SHOCK WAVES By H. 0. PRITCHARD SHOCK waves arise in air because a compressive disturbance can become more and more sudden as time goes on owing to the faster propagation of the high-pressure parts of the disturbance. Weak shock waves are produced by the clap of a hand or the crack of a whip; strong shock waves are equally familiar to us and are associated with for example thunder the motion of supersonic aircraft and projectiles and with explosions of all kinds. The way in which a shock wave builds up can be shown by consider- ing the motion of a wave in which the pressure variation is initially sinusoidal. We consider the disturbance entering a gas at the left-hand side of Fig. 1 and travelling towards the right. Any small pressure disturbance is propagated through the medium with the local velocity of sound and it is a property of any fluid that the velocity of sound increases with pressure.Thus the more intense parts of the disturbance will travel more quickly weaker parts so that the wave-form of the pressure variation as (CHEMISTRY DEPARTMENT UNIVERSITY OF MANCHESTER MANCHESTER 1 3) throughany point in the gas will be a distorted sine wave. This t b c 3 3 m w 4 than the it passes f i m r distonce FIG. 1 distortion increases until after a sufficient distance the high- and low- pressure disturbances arrive simultaneously i.e. the pressure rise becomes instantaneous; this is a shock wave. In fact all sound waves will degener- ate into small periodic shock waves after travelling a few hundred wave- lengths unless sufficiently attenuated by dissipative effects (i.e.diffusion and thermal conduction from the wave). Whilst this effect is of little practical concern a knowledge of the properties of shock waves is of crucial importance in other fields of technology most of them military; like several other techniques in physical chemistry the use of shock waves has filtered through as a by-product of military necessity. The shock tube The behaviour of shock waves is most conveniently studied by using a shock tube. The design of such tubes varies but one suitable for kinetic studies might consist of a metal tube about 6 in. in diameter and say 20 feet long. It is divided into a high-pressure and a low-pressure com- partment by a thin diaphragm (Fig. 2); this diaphragm may be of metal foil celluloid cellophane or some similar material depending on the 46 PRITCHARD SHOCK WAVES 47 High pressure Low pressure (dri v or) tion of the higher-pressure disturbance it becomes sharper until in the sixth profile we have a shock wave.This shock continues to travel along the tube in a uniform manner provided the internal walls of the tube are not too rough. At any instant during the experiment there are four distinct regions in which the local conditions differ very markedly. If we consider the final profile there are the two regions in which the gases are stationary and in the same condition as they were before the experiment started i.e. the as yet unexpanded driver gas at the extreme left and the as yet uncompressed See Payman and Shepherd Proc. Roy. SOC. 1946 A 186,293 for historical references. * White J. Fluid Mechanics 1958 4 585.48 QUARTERLY REVIEWS gas at the extreme right. These two regions may be characterised thermo- dynamically by their pressure density and temperature so that we have Pi(‘) pi(‘) Ti(‘) and Pi pi Ti respectively where the initial temperatures of the driver Ti(‘) and the driven gas Ti are usually the same. We then have a region to the left of the composition boundary which consists of expanded driver gas characterised by Pf(d) p P Tf(d). Finally there is the region which consists of gas which has been compressed characterised by P f pf Tf with Pf = Pf(d); this is the region in which we are interested. This gas has been suddenly compressed and its temperature has risen. The mag- nitude of the temperature rise can be calculated from the Rankine- Hugoniot relations,lPs which are a consequence of the fact that mass momentum and energy must be conserved across the shock front; i.e.if we consider a frame of reference which moves along with the shock front then the mass momentum and energy of the unshocked gas entering from the right must be the same as for the shocked gas leaving to the left. In essence where ,$ is the “pressure ratio” Pf/Pi and+ is a linear function of the average specific heat of the gas between the two temperatures Ti and Tf; in the case of a monatomic gas is independent of time and the pressure ratio 5 can be eliminated if the velocity V of the shock wave is known since v2=- PI t4 + 1 pi 4 - 1 For a weak shock (6 E l) V is only a little greater than the velocity of sound in the unshocked gas but for strong shocks ( f $ l) Vcan be several times the speed of sound and is usually described by a Mach number (i.e.a number of multiples of the velocity of sound in the unshocked gas). Thus if we know the specific-heat function #and the initial state Pi pi Ti of the unshocked gas we can calculate the final temperature if we measure the velocity Y of the shock wave; this is one use for the observation stations at the right-hand end of the tube in Fig. 2. The energy which causes the rise in temperature is derived from the energy of flow of the driver gas down the tube and anything which in- creases the speed of flow of the driver into the low-pressure section will result in a higher value of P&d) (and therefore 5) and consequently a bigger temperature rise. To some extent increasing the driver gas pressure is advantageous but it causes difficulties with diaphragm materials etc.The relevant equations are given in a number of places e.g. (a) Bleakney and Taub Rev. Mod. Phys. 1949 21 584; (b) Bleakney Weimer and Fletcher Rev. Sci. Inst. 1949 20 807; (c) Penney and Pike Rep. Progr. Phys. 1950 13 46 (d) Griffith and Bleakney Amer. J. Phys. 1954 22 597; (e) Hirschfelder Cuttiss and Bird “Molecular Theory of Gases and Liquids” Wiley New York 1954. PRITCHARD SHOCK WAVES 49 Increasing the actual velocity of the driver gas molecules is also useful so that hydrogen or helium is the most efficient driver and it is possible to gain a little extra by heating the driver gas to a high temperature before- hand; this can be done either physically (e.g. an electric heater inside the high-pressure chamber) or chemically (the ignition of a mixture of hydrogen and oxygen in the driver section has been used to initiate the flow4) Another device which roughly doubles the temperature rise is to allow the shock wave to be reflected at the right-hand closed end of the tube whereupon it then begins to move leftwards through the already shocked gas and raises its temperature again ; the quantitative interpretations of reflected shock studies are however open to some criti~ism.~ We can now see what considerations determine the size of the two compartments in a chemical shock tube.Owing to the non-ideal bursting of the diaphragm a good shock is not produced until the compression has moved several diameters down the tube. Then if we wish to study chemical reactions taking place in the hot zone behind the shock sufficient gas must be shock-heated so that the necessary observations can be made before the cold front arrives at the observation post.This determines the length of the low-pressure section and in consequence the driver section must be sufficiently long for the left-moving rarefaction wave not to be reflected back down the tube so as to interfere with the observations. The scope of shock-tube measurements If an inert gas say argon is shocked we have a sharp rise in the temperature pressure and density across the shock front and then a uniform region of hot gas. The discontinuity is very sharp and the distance between uniform unshocked gas and uniform shocked gas is only a few mean-free-paths; i.e. the shock front is only of the order of a micron 0 /O 20 Mach number FIG.4 thick. As the shock strength is increased the shock velocity and the temperature increase until at about Mach 10 the temperature is about 8000"~ (Fig. 4). For stronger shocks however the temperature tails off Resler Lin and Kantrowitz J . Appl. Phys. 1952 23 1390. Strehlow and Cohen J. Chem. Phys. 1959 30 257. 50 QUARTERLY REVIEWS because of the thermal ionisation of the argon atoms; at higher tempera- tures still doubly ionised atoms have been observed in thermal equilibrium with their surroundings. Thus the specific heat of the gas (and the function +) increases by successive steps as the successive ionisation processes become important. If the gas is diatomic other things can happen. Starting with a weak shock travelling only a little faster than sound we can observe effects due to the sort of processes which cause anomalous dispersion in sound waves e.g.rotational and vibrational relaxation. The gas is heated suddenly to a new temperature but it takes many collisions before the molecular rotation and vibration come to thermal equilibrium with the translational motion. Thus the gas behind the shock does not become uniform immediately and by measuring the thickness of this non-uniform region the rate of these equilibration processes can be inferred. At stronger shock strengths temperatures are reached where the diatomic molecule begins to dissociate; this is again a slow process and the rate can some- times be studied under suitable conditions. It may also be possible to study the further reactions of these atoms once they have been produced.At higher temperatures still ionisation again occurs and even this is a slow process; however although rates of ionisation (about 1 psec. at 1 cm. pressure) and recombination have been measured4y6 these are not quantities which have yet found their way into chemical thinking. In addition there is radiation of energy from the shocked gas at most temperatures so that spectral information can be obtained. Shock-tube instrumentation Apart from the obvious pressure-measuring and pumping equipment most of the instrumentation is concerned with the detection of the shock wave the measurement of its velocity and following the variations behind it. If the shock front can be detected and its arrival at the observation post converted into an electrical pulse then the measurement of the velocity simply reduces to the need for a suitable device to time the progress between two adjacent stations.Since the velocity of the shock front is of the order of lo5 cm./sec. and the two observation stations may be 10 cm. apart we have to time an interval of about lo-* sec.; thus to obtain the velocity to better than 1 % needs sub-microsecond electronic techniques. One interesting technique for strong shocks and blast waves is to direct 3 cm. radar waves upstream at the approaching shock and measure the Doppler change in frequency of those waves reflected back by the ions in the shock front.' There are a great variety of methods available for the detection of the arrival of the shock front; they depend on observing the sharp change ' (a) Niblett and Blackinan J. Fluid Mechanics 1958 4 194; (b) Manheimer-Timnat and LOW J.Fluid Mechanics 1959 6 449; (c) Lamb and Lin J. Appl. Phys. 1957 28 754; (d) Toennies and Greene J. Chern. Phys. 1957,26,655. Cook Doran and Morris J. Appl. Phys. 1955 26,426. PRITCHARD SHOCK WAVES 51 in temperature pressure density or in strong shocks conductivity associated with the shock. The detection of a change in electrical conduct- ivity can be particularly simple requiring only a couple of electrodes with a potential across them and a suitable amplifier ;8 automobile sparking plugs can even be used. The method works down to temperatures of 700”~ where there should be no thermal ionisation but the reason for this is not known.9 On the other hand the measurement of the temperature change across the shock is not easy but thin films of platinum or gold sputtered on a Pyrex surface have been used as resistance thermometers;1° the particular thermometers described have time lags of less than 1 psec.Nor is the measurement of the pressure change particularly easy but piezoelectric microphones hot-wire anemometers and mechanical pressure switches have been successfully used. Most of the methods of detection (and measurement) make use of the change in density. There are two optical techniques which give essentially direct pictures of the shock front-the shadowgraph and the schlieren method. In the former method all that is necessary is to trigger an intense flash of light as the shock passes the observation post; the light is colli- mated so as to be parallel when passing through the shock tube and then falls directly on a photographic plate.A shadow is cast by those regions in which the optical depth (i.e. density) has a non-zero second derivative in the plane perpendicular to the light beam.ll In the schlieren method the light from the triggered flash is focused on a second slit after passing through the shock tube and then into a camera; if there are regions in the optical path in which the optical depth (density) has a non-zero first derivative,ll light will be deviated from the observation slit and so cause a shadow to be cast on the photographic record. These two techniques give good qualitative representations of the density change in the shock wave but are of little use for quantitative purposes. However with a third optical technique it is possible to measure the actual change in density across the shock this is the Mach-Zehnder interferometer.12 In this case the light from the triggered spark is collimated and then split into two parallel beams by use of half-silvered mirrors; half the light passes through the shock tube and half through a dummy sample of the un- shocked gas.The two beams are then recombined and interference fringes are obtained. When the density in the shock tube changes the fringes will move and the position of the shock front is therefore indicated by a sharp discontinuity in the fringes. If the beam is off-set so as to make an angle of 1” or 2” with the shock front the discontinuity is spread out and it is * Knight and Duff Rev. Sci. Inst. 1955,26 257. lo (a) Blackman J. Fluid Mechanics 1956,1 61 ; (b) Rabinowicz Jessey and Burtsch l1 Liepmann and Puckett “Introduction to the Aerodynamics of a Compressible l2 Winckler Rev.Sci. Znst. 1948,19,307; Curtiss Emrich and Mack Rev. Sci. Inst. Manheimer and Nahmani Rev. Sci. Inst. 1956,27 174. J. Appl. Phys. 1956 27 97. Fluid” Wiley New York 1947. 1954 25 679. 52 QUARTERLY REVLEWS possible to trace the individual fringes through the shock thus giving an absolute measure of the change in density. Excellent examples of photo- graphs taken by all these three techniques are given in refs. 3(a) 3(6) and 3(4 and in many of the other references quoted in this Review. Another important method of measuring density changes was developed in the study of detonation waves.13 This depends on the change in attenua- tion of X-rays by a gas as the density changes and by using a triggered X-ray flash it is possible14 to measure the ratio of the densities on the two sides of the shock to about &l%.All these methods work with transparent gases. Clearly if the shocked gas is coloured e.g. a halogen relatively simple photometric methods will work; these howeverd will be discussed in relation to the particular problem involved. Spectra and shock waves Since very high temperatures can be attained in strong shocks molecular fragments may be formed in states of high excitation and they will then emit radiation as they fall back to the ground state. For example strong shocks in methane and ammonia emit the spectra of C2 and CN presum- ably formed via C and N atoms.15 If fine dusts (e.g. MgO A120,) are present in the tube even quite moderate shocks (2000"~) will excite the diatomic molecular spectra but much stronger shocks are usually required before the atomic lines appear;le such spectra are of interest for comparison with the emission of meteoric dusts.Quite often spectra are produced from trace impurities in the shocked gas for example strong shocks in argon or krypton have been known to give the Swan bands of carbon and the spectra of CN Hg Ca and Na; the mercury lines appear at a later time than the C2 or CN bands indicating that electronic excitation of mercury atoms by collision is a relatively slow process.17 The sodium-atom spectrum is fairly easily excited and the emission has been used to measure the temperature as a check on the shock-tube equations for the temperature rise.l* In very strong shocks e.g. argon at 18,000"~ the atomic lines suffer broadening and a red shift due to the perturbation of neighbouring ions and e1ectr0ns.l~ Strong shocks in the inert gases also give rise to a continuous spectrum which is emitted after an induction period of some tens of microseconds.This induction period is temperature dependent and in the case of xenon the temperature coefficient over the range 6000-1 1 ,OOO"K corresponds Is Kistiakowsky and Kydd J. Chem. Phys. 1956,25 824. l4 Knight and Venable Rev. Sci. Inst. 1958 29 92. l6 Charatis Doherty and Wilkerson J. Chem. Phys. 1957 27 1415. l6 Nicholls and Parkinson J. Chem. Phys. 1957 26 423. 17 Turner and Rose Phys. Rev. 1955,99,633 ; Rose quoted in Clouston and Gaydon 18 (a) Losev Proc. Acad. Sci. (U.S.S.R.) Phys. Chem. Sect. 1959 120 467; (6) 19 Petschek Rose Glick Kane and Kantrowitz J.Appl. Phys. 1955 26 83. Spectrochim. Acta. 1959 14 56. Clouston Gaydon and Glass Proc. Roy. SOC. 1958 A 248,429. PRITCHARD SHOCK WAVES 53 to an activation energy of 8.3 ev which is the excitation potential of one of the excited states of the xenon atom. These observations are interpreted20 to mean that the Xe atom is excited by collision to Xe*(5s25p56s) and that a stable excited state of Xe is formed by the reaction Xe*+Xe-+Xe,*; this then falls back to its ground state Xe which is repulsive and consequently the radiation emitted must be continuous. The same phenomenon occurs in argon but the excited state is more than 11 ev above the ground state. A continuous spectrum is also emitted from shocks in bromine between 1300" and 2300"~ at pressures of 1-2 atm.21 This arises from a two-body recombination of bromine atoms; no radiation is observed which arises from the normal three-body recombination.Two processes i.e. Br(2P,,2) + Br(2P,,2) and Br(2P,,& + Br(2P3,2) appear to be important; they lead to the formation of excited states of the bromine molecule and these emit continuous radiation in falling back to the ground state. A study of the temperature coefficient of the emission at various wavelengths leads to some information on the actual form of the potential-energy curves for these excited states. Emission however is not confined to the visible and the ultraviolet region. Radiation has been observed in the infrared but measurements are much more difficult because of the lack of suitably fast infrared detectors.However with a lead sulphide detector of 30 psec. response time the infrared emission of the 2-2-0 band in CO has been studied at 2 ~ 3 5 p . ~ ~ The emission builds up rather slowly in pure CO (relaxation time of 77 psec. at 0.24 atm. and 1470"~) but it is not possible because of the experimental difficulties to decide whether the excitation takes place directly i.e. v=0+2 or stepwise i.e. v=0+1-+2. As is common to many of these relaxation processes there is a considerable acceleration by traces of water. Spectral measurements on shocked gases can also be made in absorption. For example air in the range 2000-6000"~ shows the Schumann-Runge bands in abs~rption,~~ and at the higher temperature can be shown to contain about 5 % of NO.24 Shocks in hydrocarbon-oxygen mixtures exhibit absorption corresponding to C and CH for the first 30 psec.but after this only the absorption spectrum of OH persists; on the other hand in shocks using oxygenated compounds e.g. acetaldehyde the C2 and CH spectra do not appear until after the OH has di~appeared.,~ Such obser- vations will help in the interpretation of combustion and explosion processes; clearly they are complementary to the study of spectra in flame gases and explosion products. 2o Roth and Gloersen J. Chem. Phys. 1958 29 820. 21 Palmer J. Chem. Phys. 1957 26 648. 28 Wurster Treanor and Glick J. Chem. Phys. 1958 29 250. e4 Wurster and Glick J . Chem. Phys. 1957,27 1218. l5 Campbell and Johnson J. Chem. Phys. 1957,27 316. Windsor Davidson and Taylor J. Chem. Phys. 1957 27 315. 54 QUARTERLY REVIEWS Vibrational and rotational relaxation in shock waves As mentioned earlier it is possible to study relaxation processes by measuring the thickness of the shock front.In light diatomic molecules the conversion of translational energy into rotational energy may be observed ; in more complicated molecules the equilibration between translational and vibrational energy is important in the shock front. If the rotations were not easily excited the density profile across the shock would be represented by curve 1 in Fig. 5. On the other hand if the Dittonee FIG. 5 rotations take up their energy immediately we have a larger specific heat; thus the temperature rise is not so great and so for the same pressure ratio there is a greater increase in density as in curve 3. In diatomic molecules the rotations come to thermal equilibrium in less than 150 collisions and the density profile is represented by curve 2; we have an initial rise in density similar to that in curve 1 followed by a gradual cooling i.e.a further gradual increase in density until the final state represented by curve 3 is reached. The same happens in the case of vibrational equilibration. In both processes the shock front or region of non-uniform density becomes extended and in the case of vibrational relaxation in very weak shocks may even extend over the better part of a centimetre.26 Three methods have been used to measure the thickness of the front. If it is reasonably thick then the standard interference fringe method can be ~ ~ e d ~ ~ ~ * ~ ~ p ~ ~ with the light beam of course being exactly per- pendicular to the motion of the shock.The second method which has been used fairly extensively is to measure the reflection of a light beam projected at grazing angle to the shock front;28 in the steady state no light is reflected into the detector (apart from some scattering) but there is substantial scattering by the shock front and the duration of this reflection pulse together with the known speed of the shock gives the thickness. The third method which has been used at low densities makes use of the attenuation of an electron beam directed across the tube.29 26 Griffith and Kenny J. Fluid Mechanics 1957 3 286. e7(4Griffith Brickl and Blackman Phys. Rev. 1956 102 1209; (b) Smiley Wider and Slawsky J. Chem. Phys. 1952,20,923; 1954,22 2018. z8 Greene Cowan and Hornig J. Chem. Phys. 1951 19 427; Greene and Hornig ibid.1953,21,617; Anderson and Hornig ibid. 1956,24,767. 29 Ballad and Venable Physics of Fluids 1958 1 225. PRITCHARD SHOCK WAVES 55 The results obtained by these methods are in general agreement with those obtained by other measurements i.e. ultrasonic dispersion pro- jectile studies and impact or pitot-tube measurements. Rotational relaxa- tion in hydrogen takes about 150 collisions and less in other molecules e.g. about 20 collisions in nitrogen or oxygen. Vibrational relaxation in simple molecules is very slow e.g. many thousands of collisions in N, 0, CO, N,O etc. but relatively fast in more complex molecules such as CH or CF2C12. Again the well-known catalytic effect of water is found but it is suggested27a that this effect is confined to bending modes of vibration only; it has long been thought that relaxation occurs via the lowest vibrational mode in the molecule and this would seem to fit in with that idea.Chemical reactions in shock waves The problem of studying a chemical reaction in a shock wave is in general one stage more difficult than the experiments so far described. It is not sufficient just to study the density change; it is necessary to follow the fate of one individual species in the shocked gas and except in the special cases of molecules with relatively intense absorption spectra this is very difficult indeed. One of the earliest reactions to be studied by light absorption was the thermal decomposition N,04+2N0 ;30 this reaction had previously been investigated by ultrasonic dispersion measurements. The shocked gas consisted of a mixture of N2 at 1 atm.containing about 1 % of N204. Although pure N204 could in principle be used admixture with a large excess of a permanent gas means that the shock is moving through an almost perfect gas and this is more convenient because the shock-tube equations in their simplest form apply to perfect gases; the properties of shocks in nitrogen are readily calculable and the presence of 1% of N204 causes only minor corrections to the expected temperature rise. When 2 atm. of N was used as the driver a shock of Mach 1.12 was obtained giving a temperature rise of about 25". The light absorption was measured with a photomultiplier using mercury radiation at about 4000 A. In order to get a reasonable signal to noise ratio it was necessary to use a beam of 1 mm.width and this sets a lower limit on the time resolution attainable at Mach 1 the shock passes a 1 mm. beam in about 3 psec. so that any processes taking place in less than 3 psec. are not observable. As the N,04 is heated its vibrations are excited very quickly and then it begins to dissociate to NO which is coloured and causes a response on the photomultiplier. Above 30°c this rate of dissociation is too fast to measure and the whole shock tube was cooled to -35"c before the beginning of each experiment then over the range of about 20" either side of O"c it was possible to follow the appearance of NO2 over a time measured in a few tens of microseconds. The rate of dissociation was given by k[N,O,] [NJ 9o Carrington and Davidson J. Phys. Chem. 1953,57,418. 56 QUARTERLY REVIEWS with an activation energy of 11.0&0-6 kcal./mole the dissociation energy of N,O is 13 kcal./mole but as we shall see it is common in kinetic dissociation measurements for the activation energy to be rather less than the heat of the reaction.The rate of this dissociation has since been con- firmed by expansion of N,O at a supersonic The dissociation of halogen molecules has been studied by very similar techniques. Iodine,32 for example in high dilution with inert gases dissociates at a convenient rate in the temperature range 1000-1600"~ the rate of dissociation being measured by the decrease in light absorption. The change in light absorption at an observation station as shown on an oscilloscope is represented diagrammatically in Fig. 6. The current before ZQfO ~bsorption t i m e - FIG.6 the shock is determined by the initial I concentration; as the shock arrives the absorption rises sharply owing to the compression of the gas and thereafter begins to fall relatively slowly as the iodine molecules dissociate the rate of dissociation being determined from the initial slope 8. The problem however is not quite as simple as this. The absorption coefficient of any molecule is temperature dependent and it is therefore necessary to measure the variation of absorption with temperature; this can be done by conventional methods at relatively low temperatures but the necessary high-temperature coefficients are obtained from the shock tube traces on the (reasonably valid) assumption that the iodine comes to vibrational equilibrium with its surroundings before it begins to dissociate.In addition allowance has to be made for the fact that as the gas dissociates it cools giving rise to an increase in density and so an increase in absorption; at high I concentrations this can more than offset the decrease due to the reduction in the number of absorbing molecules.33 A correction has also to be made for the contraction which occurs in the time scale at some instant after the shock has passed we are observing a body of gas which was heated not when the shock passed the slit system but at some earlier s1 Wegener Marte and Thiele J. Aeronautical Sciences 1958 25 205; Wegener J . Chem. Phys. 1958,28 724. 32 Britton Davidson and Schott Discuss. Faraday Soc. 1954 17 5 8 ; Britton Davidson Gehman and Schott J. Chem. Phys. 1956,25,804 39 Palmer and Hornig J.Chem. Phys. 1957,26,98, PRITCHARD SHOCK WAVES 57 time because the gas is moving very rapidly along the tube behind the shock; thus gas which was heated about 600 psec. previously will show up on the oscilloscope trace only about 200 psec. after the shock has passed. The initial rate of dissociation is given by where kA is the rate constant for dissociation by collision with argon and k~~ is that for dissociation by collision with another iodine molecule; extrapolation to zero [I,] gives k~ and k1,. As is to be expected from our previous knowledge of collision efficiencies (flash photolysis and other kinetic energy-transfer studies) collisions with iodine are more effective in bringing about dissociation than are collisions with argon. Other gases can be used as diluents and their relative efficiencies measured.The activation energy for the dissociation of iodine comes out to be rather (about 4 kcal.) less than the dissociation energy. Similar measurements have been made on b r ~ m i n e ~ ~ ’ ~ ~ and again the activation energy (31 kcal.) for dissociation is substantially less than the dissociation energy (45 kcal.) ; oxygen also shows this type of behaviour the rate of dissociation being 150 times the maximum rate it could have if the activation energy were equal to the endothermicity.lsa This phenomenon of dissociation with less activation energy than the heat of the reaction appears to be quite common and one suggestion is that the energy of activation need not be solely concentrated in the molecular vibration for the dissociation to take place,33 i.e.some molecules can dissociate by rotation. If we don’t specify any particular energy division the probability that we will find an iodine molecule after a collision with an argon atom having the dissociation energy D concentrated in a specified number n of “effective oscillators” is n-1 e-D/RT A ( 2)‘ 1 RT r=0 \ ’ (2 rotations 1 effective oscillator). The Arrhenius temperature depend- ence of an expression like this is substantially lower than D if n is at all appreciable; in the simple collision we have considered n is very limited but if we consider collisions between pairs of diatomic molecules and allow all their degrees of freedom to contribute to the dissociation of one of them then there is more latitude. Even so it is necessary to strain somewhat the number of important vibrations and rotations in order to get numerical agreement with experiment.An alternative approach to the problem is to consider the mechanism of the reverse reaction i.e. the recombination of the atoms. These have been studied by flash photolysis at lower temperatures and have been shown to have negative temperature coefficients. If we take the shock-wave 84 Britton and Davidson J. Chem. Phys. 1956 25 810. 58 QUARTERLY REVIEWS data and assume a reversible system then the ratio of the forward and reverse rate constants is the equilibrium constant of the reaction and the heat of the reaction is the difference between the two activation energies; since E for dissociation is less than D then E for combination must be negative. However the value obtained from shock measurements at high temperatures is much more negative than that obtained at low tempera- tures from flash photolysis (see Fig.7). The observed activation energy is moo 500 33.3 250 JtK) R G . 7 the difference in average energy between those molecules which react and all those which are present in the system; therefore the meaning of a negative activation energy is that those molecules which react have a lower average energy than the average energy of all the molecules in the system. In a reaction I + I + M -+ I + M the third body M has to carry some energy away to bring the relative I + I energy below the dissociation limit; thus the more energetic the collision between I + I the more energy M must take away. But M is much more likely to take away only a small amount of energy than a large amount.If we make the very simple assumption that M can only take away very small amounts of energy then the average energy of the reacting I atoms is approximately zero; on the other hand the average energy of all the I atoms is RT i.e. 4 kcal. at 2000°K and 1 kcal. at 500"~-hence E at 2000°K is about -4 kcal. and at 500°K about -1 kcal. The Arrhenius curve for such a system has the shape of the broken line in Fig. 7 which is in qualitative agreement with the experimental results but the predicted activation energies are rather especially in the bromine case. We see that neither theoretical approach to this problem is really satisfactory and there is considerable scope for further investigation both in its theoretical and its experimental aspects. Several other dissociation reactions have been investigated directly by light absorption e.g.the dissociation of N205 to NO + of NO2 35 Husain and Pritchard J. Chem. Phys. 1959 30 1 101. 38 Schott and Davidson J. Amer. Chem. Soc. 1958,80 1841. PRITCHARD SHOCK WAVES 59 to NO and 0,37 and of 0 into 0 and O;38 in all these three studies data were also accumulated on some of the subsequent reactions of the dissocia- tion products (e.g. NO2 + NO -+ NO + NO + 0,; NO + NO -+ 2N0 + 0,; NO + 0 +NO + 0,; 0 + 0 -+ 2Ob. In many cases it may not be convenient to study a dissociation reaction by light absorption but nevertheless there are ways in which some relevant information can be obtained. For example it is possible to measure the heat of dissociation as opposed to the activation energy. If the shock is strong enough to dissociate all the molecules then the dissociation energy becomes part of the specific heat function 4 and thereby affects the shock velocity.Thus by measuring the effect of the dissociating gas on the velocity of shocks in say argon one can calculate the contribution the dissociation makes to the high-temperature specific heat and so get the dissociation energy. This has been done for F, N, and CO where the accepted values have been in doubt until recently and values of - 31,39 - 225,6d and - 2566d940 kcal. respectively were obtained. Alternatively one may quench the shock and analyse the products by standard chemical methods. This can be done simply by allowing the shock to expand into a large vessel at the end of the shock tube or better after a sufficient reaction time opening the tube up to a very large evacuated tank by bursting a second diaphragm thereby quenching the reaction by an expansion wave.This method has been used in the study of the pyrolysis of simple hydrocarbons; it has been found that methane cracks with an activation energy of about 101 k ~ a l . ~ 1 (ie. CH -+ CH + H D M 102 kcal.) and also that some curious molecular reactions take place fairly easily,42 e.g. 2C,H2 -+ C,H + H (E E 30 kcal.) and 2CH4 -+ C2H6 + H,. Also in reflected shocks the method has been used in the study of the reaction N + 0 + 2N0 at high temperatures., It appears that the reac- tion is a chain reaction ; oxygen having much the lower dissociation energy decomposes into atoms and the rate-determining step is 0 + N -+ NO + N; this reaction has an activation energy of about 74 -+ 5 kcal.compared with the endothermicity of about 76 kcal. at 2500"~. This technique of shocking a mixture of gases one of which has a much lower dissociation energy than the other lends itself to the study of atomic reactions and has been used to study the reaction Br + H2 by using bromine-hydrogen mixtures., Similarly in using hydrogen-oxygen mixtures,45 the hydrogen dissociation predominates and it is possible to follow the rate of formation of OH radicals by the reaction H + 0 -+ OH . 37 Huffman and Davidson personal communication. 38 Jones and Davidson personal communication. 39 Wray and Hornig J. Chem. Phys. 1956,24 1271. 40 Knight and Pink J. Chern. Phys. 1958 29 449. 41 Skinner and Ruehrwein J. Phys. Chem. 1959,63 1736. 42 Greene Taylor and Patterson J.Phys. Chem. 1958 62 238. 43 Glick Klein and Squire J. Chem. Phys. 1957 27 850. 44 Britton and Davidson J. Chem. Phys. 1955 23 2461. 45 Schott and 'ECinsey J. Chem. Phys. 1958,29 1177. 60 QUARTERLY REVIEWS + 0. There is an induction period before the radicals are detected but this is not an induction period in the true sense the concentration of radicals is followed by their ultraviolet absorption and it takes time for this concentra- tion to build up to 1 x mole/l. which is the minimum detectable; from the subsequent build-up the activation energy for H atom attack on oxygen molecules was found to be 17 kcal. The close relation of this experiment to detonation studies need hardly be emphasised. Although it is possible as we have seen to study a number of chemical reactions some of which cannot be investigated by other methods or alternatively can only be observed in some other temperature range yet these experiments are fairly tedious and subject to considerable in- accuracies.For one thing it is not easy to estimate concentrations very precisely from cathode-ray tube traces and the mainly electronic problem of time resolution is aggravated somewhat by the time contraction which occurs. Mention has already been made of the variation of spectral absorp- tion coefficients with temperature and the cooling effect the reaction may have if it is dissociative. In addition suppose that it is possible to measure the shock velocity to 1 % which is about as good as can be expected the temperature rise depends roughly on the square of the velocity i.e.we have an uncertainty of about 2% which on a temperature rise of 1500” is &30”. This makes the temperature scale for activation energy plots a little less precise and in some such experiment as say the reaction of H with 02 the calculated H atom concentration is subject to significant un- certainty. Finally mention should be made of the simple physical difficulty of making a large metal shock tube vacuum-tight and the length of time it takes to pump it out to say mm. before each experiment can begin. These limitations however have not prevented the accumulation of a substantial body of important information. Other applications of shock waves So far in this Review our attention has been confined to shock waves in gases. Shocks can also be propagated through liquids and solids and have been used to measure compressibilities and derive equations of state.One of the more interesting chemical aspects of shocks in solids is the possibility of so compressing a non-metallic solid that it becomes metallic -for example at shock pressures of 250,000 atm. phosphorus shows an electrical conductivity characteristic of a metal ;46 a similar observation has been made with sulphur.47 A further application of shock waves in solids is in the production of what are known as “tactical” nuclear weapons. An amount of fissionable material which is less than the critical mass is surrounded with a shell of trinitrotoluene. When the conventional explosive is detonated a shock wave moves towards the centre of the 48 Alder and Christian Discuss. Faraday SOC. 1956 22,441.47 David and Hamann J. Chem. Phys. 1958 28 1006. PRITCHARD SHOCK WAVES 61 system and compresses the fissionable material above its critical density so causing a sub-critical amount of material to explode.48 Mention has already been made of the crucial importance of a knowledge of the behaviour of shocks caused by supersonic aircraft and rocket nose- cones and of the importance of knowing how hot (and how corroded) the structure will become as a result of its interaction with the hot nitrogen and oxygen ions or atoms which are produced.49 Other war-time studies were concerned with the effect of blast waves on buildings and upon animal and human life-for example to find out what sort of shock pressures cause the collapse of an ear-drum or hzmorrhage of the In astrophysics the coalescence of masses of interstellar gas appears to lead to shock waves and it is possible that solar flares are some sort of shock phenomenon; an attempt has been made to explain the difference in electronic and kinetic temperatures of the sun in such terms.50 Finally mention should be made of the field of magnetohydrodynarnics and the production of very strong shocks.Supposing we have a glass tube with a single-turn copper coil around it,6a and discharge a suitable con- denser through the coil. A rapidly varying magnetic field is produced (dH/dt E 70,000 gauss/psec.) and this induces an electric field which is intense enough to ionise the gas inside the tube. The resulting current of ions is then accelerated by the intense magnetic field to very high velocities up to about Mach 90 in the experiment quoted.The production of these very high Mach numbers leads to the possibility of thermonuclear fusion reactions taking place in a shock tube. Attempts are being made to reach temperatures of several million degrees in this kind of way by producing an ionised gas (plasma) and subjecting it to an intense magnetic shock. One of the technical problems involved is to get a sufficiently fast build-up of the magnetic field say to 1500 gauss in 0.2 psec. ; this requires electrical circuits of sufficiently low impedance for the current to build up at the rate of lo6 amp./psec. or more. These and other related problems are discussed in the first few papers of the Conference on Extremely High Temperatures held in Boston in March 1 958.51 48 Pauling “No More War!” Dodd Mead New York 1958. 49 Hertzberg Jet Propulsion 1956 26 549. 6o Sen Phys. Rev. 1953 92 861. 51 Fischer and Mansur (editors) Conference on Extreme:y High Temperatures Wiley New York 1958.