a48
Communications to the Editor
clearly indicated in Figure 1. A reduced mass dependence has recently been predicted by O’Reilly.17
Acknowledgment. This work was supported in part by a grant from the Australian Research Grants Committee. The authors are grateful for helpful discussions with Professor H. L. Friedman, Dr. D. E. O’Reilly, and Dr. K. R. Harris.
References and Notes (1) G. G. Allen and P. J. Dunlop, Phys. Rev. Lett., 30, 316 (1973). (2) S. Chapman and T. G. Cowling, “The Mathematical Theory of Nonuniform Gases, Cambridge University Press, New York, N. Y., 1952. (3) J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids,” Wiley, New York, N. Y., 1954.
(4) K. R. Harris, T. N. Bell, and P. J. Dunlop, Can. J. Phys., 50, 1874 (1972). (5) R. Fox and J. N. Sherwood, Trans. Faraday Soc., 67, 1 (1971). (6) L. B. Eppstein and J. G. Albright, J. Phys. Chem., 75, 1315 (1971). (7) M. J. Pikal,J. Phys. Chem., 76, 3038 (1972). (8) R. H. Stokes, J. Arner. Chem. SOC.,72, 763 (1950). (9) K. R. Harris, C. K. N. Pua, and P. J. Dunlop, J. Phys. Chem., 74, 3518 (1970). (IO) T. N. Bell, E. L. Cussler, K. R. Harris, C. N. Pepela, and P. J. Dunlop, J. Phys. Chern., 72, 4693 (1968). (11) P. J. Dunlop, unpublished data. (12) H. D. Ellerton, G. Reinfelds, D. E. Mulcahy, and P. J. Dunlop, J. Phys. Chem., 68, 403 (1964). (13) H. C. Longuet-Higgins and J. A. Popie, J. Chem. Phys., 25, 884 (1956). (14) R. C. Brown and N. H. March, Phys. Chem. Liquids, 1, 141 (1968). (15) H. G. Hertz, Ber. Bunsenges. Phys. Chern., 75, 183 (1971). (16) See eq 14 of H. L. Friedman in “Molecular Motion of Liquids,” J. Lascombe, Ed., Reidel Publishing Co., Dordrecht, Netherlands, 1974. (17) D. E. O’Reilly, J. Chern. Phys., in press.
COMMUNICATIONS TO THE EDITOR
Relaxation Spectra of 6-Methylpurine in Aqueous Solution
’
Publication costs assisted by the National Science Foundation
Sir: Numerous studies dealing with the molecular interactions which maintain the secondary structure of nucleic acids have appeared in recent years. Work by Ts’o and others on the monomeric units of nucleic acids in aqueous solution2 indicate that (a) mononucleosides associate in “stacks” made up of layers of the essentially planar base moiety, (b) the stacks are held together primarily by so called “hydrophobic” interactions rather than by hydrogen bonding, and (c) the formation of stacked bases can be described by a model which assumes that the free-energy change and enthalpy change for the addition of a single base molecule to a stack is independent of the size of the stack. In order to elucidate the dynamics of the stacking process we have measured the sound absorption spectra of aqueous solutions containing 0.025-0.22 M 6methylpurine at 25”. The measurements, which employed a pulse technique covering the frequency range of 7-500 MHz, show excess absorption due to the presence of solute. Although the resulting relaxation curves are somewhat wider than allowed by a single relaxation, the absorption data can be used to calculate an observed, or average, relaxation time 7 and amplitude A according to
measured; Table I gives the least-squares values of the relaxation parameters as a function of formal concentration of solute. The background absorption for all solutions is equal to that of pure water, so that the relaxation time observed is the shortest time of the chemical system. A number of equilibrium studies3-5 have been done in which the data are evaluated by considering a step-wise association model
P,
(2 1
j 2 1
+
1)mer from jmer and is related to the concentrations of the reacting species by K]+l
=
c]+l/clC,’
C1, C,, and C J + l are the molar concentrations of monomer, jmer, and (j l)mer, respectively. The model is usually applied by assuming that the free-energy change for the addition of a monomer to a stack is independent of the size of the stack, i.e.
+
K,,
=
KZ3 = ... = K,’,,’ + I
=
... = K ,
K , is thus the common association equilibrium constant for the aggregation of solute molecules. The rate equations for the kinetic model are
dt
The Journal of Physical Chemistry, Vol. 78, No. 8, 1974
PI+,
K J , ] +is~ the equilibrium constant for the formation of (I’
-dC,’+ where a is the absorption coefficient and f is the sound frequency. Since r is concentration dependent, indicating a second-order process, the observed relaxation is attributed to the aggregation of purine molecules. Figure 1 shows plots of a/f“ us. log f for several of the solutions
+ PI Z
I -‘I
,’+lclc]
-
(‘I+,,,’
+ ‘,’+lI+,C1)Cj+, + k,+2,+lC,+1
j 1 1
The rate constants of the model are represented by the various k; for example, the forward and reverse rate constants of reaction 2 are k J , ] + land k J + 1 , , , respectively, and are related to the equilibrium constant by K J , J + =~
849
Communications to the Editor
jx l O ' l r e c % m - ' 40
30
20 5
10
20
50
100
200
500
f,MHz
Ultrasonic absorption spectra of 6-methylpurine dis0.10 M; 0 , 0.22 M. The arrows solved in water: *, 0.05 M ; ., indicate the inflection points of the curves, corresponding to the relaxation times. Figure 1.
0,025 0.05 0.10 0.15 0.22
3.5 6.3 13.6 15.5 18.0
x
I
=
... = k ,
where kd is the common dissociation rate constant. If this assumption is introduced into eq 3, it can be shown that the absolute value of the largest eigenvalue ( i e . , the shortest relaxation time) becomes equal to kd as cF,formal concentration of solute, approaches zero
7,
10-17
Figure 2. Reciprocal relaxation time plotted against formal concentration of 6-methylpurine.
k,l = k,, = ... = k ,
= 5 . 6 x 10-9
A, =l/crn
Liter
then that
TABLE I: Ultrasonic Relaxation Parameters Resulting f r o m Fitting the Data to E q 1 by Means of a Least-Squares Procedurea CF, M
0.2
0:1
CF , Moles
4.9 4.1 3.7 3.1
In all cases the background absorption was found to be equal to 23.0 X 10 -17 sec*/cm.
kj,j+l/kj+l,j. The parameter cp equals 2 w h e n j = 1 and 1 otherwise. Introducing the perturbation of the concentrations from their equilibrium values, Cj = Cj ACj, a set of linearized rate equations is obtained
+
which may be written in matrix notation as
(3)
a = Aa
a is a concentration vector whose elements are the ACj introduced above. a is the time derivative of a and A is a coefficient matrix whose elements consist of rate constants, equilibrium constants, and C j . The relaxation times of the chemical reaction system b e obtained as the negative reciprocal eigenvalues of A.6 A similar kinetic model has been used to describe the association of solutes due to hydrogen bonding.7 *a Despite the complexity involved this model may be evaluated by making an assumption analogous to that made above in the equilibrium model. We assume that the rate constants for the association of any given stack with a monomer is independent of the size of the stack
k,, = k23 = ... = k,,I + 1
... = k,
ka is the common association rate constant. It follows
Figure 2 shows the inverse relaxation time plotted against formal concentration of solute. Extrapolation to CF = 0 gives kd = 1.6 x 10s sec-a. This result, together with that of Porschke and Eggers,g suggests that the rate of aggre: gation of purine bases in aqueous solutions (and probably of the nucleosides as well) is a diffusion-controlled process, with the stability of the complex being reflected in the dissociation rate constant. The multistep mechanism (given by eq 2), which has previously been used in conjunction with equilibrium measurements, can be seen toexplain kinetic results as well, at least as far as the mechanism has been tested in this work. The mechanism does predict several relaxation times, and indeed the absorption spectra show relaxation curves slightly broader than would be expected on the basis of a single relaxation time. This also seems to be the case for P,W-dimethyladenine.g Additional work is necessary before the observed relaxation can be rationalized in terms of the amplitudes and distribution of the predicted relaxation times. With additional thermodynamic and kinetic measurements it will be possible to simulate the sound absorption spectra6 thus providing a check on the mechanism. Acknowledgment. The authors take pleasure in acknowledging the generous assistance of Professor Gordon Atkinson in providing the laboratory facilities which made this work possible. They also wish to thank Mr. Kerry Sublett for technical assistance in carrying out this project. This work was supported by Grant No. GP-33781X from the National Science Foundation. References and Notes (1) Presented in part at the 165th National Meeting of the American Chemical Society, Dallas, Tex., April 1973. The Journal of Physical Chemistry, Vol. 78, No. 8, 1974
850
Communications to the Editor
(2) P. 0. P. Ts’o in “Fine Structure of Proteins and Nucleic Acids,” G. D. Fasman and S. M. Timesheff, Ed., Marcel Dekker, New York, N. Y., 1970, pp 49-190. (3) P. 0. P. Ts’o and S. I . Chan, J. Amer. Chem. SOC.,86,4176 (1964). (4) A. D. Broom, M. P. Schweizer, and P. 0. P. Ts’o, J. Amer. Chem. SOC.,89, 3612 (1967). (5) S. J. Gill, M. Downing, and G. F. Sheats, Biochemistry, 6, 272 (1967). (6) F. Garland, R . C. Patel, and G. Atkinson, J. Acoust. SOC.Amer., 54, 996 (1973). (7) J. Rassing and 6.M. Jensen, Acta Chem. Scand., 24,855 (1970). (8) J. Rassing and F. Garland, Acta Chem. Scand., 24, 2419 (1970). (9) D. Pdrschkeand F. Eggers, Eur. J. Biochem., 26,490 (1972).
Department of Chemistry University of Oklahoma Norman, Oklahoma 73069
Frank Garland* Ramesh C. Patel
0.54
/
O
I
D/s 0.3-
F4
-
0.2
NF3 F6
Received November 5. 1973
0.1
Isotope Effect in Energy Losses for Deactivating Collisions of Tetrafluoromethane with Chemically Activated Fluoroethyl Radicals C H 2 1 8 F C H 2 and CD218FCD2 Publication costs assisted by the Dwsion of Research, U S. Atomic
-
0 0
0.5
1.0
2.0
1.5
0.89. 1.78 2.67 1.29 2.58
5.87
CF4
lO3/P
NF3 F6
(TORR)
Figure 1.. Graph of decomposition/stabilization vs. (pressure)for CH218FCH2 and CD2”FCD2 in sF6, CF4, and NF3. Different (pressure)-’ scales are used for each gas, chosen to give the same visual slope for CD218FCD2 in all three gases.
Energy Cornmiss/on
Sir: The magnitude of collisional energy transfer from chemically activated molecular species is often evaluated from the deviations from linearity at very low pressures of graphs of decomposition/stabilization (D/S) ratios us. (pressure)-l, and can be expressed in terms of a characteristic energy loss, e.g., step size in a step-ladder deexcitation mode1.l As yet, few measurements of step size exist for isotopic activated species in collision with the same bath gas, and these measurements have not indicated any isotopic differences in energy 1 0 ~ s . ~We have formed CHzisFCH2 and CFz18FCD2 by addition of thermal i8F to C2H4 and to C2D4 in the presence of excess NF3, CF4, and SFg,4-6 and have observed a different ratio (4.2 i 0.4) of (D/S)H/(D/S), for CF4 from that (6.2 f 0.7) found for NF3 and SFe, as summarized in Table I and Figure 1. The (D/S) graphs have been characterized by the slopes of linear plots, and are expressed as extrapolated pressures for half-stabilization. This difference in magnitude of the isotope effect requires that there be an isotope effect in the energy removal by collision with either CF4 or with SF6 and NF3 (or with all three). The molecules NF3, CF4, and SFe increase in size in that order and should show a corresponding decrease in the lifetimes of excited species toward stabilization. However, since the pressure for halfstabilization in CF4 is appreciably higher than for SF6, we conclude that (a) CF4 is a “weak collider,” i.e., that activated species are frequently still able to undergo decomposition despite one collision (or more) with CF4 as bath gas; and (b) that the average energy loss per collision with CF4 (corresponding to step size for the step-ladder model) is less for CD2l8FCD2 than for its isotopic counterpart CHz18FCH2. The experimental procedures have been described in detail earlier for the addition of 18F to C2H4 in SFs or CF4,e and are essentially unchanged with the substitution of C2D4 and/or NF3. The (D/S) ratios are determined through radio gas chromatographic measurements of the relative yields of CH2=CH18F(D) us. CH3CH218F (S, 3 3
The Journal of Physical Chemistry, Vol. 78, No. 8, 1974
TABLE I: Extrapolated Pressures for Half-Stabilization for Fluoroethyl Radicals i n NF,, CFa,and SFBBath Gases Extrapolated half-stabilization preeaures, Torra Bath gas
CHz’aFCHz radical
CDz’aFCD2 radical
Ratio H / D
NFI CFa SFe
117 f. 6 144 f 10 80 f 6
19 f 2. 34 f 3 13 f. 1 . 5
6 . 2 i. 0 . 7 4.2 & 0.4 6.2 f 0.8
a Pressure at which (D/S) = 1.0, if linear extrapolations are made for data in Figure 1. Note that none of the measurements have been made below 250 Torr.
followed by abstraction of H from HI), or of their tetradeuterio counterparts. The physical characteristics of the experiment (chiefly, the path length required to thermalize l8F atoms with > l o a eV initial kinetic energy us. the dimensions of the fast neutron generator irradiation facility) make accurate experiments impractical below about 400 Torr total p r e s s ~ r e , so ~ - that ~ all (D/S) measurements have been carried out under conditions in which stabilization is heavily dominant. The pressure range of measurement is approximately 400-4000 Torr for all systems. Experiments with varying ratios of CF4/C2H4, etc., have confirmed the earlier finding in the SFs/C2H4 systeme that nonthermallsF atom addition is of negligible quantitative importance to (D/S) ratio measurements when the mole fraction of bath gas is >0.90. The experimental data have been graphed in Figure 1 with different reciprocal pressure scales for each bath species, chosen so that the slopes of the graphs of CD218FCD2 will all be visually the same. The differences in slope for CH218FCH2 with CF4 and with SFe/NF3 are then clearly shown. In each system, the observed (D/S) ratio reflects the competition between the rate constant for decomposition, kdHSFs, and that for stabilization, kSHSFe, such that the isotopic ratio of (D/S) values therefore includes four rate
