MOLECULAR CONFIGURATION AND HYDROCARBON REACTIVITY BY A. R. UBBELOHDE AND J. C. MCCOUBREY Received 21st February, 1951 Various modes of ‘ I action at a distance ” in saturated hydrocarbons are discussed in relation to the comparative reactivity of homologues and isomers. Electronic effects and the influence of vibration coupling on reactivity are summarized. Detailed consideration is given to the average degree of coiling of n-paraffins . Experimental results quoted include infra-red and Raman measurements on crystal and melt, molar volumes of the liquids at the boiling points and critical temperatures, entropies of vaporization of the liquids, viscosities and temperature coefficients of viscosities of the vapours, thermal conductivities of the vapours and the second virial coefficients of the vapours.These results show that in the vapour phase flexible polymethylene mole- cules are coiled till the space occupied is about the same as for the corresponding isoparaffins. A moderate degree of uncoiling takes place on forming the liquid, but on average the fully stretched molecules are only found in the crystal. Various consequences of this molecular coiling for the reactivity of paraffins incIude steric and energy transfer effects. In hydrocarbon chemistry, processes such as bond rupture are formally similar at various parts of the molecule, and are also similar in homologues and isomers. This gives particular importance to detailed examination of the ways in which remoter parts of a molecule can affect the reactivity of specific bonds. In polpethylene hydrocarbons, two modes of “ action at a distance ” have previously been discussed in some detail in the light of the quanti- tative evidence available at the time.l To summarize these two modes briefly : (i) With reference to electronic action at a distance, it has been noted that in a series of 35 isomeric nonanes the molecular refractivity shows a progressive drift from about 43-9 units for the least branched to about 43.0 units for the most branched nonanes.However, electronic influences on bond strength fall off quite rapidly as the bond becomes more remote. For example, there is a constant increment to the heat of formation for each CH, group added beyond n = 4, showing that the end CH, groups have little effect on the more central bonds beyond this order of remote- ness.Again, ionization potentials of n-paraffins tend to a limiting value beyond about n = 4.2 (ii) Owing to the similarity of fundamental vibration frequency of the C-C bonds, the skeletal vibrations of the carbon atoms in a polymethylene hydrocarbon are coupled.8 This vibration coupling has a number of con- sequences. In polymethylene hydrocarbons : (a) Skeletal vibrations of longer wavelength than the fundamental are appreciably excited thermally at substantially lower temperatures than the C-C vibration in ethane, for which the characteristic temperature is Ubbelohde, Proc. Roy. SOC. A , 1935, 152, 361 ; Rev. Inst. Franpis Pitrule Honig. J . Chew. Physics, 1948, 16, 110. For experimental evidence, cf. Brown, Sheppard and Simpson, Faraday Ann. Combust.Liquides, 1949, 4, 488. SOC. D ~ S C U S S ~ O ~ S , 1950, 10, 000. 94A. R. UBBELOHDE AND J. C. McCOUBREY 95 around 8 = 1300~ K. The average zero point energy per C-C bond de- creases and the average vibrational energy increases at ordinary reaction temperatures, with increasing n. (b) Coupled vibrations can act at a distance by transmitting energy t o any part of the coupled system. But the coupling is interrupted whenever there is a substantial break in the vibrational system, as at a double bond, or where C is joined to a group such as NHa or C1. Activation processes can only draw readily on the reservoir of vibrational energy if the bond forms part of a strongly coupled system. Thus the pyrolysis of the C-X bond in C,H,,+,X, where X is a halogen or NHa or OH, or of should show quite a different dependance on n from the pyrolysis of hydrocarbons.Evidence has recently been obtained of activation in- volving coupled vibrations in the pyrolysis of n-~araffins.~ Molecular Coiling and Hydrocarbon Reactivity.-A third mode of action at a distance is possible in flexible hydrocarbons. The idea is that if these coil up so as to bring remoter groups into the neighbourhood of the bond whose reactivity is under consideration, the van der Waals forces can : (a) smudge the quantum levels of the bond by providing a polariz- able medium with variable interaction according to distance ; (b) affect transition probabilities in vibrational and electronic excitation of the bond. At the time this suggestion was first put forward, only indirect estimates could be made of the degree of coiling of homologous normal paraffins. This gap has since been filled from a number of sources of evidence. (I) Infra-red and Raman measurements on crystal and melt of normal paraffins show that whereas the molecules are stretched planar zig-zags in the crystal, in the melt crumpling takes place to form one or more “ rota- tional isomers ”. The Raman spectra of liquid n-hydrocarbons C 4 4 , are found to con- tain more lines than can be interpreted on the basis of a single configur- tion .s AH for a change from one rotational isomer to the next on progressive coiling is estimated to be about 500 cal./mole.In the vapour the con- figuration is probably similar, from the similarity of the infra-red absorp- tion spectra, which do not, however, permit quantitative comparisons.It should be noted that second virial coefficients for the hydrocarbons indicate some temporary dimerization in the vapour phase.6 (2) Pyknometric measurements of molecular volumes have shown that the n-paraffins occupy practically the same volume in the liquids as do the corresponding isoparaffins at the respective boiling points.’ Illus- trative data are recorded in Table I for C, and Cs ; much the same con- clusions have been reached with the intervening paraffins. Ratios of the critical volumes show the same effect. From the similarity in volumes and the similarity in entropies of vaporization it seems likely that the n-paraffins are “bunched” or “ coiled ” in both liquid and gas phase, to an extent such that they occupy about the same average space as the corresponding isoparaffins.(3) Measurements have been made on the viscosities and the tem- perature coefficients of viscosities of vapours of paraffin homologues and isomers.’ The results again show that the molecules of the %-paraffins must, on average, be quite highly coiled in the gas phase. Some of these features are illustrated in summarized form in Table 11. C,.H,,CH = CHC,H,, These are further discussed below. Cf. Ingold, Stubbs and Hinshelwood, Proc. Roy. SOC. A , 1950, 203, 486. Sheppard and Szasz, J. Chem. Physics, 1948, 16, 704 ; 1949, 17, 86 ; Rank 6 Hirschfelder, McClure and Weeks, J . Chem. Physics, 1942, 10, 201. 7 McCoubrey, McCrea and Ubbelohde, J . Chem.Soc., (in course of publication). and Axford, J. Chem. Physics, 1949, 17, 430.96 CONFIGURATION AND REACTIVITY TABLE I.-RATIOS OF MOLAR VOLUMES AND ENTROPIES OF VAPORIZATION 13 Paraffin n-Butane : isobutane . n-Pentane : isopentane . n-Hexane : isohexane (di-iso- %-Octane : iso-octane (2 : z : 4- %-Octane : iso-octane (di-iso- ProPYl) - trimethyl pentane) . butane) . Molar Volumes Ratio at b.p. - 1.0035 - 1.0148 - Ratio of Entropies of Vaporization - 1.0262 1'0532 1.052 Molar Volumes Ratio at Critical Temperatures 1.004 1'01 I 1'028 1.017 TABLE II.-RATIOS OF VISCOSITIES OF ISOMERIC PARAFFINS Normal: isoButane . Normal : isoPentane Normal : isoHeptane : (z : z : 3-trimethyl butane) . Normal : iso-Octane : (2 : 2 : 4-trimethyl pentane) . . . TOK 291.1 373'1 393'1 298.1 373'1 380.1 398.1 416.9 436'5 398.1 4 16.9 436.5 Ratio 0.993 1'000 I '000 0.973 0.978 0.939 0.938 0'945 0.95 1 0.955 0.954 0.955 739 947 998 676 ,341 729 763 800 83 9 724 757 785 Facts of importance for the reactivity of hydrocarbons can be obtained from Table 11.In the simplest form of kinetic theory of momentum transfer, the molecular u diameter is related to the viscosity by the equation, Inspection of the ratios of viscosities shows that at any rate so far as momentum transfer is concerned, the n-paraffin molecules have an average ma with respect to molecular collisions, which is only from 0-5 % larger than that of the branched isomers. This must imply that the normal paraffins behave predominantly as coiled molecules in the gas phase. A similar conclusion has been put forward from more restricted data on diffusion of the polymethylene chains C,,-C,, in air.s A further fact from Table I1 is that no large temperature coefficient is observed in the ratio of viscosities. This indicates that an explanation of the observed coiling in terms of repulsion potentials between 8 Molar volumes, McCoubrey, McCrea and Ubbelohde, ref.(7). Critical volumes, quoted by Partington, An Advanced Treatise on Physical Chemistry, VoE. I (Longmans, 1949) p. 645. Entropies of vaporization, Nut. Bur. Stand., 1947, Project 44. =aa = $1/(K/N.r) . 1/(MT)/q = 5.694 x I O - ~ ~ 1/(MT)/q. (1) Bradley and Shellard, Proc. Roy. Soc. A, 1949, 198, 239.A. R. UBBELOHDE AND J. C. McCOUBREY 97 adjoining CH, groups lo cannot form a complete theory of the effect, since Taylor's theory requires the diameter of a flexible molecule to decrease as the temperature rises.The observed temperature coefficients of viscosities permit calcula- tion of apparent collision areas according to the Sutherland equation, 1-594 X I O - ' ~ ~ / M . Alternatively, the method K where the collision area, A = of Hirschfelder, Bird and Spotz can be used. Values as established from the new data and from previocs observations are summarized in Table 111.' TABLE I11 Hydrocarbon n-Butane . isoButane . n-Pentane . isoPentane . n-Hexane . n-Heptane . isoHeptane . n-Octane . iso-Octane . Hirschfelder Collision Area (AZ) I 9-6 22-4 26.2 - 27'4 - - 34'7 - Sutherland Collision Area A (A? I 6-6 17-1 19-6 I 8.9 25'4 26-7 31.1 2 7'9 32-6 From Table I11 the Sutherland collision diameters of the n-paraffins in the gas are rather smaller than for the corresponding isomers, in con- trast with Table I1 in which the diameters appear slightly larger.This is because the Sutherland collision areas do not refer to quite the same molecular quantity as the momentum transfer collision areas at any one temperature (eqn. (I)). From the way they are defined, the smaller Sutherland values indicate a greater " compressibility " of n-paraffins on collision, compared with isoparaffins of the same molecular weight. The Hirschfelder collision areas refer to zero velocity of approach of the mole- cules and again suggest that n-paraffins are somewhat more compressible than isoparaffins in a molecular collision. Although the information de- tailed in Tables I1 and I11 does not refer to collision diameters defined in quite the same way, the figures in all cases point to quite considerable crumpling of the n-paraffins.Evidence* for some further coiling on vaporization can be obtained from a comparison of the entropies of vaporization of isomers (cp. ref. (I) and Table V) and from the difference in attraction potentials between molecules in liquid and gas (Table IV). If the flexible mole- cules were fully extended the force constants Elk would increase linearly with n. It will be seen that at the critical temperature there are some indications of an increasing trend of E/k with n. But in the gas there is no definite trend. This agrees with the view that the flexible molecules are crumpled somewhat more in dilute gas phase than in the liquid.The observed increase of viscosity with temperature implies a smaller average collision diameter for momentum transfer and a smaller average collision frequency as the temperature rises. Unless account is taken of lo Taylor, J . Chem. Physics, 1948, 16, 258. * From ref. (6), p. 207. D98 Force Constant e l k ~ in Liquid (Critical 1 Temperatures) CONFIGURATION AND REACTIVITY TABLE IV.-COMPARISON OF FORCE CONSTANTS FOR MOLECULAR ATTRACTION BETWEEN LIKE MOLECULES Molecule Force Constant elk in Gas (Viscosity Data) TABLE V.-~OMPARISON OF ENTROPIES OF VAPORIZATION OF ISOMERIC OCTANES AT THE BOILING POINT Molecule n-Octane . 3-Ethylhexane . 2-Methylheptane . 2 : e-Dimethylhexane . 2-Methyl-3-ethylpentane .2 : z : 3-Trimethylpentane . 2 : 2 : 3 : 3-Tetramethylbutane . hIoIar Entropy of Vaporization (Cal./mole deg.) 20.96 20.9 I 20.5 5 20'34 20'2 I 20.08 19-92 this effect a spurious temperature coefficient may be introduced in hydro- carbon kinetics. For bimolecular collisions in butane the temperature coefficient of collision frequency from this cause would simulate an activation energy of about 600 cal., which is usually less than the experi- mental error. Some Consequences of the Coiling of Flexible Hydrocarbons for Reactivity.-The coiling of the n-paraffin molecules in the vapour phase can have a number of important effects on the reactivity of individual bonds. (a) STERIC EFFECTS.-on average, the end methyl groups in a poly- methylene chain will have not less than tw9 C-H bonds available for direct reactions such as the radical-forming process, I 1 I I I I I I 4 - H + X -+ XH + -C .. . where X is an atom or free radical, or for bond rearrangement reactions such as -C--H + C1, + HC1 + -C-Cl. In some of the crumpled configurations, intermediate CH, groups may have one or both -C-H bonds blocked owing to the coiling. It is true that the energy required in a collision in order to uncoil a molecule is not large. But the probability of uncoiling is small for geometrical reasons, except for end-onA. R. UBBELOHDE AND J. C. McCOUBREY 99 collisions. Furthermore, in the time required for uncoiling the collision energy' primarily transmitted to the paraffin will tend to be redistributed throughout the coupled vibrators.As a consequence, direct reactivity of the end groups immediately following a collision is sterically favoured in spite of the somewhat lower bonding energy of secondary and tertiary C-H bonds. This seems to be the explanation of " end attack " on n-paraffins, to which reference has been made in previous papers.12 It also appears to account for the higher steric factors which compensate for higher activation energies in relative reaction rates of primary', secondary and tertiary C-H with methyl radicals.13 Indirect reactivity which follows on the primary activating collision only after some redistribution of energy within the molecule does not necessarily favour the end groups, apart from a possible " organ-pipe " effect previously mentioned.1 It seems likely that uncoiling will in many cases precede sorption into capillaries of the molecular sieve type 14 and may influence the kinetics of sorption of flexible hydrocarbons.15 (b) POLARIZATION EFFECTS DUE TO CoILING.-Points previously dis- cussed need only be briefly summarized here. (i) Owing to coiling, the CHB groups form an environment akin to that of a solvent around certain bonds.This " smudges " quantum re- strictions on certain processes, such as the postulated peroxide radical formation in gaseous oxidation of hydrocarbons,l RCH2 + 0 2 + R-CH,-O-O-. gas gas When small, a single molecule formed from a binary collision would only have very short life unless it is stabilized by collision with a third body. But in the longer ut-paraffins crumpling and vibration coupling facilitates energy storage and the satisfying of quantum conditions by smudging the sharpness of the energy levels rather similarly to the smudging of quantum conditions in a liquid.(ii) Comparison of infra-red and Raman spectra of molecules in gas and in solution l 6 shows that a polarizable medium in the neighbourhood of the absorbing bond can markedly affect relative probabilities of excita- tion. Molecular coiling must to some extent produce this effect likewise, and can in consequence modify reactivity in certain hydrocarbon re- actions. (c) ENERGY TRANSFER AND MOLECULAR CoILING.-Though some of the effects discussed below refer to data which at present are rather frag- mentary, they are included on account of their experimental and theoretical interest.The transfer of a few quanta of rotational or vibrational energy does not necessarily follow the rules that apply for activation sufficient to produce reaction." It is nevertheless interesting to review informa tion on energy transfer as a function of the number of carbon atoms and flexibility of the molecule, and as a function of the structure of isomers. Two experi- mental techniques can give information. (a) ACOUSTIC MEASUREMENTS OF THE ADIABATIC C,/C, = y AS A FUNCTION OF FREQUENCY OF VIBRATIONS.-AS is well known, gases such as C02 and C2H, show relaxation effects when the frequency of the sound exceeds about 105 c./sec. This is attributed to restrictions on the transfer l2 Ref. (I) : cf. 2. Elektrochem., 1936, 42, 468. l3 Steacie, Darwent and Trost, Faraday SOC.Discussions, 1947, 2, 86, but see Trotman-Dickenson and Steacie, J.Chem. Physics, 1950, 18, 1097. l4 Barrer, Quart. Rev., 1949, 3, 293, Is Colloque sur E'Adsorptron et La Cinetique Heterogzne, Lyon, 1949. l6 E.g. Herzberg, I%fra-red and Raman Spectra of Polyatomic Molecules 1' CasteIIan and HuIburt, J . Chem. Physics, 1950, IS, 312. (Van Nostrand, 1945).I00 CONFIGURATION AND REACTIVITY of vibrational energy in molecular collisions. No evidence of any dis- persion regions of this kind have been found la for the molecules propane or n-hexane or cyclohexane up to 40 x I O ~ c./sec. Ultrasonic dispersion was found with ethane, benzene, and cyclopropane. Restrictions on the interconversion of translational and vibrational energy appear to be prominent for rigid molecules in which vibrations of low frequency are absent.At first sight the direct excitation of vibrational energy of a bond in a paraffin as a result of molecular impact should be subject to restrictions not very different in degree from those in ethane, where dispersion effects are observed. However, a flexible molecule can store some of the energy of collision in the form of torsional oscillations. These can subsequently be redistribhted within the spectrum of internal molecular vibrations, in accordance with the degree of coupling of these vibrations. As a result, the metrical conditions for the indirect activation of vibrational energy in molecular collisions can be much less rigorous than for non-flexible mole- cules. This may explain the distinction between ethane and hexane ob- served by' Lambert and Rowlinson, though further experimental data are desirable to test this suggestion.(b) MEASUREMENTS OF THERMAL CONDUCTIVITY K.-As has been pointed out previously la restrictions on the transfer of vibrational energy can be examined from thermal conductivity data. If the overall thermal conductivity of a gas is split into the terms referring respectively to the transport of translational, rotational and vibrational energy K = Ktram f Krot f Kvib ; then according to the Chapman-Enskog formula Ktram = 2.5 &trans and according to Eucken's hypothesis Krot = VCrot. If vibrational energy contributes without restrictions to heat transfer, Kvib = &vib. But in the extreme case, restrictions on the translational + vibrational process lead to the suppression of this term.The observed thermal con- ductivity may be expected to lie between the extreme values K(norestrictions) = 77(2*5ctram + Crot + Cvib) K(vibrationa1 restrictions) = 7)( 2'5ctrans + crot) - ce = ctrans -f- Crot + Cvib and Writing and the thermal conductivity will lie between the extreme values (referred to I mole in lieu of I g. where M is the mol. wt.), MKmxl~ = Ce + 1.5Ctrans = C, + 4.5, MKminlT = 2.5Ctrans + G o t = 10.5. Ctmm = G o t = 3R/2, Values of K and Cv are somewhat variable in quality but Table VI collects the information available. It illustrates the trend in normal paraffins with increasing number of carbon atoms. By comparing the last column with the values of M K / q i t will be seen that there is no evidence of any restricted transfer of vibrational energy in the thermal conductivity of the n-paraffins.There is in fact evidence, particularly for the higher paraffins, of a correlation such that the la Lambert and Rowlinson, Proc. Roy. Soc. A , 1950, 204, 424. l9 Ubbelohde, J . Ckem. Physics, 1935, 3, 219.A. R. UBBELOHDE AND J. C. McCOUBREY I 0 1 ' I hottest '' molecules translationally also contain more than the average vibrational energy since the experimental behaviour suggests . - where a > I. More reliable data are required to test this possibility, which could have important consequences for preferred energy transfer in the chain reactions of hydrocarbons.20 TABLE VI.-TEST OF RESTRICTIONS ON VIBRATIONAL ENERGY TRANSFER IN MOLECULAR COLLISIONS IN RELATION TO THERMAL CONDUCTIVITIES OF NORMAL PARAFFINS (GAS PHASE) Molecule CH, .C2H6 C,H8 - n-C4Hlo . n-C,H12 . n-C,H14 . ~so-C~H~O. M 16.032 30.048 58.080 58.080 72.096 86.112 44'044 (1) K x 1o6 7-2 I 3-60 3-22 3'32 3'12 2-96 4'36 ( 2 ) q x I@ 10'22 8.5 I 7'46 6.86 6-86 6-21 5.86 MKIrl) I 1-31 15'39 21.3 27'3 27'3 36.2 43'5 (6.34) 9'72 14-16 19-17 24'9 29'9 - -- co + 4'5 ( 10.84) I 3.2 18.6 24-2 29'4 34'4 - (I) At oo C : quoted by Partington, Advanced Treatise on Physical Chemistry. I (2) At oo C : from Schuil, Phil. Mag., 1939, 28, 679. (3) At oo C : calculated irom values of C, (Pitzer, Ind. Eng. Chem., 1944, 36, 829) and Berthelot's equation using values of p c and To quoted by Partington above). Other Collision Diameters in Relation to the Molecular Flexibility of Hydrocarbons.-Any molecular collision process can in principle be affected by molecular flexibility and the coiling of n-paraffins.According (Longmans, 1949)~ p. 893. TABLE V I I . 2 1 - E ~ ~ ~ ~ ~ ~ ~ ~ COLLISION DIAMETERS FOR QUENCHING Hg LINE (A2537 A) Molecule C3H8 - n-C,H,o ~ s o - C ~ H ~ ~ . n-C,H,, . iso-C6H1z . neo-C6H12 . 2-Methylpentane . 2 : 2-Dimethylbutane . n-C,H16 . n-C6H14 . u x 108 (cm.) I-- - 0.33 1-13 1-73 2-2 I 2-94 3'52 1-22 4.0 I 4'54 2'39 5'39 I to the process envisaged, the relative collision diameters of homologues and isomers may show a different sequence. Systematic studies are not at present very numerous. Optical studies give some information Zo Cf. Ubbelohde, ref. (I), p. 369. 21 Darwent, J. Chem. Physics, 1950, 18, 1532.I 0 2 CONFIGURATION AND REACTIVITY about ‘ I quenching diameters ” in fluorescence and about effective diameters for collisions of the second kind with excited atoms.Pressure broadening measurements on infra-red and micro-wave ab- sorption lines due to collision with paraffins does not at present appear *, to have been carried beyond C,. The effective diameters for the quenching emission from metastable molecules have been evaluated for a number of hydrocarbon homologues and isomers. Generally the effective diameter is larger for the isoparaffins, presumably’ owing to the greater proportion of secondary and especially tertiary C-H bonds, Bond rupture occurs in the quenching process, and collision diameters do not appear to depend primarily on the volume of the molecule but on a summation of the bonds present. Although no process appears to have been identified in general hydrocarbon reactivity which can be immedi- ately compared with this type of collision, the possibilities may arise in certain chemiluminescent reactions. DifPerence between Homo-molecular and Hetero -molecular Colli - sions.-Precise collision diameters depend on the degree of interpenetration of the molecules. Certain heteromolecular collisions show about the same collision diameter independent of the second molecule. Thus di-butyl- phthalate diffusing in air has u = 8-94 A, in H, CT = 9-4 A, and in f r e ~ n , ~ ~ u = 10.5 A. On the other hand when specific interaction is suspected, as for H, with C,H, distinctive effects are observed. TABLE VIII.-RATIO OF HOMO-MOLECULAR COLLISION DIAMETERS TO COLLISION DIAMETERS WITH H, -- I Molecule I Ratio -- I- (1’00) 1-34 1-57 1-70 1-83 This aspect of collision processes is under investigation for flexible molecules, in view of the special role of H, in certain hydrocarbon re- actions. 25 Department of Chemistry, Belfast. Queen’s University, a2 Coggeshall and Sair, -1. Chem. Physics, 1947, 15, 65 ; Bleaney and Penrose, 23 See also Darwent and Steacie, J . Chem. Physics, 1948, 16, 381. ,4 Birks and Bradley, Proc. Roy. SOC. A , 1949. 198, 226. 25 Cf. Small and Ubbelohde, J . Cham. Soc., 1950, 723. Proc. Physic. Soc., rg48, 60, 83.