309
Communicationsto the Editor
iood
/
i
Figure 2.
The esr spectra of Cu(giycinate)z-loadedrayon fiber observed with the maanetic field DerDendiCUh' to (solid line) and parallel to (broken line) the fiber: T h e arrows indicate the parallel components, a quartet due to hyperfine interaction with 63Cu and "Cu (both I = 3/2).
The esr spectra of Cu(g1ycinate)z-loadedcellulose film observed with the magnetic field perpendicular to (solid line), and parallel to (broken line) the plane of the film. The arrows indicate the parallel components.
gether to form a crystallite or an elementary fibri1.l Swelling with LiOH solution is known to increase the interplatellite spacing and to facilitate occlusion of foreign material. In fibers, the individual chain within each platellite runs parallel to the direction of the fiber. It thus follows that the plane of the platellite is also parallel to the direction of the fiber. The present result with the fiber suggests that V 0 2 + ion complexes with individual cellulose chain in such a manner where the V-0 internuclear direction is perpendicular to the chain. The result with Cu(g1ycinate)a can be understood if the large, planar copper complex interacts with the planes of the platellites. The results obtained from the film suggest that not only is the integrity of the platellites maintained within the film, but there exists a coherence between the planes of the microscopic
platellites and the macroscopic plane of the film. The lack of orientation effect of the V 0 2 +ions in the film is attributed to the two-dimensional randomness of the platellite arrangement within the film. The present study thus demonstrates a possibility of probing by esr the morphology of cellulose and related materials using paramagnetic species of different sizes as well as configurations.
Figure 3.
References and Notes (1) See, for example, the Proceedings of the Seventh Cellulose Conference, J. Polym. Sci., Part C, 36, 343 (1971). (2) P. J. Baugh, 0. Hinojosa, J. C. Arthur, Jr., and T. Mares, J. Appl. Polym. Sci., 12, 249 (1968). (3) See, for example, the esr spectrum of V 0 2 + acetylacetonate in glassy matrices reported by H. R . Gersmann and J. D. Swallen, J. Chem Phys., 36,3221 (1962).
COMMUNICATIONS TO THE EDITOR
Comment on "Triplet Formation in Ion Recombination in Spurs" by J. L. Magee and J-T. J. Huang
Sir: Magee and Huangl have recently calculated the yields of singlet and triplet states in spurs produced by high-energy radiation. In the simplest case, they assume that no spin relaxation occurs, ie., a singlet ion pair (n = 1) undergoing geminate recombination can only give singlet states if the initial molecule is in a singlet state; spin relaxation is expected to be negligible in mobile liquids.2 If the electron spins were not initially correlated, the probability, PT, of obtaining a triplet state would be 3/4. In the case of a spur containing two ion pairs ( n = 2), Magee and Huang would argue as follows: the overall state of the system must remain singlet, but four spins can be paired in two different ways to give a resultant S of zero; these
correspond to the two individual molecules in singlet states and the two in triplet states with opposed S vectors; after recombination the two states are equally probable so PT = lb. This result is generalized to give
pT= 314p - i/(zn
- 111
(1)
(In practice, of course, there are a number of complications;lJ N.B. the orbitals involved are not considered; recombination will release enough energy to produce excited states.) Using a more detailed wave-mechanical description of spur recombination, Higashimura, et d , 3 obtained a different result
pT = 3/4(1- i / n )
(2)
In this note, a simple statistical argument is used to show that (1) is correct for neutral radical recombination, and (2) for radical cation-electron recombination. For simplicity, consider two ground-state hydrogen molecules, The Journal of Physical Chemistry, Vol. 78, No. 3. 1974
Communications to the Editor
310
AI3 and CD, split into four neutral atoms. These may pair up (i) AB, CD giving two singlet molecules, (ii) AD, CB, or (iii) AC, BD; ii and iii will each give Y2 singlet, 3/2 triplet on the average. If i, ii, and iii are equally probable, the net result is PT = I,; this can be generalized to give eq 1. Now consider two ion pairs: A, C are now cations, B, D are electrons; processes i and ii can occur but not process iii; it is not a neutralization but leads to two doubly charged species. So PT = 318 in this case; the argument may be generalized to give eq 2 . The difference is not in the number of overall singlet spin states ( 2 for n = 2 ) as is shown by the agreement when all pairings are allowed; rather, it concerns the efficiency with which the system can pass from one to another. It may be argued that the present treatment ignores the indistinguishability of electrons, but the only distinction made is between electrons in radical cations and free electrons. Acknowledgment. The authors thank Professor Magee for a preprint of his paper. References and Notes (1) J . L. Magee and J-T. J . Huang, J. Phys. Chem., 76, 3801 (1972). (2) B. Brockiehurst, Nature (London), 221, 921 (1969). (3) T. Higashimura, K . Hirayama, and K. Katsuura, Ann. Rep. Res. Reactor Inst. Kyoto Univ., 5, 11 (1972).
Chemistry Department The University Sheffield, S3 7 H F United Kingdom Reactor Research Institute Kyoto University Kumatori-Cho Osaka, Japan
6 . Brocklehurst*
T. Higashimura
Received February 7, 1973; Revised Manuscript Received September 7, 1973
Reply to the Comment by B. Brocklehurst and T. Higashimura on “Triplet Formation in ton Recombination in Spurs” Publication costs assisted by The U. S. Atomic Energy Cornmission
Sir: The comment of Brocklehurst and Higashimural on our paper entitled “Triplet Formation in Ion Recombination in Spurs”2 reflects a misunderstanding of our model. Contrary to their conclusion, this model2 does indeed apply to the case of cation-electron neutralization. It can also be extended to neutral radical recombination, as they suggest, but further assumptions must be made and this case is not considered in our paper. The problem of estimation of the numbers of triplets formed on the charge recombination in irradiated systems is actually quite complicated and involves several parts. We have focused on the combinatorial aspects of the problem. We attempted to state the necessary limitations of our model and we believe that within the framework in which it was presented our treatment is correct. The basic point of conflict seems to be the recognition of indistinguishability of electrons. In our paper2 we have taken into account the fact that electrons are identical fermions, whereas Higashimura, Hirayama, and Katsuura,3 and Brocklehurst and Higashimural have not done so in a consistent way. The simple statistical argument The Journal of Physical Chemistry, Voi. 78. No. 3, 1974
n n D
A---
(b) Figure 1. Rumer diagrams of a spur with two ion pairs. Ion orbitals ( A and C) and electron orbitals (B and D) are placed alternately. Each line represents two electrons with antiparallel spins. T h e physical molecules AB arid CD are indicated.
presented in ref 1 (immediately following eq 2) is based on the assumption that the electrons are distinguishable and thus we believe it to be misleading. Although they get the correct result for the case of two radical pairs, the fortuitous result cannot be generalized by their methodl to obtain our formula (eq 1)as seems to be implied. Another source of confusion seems to be the failure of Brocklehurst and Higashimura to realize that Rumer dia g r a m ~do~ not represent geometrical arrangements of orbitals in space (of course except fortuitously) but rather couplings between electron spins. According to Rumer’s method4 the orbitals are placed in an arbitrary sequence around a circle and all possible diagrams with noncrossing bonds form a complete basis set of linearly independent state functions. The orbitals are distinguishable but the electrons are not. It is usually true that some particular arrangement of orbitals makes a problem more tractable and in our case it is most convenient to place the cations around the circle alternating with the free electron orbitals as in Figure 1, where A and C are the cations and B and D are the free electron orbitals. Of course, in the recombination, the charge pairs sort themselves out and we take A and B as a combining pair and C and D as the other combining pair. Thus the physical molecules are given by AB and CD. The first Rumer diagram (a in Figure 1) corresponds to both re-formed molecules in singlet states and the second diagram (b in Figure 1) to both in triplet states, after orthogonalization with respect to the first diagram. There is no significance at all of the “double charged” species AC and BD. In our model2 all possible final (orthonormalized) wave functions under spin conservation are given equal statistical weight, since neutralization usually can be expected to release enough energy to populate excited states. If for any reason energy barriers exist, the model does not apply! Wave functions need not appear explicitly in our treatment, and the somewhat more realistic problem of spur recombination in which there is also direct triplet formation by low-energy electron impact can be easily tackled (see section I11 of ref 2 ) . References and Notes (1) B. Brockiehurst and T. Higashimura, J. Phys. Chem., 7 8 , 309 (1974). (2) J. L. Magee and J-T. J. Huang, J. Phys. Chem., 76, 3801 (1972). (3) T. Higashimura, K. Hirayama, and K. Katsuura, Ann. Rep. Res. Reactor Inst. Kyoto Univ., 5, 11 (1972). (4) For example, see H. Eyring, J. Waiter, and G. E. Kimbaii, “Quantum Chemistry,” Wiley, New York, N. Y . , 1944, p 240. (5) The Radiation Laboratory of the University of Notre Dame is operated under contract with the U. S. Atomic Energy Commission. This is AEC Document No. COO-38-934.
Radiation Laboratory5 University of Notre Dame Notre Dame. Indiana 46556 Received March 21, 1973
J. L. Magee* J-1. J. Huang
