J. Phys. Chem. 1984,88, 6353-6356
6353
This model of part dehydration of the bases is not valid for the nucleosides. A large part of the nucleosides, the ribose unit, is hydrophilic. This part of the molecule will probably be hydrated even in the stacks. The bulky, fully hydrated ribose unit probably requires much space, leading to less efficient packing of the nucleosides when they form stacks. The nucleosides are amphiphilic molecules containing a hydrophilic part, the ribose unit, and a hydrophobic part, the base. In this respect they resemble micelle-forming surfactants. Both types of compounds also exhibit positive AVvalues when they form aggregates, micelles or stacks. Perhaps this is a general feature of amphiphilic aggregation in water as opposed to purely hydrophobic compounds. Normally, negative volume differences for a process lead to negative compressibility changes as well and positive volume changes to positive compressibility change^.^'^^^ This is not observed for the nucleobases. They exhibit negative AV, and positive AK, values. Further the AK, values of the nucleosides are unusually large, especially for uridine. Normally the solutes are considered incompressible; Le., the intrinsic compressibility is zero. The observed compressibilities are ascribed to the compressibility of the hydration sheath. For the stack as an entity the intrinsic compresibility need not be zero. The distance between the monomers may well be reduced by pressure. This will explain the large partial molar compressibilities obtained for the nucleobases and especially the nucleosides of the stacks. Registry No. Purine, 120-73-0; caffeine, 58-08-2; cytidine, 65-46-3; thymidine, 50-89-5; uridine, 58-96-8.
compressibility of this compound. Table I1 shows AV,O and M: for the stacking process calculated on the basis of both the SEK and AK models. There is only a very moderate model dependence. The AK model yields systematically lower values, but the differences are practically within the experimental error. Cesaro et aL2*have calculated AVg for caffeine by assuming only dimer formation, and even then the result remains the same. It thus seems safe to conclude that the AV: and AK: values are real and not model dependent. The difference between the bases and the nucleosides also shows in the AV: and AK: values. Purine and caffeine exhibit negative AV: values, and the nucleosides positive values (zero for thymidine). All AK: values are positive, but they are 1 order of magnitude larger for the nucleosides. Stacking of the bases leads to a volume contraction. The monomer is more efficiently incorporated in the stacks than in water. If hydrophobic solutes are dissolved in water, either they form a separate phase above a certain concentration or, if they are amphiphilic, they form micelles. A volume increase is observed in both cases. This suggests that hydrophobic solutes occupy interstitial positions in the water structure, requiring little extra volume.37 If this is also the case for the nucleobases, it is difficult to explain the negative volume changes of stacking of the nucleobases. Kasarada30 suggested that AV, still can be negative for very small aggregates. Gaarz and L ~ d e m a n , on ~ ' the other hand, have argued that this comparison of the association into stacks with the formation of a separate phase is questionable. The process to be considered as a parallel to stacking is the approach of two monomeric hydrophobic solutes from infinity to close contact. Such a process must involve removal of only part of the hydration sheath of both molecules. Such a process may well be connected with a volume decrease as seen for the nucleobases. It has been observed that the excess volumes of many hydrophobic solutes in water do in fact decrease with concentration up to a minimum value, the minimum occurring a t mole fractions between 0.1 and 0.2.39*40
(39) Hvidt, A, J. Theor. Biol. 1975, 50, 245. (40) Franks, F. In "Water: A Comprehensive Treatise"; Franks, F., Ed.; Plenum Press: New York, 1975; Vol. 4. (41) H~iland,H.; Vikingstad, E. J . Chem. SOC.,Faraday Trans. 1 1976, 72, 1441. (42) H~iland,H.; Ringseth, J. A.; Brun, T. S.J . Solution Chern. 1979, 11. 719.
Cation Charge Effect on the Rate of Complexation of Crown Ethers: Ba(CIO,), In DMF
+ 18C6
William Wallace, Edward M. Eyring, and S. Petrucci" Department of Chemistry, Polytechnic Institute of New York, Brooklyn, New York 11201, and Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 (Received: June 1 1 , 1984; In Final Form: August 6, 1984)
Ultrasonic absorption spectra in the frequency range 1-500 MHz for barium perchlorate-18-crown-6 solutions in dimethylformamide in the concentration range 0.1-0.5 M, at various temperatures, are reported. The ultrasonic spectra are described by two Debye relaxation processes. Independence of the relaxation frequencies on concentration and the linearity of the excess maximum sound absorption coefficients per wavelength with concentration lead to interpretation of the data in terms of the Eigen-Winkler mechanism k
k
k-2
k-3
Me2+.-C 1, MeC2+
(MeC)2+
where the species Me2+-.C, MeC2+,and (MeC)2+symbolize three different metal ion-crown ether complexes. The forward rate constants k2 and k3 are larger for Ba2+than for K+ in DMF despite the fact that the two ions have similar ionic radii. Differences are tentatively rationalized in terms of an ion-dipole charge-enhanced potential affecting the rate constants. The situation is different in water where the reported complexation rate constant is larger for K+ than for Ba2+ and the rate-determining process of the complexation appears to be removal of water from the first coordination sphere of the cations. The same Eigen-Winkler mechanism applied to the removal of water dipoles from the first coordination sphere of the ions seems to account for the findings in water.
Introduction The kinetics of complexation of alkali metal ions with the crown ether 18C6 in the solvent dimethylformamide (DMF) have been *Department of Chemistry, Polytechnic Institute of New York.
recently studied'J by ultrasonic relaxation techniques with the results corroborated by ancillary Raman spectra' and backed by (1) K. J. Maynard, D. E. Irish, E. M. Eyring, and S . Petrucci, J . Phys. Chem., 88, 729 (1984).
0022-3654/84/2088-6353$01.50/00 1984 American Chemical Society
6354
Wallace et al.
The Journal of Physical Chemistry, Vol. 88, No. 25, 1984
TABLE I: Ultrasonic Parameters p,, fI,bII,fIr,B , and Sound Velocity u for Ba(C104)2 + 18C6 in DMF at the Various Concentrations and Temperatures Investigated"
T, OC 25
25 25
CBa(C104)p
ClSC6,
M
M
0.50
0.50 0.40 0.30
0.41 0.29 0.20
25
15 33
0.41
40
0.41
MHz 120 120 120
170 150
125 85 170
0.20
0.40 0.40 0.40
0.41
h?
x 105
120 110
MHz
10176, cm-' s2
10-5U: cm s-I
12 12 12 12 8 17 24
47 43 35.5 32.5 42 42.5 45
1.491
hI3
x lo5
PI1
350
290 220
120
140
90 140
280 300
175
300
1.489 1.480 1.476 1.528 1.467 1.438
cm-l s2. The values of "The values of p,, fr, plI, and firare affected by an average error of 5%. The values of B are precise within f 0 . 5 X u are urecise within *1 to 2%. b~ = (1.465 + 0.05,c) lo5 cm s-I, r2 = 0.97 for 0.2 IC I0.5 M at 25 OC. u = (1.5800 - 0.0035T) lo5 cm d,r2 = 0.965 for 15' It 5 40 O C at C = 0.4, M. parallel calorimetric titrations aimed at determining complexation stability constants. The is in mechanism
+
MenC C
k
k-I
Me"+.-C
kl k-2
Me@
k
2 (MeC)"' k-3
0.40M in DMF, !=33'C
(I)
describes the data adequately. In addition, the data suggest that the rearrangement of the ligand is the rate-determining step for the overall process leading to the species (MeC)"+, where the metal is encapsulated in the ligand cavity. No kinetic data exist in D M F for divalent cations reacting with 18C6. This is in contrast to our knowledge of aqueous solutions of these solutes wherein the rate-determining step for the divalent metal cation crown ether complexation process is believed4J to be the removal of water from the first coordination sphere of MeZ+. If the rate-determining step is the final ligand attack in D M F rather than solvent removal as in water, a charge effect could influence the potential barrier for the rate constant k3 in opposite directions in the two solvents as will be shown below.
1
1
2
5
10
1
1
,
50 100 200 500 f(MHz)
20
B%C104)t 0.29M + 18C6 0.30M In DMF. 1=25'C
Experimental Part The equipment and procedures have been described elsewhere.'q2 AnThe materials D M F and 18C6 were purified as hydrous Ba(C104)2(Smith, Cleveland, OH) was redried in a torr vacuum at room temperature.
I
Results Figure 1 shows representative plots of the quantity fi = aexcX, the the excess sound absorption coefficient per wavelength, where p = (a- Bf )u/J vs. frequency$ In the above CY is the sound absorption coefficient (neper (Np) cm-'), B is the background sound absorption at f >>f, wheref, is the relaxation frequency (or frequencies) for the processes under examination, and
Ba[C10al10.4lM+l8C6
'i __ 1----
-/'
5
The variable u is the sound velocity, and f is the frequency of the sound wave. The solid lines in Figure 1 correspond to the sum of two Debye relaxation processes according to the function:
*-.
1 0 20
--__
50 IO0 ZOO
500
f(MHz)
I
'
Figure 1. Representative plot of p = aexcXvs. the ultrasonic frequency ffor Ba(C104)2+ 18C6 in DMF: (a) 0.41 M Ba(C104)2+ 0.40 M 18C6, T = 33 O C ; (b) 0.29 M Ba(C10& + 0.30 M 18C6, T = 25 OC; (c) 0.41 M Ba(C10& + 0.40 M 18C6, T = 15 OC.
the sound velocities for the systems investigated.
In Figure 1 the dashed lines correspond to the contributions of the two Debye relaxation processes to k. The arrows indicate the positions of the two relaxation frequenciesh andfII. pI and wII are the maximum values of pl and p2 for f = fi and f = fI1, respectively. Table I reports all the ultrasonic parameters and (2) C. Chen, W. Wallace, E. M. Eyring, and S . Petrucci, J . Phys. Chem., 88, 2541 (1984). ( 3 ) H . Rushton, H. Rohrs, R. Adamic, S.Petrucci, and E. M. Eyring, unpublished data. (4) G. W. Liesegang, M. M. Farrow, N. Purdie, and E. M. Eyring, J. Am. Chem. SOC.,98, 6905 (1976). ( 5 ) L. J. Rodriguez, G. W. Liesegang, M. M. Farrow, N. Purdie, and E. M. Eyring, J. Phys. Chern., 82, 647 (1978).
Calculations One may write the Eigen-Winkler mechanism in terms of the three equilibrium constants K , , Kz, and K3 as
Men+ + C
G=
Me"+-C
Kl
K2
MeC"'
2 (MeC)"'
(111)
If the overall Kz = K l ( l + Kz + K2K3) >> 1, and K , >> 1 , K2 >> 1, K3 >> 1, it results for loosely coupled steps (fI >>fi~) that the two observed reciprocal relaxation times are given by kz = kT
7I-l
q1-1
N
e-ml*~RTe~l*~R
kT ~ - A H I ' / R T ~ ~ S , * I R k =3 h
(IV) (VI
The Journal of Physical Chemistry, Vol. 88, No. 25, 1984 6355
Charge Effect on Rate of Crown Ether Complexation
In(r;h/T)vs. 1/T for Ba(C104),tlBC6 in DMF
- 13.5 I-
\
TABLE II: Kinetic and Thermodynamic Parameters for the Observed Ultrasonic Process in the System Ba(CI0.)2 + 18C6 in DMF k2 = 7.5 X lo* s-I at T = 298.2 K AH2* = 4.1 kcal/mol AS2*= -4.4 cal/(K mol) AH, = 3.8 kcal/mol
--
-13.0r
k3 = 7.5 X lo7 s-' at T = 298.2 K
bH E
14.01
13.5
c
3.1
3.2
Figure 2. In DMF.
3.3 3.4 (10 3 1 ~ )
( ~ f l / q and
-231
3.5
- 1 2.5
AH3* = 7.2 kcal/mol AS3* = 1.8 cal/(K mol) AH3 = -1.9, kcal/mol
71 2.0
wavelengthp.,and pn vs. concentration t-25'C
3.6 200
In ( q C I / T ) vs. 1/T for Ba(C104)2
+ 18C6 in
100 0.1
In(p,T/u2), and In(p,T/u2) VI. 1/T for Ba(CI04)2+18C6 In DMF
Figure 4. DMF.
'Slow'process
n
-25 3.1
I
3.2
I
0.2
0.3
0.4
0.5
C ( rno Ie / d rn3)
1
I
3.3 3.4 (1031~)
3.5
Figure 3. In ( p I T / u 2 )and In ( p I r T / u 2vs. ) 1 / T for Ba(CI04), in DMF.
3.6
wl and pLII vs. the concentration C for Ba(C104),
+ 18C6 in
first-order or pseudo-first-order processes VI according to eq VI1 and VIII. Linear regression applied to the p vs. C data forcing the intercept through the origin (50% statistical weight to the origin) gives for pIvs. C a n 9 = 0.984 and slope = 3.63. For the pII vs. C data by the same procedure one obtains 9 = 0.998 and slope = 7.14. From eq VI1 and VI11 one obtains
+ 18C6
112
K2K3)
= (2.75K2K3)'I2
In the concentration range where ultrasonic measurements are feasible, the concentration of free Me"+ and C is low under the above conditions. Then one is justified in using the simpler expression Me"+--C S Me@ S (MeC)"+ K2 4 It has been shown then1.2,6that for process VI PI
= 7r
(AVsd2 R T (1
I -
2/3,
K2C
(VI)
+
c -_--(Av81)2 R T K2K3 ?r
+ K2)(1 + K2 + K2K3) = 2/3,
(VII) KII
?r (AvsII)2 ( l + K2)K2K3c ?r (AvsII)2 c = -20s R T (1 K2 K2K3)2= 2/38 R T K3 (VIII)
+ +
N
A
P
-
for K2, K3 >> 1. A plot of In ( T < ~ / Tvs. ) 1 / T is shown in Figure 2. The solid line has been calculated by linear regression analysis. The results are coefficient 9 = 0.99, slope = -2036, and intercept = 21.56, from which AS2* = -4.4 cal/(K mol) and AH2*= 4.1 kcal /mol. Similarly in Figure 2 a plot of In ( T ~ ; I / T ) vs. 1 / T is shown. From linear regression analysis one obtains rz = 0.99,, slope = -3641, and intercept = 24.68, from which it follows that AS3* = 1.82 cal/(K mol) and AH3*= 7.2 kcal/mol. A plot of the quantity In (pIT/u2) vs. 1 / T is shown in Figure 3. Linear regression gives 3 = 0.89, (l/R)(AH2 + AH3) = slope = 924, and intercept = -27.78, from which one calculates (AH2 AH3) = 1.84 kcal/mol. Similarly from Figure 3 and the plot of In (p11T/u2) vs. 1 / T one calculates by linear regression: r2 = 1.OO,(1/R)AH3 = slope = -993, and intercept = -20.64 from which AH3 = -1.97 kcal/mol. Then AH2 = 1.84 - AH3 = 3.8 kcal/mol. Table I1 collects all the thermodynamic and kinetics parameters which were extracted from the above analysis. Figure 4 shows the quantities w1 and pII plotted vs. C. Linearity confirms the
+
Unfortunately, the lack of knowledge of the quantities K2 and K3 prevents further progress on this point. It should also be noted that we have measured both the systems Mg(C104)2 18C6 and Ca(C104)2 18C6 at concentrations of 0.3 M and molar ratio R = (Mez+)/(18C6) = 1 by ultrasonic absorption. Very small effects in terms of excess sound absorption with respect to the solvent have been observed. This may indicate that the effects exist in a frequency range inaccessible to us or that the complexation stability constant between Mg2+ or Ca2+ and 18C6 is small. A more pronounced selectivity of the alkaline earth ions with respect to the alkali ions when reacting with 18C6 in water has been previously reported. Specifically, the logarithm of the stability constant when plotted vs. the ratio (diameter cation/diameter cavity) shows more than three orders of magnitude change in going from Ca2+to Ba2+ but only a little more than one order of magnitude change in going from Na+ to K+.6
+
Discussion The effect of the charge of Ba2+ on the reaction with 18C6 in D M F may be tentatively rationalized as follows: For K+ reacting with 18C6 at comparable concentrations at 40 O C in DMF solvent, it has been reported2 thafIK cz 30 M H z andfIIK 3 MHz compared to the present valuesfIBa = 175 M H z andfIIBa= 24 MHz for Ba2+ 18C6 in D M F at 40 OC. ThusfIBa/fIK= 6 and hlBa/fIIK = 8. It is clear that since the solvent is more strongly bound to alkaline earth ions than to alkali ions of the same approximate radius, if the solvent removkl were the rate-determining step for
+
(6) (a) H. Schneider, S.Rauh, and S. Petrucci, J . Phys. Chem., 85, 2287 (1981). (b) J. D. Lamb, R. M. Izatt, J. J. Christensen, and D. J. Eatough in "Coordination Chemistry of MacrocyclicCompounds", G. A. Melson, Ed., Plenum Press, New York, 1979, Chapter 3, p 148.
Wallace et al.
6356 The Journal of Physical Chemistry, Vol. 88, No. 25, 1984 the complexation process with 18C6, one could not rationalize easily the above experimental ratios. We however, that for K+ the ligand rearrangement was the rate-determining step in DMF. The radius of the two cations cannot be the leading factor in the above difference, because the two cations have similar cm; r B p= 1.43 X ~ m ) .We ~ ionic radii (rK+= 1.33 X propose that the difference may arise through the charge effect in the ion-dipole potential affecting the rate constants. Recalling from (IV) and (V) that 7f1 k2 and q I - l N k3, one may write for both the fast and slow processes
=
L(Ba) -=-= f,(K)
ki(Ba) ki(K)
[(kT/h) ex~(-AG*i(Ba)/kr)I (IX) [(kT/h) e~p(-AG*~(K)/kTll
with i = 2, 3. One may split the AG*[s into two components: a nonelectrostatic contribution and an electrostatic contribution, tentatively identified with the ion-dipole potential U = -Zep/t$, with Z the cation valency, e the electronic charge, e the solvent permittivity, and r the cation-own ether distance in the activated complex. Then by assuming AG*,,,(Ba) = AG*nos(K),for the nonelectrostatic contributions to the AG* values, one obtains AG*(Ba) - AG*(K) kT
2ep - ep
ep
er2kT
er2kT (X)
E-=-
-
By choosing reasonable parameters such as p = 5.5 X esu cm, e = 36.6 (for DMF), one obtains (ep/t?kT) cm, r = 3 X = (8.015 X 10-14)/(4.32 X = 1.86, namely, the ratio V;(Ba)/f,(K)] = 6.4 which is of the expected order of magnitude at 40 OC. Numerical agreement with the experimental ratio should not deemphasize the naivety and simplistic approach of the above calculation. In addition, the functional form of the ratio which depends on an exponential allows for a wide fluctuation of the result by altering the ratio p / $ . Nevertheless the calculation offers an alluring rationalization of the results and an indirect confirmation that the removal of the solvent is not the rate-determining step of the overall complexation process for the alkali and alkaline earth cations in DMF. One should also take notice of the case where the removal of the solvent is the rate-determining step. This has been reported for alkali4 and alkaline earth ions5 reacting with crown ethers in water. Thus from the relation ~11-l
= (27rjJ-l
s-l. Hence in aqueous solutions, complexation of 18C6 with metal cations involves a decrease of rate constant with increasing cation charge for the two cations K+ and Ba2+(at variance with the DMF solvent), the ratio being [k23(Ba2+)/k23(K+)] = 0.3. This behavior may be rationalized if one retains the c o n c l ~ s i o n ~ ~ ~ that the rate-determining step is the removal of water coordinated around the cation. The “event” that determines the reaction rate is the separation of several water molecules from the cation in the activated state. Hence the energy barrier of the reaction might be increased by an approximate amount
k23((Mn+)+ (C))
+ k32
(XI)
where (C) is the total concentration of the free crown ether, it has been reported for K+ reacting with 18C6 in water4 at T = 298 K that kz3 = 4.3 X loEM-’ s-l, whereas for Ba2+ reacting with 18C6 in water5 at T = 298 K one has kzs = 1.3 X 10’ M-’ (7) F. Basolo and R. G. Pearson, “Mechanism of Inorganic Reactions”, 2nd ed, Wiley, New York, 1967, p 81.
with respect to neutral particles. In the above 2 is the charge (valency) of the cation, p is the dipole to be separated from the cation, r the cation to solvent-dipole distance, and t the solvent permittivity. We will estimate the following quantities: r N 2.8 X cm (the sum of the radius of a water moleculeE taken as 1.45 X cm and the cation radius taken on the a dipole 1.4 X cm); p = 1.85 X esu ~ me = ; 78.5; ~ average at and n = 4 which corresponds to a coordination of the crown ether on a plane, a model that relies on some of the solid state findings.1° Thus one obtains
--
kHz0(Ba) -kH20(K) In
kH20(Ba) ~
kHzo(K)
-
enp er2kT
- exp(U/kTj
exp(U/k r )
- - 4(1.44
X
10-14)
4.11 x 10-14
= - 1.40
or kH20(Ba)/kH20(K) = 0.25, in good agreement with the experimental ratio. Changing n to a value of six, which corresponds to total cation desolvation, will result in a ratio equal to 0.12, which is still an acceptable result. Despite the agreement, the calculation can be subjected to the same criticisms as for the previous case in DMF. It should be taken as a possible, tentatiue rationalization of (a) the experimental finding that Ba2+ reacts slower than K+ with 18C6 in water but faster in DMF, and (b) the derived conclusion that removal of waters of solvation in ~ a t e r and ~,~ rearrangement of the ligand in DMF1n2 are respectively the rate-determining steps in the two solvents. Acknowledgment. The authors express their gratitude to the N S F for generous support through grant no. CHE8108467. Registry No. DMF, 68-12-2; 18C6, 17455-13-9; Ba, 7440-39-3. (8) J. Morgan and B. E. Warren, J . Chem. Phys., 6, 670 (1938). (9) R. W. Gurney, ’Ionic Processes in Solution’’, McGraw-Hill, New York, 1953, pp 50 and 266. (IO) J. D. Dunitz and P. Seiler, Acta Crystallogr., Sect. E , 30, 2739 (1974); P. Seiler, M. Dobler, and J. D. Dunitz, Ibid.,30,2744 (1974); M. Dobler. J. D. Dunitz. and P. Seiler. Ibid., 30. 2741 (1974): M. Dobler and R. P. Phizackerley, Ibid.,30,2746, 2748 (1974); J. D. Dunitz and P. Seiler, Ibid.,30, 2750 (1974).
