Determination of the Number of Separated Ion Pairs Produced in the Irradiation of a Liquid BY A. 0. ALLEN AND ANDIUES HUMMEL Chemistry Dept., Brookhaven National Laboratory, Upton, L.I., New York, U.S.A. Received 4th June, 1963 The degree of ionization of irradiated hexane in the absence of an applied field has been studied by means of determinations of the electrical conductivity in extremely low fields at known radiation intensities, and of the ionic mobilities. The number of separated ion pairs formed by 1.5 MeV X-rays is 0.09 per 1OOeV absorbed by the hexane, with a probable uncertainty of 50 %. This low value indicates that practically all sub-excitation electrons are captured by their parent positive ions before they can escape into the bulk of the liquid. The electrical conductivity of irradiated liquids has been much studied.The curve of current against voltage bends over with increasing voltage as in an irradi- ated gas, but instead of approaching a saturation value, the current in liquid continues to increase until breakdown occurs at very high voltages. Most interest has been in the high-voltage region in which the applied field is apparently interfering with the normal process of initial recombination. Mohler and Taylor 1 studied the curve for carbon disulphide and extrapolated the data from moderately high field strength to infinite voltage, obtaining a total ion yield approximately equal to that determined from the saturation current in carbon disulphide vapour. Of perhaps more interest is the number of ions set free by irradiation of a liquid in the absence of an applied field.This number does not appear to have been determined. Its value should offer a clue to the important question of how many subexcitation electrons are able to escape primary recombination with positive ions in the liquid. The present paper presents data on this point for liquid hexane irradiated with hard X-rays generated at 1500 kV. PRINCIPLE OF THE METHOD The method essentially makes use of the limiting conductivity of the irradiated liquid at zero voltage, i.e., the initial slope of the current-voltage curve, which is linear as long as the current is so low that the number of ions going to the elec- trodes is very small compared to the number which are formed by the irradiation and disappear by general volume recombination.Under these conditions, the conductivity is equal to the ionic concentration multiplied by the mobility, whence icL/VS = uC, where C is the number of ions of either sign per cubic centimetre, u = zc+ + 1 ~ - is the sum of the mobilities of the positive and negative ions, ic the current in the conductivity cell expressed in ions/sec (=A x 6.24 x 1018), V the applied voltage, L the distance between the parallel electrodes and S their area. At steady state the rate of ion generation equals the rate of ion disappearance by volume recombination : IG/100 = kC2, (2) 9596 NUMBER OF SEPARATED ION PAIRS where I is the dose rate in eV cm-3, G = lOO/W is the number of ions of either sign formed per 100eV of energy dissipated in the liquid by the X-rays, and k is the ion recombination coefficient in cm3/ion-sec.From (1) and (2), we find G kizL2 100 I u v2s2' -=- (3) To evaluate k/u, the rate of decrease of the current is determined when the irradi- ation is suddenly interrupted ; then - dC/dt = kC2. Integrating and substituting from (1) : 1 1 kL - - - + - t , - i, i," uVS (4) where i: is the steady-state current. the target current it in the X-ray generator, to which it is proportional : Experimentally, the dose rate is monitored by I = ai,. ( 5 ) Determination of the ion yield G then requires four separate determinations: (i) a dosimetry measurement to determine a ; (ii) a determination of the drift mobility of the ions, us and u- ; (iii) a determination of ic as a function of I and V-if the as- sumptions are correct, ic should be exactly proportional to Y and Z* ; (iv) determin- ation of the rate of current decay when the X-ray beam is suddenly interrupted -if the assumptions are correct, this rate should be exactly second-order.EXPERIMENTAL ION MOBfLITIES Hexane is distilled into a glass cell, the upper end of which consists of a thin plate of beryllium, 2-2cmdiam., cemented to the glass. Parallel to this is a platinum electrode, which is split into a central circle, 1-5 cm diam., and a 0.25-cm guard ring. A metal bellows, sealed to the glass, allows the interplate distance to be varied between 0.5 and 3 cm. The cell is placed with the beryllium plate beneath the beryllium window of a Picker X-ray machine, which is run at its lowest feasible peak voltage, about 6 kV.Ionization of the hexane is thus confined to a region within about 2 mm of the beryllium plate. In operation, the X-rays are turned on for a brief time. Then actuation of a relay switches off the X-rays ; applies a potential, which may be adjusted from 100 to 2000 V positive or negative, to the beryllium plate ; and simultaneously triggers an oscilloscope which is arranged to respond to the current passing between the beryllium electrode and the lower, grounded, electrode. Fig. 1 shows typical oscilloscope tracings of the current as a function of time. Theoretically, one expects an initial surge, composed of a charging current. due to the capacitance of the cell, and an ion current generated as the ions of opposite sign to the charge on the beryllium are drawn to that electrode.The surge quickly dies away as all these ions disappear by neutralization at the electrode or by recombination. A layer of ions of the other sign will be left, and will slowly drift in the field toward the lower electrode. A constant drift current should then appear, which should begin to decrease and tail off to zero as the ions reach the electrode? The quantity measured is the average drift time required for the ions to reach the lower electrode ; the mobility is equal to the distance from the ionized region to the lower electrode, divided by the average drift time and by the field strength. In practice, the surge quickly dies down as expected, but the drift current is not constant ; it rises with time to a maximum betore tailing off.We do not understand the reason for this maximum. The average drift time is taken as the time from application of the voltage to the time of the last inflection point. These times are reproducible to f5 %; and they are within this same precision inversely proportional to the applied field, when the interelectrode distance is held constant. Since we do not understand the cause of the maximum in the current, the absolute significance of these drift times might be questioned. However, we haveFIG. 1 .-Typical oscilloscope traces of current against time in ion mobility measurement. Positive ions, L = 1.1 cm. Top, V = 1000, time-scale (left to right), 0.5 sec per division ; time to inflection [To face page 96. point, 2-6 sec. Below, V = 500, 1 sec per division, time to inflection point, 5.0 sec.A .0. ALLEN A N D A . HUMMEL 97 also changed the interplate spacing, and calculated the mobility by dividing the diflerence in the interplate spacing by the diflerence in the times to reach the inflection point, when the field strength in V/cm was the same. This difference method would seen1 to reduce the absolute uncertainties involved. The difference method, however, gave the same results for the mobility (within f5 %) as the use of the absolute time to attain the inflection point. CONDUCTIVITY MEASUREMENTS The radiation source was a Van de Graaff electron accelerator ; the X-rays were generated at 1500 kV on a gold target. Most of the conductivity data were obtained either with the same cell used for the mobility determination, or with another parallel-plate cell with adjust- able interplate distance, the electrodes being of aluminium.Currents through the cell, which were generally 10-13-10-12 A, were read by a Cary vibrating reed electrometer, using a calibrated lOlo-ohm resistor. The electrometer was shielded from radiation by lead bricks. The output of the electrometer was read on a millivoltmeter, a recorder or an oscilloscope. Either of the latter two could be used to follow the decay of the cell current with time when the radiation was interrupted, while the voltage across the cell was maintained. Instantaneous interruption of the electron beam in our generator is accomplished by application of a small potential to an appropriate point within the electron gun, which stops the beam at its source.Dosimetry was done in three ways. (i) Ampoules of ferrous sulphate were placed within the cell, and the oxidation rate determined as a function of target current. This method was feasible only for intensities orders of magnitude higher than those used in most of the hexane work. (ii) The cell with A1 electrodes, filled with air, was used as an extrapola- tion ionization chamber. The saturation ionization current per unit volume was determined at constant target current for different interplate distances, and extrapolation to zero distance provided a measure of the rate of energy absorption in aluminium. (iii) A portable X-ray Dosemeter by Electronic Instruments Ltd., fitted with a 350-cm3 ionization chamber, read the radiation intensity directly in r/sec when the chamber was placed with its centre as near as possible to the point ordinarily occupied by the centre of the conductivity cell.These methods agreed within 3 % (under the assumption that air, water and aluminium absorb energy from these X-rays proportionally to their electron densities), and showed that the dose rate and target current are proportional over five orders of magnitude. The dose rate to hexane in the cell was calculated to be 8.0~ 1016 eV cm-3 sec-1 A-1 of target current. PURIFICATION OF HEXANE After preliminary purification, the hexane was distilled from sodium or sodium-potassium alloy in vacuo into a bulb fitted with metal electrodes. A potential of about 1000V was applied for some hours to get rid of residual conductive impurities by electrolysis.The hexane was then distilled into the conductivity cell. If the resistance of the hexane was still thought too low, it was poured back into the electrolysis bulb for further treatment. The specific resistances of the samples used lay in the range 1015-1017 ohm cm, when measured at 300 V/cm. Vapour-phase chromatographic analysis of the hexane preparations used here showed a small peak corresponding to the presence of about 0.3 % of methylcyclopentane. One preparation, called F2, was found, after sonie electrical measurements were made, to give a faint yellow colour to sulphuric acid, indicating the presence of unsaturation. The chro- matogram was not noticeably changed, however, by extracting the unsaturates with H2SO4. The unsaturated material was probably mostly hexene-2, which appears at the same point as methylcyclopentane in chromatography, so that its peak would be covered by that of the larger impurity.It must have been present to an extent less than 0.03 %, otherwise the size of the methylcyclopentane peak would have been noticeably decreased by its extraction. A later preparation, called F3, was properly treated with sulphuric acid before distillation to remove unsaturates. Research-grade hexane (called RG) was also used ; like F3, it apparently contained some methylcyclopentane but no unsaturates. Preparations F2 and F3 gave very different results for the ionic mobility, despite the fact that the concentlation of unsatur- ates present in one but not the other was very small. D98 NUMBER OF SEPARATED ION PAIRS RESULTS AND DISCUSSION MOBILITIES Table 1 shows results of our mobility determinations, together with values froin the literature.Our values for the purer preparations were the same, whether the material was air-saturated or vacuum-distilled. The negative ions in this experi- ment move tremendous distances on the molecular scale, and their charge should shortly attach itself to any trace of oxygen remaining in the evacuated liquid; so it seems probable that in both cases we are dealing with negative oxygen ions. The TABLE IONIC MOBILITIES IN HEXANE AT ROOM TEMPERATURE ref. hexane air mobilities (cm2/V sec) x 104 preparation present U- u+ RG no 7.6 3.8 present work F3 Yes 7.5 4.0 present work F2 Yes 1.8 3-3 present work 3Q - no 10 - - ? 9-2 5.8 4 - ? 13 4.1 2 - no 12.5 - 5Q a negative ions generated by a pulse of ultra-violet light incident on the cathode.presence of a trace of unsaturation (preparation F2) causes a remarkable decrease in the negative ion mobility. Presumably 0; attaches to hexene, forming a large, sluggish ion. Literature values for u- are not in good agreement but all are slightly higher than ours. It is possible that their preparations were purer. The nature of the negative ion in hexane has been much argued; because of the difficulties of getting rid of the last traces of oxygen, it may be an oxygen ion in all cases. For our calculation of G, we use our own determination, and take u = u+ + u- as 1-14 x 10-3. CONDUCTIVITY Fig. 2 is a typical plot of cell current against applied voltage, under constant radiation intensity.The current varies linearly with voltage, passing smoothly through zero. The current at zero appiied voltage is caused by irradiation of the lead-in wires, and varies in magnitude and sign when the cell is removed and re- placed. Fig. 3 is a typical plot of the slopes of such conductivity lines against the target current (which is proportional to the radiation intensity), on a log-log scale. A line of theoretical slope 3 is drawn through the points. A line of slightly greater slope, say 0.54, would be a better fit, but there is no doubt that, for any particular cell filling, the conductivity is at least very nearly proportional to the square root of the radiation intensity. For the determination of the yield of ions, the important quantity is just this proportionality constant, or its square, which we may express as u2/it, where IC = icL/VS and it is the target current.This ratio unfortunately has so far proved to be not very reproducible, even for different fillings of the cell from the same source. Values for apparently good preparations ranged from 1.4 x 10-21 to 2.9 x 10-21 Q-2 cm-a/A. We suppose the variations to arise from variable traces of impurity, perhaps arising in part from radiolysis as well as im- perfect cleaning of the cell. Since impurities tend to lower u and hence ii, the higher values are perhaps more reliable; but some weight should be given to the more numerous lower values. Further work is required on comparison of carefully purifiedA .0. ALLEN A N D A. HUMMEL 99 samples in thoroughly cleaned cells. We tentatively take ~ 2 / & as 2.2 x 10-21 with a probable error of 0.7 x 10-21. 4 2 0 m H 0, 2 -2 - 4 -6 -0.5 0 t 0.5 V FIG. 2.-Cell current against applied voltage, hexane, 1500 kV X-rays, dose rate 4.5 x 1010 eV cm-3 sec-1, L = 0.131 cm. m r( E: X t I I I 1 I11111 I I I I l l l l l I I I 1 1 1 1 1 1 2 4 5 2 4 6 2 4 it, A FIG. 3.-Conductivity of irradiated hexane against target current in X-ray generator. DECAY CONSTANT klu If the decay of the cell current (after the radiation is interrupted but voltage across the cell maintained) is due to second-order ion recombination, then a plot of l/ic100 NUMBER OF SEPARATED ION PAIRS against time should be a straight line. We have made many such plots, of which fig.4 is typical. The points are read from a recorder tracing of the current. Values of k/u in Vcm are obtained from the slopes of such lines by multiplying by the 0 10 2 0 30 40 t (sec) 5 0 FIG. 4.-Reciprocal cell current against time after interruption of radiation, V = 5.0, L = 0.35 cm. applied voltage and dividing by the cell constant L/S and by 6.24 x 1018. The resulting figures are not in very good agreement, even for successive readings taken with the same cell. Typical values, taken from the better runs, are 1-31, 1-43, 1-47 x 10-6 V ern. There is a simple theory6 which should give an accurate value of k/u for solvents of low dielectric constant. Ions should combine whenever they approach within a critical distance rc, at which their mutual Coulomb energy equals the energy of thermal agitation kT.Then re = e2/ckT, where e is the electronic charge and E the dielectric constant, 1-89 for hexane. In our case, rc = 260& which is so large that the actual size, shape and character of the ions can have little effect on the interaction. Then the rate constant k = 471rC(D+ + D-), where D+ and D- are the diffusion coefficients of the re- acting ions. There is also the general relation D/u = kT/e, Combining, we have klu = 4nelc. This quantity, ex- pressed in V cm, is equal to 0.96 x 10-6. Our measured values are around 50% higher than the theoretical value. It is difficult to see why the true ion recombination coefficient should differ appreciably from the theoretical value. The ion concentration in our experiments is of the order of only 109 6111-3 or less, so that " ionic strength " effects can be of little importance.Possibly the experimental values are vitiated by polarization effects. As decay proceeds while current continues to pass, a layer next to the elec- trodes is depleted of ions more rapidly than the bulk. The electrical potential thus might fall appreciably more rapidly across these layers than across the rest of the solution; and the field acting on the bulk of the ions would be less than V/L, to an extent which should increase with time. Then the ratio of the measured current to the ion concentration should decrease with time, and the current should decay more rapidly than the ion concentration. Provisionally, we assume that the true value of Jc/u is close to the theoretical, 0.96 x 10-6 V cm.THE ION YIELD Putting the above numbers into eqn. (3), we find G = 0.09, with a probable error of perhaps 50 %. If the experimental value of 1-4 x 10-6 for klu were used, G would be increased to 0.13. While this work was under way, a note by Freeman 7 appeared, giving a valueA . 0. ALLEN AND A. HUMMEL 101 of G for hexane of 0.2. This was calculated from an extrapolation to zero field of the conductivity observed at very high fields, a sort of extrapolated saturation current, the physical significance of which appears to us very dubious. Similar methods were used in two papers 8 9 9 presented at a recent meeting; their results for hexane, calculated in terms of G, were 0-09 for X-rays of various energies and 0.07 for tritium 0-rays.The present method, though difficult to apply with pre- cision, seems to us to be in principle the correct one. The number of ions escaping initial recombination in liquid hexane is about 4 % of the number formed in gases, and presumably also formed transiently in the liquid. Most or all of the observed charge separation may be attributed to the higher-energy delta rays. The beginning of a delta-ray track must have one excess positive charge, the end must have one excess negative. If the two ends are separ- ated by more than rC = 260& then a separated pair of ions must result. It appears that, apart from this delta-ray effect, almost none of the sub-excitation electrons produced by ionization escape recombination, or become thermalized at a distance greater than 260A from a positive ion.This result may seem surprising since it is difficult to imagine a mechanism for the rapid thermalization of electrons in hexane below the molecular vibrational energy level of around 0.1 eV. The mechan- ism of Frohlich and Platzman 10 should be of little importance in a non-polar liquid like hexane. It seems more likely that the great majority of the electrons are never completely thermalized, but are rapidly reduced, by loss of energy to molecular vibrations,ll to some epithermal energy E (of about 0.2 eV) while still at a distance from the positive ion small compared to e2/&E. They must then, as pointed out by Samuel and Magee,l2 return to the positive ion and neutralize it, the energy of neutralization being dissipated in the form of molecular fragmentation and of heat. This research was performed under the auspices of the U.S. Atomic Energy Commission. 1 Mohler and Taylor, J. Res. Nat. Bur. Stand., 1934, 13, 659. Taylor, J. Res. Nat. Bur. Stand., 2 Gzowski and Terlecki, Acta Phys. Polon., 1959, 18, 191. 3 Chong and Inuishi, Tech. Reports Osaka Univ., 1960, 10, 545. 4 Gzowski, Z. physik. Chem., 1962,221, 288. 5 Le Blanc, J. Chem. Physics, 1959, 30, 1443. 6 Debye, Trans. Electrochem. Soc., 1942, 82, 265. 7 Freeman, J. Chem. Physics, 1963, 38, 1022. 8 Adamczewski and Januszitis, Conf. Electronic Processes in Dielectric Liquids (The Institute of Physics and The Physical Society, University of Durham, 23-25 April, 1963), paper no. 6.3. 9 Gzowski and Chybicki, (Conf. Electronic Processes in Dielectric Liquids (The Institute of Physics and The Physical Society, University of Durham, 23-25 April, 1963), paper no. 6.4. 1936, 17, 557. 10 Frohlich and Platzman, Physic. Rev., 1953, 92, 11 52. 11 Chen and Magee, J. Chem. Physics, 1962,36, 1407. 12 Samuel and Magee, J. Chem. Physics, 1953,21, 1080.