J. Phys. Chem. 1983, 87, 5339-5345
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Nuclear Magnetic Resonance Study of the Rotational Motion of [Co(en),13+ in Aqueous Solution, with Particular Reference to Dynamic Features of Ion-Ion Interaction Yulchl Masuda and Hideo Yamatera’ Department of Chemistry, Faculty of Science, Nagoya University, Chlkusa-ku, Nagoya 464, Japan (Received: February 15, 1983; In Final Form: Aprll28, 1983)
The rotational correlation times, 7,,of the [Co(en),13’ (en = ethylenediamine) ion in the DzO solutionsof various salts were obtained by measuring the spin-lattice relaxation times of 13Cand IH of the methylene group. The 7, values of the [Co(en),13+ ion (extrapolated to infinite dilution) at various temperatures followed the Stokes-Einstein equation. Remarkably higher 7,values with significant anisotropy were observed for the complex ion in the presence of dinegative anions such as suc2-(succinate ion), L-tart2-(L-tartrate ion), and S042-.These features of the rotational motion of [Co(en),l3+were explained by the ion-association model. The rotational motion of the C3 axis of [Co(en),13+was largely retarded by ion pairing with Sod2-, L-tart2-, and suc2-, while the rotation around the C3axis was only slightly influenced by the ion pairing. The high T , value and its anisotropy for the [ C 0 ( e n ) ~ ] ~ + . Sion 0 ~pair ~ - were reasonably explained by regarding the ion pair as a rigid prolate and dealing with the rotational motion of that prolate on the basis of the hydrodynamic model.
Introduction Useful information regarding dynamic structures of electrolyte solutions can be obtained by the investigation on mobilities of ions in solutions. Many authors have investigated translational motions of various ions by measuring diffusion coefficients, electric conductivities, etc., and related them to solvation and ion-ion interacti0n.l Rotational motions of ions can also be expected to give information about dynamic structures of electrolyte solutions, in particular, dynamic features of solvation and/or ion-ion interaction. However, it is very difficult to relate quantitatively the rotational motions of the ions to these interactions. The rotational motions of metal complex ions in solutions have previously been studied for [co(CN),l3-, [Co(NH3)6]3+,and [Co(en),13+by 59C0and 14Nnuclear magnetic relaxation2 and for [Co(a~ac)~] (acac = acetylacetone) by 13C nuclear magnetic r e l a ~ a t i o n . ~However, these studies aimed mainly at the elucidation of the relaxation mechanism and the quadrupole coupling constant of the 59C0 nucleus. Although no detailed studies have so far been made on the relations between the rotational motions of metal complexes and the ion-ion or ion-solvent interactions, the metal complex ions have characteristics favorable for such studies; the size, geometrical structure, electric charge and its distribution, etc., can be easily changed by selecting the ligands or metal ions. We have chosen aqueous solutions of [Co(en),13+salts for the nuclear magnetic resonance study of rotational motions of ions for reasons to be described below. The rotational correlation time of a molecule or an ion, 7,,has often been used to represent rotational motion and has been obtained by the methods of depolarized Rayleigh light scattering: Raman scattering: and NMR relaxation., (1) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions”, Butterworth, London, 1959. (2)R. Ader and A. Loewenstein, J. Mugn. Reson., 6,248 (1971). (3)D. M.Doddrell, M. R. Bendall, P. C. Healy, G. Smith, C. H. L. Kennard, C. L. Raston, and A. H. White, Aust. J. Chem., 32,1219(1979). (4)G.R.Alms, D. R. Bauer, J. I. Brauman, and R. Pecora, J. Chem. Phys., 68, 5570 (1973);69,5310,5321 (1973);G.D. J. Phillies and D. Kivelson, ibid. 71, 2575 (1979). (5) F. J. Bartoli and T. A. Litovitz, J. Chem. Phys., 66,413 (1972);K. Tanabe, J. Phys. Chem., 86, 319 (1982). (6)B. Ancian, B. Tiffon, and J. E. Dubois, J. Chem. Phys., 74 5857 (1981);B. Tiffon and B. Ancian, ibid., 76,1212 (1982). 0022-3654f 8312087-5339$01.SO10
The 7,value for the nonpolar molecule is usually treated by using the hydrodynamic model. When a rotating molecule is sufficiently large to regard the solvent as a continuous medium, the value of 7c can be predicted by the Stokes-Einstein equation, which has been derived from hydrodynamics by using the stick boundary c0ndition.l When the molecule becomes so small that the solvent cannot be regarded as a continuous medium, the hydrodynamic boundary shows the nature of slipping. Pecora et al.s reported that the rotational correlation time of the molecule could be well evaluated with the condition of the slipping hydrodynamic boundary, when the molecule was as large as the solvent molecule. Dote et al.9 were successful in describing 7, of various molecules in organic mixtures with the quasi-hydrodynamic free-space model. In many cases, the hydrodynamic model has been proved to be useful to estimate the 7c value unless specific interactions exist between solute molecules or between solute and solvent molecules. As for ions in solutions, the studies on their rotational motions are limited to only a few cases, i.e., for the NO3(ref 10 and 11) and SCN- (ref 11) ions studied by the methods of depolarized Rayleigh light scattering’l and Raman scattering.1° In these cases, dependences of 7c on the temperature and the salt concentration of the solutions are not always explainable by the hydrodynamic model. The hydration and the ion-ion interaction may have large effects on the rotational motion of the ion. However, no quantitative treatments have so far been carried out on those effects. In order to investigate the rotational motion of cations in the presence of various anions, we selected aqueous [Co(en),]X, (en = ethylenediamine, X = C1-, I-, C104-, AcO-, SO:-, L-tartz-, and suc2-) solutions as the samples. Selection of this series of systems allows us to make the following simplified treatment: (i) [Co(en)J3+ is a rela(7)A. Einstein, “Investigation on the Theory of Brownian Movement”, Dover, New York, 1956,p 19. (8)D. R. Bauer, J. I. Brauman, and R. Pecora, J. Am. Chem. Soc., 96, 6840 (1974). (9)J. L. Dote, D. Kivelson, and R. N. Schwartz, J. Phys. Chem., 86, 2169 (1981). (10)D. James and R. L. Forst, Faraday Discuss. Chem. Soc., No.64, 48 (1977);T. Kato, J. Umemura, and T. Takenaka, Mol. Phys., 36,621 (1978). (11)M.Whittle and J. H. R. Clarke, Mol. Phys., 44, 1435 (1981).
0 1983 American Chemical Soclety
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The Journal of Physical Chemistry, Vol. 87, No. 26, 1983
tively large ion compared with a water molecule. This permits one to regard the solvent water as a continuous medium. Thus, the sticking boundary condition can reasonably be applied to the rotational motion of the [Co(en),],+ ion if no specific interactions exist between the cation and solvent molecules or anions. (ii) The Stokes radius of the [Co(en),13+ion for the translational motion is approximately equal to its crystal radius.12 (iii) The interaction between [Co(en),13' and its counteranion can be observed even in dilute solutions (10-3-10-1 mol drn-,), where a relatively simple treatment of the ion-ion interaction can be made in investigating the rotational motion of the ion. Another advantage of these systems is a wealth of information as to the interaction between [Co(en),l3+ and anions.13J4 Although the information is mainly concerned with the static structure of the ion pairs between [Co(en),13+and several anions, it is of much use in the investigation of the effect of anions on the 7c value of [Co(en),13+. The proton NMR relaxation method is very effective for obtaining the 7,value of an ion in dilute solutions below 0.1 mol drn-,. 13Crelaxation measurements can also give 7,values in dilute solutions, if the sample is highly enriched with 13C. In this study, we measured the lH and 13C relaxation for the methylene group of [Co(en),13+and determined the 7,values of [Co(en),13+in 10-3-10-1 mol dme3 D20 solutions. Experimental Section Materials. [ C ~ ( e n ) ~ ]was C l ~prepared by the literature method.15 For the synthesis of 13C-enriched [Co(13C-en),]C13,2.2 mmol of 90 atom % enriched ethylenediamine-l,2-13C2 dihydrochloride (Prochem Co. Ltd.) was dissolved in an aqueous solution containing 4.3 mmol of NaOH, and then 0.7 mmol of [Co(NH3),C1]C12and active charcoal were added to this ethylenediamine solution. Crystals of [Co(13C-en),]C13were obtained in a manner similar to that for ordinary [Co(en),]Cl,. The yield of [Co(13C-en),]C1,based on the ethylenediamine-1,2-13C2dihydrochloride was about 80%. The A-[Co(en),13+(for use as L-tartrate) was obtained by ion-exchange chromatography on SP-Sephadex.16 Conversion of [Co(en),]Cl, to the other salts was also executed by the ion-exchange technique. Each salt of [Co(en),],+ was twice recrystallized. The amine protons of [Co(en),13+were deuterated by repeated recrystallizations from D20 before measuring NMR spectra. NMR Measurements. The 13C and lH NMR spectra were obtained on a JEOL FX-60 Fourier-transform spectrometer operating at 15.0 and 60.0 MHz, respectively. the spin-lattice relaxation time (TI) was obtained by the inversion-recovery method, using the pulse sequence of (-180" pulse -t-90° pulse-T-),. For the measurement of T1, more than 10 different pulse intervals ( t )were used and the delay time (7')was 5 times as long as T1. Errors in measuring T1 were less than 3%. The NOE (nuclear Overhauser effect) in 13C NMR was measured by the grated decoupling method with errors of about 3%. The measurements of NMR were performed by using 10-mm (diameter) tubes a t 33.0 "C unless otherwise stated; the (12) K. Kurotaki and S. Kawamura, J. Chem. Soc., Faraday Trans. 1, 71, 217 (1981).
(13) Y. Yoshikawa, Chem. Lett., 1385 (1980). (14) (a) S. F. Mason and B. J. Norman, J. Chem. SOC.A , 307 (1966); (b) Y. Yoneda and T. Taura, Chem. Lett., 63 (1977). (15) S. M. Jorgensen, J. Prakt. Chem., 39, 8 (1889). (16) Y. Yoshikawa and K. Yamasaki, Inorg. Nucl. Chem. Lett., 6, 523 (1970).
Masuda and Yamatera a
b
loHzT 1 = 0 . 7 8 s
-
0 5.2
% T1=0,83s lHz
Flgure 1. I3C and 'H NMR spectra of the methylene group of Ndeuterated [Co(en)$+ for spin-lattice relaxation time measurements by inversion-recovery method (-180" pulse-t -90' pulse-T-), . (a) I3C spectra of 0.0073 mol dm-, [Co(13C-en),](CI0,), (90% enriched with I3C) in D,O, n (number of the pulse sequence) = 1200 and T (delay time) = 5.0 s. (b) 'H spectra of 0.0051 mol dm-, [Co(en),]CI, in D,O, n = 1000 and T = 5.2 s.
- 2,o
Flgure 2. Relationship between the I3C spin-lattice relaxation rate in DO , at 33.0 "C and the concentration of [c~(en)~]X,,, (cM).The values for A-[Co(en),13+ are plotted for X"- = L-tart2-. No significant difference was observed in the RDi, values between A and racemic complexes.
accuracy in temperature was within 0.3 "C. The sample solution of the complex salt in D20 was bubbled with nitrogen gas for 10 min just before each NMR measurement in order to remove oxygen gas from the solution. The concentration of [Co(en),13+in the sample solution was determined by measuring the absorbance a t 21 300 cm-l (log E = 1.94). Viscosity Measurement. The viscosity of the aqueous solution of each [Co(en),13+salt was determined a t 33.00 f 0.01 "C with a Canon-Fenske capillary viscometer. The viscosity of the D20 solution was obtained by multiplying the measured viscosity of the aqueous solution by 1.20, the ratio of the D20 to the H 2 0 viscosity a t 33.00 "C. Results a n d Discussion 1. lH and 13CRelaxation. Figure 1shows representative examples of the 13Cand 'H relaxation-time measurements for the methylene group of ethylenediamine ligands of [Co(en),l3+in aqueous solutions. The 13Cand IH spectra for solutions of other concentrations and other salts were obtained in a similar signal-to-noiseratio by appropriately accumulating the fid signals. The dependence of the 13Cand lH relaxation rates, Rlc and RIH, on the complex-salt concentration is shown in
Rotatiohal Motion of [Co(en),13+ in Aqueous Solution
I
0,05
I
The Journal of Physical Chemlstry, Vol. 87, No. 26, 1983
5341
I
0,lO
0,15 c, / mol d ~ n - ~
Flgure 3. Relationshlp between the 'H spin-lattice relaxation rate in D20at 33.0 OC and the concentration of [Co(en),]X, (cM). The values for A-[Co(en)J3+ are plotted for X"- = L-tart2-. No significant difference was observed in the R , , values between A and racemic complexes.
Figures 2 and 3, respectively. These results are treated as follows. 13CRelaxation. For the 13Cnucleus with directly bonded protons, the main relaxation mechanism is dipolar interaction with these protons. The dipolar relaxation rate caused by this mechanism (RDlc)under the condition of proton noise decoupling is generally represented by1' RDic(k)= y~'y~'h'Cr~(k)~(i)~~~(k)~(i)(1) where Y~ and yc are the gyromagnetic ratios of lH and 13C, ) ~the ( ~rotational ) correlation time of respectively, T ~ ( ~ is the dipolar C(K)-H(i) vector ( r C ( k ) H ( i ) ) ,and rC(k)H(i) is the internuclear separation between the carbon atom and a m), proton; rC(k)H(i) was taken to be 1.09 A (=1.09 X as usually assumed.13J8 The RDlc value can be obtained from the measured nuclear Overhauser effect ( ~ ~and 0 the ~ )observed spinlattice relaxation rate of 13C (&) according to the relaxationlg
RDic = ( V N O E / ~ . ~ ~ ~ ) R I C
(2) All the measured TNOE values were in the range of 1.97 f 0.05. The RDlc values obtained are shown in Figure 2. 'HRelaxation. The 'H NMR spectrum for the methylene protons of N-deuterated [Co(en),13+in D20 solution gave a broad singlet signal. This may result from line broadening due to the spin coupling with the cobalt-59 nucleus and also from the collapse of the AzBzpattern (A = H ( l ) and H(4); B = H(2) and H(3), see Figure 4) resulting from the conformational exchange of the ethylenediamine chelate ring between the 6 and the X conformation.'O This broad signal gave only a single relaxation time over the pulse intervals up to 3T1, in spite of the presence of inequivalent protons, A and B. This obser(1'7) J. R. Lyerla, Jr., and G. C . Levy in "Topics in Carbon-13 NMR Spectroscopy", Vol. 1, G. C. Levy, Ed., Wiley, New York, 1974, p 96. (18) The value obtained by the conformation analysis of the free ! C ~ ( e n ) ~ion ] ~ +was used (ref 13), because the structure of the complex ion obtained by the X-ray diffraction of the crystal may have been influenced by its counteranion. The numerical values for the structure of [Co(en)#+ are due to a private communication from Y. Yoshikawa. (19) K. F. Kuhlmann, D. M. Grant, and R. K. Harris, J. Chem. Phys., 52, 3439 (1970). (20) J. L. Sundmeier and G. L. Blackmer, J. Am. Chem. SOC.,92,5238 (1970).
= the angle between the r,, vector and the C , axis. Geometrical data for the le/,-type A-[Co(en),l3+ ion are listed; the geometrical structure of the ob chelate ring is slightly different from the above. Since the /e/ conformation predominates in aqueous solution (ca. go%), the calculation was carried out by assuming that all of the chelate rings were of the le1 type.
vation indicates that the spins of the A and B protons have almost the same relaxation time. The relaxation of a methylene proton in [Co(en),13+can be considered to be mainly caused by the dipolar interaction with nearby protons. For example, the H( 1)proton shown in Figure 4 is relaxed by the interaction with the other protons of the same ethylenediamine ligand, H(2), H(3), and H(4). When a proton under observation and the protons interacting with that proton have practically the same relaxation rate, as is the case here:' the 'H relaxation rate is represented byz2 RIH(i)
=
(3/2)yH4h2
rH(i)Hb)-6TH(i)HQ)
(3)
$+I
where, rH(1)HQ)is the distance between H(i) and H(j) and T H ( ~ ) H ~is) the rotational correlation time of the dipolar vector, ~ H ~ ) H Q The ). values of rH(l)Hb)used in this study are listed in the caption of Figure 4. 2. Anisotropic Rotational Motion of the [Co(en),13+Ion. If the [Co(en),13+ion has an anisotropic structure or has an anisotropic interaction with solvent water molecules or with its counteranions, the rotational motion of the [Coion should be anisotropic. We assume that the geometry of the [Co(en),I3' ion can be approximated by a cylindrical symmetry whose main axis is the C, axis of the [Co(en),13+ion (see Figure 8). Then, the rotational correlation time of each dipolar vector should show a characteristic value, depending on its direction with respect to the C3 axis. An anisotropic rotational motion of a cylindrical molecule is characterized by two rotational diffusion coefficients, D,, and D,, the rotational diffusion coefficients about axes parallel and perpendicular to the C3 axis, respectively. The relaxation rate of the anisotropic rotational D,, and other parameters motion has been related to D,,, (21) The H(l)-H(2) and H(l)-H(3) dipolar interactions are equivalent to the H(3)-H(4) and H(2)-H(4) interactions, respectively. If the slight difference between the weakest interactions, H(l)-H(4) and H(2)-H(3), is disregarded, the values of RIH(i) (i = 1,...,4) should be practically equal to one another. (22) K. Akasaka, J. Mugn. Reson., 18, 328 (1975).
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Masuda and Yamatera
by S h i m i z and ~ ~ ~Huntress.23b ~ The equation given by the latter author for the NMR quadrupolar relaxation of a symmetrical rotor (eq 5.9 of ref 23b) was applied to the present case of dipolar relaxation with necessary modifications. Thus we have
for the rotational correlation time of a vector at an angle of 0 with the C3 axis. Substituting the relations l/rcll = 6Dlland 1r/Ci = 6D, for the rotational correlation times around the axes parallel (rcll) and perpendicular (7,J to the C3 axis, we obtain
With eq 4, T ~ ( ~ and ) ~ ( T~H ()~ ) H ( Iin ) eq 1 and 3 can be rewritten by 7,ll and T,,. Using the Rhlc and R1H values obtained from observed relaxation rates and the 8ij values for r C ( k ) H ( i ) and r H ( i ) H G ) listed in the caption to Figure 4, we can solve two simultaneous equations in rcIl and r,,, eq 1 and 3. In this way, we obtain the two rotational correlation times, rCll and r,,, of the [Co(en),13+ ion. 3. Rotational Motion of the [Co(en),13+Ion i n a Solution of Infinite Dilution. The relaxation rates of 13Cand lH a t infinite dilution, RDIC(M) and R1H(M)(M stands for the [Co(en),13+ion), were determined by extrapolating the RDlc and R1H values a t different concentrations of [Co(en)3](C104)3to zero concentration. The extrapolation gave the values of 1.28 and 1.21 s-l for f t D I C ( M ) . and R1,(~j,respectively. Two rotational correlation times at infinite dilution, Tcl1(M) and T,,(M), characteristic of the rotational motion of the [Co(en),13+ ion were calculated with the measured RDIC(M) and R 1 H ( M ) values (see section 2). The values of Tcll(M) and rCI(M)were thus found to be 3.15 X and 3.23 X lO-l's, respectively. The approximate equality between the values for r c I l ( M )and T,,~M) indicates that the rotational motion of the [Co(en),13+ion is nearly isotropic. The rotational correlation time obtained by NMR technique can be well represented by the semiempirical relati~n~,~~ r, = ( C V q / k T ) + r,O
(5)
where V is the molecular volume, q the viscosity of the solution, k the Boltzmann constant, T the absolute temperature, C an experimentally determined dimensionless parameter which is concerned with the shape of the rotating molecule and the hydrodynamic boundary condition, and r,O the zero-viscosity intercept which was found to be nearly equal to the classical free-rotor reorientation time. The temperature dependence of rc in eq 5 is determined dominantly by q / T ; the other parameters do not appreciably depend on the temperature. Figure 5 gives a plot of the r, values of the [Co(en),13+ ion a t infinite dilution in D 2 0 against the q/T values at various temperature^.^^ The value of rc a t q/T = 0, 72, is shown to be nearly zero and r, of the [Co(en),13+ion to be approximately proportional to q/T. By assuming that the [Co(en),13+ion is a sphere with a radius of 3.6 A,12we found the parameter C in eq 5 to be 0.9 from the results (23) (a) H. Shimizu, J. Chem. Phys., 40, 754 (1964); (b) W. T. Huntress, Jr., Adv. Mugn. Reson., 4, 1 (1970). (24) P. A. Madden, Annu. Rev. Phys. Chem., 31, 523 (1980). (25) The T, values at the temperatures other than 33.0 "C were obtained from RIH by assuming isotropic rotational motion.
Flgure 5. Relationship between the rotational correlation time of the [Co(en),13+ ion at infinite dilution and the value of 9T-I (1 CP = lo-, kg m-' s-I).
shown in Figure 5. This value is close to 1.0, the value predicted for the rotational motion of a spherical molecule with a sticking hydrodynamic boundary.24 In other words, 7,of [Co(en)J3+follows approximately the Stokes-Einstein relation7 r, = V q / k T (6) which describes the rotational motion of a sphere in a continuous medium. This fact may result from the large radius of [Co(en),13+ compared with that of the solvent water molecule and the weak hydration of the [Co(en),13+ ion. A similar result for the translational motion was previously obtained by conductivity experiments.12 4. Rotational Motion of the [Co(en),13+Ion in Solutions of Various Complex Salts. First, we examine whether or not eq 5 is followed by the rotational correlation time, r,, of [Co(en)J3+ in aqueous solutions of its salts. For this purpose, the relaxation rate divided by the relative viscosity of the solution, Rl/qr (7, = q/q,,! qo being the viscosity of the pure solvent), were plotted agtunst the concentration of the complex salt (Figures 6 and 7). If rc followed eq 5 with a negligibly small value of r,O as was the case for the [Co(en),13+ion a t infinite dilution (Figure 5 ) , Rl/qr (proportional to rc/qr)could be expected to be independent of the concentration of the complex salt. The results shown in Figures 6 and 7 did not meet this expectation, especially in the systems containing dinegative ions. The Rl/q, value largely depended on the concentration of the complex salt for the sulfate, L-tartrate, and succinate systems, while the chloride and perchlorate solutions showed only a slight concentration dependence of the RI/Vr value. The rotational correlation time of the complex ion in the solution of its salt cannot in general be described by a simple hydrodynamic model. Similar behavior of the rotational correlation time was also reported by Whittle et al. for NO3- and SCN- in dilute aqueous solutions of NH4N03and NH4SCN.11 They attributed such behavior to the hydration of the ions. However, the anomaly of 7, for the [Co(en),13+ ion cannot be attributed to the hydration of this ion, since no remarkable anomaly was observed for the chloride and perchlorate solutions. The interaction with the counterion must be responsible for the anomaly.
The Journal of Physical Chemistry, Vol. 87, No. 26, 1983
Rotational Motion of [Co(en),13+ in Aqueous Solution
TABLE I : Ion- Association Constant a t Infinite Dilution and t h e F?,(MxJ/TI~ Ratios of t h e [Co(en),I3+.XnIon Pair a t 33 C
so42-
2.0
Xn-
-
L - tart2-
log K M X o this study lit. ( r e f )
c10,-
IAcOsuczL-tartz-
a a 1.3 1.6 2.8 2.9
so,2-
3.0
c1SUC N
I \ 7
I
L
c0
0-
A-A-
a:
AcO-
I
0.10
0.15
cM / m o l d ~ n - ~ Figure 6. Relationship between the ratio RDlclqr in D,O at 33.0 OC and the concentration of [Co(en),]X, (c,.,).
2.0
,.,, 2-
N
r \ 7
I
c
I 7
E
1.5
L
0.05
1.5 (30)
2.8 2.5 3.5 3.1
(31)' (32p (33) (34)d
'H
13C
1.22 1.26 1.35 1.48 1.85 1.82
1.33 1.38 1.46 1.73 2.02 2.03
1.84
2.25
I
I
0.10
0.15
its counteranion, and their ion pair, respectively, and Km represents the association constant for the [ C ~ ( e n ) ~ l ~ + - X " ion pair. Here, discrimination cannot be made between contact and solvent-separated ion pairs; however, because of the high charge of [Co(en),13+,it is reasonable to assume that contact ion pairs predominate at least for n = 2. For the sake of simplicity we tentatively regard all the ion pairs as contact pairs. The second assumption is that characteristic r, values, T , ( ~ and ) T ~ ( ~are ~ )defined , for the unassociated and ionpaired [ Co(en),l3+ ion, respectively, over the whole range of complex-salt concentrations examined. The third assumption is that T ~ ( can ~ be ~ )described by eq 5 with a negligibly small value of the zero-viscosity intercept. This is an assumption which is valid for T , ( ~ ) . In this assumption, the rotational correlation times divided by the relative viscosity, rc(M)/qr and rC(Mx)/qrshould be independent of the complex-salt concentration. With eq 1-3, the relaxation rates divided by the relative viscosity for the unassociated and the ion-paired [Co(en),13+ ion, R ~ ( M ) and / v ~R1(MX)/qr,should also be independent of the complex-salt concentration. Then, the observed relaxation rate divided by the relative viscosity, Rl/qr, can be written
where cM is the total concentration of the metal complex. The value of Pm is determined by cMand Km, which can be expressed by
c104-
0
1.4 (30)
1.7 (30)
( R(MX)/qr)/s-' ~
a See ref 27. The values for the A-[Co(en),I3+.Ltart*- ion pair. The values were calculated from concentration ion-association constants a t an ionic strength of 1.10. The values were calculated from concentration ion-association constants a t an ionic strength of 0.07.
4
0.05
5343
cM /mol d ~ n - ~ Figure 7. Relationship between the ratio R,,lq, in DO , at 33.0 OC and the concentration of [Co(en),]X, (c,.,).
5. Effect of the Ion-Pair Formation. The [Co(en),13+ ion is known to form ion pairs with various anions.14a We introduce the concept of ion association in order to explain the dependence of the r, value of [Co(en),13+on the concentration. As a first assumption, we consider the equilibrium M3+ + x n M3+.XnKMX
= [M3'-Xn-]/([M3+][Xn-]J
(7)
where M3+,Xn- and M3+.Xn-denote the [Co(en),13+ ion,
where Kmo is the association constant at infinite dilution and f M , for example, denotes the activity coefficient of M3+, which was calculated by means of the extended DebyeHuckel equation.26 In effect, eq 8 contains two unknown parameters R1(MX)/qr and KMxo. Their values were determined so as to give the best fit to the measured RDlc and R ~ values. H The values of KMxo and R1 Mx)/or deand the termined in this manner are listed in Table 1211,28 (26)For example
log f~ = (4).5115~~~1'/~)/(1 -t 0.3291~1'/~) +0.1~~~1 where I is the ionic strength and zM is the charge of the M3+ ion. The ion size parameter, a, was taken as 6 A, the value used in ref 30.
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TABLE 11: T ~ I I / TaIn~d 7 ~ ~ Ratios / 7 ~f o r the [Co(en),l3+.Xn- I o n Pairs at 33 "c ( s)
c10,c1-
IAcOsuc2L - t ar t '-
s0,z-
unassociated
MX 3.2 3.3 3.3 3.3 4.5 4.1 3.5 M 3.15
c3
3.2 3.4 3.8 5.2 5.4 5.8 8.7 3.23 (a)
(b)
calculated RDlcand RIHvalues on the basis of these KMxo Flgure 8. Simplified geometries of the free [Co(en),13' ion (a) and the and R1(MX)/qr values are shown by solid lines in Figures [Co(en),13+.X"- ion pair (b). 2 and 3. The KMxo values for Xn- = S042-,L-tart2-, and I- show a reasonable agreement with the values obtained T A B L E 111: Length ( A ) of the Longer and Shorter Axes by other method^.^^-^^ of the Ellipsoid o f the [ Co(en),13+.Xn- Ion Pair The R1(MX)/qrvalues obtained for the ion pairs with Xnrl(MX) rs,MX) rXa rM+Xa S042-,suc2-, L-tart2-, and AcO- were appreciably greater than the R1(M)/qrvalue for the unassociated complex ion. c10,3.4 3.4 2.4 6.0 c13.5 3.4 1.8 5.2 These greater Rl(m)/qrvalues indicate that the rotational 13.7 3.4 2.2 5.8 correlation time is increased by ion pairing with those AcO4.1 3.4 2.4 6.0 anions. suc24.4 3.7 3.0, 4.0b 6.6 6. Anisotropic Rotational Motion of the [Co(en),l3'-XnL-tart'. 4.7 3.8 3.0, 4.5b 6.6 Ion Pair. In section 3, we showed that the rotational so,25.9 3.5 2.3 5.9 diffusion of the [Co(en),13+ion at infinite dilution is nearly rl, s (M) r(M P isotropic. In order to examine whether or not the rotaunassociated 3.4 3.6 tional motion of the ion-paired [Co(en),l3' ion is isotropic, the two rotational correlation times, T,~~(Mx)and TCi (MX), a rx, r M , a n d r M + X are t h e crystal radii of X"-, were calculated by the method mentioned in section 2. [Co(en),]'+, a n d t h e s u m of t h e m , respectively, The smaller a n d larger values are t h e X"- radii parallel a n d These correlation times divided by the relative viscosity, perpendicular to t h e C, axis of [Co(en),13' i o n paired ~ , l l ( M X ) / q and ~ T ~ ~ ( M Xare ) / ~shown ~ , in Table IL2* with X n - , respectively. The 7c1(MX)/qrvalues obtained were different for the ion pairs with different anions, while the T,ll(MX)/~, value for each ion pair is only slightly different from the T ~ ~ I ( M ) / ~ ~ placed on the C3 axis of [Co(en),13+. Such a structure of the [Co(en),13+.X"- contact ion pair was proposed by sevvalue. It is known that, in the formation of the ion pair, eral authors in the cases of Xn- = S042-, Po43-,and Lan anion tends to approach [Co(en),13+along its C3 tart2-.13,14 It can be expected that the presence of an anion on the We first consider the case in which the lifetime of the C3 axis causes an increase in the friction for the rotational ion-pair structure is longer than T ~ ~ and ~ T( , ~~( M x~ ) . !The diffusion of the C3 axis and accordingly an increase in the [Mg(H20)6]2+.S042"contact" ion pair is known to have a ~ ~ ~ value. ( ~ The ) / experimental q ~ results given in Table lifetime of 10-s-10-9 s from ultrasonic absorption meaI1 are in accord with this expectation. s u r e m e n t ~ . This ~ ~ permits one to presume that the anion 7. Ellipsoidal Approximation of the [Co(en),13+.X" Ion of the [ C ~ ( e n ) ~ ] ~ +ion e Xpair ~ - stays in contact with the Pair. The NH hydrogens of the complex ion can take part [Co(en),13+ion for a time interval of the order of a t least in the hydrogen bonding with an anion to form the [Cos or that a structure of the [Co(en),l3+.Xn-ion pair (en)3]3+-Xnion pair, in which the x"-anion is likely to be is maintained for that time interval (at least for n = 2). The rotational correlation time of the ion-paired [Co(27) In the cases of X" = C10,- and C1-, the KMXOvalues reported in ( e r ~ ) ~can ] ~ ' be estimated by approximating the shape of r and also the ref 30 were used in the calculation of the R 1 ( ~ x ) / qvalues the [ C ~ ( e n ) ~ l ~ + . X ion" -pair by a prolate the longer axis r,lI(~x)and r C l ( ~ xvalues, ) because the KMX"values obtained in the of which is the C3 axis of [Co(en),13+ (Figure 8). The present study were accompanied by large allowances. (28) The KMxovalues listed in Table I are those for total ion pairs values of parameter C in eq 5 for the rotational motion of including both contact and solvent-separated pairs, while each R:(MX)/qr such an ellipsoid were given by Perrin36and Z ~ a n z i g for ,~ value in Table I is the weighted average of the values for the different the sticking and slipping hydrodynamic boundaries. In types of ion pairs or the lower limit for the contact pair. (For systems section 3, the rotational correlation time of the [Co(en),13+ containing anions of 1- charge, in particular, one cannot ignore the contribution to R i ( M X ) from solvent-separated ion pairs, for which the reion at infinite dilution has been shown to be well reprelaxation rate may not appreciably differ from that for unassociated comsented by eq 6, the Einstein-Stokes equation. That is, the and 7cL(m) and for and r B ( m ) plex ions.) The same is true for rcl,(m) hydrodynamic boundary for the rotational motion of the given in Tables I1 and 111, respectively. (29) The association constants given in ref 31, 32, and 34 are the [Co(en)13+ion is nearly sticking. Therefore, on the conconcentration association constants. The values of KMXowere recalcudition of the sticking boundary for the rotational motion lated by considering the ionic strength (see the footnote of Table I). of the [Co(en),l3+.X" ion pair, the lengths of its longer and (30) T. Takahashi and T. Koiso, Bull. Chem. SOC.Jpn., 47, 2784 (1976); 51, 308 (1978). shorter axes, rl(MX) and rB(Mx), were calculated from the
(31) H. Yoneda, K. Miyoshi, S. Suzuki and T. Taura, Bull. Chem. Sac. Jpn., 47, 1661 (1974). (32) B. Norden, Acta Chem. Scand., 26, 111 (1972). (33) I. L. Jenkins and C. B. Monk, J. Chem. SOC., 68 (1951). (34) N. Tanaka, Y. Kobayashi, and M. Kameda, Bull. Chem. SOC. Jpn., 48, 2839 (1967).
(35) (a) M. Eigen and T. Tamm, Z . Elektrochem., 66, 107 (1962); (b) G. Atkinson and S. Petrucci, J.Phys. Chem., 70, 3122 (1966). (36) F. Perrin, J. Phys. Radium, 5, 33 (1934); 7, 1 (1936). (37) C. Hu and R. Zwanzig, J. Chem. Phys., 60,4354 (1974).
J. Phys. Chem. 1983, 87, 5345-5354 T ~and T~ ~ ~~values ~ ~ (according ~) ! to Perrin.% The results are summarized in Table III.2s In the case of X" = SO-,: the values of rl(m)and r,(Mx) derived from relaxation experiments were close to the sum of the radii of [Co(en),l3' and SO-: and to the [Co(en),13+ radius, respectively. These results are consistent with the model that the [C0(en),]~+-S0~~ion pairs are mostly contact ion pairs, which are rotating like a rigid prolate as shown in Figure 5 at least for the order of s. In each case of X"- = suc2- and L-tart2-,the rl(m) value from relaxation experiments is somewhat smaller than the sum of the [Co(en),13+ and Xn- radii, while the r,(Mx)value is slightly larger than the [Co(en),13+ radius and slightly smaller than the Xn- radius. The smaller qMX) value may be interperted as resulting from the relative lability of the structure of these ion pairs compared with the [Co(en)3]3+-S042ion pair; the labile structure may cause a reduction in the effective length of the longer axis of the ellimoid of the ion Dair. The case of X" = AcO- mav also be explained in a similar manner except that the r,(Mx) was to the [Co(en)313+radius because Of the radius Of the acetate ion*38Contrary to the above cases, the ion pair with C104- shows rl((Mx) and r,(m) values
5345
approximately equal to the radius of [Co(en),13+. This indicates that the lifetime of the ion-pair structure is smaller than T , ~ ~ ( M Xand ) or that no directed interaction exists between the ions of the ion pair. At any rate, the C104- ion scarcely gives friction for the rotational diffusion of the [Co(en),13+ ion in the ion pair. For the ion pairs with C1- and I-, the situation is more or less similar to the last case, although a slight influence of ion Dairina is indi~ated.,~ Acknowledgment. We thank Dr. Y. Yoshikawa for providing unpublished numerical values for the structure of the [Co(en),13' ion. This work was partially supported by Grant-in-Aid for Scientific Research No. 56470039 from the Ministry of Education, Science, and Culture, Japan. Registry No. [C0(en)~]~+C10~-, 52672-84-1; [Co(en),13+C1-, 18372-70-8;[Co(en),13+I-,31011-74-2;[Co(en),I3+AcO-,87461-87-8; [ C ~ ( e n ) ~ ] ~ ' s u c87461-88-9; ~-, [Co(en),13+~-tartZ-, 62109-98-2; [C0(en),]~+S0~~-, 18372-71-9; [Co(en),13+,14878-41-2. (38) The smaller values of r I ( M X ) for n = 1 may be partly due to the lability of solvent-separatedion pairs, which may exist in an appreciable proportion because of weaker electrostatic attraction between the anion and the complex ion.
Synthesis and Characterization of a Benzylviologen Surface-Derivatizing Reagent. N ,N'-Bis[ p - (trimethoxysilyl)benzyl]-4,4'- bipyridinium Dichloride Raymond N. Domlney, Thomas J. Lewls, and Mark S. Wrighton" Department of Chemistry. Massachusetts Institute of Technology, Cambridge, Massachusetts 02 139 (Received: February 22, 1983)
N,N'-Bis[p-(trimethoxysilyl)benzyl]-4,4'-bipyridiniumdichloride, I, can by synthesized by reaction of 4,4'bipyridine with p-(trimethoxysily1)benzyl chloride in refluxing CH3CN. Reagent I can be used to functionalize electrode surfaces forming a redox-active polysiloxane, [ (BPQ2+),],,f, via hydrolysis of the Si-OMe bonds. Pt, W, n-Si, and SnOz electrodes derivatized with I have been characterized by electrochemical techniques and surface-sensitive spectroscopies. In aqueous electrolyte the E"' for the [ (BPQ2+~+),],,,fsystem is -0.51 f 0.05 V vs. SCE. Both [(BPQ2'),],,,f and [(BPQ+),],,,f are durable when exposed to aqueous electrolyte solution. Further reduction to [(BPQo),],,~, E"' i= -0.9 V vs. SCE, leads to relatively rapid loss of electroactive material. Optical properties of SnOz/[ (BPQ2+/+/0),]surf show that the surface-confined polymer from I is a promising electrochromic material based on the [(BPQ2+)n],,,~(colorless)+ [ (BPQ+),],,,f(blue-violet) interconversion. cmz/s for Effective diffusion constants for the [(BPQ2+),],,,f [ (BPQ+),],u,fprocess are approximately a coverage of 1 5 X mol/cm2. Even at lo-' mol/cm2, greater than 50% reduction of [(BPQ2+),lsurfcan be effected in 20 mA/cm2 can pass through a [(BPQ2+~+),],,,fsystem at a coverage of -3 X mol/cm2. The [(BPQ2+)n]surf will bind transition-metal complexes in the following ordering of binding strength: M o ( C N ) ~ ~ > - / ~R-u ( C N ) ~ ~ ->/ ~CO(CN)~~> Fe(CN)63-/4-> IrClS2-13->> C1-. The bound complexes have nearly the same E"' as when dissolved in solution, consistent with the conclusion that both halves of the redox couple are equally firmly bound.
-
I terization of electrode surfaces functionalized with it. The surface-derivatizing reagent 1 is a derivative Of benzylviologen capable of polymerizing via hydrolysis of the Si(OMe), groups to form a polysiloxane and covalent attachment to surfaces via reaction of surface OH with the Si(OMe), groups. A closely related benzylviologen derivderivative, 11,2 ative' and an N,"-dialkyl-4,4'-bipyridinium
for derivatizing surfaces have been previously reported. Electrodes derivatized with the viologen reagents1t2 have been demonstrated to be useful in hydrogen~evo~ution catalysis on p-t-e semiconducting photocathodes,2-6 ca-
-- (1) Willman, K. W.; Murray, R. W. J.ElectroanaL Chem. 1982,133, 211.
(2) Bookbinder, D. C.; Bruce, J. A.; Dominey, R. N.; Lewis, N. S.; Wrighton, M. S. Proc. N a t l . Acad. Sci., U.S.A. 1980, 77, 6280.
0022-3654/83/2087-5345$01.50/00 1983 American Chemical Society
