J. Phys. Chem. 1984, 88,129-136
729
Raman Spectra and Kinetics of Complexation of Sodium and Potassium Ions with 18-Crown-6 Ether in Dimethyiformamide Kevin J. Maynard,' Donald E. Irish,' Edward M. Eyring,* and Sergio P e t r ~ c c i * ~ Polytechnic Institute of New York,Farmingdale. New York 11735; University of Waterloo, Waterloo, Ontario, Canada N2L 3G1: and University of Utah, Salt Lake City, Utah 84112 (Received: January 17, 1983; In Final Form: May 12, 1983)
Ultrasonic absorption data are reported in the frequency range 10-300 MHz for solutions of NaSCN and KSCN added to 18-crown-6 ether (18C6) in molar ratio R = 1, in the solvent dimethylformamide (DMF) at t = 25 " C . A Debye single relaxation process describes the data in the frequency range covered. The relaxation frequency seems independent of concentration. The relaxation strength, characterized by the maximum excess absorption coefficient per wavelength p,,,, is linear with concentration within experimental error. The relaxation process appears to be independent of the nature of the anion, NaC10, giving the same results as NaSCN (although Raman spectra show the latter electrolyte and KSCN to be associated in DMF). The observed relaxation process is interpreted as an interaction between the cations and the crown ether. The mechanism of the metal ion-crown ether complexation is believed to be the one proposed by Eigen and Winkler. In particular the observed relaxation process is ascribed to the second step of the Eigen-Winkler mechanism. A final molecular rearrangement of crown ether around the cation with simultaneous cation desolvation may be a slower process than observable with the presently available techniques of pulsed ultrasonics. In fact, when the temperature is raised to 45 "C, a new process for both NaSCN and KSCN added to crown ethers becomes observable. The isomeric relaxation of 18C6 in DMF has been observed and characterized. Study of its temperature dependence and determination of its activation parameters AHo* and ASo' suggest similarity in the order of magnitude between the isomerization rate constant ko and estimated rate constant k3 for the final step of the metal complexation with the crown ether. Raman spectra of the u3 (735-cm-l) line of the SCN anion of NaSCN and KSCN have been analyzed as a sum of two band components centered at 735 (free thiocyanate) and 754 (Na') or 746 (K') (bound thiocyanate) cm-I. Quantitative integrated intensity data give for NaSCN a complexation constant K = 1.46 & 0.10 M-I. Addition of 18C6 in molar ratio R = 1 to either NaSCN or KSCN in DMF at 25 OC causes the 754- or 746-cm-I band to practically disappear.
Introduction Understanding the mechanism of complexation of alkali metal ions with macrocyclic ligands such as crown ethers is of relevance to the biophysics of transport of ions through membranes, a phenomenon induced by nerve impulses. Current ideas envisage macrocyclic antibiotics such as valinomycin stripping the ion from its aqueous solvation shell and 'dressing it" with a lipophilic hydrocarbon shell (the polar group pointing inward toward the ion). This new configuration would enable the ion to pass through the cell membrane, by virtue of being soluble in it, to be then released to the aqueous medium inside the cell. The above might cause one to think that the study of the kinetics of complexation of alkali metal ions with macrocyclic ligands in water is the only topic of relevance, the ion being already in the complexed form when passing through the membrane. However, it has been shown4 that at least two mechanisms fit the existing data equally well, both being kinetically indistinguishable from each other. One, the so-called Eigen-Winkler mechanism, was applied to the study of valinomycin complexing with alkali metal ions in m e t h a n ~ l . ~In this mechanism the rearrangement of the ligand around the cation is considered to be the rate-determining step Me+
+ V + Me.-.V
e MeV
(1)
MeV is the final form of the complex, Me.. .V is an intermediate encounter complex, and Me+ is the solvated cation. The second mechanism, the so-called Chock's mechanism: predicts at least two forms of the macrocyclic ligand in rapid (1) University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. (2) University of Utah, Salt Lake City, UT 841 12. (3) Polytechnic Institute of New York, Route 110, Farmingdale, NY 11735. (4) Farber, H.; Petrucci, S. J. Pfiys. Cfiem. 1981, 85, 1396. (5) Grell, E.; Funk, T.; Eggers, F. In "Membranes"; Eisenman, G., Ed.; Marcel Dekker: New York, 1975; Vol. 111, p 1. (6) Chock, P. B. Proc. Natl. Acad. Sci. W.S.A. 1972, 69, 1939.
0022-365418412088-0729$01SO10
equilibrium; only one form reacts with the metal ion C1 C2 fast
*
Me+ + C2
MeC2+
slow
(11)
In this mechanism, the rate-determining step is the complexation to form MeC2+rather than the rearrangement of the ligand. This last mechanism has been used4 successfully to interpret ultrasonic data for complexation of alkali and alkaline-earth ions with synthetic macrocyclic ligands such as crown ethers' in water. The presence of the equilibrium C1 F! C2 and its experimental observation is insufficient to prove Chock's mechanism. The steric requirements of rearranging the ligand around the cation may be different from the isomeric rearrangement of ligand alone (possibly involving the solvent) for the C, s C2equilibrium. This was the conclusion of a recent study with solvent methanol* where, at variance with water, the equilibrium constant of metal complexation is so large that eq I could be written Me..-C
G
MeC
(111)
in the concentration range of the ultrasonic technique. It was in fact verified that a first-order reaction was observed in the ultrasonic relaxation between Li', Na+, or K+ complexing with 18C6 in methanol. Further, an isomeric relaxation of the type C I + C2 was a process much faster than the complexation with the metal. Both q I and I1 may be oversimplifications of the actual process which might be more complicated and multistage if the barrier of energy of desolvation is quite different from that of ligand rearrangement and if the latter involves more than a simultaneous and single chain rearrangement. It was with the latter ideas in mind that we engaged in the present work with dimethylformamide as a solvent. Its choice was suggested by several factors. It was (7) Liesegang, W. G.; Eyring, E. M. In "Synthetic Multidentate Macrocyclic Compounds"; Academic Press: New York, 1978 and literature quoted therein. (8) Chen, C.;Petrucci, S. J . Phys. Cfiem. 1982, 86, 2601.
0 1984 American Chemical Society
I30
The Journal of Physical Chemistry, Vol. 88, No. 4, 1984
Maynard et al.
TABLE I: Ultrasonic Relaxation Parameters);, A, E , and pm and Sound Velocities u for NaSCN and KSCN Added to 18C6 Ether at the Concentrations and Temperatures Investigated in DimethylformamideC
NaSCN t, O C 25 25 25 25 25 25 1 10 35
CNaSCN,
0.80 0.60 0.40 0.20 0.40 0.40 0.6 0.6 0.6
C1aCs9
0.80 0.60 0.42 0.20 0.80 0.20 0.6 0.6 0.6
+ 18C6a
A, MHz
lO"A, sz /cm
1017~1,
s2/cm
10-5u: cmis
1 0 5 ~
65 60 55 55 65 60 35 43 65
330 28 0 190 100 184 110 660 470 215
50 50 44 40 48 42 50 45 50
1.525 1.507 1.484 1.467 1.478 1.424 1.615 1.563 1.473
1636 1266 775 403 884 470 1865 1579 1029
KSCN
+ 18C6b
t, OC
CKSCN,
CUC6 1 M
G, MHz
1017~, sz/cm
10178, s* /cm
103, cm/s
1 0 5 ~
25 25 25 25 15 35
0.40 0.30 0.20 0.10 0.4 0.4
0.40, 0.32 0.20 0.10 0.4 0.4
25 25 25 30 20 32
380 310 215 80 419 310
35 30 30 28 35 35
1.486 1.484 1.460 1.398 1.527 1.464
706 575 392 168 640 7 26
a u = 105(1.607 - 0 . 0 0 3 7 ~ ) . r z = 0.98 for R = 1, c = 0.6 M. u = lO'(1.571 - 0.0032t). r z = 0.988 for R = 1, c = 0.4 M. The relaxation parameters A, E , andJ, were determined with an average error of =5-10%. The sound velocity 11 was measured with an average error of about 0.5-17i.
our wish to carry out parallel Raman work looking at the effect of the crown ether on the C-S stretch region (at 2735 cm-l) of the SCN- ion, the latter found to be partially associated with the alkali metal ions. DMF has a Raman spectroscopic window around 735 cm-' where the v(C-S) vibration of SCN-occurs. This vibrational mode can be used to monitor ion pairing. Further, the donor numberg of DMF is higher than those of methanol and of the ethers used so far,4 but its permittivity is lower than that of water by a factor of about 2. This causes formation constants to be high, but there was hope that one might distinguish between the desolvation step and the rearrangement of the ligand. As shown below there is some indication that this might be the case. For the sake of clarity, after the Experimental Section the portions of the work dedicated to ultrasonics and Raman spectra are reported separately. Experimental Section The equipment and the procedure have been described before.I0 DMF (Baker) was distilled over P 2 0 5 in vacuo in an all-glass apparatus without grease on the joints. The solvent was kept in sealed bottles in a desiccator over anhydrone and so also were the solutions, which were used shortly after preparation. LiSCN was dried in vacuo by raising the temperature slowly to 110 OC. NaSCN, NaClO,, and KSCN were dried at 110 OC. 18C6 was recrystallized from spectrographic-grade acetonitrile. 18C6 (Aldrich) was dissolved in the minimum amount of acetonitrile by warming gently up to 250 OC. It was then recrystallized by quenching the solution and filtering quickly. The 18C6-CH3CN adduct was subjected to vacuum for 12 h. The melting point of the white crystalline powder was 39-40 OC. Raman spectra were excited by the 514.5-nm line of a Spectra-Physics argon ion laser and recorded by a Jarrel-Ash spectrometer" interfaced to a 32K byte Commodore computer.
Results and Discussion Metal Ion Complexation. Figure 1 shows representative plots of the quantity a / f vs.ffor NaSCN + 18C6 and for KSCN
+
( 9 ) Gutmann, V . 'Coordination Chemistry in Non-Aqueous Solutions"; Springer-Verlag: Wien, 1968. ( ! O ) Onishi, S.;Farber, H.; Petrucci, S. J . Phys. Chem. 1980,84,2922 and previous literature quoted therein. (1 1) Irish, D. E.; Tang, S. Y . ;T a b , H.; Petrucci, S. J . Phys. Chem. 1979, 83, 3268.
+
NaSCN 18C6 In DMF t = 25'C
t
300
ih r
Legend 0 NaSCN 0.8M 18C6 0.8M
+
A NaSCN 0.4M
+
8
5 200
0.4,M
18C6
I .
c
rNaC104 0.4M
II
-X
+
100
\ c(
A
01 10
20
50 100 f(MHz)-
KSCN
A
200
500
+ 18C6 in DMF: t =2S0C
Logene A KSCN 0.4M 18CI 0.40M In DMF
+
0
10
B
20
KSCN 0.20 +18C6 0 . 2 0 In DMF
50 100 f(MHz)---
Figure 1. Plot of a/f vs.ffor NaSCN DMF at 25 O C .
200
500
+ 18C6 and KSCN + 18C6 in
18C6 in molar ratio R = 1 at 25 OC in DMF. The solid lines are the calculated Debye functions for a single relaxation process according to the expressionI2
C Y f/ = A / ( l + (f/f,)*I
+B
(IV)
The arrow in the figure indicates the position of the relaxation frequencyf,. In the above CY is the absorption coefficient (Np/cm), (12) Petrucci, S. In 'Ionic Interactions"; Petrucci, S., Ed.; Academic Press: New York, 1971; Vol. 11, Chapter 2.
Complexation of Sodium and Potassium Ions with 18C6
The Journal of Physical Chemistry, Vol. 88, No. 4, 1984 731
Legend: o NaSCN 0.4M 18C6 O.8M in DMF
Pa+
+
t
;n ' E,
l5O0I
+
300/A
ANaSCN 0 . 4 M 18C6 0.4,M in DMF t = 25OC
c
200
t
z X
c
2
x
Legend:
/
I
5001 100
1
II
\
0 10
50 100 f(MHz)-
20
1
0
+
oLiSCN 0.48M 18C6 0.48M in DMF; t = 25OC ALiSCN 0.47M in DMF; t = 25OC 0
0.6 0.8 c x 1O~(molo/cm~)-
Figure 3. p,,,vs. concentration c (mol/cm') for NaSCN and KSCN 18C6 in DMF at 25 "C. 1400/
+
21000
NaSCN 0.6M in DMF: t = 45oc &18C6 0.6M in DMF; t = 45%
c
b 600
20
50 f(MH2)
-
100
200
400
Figure 2. (A) Plot of a/f vs.ffor 0.4 M NaSCN + 0.8 M 18C6 (open points) and for 04 M NaSCN 0.42 M 18C6 (closed points) in DMF at 25 OC. (B) Plot of a/f for 0.48 M LiSCN 0.48 M 18C6 in DMF at t = 25 OC and for 0.47M LiSCN in DMF at 25 OC.
+
3
Y
0 1
5
2
A
+
+
10 2 0 f (MHz)
-
50 100 200
+
KSN 0.4M 18C6 0.40M in DMF; t = 45%
f is the frequency (hertz), and A , B, and fr are the relaxation parameters.I2 A contains the thermodynamic information pertinent to the relaxing process; B is the background absorption at f>>fr, namely, Ia/flD,L. In Table I the quantities A , B, andf, together with the sound velocity u (cm/s) and the maximum excess sound absorption per wavelengthI2 pm = (1 / 2 ) A u f , are reported for all the concentrations investigated. Note that there is no relaxation in this frequency region for the salt/solvent system in the absence of 18C6. The ion-pair formation detected by Raman spectroscopy is not responsible for the ultrasonic process. Further, Figure 2 reports the quantity of a/f vs.fand the fitted Debye functions for NaSCN + 18C6 in the molar ratio RI(NaSCN)/ (18C6)) equal to 0.5. From Table I it may be seen that the relaxation strength characterized by the parameter A is dependent on the component in defect; thus, 0.4 M NaSCN + 0.8 M 18C6 shows an ultrasonic relaxation equal, within experimental error, to the 0.4 M NaSCN 0.4 M 18C6. This suggests that the effect corresponds to a 1 to 1 interaction between electrolyte and crown ether and that the equilibrium constant K z of complexation between electrolyte and crown ether must be large. Figure 1 also indicates that for NaC104 and NaSCN within experimental error the anion does not affect the results (although Raman spectra show interaction between Na+ or K+ and NCSin the absence of 18C6). Figure 2 shows also that 0.5 M LiSCN in D M F undergoes a relaxation process (0.6 M NaC104 shows no relaxation, but only an increase of B with respect to the solvent absorption at 25 "C). However, addition of 18C6 in molar ratio R = 1 to LiSCN does not affect significantly the relaxation with the exception of alteration of the background absorption. Raman spectra described later also illustrate the inability of the 18C6 to compete with NCS- in the presence of Li+. This lack of interaction with LiSCN may be due to the large mismatch between cation radius and crown ring size and to the relative affinity of SCN- and 18C6 toward Li+. Table I shows that the relaxation frequency seems independent of concentration within experimental error. Further, the quantity M~ when plotted vs. the concentration c (mol/cm3) shows a linear
+
OMSCN 0.6M 18C6 0.6M in DMF; t = 45%
\
A 8
10
1
0.4
0.2
500
200
+
KSCN o and NaSCN 18-C-6 (R=l) in DMF. t=25OC R = CAlkSCNI/C18-C-61 A R = 0.50 NaSCN R = 2.0
c
z
X
100-
n L \
0
Y
e
01 10
20
50 100 f(MHz)-
200
500
Figure 4. (a) 0.6 M NaSCN + 0.6 M 18C6 in DMF; f = 45 O C . (b) 0.4M KSCN 0.4 M 18C6 in DMF: f = 45 O C .
+
correlation (Figure 3). This information seems to suggest a firstor pseudo-first-order process.s We advance the hypothesis, as we did in the case of methanol as ~ o l v e n tthat , ~ we are observing the second step of the Eigen-Winkler process I, namely, process 111. We also assume the existence of an isomeric relaxation of the crown ether alone in DMF. The experimental proof of this last assumption is given below. At variance with what was observed in methanol, however, we have raised the temperature to 45 "C for 0.6 M NaSCN 0.6 M 18C6 and for 0.4 M KSCN + 0.4 M 18C6. The results in terms of the quantity a/f vs.fare shown in Figure 4. Two Debye relations can fit the data as the depicted solid line shows. The dashed lines show the contribution of the Debye process centered at the upper relaxation frequency. The solid line is the sum of both Debye relaxation processes. The process responsible for the relaxational low frequency is not specific for NaSCN since 0.2 M NaC104 added to crown ether (0.2 M 18C6) shows a similar effect. This process appears at 45 "C only if the cation (Na' or K+) and 18C6 are simultaneously present. It appears therefore that another process, slower than the one observed and characterized already, exists. Unfortunately,
+
732 The Journal of Physical Chemistry, Vol. 88, No. 4 , 1984
Maynard et al.
+
NaSCN 0.6M 18C6 0.6M and KSCN 0.4M +18C6 0.4M in DMF
with the available pulse technique, it is not possible to characterize adequately this new process. The determination of its existence and position depends on a few points at the low-frequency end of our accessible instrumentation range. At present we are trying to develop resonator techniques which will allow us to return to this problem at a later time. It is possible that the Eigen-Winkler mechanism in some solvents (depending on the relative barrier of energy of desolvation and of ligand rearrangement) should be written for large 4 ' s as follows: Me. - 4Z&
k
k-1
k
MeC & (MeC)
(V)
k-3
the quantity (MeC) symbolizing the metal complex in the final wrapped configuration. If this is the case, we are observing the second step Me. * .C F? MeC (k2, k-2),mainly due to initial ligand rearrangement and/or desolvation. For the time being we will analyze only the process that we observed and adequately characterized; Le., we will deal with the observed process according to the first step of eq V, using the relevant equations for two first-order step processes (both first order) taken from the 1iterat~re.l~ 7;'
= 2aA = k2
+ k-2
-221 c
E
/
(VI) where 0, = (l/pu2), C2 = [Me...C], C3 = [MeC], and C, = [(MeC)]. Further, K2 = C3/C2 and K3 = C4/C3. From the mass law and mass conservation rule, one has (AVSd2
K
(VII)
Calorimetric titrationsL4for NaC104 and 18C6 in DMF at 25 OC indicate that the overall complexation constant K , = 1.2 X lo3 M-I. Also, Kx = K I ( l + K2 + K2K3) ands K L = K F = (4aLa3/3000) exp[ep/(a2ekT)] = 1-10 M-l, with p the dipole moment of 18C6, and a the collision distance between Na+ (or K+) and 18C6. Raman spectra to follow show that, when R = 1, the anion NCS- is spectroscopically free. The latter information signifies that Na+ (or K+) is practically all bound to 18C6 at R = 1, namely, that C1 (the free ions and free crown ether ion concentration) and C2 are small with respect to C3 and C,. The above indicates that K2 and K3 are large with respect to 1. Then
(VIII) Then we can write
= k2 = (kT/h)eA+%'/Re-Aff2*/RT
d In ( s ' / T ) / d ( l / T )
3.4 (
iovn-
3.5
3.6
3.7
Figure 5. (A) In ( r - ' / T ) vs. 1 / T for 0 . 6 M N a S C N + 0.6 M 18C6 in DMF and for 0.4 M KSCN 0.4 M 18C6 in DMF. (B) In ( F ~ T / U * ) vs. 1 / T for 0.6 M NaSCN + 0.6 M 18C6 in DMF and for 0.4 M KSCN + 0.4 M 18C6 in DMF.
+
K2
c prnl= 2/3, RT (1 + K2)(1 + K2 + K2K3)
7-1
3.3
3.2
B
(1x1
= -AH2*/R
(X>
Further d In (fimT/U2)/d(l/T) = (l/R)(AH2 + AH31
(XI)
From the data of Table I one may produce Figure 5, depicting In (7-l/7') vs. 1/Tand In (pmT/u2)vs. l / T f o r NaSCN 18C6 and KSCN + 18C6 in DMF. The solid lies calculated by linear regressions give the following results. For NaSCN + 18'26, from In ( 6 l / 73 vs. 1/ T one obtains slope = -1207, intercept = 18.01, r2 = 0.995. From these data one cal_culatesAH2* = 2.4 kcal/mol, AS2* = -1 1.4 eu whereas k2 = 2aA = 3.7 X lo8 s-l. Further, the plot of In (pmT/u2)vs. 1 / T
+
(1 3) Schneider, H.; Rauh, S.; Petrucci, S. J . Phys. Chem. 1981,85,2287. (14) Rushton, H. J.; Grey, G. C.; P e t y i , S.;.Graham, R. C.; Eyring, E. M., in preparation.
(Figure 5B) gives slope = 665, intercept = -24.7,, r2 = 0.954. From these data one calculates AH2 + AH3 = 1.3 kcal/mol. Finally, the plot of pmvs. c (expressed in mol/cm3), Figure 3, assigning 50% statistical weight to the origin gives r2 = 0.998, slope = 20.6. For KSCN + 18C6, from In (T-'/ T) vs. 1/ T, Figure 5A, one obtains slope = -1789, intercept = 19.19,G = 0.998. From these data one calculates AH2*= 3.55 kcal/mol, AS2* = -9.1 eu whereas k2 = 2 r T = 1.6 X 108s-'. The plot of In ( h T / u 2 )vs. 1/T, Figure 5B, gives slope = -1236, intercept = -18.96, r2 = 0.957. From these data one calculates AH2 AH3 = -2.4, kcal/mol. Finally, the plot of pmvs. c (expressed in mol/cm3), Figure 3, gives (with 50% statistical weight to the origin) 9 = 0.996, slope = 18.3. From the above one may notice the similarities and the differences between the two systems. The slopes of I, vs. c are very close as is also evident from Figure 3. Further, the two (AH, + AH3)'s are contrary in sign as the slopes of Figure 5B indicate. Although we do not know the value of K2K3, it may be of interest, by using an educated guess, to predict an order of magnitude for AV,. For Na+ + 18C6 it is known that K , = 1.2 X lo3 M-'.14 Assuming this value and K , 1-10, one obtains K2K3 lo2 as an order of magnitude. Then from eq VI11
+
-
-
AV, =
(
TW,RT K ~ K ~ ? ) ' ~ ~= 39.1 cm3/mol
having used u = 1.5
os=--'
X
- 47.1
lo5 cm/s, p = 0.944 g/cm3 and X
cm s2/g (or dyn-' cm2)
PU2
Isomeric Relaxation of 18C6. Figure 6 shows a representative plot, in the form of a/f vs. the frequencyf, of the relaxation of 18C6 in DMF at t = -10 OC. The effect vanishes at a few degrees above 0 OC. Solubility becomes low below -20 O C . In this limited temperature range it is possible to collect relaxation parameters
Complexation of Sodium and Potassium Ions with 18C6
The Journal of Physical Chemistry, Vol. 88, No. 4, 1984 733 TABLE 11: Ultrasonic Relaxation Parameters A , fi,B , and p m and Sound Velocities L( for 18C6 a t the Concentrations and Temperatures Investigated in DMF
18C6 0.6M in DMF t=-lO°C
t
f, O C
ciSc6, r;,
-10 -10 -10 -10 0 -15 -20
M
MHz
0.20 0.40 0.60 0.80 0.20 0.20 0.20
90 90 80 90 150 75 45
1 0 1 7 ~ 1 0 1 7 ~ , 10-5u, s'/cm s*/cm cm/s 49 85 116 144 23 77 140
36 45 52 60 31 32 32
1.594 1.600 1.594 1.606 1.555 1.586 1.616
1 0 5 ~
35 1 612 740 1041 268 458 5 09
1
10
-
20
50 100 WHZ)
500
200
Figure 6. Plot of a/f vs. f f o r 0.6 M 18C6 in DMF at
1
18C6 0.2M h DMF
= -10 "C.
t
15
c.
for the process. The results of the analysis of the data and of the sound velocities are recorded in Table 11. One notes that the relaxation frequency f, is independent of concentration, in the investigated range at the temperature of t = -10 "C. Further, the maximum excess sound absorption per wavelength p, is roughly linear with concentration. The above indicates a first-order or pseudo-first-order process.8 We propose that the observed process is represented by the isomeric conformational scheme
c, e c2
7-1
= k,
+ k4
k
14
13
A
= k*(l
I
I
I
3.7
3.8
3.9
I
4. L
+ KO)
1
3.6
(1031~)-
(XII)
C I and C2 being two isomeric forms of the crown ether. The following equations apply for this process: 7-l
t
18C6 0.2M in DMF
-231
= kTe~+*/Re-Afi+'/RT(1 + KO) h = 5.5 x IO8 s-l at -10 "C
d In ( T - I / T ) d(l/7')
-25
- -AH+,* R
(XIII)
(1
+ K0)R
= -3765 (XIV)
3.6
3.7
B
I The numerical values above for eq XIV and XV have been obtained by linear regression analysis of In ( T - ~ /7') vs. 1 / T and of In ( h T / u z )vs. 1/T, respectively (Figure 7, A and B). Specifically from the former plot, one obtains r2 = 0.968, intercept = 28.88, slope = -3765. From the intercept = In ( k / h ) + AS4*/R,one calculates A&,* = 10.2 eu. From the latter plot (Figure 7B) one calculates r2 = 0.945, intercept = -30.93, slope = AHo(Ko l ) / R ( K o+ 1 ) = 1829. Excluding KO= 1 since eq XV is different from zero, values of KO= 10 and KO= 100 give parameters AH4* that, when substituted into eq XIII, result in 7-1 of the order of l O I 3 s-l, inconsistent with the experimental value T ~ , ~=~ 5.5 ( ~X KO= 0.1 leads to 7-l = 2.9 X lo8 s-l, whereas convergence with the experimental value is obtained with KO = 6.5 X With this value KO = 6.5 X it results that AHo = -3.7 kcal/mol, AH4* = 7.5 kcal/mol, and 7-l = 5.4 X lo8 s-l. The above results are summarized as follows: K~ = 6.5 x 10-3
38
3.8
(l+/l* 18C6 h DMF 1:-10'C
0 0.1 0.2 0.3 0.4 0.6 0.6 0.7 0d
C
cx
103 (md.1~m3)-
Figure 7. (A) In ( 7 - l / T ) vs. 1 / T for 0.2 M 18C6 in DMF. (B) In ( p , T / u 2 ) vs. 1 / T for 0.2 M 18C6 in DMF. (C) pm vs. c for 18C6 in DMF at t = -10 OC.
weight to the origin) gives r2 = 0.987, slope = 12.94. One then may write
= 34 cm3/mol at -10
O C
AHo = -3.7 kcal/mol AH+*,
= 7.5 kcal/mol
AS4* = 10.2 eu k , = 5.5 x lo8 s-I at t = -10
O c
Further, one can extract ko = 3.6 X lo6 s-I at -10 OC and AHo* = 3.8 kcal/mol. One can also evaluate the parameter AV, for the isomerization reaction. From Figure 7C depicting p, vs. c expressed in mol/cm3 linear regressions (with 50% statistical
having used pDMFZ5 = 0.94 g/cm3 (the value of p at -10 "C is not known), w = 1.6 X lo5 cm/s and consequently p, = 41.4 X IO-'* cm s2/g. From KO= 6.5 X and the relation AGO= -RT In KO,AGO = 2.6 kcal/mol at t = -10 O C . Given AHo = -3.7 kcal/mol it follows that A S 0 = -24.0 eu. Then a,* = + AS+* = - 1 3 . 8 eu. Calculation of ko at 25 "C with the above activation parameters AHo* and ASo* (although they refer to -10 O C being based on KOat -10 "C) leads to ko = 9.9 X lo6 s-l = lo7 s-I. This figure is lower by 1 order of magnitude than the values of k2 above,
134
Maynard et al.
The Journal of Physical Chemistry, Vol. 88, No. 4, 1984
I
3. 5 M LISCA/OMF
I
1
1
\
I
I 600
718
730
710
730
750
770
730
E;;@
770
7:1!
d.2
770
190
d.0
ne
./ad
CM- 1
a) 690
750
0 . 4 M KSCN/DMF
CM- i Figure 8. Raman spectrum (u3 line) for NCS- anion. System: NaSCN in DMF at 25 OC.
namely, k,(Na+) = 3.7 X lo8 s-l and k2(K+) = 1.6 X lo8 s-l. Further, ko = lo7 s-' is close to what is expected for k3 based on the presence of the lower relaxation at -4 MHz for NaSCN and KSCN 18C6 although these data are at t = 45 "C (Figure 4). It would appear therefore that the rearrangement of the ligand in DMF is the rate-determining step for the complexation process in accord with the Eigen-Winkler mechanism. Further confirmation of these surmises will have to wait for future studies of the lower relaxation with alkali metal and 18C6 by ultrasonic resonator techniques. Raman Spectra. Thiocyanate ion (&) has three coincident Raman and infrared spectral lies normally at v1 (CN, 2060 cm-'), u2 (degenerate bend, 480 cm-I), and u3 (CS, 735 cm-I). Upon coordination via either the nitrogen or sulfur end (thiocyanate ion is known to be ambidentate), certain characteristic changes in the vibrational spectrum occur and can be used as accurate criteria in determining its mode of attachment. Specifically, N-coordination increases u3 (as much as 100 cm-' in solid com~ ~ *vibrational ~ ~ plexes) while S-coordination decreases Y ~ . These frequency shifts can be explained by resonance structures which depict electronic redistribution in the molecule
+
SEC'ZN
/ \
s=c=N-
I OM
738
750
CM- 1
0.4M NH4SCN/DMF
I
I
ma
7ia
C)
N-banded
S- banded
71#
b)
738
750
I 'ID
CM- 1
Figure 9. Raman spectrum ( u 3 band) for (a) 0.5 M LiSCN in DMF at 25 OC, (b) 0.4 M KSCN in DMF at 25 OC, and (c) 0.4 M NH4SCN in DMF at 25 ' C .
/S-c=N
Note that the changes in bond order account for the observed spectral behavior. In this study, the u3 region (C-S stretching region) was studied most intently; the u1 region has a nearby weak solvent band which hinders quantitative analysis, and the u2 region is obscured by strong DMF absorptions. The u3 band was also found to be the most diagnostic with respect to coordination of cations in solution. Figure 8 shows the u3 region of sodium thiocyanate in N,N-dimethylformamide at concentrations of 0.2-0.8 M. Spectral intensities are normalized at 735 cm-' to aid comparison. Each spectrum is comprised of two components: a band at 735 cm-' assigned to "freen (solvated) SCN- and another band at 754 cm-I assigned to the Na'NCS- contact ion pair. The "bound"-SCN band is higher in frequency relative to the free-SCN band and is therefore assigned as an N-bonded thiocyanate ion pair.I6 Spectra of LiSCN, KSCN, and NH,SCN in the u3 region also show evidence of contact ion pairs, with the bound band appearing at 768,746, and 760 cm-l, respectively (Figure 9a-c). For all the thiocyanates studied, a two-component-band analysis of the u3 region was found to best fit the envelope. Species concentrations in the NaSCN/DMF solutions were obtained as follows. With use of a computer program utilizing (15) Gam, P."Vibrating Molecules";Chapman and Hall:London, 1971; p 192. (16)Paoli, D.;Mucon, L.; Chabanel, M. Spectrochim. Acra, Part A 1978, 34, 1087.
an exponential-polynomial function, the residual background intensity was subtracted. The resultant difference spectra were curve resolved into two components with the program BNDFT, which uses Cauchy-Gauss product functions. To determine a molar intensity (J) for the SCN- ion, the relative total Raman intensity ( I , = (AT/A,)C,where C, is the DMF concentration) from the u3 region was plotted vs. the total thiocyanate concentration C,. A straight line of slope J = 1.55,g = 0.994, and zero intercept was obtained. (The area of the intense 660-cm-' band of DMF A, was used as an internal intensity standard.) The fact that the resultant plot is linear over the concentration range studied suggests that J = J f = Jb (where f free, b bound), i.e. Af Cf = 4- cJ ,r
Ab
c, = -e, AsJb
c, = c, + c,
But
thus AbCs AfCs c, = + -A,J A,J when J = J f = Jb. The molar intensity Jf has been obtained in previous work" from a series of solutions of a thiocyanate salt
Complexation of Sodium and Potassium Ions with 18C6
The Journal of Physical Chemistry, Vol. 88. No. 4, 1984 735 0. 2M NASCN/DMF
TABLE 111
[NaSCNl , M
K , M-’
[NaSCN], M
0.176 0.282 0.389 0.480
1.47 1.46 1.41 1.45
0.555 0.683 0.826
-~
K, 1.44 1.66 1.31 K,,= 1.46 t 0.10 M-’
W I T H 0. 2V C18I-CROWN-6
for which no ion pairing occurs. For D M F solutions even NH4SCN is not completely dissociated and thus the total intensity was used. The use of the molar intensity value with the resolved areas from the v3 region allowed concentrations of free and bound species to be determined. Assuming a single equilibrium the following equilibrium constant is defined: Na+ Cf
+ SCN-
K
Cf
Na+NCS-
710
730
750
770
790
810
77E
798
810
CM- 1 0.614 NASCN/GMF
cb
K = [Na+NCS-]/{[Na+][SCN-]] = Cb/C:
(XVI)
Table I11 lists the calculated values for the equilibrium constant K at each thiocyanate concentration studied. For the solutions of sodium thiocyanate in D M F containing 18C6, the Raman spectra in the u3 region are markedly different. Figure 10 displays the v3 (CS) region of NaSCN with an equimolar amount of 18C6 present. The spectral region now consists of essentially one line at 735 cm-’ due to the free thiocyanate ion. The “disappearance” of the 754-cm-I band (due to the Na’NCS- ion pair) may be explained as a competition between SCN- and 18C6 for the metal ions.
+ SCN- 2 Na+NCSK, Na+ + 18C6 S (Na18C6)’ Na+
690
K
It is known from the literature” that K z is generally large (i.e., K2 >> K ) , such that the sodium ion greatly favors binding with the 18C6 rather than with the thiocyanate ion. In effect, when the stoichiometric concentration of 18C6 is equivalent to that of NaSCN, the concentration of bound S C N species in solution is very low. Hence, the absence of the 754-cm-I band in the Raman spectrum of such solutions. Similar effects are evident in the spectra of KSCN/18C6 in DMF solutions, where again, Kz >> K. In the case of ammonium thiocyanate, the intensity of the 760-cm-’ band is approximately halved upon addition of the equimolar crown ether and with lithium thiocyanate no changes occur. The experimental observations may be justified solely on the relative magnitudes of K and K2. Results thus far have focused on observation of (a) cation-anion interaction (directly) and (b) cation-crown ether interaction (indirectly) from changes in the v3 band of SCN. There is also evidence of cationsolvent interaction (directly) and cation-crown ether interaction (indirectly) from changes in the bandshape of the 660-cm-’ line of the solvent. Besides the main intensity there is a shoulder visible at 673 cm-’ when LiSCN is present, and a definite asymmetry when NaSCN is present. Both effects are directly related to solute concentration. To investigate the asymmetry in the NaSCN/DMF case, the centroid (center of mass) and peak frequency of the 660-cm-’ band from a series of solutions (0-1.1 M Na’) were determined with a PC computer program. The asymmetry of the spectral envelope ~ ~ ) called Av. This quantity is zero for is related to v ( , , ~ ~ -~ qp0, neat DMF and increases with increasing NaSCN. With NaC104 added to the NaSCN, Av is even larger. D M F is known to strongly solvate cations and this interaction is believed to be the cause of the asymmetry of’ the 660-cm-l band, which is an OCN deformation mode.I8 When solvent is replaced by 18C6 in the (17) Christensen, J. J.; Eatough, D. J.; Izatt, R. M. Chem. Rev. 1974, 74, 351. (18) Kauffmann, G.; LeRoy, M. J. F. Bull. SOC.Chim. Fr. 1967, 402.
690
710
73D
758
CM-- 1 Figure 10. Raman spectrum (v3 region) for NaSCN with and without added 18C6 ( R = 1) at concentrations c = 0.2 and 0.6 M in DMF at 25 OC.
solvation shell of Na’, the band symmetry is reestablished. Spectral Changes with Time The above spectral study and quantitative analysis were based on spectra obtained soon after preparation of the solutions from pure components. However, spectra collected at later times show significant changes in the v3 region. Specifically, a band at 747 cm-’ appears in the spectrum where no band was present initially. The frequency of this new component was independent of the cation studied. The process of concern is thought to be chemical in nature, possibly involving a slow reaction between the thiocyanate ion and dimethylformamide. Raman spectra of solutions containing equimolar amounts of 18C6 and NaSCN were obtained in short scans and the resultant data checked for consistency. With this assurance of reproducibility with time, the short scans were mathematically co-added to produce the final spectrum. This exercise showed that no detectable change occurred in the Raman spectrum during the time needed to obtain the spectrum itself. Conclusions It appears that in DMF the Eigen-Winkler mechanism can best explain the observed phenomenon. This is interpreted as due to the second step of the Eigen-Winkler mechanism. Another process slower than the one characterized appears to exist. It is surmised that it corresponds to the final desolvation of the metal cation and to the crown ether conformational rearrangement around the cation. The isomeric relaxation of the crown ether alone has been observed and characterized. The activation parameters for the C2 lead to the calculation of k , = lo7 s-l at forward step C, 25 O C . This figure is comparable with the values estimated for k,, the rate constant for the final metal-crown ether complexation. It would appear therefore that the rearrangement of the ligand 18C6 in D M F is the rate-determining step for the complexation process in accord with the predictions of the Eigen-Winkler mechanism. The Raman data are interpreted in terms of two competing equilibria:
-
Me+ + SCN-
K
MeNCS
J. Phys. Chem. 1984, 88, 736-743
736 Mef
+ 18C6
4
(Me18C6)+
The thiocyanate and donor atoms of the crown ether compete for the coordination sites about the solvated cations. For NaSCN/ 18C6 and KSCN/ 18C6 it appears that K < K z , Most of the bound thiocyanate has been r e p l a d with crown ether and the v3 region appears as essentially a single line at 735 cm-I. The converse situation (with K > Kz and most of the thiocyanate remaining bound with little change occurring in the v3 region upon addition of 18C6 to R = 1) appears to be the case for LiSCN/18C6 as well as for LiSCN/15C5 and LiSCN/12C4. The intermediate situation K = K z with significant changes oc-
curring in the Raman spectrum appears to occur for NH4SCN/18C6 NH4SCN/15C5 and NaSCN/15C5. The ammonium ion is of interest in the above list because it can interact with the crown ether by hydrogen bonding in addition to the Coulombic forces. Acknowledgment. E.M.E. and S.P. thank the National Science Foundation (Grant No. CHE-8108467) and (D.E.I. and K.J.M.) the Natural Sciences and Engineering Research Council of Canada for their generous research support. Registry No. Na, 7440-23-5; K, 7440-09-7; NaSCN, 540-72-7; KSCN, 333-20-0; 18-crown-6, 17455-13-9.
Dlffuse Reflectance Spectroelectrochemistry as a Probe of the Chemically Derivatked Electrode Interface. The Derlvatlzed Nickel Electrode Brian D. Humphrey, Sujit Sinha, and Andrew B. Bocarsly* Department of Chemistry, Frick Laboratory, Princeton University, Princeton, New Jersey 08544 (Received: February 3, 1983; In Final Form: September 14, 1983)
Diffuse reflectance spectroelectrochemistryhas been employed to directly monitor the interface charge-transfer (CT) behavior of surface-bound [Ni"(NC)Fe"~"'(CN)~]*-/on a nickel electrode. The technique is shown to be species specific and sensitive to the amount of surface-confined material and the oxidation state of the surface-attached species. It is therefore of utility in observing the time-dependentbehavior of the surface species under transient potential conditions. This technique is compared with chronocoulometry carried out on the same system. The two techniques are used to obtain values of apparent diffusion coefficients for the derivatized surface. In the short-time limit both techniques are shown to follow the Cottrell equation. However, it is necessary to incorporate time-dependent diffusion coefficients to obtain agreement for long-time data. The reflectance technique is shown to be superior to chronocoulometry in that it can discriminate against current not associated with the surface species of interest.
During the past decade, spectroscopic techniques have proven to be powerful tools in understanding electrochemical processes. In situ spectroelectrochemical monitoring has yielded a wealth of information about the kinetics and mechanism of a variety of charge-transfer reactions between an electrode and a solution species.' Relatively little effort has been aimed at probing the nature and reaction dynamics of chemically derivatized electrodes using these techniques. However, spectroscopy offers access to information on both surface structure and kinetics not directly obtainable by using pure electrochemical techniques. Further, since spectroelectrochemical techniques are species specific, they offer a specific advantage when dealing with the small quantities of materials associated with the derivatized electrode interface. In particular, both nonfaradaic processes and faradaic processes not associated with the surface-attached species can be discriminated against. Both these items may be a sizable component of the total cell current associated with charge transfer to mol/cm2 of surface-attached material. Standard spectroelectrochemical techniques require the use of an optically transparent electrode (OTE). Unfortunately, both the minute sample size and the fact that the actual interface constructed is often a strong function of both the electrode material and its physical condition suggest that the application of OTE techniques will not necessarily yield the desired results. A limited number of spectroelectrochemical investigations have been carried out at OTEs coated with relatively high coverages of polymersZd or Prussian blue and
-
(1) (a) Kuwana, T.; Heineman, W. R. Ace. Chern. Res. 1976, 19, 241. (b)
Kuwana, T.;Winograd, N. "Electroanalytical Chemistry"; Bard, A. J., Ed.; Marcel Dekker: New York, 1974; Vol. 7, p 1.
(2) Scott, N. S.;Oyama, N.; Anson, F. C. J . Elecrroannl. Chem. 1980, 1IO, 303. (3) Kaufman, F. B.; Engler, E. M. J. Am. Chem. Soc. 1979, 101, 347.
0022-3654/84/2088-0736$01.50/0
its analogue^.^^^ These studies have yielded promising results; however, the techniques employed are limiting and cannot be applied to the general derivatized electrode containing (1-500) monolayers on a nontransparent substrate. Such systems are susceptible to optical studies, though, if reflection techniques are employed. This approach has previously been used to study chemisorption on various electrode and solid surface^.^ Quite recently, Murray demonstrated that specular reflection techniques are capable of identifying the spectroscopic features of a chemically modified, polished platinum electrode, containing 5 X mol/cm2 of a silylporphyrin.I0 Specular reflection greatly expands the utility of surface spectral probes; however, it still is not a general technique for probing chemically modified electrodes due to the requirement that a mirrored surface be employed. We therefore report on the application of diffuse reflection techniques to characterize the surface derivative and to investigate the charge-transfer kinetics of a new chemically derivatized electrode interface: nickel modified with K3Fe(CN),. To date, most of the chemically modified surfaces which have been reported are based on the surface confinement of a welldefined molecular species, and thus very little effort was necessary to establish that the surface-attached species was the intended species." For example, interface formation based on either
-
(4) Kaufman, F. B.; Schroeder, A. H.; Engler, E. M.; Kramer, S. R.; Chambers, J. Q.J . Am. Chem. Soc. 1980, 102, 483.
(5) White, H. S.; Murray, R. W. Anal. Chem. 1979, 51, 236. (6) Willman, K. W.; Murray, R. W. J . Eleetroanal. Chem. 1982,133,211. (7) Rajan, K. D.; Neff, V. D. J . Phys. Chem. 1982, 86, 4361. (8) Itaya, K.; Ataka, T.; Toshima, S.J . Am. Chem. Soc. 1982, 104, 4767. (9) "Symposia of the Faraday Society"; The Faraday Society and contributors: London, 1971; Vol. 4. (10) Willman, K. W.; Rocklin, R. D.; Nowak, R.; Kuo, K. N.; Schultz, F. A.; Murray, R. W. J . Am. Chem. Soe. 1980, 102, 7629. (11) Murray, R.W. Ace. Chem. Res. 1980, 13, 135.
0 1984 American Chemical Society
