumed to have reached astationary value. This is equivalent to assuming that the lifetimeof the active polymer is short compared with the half life of thereaction.(Exceptions to this behaviour will be discussed below.)Hence the simple equation becomesfor polymer P, [P,] = I - kp,[Pl][M] - k,,[P,][M] = 0and for P,and, in general, rki = kpT- ,[E - 1 ~ [ ~ ~ - I~,~[P,I~MI - ~,JP,I[MI = 0Therefore I = =prI[MI.P21 = k p l r p l i [ ~ i - I%,,[P,I[MI - ~,,CP,I[MI = 0As it stands this expression is not of much value for obtaining-d[M]/dt, but if the eminently reasonable assumption is made thatktJkpl = ktr/kpr = A, then it can be easily shown thatand therefore- d[M]/dt = IZ(1 + A)-?- d[M]/dt = 1(1 +if the chain length of the polymer is long. Thus it is seen that alarge number of stationary concentration equations are easily dealtwith by making this assumption.For any other type of initiationor termination process the corresponding equations may be deducedand compared with the experimental findings so that a mechanismmay be formulated. Naturally such a method precludes thepossibility of determining the magnitudes of the individual valuesof kp or of kl. For that purpose a different technique must beemployed. As will be seen later, an extension of this procedureenables molecular-weight distribution curves to be obtained.Returning to the polymerisation of acetylene, it may be shownthat the above-mentioned kinetics are only consistent with monomertermination. Apart from this not much more may be said abouMELVILLE : CHEMICAL KINETICS. 71the details of this reaction. Dideuteroacetylene polymerisesmore slowly that acetylene and with a shorter chain length.2' Thereason for the difference is probably due to the higher energy ofactivation of the propagation reaction.Methyl radicals from photodecomposing acetone also inducepolymerisation of acetylene,28 but the chain length is very short-2 to 5-at high temperatures, with the result that it is ratherdifficult to arrive at a mechanism except to say that the methylradical produces a larger free radical by reaction with acetyleneand this grows further by the addition of monomer.Providingthe iodine atoms be removed by mercury, ethyl radicals fromphotodecomposing ethyl iodide will also induce p~lymerisation.~gThe photopolymerisation of methylacetylene is rather less rapidthan that of acetylene.30Ethylene does not polymerise thermally at ordinary pressures,but at pressures of the order of 100 atm.it forms a wax-likepolymer ; 31 unfortunately no kinetic data are available to yieldany mechanism, except that it is not improbable that oxygencatalyses the reaction. In view, therefore, of the possibilityof the formation of ethylene oxide and its subsequent decom-position into free radicals, it is not unlikely that the ethylene ispolymerised by the free-radical mechanism, as happens a t ordinarypressures under suitable conditions.On being irradiated, ethylene decomposes in addition to formingsmall amounts of polymer.32 If it dissociates into acetyleneand hydrogen the polymer will simply be that of acetylene ; if it dis-sociates into 2CH2, for which there is some spectroscopic evidence,33polymerisation might occur by the primary reaction of CH, withC,H, and the subsequent addition of C,H,.Likewise, in the poly-merisation by excited mercury atoms there is probably first dis-sociation to hydrogen and a~etylene.~, Here, too, the acetylene ispolymerised, but it may be hydrogenated by atomic hydrogenproduced by mercury sensitisation, thus giving a polymer of a com-position approximating to that of ethylene itself.252 7 J. C. Jungers and H. S. Taylor, J . Chern. Physics, 1935, 3, 338.28 Idem, Trans. Paraday Soc., 1937, 33, 1353.29 G. Joris and J. C. Jungers, Bull. SOC. chirn. Belg., 1938, 47, 135.30 S. C. Lind and R. S. Livingston, J . Amer.Chem. SOC., 1933, 55, 1036.31 B.P. 471,690.32 R. B. Mooney and E. B. Ludlam, Trans. Paraday SOC., 1929, 25, 442;33 H. J. Hilgendorff', 2. Physik, 1935, 95, 781; W. C. Price, Phystkl Rev.,34 A. R. Olson and C. H. Meyers, J. Amer. Chem. SOC., 1926, 48, 389; J. R.R. D. McDonald and R. G. W. Norrish, Proc. Roy. SOC., 1936, A , 157, 480.1934, 45, 843; 1935, 47, 444.Bates and H. 8. Taylor, ibid., 1927, 49, 243872 GENERAL AND PHYSICAL CHEMISTRY.It is said that hydrogen atoms polymerise ethylene since C,hydrocarbons are one of the main products of the reaction at 20",but this is probably due to the combination of ethyl radicals formedby the addition of hydrogen atoms to the eth~lene.3~ Higherhydrocarbons, which would imply true polymerisation, are notpresent in any large quantity.At higher temperatures-up to300"-methyl radicals from thermally decomposing azomethane,36from photodecomposing acetone,,* from thermally decomposingmetal alkyl~,~' and ethyl radicals from photodecomposing ethyliodide29 polymerise ethylene to hydrocarbons up to C20. Inthese reactions the free radical adds on to the ethylene molecule,thus forming a larger free radical CH3*CH,*CH,-. Further mole-cules of ethylene then add on until the free radical reacts withanother of its kind by one of two mechanisms : (a) combination or(b) disproportionation, R*CH,CH,* -CH,*CH,R --+ R*CH:CH,CH,*CH,R. Depending on conditions, however, it happens that thefree radical may disappear a t a rate proportional, not to the squareof its concentration, but to the first power.Such a reaction mightwell be wall recombination of the radicals. An examination of thedata on the azomethane-catalysed polymerisation shows that if theassumption is made that the disappearance of the radicals is temper-ature-independent, the mean energy of activation for the propagationreaction is 8.6 kg.-cals. This is a comparatively small value, andwould indicate that marked polymerisation should occur a t temper-atures much below those, vix., 200-300°, normally employed tostudy the reaction. If, however, the interaction of free radicalsrequires activation the above figure will be correspondingly in-creased. At present there is no published evidence to settle thisquestion.The direct photopolymerisation of butadiene has not yet beeninvestigated, but since the gas is transparent compared with mercuryvapour a t 2537 A., the mercury-sensitised reaction may be con-veniently studied.38 Kinetically its behaviour is similar to that ofacetylene.The quantum yield is, however, less than unity, althougha brown non-volatile product is deposited, and hence it must besupposed that the activation of butadiene molecules is not at allefficient. Here, too, the excited mercury atom enters into chemicalcombination with the butadiene molecule, and the polymerisationis brought to a stop by collision of the active polymer with a monomer-by what type of collision is not known. The polymer would35 H. S. Taylor and D. G. Hill, J . Amer. Chem. SOC., 1929, 51, 2922.36 0.K. Rice and D. V. Sickman, ibid., 1935, 57, 1384.37 H. S. Taylor and W. H. Jones, ibid., 1930, 52, 1111.38 G. Gee, Trans. Paraday SOC., 1938, 33, 712MELVILLE : CHEMICAL KINETICS. 73appear to be complex in structure and extensively cross-linked,for it is insoluble in all the usual solvents. Accompanying thepolymerisation there is some decomposition to hydrogen and a resi-due and also the formation of dimer. Polymerisation proceedsfor a short period in the dark after the light is cut off.It will be evident from the above remarks that the polymerisationof hydrocarbons is not a reaction which occurs at all readily. If itis accelerated by employing higher temperatures, the product is notstable. Hence for more exact kinetic study it would seem that othervinyl derivatives may be suitable for experiment.There are a tleast two advantages to be gained by the substitution of the hydrogenatoms with groups such as CO,Me, CN, Cl, COMe, etc. : the poly-merisation velocity is increased and also the absorption spectrumof the molecule is extended to longer wave-lengths. Early experi-ments 39 on styrene and vinyl acetate had demonstrated that thesemolecules polymerise readily under the influence of radiation,showing typical chain characteristics, vix., high quantum yield andsensitiveness to inhibition by substances which are well recognisedas having this effect on chain oxidations. Fortunately, a numberof these vinyl derivatives have a high enough vapour pressure tomake practicable the study of their polymerisation in the vapourphase.Methyl methacrylate, for example, polymerises with ultra-violetlight of wave-length shorter than about 2600 A.sufficiently readilyto produce an easily visible cloud of solid polymer in the v a p o ~ r . ~ ~If too short wave-lengths (< 2300 A.) are used the molecule tendsto dissociate rather than polymerise, and hence it would appearthat such a molecule will only contain a limited amount of energyin order to excite the molecule in such a manner as to lead to poly-merisation. The energy limit cannot be fixed on account of the factthat the absorption at long wave-lengths is too minute to cause anypolymerisation. In the section on dimerisation it was seen that theactivation energies involved may lie as low as 20,000 cals., andtherefore it is not impossible that with methacrylate the energyrequired to start polymerisation may have a lower limit of thismagnitude.The curious thing is that the polymer so depositedis reactive long after the light is cut off, the monomer continuingto polymerise for several days afterwards. This activity maybe destroyed by atomic iodine and atomic hydrogen, i.e., sub-stances capable of reacting with double bonds or free radicals.The process is undoubtedly a condensed-phase reaction between39 H. W. Starkweather and G. B. Taylor, J . Amer. Chem. SOC., 1930, 52,40 H. W. Melville, PTOC. Roy. SOC., 1937, A , 163, 511.4708; H. S. Taylor and A. A. Vernon, ibid., 1931, 53, 252774 GENERAL AND PHYSICAL CHEMISTRY.absorbed monomer and polymer ; its overall temperature coefficientgives an apparent energy of activation of - 5.6 kg.-cals., but whenthis is corrected for desorption of monomer the real value of theactivation energy is 2.7 kg.-cals.Although molecular-weightmeasurements have not yet been made, it is probable that themolecular weight increases with time, and thus theoretically amolecule of any given size may be constructed. When anactive molecule possesses such a long lifetime, the rate of formationand destruction of these centres plays no part in the rate of poly-merisation, which is then solely determined by the velocity ofthe propagation reaction. In a way it is unfortunate that thereaction occurs in the solid phase, since its absolute efficiencycannot easily be determined.The activation energy is, however,comparable with that of other polymerisations. In treating thekinetics of reactions of this type, which at the moment are confinedto polymerisation, the stationary-state method indicated above canno longer be employed.Attempts41 have therefore been made to devise a system ofkinetics to suit this case. Suppose we deal with a finite initialconcentration of monomer [MI,, and that the active centres are pro-duced at a rate Ei[M], and further that the propagation coefficient(A$ does not vary with molecular size. There is no experimentalevidence for this assumption; in fact, Ep has been assumed to de-crease with increasing size and even to so small a value as to stopreaction altogether, but this is going too far.With methacrylate 40and chloroprene it would appear that there is no variation in kpover a very large range of molecular weights. Hence the mechanismof the reaction will beM-+ PI ktM + PI-+ p2 } k pand in general M + p, --+ P T f l JIf therefore [PI is written for C[P,] thenandOn solving for [PI, we haveThus the reaction will exhibit an induction period. Naturallyif [PI reaches a well-defined and maximum value, as, e.g., when asurface becomes completely covered with active centres, the ratewill then attain a constant value. For any other type of4 1 See, e.g., H. Dostal and H. Mark, Trans. Paraday Soc., 1936, 32, 54;G. Gee and E. K. Ridesl, ibid., p. 656MELVILLE : CHEMICAL KINETICS. 76initiation process the corresponding rate equation may be deduced.Similarly, if the number of centres gradually as, e.g.,by mutual destruction, and there is bimolecular initiation, thend[P]/dt = k1[MI2 - L2[P12- d[M]/dt = kp[P][M]whenceTherefore every type of long-lived polymer may be dealt with ina precisely analogous manner. Unfortunately, experimental dataare as yet too meagre to be of much use in formulating representativereaction schemes.The above discussion has emphasised the fact that, before con-ducting a kinetic analysis of a polymerisation reaction, the firstnecessity is determination of the lifetime of the active polymer.This is in general a fairly easy matter with photochemical reactions,at least in so far as discriminating between short and long lifetimes,but it is much more difficult for thermal or catalytic reactions inwhich the rate of the initiation reaction cannot be independentlycontrolled.In absence of this definite criterion, there is the possi-bility of determining the molecular weight of the product during thereaction. If this increases with time continuously, there is somereason to suppose that the lifetime of the active polymer is at leastcomparable with the half life of the reaction, and that thereforethe non-stationary kinetic method must be applied. In thosephotochemical polymerisations, e.g. , that of butadiene, where thereis a dark reaction with a half life of a few minutes, it may be difficultto decide which system to employ.Moreover, the reaction may becomposite in that the dark reaction is entirely separate from thelight reaction even though both are initiated by radiation.Gaseous methyl methacrylate may also polymerise on additionof hydrogen atoms. This is undoubtedly a free radical reactionin which the hydrogen atom adds on to the methacrylate moleculeto give CH,*CMe(CO,Me)*. Further molecules of monomer addon until two such radicals combine, whereupon the polymerisationstops.sec. , and therefore this free-radical polymerisation is entirely differentfrom that occurring by direct photoexcitation of the methacrylatemolecule.One of the problems arising in the polymerisation of vinyl de-rivatives as a whole is the nature of the active polymer. Opinionhas been divided between two mechanisms which may be likened to42 P.J. Flory, J . Amer. Chem. Soc., 1936, 58, 1877.The lifetime of these radicals is only of the order o76 GENERAL AND PHYSICAL CHEMISTRY.the ‘‘ hot ” molecule and radical chain of the early days of chainreactions. Here it is necessary to distinguish between the twopossible ways of activating a double bond, zfix., (a) by forming adi-radical, the mechanism of polymerisation then being*CH,*CHX* + CH,:CHX --+ *CH,*CHX*CH,*CHX*and (b) by exciting the double bond so as to facilitate addition ofa molecule of monomer, that is, reduce the energy of activation :CH2:CHX + CH2:CHX -+ CH,*CHX*CH:CHXIn the latter mechanism the distinguishing feature is that each timeaddition of monomer occurs a hydrogen atom must migrate.Somehave argued that such a process would require so much activationenergy that the polymerisation would revert to the so-called step-wise rather than the chain mechanism. In the former the activationenergies for the individual steps are of the same order of magnitudeas that of the initial step, and thus the activation of one moleculedoes not necessarily lead to the polymerisation of a large numberof monomeric molecules. The main characteristic of the chainmechanism, on the other hand, is that once the first molecule isactivated the activation energy for subsequent addition is materiallydiminished.In the polymerisation of methyl methacrylate it is very probablethat the kinetics of the di-radical mechanism would be similarto those of the reaction induced by hydrogen atoms, and thereforethe normal polymerisation should occur by the double-bondmechanism.Although this seems the most reasonable explanation,it is somewhat difficult to see why the activity persists for so long aperiod; yet in absence of evidence to the contrary this mechanismmay be provisionally accepted. Thus a molecule containing only asingle double bond may polymerise by at least two mechanisms.There is evidence in the liquid-phase polymerisation of styrenethat the two mechanisms may operate, for, under one set of conditionsa long-chain molecule is obtained whereas in another di- or tri-styrene is the product.43 The first may go via free radicals and thesecond by double bonds.Likewise in the polymerisation of methylisopropenyl ketone both long-chain molecules and dirner areformed.44Methyl acrylate polymerises rather more readily than the meth-acrylate but the greatest difference is that the lifetime of the activepolymer is short. On analogy with methacrylate it presumablypolymerises by the double-bond mechanism, and chain terminationis brought about by mutual destruction. This could easily be43 H. Staudinger, Trans. Faraday SOC., 1936, 32, 97.** T. T. Jones, private communicationMELVILLE : CHEMICAL KINETICS. 77explained by the radical mechanism but is equally probable withthe double-bond mechanism, for the two ends of the polymer mayreact thus--CH=CHX + CHX=CH,-' + ---CH2-CX=CX-CH,-One of the most surprising features of the reaction is its negativetemperature coefficient.If the active polymers are destroyed bythe addition of a small amount of oxygen or butadiene the temper-ature coefficient becomes positive. On the assumption that in-hibition is temperature-independent, the energy of activation forpropagation is computed to be about 4 kg.-cals. Thus the negativeoverall energy of activation must be due to the fact that the termin-ation reaction possesses an energy of activation greater than that forpropagation. A measure of the chain length in the photopoly-merisation may be obtained in the butadiene inhibited reactionfrom the ratio of acrylate molecules polymerised to butadienemolecules used up.The chloroprene photopolymerisation exhibits many unusualtypes of b e h a ~ i o u r .~ ~ . 46 As with methacrylate the polymerisationcontinues in the dark. Similarly, if light much shorter that 2500 A.is used for irradiation the molecule is decomposed and no poly-merisation occurs. Excited mercury atoms cause polymerisation,being simultaneously incorporated in the polymer. The photo-polymerisation occurs wholly in the polymer itself after a smallamount of this is deposited on the walls of the reaction vessel.There are two simultaneous reactions-one in which the life of theactive molecules is short and the polymerisation is terminated by theinteraction of two active ends of a molecule, and the other in whichpolymerisation continues indefinitely (over 3 weeks has been re-corded) in the dark.The energy of activation for polymer growthis again about 3 kg.-cals. Since the lifetimes of the methacrylateand chloroprene polymers are so long it is practicable to make mixedpolymers by growing methacrylate on chloroprene and vice versa.On the other hand, butadiene refuses to interpolymerise with eitherof these molecules under these conditions.Liquid-phase Polymerisation.-Much more work has been done 011liquid-phase than on gas-phase polymerisation, though it cannotbe said that the results are more illuminating kinetically. Threemolecules have received most attention, vix., vinyl acetate, methylmethacrylate, and particularly styrene. Pure styrene may bepolymerised thermally as a, liquid or in solution with or without45 W. H.Carothers, I. Williams, J. E. Kirby, and A. M. Collins, J. Amer.Chem. Soc., 1931, 53, 4203.46 J. L. Bolland and H. W. Melville, Proc. Rubber Tech. Conf., London,1938, 23978 GENERAL AND PHYSICAL CHEMISTRY.the addition of a catalyst such as benzoyl peroxide, stannic chloride,etc.In presence of air, pure liquid styrene polymerises at about 100"as a homogeneous liquid-phase reaction, the evidence being thatthe rate of reaction and molecular weight of the product are notchanged by alteration of the surface/volume ratio of the reaction~esse1.~7*~8 There is no induction period, and the rate of reactionconforms to a first-order equation.49 The average energy of activ-ation is 23.2 kg.-cals., and the molecular weight of the polymer, whichremains substantially constant during any one runso a t a constanttemperature; decreases with increasing temperature according tothe relationship M = const.e570°'RT. If the polymerisation is carriedout in an atmosphere of nitrogen, the kinetics of the reaction are notmaterially altered.51 If the temperature of the mixture of monomerand polymer is suddenly reduced the polymerisation immediatelyceases. This fact, and also the observation of the constancy ofmolecular weight, are strong indications that the lifetime of thepolymer is short compared with the half life of the reaction, andthat therefore the stationary-state method may be applied todetermine the mechanism. Here there is a difficulty, for althoughthe reaction proceeds according to a first-order equation, it is difficultto see what significance this observation can have since presumablyin the pure liquid phase the concentration of styrene remainsconstant. It is, however, probably true to say that the concen-tration of the polymer increases according to the equationc = c,(l - e-kt), where c and c, are the concentrations of deadpolymer at time t and at the end of the reaction. Hence, no con-clusion can be arrived at with regard to the collision mechanismof the initiation and termination processes.Assuming, as has beendone, that there is mutual termination of the growth of the polymer,then by employing the method indicated on p. 70 it can be shownthat R = P(I/T)l12 and M-P(IT)-'I2, where I , P, and T are theinitiation, propagation, and termination factors respectively.Since each factor is temperature-dependent, then from the datathe following relationships a t once hold : 23-2 = E, + +EI - QETand - 5-7 = Ep - $EI - $ET or EI = 28.9 kg.-cals.(XI, etc.,are the corresponding energies of activation). As will be seen, evenwith this assumption there are three unknowns and only two equa-tions; ET cannot arbitrarily be put equal to zero, as may be done47 J. W. Breitenbach and W. Jorde, 2. Elektrochem., 1937, 43, 609.48 H. Dostal and W Jorde, 2. physikal. Chem., 1937, A, 179, 23.4a G. V. Schulz and E. Husemann, ibid., 1936, B, 34, 187.50 H. Staudinger and W. Frost, Ber., 1935, 68, 2351.5 1 G. V. Schulz and E. Husemann, 2. physikal. Chem., 1937, B, 36, 184MELVILLE : CHEMICAL KINETICS.79often in ordinary chain reactions. If it were, E, would then amountto the rather high value of 17.5 kg.-cals. Consequently the con-clusion is that E, must amount to several thousand calories.It would appear, therefore, that in order further to elucidatethe mechanism it would be desirable to conduct the polymerisationin solution, so that the concentration of monomer would be betterdefined. Furthermore, the addition of a catalyst might thenenable a check to be kept on the initiation reaction. The uncatalysedpolymerisation in solution has been studied in a number of solventswhich exert a well-marked influence on the rates.although the overallenergy of activation is not changed. 52 The rates increase in the orderbenzene, toluene, hep tane , ethylbenzene, diet h ylbenzene, styrene,dichloroethane, trichloroethane, and carbon tetrachloride, but asufficiently detailed analysis is not given to explain what process orprocesses are affected by the solvent or whether the solvent acts asan inhibitor.A more detailed analysis of the benzoyl peroxide-catalysed reaction in toluene gives a better idea of the mechanismof the reaction.53 Again, the degree of polymerisation remainsconstant and is inversely proportional to the square root of thecatalyst concentration. The rate is correspondingly directlyproportional to the square root of the benzoyl peroxide concentra-tion. These facts definitely prove that the mechanism of thecessation of growth involves the interaction of two active polymers.It would appear that an endothermic catalyst-monomer complexis formed which initiates polymerisation. Whether the benzoylperoxide is eliminated on termination of growth is not known.Thisinvestigation also proves that toluene has nothing to do with thetermination reaction. Any effect it may exert is thus confined to thealteration in the equilibrium constant for complex formation or thevelocity coefficient for propagation.Stannic chloride catalyses the polymerisation of styrene moremarkedly than benzoyl peroxide, measurements of velocity beingpracticable in carbon tetrachloride at 25". 54 Provided the stannicchloride be absolutely free from hydrogen chloride, which is astrong inhibitor, there is no induction period and the rate is approxi-mately proportional to the concentration of the catalyst; also themolecular weight, though small, does not vary during the reactionand is independent of catalyst concentration.These kinetics wouldindicate that the active polymer is destroyed at a rate proportionalto its concentration-possibly by reaction with carbon tetrachloride.52 H. Suess, K. Pilch, and H. Rudorfer, ibid., 1937, A , 1'79, 361 ; H. Suessand A. Springer, ibid., 1938, A, 181, 81.53 G. V. Schulz and E. Husemann, ibid., 1938, B, 39, 246.64 G. Williams, J., 1938, 246, 104680 GENERAL AND PHYSICAL CHEMISTRY.As with benzoyl peroxide, some complex is formed between catalystand monomer which starts polymerisation. In view of the factthat there is no induction period, the time for the formation of theequilibrium amount of the complex is short compared with the timefor polymerisation.An interesting use can be made of the inhibi-tion by hydrogen chloride since by observing how the length of theinduction period varies with the concentration of this substanceand assuming that the hydrogen chloride reacts with the activepolymer, it is possible to calculate how many active polymers areproduced per unit time. The ratio of rate of polymerisation to therate of this process should then give the mean degree of polymeris-ation. There is, in fact, good agreement with the value determinedfrom the molecular weight of the polymer.What the precise nature of the active polymer is under theseconditions of polymerisation has been and still is a matter for specula-tion, but it is interesting to observe that G.V. Schulz and G. Wittig 55have succeeded in inducing a free-radical polymerisation of styreneby adding to it the free radical CPh,*CN from tetraphenylsuccino-nitrile. Moreover, the free radicals combine finally to stop thegrowth of the polymer chain.The polymerisation of vinyl acetate seems to be rather morecomplicated than that of styrene. The early observations do notpermit of a detailed analysis.39 Some have questioned the homo-geneity of the reaction.56 A more detailed analysis has shown thatwhen suitably purified reactants are used the reaction is homogeneous,and is catalysed by benzoyl peroxide, an induction period beingcharacteristic of the polymerisation.57 During the inductionperiod the catalyst interacts with the monomer to form a complexwhich on breaking down initiates a polymer chain. The kineticanalysis shows that termination is again due to mutual interactionof the active polymers. Further complication appears to arise, fora t high temperatures the polymer is insoluble, from which it isconcluded that branching and cross linking of the molecular chainsThe kinetics of the polymerisation of methyl methacrylatecatalysed by its ozonide and also by benzoyl peroxide have beenexamined.58 Here the reaction is of zero order until isothermalconditions cease to apply to the system. The rate of polymerisationis proportional to the square root of the catalyst concentration,occur.55 Naturwiss., 1939, 27, 387.56 J.W. Breitenbach arid W. Jorde, Z . lClektrochem., 1937, 43, 609.5 7 A. C. Cuthbertson, G. Gee, arid E. K. Rideal, Proc. Roy. SOC., 1939, A ,58 R. G. W. Norrish and E. E. Brookman, ibid., 171, 147.1’70, 300MELVILLE : CHEMICAL KINETICS. 81which implies mutual destruction of the active polymers whateverthese molecules may be. The molecular weight under the conditionsemployed tends to increase during polymerisation. This was a tfirst taken to mean that the life of the polymer was long, but maybe more simply explained by supposing that the lifetime of theactive polymer is short, in conformity with general experience inliquid-phase polymerisations, and that the catalyst concentrationgradually falls during the reaction owing to its decomposition.59The kinetics of the polymerisation of mixtures of styrene andmethyl methacrylate are peculiar in that there is a non-linearrelation between rate and mo1.-fraction of the components.58Interpolymerisation may occur but the precise interpretationof the data is at present rather difficult owing to lack of knowledgeabout the kinetics of the individual reactions themselves.There are two matters finally to be discussed in connection withthe kinetics of polymerisation. The first concerns branching.In ordinary gas kinetics branching of chains was first introducedto explain the appearance of sharp explosion limits, but in polymersthe idea was introduced from an examination of substances whosestructure consisted of a three-dimensional network of atoms.I npolymers, therefore, branching is detected structurally, and thequestion arises as to whether there is any way of detecting itsoccurrence during a polymerisation reaction by some characteristickinetic feature. At present there is no published evidence pointingto any deviation in normal kinetic behaviour which may be conclu-sively ascribed to branching, although products have been obtainedwhich appear to be cross-linked. This may be due to the fact thatmost polymer growth stops by mutual deactivation in pure systems.But branching can only become noticeable if the reaction goesabnormally quickly as some parameter such as concentration ortemperature is increased, and such an event only becomes possibleif the kinetic order of the branching process with respect to theactive polymer concentration is greater than the order of thereaction responsible for the destruction of the polymer.Whenactive polymer destruction is already of the second order it is thusimpossible for this condition to be fulfilled. Unless thereforebranching is brought about by the addition of some specificnew component to the system, its detection kinetically seemsunlikely.Molecular..weight distribution in synthetic polymers and its re-lationship to mechanism is still a virgin field. The ultra-centrifugalmethod of separation has been applied to polystyrene.60 G. V.59 G. Gee, Trans. Paraclay SOC., 1939, 35, 1085.6o R. Signer and R. Gross, Helv. Chim. Acta, 1934, 17, 59, 335, 72682 GENERAL AND PHYSICAL CHEMISTRY.Schulz has separated polymers by fractional precipitation andcompares such distributions with his theory, whereas H.Dostaland H. Mark 62 and P. J. Flory 63 have made calculations on suchdistributions. From the general theory of the polymerisationgiven on p. 70, it may be indicated how this kind of calculationcan be carried out. The last term in each differential equationfor the active polymer gives the concentration of '' dead " polymerorHenceand consequently the weight fraction w, is given byd[M,]/dt = ~~r[P,I[Ml = hf(l)/(l + A)?[Mrl = h2([MlO - [Ml)/(I + 1Y-lw, = P r / ( l +As a result of these calculations two kinds of average chain lengthmay be defined,64 vix., (a) a number average v, = Zr[M,]/C[M,] = I - 1,which is determined by kinetic methods, i.e., end-group determin-ations, and ( b ) a weight average v, = Cr2[&]/Zr[i&] = 2 / h , de-termined by viscosity measurements.For this particular mechan-ism it will be seen that v, is twice v,. Naturally, for each kind ofmechanism appropriate distribution functions may be derived.Whether the reverse process may be practised, vix., the confirmationof reaction mechanism by distribution measurements, is yet to beseen.This brief survey of polymerisation will have indicated thatalthough the problems encountered are innumerable and often diffi-cult of solution, the kinetic attack on the question, supplementedwhenever possible by determination of the structure of the resultantpolymer, does show some promise of successful solution.H.W. M.4. THE RGLE OF THE SOLVENT IN REACTION KINETICS.The effect of different solvents upon the velocity of chemicalreactions was one of the earliest kinetic problems to be studiedexperimentally, as, for example, in the work of Menschutkin.1Numerous attempts were made to establish empirical relationshipsbetween the reaction velocity and physical properties of the solvent61 2. physikal. Chem., 1935, B, 30, 379.62 Trans. Paraday SOC., 1936, 32, 54.63 J . Amer. Chem. SOC., 1936, 58, 1877; 1937, 59, 241.64 E. 0. Kraemer and W. D. Lansing, J . Physical Chew&., 1935, 57, 1369.1 2. physikal. Chem., 1890, 8, 41BELL: R6LE O F THE SOLVENT IN REACTION KINETICS. 83(such as the dielectric constant), but these relations had no theor-etical basis and had no wide range of applicability even in a qualit-ative sense.Later, experimental advances made it possible to studyhomogeneous gas reactions, and modern theories of reaction velocitywere applied in the f i s t instance to these on account of their greatersimplicity from a theoretical point of view. More recently, however,the focus of attention has to some extent returned to reactions insolution, partly because of the increase in our general knowledge ofthe liquid state, and partly because of the bearing of such velocitieson modern theories of organic chemistry. Most of the theoreticaladvances have been framed in terms of either the collision theory orthe trunsition-state theory.The separate application of these twomethods often leads to results which appear at first sight to bedifferent, or even contradictory, but it is gradually being realisedthat the two methods of treatment are essentially equivalent, andmust lead to the same results if correctly applied. One of theobjects of this Report is to emphasise this equivalence in the problemof solvent effects, and to indicate how each method has someadvantages in dealing with particular aspects of this problem.*It is, of course, impossible to give any complete review of theexperimental data. I n the f i s t place, this article will deal almostentirely with bimolecular reactions, since it is for this type of reactionthat the effect of the solvent is most clearly understood.We shallconsider, in particular, cases in which a direct comparison has beenmade between the reaction velocities in the gas phase and in solu-tion-clearly an important type of investigation for our presentpurpose-and also reactions which have been studied in a wide rangeof solvents. Such results provide a much more useful basis fortheoretical discussion if they refer to a range of temperatures, and thetemperature variation of the velocity has almost always beenexpressed in terms of the Arrhenius equation, Ic = Ae-E”RT, where Eis the activation energy, and A will be termed the collision factor.The effect of the solvent on E and A separately should then consti-tute a simpler problem than the effect on the velocity as such. Itshould, however, be mentioned that there are certain grounds forregarding the Arrhenius equation as only a good f i s t approximation.From a theoretical point of view the activation energy defined byE = RT2 d(1og k) /dT is the difference between the average energy ofthe reacting molecules and the average energy of all the molecules,and this difference may be expected to vary with temperature in thesame way as any heat of reaction.This fact has been realised for a* Both the apparent divergence and the essential equivalence of the twomethods are well illustrated by two discussions held recently; J., 1937, 629;Trans. Faraday SOC., 1938, 34, 1-26784 GENERAL AND PHYSICAL CHEMISTRY.long time 2 and has been more recently emphasised by V. K. LaMer,3who also pointed out that deviations from the Arrhenius equationwill be more likely if different activated states have different prob-abilities of reaction.This possibility applies particularly to reactionsinvolving the movement of light nuclei (Le., protons) where, accord-ing to quantum theory, the probability of reaction is a continuousfunction of the energy.4 On the other hand, the reported experi-mental deviations from the Arrhenius equation (apart from thosedue to a composite chemical mechanism) are neither numerous norconvincing, and even recent low-temperature measurements onproton-transfer reactions have failed to reveal such deviations. I nthis Report we shall therefore follow the usual practice of using thesimple Arrhenius equation, though it should be borne in mind thateven deviations too small for experimental detection may affect theexact interpretation of the experimental values of A and E.'There are obvious experimental difficulties in measuring thevelocity of a reaction both in the gas phase and in solution, andalthough a fairly large number of such comparisons have beenattempted, the results are often inaccurate and difficult to interpret.The following bimolecular reactions have been investigated : (a) thereaction between amines and alkyl iodides, (b) that of aceticanhydride with alcohol, (c) various esterification reactions, (d) thedimerisation of keten, ( e ) the catalysed decomposition of trioxy-methylene, (f) the hydrolysis of oxalyl chloride, (9) the decompositionof ozone, (h) the reaction between ozone and chlorine, (i) the decom-position of chlorine monoxide, (j) the decomposition of ethylenedi-iodide, (k) the dimerisation of cyclopent,adiene.Cf.F. E. C. Scheffer and W. F. Brandsma, Rec. Truw. chim., 1926, 45,522;W. F. Brandsma, ibid., 1928,47,94; 1929,48,1205.J . Chem. Physics, 1933, 1, 289.For a summary, see R. P. Bell, Trans. 3'uruday Soc., 1938, 34, 232, 259;J. 0. Hirschfelder and E. Wigner, J . Chem. Physics, 1939, 7 , 616.Cf. V. K. LaMer, J . Amer. Chem. SOC., 1935, 57, 2662, 2669, 2674; 1936,58,2413; G. F. Smith, J., 1936,1824; W. I?. K. Wynne-Jones, Trans. FuradaySOC., 1938, 34, 250. R. P. Bell and J. K. Thomas, J., 1939, 1573.R. P. Bell, Trans. Faraday SOC., 1938, 34, 232.( a ) E.A. Moelwyn-Hughes and C. N. Hinshelwood, J., 1932, 230 ; H. W.Thompson and E. E. Blandon, J., 1933, 1237; A. Gladishev and J. Sirkin,Actu Physicochim. U.R.S.S., 1938,8,323; ( b ) E. A. Moelwyn-Hughes and C . N.Hinshelwood, Zoc. cit. ; (c) C . A. Winkler and C. N. Hinshelwood, Trans. B'arudaySOC., 1935, 31, 1739; (d) F. 0. Rice and J. Greenberg, J . Amer. Chem. Soc.,1934,56,2132 ; ( e ) R. P. Bell and R. le G. Burnett, Trans. Puruduy Soc., 1939,35, 474; (f) F. Daniels, Chem. Reviews, 1935, 1'7, 8 2 ; (9) and (h) E. J. Bowen,E. A. Moelwyn-Hughes, and C . N. Hinshelwood, Proc. Roy. Soc., 1931, A , 134,211; ( i ) E. A. Moelwyn-Hughes and C. N. Hinshelwood, ibid., 1931, A , 131,127; ( j ) M. J. Polissar, J . Amer. Chem. SOC., 1930, 52, 956; H.J. Schumacher,ibid., 1930, 52, 3132 ; L. B. Arnold and G. B. Kistiakowski, J . Chem. PhysicsBELL: R ~ L E OF THE SOLVENT IN REACTION KINETICS. 85Of these reactions, (a)-(e) take place on the walls of the vessel inthe absence of solvent, whereas (f) and (9) proceed by complicatedmechanisms which are not the same in solution and in the gas.Reaction (h) is a complicated chain reaction, but in the gas phase thevalues of A and E for the rate-determining bimolecular process canbe estimated. At 50" the observed rate is almost the same in the gasand in carbon tetrachloride solution, but there is such a largedifference in the temperature coefficients that the reactionmechanism can hardly be the same in the two phases. Reaction(i) is not strictly of the second order, and the numerical values of Aand E cannot be determined; however, both the rate and thetemperature coefficient are much the same in the gas and in carbontetrachloride solution, so the A and E values are probably verysimilar in the two phases. Reaction (j) is a chain reaction, but thevelocity constant of the rate-determining bimolecular process can beestimated both in the gas and in solution. The A and E values arereported to be the same in the two phases, but the accuracy is low,i.e., about h 1 .3 in log,,,A, and &3 kg.-cals./mol. in E . Reaction(k) has been studied over a wide range of temperature in the gasphase and in eight different solvents : the velocities vary only by afactor of about 4 throughout, and the values of A and E me constantwithin the experimental error.The study of reaction velocity in a wide range of solvents offersfew experimental difficulties, but although the mass of experimentaldata is large, the number of different types of reaction coveredis regrettably small.Reaction (a), often referred to as theMenschutkin reaction, has been studied by a large number of authorsin some 20-30 different solvent^.^There is some disagreement between the individual values ofdifferent authors, but it is clear in general that the velocity can bevaried by a factor of about lo3 by change of solvent, there being ageneral tendency for higher rates in solvents of a polar type. Theeffect of the solvent appears in the values of both A and E, and thereis little correlation between the variation of the two factors.Similar1933, 1, 166; R. A. Ogg, J. Amer. Chem. SOC., 1936, 58, 607; (Ic) (Miss) B. S.Khambata and A. Wassermann, Nature, 1936, 137, 496; 1937, 138, 368;A. Wassermann, J., 1936, 1028; G. A. Benford, (Miss) B. S. Khambata, andA. Wassermann, Nature, 1937,139,669; A. Wassermann, Trans. Faraday Xoc.,1938, 34, 128; H. Kaufmann and A. Wassermann, J., 1939, 870.9 See especially H. G. Grim, H. Ruf, and H. Wolf, 2. physikal. Chem., 1931,B, 13, 299; N. J. T. Pickles and C. N. Hinshelwood, J., 1936, 1353; R. A.Fairclough and C. N. Hinshelwood, J., 1937, 538, 1573. Other papers arethose of H. W. Thompson and E. E. Blandon, J., 1933, 1237 ; J. W. Baker andW. S. Nathan, J., 1935, 519; W. C. Daviesand12.G. Cox, J., 1937,614; V. A.Goldschmidt and N. K. Voroviev, J. Phys. Chem. Russia, 1939, 13,47386 GENERAL AND PHYSICAL CHEMISTRY.results were obtained by studying a reaction of somewhat similartype, the benzoylation of m-nitroaniline, in eight different solvents.1°It has already been mentioned that the dimerisation of the non-polarmolecule cyclopentadiene has the same A and E values in the gas andin 8 diverse solvents. The addition of cydopentadiene to the fairlypolar molecule benzoquinone has also been studied in 8 solvents,11and although there are some discrepancies between the values ofdifferent authors it is clear that a change of solvent leads to a vari-ation of rather less than 100-fold in the velocity, and that thisvariation involves both the factors A and E.The above data form a slender basis for generalisation, but(together with other experimental results of a less systematiccharacter) they suggest the following tentative conclusions. Bi-molecular reactions in which both the reactants and the products areof low polarity take place a t approximately the same rate in the gasphase as in solution, and their rate varies little with the nature of thesolvent. This constancy also applies to the values of the factors Aand E under different conditions.If, on the other hand, the reactioninvolves polar molecules, then attempts to study it in the gas phasereveal only a surface reaction, and change of solvent causes largevariations of rate, these variations appearing in both the factors Aand E.Apart from these generalisations, the absolute value of the factorA in solution is of theoretical interest, and a recent survey 12 showsthat for bimolecular reactions (excluding reactions between twoions) A has values ranging from about lo3 to 1011 l./g.-mol.see.-1.All intermediate values are found, and there appears to be nofoundation for the view once held l3 that bimolecular reactions insolution could be divided into two classes, “ normal ” reactions inwhich A loll, and “ slow ” reactions with A several powers of tenlower.We must now consider the theoretical interpretation of these facts.The collision theory of bimolecular reactions is too well known toneed any description here. The reaction velocity is written in theform k, = PZe-E”RT, where Z is the collision number and P atemperature-independent factor less than unity which allows forrestrictions as to the mutual orientation and internal phase of thereacting molecules.The experimental factor A is thus written as thelo N. J. T. Pickles and C. N. Hinshelwood, J., 1936, 1353.l1 A. Wassermann, Ber., 1933, 66, 1932; Trans. Faraday SOC., 1938, 34,128; (Miss) B. S. Khambata and A. Wassermann, Nature, 1936, 137, 496;R. A. Fairclough and C. N. Hinshelwood, J., 1938, 236.12 C. N. Hinshelwood and C. A. Winkler, J., 1936, 371.13 Cf. Ann. Reports, 1934, 31, 51BELL: ROLE OF TRE SOLVENT IN REACTION KINETICS. 87product of P and 2. The value of P could in principle be calculatedif sufficiently detailed information were available as to themechanism of the reaction and the interatomic forces involved.This is not possible in practice, but we can conclude from the experi-mental data for gas reactions that P is between about 0.03 and 1.0 forreactions between simple molecules, whereas for more complexmolecules it may be as low as lo4.The transition-state theory of reaction velocity has been previouslyfully discussed in these Reports and e1~ewhere.l~ The reactionvelocity is written in the form k, = K(kT/h)K where K is.a trans-mission coefficient, and K represents a constant for the equilibriumbetween the reacting molecules and the transition state (or " criticalcomplex '7. K can be written as the product of e-E'nT and aproduct of partition functions F which (like K ) can in principle beevaluated if enough is known about the detailed course of thereaction.The necessary information is equivalent to that requiredin order to calculate P in the collision theory.In spite of their failure to give an absolute prediction of reactionvelocities in gases, both theories are useful in indicating the possibleways in which the solvent can affect the velocities. The interactionbetween the solvent and the reacting system can be of varyingdegrees of intimacy, ranging from a purely physical interference to anactual chemical combination with reactants or products. We shallfirst consider the case in which the nature of the interaction betweenthe solvent and the reactants is not appreciably modified when thereactants collide to form the " critical complex." This condition islikely to apply when both the reactants and the products are mole-cules of low polarity.According to the collision theory there arethree factors, E, P, and 2, which may be modified by the presence o fsolvent. If the activation energy E depends on short-range forcesrather than on Coulomb forces it is likely to be little affected by thepresence of solvent, and this conclusion is borne out by the experi-mental results. The steric factor P is also likely to be unaffected,since it depends on the mutual orientation of the reacting molecules.The collision number in solution has been the subject of muchdiscussion. It will depend on the translational energies and dia-meters of the solute molecules and upon the space in which they arefree to move.While the first two quantities have the same values asin the gas, the free volume will be decreased by the presence of thesolvent, with a consequent increase in collision number. It is verydifficult to make any quantitative estimate of this free space factor,l4 Ann. Reports, 1935, 33, 94 ; 1936, 34, 86 ; cf. the discussions indicated infootnote, p. 8388 GENERAL AND PHYSICAL CHEMISTRY.but a consideration of various models of the liquid state leads to theconclusion that it should certainly be less than 10, and is probablyless than 4.15This conclusion is in agreement with the inadequate experimentalevidence mentioned above, and it also receives support from measure-ments on the rate of change of pars- into ortho-hydrogen, catalysedby paramagnetic molecules.16 This change takes place a t ameasurable rate, since only a small fraction of the collisions betweenpara-hydrogen and the paramagnetic molecule are effective, but thisfraction does not depend on the temperature (i.e., does not involvean energy of activation) and would be expected theoretically to beunaffected by the presence of solvent.It is found experimentally 1 7that the conversion by nitric oxide and oxygen takes place 1.2-2times as fast in aqueous solution as in the gas phase, which providesgood evidence that the collision numbers in the two phases are aboutin the same ratio. This conclusion is further supported by a generalsurvey of the values of A in solution : - there are a large number ofcases in which A is approximately equal to 2 (calculated for a gasreaction), and very few in which A exceeds 2 by more than a factorof 10."In the formulation of the transition-state theory the effect of thesolvent appears as its effect on the equilibrium constant K , and maybe split into two factors : AE, the change in activation energy(altering the velocity by a factor e-AEIRT) ; and AX, the change in theentropy of activation, which appears in the product of partitionfunctions and alters the velocity by a factor e+ASIR.The wholesolvent effect may be conveniently expressed in terms of activitycoefficients : thus for a bimolecular reaction in solution betweenmolecules A and B we can write k2 = K(kT/h)K = (fafB/f&?2,where X is the critical complex and the index o refers to the gasl5 Cf., e.g., M.Jowett, Phil. Mag., 1929, 8, 1059; E. Rabinowitch, Trans.Faraday SOC., 1937, 33, 1224; R. H. Fowler and N. B. Slater, ibid., 1938, 34,91 ; R. P. Bell, ibid., 1939,35,324. Some of the difficulties concerned with thefree space factor depend on the different sizes of the solute and the solventmolecules, a, problem which also arises in connection with the positionalentropy of binary liquid mixtures. The latter problem has recently beentreated with some success; cf. R. H. Fowler and G. 8. Rushbrooke, Trans.Faraday SOC., 1937, 33, 1272; T. S. Chang, Proc. Camb. Phil. Soc., 1939, 35,265.l6 Cf. Ann. Reports, 1933, 30, 41.1' L. Farkas and H. Sachsse, 2.physikal. Chesn., 1933, B, 23, 1 ; L. Parkasand U. Garbatski, Trans. Faraday SOC., 1939,35,263.* The different conclusion reached by M. G. Evans and M. Polanyi (Trans.Faraday SOC., 1935, 31, 875) is due to a confusion of units : their calculated 2values refer to a pressure of 1 atm., whereas the observed A values refer to aconcentration of 1 mol. /1BELL: R ~ L E OF THE SOLVENT IN REACTION KINETICS. 89phase, in which all the activity coefficients are by definition unity.This equation is identical in form with the one proposed by Bronstedto describe salt effects in ionic reactions,l* though Bronsted himselfdid not consider that the activity factor would apply to the effect ofthe solvent itself. In dealing with the effect of electrolyte con-centration on an ionic reaction, the activity coefficient of the criticalcomplex can be predicted in terms of its charge, but in the moregeneral problem of solvent effects and uncharged reactants no suchprediction is possible.If an idealised model of the liquid state istaken, then the treatment is of course exactly analogous to that ofthe collision theory outlined above, and will give the same results.There is, however, another method of approach, namely, to treat thecritical complex as an ordinary molecule, and to apply empiricalgeneral laws about activity coefficients in solution derived fromexperimental data on vapour pressures and gas solubilibies. This hasbeen done by M. G. Evans and M. Polanyi l9 and by W. F. K. Wynne-Jones and H.Eyring,20 who conclude that for reactions betweenmolecules of low polarity the collision factor should be 100-1000times as great as in the gas phase, a result which conflicts with thepredictions of the collision theory and with the experimental data.However, it has been recently shown that the method employed bythese authors involves an over-simplification, and that when dueregard is taken of the relations known t o exist between the heats andentropies of solution,22 the transition state theory predicts thatA(so1ution) /A(gas) 2 2-3, in excellent agreement with the collisiontheory and with experiment.The above conclusions refer to the total number of collisionsbetween solute molecules, and the viscosity of the solvent has not sofar entered into consideration.On the other hand, the viscosityplays a decisive part in determining the grouping of these collisions.This may be seen by considering very viscous systems : two solutemolecules originally far apart will take a long time to diffuse towardseach other, but when they have met they will be surrounded by A“ cage” of solvent molecules and will undergo a large number ofrepeated collisions before parting company. Such a group ofrepeated collisions is conveniently termed an encounter. In asufficiently dilute system (i.e., a gas) 2~ repeated collision is a very rarel8 Cf. Ann. Reports, 1927, 24, 332 ; 1934, 31, 67.l9 Trans. Faradmy SOC., 1935, 31, 875.*o J . Chem. Physics, 1935, 3, 492.21 R. P. Bell, Trans. Faraday SOC., 1939, 35, 384.22 MI G.Evans and M.Polanyi, Trans. Farachy SOC., 1936,32,1333; J. A. V.Butler, ibid., 1937, 33, 171, 229; It. P. Bell, ibid., p. 496; I. M. Barclay andJ. A. V. Butler, ibid., 1938, 34, 144590 GENERAL AND PHYSICAL CHEMISTRY.event, and the collision number and the encounter number are almostidentical. As the system becomes more viscous the encounternumber decreases, but there is a corresponding increase in thenumber of collisions in each encounter and the total collision numberremains substantially the same. The bearing of this aspect ofcollision processes on reaction kinetics has been recently consideredby a number of authors,23 some of whom have used ingeniousmechanical models to illustrate the problem. In a process where alarge proportion of the collisions are effective? the rate will bedetermined by the encounter number rather than the collisionnumber, since only the first few collisions in each encounter will be ofimportance.This is true of the coagulation of colloids 24 and thequenching of fluorescence by solute both of which aregoverned by the. viscosity of the medium. In these cases theequiIibrium molecular distribution is much disturbed by the pro-cesses taking place, thus making it impossible to apply either thesimple collision theory or the transition-state theory, both of whichassume that the distribution is governed by the laws applying to anequilibrium state. On the other hand, if only a very small propor-tion of the collisions are effective? it is clearly a matter of indifferencewhether they occur in large or in small groups, the rate dependingonly on the total number of collisions.This applies to the majorityof chemical reactions in solution : for instance, it can be roughlyestimated that for liquids of ordinary viscosity the grouping ofcollisions will only be important if E < 2 kg.-cals./mo1.,26 while ifE = 20 kg.-cals./mol. the viscosity has to approach that of thevitreous state .27In many cases the interaction between the solvent and the reactingsystem will be a more intimate one than we have so far supposed, andthis will be especially so for reactions involving ions or molecules ofhigh polarity. The factor affecting the reaction velocity will be thechange in interaction when the reactants A and B pass into thecritical complex X.Thus in a reaction between two ions A+ and B-23 M. Leontovitch, 2. Physik, 1928, 50, 58; J. Weiss, Naturwiss., 1935, 23,229; E. Rabinowitch and W. C. Wood, Trans. Faraday SOC., 1936, 32, 1381 ;B. I. Svesnikov, Compt. rend. Acad. Sci. U.R.S.S., 1936, 3, 61 ; E. Rabino-witch, Trans. Paraday Soc., 1937, 33, 1225; R. A. Fairclough and C. N.Hinslielwood, J . , 1939, 593.24 I. Smoluchowski, Physikal. Z., 1916, 17, 594; 2. physikal. Chem., 1917,92, 129.26 S. I. Wawilow, 2. Physik, 1929,524 665; J. M. Franck and S. I. Wawilow,ibid., 1931, 69, 100; B. I. Svesnikov, Acta Physicochim. U.R.S.S., 1935, 3,257; 1936, 4, 453; 1937, 7, 755; E. J. Bowen, Trans. Faraday SOC., 1939, 35,15. 26 E. Rabinowitch, ibid., 1937, 33, 1228.27 M.G. Evans and M. Polanyi, ibicl., 1936, 32, 1353BELL : RdLE OF TRE SOLVENT I N REACTION KINETICS. 91the critical complex will have a zero net charge, and its formationfrom A+ and B- will involve a decrease in the orientation of the sol-vent molecules attached to the ions. This de-solvation will clearlycontribute to the activation energy, causing it to differ from the valuein the gas phase. Moreover, it will also affect the factor A , as maybe seen either from the transition-state theory or from the collisiontheory. According to the former theory the process of de-solvationinvolves a decrease in order and hence an increase in entropy, whichappears as an increase in the factor A.28 From a kinetic point ofview the co-operation of the solvent molecules causes the activationenergy to be distributed among a larger number of degrees offreedom (ke., the bonds holding the solvent molecules to the ions),thus increasing the fraction of collisions possessing the necessaryenergy by a factor which is roughly independent of temperature.29In the same way it can be predicted that in a reaction between ionsof like charge the effect of the solvent will be to produce a decrease inthe value of A .The same qualitative conclusions have been reachedby a purely electrostatic treatment, in which the solvent is treated asa uniform diele~tric.~~ The physical basis of this treatment isessentially the same as that outlined above, since the calculatedeffect involves the temperature coefficient of the dielectric constant,and this in turn depends on the orientation of the solventdipoles.In the case of reactions between ions it is not possible to make anexperimental comparison between the velocities in solution and in thegas phase, and there are not even data to illustrate the effect ofchange of solvent.However, the experimental values of A inaqueous solution can be compared with the theoretical collisionnumbers, and it is, in fact, found that reactions between ions of likecharge give P factors as low as lo-* (for multiply charged ions),whereas for reactions between oppositely charged ions P can becomeas great as lofs.Even in the absence of a net charge on the reactants there may bea large change of polarity during the reaction and hence a change inthe extent of solvent orientation.Considerations of this kind werefirst applied to reactions of the type NR, + RI -+ [NR,]+I-, wherethe critical complex may well be much more polar than the initialstate, and hence more solvated. The necessity for this solvent28 W. F. K. Wynne-Jones and H. Eyring, ref. (20).29 Cf. C. N. Hinshelwood, “Kinetics of Chemical Change in GaseousSystems,” p. 24 (Oxford, 1933) ; R. H. Fowler, “ Statist.ica1 Mechanics,” p. 707(Cambridge, 1936).30 E. A. Moelwyn-Hughes, Proc. Roy. h’oc., 1936, A , 155, 308; V. K. LaMor,J . Pranklin Inst., 1938, 225, 70092 GENERAL AND PHYSICAL CHEMISTRY.orientation appears as a small P factor (or a negative entropy ofa,ctivation) and should lead to low A values varying with the solvent.The chief experimental evidence on this type of reaction has beenoutlined a t the beginning of this Report, and although no directcomparison with the gas phase can be made, the A and E values varyfrom one solvent to another and the A values are lo4-lo9 timessmaller than the calculated gas values.The part played by solva-tion is further illustrated by the auto-catalytic effect exerted by thepolar reaction products when the reaction takes place in a non-polarsolvent .31The same kind of behaviour is found in reactions between aminesand acyl chlorides : on the other hand, the formally similar reactionEt,S + EtBr -+ [Et,S]+Br- has a P factor near to unity 32 (indicat-ing a critical complex of low polarity), so that it is clearly dangerousto attempt a priori conclusions as to the nature of the critical com-plex.It may be noted that the absence of any measurable homo-geneous reaction for the Menschutkin reaction in the gas phase * wasoriginally taken to indicate a low A value even in the absence ofsolvent. However, there is no experimental evidence as to thevalue of the activation energy in the gas phase, and the low velocitymay equally well result from a normal A value and a high energy ofactivation. Approximate calculations show that the solvation of apolar critical complex can materially reduce the activation energy,=and even the proximity of a surface may lower the necessary energyby several thousand calories per mol., and thus favour a wall reactionrather than a homogeneous one.=A large number of the reactions of organic chemistry are nowbelieved to take place by an ionic mechanism,35 so that when boththe reactants are uncharged molecules the formation of the transitionstate will usually involve an increase of polarity. According to theabove arguments, this will lead to a low collision factor in solution,which is found to be the case for most reactions of this type. It isnoteworthy that the reaction between lead tetra-acetate and ethyleneglycol has recently been shown to have a collision factor in acetic acidsolution which is roughly equal to the collision number calculated for31 E.A. Moelwyn-Hughes and C. N. Hinshelwood, J., 1932, 231 ; N. J. T.Pickles and C. N.Hinshelwood, J., 1936, 1353 ; G. E. Edwards, Trans. FuradaySOC., 1937, 33, 295 ; V. A. Holzschmidt and I. V. Potapov, Acta Physicochim.U.R.S.S., 1937, '7, 778.32 R. F. Corran, Trans. Faraday SOC., 1927, 23, 605.33 R. A. Ogg and M. Polanyi, Trans. Faraday SOC., 1935, 31, 605; A. G.34 R. P. Bell and R. le G. Burnett, Trans. Faraday SOC., 1939, 35,474.35 Cf. H. B. Watson, Arm. Reports, 1938, 35, 208.* LOC. cit., ref. (Sa).Evans and 35. G. Evans, ibid., p. 86BELL: RGLE OF THE SOLVENT IN REACTION KINETICS. 93the gas phase : 36 the mechanism of this reaction probably involvesradicals rather than ions.37On the other hand, for a reaction between an ion and a neutralmolecule the displacement of charge due to an ionic mechanism willhave only a small effect on the solvent orientation.This view issupported by the large number of reactions of this type in which A isapproximately equal to the gas collision number.The intervention of the solvent has so far been supposed to takeplace in an equilibrium manner ; ie., we have assumed that solvationequilibria are completely set up throughout and that the equilibriumenergy distribution is not disturbed by the reaction. (This assump-tion is involved in both the transition-state theory and the simplecollision theory.) It has been suggested that in reactions of theMenschutkin type the solvent may take part in a rate-determiningstep such as the removal of energy from the nascent un-solvatedproduct, thus stabilising it and preventing the reverse reaction.38This would lead to collision factors varying from one solvent toanother, and in general will account for many of the phenomenaassociated with this type of reaction.At first sight the hypothesisseems improbable owing to the high concentration of solvent mole-cules, but it must be remembered that the transfer of energy betweendifferent degrees of freedom is often a specific and very inefficientprocess.39 I n the case of reversible reactions it should be possible todecide between the two types of explanation. The position ofequilibrium cannot be affected by the rate of energy transfer, so thatif this process is rate-determining in the bimolecular reaction itseffect will also appear in the reverse unimolecular reaction. In thefew cases where data are available 40 the A factor of the unimolecularreaction appears to have a normal value, thus favouring the equi-librium explanation of the solvent effect in the bimolecular reaction.More experimental work on this point is to be desired.R. P. B.36 R. P. Bell, J. G. R. Sturrock, and R. L. St.D. Whitehead, J., 1940, 82.37 R. Criegee, L. Kraft, and B. Rank, Annalen, 1933, 507, 159; W. A.38 C. N. Hinshelwood, Trans. Furaduy Soc., 1936, 32, 970 ; G. E. Edwards,39 A. Eucken and H. Jaacks, 2. physikal. Chemn.., 1936, By 30, 85.40 H. Essex and 0. Gelormini, J . Amer. Chern. SOC., 1926, 48, 882; W. C .Davies and R. G. Cox, J., 1937, 614; J. K. Sirkin and M. A. Gubareva,J . Phys. Chem. Russia, 1938,11, 285.Waters, J., 1939, 1805.ibid., 1937, 33, 29594 GENERAL AJSfD PHYSICAL (IHEMISTBY.5.SURFACE CHEMISTRY.Physical Properties of Monolayers.Recently, research on monolayers has expanded to such anextent that any paper which summarises all their physical propertiesand correlates these properties directly to their three-dimensionalcounterparts in a concise and rigorously defined manner does agreat service to a student in this field. Such a paper has beenpublished by D. G. Dervichian,l and since it summarises our entireknowledge, with many new aspects, of the physical properties offilms in general, it is quoted in some detail.The method employed was to study the pressure, compressibility,viscosity, and surface potential of the same film over a wide variationin area per molecule, vix., from 100,000 A . ~ to 18.5 A . ~ . This necessit-ated measuring extremely low surface pressures of the order of0-001 dyne/cm. A simple apparatus for this purpose was con-structed by J. Guastalla,2 who magnified the movement of a greasedsilk thread on the surface of the water. This thread could besubjected to different strains by a suitably placed torsion wire.Calibration can be made geometrically and by known two-dimen-sional transition pressures, vapour-liquid. (Guastalla also usesthe damping of a surface pendulum to measure very low pressureswithout any optical magnification.) Two methods were employedfor measuring the surface viscosity :S. E. Bressler andD. L. Talmud first studied the fall of pressure with time for differentfilms, when these are caused to flow through a canal, and noticeddiscontinuities occurring at certain pressures.have adapted to the two-dimensionalsystem the ordinary measurements of viscosity by this method ofcapillary flow.The very small pressure drop through the narrowcanal was kept constant and well defined, the flow was neverturbulent, and a systematic study was made, the different factorsbeing varied. They concluded that the flow per second is pro-portional to the pressure drop and inversely proportional to thelength of the slit; but they pointed out that there is no simplelaw analogous t o Poiseuille’s law in respect to the width of the slit.They showed that there are two phenomena which are super-1. The two-dimensional capillaryjlow method.Dervichian and M.JolyJ. Physical Chern., 1939,7,931 (cf. Harkins and E. Boyd, J. Chern. Physics,Compt. rend., 1939,189, 241 ; 1938, 206, 993; 1939, 208, 973.LOG. cit., 1939.Phy&kal. 2;. Sovietunion, 1933, 4, 564.Cmpt. rend., 1937, 204, 1318.1940, 8, 129)SCHULMAN SURFACE CHEMTSTRY. 95imposed : two-dimensional viscosity of the film and entrainment ofthe substrate. A study by R. M6rigoux proves that there is afriction without slip between film and substrate, and J. H. Schulmanand T. Teorell7 have shown that, in fact, the film does carry waterwith it while flowing. The result is that the true viscosity of thefilm is gradually masked as the slit becomes wider.8R. J. Myers and W. D. Harkins 9 have used the same method and,assuming a two-dimensional Poiseuille equation with the thirdpower (a3) of the width of the slit, have published quantitative datafor the surface viscosity.Later, Harkins and J. G. Kirkwood 10proposed a new formula for the calculation of the viscosity, justifyingthe law in d3. Dervichian and Joly l1 point out that this calculationis not generally justsed : the law in d3 being a limiting law only forslits with widths smaller than 0.5 mm., at greater dimensions itgradually changes to d2 and finally becomes linear towards 5 mm.Dervichian and Joly l1 have improved upon a theory first given byTalmud and Bre~sler.~ This gives a better quantitative accord withthe experimental data even for wide slits. Harkins and Kirkwood,10however, disagree with some of this work.A detailed review of the different theories and an empiricalmethod for the calculation of the surface viscosity has been givenby J01y.l~Using a new device which enables the pressures at the entranceand exit of the slit to be maintained very constant and to producea flow under a very weak pressure gradient, Dervichian and Joly 13have been able to study with precision the variation of viscositywith the pressure for different fluid monolayers.Points of dis-continuity have been thus detected at definite molecular areas (seeDervichian 1).2. The oscillation damping method. This is a two-dimensionalapplication of the Coulomb method, the damping of oscillationsbeing measured by a viscous medium. A disc or a cylinder issuspended by a vertical torsion wire and brought into contact withthe surface.The system oscillates as a torsion pendulum. Theviscosity of the film is determined by the difference in the damping(logarithmic decrement of the successive oscillations produced bythe clean surface and the surface covered by the film). This methodCompt. rend., 1936, 202, 2049; 203, 848.Trans. Faraday SOC., 1938, 34, 1337.8 See also Joly, J . Physique, 1937, 8, 471.J . Chem. Physics, 1937, 5, 603; Nature, 1936, 140, 465.10 J . Chem. Physics, 1938, 6, 153; Nature, 1938, 141, 38.11 J . Chem. Physics, 1938, 6, 226; Nature, 1938, 141, 975.12 J . Physique, 1938, 9, 345; see also J. J . Hermans, Physica, 1939, 6, 313.l3 Compt. rend., 1938,806,326 ; 1939,208,1488 ; J.Physique, 1939,10,37596 GENERAL AND PHYSICAL CHJiXNISTRY.has been used by I. Langmuir and V. J. Scliaefer l4 and by Myersand Harkins.9The method is too insensitive to give very accurate measurementson fluid films, but on the other hand it is of great use with veryviscous or plastic monolayers; Langmuir and Schaefer l5 haveemployed it for the study of protein monolayers. L. Fourt andW. D. Harkins l6 have investigated changes of state in condensedfilms of long-chain alcohols. In the latter case and in some caseswith proteins, the measurements do not give the viscosity butrather the plasticity or rigidity of the film. In fact, although witha true liquid film the viscosity is independent of the amplitude, thisis not the case with solid or gel films.A plot of the logarithm ofthe amplitude against the number of swings gives, with fluid films,a straight line slope, the slope of which is a measure of the viscosity ;with non-fluid films, the line is curved.In order to reduce the damping due to the substrate to a minimumand increase the sensitivity of this method, Joly l7 has recently useda very narrow flat ring of mica bound to a torsion wire, but floatingon the surface. This is surrounded by a fixed and larger ring alsofloating on the water. The distance between the two concentricrings is variable according to the viscosity of the film which isspread in the free space. A special device enables the compressionof the film and measurement of the surface pressure to be under-taken by the ordinary methods.With this apparatus, the viscosityof protein films has been studied in the region where they are stillfluid, and the ageing and the existence of two types of these filmshave been noticed. l8Thermodynamical DeJinition of Transformations of DiflerentOrder.-The points of transformations of different orders have beenconsidered by P. Ehrenfest l9 as corresponding to discontinuities ofthe derivatives of different order of a thermodynamical function.has introduced in thedefinition of this function a term corresponding to the surface energy.If y is the surface tension of the surface covered by a film and yothat of the clean surface, the work done by an infinitesimal dis-placement of the barrier which changes each of the two areas bydA and - dA respectively is dwS = ( y - yo)dA.Introducing thesurface pressure x = yo - y, we have dwS = - x . dA. If XFor the surface phenomena Dervichianl4 J . Amer. Chevn. Soc., 1937, 59, 2400; Langmuir, Science, 1936, 34, 379.l6 Chem. Reviews, 1939, 24, 181.l6 J. Ph.ysica1 Chem., 1938, 42, 897..l7 J . Chim. physique, 1939, 38, 285.l8 LOC. cit.; Compt. rend., 1939, 208, 975.l9 Proc. K . Akad. Wetensch. Amsterdam, 1933, 38, 115SCHULMAN S CJRFACE CHEMISTRY. 9 7represents the t,otal entropy (surface and bulk) of the systeni, thevariation of the total energy is defined by dE = T . dS - P . du -i5 . dA. When T, P, and x are considered as independent variables,one can adopt, as thermodynamical function, the thermodynamicpotential G of Gibbs, in which one can introduce a term correspond-ing to the surface energy analogous to the term :PY : G = F +PV + xA, where F is the free energy F = E - TX, which givesG = E - - T T X + P V + x A and d G = - B .d T + V.dp+Adx,which enables successive partial derivatives to be calculated, vix.,An ordinary change of state will be called a transformation of thefirst order, since it is characterised by a discontinuity in the area ,4and consequently corresponds to a discontinuity in the first deriv-ative of G. Likewise, a transformation in which A does not undergoany sudden variation, but in which the compressibilityshows a discontinuity, will be a transformstion of the secondorder, etc.This leads to one of the most important new aspects of Der-vichian's paper,l vix., that areas corresponding to ordinary phasechanges are found as points of discontinuity of higher order in thosephases which exist at higher temperatures.Thus the area 20.5 A . ~ ,which in three dimensions exists as the B-crystal form of a fattyacid, is the sublimation point in the solid state for two-dimensionalfilms. It is found as a point of second order in the mesomorphousstate as shown by discontinuities in the compressibility-, viscosity-,and electric moment-area curves, when this specific area is reached.The table on p. 101 shows a whole series of transformation points inthe various phases, some of which have known three-dimensionalanalogies, a t given areas. This very significant analogy seems tohave been neglected by previous workers in' force-area diagrams andis extremely helpful in explaining and anticipating the various dis-continuities, on a physical basis.In the figure a combined two-dimensional phase diagram is givenfor long-chain hydrocarbon compounds for the case where thecritical temperature of crystallisation is greater than the criticaltemperature of liquefaction (except for curve VII, where the inverseholds) ; the areas given all have significant three-dimensionalanalogies irrespective of the substance, but respective to the hydro-carbon chain, t'hese appear as discontinuities in phases existing athigher temperatures. Films of the following substances give thetypical force-area curves (room temperature) : curve VI, tri-caproin ; curve VII, oleic acid ; curve V, ethyl palmitate ; curve IV,K = (l/A)(dA/dx)REP.-vOL.XxXvI. 98 GENERAL AND PHYSICAL CHEMISTRY.myristic acid ; curve 111, palmitic acid (25') ; curve 11, stearic acid ;curve I, eicosyl alcohol.Substances giving typical gaseousfilms with no condensation to the liquid state are the short-chainglycerides, which Guastalla has measured up to very large areas,Gaseous state (curve VI).showing that they obey the gas law TCA = RT. He has used thistechnique to determine the molecular weight of proteins, by measur-ing the X-A curves at pressures of 0.001 dyne/cm., where theproteins exist as a two-dimensional vapour. Guastalla found 110evidence for association as measured by S. A. Moss and E. K.Rideal,20 who obtained R/2 for the gas constant; the latter used a2o J., 1933, 1525SCHULMAN : SURFACE CHEMISTRY.99metal trough for fatty acids a t large areas. It is noteworthy thata higher-order transformation point, obtained by measuring theviscosity or surface potential of the gaseous films, appears at anarea of 3 8 ~ . ~ per hydrocarbon (for triglycerides at 115a.). Thesignificance of the area which Dervichianl relates t o the triplepoint M has no known three-dimensional counterpart ; it is probablyrelated to some structure in liquids.The triple point. This refers to the junction of the mesomorphous,liquid, and gaseous states which occurs at 38-39 A . ~ per straighthydrocarbon chain. This point reappears in the higher-trans-formation points in the viscosity, surface potential, and com-pressibility curves for the liquid or gaseous state at this area perhydrocarbon chain.A good example of this is found in theviscosity curve of triolein a t 115 A . ~ , which is given as curve VII inthe phase diagram.The liquid state. The curve MP of the phase diagram typifies theliquid state wit,h no transition to a solid state (oleic acid). Der-vichian draws a, very interesting conclusion from the similarity of theinterfacial tension at the point P to that a t the water-oil interfaceof an oil drop, vix., that the structure of the molecules at P isidentical with the structure of the surface of a liquid; i.e., the pointP represents a drop one monolayer thick. On expansion of thefilm from point P to M y the number of molecules decreases fromthat at the surface of a liquid t o that at the interior of the liquid.The proof that the point M represents the concentration of themolecules in the interior of a liquid is given by the fact that themolecular volume of the molecule to the power of 2/3 is equal t o thearea for any given substance at that point. Dervichian showsthat V2’3 equals the area occupied by the molecule at the point Mfor a whole series of substances, thus re-establishing the significanceattached to these correlations by earlier workers in this field.It isastonishing that the presence of the water has so little effect on themolecular forces involved in establishing the mean moleculardistances either on the water surface or in the interior of the liquid.It has been shown by F.Sebba and H. V. A. BriscoeY21 dealing withthe ageing of films at the air-water interface, that water does peptisethe polar groups in time and expands the film markedly. Thisis especially marked with long-chain alcohols and acids.There has been muchcontroversy as to whether tlhis transition region is electricallyhomogeneous (for the case of myristic acid) or no. Dervichian,by a self-recording device, definitely establishes that it is electricallyinhomogeneous, and suggests that this is due to islands of the solidIl’rasasition : liquid+nesomorphous states.21 J., l O W , 128100 GENERAL AN0 PHYSICAL CHEMISTRY.state floating in the liquid state. The packing of the molecules, andconsequently their number per unit area, being markedly differentin the two states, would cause large surface-potential fluctuations,even if the apparent dipole moment of the molecules in the twostates were similar.Secondly, as to whether this transition is flator gives a horizontal isotherm, Dervichian gives examples showingthat this transition, in equilibrium, over a considerable change inarea per molecule is flat, as the theory demands, and is similar tothe gas-liquid transition.Solid states. The solid state has three well-defined areas forhydrocarbon chain compounds which have significance in threedimensions. The sublimation point, where the solid is in equi-librium with its vapour pressure, is 20.5 A . ~ or a multiple of thisnumber for the glycerides. This area corresponds in threedimensions to the B-crystalline form of the fatty acids or glycerides,and appea,rs as a second-order transformation point in the meso-morphous state.There is a second transformation point in the solid state a t19.5 A.Z, which corresponds to the A-crystalline form. The filmbreaks a t 1 8 - 5 ~ .~ , which is the cross-sectional area of the unitcrystal, showing that on compression of the solid state a tilting ofthe chains takes place until they are in the vertical position.The mesomorphous state corresponding toa liquid crystal extends up to 2 3 - 5 ~ . ~ , which in three dimensionscorresponds to the C-crystalline form of the fatty acids andglycerides. There is a second-order transformation point at 22 A .~ :which has a t present no three-dimensional counterpart. There isan expansion of the mesomorphous state from 23.5 to 27 A. atconstant pressure before true two-dimensional melting takes placeand the liquid state commences at point M on the diagram. Thisexpansion is what Labrouste first observed, and is really an expandedmesomorphous state and is especially noticeable in trimyristin.This point, 27 A . ~ , appears beautifully as a higher-order trans-formation in the viscosity curve of a palmitic acid film whichexists over the expanded mesomorphous state at 25" and also as ahigher-order transformation point in the gaseous state. .Two-dimensional and three-dimensional melting points. Dervichiandefines the two-dimensional melting point as the temperature atwhich the liquid state appears a t the end of the Labrouste trans-formation. This temperature in many cases (such as with cetylalcohol) agrees with the known three-dimensional melting point ;but with the glycerides and acids the two-dimensional is much lowerthan the normal melting point.In order to explain this difference,Dervichian finds that the glycerides possess a vitreous form whichMesomorphow stateSCHULMAN : SURFACE CHEMISTRY. 101melts a t the two-dimensional m. p. Them. p. of this form agreeswith considerable correlation with the film m. p. for a whole range ofsubstances (thus the vitreous form is more stable under monolayerthan under ordinary conditions). He suggests that for the acidsthe vitreous form only exists in two dimensions, although there isdistinct evidence for a vitreous form for palmitic acid. Oneinteresting point is that the vitreous form of the glycerides spreadsspontaneously on to the water surface from the solid, whereas thecrystalline form spreads extremely slowly.Labrouste showed that the triglyceride films compressed to thesolid and removed from the surface melted a t the vitreous formtemperature, and that these solidified films after a while gave thethree-dimensional crystalline m.p.The following two tables are taken from Dervichian's paper andsummarise all the physical characteristic areas of films as deter-mined by force-area, viscosity, compressibility, and surface potentialmeasurements with their three-dimensional correlations.Characteristic three -dimensional areas, in A .~ .18-5, cross section crystalunit .....................19.5, A-crystal form ......20.5, B-crystal form ......22, unknown form .........23.5, crystal form C ......27-30, area of moleculesurface of liquid .........38, triple point ............V/72/3, vol. of molecule, in-t,erior of liquid .........Meso- ExpandedSolid morphous mesomor- Liquid Gaseousfilms. films. phous films. films. films.18.6 18.5 18.5 I -19-5 19.5 19.520.5 30.6 90.6 -- -6) <> 22 - -- 23.5 23.5 - -- -i d -Two-dimensional Three-dimensional m. p.'s.m. p. Vitreous state. Crystalline state.- Tristearin ............... 5 5 O 55"Tripalmit in ............ 45 46Trimyristin ............29 32Trilaurin ............... 2-14 14 -Cetyl alcohol ......... 50 - 49-5O--Surface Potentiak.Gatty 22 raised in the October 1939 meeting of the Faraday Societyon the Electrical Double Layer 23 a very interesting suggestion asto the meaning of " surface potentials " a t the air-water interface,quite contrary to the previously accepted view that a film oforiented molecules acted as an electrical condenser. Dean,Gatty, and Rideal 24 showed that under thermodynamical equi-librium conditions the spreading of a monolayer a t an interphase22 See also Trans. Paraday SOC., 1937, 33, 1087; 1940, 36, 173.23 Ibid., 1940, 36, 1. 24 Ibid., p. 161102 GENERAL AND PHYSICAL CHEMISTRY.plane between two phases, insoluble in both phases, and permeableto at least one ionic species, whilst producing a transitory surge ofpotential, cannot alter the interfacial potential. If diffusion istaking place between the two phases, the diffusion potential canonly be affected if the monolayer sufficiently affects the resistanceto the passage of a t least one ionic species.Gatty showed that by passing a saturation current (ca.8 x 10-l1amp.) through a stearic acid film a t an air-water interface for morethan 33 hours, no change in the surface potential of the film tookplace (to within 1 mv.); furthermore, films of various substanceshave been left for periods of a week, showing, likewise, no change insurface potential.On calculation, this shows that the capacity of the monolayermust be greater than 90 p F.cm.-2, so that if the film correspondsto a parallel plate condenser with a dielectric of 1, a separation of(2.1 A. would be necessary. A capacity of this magnitude would beimpossible for a film of stearic acid on a strong ionic solution.Alternatively, this result might show that the film has a low resistanceof the order of lG9 ohms/cm.2 at the most. On this basis, areasonable capacity being assumed for a parallel plate condenser, thesurface potential should have fallen l/eth of its value in 14 hours( E = Eoe-t’m), but since no change occurs over periods at least tentimes longer, the low resistance alternative being also excluded, allconceptions of the film’s acting as a condenser must be ruled out.Gatty further shows, by enclosing an area of the film and theair above it by a glass tube, letting the air become saturated withwater vapour, and obtaining likewise no change in the surfacepotential under these conditions, that the potential cannot be dueto diffusion of charged water ions.Gatty therefore offers the following explanation for the surfacepotential.Upon deposition of a monolayer on the surface of thewater, a diffuse layer can be immediately built up in the aqueousphase, but no such diffuse layer can be built up in the air phaseto neutralise the potential difference due t o the film, since ions inthe immediate vicinity of the film in the air would be sucked intothe aqueous solution. Gatty calculates this from consideration ofthe mirror-image forces that these ions would create in the aqueousphase-forces which on purely electrostatic grounds would suck theions into the solution.Gatty, Dean, and Dean23 show that, by replacing the air phaseby an oil in which ions can be dissolved such as amyl acetate or octylalcohol, a surface potential can be obtained by spreading films atthe interface, which decays with time to an equilibrium zero value,as would be expected from the general theorySCHULMAN : SURFACE CHEMISTRY.103Dean 23 shows that the electrical resistances of films a t an inter-face are negligible compared t)o those of the two bulk phases.Further, a stable potential can be obtained if the interface resists thcdiffusion of one ionic species (Donnan potential) as with certain dyes.A poorly oil-soluble electrolyte cannot diffuse rapidly into the oilphase and so leaves " negligible diffusion " potential in the aqueousphase, but after diffusing through the region of Donnan potentialsit is able to set up a diffusion potential in the oil phase in regionswhere its concentration is not less than that of the oil ions them-selves.Dean justifies this experimentally by controlling theseparation of two protein-covered water drops in an oil-phasemedium.These experiments appear to rule out the theories expressed by 0.Bauer and G. Ehrensviird and L. G. Sill& 25 on adsorption potentialsa t oil-water interfaces, although these workers are right in expressingthe view that the potential gradient is located very close to theinterface.Multila yers .General Properties.-The most recent development in the studyof built-up films is the investigation of compounds other than thoseof the fatty acids, which have been used exclusively by theAmerican scientists, who discovered this very interesting propertyof monolayers.26Owing to the various ways in which a film can be deposited from anaqueous solution on a solid, considerable difficulty has arisen as toa general nomenclature for different types of built-up multilayers.There are three different types of deposition, which must in noway be confused with the type of the ultimate structure of themultilayer, since the method of deposition has no bearing on thestructure of the multilayer which is entirely dependent on thechemical properties of the sub~tance.~7It is termed an X-deposition when the film comes on onlyon the downward movement of the slide through the watersurface, a Y-deposition when the film is deposited on both thedownward and the upward movement, and a 2-deposition when26 Nature, 1938, 141, 789.26 I?.M . Blodgett, J . Amer. Chem. Soc., 1935, 57, 1007; I. Langmuir, J .Pranlclin Inst., 1934, 218, 143; F. 31. Blodgett and I. Langmuir, PhysicalReu., 1937, 51, 964; Langmuir and V. J. Schaefer, J . Amer. Chem. Xoc., 1937,59, 2400; €or full references see Langmuir, Proc. Roy. Xoc., 1939, A, 170, 1.27 E. Stenhagen, Trans. Paraday SOC., 1938,34,1328; C. Holley and S. Bern-stein, Physical Rev., 1937, 52, 525; C. Holley, ibid., 1938, 53, 534; I. Fan-kuchen, ibid., p. 909; G.L. Clark and P. W. Leppla, J . Amer. Chem. Soc.,2936, 58, 310104 GENERAL AND PHYSICAL CHEMISTRY.the film is deposited only on the upward movement of the slide.The film is forced on to the slide by a surface pressure; a very con-venient way of exerting a constant surface pressure is to utilise theequilibrium spreading pressure of an oil, and this remains constantso long as an excess of the substance is on the surface, irrespective ofthe change in area of the free surface due to the deposition of thefilm.Suitable piston oils have been shown by Langmuir to be oleicacid, 31; triolein, 21; castor oil, 16; and tritolyl phosphate,10 dynes/cm.The resultant multilayer can be either a single layer or a doublelayer repeat unit according to the crystal structure of the substancein three dimensions.J. J. Bikerman 28 shows that the three typesof deposition are related to the degree of wettability of the depositedfilms : X > Y > 2. Hence, the manner of deposition is related tothe contact angle, which can be changed very readily by ions in theunderlying solutions for those substances, such as fatty acids andamines, which can react with the substrate, and by simply changingthe surface pressure for those substances, such as esters and ketones,which do not react with the substrate.The film can only be deposited when the angle which it makeswith the slide is obtuse; hence, for a strongly hydrophobic surfacethe film can only be deposited on the downward movement. If thesurface be less hydrophobic, it is possible (X-film) by varying therate of the movement of the slide to obtain an obtuse angle both onthe downward (angle > 90") and during the upward movement(contact angle < 90") ; consequently a film is deposited on bothjourneys (Y-film).If the surface of the slide is relatively hydro-philic (small contact angle) an obtuse angle can only be obtained onthe upward journey, and thus deposition only takes place on thismovement (Z- film).This can be readily demonstrated with a film of octadecyl acetate,which, being very hydrophobic, will deposit as X-films, but if thesurface pressure is made very high, thus lowering the contact angle,the film deposits in the Y - f ~ r r n . ~ ~Deposition Rates.-Langmuir, Schaefer, and Sabotka 3O found thatthe ratio of the geometrical area of the slide to the area of the filmremoved from the surface of the water was unity within experi-mental error.This is irrespective of the actual area of the slide,which is usually much greater. Bikerman31 artificially grooved ametal slide and found that the deposition ratio still remained unity.Further, he was able to deposit films on wire gauzes, proving that28 Proc. Roy. SOC., 1939, A, 170, 130.30 J . Arner. Chem. SOC., 1937, 59, 1751.29 See Stenhagen, ref. (27).31 See ref. ( 2 8 ) SCHULMAN : SURFACE CHEMISTRY, 105the area of the molecule in the film has no bearing 011 the area ofthat on the slide : this can bc shown much better wibh X-rays (seelater). The monolayer behaves like a soap bubble film on the wiregauze, and when drying, bursts and forms crystallites on soap gels.Bikerman suggests that this is what occurs on deposition of afilm on t o a metal surface, the film being spanned across theundulations.Monolayer and Multilayer Thickness.Since one can only deposit films on slides when they are in thecondensed states, and further, since these states consist of differentcrystalline forms of the substance with varying tilts of the chain tothe surface, there is no reason t o suppose that the two-dimensionalcrystal should have the same form or thickness when it is in thethree-dimensional form, as in the multilayer.One of the mostextreme cases of this difference in the layer thicknesses was shownby A. E. Alexander,32 who deposited calcium oleate films a t an area of27 A .~ as compared with 19 A . ~ for calcium stearate; this gave amultilayer of 23.5 A. thickness per layer as compared with 16 A.thickness on the surface of the water with a deposition ratio ofunity. A multilayer of this material must contain at least 50% ofopen space. This was confirmed by comparing the thickness of thelayer found by optical measurements with those found by X-raymeasurements.It is noteworthy that the different substances build up single- ordouble-layer unit multilayers with either vertically orientated orinclined chains, irrespective as to whether they have been depositedin the X - or the Y-forms. For instance, the salts of the fatty acidsand long-chain amine phosphates always build double-layer latticeswith tilted chains.Octadecyl acetate films are intermediary,building either double-layer lattices with a marked tilted orientationin the long chains or vertically orientated long-chain single lattices.33The ease with which multilayers can be made with films of thisester, and the various types of multilayer it forms, renders it anexcellent subject for detailed research on the structure of multi-layers. Other esters such as the triglycerides or ethyl and methylstearates form inclined long- chain double layers. Methyl ketonesform vertically orientated single layer lattices.34Methods of Measuring Thickness of Mu1tihyers.-Optical measwe-muzts. Blodgett 35 and Blodgett and Langmuir 36 measured the32 J., 1939, 777.34 Stenhagen, private commmiication.35 J . Plhysical Chem., 1937, 41, 975; Physical Rev., 1939, 55, 391,3G Ibid., 1937, 51, 964.33 Stenhagen, ref.(27)106 GENERAL AND PHYSICAL CHEMISTRY.thickness of the multilayers and the layer spacing by interferencecolours with polarised light which set in a t the quarter wave-lengthof light, and also by interference intensities with monochromaticlight. These methods give astonishingly accurate results, differ-ences of thickness of one monolayer being easily observed. Theycompare very favourably with the X-ray results when the mono-layer thickness and multilayer lattice thickness are identical. The'interference colours are depcndent both on the thickness of thelayers and on their refractive index.The extinction of reflection formonochromatic light is dependent also on the wave-length and angleof incidence at which the light strikes the film. By varying allthese factors most of the optical properties of multilayers can beobtained.A very useful method is to make a step scale with a known sub-stance and compare the colours under identical conditions to a stepscale of an unknown substance and ascertain the number of layersat which the colours coincide, having corrected for differences inthe refractive indexes of the two substances.This technique 37 is still inits infancy as a weapon for investigating the structure of multilayers.Since the building of multilayers is an extremely easy way to obtainthe substance in a crystalline form, and also to obtain a completeX-ray picture with quantities of the order of only 0.03 mg.of thesubstance, its importance as a means of investigating crystals ingeneral and the chemical structure of unknown substances in par-t icular c annot be overestimated.Fankuchen 27 greatly improved this technique by applying hiscondensing monochromator (for the X,) X-ray beam by reflectionfrom a pentaerythritol crystal. Films can be deposited on any base,cellulose being a very convenient one, since its x-ray picture con-sists of faint diffuse rings. Knott and Schulman 38 deposited 2000layers of octadecyl acetate on a thin cellophane sheet. The axesin the plane of the slide being x and y, x being the dipping direction,and z the axis a t right angles, then photographs were taken by per-mitting the X-ray beam to travel all the three axes in turn, rotationof the slide with increasing angles, 5", 15", 25", etc., being under-taken around either the x or the y axis during the photograph.By this means pictures were taken a t various angles along the dippingdirection and at right angles to this direction, and also a transmissionpicture. This revealed the built-up multilayer to have a beautifulthree-dimensional crystal lattice.The photographs showed layerlines with spots clustered in definite regions on the layer line,37 Holley and Bernstein; Holley; Fankuchen; Clark and Lepplrc, locc. cit.,ref. 2.7,X-Ray measurements of multilayers.38 Nature, 1940, in the pressSCHULMAN : SURFACE CHEMISTRY. 107resembling in this respect the rotation photograph of C,,W,, abovethe c-axis.39 More than 30 orders were obtained for the mainspacing, and several for the side spacings.A stationary photo-,graph, with the X-rays travelling parallel to the surface of the film,showed not only distinct layer lines with rather diffuse spots, butalso the main spacings. This shows that the reciprocal pointscorresponding to the main orders of reflection are in reality finiteplane areas.Thiswork has chiefly been done by L. M. Germer and K. H. Storks4()and by E. Havinga and J. de Wael.41 Their investigations showedthat the monolayer has a two-dimensional crystal structure, andthat the multilayers have a similar structure to the crystal of thesame substance.Transmission pictures of monolayers deposited on thin Resoglaz(200 A.thick) or nitrocellulose give beautiful pictures and are veryeasily obtained once the apparatus is constructed. It would beinteresting to study mixed monolayers or mixed two-dimensionalcrystals by this method.Interesting pictures taken by Germer and Storks42 on rubbedmultilayers showed that one could only remove or displace the filmif the rubbing direction was against the tilt of the molecules, butnot in the direction of the tilt.Electron-ray measurements of mouolayers and multilayers.Skeleton Films.Avery interesting property of multilayers, shown b y B l ~ d g e t t , ~ ~ l ~ ~ , ~ is the skeletonising of multilayers. It was shown by Langmuir andSchaefer 46 that films of stearic acid containing traces of calcium orbarium ions in the underlying solution were half converted intoneutral soaps a t a pn of 5-1 and 6.6 respectively; hence, if a multi-layer of barium stearate and stearic acid containing 50yo of free fattyacid was dipped into benzene, all the free fatty acid is readilydissolved out, leaving a stable structure called a skeleton multilayerconsisting of barium stearate.The freeing of the multilayer fromstearic acid does not involve any change in its thickness but onlyin the refractive index. Blodgett 45 now found that it was possibleto dissolve back into the skeleton multilayers hydrocarbons or39 A. Miiller, Proc. Roy. SOC., 1928, A, 110, 437.40 Physical Rev., 1936, 50, 676; 1939, 55, 648; J .Chem. Physics, 1938, 6,4 1 Rec. Trav. chim., 1937, 56, 375.42. LOC. cit., 1939.44 J . Physical Chem., 1937, 1937, 41, 973.46 Physical Rev., 1939, 55, 391.46 Ibid., 1936, 58, 284.280; PTOC. Nat. Acad. Sci., 1937, 23, 390.43 Physical Rev., 1937, 51, 966108 GENERAL AND PHYSICAL CHEMISTRY.other substances such as long-chain alcohols. It was thereforepossible to obtain a film of any desired refractive index by addingsubstances or dissolving the fatty acid out of the multilayer. Acadmium arachidate multilayer from which progressive amounts ofthe free arachidic acid had been dissolved out seemed very appro-priate for changing the refractive index. Certain substances, suchas the long-chain alcohols, could not be dissolved out again veryreadily, thus denoting complex formation in the multilayer.47Blodgett 45 has utilised this technique to change the refractiveindex of the surface of glass and the thickness of the surface layer,so that the refractive index is equal to the square root of therefractive index of the glass, and the thickness equal to a quarter ofthe wave-length of the reflected light.Under these conditions theintensity of the light reflected from the upper surface of the skeletonmultilayer is equal to the intensity of the light reflected from theinterface glass-multilayer ; hence, at the quarter wave-lengththickness no reflection from a beam of light of normal incidence canoccur, and consequently the glass surface will be invisible.Another interesting use of the technique of skeleton films 44 is toshow up the conditions necessary for X - and Y-deposition of mono-layers (for the fatty acids) into multilayers.Single-component filmscomposed of barium stearate are more hydrophobic than mixedfilms of barium stearate and free fatty acid; consequently, films ofbarium stearate will deposit in the X-manner and the mixed filmsin the Y-ma~mer.~l The X-films will not therefore skeletonise,whereas the Y-films will.It has been found possible by Blodgett 43 to change the consti-tution of a multilayer in the course of its deposition ; e.g., a mixedfilm of barium stearate and stearic acid giving a Y-deposition, will,if the built-up multilayer is left in a barium solution for a veryshort time, give an X-deposition.This shows that the com-position of the multilayer has changed in the barium solution to acomplete barium stearate multilayer although a mixed film wasdeposited.Overturning of Molecules.Molecules built up into multilayers by X-deposition and whichcrystallise as doublets must in process of deposition turn over;likewise for the inverse process, in multilayers formed by Y-deposi-tion which crystallise in single layers, the molecules must also haveturned over. Further X-deposited layers always come out hydro-phobic; consequently, the inner layer must turn over a t some47 Blodgett, private communicationSCHULMAN : SURFACE CHEMISTRY. 109point during the deposition. 'It could be suggested that thisphenomenon takes place a t the triple point slide-air-~ater.~SThe attraction of polar head-groups to one another for thosecrystallising as double layers and the protection of these polargroups by a methyl group, as in the case of octadecyl acetate, forthose crystallising in single layers, must play an important part inthe mechanism.The most important part of the deposition ofmonolayers is that water must be squeezed out from between thepolar groups, presumably by polar interaction, or by associationbetween the methyl group as in the second case.Stearic acid, which has a hydrophobic layer on the outside, willbecome hydrophilic in contact with ~ a t e r , ~ g i.e., the outside layerof molecules must have overturned.A built-up multilayer of barium stearate does not become hydro-philic on contact with water, and, more remarkable, it is alsooleophobic to hydrocarbons, in spite of the fact that hydrocarbon issupposed to be oriented in this case t o the outside.Barium stearate is not soluble in hydrocarbons or water : asimilar relation must hold for both cases.If multivalent ions of ahigher valency be dissolved into the solution surrounding a built-upfilm of the stearate, the outside layer rapidly becomes very hydro-philic. For example, a barium stearate multilayer becomeshydrophilic in the presence of aluminium or thorium ions in thesolution. The multivalent ion apparently anchors a polar groupto the surface and, being not fully saturated with fatty acid radicals,the free hydroxyl groups make the surface hydrophilic. Langmuirand S~haefer,~O who found this phenomenon, utilised it to conditionsurfaces of multilayers to absorb proteins and bile acid salts.Electrical Properties of Multilayers.Langmuir 51 suggested that the surface potentials of multilayers,first measured by E.F. Porter and J. W y ~ a n , ~ ~ were due to surfacecharging of the outer layers by the recession of the water from thefilm, and not to the actual dipoles of the stearate film, as with thesurface potentials of the film on water : R. W. Goranson and W. A.Zisman,53 reviewing all previous work on electrification of multilayers,showed that the potentials are due to the absorption of ions from theunderlying solution. They further showed that X-deposition for the48 Langmuir, Science, 1938, 87, 493, describes various ways in which thisphenomenon might take place.Devaux, Ann.Report Smithsonian Inst., 19 1 3, 26 1.6o J . Amer. Chem. SOC., 1937, 59, 1400, 1762.61 Ibid., 1938, 60, 1190.63 J . Chem. Physics, 1939, 7 , 492.52 Ibid., 1937, 59, 2746; 1938, 60, 1083110 GENERAL AND PHYSICAL CHEMISTRY.fatty acid films takes place on more alkaline solutions than theY-films ; these films are therefore composed of the salts of the fattyacids, and wiU have more positive ions adsorbed into them than theY-films, which are formed on solutions of low pa and are mixedfilms of stearic acid and stearate. Consequently, the multilayersbuilt by X-deposition will have much higher charges than those builtby Y-deposition (for the fatty acid multilayers).If the multilayer is built on an insulator, an electrostatic repulsivefield is set up which, after about 500 layers, inhibits the depositionof further layers.Films of the esters such as octadecyl acetate and ethyl stearate,whether X - or Y-deposited, can produce very highly charged multi-layers,54 presumably by mechanical adsorption of ions from theunderlying solution.One interesting experiment can be done bydepositing on a built-up layer of barium stearate with a surfacecharge of + 20 volts two layers of octadecyl acetate; this reversesthe surface charge to - 20 volts. The octadecyl acetate films mustbe picking up ions of opposite sign out of the underlying solution ascompared with the barium stearate film. Hence, the surfacepotentials of multilayers are due to induced charges in the metalsupport and electrokincsis effects.Molecular Interactions in Monohyers.-Mixed Films.-Before the work of Schulman and A.H. Hughes 56 itwas considered that no interaction took place between molecules in amixed monolayer, but they showed that, if one of the componentswas ionised, strong interaction could take place, as measured bygreat differences in the surface pressure and potential calculatedmean values and the observed values. Further, if no interactiontook place, the more stable component could eject the other com-ponent out of the monolayer, leaving a one-component film.J. Marsden and J. H. Schulman 56 and Schulman 57 enlarged uponthese interactions. It appears that the attractive and repulsiveforces between polar groups in mixed films may be interpreted uponthe hypothesis that they are due to Coulomb forces acting betweenpolar groups in systems containing (graded by their energy ofassociation)ion+-ion- > ionf-dipole > dipole-dipole > ion*-ion*.Examples in the first category are long-chain amines and acids inneutral solution ; in,the second, long-chain amines and acids in acidsolution and long-chain amines and alcohols; in the third, long-chain alcohols and ethers, or esters giving no interaction; and in5 5 Bwchem.J., 1935, 29, 1243.5 7 Ibid., 1937, 33, 1116.64 Stenhagen, loc. cit., ref. 27.66 IZ’rans. Faraday SOC., 1938, 34, 748SCHULMAN : SURFACE CHEMISTRY. 111the fourth, one-component films such as amines in acid solution,which actually show (by being vapour films) strong repulsive forcesbetween the ions.The interactions in the first category are difficult t o measure bychange in surface area, since the single-component films exist bythemselves in the solid state, but they can be measured by changesin surface potential.The most striking examples are in the second category, where avapour film of octadecylamine hydrochloride (repulsion due to likeions) is condensed to a solid when mixed with stearic acid, whichon itself is in the mesomorphous state (weak interaction due to twodipoles) at pH 2.The mixed film also has a surface potential some150 mv. above the mean. Since single-component films of acids andbases are, in nearly neutral solution, partly ionised, they also obey therule applied t o an ion-dipole system and are consequently always inthe condensed state.If a component which hinders this interactionbe added to this system, an expansion of the original film takes place,as seen with an amine-alcohol mixed film at pH 7.8. Harkins andR. T. Florence 58 essentially confirm these results, and further showthat maximum condensing effect is observed with 1 : 1 mixtures of theinteracting components. They show that with mixed films of fattyacids of varying chain length, differences with the mean values ofthe surface potentials can be obtained, suggesting therefore thatthese differences do not necessarily show interactions between polargroups.Stereochemical Effects.Schulman and Hughes 55 and Schulman 57 showed that mixedfilms of saturated long-chain compounds were very much morestable than those containing an unsaturated long-chain component.That this phenomenon was most probably due to stereochemicalconsiderations in the hydrophobic portion of the molecule, firstcame out of work done on penetration of films of cis- and trans-long-chain alcohols by sodium cetyl s ~ l p h a t e .~ ~ This substance,when injected into the underlying solution, formed stable mixedfilms only with the trans-compound at high surface pressures owingto the interlocking possible between the chains, and not with thecis-compound. Schulman and S t e ~ h a g e n , ~ ~ R. T. Florence and W. D.Harkins,60 and Marsden and Rideal showed by their examinationof mixed films of cis- and tram-unsaturated long-chain compoundswith saturated long- chain compounds that an interlock or adlineationof t,he chains was most important for their association and two-5 8 J.Chem. Physics, 1938, 6, 847.5s Nature, 1938, 141, 785; Proc. Roy. SOC., 1938, B, 126, 1356.6o J. Chem. Physics, 1938, 6, 856. 61 J., 1938, 1163112 GENERAL AND PHYSICAL CHEMISTRY.dimensional crystal packing, thus supporting the views first expressedby C. G. Lyons and Rideal.62 Marsden and Rideal further showedan important characteristic of adlineated molecules, brought aboutby their orientation in monolayers, vix., that their reactivities canbe quite different from that of the same molecules in bulk solution.This is shown here by the marked differences in the packing of thefilms of the oxidation products of the trans- and cis-unsaturated C,,fatty acid.These differences were attributed to the associationbetween hydroxyl groups, brought about by the adlineation betweenthe molecules. I n the cis-compound, a pairing of two moleculescould take place by hydroxyl bonding, resulting in weak associationbetween the paired molecules in the film and consequently theformation of vapour films. On the other hand, the trans-hydroxyl compound could cross-associate and aid the packing andassociation between the molecules in the film, thus producing strongsolid monolayers. These differences are further brought out bythe availability of the double bonds in the cis- and trans-compoundsto oxidising agents in the underlying solution induced by thedifferent packing arrangements.It is interesting that this hydroxylbonding in the dihydroxy-compounds takes place in a hydrocarbonenvironment and not in an aqueous medium.Penetration of Monoluyers.It was first shown by Schulman and Hughes 55 that, if certaincapillary-active substances were injected in minute quantities undera monolayer kept at constant area, great changes in surface pressureand surface potential of the film-forming substance occurred,although the injected substance alone a t these concentrations hardlyaffected the surface tension of an aqueous solution. Schulman andRideal e3 showed that this phenomenon was very specific andrelated to two types of interaction between the film-formingmolecule and the injected molecule. This consisted primarily ofan interaction between the polar groups of the two molecules,which anchored the soluble molecule to the film-forming molecule,thus enabling the second stage of the association to take place.This consisted in the association between the non-polar portions ofthe molecules. The energy of association is of the same magnitudeas that of the polar association, under conditions in which strongassociation between the molecules can take place.On penetration, therefore, the number of molecules in themonolayer is increased, and since the stability of the complex isgreater than that of either of the two components alone a t theinterface, an equimolecular mixed film will result , thus increasingthe surface pressure markedly and increasing or decreasing the62 Proc.Roy. SOC., 1929, A, 124, 333SCHULMAN : SURFACE CIEEMISTRY. 113surface potential to the mixed-film value of the two components.Schulman and Rideal63 gave strong proof for this hypothesis byshowing that penetration of monolayers took place (by substancesinjected into the underlying solution) with the same specificity aswith components that were known to form complexes in bulk, suchas the saponin-cholesterol complex ; for instance, saponin readilypenetrates films of cholesterol or ergosterol, but not films of chole-sterol acetate, cetyl alcohol, or calciferol, giving a direct analogy totheir association in bulk solution. Similarly, sodium cetyl sulphatepenetrates cholesterol films but not those of cholesteryl acetate orcalciferol. As shown already, this compound will penetrate cetylalcohol or elaidyl alcohol, but not oleyl alcohol, at all readily, thusshowing that the phenomenon of penetration is related equally topolar and non-polar association by van der Waals forces.Schulman and Rideal 64 utilised the technique of monolayerpenetration to grade the reactivity of polar groups to react withone another. I n this case polar groups having special biologicalsignificance were chosen. On weakly associating systems the moreunstable component can be ejected from the interface by highsurface pressures which are well defined and permit a measure ofassociation between molecules. This pressure is the equilibriumpressure attained by injecting into the underlying solution a certainquantity of the reacting component at a certain surface concentrationof the film-forming compound : according to Gibbs it is related toboth these conditions, and this has been shown experimentally bySchulman and Stenhagem65Schulman and Rideal 64 showed that by injecting equimolar con-centrations of a whole series of compounds easily soluble in waterbut containing an identical non-polar portion such as a C1, long-chain hydrocarbon, t o which various polar groups were attached,a well-defined reactivity series of these polar groups in associatingwith a common polar group, such as the hydroxyl group incholesterol, could be established. The area of the cholesterolmolecule in the film was chosen so as t o enable one molecule of theinjected substance to penetrate the monolayer. This gave thefollowing reactivity series :+-NH3+ > -SO,- > -SO3- > COO- > -NMe3 > Bile acid anionThe direct analogy of this series with the biological activity of thesesubstances has been shown by Schulman and RideaL6*Schulman and Stenhagen 65 enlarged upon the monolayer pene-tration technique by measuring the phenomenon, not only atconstant area, but a t varying areas and pressures of the film-forming63 Proc. Roy. SOC., 1937, B, 122, 29.6s Proc. Roy. SOC., 1938, B, 126, 356.64 Nature, 1939, 144, 100114 GENERAL AND PHYSIC& CHEMISTRY.component and a t different concentrations of the injected component.This established two interesting properties of mixed films. (1) Thetwo components could exist in two-dimensional crystal forms witha well-defined stable ratio of the two components. The stability ofthe various mixed two-dimensional crystalline forms depended onthe associating properties of the polar and non-polar portions ofthe two components. For instance, solidification of the mixedmonolayer and marked changes in the force-area curves of films ofthe two components took place a t definite stoicheiometrical ratiosof the two compounds. (2) The stability of the mixed film, asmeasured by the surface pressure necessary to eject the penetratingcomponent or collapse the mixed film as a unit, is markedly affectedby the concentration of the penetrating component in the underlyingsolution; e.g., a pressure of only 8 dynes/cm. is necessary to ejectsodium cetyl sulphate molecules out of an equimolecular mixed filmcontaining cholesterol as the other component, but a t a concen-tration of g./c.c. of sodium cetyl sulphate in the underlyingsolution the ejection pressure is already 35 dynes/cm. At a con-centration of 2 x g./c.c. the penetrated film collapses as a unitwithout an apparent ejection of either component at pressures ofca. 50 dyneslcm., which is much greater than the collapse pressure offilms of the components alone. This emphasises the importance ofthe diffuse layer of the penetrating material underneath the mono-layer in stabilising the complex a t the interface. The significance ofthis diffuse layer in bulk solution is demonstrated by Schulman(unpublished) in work on the stability of micelles and emulsions andon phenomenon relating to reactions taking place at cell surfaces.Schulman and Stenhagen 65 further showed the marked influenceexerted by the nature of the non-polar portion of the interactingmolecules both on the penetrating ability of the molecules and onthe stability of their resultant complexes a t the air-water surface.For instance, by increasing the chain length from C,, to CIS, theejection pressure of tbe long-chain sulphate from a mixed filmcontaining cholesterol changes from 8 dynes/cm. to 30 dynes/cm.Similarly, as has already been emphasised, stereochemical arrange-ments permitting of adlineation between molecules and interactionby van der Waals forces, such as with the cis- and trans-configurationand with long-chain hydrocarbons and ring structures, play a veryimportant part in the phenomenon of penetration.Adsorption.It has already been shown that a long-chain hydrocarbon withone polar group at the end of the chain will penetrate a monolayersimilarly constituted, raising the surface pressure and changing thesurface potential of the film-forming substance in a marked manneSCHULMAN : SURFACE CHEMISTRY. 115under the specific interacting conditions. Schulman and Rideal G3* 64and E. G. Cockbain and Schulman 66 show that, if the interactingmolecule has more than one reacting polar group and these polargroups are suitably spaced, very poor penetration of the monolayertakes place, but a very strong adsorption on the monolayer isobserved. This adsorption is measured by marked changes in thesurface potential and rigidity of the film-forming component.Schulman and Rideal 63 show that penetration of a protein film bya long-chain compound is usually followed by complete dispersionof the protein film and subsequent removal from the interface, butif a dibasic fatty acid or other multiple polar reacting compound beinjected into the underlying solution, strong adsorption or tanningof the protein film is observed. It was shown that the rate ofadsorption and resultant concentration of the adsorbed molecules isgreatly influenced by the number of reacting polar groups peradsorbing molecule. Cockbain and Schulman 66 enlarged uponthese reactions, showing that the spacing of the polar groups andthe nature of the hydrophobic portion 9f the adsorbing molecule inthe underlying layer permitting of adlineation or packing of themolecules (on this occasion) in the underlying layer was mostimportant in the rate of the adsorption and stability of the resultantbimolecular film.Cockbain and Schulman summarise the various factors which cangovern the interaction between molecules in an orientated mono-layer and compounds present in the underlying solution. Thisinteraction can vary from examples where the association is so strongthat the reacting molecules can associate into a mixed monolayerwith definite stabilities measurable at simple stoicheiometrical ratiosof the two reacting components to cases where it is so weak thatonly solution effects can be measured.The extent of the interaction can depend on the following factors :(a) The chemical nature and number of the polar groups in thetwo molecular species; ( b ) the van der Waals forces between thenon-polar residues ; ( c ) surface pressure of the monolayer ; ( d ) con-centration of the dissolvcd compound; ( e ) pE of the underlyingsolution ; (f) neutral salt concentration in the solution ; (9) stereo-chemical confgurations of the two molecular species, in both theirpolar and non-polar groups.J. H. S.R. P. BELL.M. G. EVANS.H. W. M~LVILLE.W. C. PRICE.J. H. SCHULJKAN.Tram. P’araday SOC., 1039, 35, 716