JOHN ZINN AKD R. N. ROGERS
2646
Vol. 66
THERMAL INITIATION OF EXPLOSIVES1 BY JOHN ZINN AND R. N. ROGERS Unicersity of California, Los Alamos Scientijic Laboratory, Los Alamos, New Mexico Received Mag S, 1962
Theoretical calculations are described which pertain to the behavior of explosives when heated under known conditions of confinement. Effects of depletion apd pressure buildup are explicitly considered. The results are capable of generalization to a large class of reactive materials of which ex losives are a special case. Experiments are described wherein confined samples of several common explosives have been ieated and their times to explosion recorded. Themeasurements are compared with two previously published sets of data, and the results are shown to be consistent if geometry effects are properly considered. All three groups of data are in agreement with the calculations. Explosion time data are used (in Appendix A) to derive reaction rate parameters for TNT.
Introduction = a constant a t the surface or surfaces defined by Previously published data on the thermal initia- I z 1 = a. This is intended to represent a physical tion of explosives2-4 have pointed out a strong de- process such as the sudden immersion of a sample pendence of induction times on experimental geom- whose temperature is To initially into a Wood’s etry, andit has been shown that such a depend- metal bath at the temperature TI. For pure explosives the quantity Q/C is freence is to be expected on theoretical grounds.2 The data reported herein are found to correlate quently of the order of lo3 degrees, and in many with the previous data in the expected manner. cases, therefore, a large temperature increase can However, an important purpose of the present result from a very small amount of chemical reacexperiments has been to study the temperature tion. Under these circumstances the thermal dependence of explosion times at relatively low behavior of the system prior to explosion can be temperatures, and here the results have not been described adequately by the first equation alone, entirely as anticipated. In order to interpret the with w set equal to unity; Le., a zero-order reacdata it has been necessary to extend the theoretical tion can be assumed. In a previous paper,a cermodel to take account of the pressure in the sample tain numerical solutions to eq. 1 were described and also to account for the depletion of reactants for w = 1, and these mere shown to be consistent with experimental data then available. The as reaction proceeds. If a reactive material is heated or cooled, and if simple zero-order reaction model is nevertheless it simultaneously decomposes by a single first- limited in its applicability, and this paper will order rate process, then variations of temperature attempt to identify conditions under which it may and concentration within the sample will be de- or may not be a useful approximation. The zero-order reaction model permits two useful scribed by the equations quantities to be defined, viz., a “critical temperature” and an “explosion time.” The “critical bT - = kV2T Qz - we- E / R T (1) temperature,” T,, is defined as a limiting value of at C T I which, if exceeded, leads to runaway exothermic reactions (thermal explosions), and, if not exceeded, leads to temperature distributions which approach, instead, certain well defined steady s t a t e ~ . The ~ Here T is the temperature at time 1, w is the mass steady-state problem has been treated by Frankfraction of undecomposed reactant at any point, Kamenetskii6 and Chambre,’ and through their k is the thermal diffusivity in cm.%/sec.,Q is the heat analyses the critical temperature is given by of reaction per gram, C is the specific heat, Z is the “collision number,” and E / R is the activation temperature. It will be assumed that the quantities k , Q/C, Z, and E / R are constant. For configurations having one-dimensional, cylindrical, or spherical symmetry, the Laplacian operaHere r = a 2 / k ,a being the radius or half-thickness tor, v*,takes the form of the explosive sample. 6 is a dimensionless b2 m b parameter equal to 3.32 for spheres, 2.00 for cylin-+-ders, and 0.88 for slabs. 3x2 x ax In the event that TI exceeds T,, an explosion where m = 0 for the one-dimensional system, 1 takes place after a certain induction time, t,,. for cylinders, and 2 for spheres. We assume that Since in the zero-order reaction model w is assumed initially the temperature is everywhere equal to to be constant, T and dT/dt can increase without a constant, To,and w is everywhere equal to 1. limit, and texp can be precisely defined as the time The boundary condition will be taken to be T = T I when this occurs. It was found2 that the induc-
+
(1) Based on work performed under the auspices of the U. 9.Atomic Energy Commission. (2) J. Zinn and C. L. Mader, J . A p p l . Phgs., 31, 323 (1960). (3) J. Wenograd, Trans. Faraday Soc., 67, 1612 (1961). (4) H. Henkin and R. McCill, Xnd. Eng. Chem., 44, 1391 (1982).
( 5 ) We exclude from consideration those cases in which the initial temperature, To,is higher than Ti. (6) D. A. Frank-Kamenetskii. Acta Physicoehem. U R S S , 10, 365 (1939). (7) P. L. Chanibre, J. Chem. Pliys.. 2 0 , 1795 11952).
Dec., 1962
THERMAL INITIATION OF EXPLOSIVES
2617
tion times, texp, conformed to the functional relationship
reaction rate a t each point would follow the temperature without influencing it. According to eq. 5 the sample container would “explode” when the texp/T = function of (E/Tm - E/TJ (4) extent of reaction, F, reached a certain value, F*. At low temperatures such that explosion times are That is, for a fixed sample geometry and fixed To, much longer than r , the chemical reaction can be the quantity texp/. is, to a very good approximation, a function of the single variable (E/Tm - E/Tl). regarded as approximately isothermal. Under The computed relationship between texp/T and these circumstances, eq. 2 can be integrated, and (E/T,,, - E/TJ is as plotted in Fig. 3 of reference 2. leads to the expression It can be shown rigorously that texp/rdepends on -In @ only three variables, such as E, T,, and TI; howt = Z exp(-E/RT) ever, we are unable to provide an existence proof for eq. 4. In a real physical situation, the amount of un- Accordingly, the explosion time is given by decomposed explosive at any point decreases as - -In (1 - F*) reaction proceeds. It is commonly found that the texp (7) Z exp( -E/RT) decomposition is first order, so that the depletion process follows eq. 2. But if w is a continuously At higher temperatures, the isothermal approxidecreasing function of time, a true stationary state cannot exist, arid the critical temperature is not mation would not apply, and the explosion times easily defined; moreover, an “explosion” must invariably would be longer than those given by eq. 7. At much higher temperatures, heat conduction now be carefully defined. An explosion is most often associated with some would become the rate-limiting process, and chempressure effect, such as the sudden rupture of a ical reaction would proceed in layerwise fashion from sample container. Therefore, before a realistic the surface inward. At early times when only the surface region has comparison between experimental and computed explosion times can be made, it is necessary to ex- been heated, the temperature distribution is apamine the relationship between the thermal proximateds by processes described by eq. 1 and 2 and the buildup T = To (TI - To) X of presslire in the container. Suppose that the sample has a crystal density of p and the sealed container is loaded to a density of D g./cc., and suppose that N moles of gaseous products are produced per gram of explosive de- where X is the thermal conductivity (cal. deg.-l composed. If the products are assumed to obey em.-’ sec.-l). If eq. 2 is approximated by the Abel-type equation of state, V = NRT/P l / p , where V represents specific volume, then at an instant when a fraction F = (1 - a) of the total sample has reacted, the pressure in the container and T is that given by eq. 8, then it can be shown will be approximately that for a symmetric cylindrical system FNRTDp NRTDp PEP-=3E(T1 - To)F* (1 (5) p-D p-D (9) lexp = [4dGRT1~Zrexp(-E/RT1) Here @ represents the volume average of w. The container presumably will rupture at some fixed This formula is derived in Appendix B. For small value of P, which we shall designate by P*. Then values of F* and high values of T, it gives a good the experimentally determined explosion time will approximation to explosion times obtained by be the time at which the pressure reaches P*. numerical computations. Explosion times for a wide range of temperature Under many circumstances, the explosion times determined hy this criterion will be in close agree- have been computed for one such hypothetical ment with those defined by the occurrence of a Q = 0 system, using the numerical procedure to runaway exotherm. However, this is not always be described in the last section. The results are the case. Large differences can occur, especially plotted in Fig. 1 (curve A), along with the limiting times given by eq. 7 and 9 (curves Afland Afz). at low temperatures below T,. In cases where the chemical reaction is exotherIt may be noted that the process causing the pressure buildup is not necessarily related in any mic, self-heating effects can operate, tending to way to a thermal explosion. It will be useful to increase the over-all reaction rate. Then, if consider the case of a material which decomposes other things are equal, the explosion times to be to gaseous products without liberating or absorbing expected for a system with Q > 0 (exothermic) heat. The decomposition reaction will be assumed invariably are shorter than for the corresponding to follow eq. 2. If a sample of this material were Q = 0 system. The differences, however, are in heated, its internal temperature distributions would many cases small. Curve B of Fig. 1is derived from riot be influenced by the chemical reaction, and the computations of explosion times for a system that variations in temperature in the sample could be (8) R. V, Churchill, “Modern Operational Mathematics in Engidescribed by familiar heat transfer relations. The neering,” McGraw-Hill Book Co., New York, N. Y., 1944.
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2648
JOHX Z I N X A S D
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R. N. ROGERS
Vol. 66
size of the cylinder or the identity of the explosive. Equivalent statements apply to samples of other shapes. The time constant, T, is equal to a2/k, and k is, to a satisfactory approximation, the same for all the explosives studied in this paper, having a value of about 0.00066 cm.2/sec. Values of E frequently are to be found in the literature, and also can be obtained from the explosion time data in the manner shown in Appendix A. The values of T , for a given explosive in two different geometries are related by the expression
ki' /
//
(10)
I / TI x IO3 (DEG:')
Fig. 1.-Computed explosion times for cylindrical samples with 2 = 1018J see.-', E = 47.5 kcal./mole, T = 22.5, and To = 298'K: curve A, first-order reaction with Q = 0 and t,,, = time when F = 0.04; curve AI', times for F = 0.04 for isothermal reaction; curve Az' times for F = 0.04 for zeroorder reaction (high temperature limit); curve B, firsborder reaction with Q/C = 2000' and tex, = time when F = 0.04; curve C, zero-order reaction with Q/C = 2000' and tex, = time of thermal explosion.
is identical with that of curve A except that Q / C = 2000' instead of 0'. For curves A, At1, Atz, and B, an "explosion" is assumed to occur when F = 0.04. Curve C of Fig. 1 is the explosion time curve for a system equivalent to that of curve B, except that it has a zero-order reaction (w = constant = l), and an explosion is identified with a runaway exotherm. This curve was generated from the reduced explosion time curve for cylinders shown in Fig. 3, ref. 2. Over a range of approximately 100°K., curves A, B, and C of Fig. 1 are remarkably similar in shape and position. Therefore, within this range, self-heating and depletion effects do not play a dominant role in determining explosion times. Over much of the range, curve B is almost coincident with curve C, the zero-order reaction curve. This shows that thermal explosions are generally well under way by the time F = 0.04. Although at higher temperatures curve B most closely resembles curve C, below T , the resemblance ceases, and B then approaches the Q = 0 curve (curve A). Below T,, thermal explosions are impossible, and with further lowering of T I the influence of self heating continuously decreases. Far below Tml the explosion time curve merges with the isothermal line, A'1.
Geometry Effects When the zero-order reaction model is applicable, eq. 3 and 4 provide a means of reducing to a common basis explosion time data for different explosives and different sizes of sample. According to eq. 4, if the data for all cylindrical explosive samples are plotted at t e , p / r US. (E/Tm - E/?',), the points all should fall on the theoretical curve for cylinders given in Fig. 3, ref. 2, regardless of the
where the subscripts (1) and (2) refer to the two geometries. This equation follows directly from eq. 3. There remains only to find one value of T , for each explosive. T, can be calculated from eq. 3 if QZ/C and E are known; however, for present purposes, we propose to obtain T , directly from the data. The following is a convenient procedure. If, for an explosive in a given geometry, explosion time data are available a t temperatures such that texp = T, the value of TI for which texp = T can be obtained by interpolation. According to Fig. 3, ref. 2, when texp = r, the correspondingvalue of ( E / T , - E / T J (for cylinders) is 1.6. Since the appropriate T1 is an experimental quantity and an approximate E is presumed to be known, T , follows. The T , for other geometries then can be obtained from eq. 10. Experimental Apparatus.-The experimental arrangement is similar to t,hat of Henkin and McGill,4 with the important difterence that the sample is tightly confined. Procedure.-Weigh the desired sample, usually 40 mg., into a new, empty, no. 8 blasting cap shell (6.5 mm. i.d., 0.2 mm. wall thickness, copper). Insert the shell into a suitable die, and ram one 6.5 mm. gascheck (a small metal cup used to protect the base of a lead alloy bullet in reloading ammunition) part way into the shell. Place one 00 cork into the shell and ram both to the level of the sample. Place a second gascheck over the cork, and press the assembled shell to an applied force of 300 lb. (approximately 6000 p.s.i.). Eject the shell from the die, and, using a dull tubing cutter, crimp the walls of the shell just above the upper and lower gaschech. The resulting sample depth is 0.75 to 1.0 mm., depending upon sample density and crystal habit. As in the original method of Henkin and McGill, times to explosion are determined by dropping the samples into a Wood's-metal bath a t fixed temperatures and measuring the time required for the sample cell to rupture. The temperature of the bath should be controlled to f 0 . 2 5 . Measurements of the mechanical force necessary to unseat the gaa checks lead to an estimate of 15,000 p s i . for the failure limit of the container. Loading densities of the samples are estimated to be approximately 90% of crystal densities. Experimentally determined explosion times are reported herein for six pure explosives: TNT (2,4,6-trinitrotoluene), RDX (hexahydro-1,3,5-trinitro-s-triazine), HMX (octahydro-l ,3,5,7-tetranitro-l,3,5,7-tetrazocine, 99 .5y0purity), tetryl (N-methyl-N,2,4,6-tetranitroaniline), PETN (pentaerythritol tetranitrate), and ammonium nitrate. The raw data are plotted in Fig. 2 . Additional data on mixed explosives will be reported elsewhere.9 (9)
R. IlT. Rogers, Ind.
Eng. Chent., Prod. Res. Der., 1, 109 (1962).
THE~~M IXITIATIOS AL OF EXPLOSIVES
Dec., 1962
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-
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-
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-
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2649
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JOHN ZINN AND R. N. ROGERS
2650
I
/
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/
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1'01. 66
/
+
TNT t =2419SEC TNT t = 3 4 SEC TNT te0.12 SEC RDX t = 2 4 1 9 S E C RDX r.34 SEC AN t . 3 4 SEC PETN r =34 SEC PETN t =0.12 SEC
A A
TETRYL t =34 SEC (THIS PAPER) TETRYL ~ ' 0 . 1 2SEC ( REF.3
0
0
0
v 0
-
(REF.2) (THISPAPER) (REF.3) (REF. 21 (THIS PAPER) (THIS PAPER) (THIS PAPER) (REF. 3
-
-
-
-
0 -
I
4
6
Fig. 3.-Combined plot of telp/r us. E ( l/Tm
8
l
l
l
IO
I
l
/
12
14
16
20
18
22
- 1/Tl) for various explosives in three different geometries.
The values of T, so derived are listed in Table I. It will be note2 from Fig. 3 that explosions were recorded for TNT, PETN, RDX, and €IMX, a t temperatures below the T, listed in Table I, and that in all cases except that of HMX these are believed to be of the non-thermal type described in the Introduction. In the case of RDX, the value of tern in this region corresponds fairly closely to the expected value of F* = 0.04. The texp measured for TNT in the same region corresponds more nearly to F* = 0.3. If E and Z are known, an approximate value of F* can be obtained from measured explosion times by the use of eq. 7. The experimental texp data used for this purpose should be 57 or longer. The results of three such calculations are listed in Table 11, where F" has been obtained for RDX, PETN, and TNT. The behavior of HMX is believed to be essentially different from the rest of the explosives studied, and will be discussed separately. It will be of interest to compare the present experimental results with earlier data reported in ref. 2 and 3. The measurements in ref. 2 were made in cylindrical containers of 1.27 cm. inner radius; those of ref. 3 used a cylindrical geometry of 0.0089
VALUESOF T,
FOR
TABLE I THREEEXPERIMENTAL GEOMETRIES
Explosive Measured Ti for t e x p = T (r 34
-
E (kcal./mole) T m (OK.) for 7 = 2419 34 0.12
sea.)
sea.
561'K. 486 462 484
TNT RDX PETN
",Nos Tetryl 4i'O
sec.
8ec.
41.1 (this paper) 491 549 653 47.5 (ref. 11) 439 478 47.0 (ref. 12) 455 513 38.3 (ref. 13) 475 34.9 (ref. 14) 460 545
TABLEI1 CALCULATIONS OF F* Explosive
RDX PETN TNT
t e x p (sec.)
120 110 1130
Tj (OK.)
473 449 538
E (kcal./ mole)
47.5 47.0 41.1
Z (sec.-1)
1019.8
P*
0.04 0.09 0.3
(11) A. J. B. Robertson, Trans. F a r a d n ~Sac., 46, 85 (1949). (12) A. J. B. Robertson, J . Soe. Chem. Ind. (London). 61, 221 (1948). (13) M. A. Cook and M. T. Abegg. I n d . EnQ. Chem., 48, 1090 (1956). (14) E . K.Rideal and A . J. B. Robertson. Proc. Roy. SOC.(London), 8196, 135 (1948).
Dec., 1962
THERMAL INITIATION OF EXPLOSIVES
cm. radius. If IC = 0.000666 cm.2/sec., then the time constants, 7, for these two systems are 0.12 and 2419 sec., respectively, as compared to 34 sec. for the present system. Values of T, for various explosives in the present geometry having been obtained, 1,he corresponding T, for the other two systems can be calculated by eq. 10. The results are listed in Table I. Having estimates of T and T, for each set of experiments, and assuming the values of E given in Table I, one can calculate the quantities t q x p / T and (E/Tm - E/TJ for each measurement of tern and TI. According to eq. 4, if all the data from the three sets of experiments are plotted as tern/. vs. (E/T, - E/TJ, the points all should fall on the same curve. Such a plot is shown in Fig. 3, which contains the aggregate of points for T N T in all three geometries, PETN and tetryl in the 34 sec. and 0.12 sec. geometries, RDX in the 2419 and 34 sec. geometries, and ammonium nitrate in the 34 sec. geometry. Also shown is the theoretical zero-order reaction curve for cylinders, as given in Fig. 3 of ref. 2. The width of the band of points is not appreciably greater than the s c a t t e ~within any single set of measurements; moreover, the theoretical curve is in good agreement with the data over the entire range of positive values of (E/Tm - E/TI). In view of the fact that the several groups of data are scattered over a range of' seven powers of ten in explosion time and a temperature range of 550°, this degree of agreement is felt to be quite remarkable. The data for IIMX have not been included in Fig. 3, and must be considered separately. It can be noted from the raw data of Fig. 2 that the Lev us. l/T1 curve for this explosive is steeper than equivalent curves for the other materials. HMX is the only one of the organic explosives studied which is still a solid in the experimental temperature range, and much of its unusual behavior is attributable to this fact. The rate of decomposition of the pure crystalline solid is believed to be considerably slower than that of the melt, or of the mixed phase formed between the explosive and its decomposition products. It therefore would be expected that a small amount of decomposition in a confined sample would tend to catalyze further decomposition. If autocatalysis of this sort does indeed take place, it could account for the extraordinary steepness of the t, US. 1/T1 curve and the extremely long explosion times recorded below T,. A few auxiliary facts can be noted in this connection. It is found that thermal initiation of Hh4X is greatly accelerated by the admixture of other explosives or the presence of minor impurities. The tax,, vs. 1/T1 curve for standard production HMX containing 5% RDX is displaced downward in temperature by 11' from the curve for 99.5% HMX shown in Fig. 2. The curve for octol, a 7Fi:25 mixture of HMX with TNT, is displaced downward by 17'. N o parallel effect can be noted with mixtures of RDX with T N T ; the curve for cyclotol, a 75:25 mixture of RDX and TNT, is coincident within experimental error with the curve for RDX alone. Numerical Computations.-Except within the limited range where the isothermal approximation
2651
can be used, solutions of eq. 1 and 2 must be obtained numerically. The differential equations are conveniently integrated by means of the finite difference approximations T,n+l = 6Tj-i
+ (1 - 26)Tjn + 6Tnj+i +
and
w l n f l = w , [I~ - Z A ~~x ~ ( - . E / R T ) ~ )(12) ] Here superscript n is the time index, and subscript h is the (constant) mesh interval, so that z = j h ; At is the time interval, so that t = nAt. 6 = kAt/h2, At being so chosen that 6 is in the vicinity of 0.16. This system is stable as long as 6 < 0.5. The region 0 5 x 5 a is divided into J equal intervals of width h, where J has been given values between 10 and 200, depending on the problem. The physical magnitude of h is given by h = a / J . The initial conditions are described by Ti0 = To = constant, and wjo = 1. The boundary condition is Ton = Tl* = constant. The condition bT/bx at x = 0 is maintained by setting Ton = Tin. The computations were performed with an IBM 704 digital computer. The present method of computation differs from that described in ref. 2, and is in most cases faster. Experimental runs designed to compare the two methods showed them to be in good agreement. The appropriate mesh spacing to be used for a given problem ww determined by trial and error. Progressively smaller mesh intervals were necessary as T1 was increased. This computational method was used to obtain curves A and B of Fig. 1.
j , the space index.
Conclusions
It is concluded that a t least the gross features of the temperature dependence of explosion times can be understood on the basis of the simple model expressed by eq. 1 and 2, and that for certain ranges of conditions this model can be further simplified. Earlier calculations based on the assumption of a zero-order reaction lead to quite accurate predictions of explosion times within the range 0.17 < texp < r. At temperatures appreciably lower than the hypothetical critical temperature, the isothermal assumption can be used. The agreement between the predicted and observed behavior is suf%cient to permit reasonable extrapolations of the data to larger or smaller geometries. Appendix A Determination of Rate Parameters for TNT.The present type of experiment is potentially useful for the determination of rate parameters. It offers definite advantages in the case of volatile materials, where techniques based on gas evolution are complicated by the effects of vaporization, and it also is advantageous for studies of reaction rates a t high temperatures. Since the theoretical treatment of the data will take explicit account of effects due to temperature gradients and self heating, these will not be a source of confusion.
JOHXZIXJ
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Whereas “isothermal” experiments are restricted It will be convenient to subst’itute the variables to situations where the times involved are much 0 = t / r = kt/u2, $ = x/a, and 4 = E(T - Ti)/ longer than r , the present method is not so re- RT12. Then eq. 8 becomes stricted. A case in which the present method has distinct advantages is that of TNT, where the existing published datai3.’6 are in poor agreement. The previous measurements apparently were compliThe Arrhenius expression, exp (- E/RT) , can cated by both vaporization and self heating effects. be approximat,ed by exp(-E,/RTl)exp 4, so that, Given two data points (fexp, Ti), and the perti- eq. 2’ becomes nent sample dimensions, the corresponding values bw of (E/Tm - E/TJ can be obtained from Fig. 3 - - -_ of ref. 2. If these are denoted by A(1) and A(%,, bo and the corresponding values of T1 are denoted by and Tlc2), it then follows from eq. 10 that For cylindrical samples the volnme average of u is given by A(1) - A ( 2 , R In (a2~2~8(1)/u2~1)6(*))
+
+
But since w = 1 everywhere except where { is nearly eqiial to 1,this becomes The experimental values of t,, used for this purpose should preferably be between 0.1 and 1.07. It also is advantageous, as in any determination of E, for the two data points to be taken at widely different temperatures. These two requirements, to be compatible, entail the further requirement that the two measurements be made with very different sizes of sample. For the case of TNT, the two data points which have been chosen are
texp = 250 sec.,
=
T
texp = 0.030 see.,
T
2419 sec., 6
=
0.12 sec., 6
2.00, TI = 571OK. (ref. 2)
Therefore
=
57 = 2 Jol
= 2.00, TI = 763°K. (ref. 3)
[1 - (Zre-e’RT1) Jo’
ebd8] d[ - 1
= I - (2Zre-E/RT1)$‘J1 0 0 eOdf do (B4)
We define the new variable z = (1 - 5 ‘ ) / 2 4 5 , Then by eq. ,41 we obtain E = 41.1 kcal./mole. so that Substituting this value of E in eq. 3, we obtain QZ/C = 10i6.2deg./sec. The above value of E is intermediate between the values quoted in ref. 15 and 13. The two data points used are separated in temperature by 192”, and thereby provide a large amount of leverage for determination of E. The values of 2$,& which are of interest are The slope of a In texp us. 1/T plot should not be used as ameasure of E/R. It will benoted from Fig. generally of the order of -20; therefore exp(4) 1 (curve B) that this slope is almost always less decreases rapidly with increasing z, and the integral than E/R. Joze+ddz has effectively a constant value for values Appendix B of z greater than about 0.2. Within the range 0 An Approximate Expression for Explosion Times 5 z 5 0.2, 4 is approximated closely by $ = at High Temperatures.-The early stages in the 24oz,/d/?r. I t follows that, for values of 0 less than heating of a sample with Q = 0 can be described I anproxirnately by the equations T
To
+ (Ti - To) X
Therefore and Referring to eq. B4, the value of (15) A. J. B. Robertson, Trans. Faraday SOC.,44, 977 (1948).
by
then is given
Dcr., 1062
nIliECTED
SOLUTE-SOLVEST
ISTER.4CTIOXS I S
BENZENE SOLUTIONS
2653
DIRECTED SOLUTE-SOLVENT INTERACTIOSS I N RESZENE SOLUTTONS‘ BY W. G. SCHKEIDER Division of Pure Chemistry, National Research Council, Ottawa, Canada Received May
8, 1968
By means of proton magnetic resonance techniques it has been possible to demonstrate directed molecular interactions between polar solute molecules and benzene solvent molecules. The pronounced sensitivity of the proton resonance method for this purpose is due to the large magnetic anisotropy of the benzene solvent, which greatly magnifies the solute proton shifts arising from non-randomization in the solution. For polar alkyl-X and vinyl-X solutes the interaction with benzene is interpreted in terms of a dipole-induced dipole interaction, which leads to preferred mutual orientations of the solute and solvent molecules. The magnitude of the interaction appears to depend on the magnitude of the molecular dipole moment of the solute, as well as its molecular volume; molecular shape of the solute molecule is not a determining factor. With phenyl-X solutes in aromatic solvents the interaction is more extensive and cannot be adequately accounted for in terms of a simple dipole model.
The molecula,r force field of benzene, and of aromatic molecules generally, has a pronounced directional character. The r-electron system in such molecules represents a relatively exposed region of electronic charge directed normal to the molecular plane. Accordingly, when a second molecular species interacts with benzene, the interaction will be primarily through the a-electrons, and in the resulting complex the interacting molecules will tend to have preferred mutual orientations. It turns out that nuclear magnetic resonance techniques provide us with a method of extraordinary sensitivity for studying systems of this kind. The reason for this is the large anisotropy in the magnetic susceptibility of aromatic molecules, also commonly referred to as the “ring current effect.”2 I n order to illustrate how the ring current effect influences nuclear magnetic resonance measurements we consider a very simple model, shown in Fig. 1. In this model we regard the aromatic ring as a, simple circular conducting loop. X magnetic field Ho applied normal to this loop induces a circular current, which generates a secondary magnetic field opposed in direction to that of the applied field. We can approximate this very crudely by a dipole placed a t the center of the ring. This dipole has magnetic lines of force as illustrated by the dotted lines. Suppose now we are measuring the proton resonance of the hydrogen atoms in benzene, only one of which is shown here. The component of the secondary field a t this proton is in the same direction as the applied field, i.e., it enhances. the a,pplied field Ho. Therefore to bring this proton into resonance we will require an external field H which is less than Ho, or, in
other words, the resonance is shifted to lower applied field. On the other hand protons which find themselves in positions immediately above or below the plane of the aromatic ring will have their resonances shifted to higher applied field. This is because here the component of the secondary field is opposed to that of the applied field and hence to bring such protons into resonance we have to apply a field H greater than Ho. We have here considered a fixed orientation of the aromatic ring with respect to the external field. If the external field is applied parallel to the plane of the ring there will be no induced ring current and no resonance shifts. So even after averaging over all directions we will still observe a net effect as indicated. A simple example of the kind of behavior discussed here is provided by the proton resonance of CHCh contained in a dilute solution of benzene. This is illustrated in Fig. 2. When CHCla is dissolved in cyclohexane, there will be no specific interaction with the solvent, other than relatively weak van der Waals and dipole interactions. For the present purpose we may regard the cyclohexane solvent as an inert medium and accordingly we arbitrarily assign the chloroform resonance in this case the value zero. I n ether, which is an n-type donor, the chloroform hydrogen interacts by forming hydrogen bonds with the ether oxygen, giving rise t o a shift of the chloroform proton resonance to lower applied field.a This low-field shift is quite characteristic of all hydrogen atoms involved in hydrogen bonding with n-type donors. In benzene we observe the chloroform proton resonance shifted very much to higher field. We interpret this to mean that the chloroform is here also forming a
(1) Presented a t the Prof. Hildebrand 80th Birthday Symposium a t Berkeley, Calif., September 11th a n d 12, 1961. (2) (a) L. Pauling, J . Chem. Phys., 4, 673 (1936): (b) J. .1. Pople. ibid., 24, 1 1 1 1 (19%).
(3) The proton resonance of the CHClzin ether, as well a8 in benzene, was measured relative to the proton resonance of cyclohexane, a small amount of which was added t o the solutions to serve as a n internal reference.
