J. Phys. Chem. 1989, 93. 6357-6363 transfer into two separate steps. This could be done in a molecular shift register as well. A system designed so that a /3 transfer y transfer is driven by is driven by a wavelength A,, while /3 X2, would have the desired property. This might be thought of as a rough analogy to green plant photosynthetic reactions (which use two light initiated reactions) rather than bacterial photosynthetic reactions. In practice, pulses of AI and X2 would alternate. The advantage of this scheme is that the light pulses need not be short compared to electron-transfer times, since there can be a maximum shift of only one monomer unit per clock cycle regardless of how long the light pulses last. Both the demands on the laser and the possible problems arising from multiphoton effects are simplified by such a scheme. Light is an answer to the clock and power supply problems. With light, the fabrication problems of a real device appear to lie within understood chemistry, VLSI, and physics. Light is quite possibly not the answer. As others have noted, diffusing energetic molecules (playing the role of ATP) could in principle be a much better power supply. Molecular wires might solve both the clock and/or power supply problems. However, such solutions involve technical problems that are unresolved at present. An (.By), shift register polymer with high efficiency would be interesting in its own right. The general question of light-driven shift polymers can be investigated with far shorter oligomers tethered at only one end, and without the need for microfabrication. The materials science and chemical synthesis questions raised in such schemes are also of interest for more conventional electronics. For example, much more simple electron-transfer +
-+
6357
polymers could be made to serve as molecular wires over short distances in conventional VLSI without the need for light as a driving source. Short-range self-wiring with such molecules might replace certain metallization or polysilicon layers. This would be particularly attractive if a class of specific surface-to-polymer end bindings (through which electrons could be transferred) were developed.3s Such an approach relates also to neural network chip architectures, where the connectivity is complex, where wiring faults can be tolerated, and for which connections having a large resistance can be a central part of a computational circuit.36
Acknowledgment. We thank H. B. Gary and H. H. Thorp for useful discussions and acknowledge the Office of Naval Research (Contract N00014-K-0377), the Department of Energy’s Energy Conversion and Utilization Technologies Division (ECUT) that supported the work at the Jet Propulsion Laboratory, California Institute of Technology, through an agreement with the National Aeronautics and Space Administration, and the Brazilian agencies FAPESP nd CNPq that supported the work in Brazil and also provided support for visits of J.J.H. and D.N.B. to Brazil. (35) Arrhenius, T. S., et al. Proc. Natl. Arad. Sei. U.S.A.1986.83, 5355. (36) A single strand of half-reduced al-a2-a3-a4... polymer 4000 units long, and having an internal electron-transfer rate ai a,+,offs-I, has an
electrical resistance of about 102’/fQ. Sincefcan be made larger than IOLo for hopping transfers between very nearby localized sites, a single strand a few microns long can have a resistance lower than 1O’O 0. A single such molecular strand has sufficient conductance to discharge a small VLSI floating gate in 1 ms.
Isomeric Relaxation Kinetics of the Macrocycles 18-Crown-6, Diara-18-crown-6, and Cryptand 222 in Acetonitrile and Methanol Licesio J. Rodriguez,+ Edward M. Eyring, and Sergio Petrucci* Weber Research Institute and Department of Chemistry, Polytechnic University, Route 1 IO, Farmingdale, New York 1 1 735, and Department of Chemistry, University of Utah, Salt Lake City, Utah 841 12 (Received: May 5, 1988; In Final Form: January 9, 1989)
Ultrasonic relaxation spectra in the frequency range 0.5-500 MHz for the macrocycles 18-crown-6 (18C6), cryptand 222, diaza- 18C6 (Kryptofix-22), and (CloH21)2-diaza18C6 (Kryptofix 22-DD) in the solvent acetonitrile are reported. A single Debye relaxation for 18C6 and cryptand 222, a double Debye relaxation for Kryptofix 22, but no relaxation process for Kryptofix 22-DD describe the ultrasonic data in the solvent acetonitrile. A single Debye relaxation, only visible at much lower temperatures, as reported before, for 18C6 in methanol, a double Debye relaxation, as reported before, for cryptand 222 in methanol, a double Debye relaxation process for Kryptofix 22 in methanol, and a double Debye relaxation process for Kryptofix 22-DD in methanol were also observed. The different behavior in the two solvents reflects the importance of the solvent in the dynamic properties of these macrocyclic ligands. In each solvent the relaxation processes are interpreted at a molecular level for the diaza compounds (Kryptofix 22) in terms of the rotation relaxation of the two nitrogens coupled with the rotational rearrangements of the side chains. When a third chain (as in cryptand 222) is added, only one process is detected in acetonitrile. In methanol, however, both processes are still visible for cryptand 222, as reported before, although the one at higher frequency is much slower than for Kryptofix 22. When two open hydrocarbon chains are substituted for the two protons as in Kryptofix 22-DD contrasted with Kryptofix 22, two processes, much slower than for Kryptofix 22 and the lower one below our accessible frequency range, appear to be present. The different behavior of Kryptofix 22 and Kryptofix 22-DD is interpreted as rising from the dragging of two long chains in the rotational relaxation of the latter compound.
Introduction Substitution of atoms other than oxygen in the polyether chains of macrocycles such as crown ethers, and their influence on the mechanism of complexation of macrocycles with alkali metal ions, is a still largely untouched problem. Before investigating this *Address correspondence to this author at Polytechnic University. On sabbatical leave from the Department of Physical Chemistry, University of Salamanca, Salamanca, Spain.
0022-3654/89/2093-6357$01 .50/0
question, it is necessary to understand the isomeric behavior of the potential ligands and the effect of the solvent on the isomeric behavior of the macrocycles. To this end, the macrocycle 18C6 (I) has been studied in the solvent acetonitrile, which is known to form an adduct in the solid state with 18C6. Substitution of the oxygen atoms in positions 1 and 10 of 18C6 with an N-H group produces diaza-l8C6 (11). This compound has been studied in both acetonitrile and methanol. Substitution of the two protons bound to the nitrogen atoms by the ethereal 0 1989 American Chemical Society
6358
The Journal of Physical Chemistry, Vol. 93, No. 17, 1989
Rodriguez et al.
I
18C6 0.075M in CH3CN, 1=25'C
Cryptand 2 2 2 0 10M in CH&N, 1=25OC 300-
p,=240~10-~
p = 4 8 0 x 1O+ 1,=8OMHr
600
1,=95MHZ
B = 5 7 x 10-'7cm-'52 u = 1 . 2 7 9 x 1 0 5 c m s-'
200-
*i s! x
l00C
O L 0 1
O0 1
05
0 2
1
2
5
10
20
50
100
200
500
J
0 2
0.5
1
2
5
10
Figure 1. Ultrasonic spectrum expressed as excess sound absorption per wavelength, p, vs frequency,f, for 0.075 M 18C6 in CH3CN at 25 OC.
-
20
l(MHz)
50
1 0 0 200
500
Figure 2. Ultrasonic spectrum expressed as p vsffor 0.10 M cryptand 222 in CH3CN at 25 OC.
chain -CHz-CHzUCHz-CHz-O-CHz-CH2- gives te cryptand 222 (111). This compound has been studied in acetonitrile. Comparison with previous studies of 18C6 and cryptand 222 in methanol were drawn. Substitution of the two protons of Kryptofix 22 by two C,,,Hz1 hydrocarbon chains yields Kryptofix 22-DD (IV). This compound has been studied in both acetonitrile and
00
I
0C 1
11
02
0 5
1
2
5
10
I(MHz)
20
-
50
100 200
500
Figure 3. Ultrasonic spectrum expressed as p vsffor 0.20 M Kryptofix in CH3CN at 25 OC.
d m
I3L
methanol. All these studies have been carried out by ultrasonic relaxation techniques.
Experimental Section The equipment for the pulse and resonator ultrasonic absorption measurements has been described previously.1~218C6 (Aldrich) was recrystallized from spectroscopic grade acetonitrile and dried in vacuo before use. Kryptofix 22, cryptand 222, and Kryptofix 22-DD were Merck products. They were used as received. Acetonitrile (Aldrich Gold Label) was refluxed over P 2 0 5for several hours and then distilled in an all Pyrex column with no grease on the joints. Methanol (Aldrich Gold Label) was distilled over an aluminum amalgam in the same distillation column. Solutions were prepared by weight in volumetric flasks, diluting to the mark with the solvent after dissolution of the solute, effected by ultrasonic stirring. For runs in the ultrasonic resonator below 15 O C a new total immersion cell, which prevented thermal lags, was used. The cell was first immersed in the thermostat after being filled with the solvent and sealed in order to avoid moisture condensation. The cell after the solvent measurements was allowed to return to thermal equilibrium wth the atmosphere, flushed four times with ( I ) Delsignore, M.; Farber, H.; Petrucci, S.J . Phys. Chem. 1986, 90, 66. Chen, C.; Wallace, W.; Eyring, E. M.; Petrucci, S.J . Phys. Chem. 1984,88, 2541.
(2) Eggers, F.; Funck, T.; Richmann, K. H.; Schneider, H.; Eyring, E. M.; Petrucci, S . J . Phys. Chem. 1987, 91, 1961.
acetone, air-dried, filled with the solution, sealed, and immersed in the bath again. Runs at 15 "C with this cell and with a cell sitting outside the thermostat, connected to it by the thermostating fluid circulation, and temperature monitored by thermistor probes gave the same results within experimental error.
Results and Calculations Figure 1 shows a representative plot of the quantity p = a,X, the excess sound absorption per wavelength vs the frequency for 18C6 dissolved in acetonitrile at 25 "C. The solid line is the function for single Debye relaxation
Equation 1 is equivalent to the alternate expression a/f = A,/ [ 1 with A, = 2p,/fu. In the above p = (a B')(u/f), a is the sound absorption coefficient (nepers per centimeter), and B is the background sound absorption ratio (a/f),,.fi at frequencies greatly exceeding the relaxation frequencyf,. wm is the maximum value of p at f =A. h = u/J where u is the sound velocity. Figure 2 shows a similar representative plot for cryptand 222 in acetonitrile at 25 O C . The solid line is the calculated function according to eq 1. Figure 3 shows a representative plot of vs f for diaza-18C6 (Kryptofix 22) in acetonitrile at 25 "C. The solid line is the sum of two Debye relaxation processes
+ cf/f,)2] + B
wherefi and frI are the two relaxation frequencies for the two Debye processes of maximum excess absorption per wavelength gI and gII, respectively.
The Journal of Physical Chemistry, Vol. 93, No. 17, I989 6359
Isomeric Relaxation Kinetics of Macrocycles
TABLE I: Relaxation Parameters and Sound Velocities for the
K r y p t o l i x 2 2 0 3 0 M ln CH30H, t=25OC
pI=300X10
Macrocycles Studied in Acetonitrile and Methanol t , OC c, M 105p,‘ f,, MHz lO”B, cm-I s2 lo%, cm
’
lI=200MH2
p n = 4 5 0 x 10.’
I
In=20MHr
B =30 x
1
300-
\
l o - ’ ’cm-’s2
” =1 l3 5 x 1 0 5 c n
\ 5-1
‘.
0
z
230-
100
-
Macrocycle, 18C6; Solvent, C H X N 90 54 0.103 600 f 5 80 56.5 0.075 480 f 5 90 56 0.050 360 f 6 0.025 150 f 6 85 56
25 25 25 25 25 15 10 5
0.0125 74.4 f 6 0.025 163 f 5 0.025 107 f 3 0.025 102 f 2
90 70 40 30
s-I
1.274 1.271 1.289 1.280 1.272 1.334 1.341 1.359
57 53 51 49
Macrocycle, Cryptand 222; Solvent, CH3CN f(MH2)-
Figure 4. Ultrasonic spectrum expressed as p vsffor 0.30 M Kryptofix 22 in C H 3 0 H at 25 OC.
25 25 25 25 35 15 5
380 f 5 300f 5 240 f 6 115f6 290f8 300f4 325 f 3
0.20 0.15 0.10
0.05 0.15 0.15 0.14
85 80 95 90 130 65 45
K i y D t o l i x 22-DD 0.10M In CH30H 1=25’C
B =32.8~10~~’cm-’s~ 1.126x105cm S-’
t , OC
c, M
25 25 25 25 35
0.20 0.15
15
5
1 0 s O ~ l MHz
1.295 1.275 1.279 1.287 1.230 1.313 1.372 I O I ~ B , io-su,
fiI,
h
A~ = I ~ . ~ X I U ” C ~ - ’ s ~ f1 = 80 MHz An= 2 3 7 0 1~O-”cm-’s2 I n = o . 1 5 MHr u
54 52 57 59 61 50 45.5
MHz cm-l s2 cm Macrocycle, Kryptofix 22; Solvent, CH3CN
250 f 11 210f 12 140f 11 70 f 11 150 f 14 100f9 120f7
0.10
0.05 0.15 0.15 0.15
105u11‘
170 600 f 2 180 450f 2 170 3 1 0 f 2 170 155 f 2 230 520f 3 130 510f 1 100 450f 1
23 25 25 25 40 17
54 53 53 59 61 49 43
10
s-I
1.281 1.284 1.288 1.271 1.248 1.329 1.376
Macrocycle, Kryptofix 22; Solvent, C H 3 0 H
0 2 ’ 011
012
0’5
;
; A
f(MHz)
-,b
2b
5b
1bo 2 6 0
’
Figure 5. Ultrasonic spectrum expressed as {a/f- BJvsffor Kryptofix 22-DD in C H 3 0 H at 25 OC.
Figure 4 shows a representative plot for Kryptofix 22 in methanol in the form of I.C vsf: A double relaxation Debye function as in eq 2 is depicted by the solid line. Figure 5 shows a representative plot of (a/f - B ) vs f for Kryptofix 22-DD in methanol at 25 OC with B = a/f forf>> fi,fir. A double Debye relaxation function describes the data. Since the calculated relaxation frequency is below the minimum accessible frequency, the fitted function and the corresponding parameters must be taken as extremely tentative, perhaps approximating the real values to within only an order of magnitude at best. Because of these uncertainties and the difficulty of raising the temperature in methanolic solutions without incurring evaporation problems, no determination was made of the temperature dependence of the ultrasonic spectra of Kryptofix 22-DD (lower temperatures would shift the lower relaxation process to even lower frequencies of sound). The spectra for this compound will then be used only for a qualitative discussion of the effect of the side chains in Kryptofix 22-DD. The ultrasonic parameters are collected in Table I. The data for 18C6 and for cryptand 222 in acetonitrile, showing a single Debye relaxation, will be considered first. For an isomerization describable by the scheme
= 2 ~ f =,
0.30 0.25 0.20 0.149 0.099 0.20 0.20 0.20
300 f 11 180 f 11 200 f 11 102f 11 65 f 11 230 f 17 200f8 150f 5 ~OI~
t, O C
c, M
25 25 25
0.10 0.077 0.050
200 200 200 200 200 300 135 85 Afi,~ ,
450 f 360 f 300 f 202f 160 f 300 f 300f 325 f
1
20 20 1 20 1 17 1 20 1.5 26.5 1 13.5 1 9.5
31 30 31 31 30 29 31
1
34.5 . .
101’AII, fiI, cm-I s2 MHz
iOi7B,
2370b 0.15’ 1770’ 0.15’ 1180* 0.15b
32.8 31.8 31.5
kf + k, = k,(l
+
K) = k T / h exp(AS,*/R) exp(-AH,*/RT}(l
+ K } (3)
1.135 1.136 1.131 1.129 1.129 1.109 1.156 -
1.182 . ..
~O-~U,
cm” s2 MHz cm-I s2 cm s-’ Macrocycle, Kryptofix 22-DD; Solvent, CH,OH
13.3 8.8 5.5
80 70 80
1.126 1.130 1.137
‘The B values are uncertain by f l X IO-’’ (cm-I s2) units in the fit by eq 10 or the equivalent one for a single relaxation process. Consequently A,, AI, and AII are uncertain by f 1 X 10-l’(cm-l s2) units. The systematic error is then calculated for fimr pI and pII,as reported above. The total average error for the above quantities is about f5-10%. The relaxation frequencies are affected by an average error of f5%. The sound velocity values have an uncertainty of f0.5%, on the average. ‘Very tentative value. Probably reliable only as an order of magnitude at the best.
with K = k f / k ,and the other symbols having their usual significance. d In ( ? ‘ / T ) d(l/ r)
AH,*
=----R
K
AH,
l+K R
(4)
(5)
with & = (pu2)-l denoting the isoentropic compressibility and AV, the isoentropic volume change due to the process d In (PmT/U2) = -AH0 K-I d(l/T) R K+l
we may write3 7-I
25 25 25 25 25 30 18 10
(3) Chen, C. C.; Petrucci, S. J . Phys. Chem. 1982, 86, 2601.
(6)
6360 The Journal of Physical Chemistry, Vol. 93, No. 17, 1989 14.5
dn(r-'IT)vs. (1IT)for in acetonitrile
\O O \
14.0
t
TABLE II: Results of Linear Regression Applied to the Systems Below, As Indicated
18C1
Macrocycle, 18C6; Solvent, CH3CN (a)
\
(b)
t .
13.5
~
Rodriguez et al.
(c)
In ( r - ' / T ) vs (l/T), Figure 6A ? = 0.89, intercept = 28.53, slope = -4184 In (fi,T/u2) vs ( l / n , Figure 6B r2 = 0.80, intercept = -15.S2, slope = -2603 p,,,
vs c (mol/cm3), Figure 6C" 0.99, intercept = 4.0 X
r2 =
slope = 61.2 cm3 mol-'
P.
N
*I-
-
(a)
C
(b)
24
(c)
+E
I
L
3-
Y
dn(p,,,TIu2) v s . (1IT) for 18C6 in acetonitrile
4
v
(a) 25
t
-
3.5 3.6 ( 1 OVT)
3.4
I
(b)
t
t l t
I
(c)
500
Macrocycle, Cryptand 222; Solvent, CH3CN In (7-'/7') vs (1/7'), Figure 7A ? = 0.9g5, intercept = 23.50, slope = -2692 In ( p , T / u 2 ) vs (l/T), Figure 7B ? = 0.98, intercept = -21.58, slope = -610 p, vs c (mol/cm3), Figure 7C" ? = 0.99, intercept = 6.4 X slope = 19.7 Macrocycle, Kryptofix 22; Solvent, CH$N In (~;~/7') vs (l/T), Figure 8A ? = 0.996, intercept = 22.28, slope = -2130 In (71f'/T) vs (1/7'), Figure 8A ? = 0.997, intercept = 25.30, slope = -3606 In (fiIT/u2)vs (1/7'), Figure 8B ? = 0.58, intercept = -17.40, slope = -2068 In ( p I l T / u 2 )vs (l/T), Figure 8B ? = 0.87, intercept = -19.39, slope = -1 120 pI vs c (mol/cm3), Figure 8C" ? = 0.995, intercept = 2.1 X slope = 13.06 pIIvs c (mol/cm3), Figure 8C' ? = 1.000, intercept = 1.4 X slope = 30.07 Macrocycle, Kryptofix 22; Solvent, Methanol
(a)
(b)
ov 0
I
0.10
(c)
c(mol/dm3) Figure 6. (A) In ( r - I / T ) vs 1/T) for 18C6 in CH3CN. (B) In (fi,T/u2) vs ( I / T ) for 18C6 in CH3CN. (C) p,,, vs concentration, c, for 18C6 in CH3CN at 25 OC. Equations 3, 4, and 6 can be combined to give the following transcendental equation4 7- I
(kT/ h)eai*lR
=
1
d In ( T - I / T ) d(l/T)
+
(4) 1677.
IO-' = [exp[-$[4184
+ (-&)2603]]1(1
slope = 9.0 slope = 14.7
"The results of linear regression apply to the concentration c expressed in mol/cm3. TABLE 111: Kinetic and Thermodynamic Parameters for the Configurational Isomerization of Macrocycles in CH3CN
Macrocycle, 18C6; Solvent, CH,CN ASf* = 9.5 cal/(K mol) AHo = kcal/mol AH; = 8., kcal/mol AH,' = 13.4 kcal/mol
+
X
vs c (mol/cm'), Figure 9C' ? = 0.95, intercept = 4.9 X pl vs c (mol/cm3), Figure 9C" ? = 0.998, intercept = 0.15 X pl
K >> 1 kf = 5.3 x 108 s-1
Once the values of AS,*, d In (r-l/T)/d(l/T), and d In (pmT/ u2)/d( 1/T) are known, a trial and error calculation with various values of K can be carried out, until the condition of equality in eq 7 is satisified. Figure 6A shows the plot of In ( T - ' / T )vs 1 / T for 18C6 in acetonitrile. Linear regression gives the correlation coefficient r2, the intercept = In ( k / h ) A S , * / R , and the slope = d In (T-I/T)/d(l/T) (see Table II), from which one calculates ASr* = 9.5 cal/(K mol). Figure 6B shows the plot of In (p,T/u2) vs (1/T) for 18C6 in acetonitrile. The solid line has been calculated by linear regression (Table 11). Since T-' = 2rfr = 5.3 X lo8 s-I for 18C6 in acetonitrile, eq 7 becomes 7.13
r2 = 0.99, intercept = 26.77, slope = -41 18 In ( p l T / u 2 ) vs (1/7'), Figure 9B r2 = 0.98, intercept = -15.56, slope = -2434
In (plIT/u2)vs (l/7'), Figure 9B r2 = 0.73, intercept = -21.70, slope = -500
-
I
0.05
In (rf'l7') vs (l/T), Figure 9A r2 = 0.99, intercept = 32.09, slope = -5003 In (qf1/7') vs (l/7'), Figure 9A
+ K) =
Petrucci, S.;Adamic, R. J.; Eyring, E. M. J . Phys. Chem. 1986, 90,
Macrocycle, Cryptand 222;" Solvent, CH3CN AS,' = -0.52 cal/(K mol) AHo = -1.54 kcal/mol AH; = 5.23 kcal/mol AV = 16 cm3/mol
K = 8.4 k , = 5.9 x 107 s-I kf = 4.9 x 108 s-' AH,* = 6.7, kcal/mol
"The results apply to the observable relaxation. Trial and error calculations of the function 4(K) for various K values leads to a finite value of K = 5.5 X lo3 that satisfies eq 8. Since K >> 1, it follows that k f > k,, which leads to kt = 7-I = 5.3 X IO* s-' at 25 "C in eq 3, d In (T-I/T)/d(l/V = A H t / R in eq 4, hence AH,' = 8.3 kcal/mol and d In (pmT/u2)/d(l/T) = A H o / R , hence AHo = -5.1 kcal/mol from eq 6. Since AH, = AHft - AHr*,it follows that AH,' = 13.4 kcal/mol. In addition, a plot of pmanvs c for 18C6 in CH3CN (Figure 6C), assigning 50% statistical weight to the origin (see results in Table 11), is shown. Since the value of K is correct only to an order of magnitude, consistent with the condition K >> 1, a value of AVfrom eq 5, based on the above data, will not be reported. Figure 6C, however, showing linearity of p, vs c, together with constancy off, with c, within experimental error proves that the process is pseudo first order. Table 111 collects all the kinetic and ther-
The Journal of Physical Chemistry, Vol. 93, No. 1 7 , I989
Isomeric Relaxation Kinetics of Macrocycles
6361
15
I n ( T - ' / T ) vs. 1 I T for C r y p t a n d 2 2 2 -in
- 13.5
acetonitrile
-tt
1'
-13.070
-
t
t-
v
I
C
t-
Y
C \
- 12.5 dn(pIT/u2) and In(pET/u2) V S . ( I I T ) f o r K r y p t o f i x 2 2 in CH3CN
-12h 3.2
-24 -25
-
3.3
2 w
3.4 3.5 (1o ~ / T )
3.2
3.6
3.3
-
3.4
p,,, v s . C for C r y p t a n d 2 2 2 in CH3CN.
600
1pIo
and pLII.vs.
concentration
for K r y p t o f i x 22 in CH,CN
I
0.1
1
I
cryptand
0.2 C(mol/dm3)
lo4 = expl-
$[2692 + -6OO])( K K- 1
0.05
0.10 C(mol/dm3)
--.
0.15
0.20
Figure 8. (A) In ( T ~ ' / Tand ) In ( T ~ ~ ' /vsT (1/T) ) for Kryptofix 22 in CH,CN. (B) In ( p , T / u 2 ) and In (pIrT/u2)vs (l/T) for Kryptofix 22 in CH,CN. (C) p1and pIIvs concentration, c, for Kryptofix 22 in CHpCN at 25 OC.
8B have been calculated with linear regression parameters collected in Table 11. Figure 8C reports pI vs c and pIIvs c for Kryptofix 22 in CH3CN. The solid line has been calculated by linear regression giving 50% statistical weight to the origin (see Table 11). Figure 9A reports the quantities In ( ~ f l / T ' ) and In ( T ~ F I / T ) vs (1/T) for Kryptofix 22 in methanol. The solid lines in Figure 9A have been calculated with linear regression parameters (Table 11).
1
+ K ) = +(K)
which can be solved by trial and error giving the solution K = 8.4 > 1. Substituting this number into eq 6, one calculates AHo = -1.54 kcal/mol. Then from eq 4 one obtains AH,' = 6.70 kcal/mol. Since k f / k , = 8.4 and kf k, = 7-l = 5.5 X lo8 s-l, it follows that kf = 4.9 X lo8 s-l and k, = 5.9 X lo7 s-'. All the calculated kinetic and thermodynamic parameters are reported in Table 111. Finally, Figure 7C shows a plot of p m vs c. Linear regression, giving 50% statistical weight to the origin (Table 11) and expressing c in mol/cm3, yields the line shown. Figure 8A reports the quantities In ( T ~ I / T ) and In ( ~ f l / T ) vs (1 / T ) for Kryptofix 22 in CH3CN. The solid lines in Figure 8A have been calculated by linear regression with the parameters reported in Table 11. Figure 8B shows the quantities In ( p l T / u 2 )and In (pIIT/u2) vs (1 / T ) for Kryptofix 22 in CH3CN. The solid lines in Figure
+
CH
at
"fast" process
100
mcdynamic parameters related to the isomeric relaxation of 18C6 in acetonitrile. Figure 7A is a plot of In (?'/T) vs (1/T) for cryptand 222 in CH3CN. The solid line was calculated by linear regression with the results collected in Table 11. From the intercept we calculate AS,' = R[ln ( k / h ) - 23.501 = -o.52 cal/(K mol). Figure 7B is a plot of In ( p , T / u z ) vs (1/T) for cryptand 222 in CH3CN. The solid line was calculated by linear regression (Table 11). Using the values of 7-l = 5.5 X lo8 s-l in eq 3 with AS,' = -0.52 cal/mol, the value d In (T-'/T)/d(l/T) = -2692 in eq 4, and the valued In (p,T/d)/d(l/T) = -610 in eq 5, one arrives at the transcendental expression X
3.6
2 200
Figure 7. (A) In ( T - ~ / Tvs ) (1/T) for 222 in CH3CN. (B) In (p,,,T/u2)vs (l/T) for cryptand 222 in CH3CN. (C) p, vs concentration, c, for cryptand 222 in CH3CN at 25 OC.
1.1 5
3.5
( 1O ~ I T )
Figure 9B reports the quantities In ( p 1 T / u 2 )and In (pIIT/uZ) vs (1/T) for Kryptofix 22 in methanol. Linear regression applied to these data (Table 11) gives the two solid lines in Figure 9B. Figure 9C reports the values of pI vs c and pI1vs c for Kryptofix 22 in methanol. Linear regression applied to these data, giving 50%statistical weight to the origin (Table 11), yields the two solid lines in Figure 9C. In a previous paperS the equilibrium scheme
(9) was applied to the isomeric relaxation of the cryptand 222 in water. The same scheme is proposed here for the Kryptofix 22 in both acetonitrile and methanol. In Table I the constancy offi andfiI with concentration within experimental error, and the linearity of pI and pI1(Figures 8C and 9C, respectively) support the idea ( 5 ) Schneider, H.; Rauh, S.; Petrucci, S. J . Phys. Chem. 1981,85, 2287.
6362 The Journal of Physical Chemistry, Vol. 93, No. 17. 1989
Rodriguez et al.
AIO and
An.
f o r Kryplotix
13.0
20
t
2000
t
w -
I
E r--
14.5
I--b-\j-
12.0
I -$.
(B
-25
/n(pIT/u2)
a n d Ln(p,T/u*)
VS.
( 1 I T ) f o r K r y p t o f i x 22 in M e t h a n o l
u
3.2
3.3
3.4
3.5
3.6
(10'/T)--
p.,o
and+,,@vs
concentration C
500 - f o r K r y p t o f i x 2 2 in
t
C(moi/dm3)
-
Figure 9. (A) In ( i , - I / T ) and In ( i 1 , - l / 7 ' ) vs (1/Q for Kryptofix 22 in methanol. ( B ) In (pIT/u2)and In ( p l , T / u 2 )vs ( l / Q for Kryptofix 22 in methanol. (C) p, and pll vs concentration, c , for Kryptofix 22 in methanol at 25 O C .
of a process involving two pseudo-first-order steps as represented in eq 9. Unfortunately, the smallness of the upper relaxation strength, as expressed by the pI values, and their relatively large error make application of the slopes and intercepts, calculated above, to evaluate the parameters k l , kl,kZ,k-2, AVI, AVII, AHl*,AH-l*, ASl*, A S l * as done b e f ~ r e an , ~ impractical task. The error propagation associated with the large uncertainty in the pIvalues renders calculated kinetic and thermodynamic parameters void of significance for Kryptofix 22 in both acetonitrile and in methanol. The results for these two systems have therefore been dealt with qualitatively. For both the acetonitrile and the methanol solutions, one must conclude that for Kryptofix 22 all three configurations (endeendo, endo-exo, and exo-exo) must be at comparable concentrations. This follows from the observation that two relaxation processes were observed in acetonitrile as well as in methanol. The fact that two relaxation processes were also found in a single experiment for 0.05 M Kryptofix 22 at 25 O C in propylene carbonate seems to indicate some independence of the concentration distribution for Kryptofix 22 from the choice of solvent at variance with what was found for cryptand 222 in the present work and Figure 10 shows a tentative plot for Kryptofix 22-DD in methanol at 25 OC of the relaxation amplitudes A I = ( 2 4 u f i ) and AII = (2prl/ufi1)vs the concentration c. The quantities AI and All were extracted from the fitting function
which is a different form of eq 2. As explained above, the plot and the numerical values for the amplitudes AI and AI, must be taken as tentative.
Discussion Comparisons are drawn below between the different relaxational behaviors of macrocycles I, 11, 111, and IV arising from their
OO3
A W
1
I
I 0 05
-
0 10 C(mol/dm3)
0
Figure 10. Plot of A, and All, the two relaxation amplitudes, for Kryptofix 22-DD in methanol at 25 "C. The A values are tentative as explained in the text.
structural differences and for the same macrocycle as a function of the two different solvents CH3CN and C H 3 0 H . Attention is first drawn to the existence at room temperature of an isomeric relaxation for 18C6 in CH3CN at variance with the case of 18C6 in C H 3 0 H , where only by lowering the temperature below -5 "C was a relaxation detected.3 Extrapolation of the data to 25 O C indicates that if a relaxation were observable for methanolic solutions of 18C6, it would have to occur at a relaxation frequency of several hundred megahertz. It is known that CH3CN forms adducts in the solid state with 18C6, and IR studies6 have confirmed these interactions through alteration of the 'CN stretch* of CH3CN. It is reasonable to assume that the solvent participates in the configurational relaxation of 18C6 in CH3CN (which appears pseudo first order because the solvent is in excess). The same may be true in aqueous solutions of 18C6 where a relaxation process at 100 M H z has been reported' at 25 OC and where infrared studies have revealed* interactions of 18C6 and water. Substitution of two of the oxygens in positions 1 and 10 of the ring by nitrogens carrying a third ethereal chain (CH2)-0(CH2)2-0-(CH2)2- as in cryptand 222 (111) produces only one detectable relaxation process in CH3CN (and in all other aprotic solvents studied so far,2 namely, propylene carbonate and dimethoxyethane). However, two Debye relaxation processes can describe the ultrasonic spectrum of I11 in the protonated solvent methanol2 (as well as in water5 and methyl cellosolve). The two relaxation processes are interpreted as due to the rotation of the two nitrogens of the rings of cryptand 222 possibly linked to rearrangements of the ethereal chains and solvation/desolvation of the macrocycle. It is possible that for the reaction scheme
-
endo-endo e endo-exo e exo-exo solvation in protic solvents causes a more even concentration distribution of the three species with appearance of both relaxation processes. Elimination of one ethereal chain of cryptand 222 and substitution of the chain by two protons produces Kryptofix 22 (11) and gives rise to the appearance of two relaxation processes in both CH3CN and CH30H. Both processes as in the corresponding case of cryptand 222 are ascribed to rotation of the two nitrogens. As pointed out before, however, the nature of the solvent does not appear to influence the concentration distribution of the three species in equilibrium (at least in CH3CN, CH30H, and propylene carbonate) to the point that one of the two relaxation processes disappears. Comparison of the relative energy barriers by comparing the slopes d In (q-l/T)/d(l/T) and d In ( r I c 1 / T ) / d ( 1 / T ) for Kryptofix 22 would lead to possibly false conclusions. These (6) Mosier-Boss, P. A.; Popov, A. I. J . Am. Chem. SOC.1985, 107,6168. (7) Rodriguez, L. J.; Ligegang, G. W.; Farrow, M. M.; Purdk, N.; Eyring, E. M. J . Phys. Chem. 1978, 82, 647. Rodriguez, L. J.; Liesegang, G . W.; White, R. D.; Farrow, M. M.; Purdie, N.; Eyring, E. M. J . Phys. Chem. 1977, 81, 21 18.
(8) McKenna, W. P.; Eyring, E. M. Appl. Spectrosc. 1986, 40, 16, 20.
J. Phys. Chem. 1989, 93, 6363-6367 slopes have a less simplistic significance than an energy barrier to a process. Indeed one must consider the importance of the unknown second terms on the right-hand side of both equation^.^ Substitution of the two protons of Kryptofix 22 by two CloHzl hydrocarbon chains leads to Kryptofix 22-DD (IV). A 0.05 M solution of this compound in CH3CN at 25 OC showed no visible relaxation effect whereas the same solution in C H 3 0 H showed a spectrum tentatively interpreted by the sum of two Debye relaxation processes. The two relaxation frequencies are much lower
6363
in value than the ones reported for Kryptofix 22 in C H 3 0 H . It appears therefore that the nature of the solvent plays a major role in the relaxational behavior of this bitailed macrocycle. Also, rotation of the nitrogens dragging a long chain appears to be a much slower process than the rotation of the nitrogens of Kryptofix 22, where only two protons are linked to the two nitrogens.
Acknowledgment. We thank the National Science Foundation (Grant CHE-85 13266) for generous support of this research.
NH(b'X+) Deactivation/Reaction Rate Constants for the Collisional Gases H,, CH,, C2HB,Ar, N,, O,, H,O, and CO, C. A. van Dijk, S. T. Sandholm, D. D. Davis, and J. D. Bradshaw* School of Geophysical Sciences, Georgia Institute of Technology, Atlanta, Georgia 30332 (Received: August 2, 1988; In Final Form: January 20, 1989)
-
The NH(blZ+) radical was produced via two-photon photodissociationof NH3 by use of an ArF excimer laser. Detection of this radical species was achieved by laser pumping the transition NH(b12+) NH(clII) at 452 nm followed by fluorescence monitoring of the NH(clll) NH(alA) transition at 326 nm. Deactivation/reactionrate constants for the process NH(blZ+) M products were measured for the following collisional gases: Ar, N2, 0 2 , C02, H20, H2, CH4, and C2H6. The measured cm3/(molecule.s)for deactivation/reaction by Ar and H20, respectively. rate constants ranged from 7.1 X 1O-I' to 1 .O X
-
-
+
Introduction As one of the prominent trace gas species in the atmosphere, there has been an increasing interest in the atmospheric chemistry of ammonia. Much of this interest has been the result of the major role this species plays in controlling the acidity of precipitati~n.'-~ For this reason, considerable effort has been expended over the past decade to develop reliable methods for detecting N H 3 under atmospheric conditions. One of these new detection methodologies has involved the photofragmentation of the N H 3 species by using 193-nm radiation from an ArF excimer laser.6 This new method involves the monitoring of the N H 3 photolysis product, NH(blZ+). The latter radical species, which has been shown to arise from a two-photon-dissociation process in NH3,' has the advantage of being metastable. Its reported radiative lifetime is 53 m s 8 Thus, laser pumping the NH(blZ+) species to the NH(clII) level can be sufficiently delayed (e.g., 2 ps) as to permit several l / e decay times of the background fluorescence produced from the 193-nm photolysis laser. However, since the NH(blB+) species may also be deactivated via collision with atmospheric gases, critical to estimating the sensitivity of the latter N H 3 detection method are the deactivation/reaction rate coefficients for NH(blZ+) with representative atmospheric gases. Presented here are the results from a study that has examined the rate coefficients for the deactivation/reaction of the NH(blZ+) radical in the presence of various possible atmospheric gases, including both major constituents as well as several of the more prominent minor gases. Experimental Section As described by Schendel et the photolytic scheme used in this study to generate and detect the NH(blZ+) species is summarized below and in the energy level diagram depicted in Figure 1. NH3
+ 2hvl
- + + - + XI = 193 nm
NH(blZ+)
hv2
NH(blZ+)
Xj
NH(c'II)
XI = 452 nm
= 326 nm
products
(1)
NH(c'II)
(2)
hv3
(3)
NH(alA)
*Author to whom correspondence should be addressed.
0022-3654/89/2093-6363$01.50/0
The detailed nature of the two-photon-generated N H ( b l Z + ) species from NH, is still not fully understood but is believed to involve the initial formation of the NH2(A) state and/or highly vibrationally excited NH2, e.g., reactions 4 and 5 and/or 6 and 7. Energetically, the formation of the NH(blZ+) radical requires
X = I93 nm
NH3
+ hvl
NH,(A)
+ hvl
h = 193 nm
+ hvl
h
193 nm
+H +H
NH(b'Z+)
h = 193 nm
N H 3 + hvl NH2*
NH,(A)
NH2*
(4) (5)
+H
NH(blZ+)
+H
(7)
the absorption of two 193-nm photons, a conclusion that was verified in this work with the observation of an approximate square power dependence in the production of the NH(b'Z+) species as a function of the 193-nm laser fluence (Le., plot of log fluorescence vs log 193-nm energy yielded a slope of 1.7 f 0.3 over the energy range of 3-30 mJ/cm2).6 A plot of the rotational level distribution versus energy, using the appropriate Honl-London expression9 and level spacing and rotational constantlo yielded a NH(blZ+)
(1) National Research Council. Sulfur Oxides; National Academy of Sciences Press: Washington, DC, 1978. (2) National Research Council. Acid Deposition; National Academy of Sciences Press: Washington, DC, 1983. (3) National Research Council. Global Tropospheric Chemistry; National Academy of Sciences Press: Washington, DC, 1984. (4) Charlson, R. J.; Chameides, W. L.; Kley, D. The Biogeochemical Cycling of Sulfur and Nitrogen in the Remore Atmosphere; Galloway, J. N., Charlson, M. O., Andreae, M. O., Rodhe, H., Eds.; Reidel: Boston, 1985. (5) Calvert, J. G.; Stockwell, W. R. Enuiron. Sci. Technol. 1983, 17,428A. (6) Schendel, J.; Stickel, R.; van Dijk, C.; Sandholm, S.; Bradshaw, J.; Davis, D. J . A m o s . Chem. To be submitted for publication. (7) Donnelly, V. M.; Baronavski, A. P.; McDonald, J. R. Chem. Phys. 1979, 43, 27 1. (8) Blumenstein, 1J.; Rohrer, F.; Stuhl, F. Chem. Phys. Letr. 1984, 107, 347.
(9) Herzberg, G. Specrra of Diatomic Molecules; Van Nostrand Reinhold: New York, 1970.
0 1989 American Chemical Society
