J . Phys. Chem. 1990, 94, 8370-8373
8370
I 3
,
, 3.4
,
#
,
,
3.8 4.2 l/Tx103 l I / K l
*
S
,
4.6
j
5
Figure 10. Arrhenius plot of the rate constant of the excimer formation of the 1-0 polypeptide in DMF ( 0 )and in THF (0).
5E7i
[?
I
..-
X
5E6
Conclusions
I
I
-
3
this polypeptide, the final (excimer) conformation cannot be specified to a single conformation. However, the decay curves were also reasonably fitted to three-component exponentials with a single rise time. The rate of excimer formation is somewhat slower than that of the 1-0 polypeptide at each temperature. The activation energy is again very small (0.9 kcal/mol in DMF, I .2 kcal/mol in T H F ) . The rates of the excimer formation in the 1-0 and 1-2 polypeptides are much slower than the time scale of a local side-chain fluctuation measured by I3C NMR relaxation method on the C@ of poly( y-benzyl i - g l ~ t a m a t eor ) ~by ~ the anisotropy decay method on the tryptophan by about 2 orders of magnitude. This is reasonable, since the range of the librational motion must be much wider for the excimer formation. The present rate is even slower than the fluctuation of the whole helix of 21 amino acid polypeptide in solution ( T = 0.6 ns) and in lipid bilayer (9 ns)., On the other hand, the relaxation time for the main-chain motion accompanied with helix-coil transition is much longer than the present Therefore, the range of the relaxation time found in the present experiment is consistent with the molecular motion proposed in Figures 2 and 3.
3.4
3.E 4.2 l/Tx103 I l / K )
4.6
5
Figure 11. Arrhenius plot of the rate constant of the excimer formation of the 1-2 polypeptide in DMF (m) and in THF (0).
out again that the activation energy is very small. The importance of the entropy term should be stressed for the excimer formation in this polypeptide system. The rise time of the excimer formation was also measured for the 1-2 polypeptide, and the rate constant of the excimer formation was calculated. The Arrhenius plot is shown in Figure 1 I . I n
Two major conclusions are drawn from the present study. First, the helical polypeptide chain is rigid enough to fix side-chain groups, including such a large chromophore as pyrenyl group. Second, the relaxation time for the local unfolding of the helix conformation was found to be on the order of 30-40 ns.
Acknowledgment. We thank Professor I. Ando of Tokyo Institute of Technology for informing us of literature on the dynamics of unfolding of polypeptides. The financial support from the Grant-in-Aid for Scientific Research from Ministry of Education, Science and Culture, Japan (No. 63470095), is acknowledged. Registry No. 1-0, 129314-68-7;1-2, 129215-26-5;Glu(OBz1) NCA, 3 190-71-4; BOC-pyrAla-OH, 100442-89-5; BOC-pyrAla-Glu(OBz1)OBzl, 121445-55-4; BOC-pyrAla-Ala,-OBzl, 129149-42-4; BOC-AlaOH. 15761-38-3;Ala-OBzl-TosOH, 42854-62-6; BOC-pyrAla-Ala2-pyrAla-Glu(OBzl),-OBzl, 129173-90-6; A'-methylmorpholine, 109-02-4. ( 2 5 ) (a) Allerhand, A.; Oldfield, E. Biochemistry 1973, 12, 3428. (b) Nagayama, K . Biophysics 1976, 16. 68. ( 2 6 ) Beppu, Y . Comptct. Chem. 1989, 13. 101.
Temperature and Solvent Effects on Viscoslty B Coefficients. Monovalent Ions in Acetonitrile at 15, 25, and 35 OC K. Ibuki and M. Nakahara* Department of Chemistry, Faculty of Science, Kyoto University, Kyoto 606, Japan (Received: November 29, 1989: In Final Form: M a y 7 , 1990)
The viscosity E coefficients were measured for Lil, Nal, KI, NaBPh,, and Bu4NBPh4in acetonitrile at 15, 25, and 35 O C , and they were divided into the ionic components by using the reference electrolyte Bu4NBPh4. The ionic B coefficients were positive for all the monovalent ions studied at each temperature in this dipolar aprotic solvent. The temperature coefficients of the B values were quite small as in other nonaqueous solvents. The experimental results were compared with the values predicted by the dielectric friction theory to clarify the effect of ionic charge. The charge effect is examined also by correlating the ionic B coefficient with the dielectric constant of solvent.
Introduction Although for a long time attention has been paid to the viscosity B coefficients for ions in aqueous solutions to investigate the effect of ions on the water structure, measurements of B coefficients in nonaqueous solutions are still scarce, in particular for its temperature dependence in aprotic solvents,' and the theoretical in0022-3654/90/2094-8370$02.50/0
terpretation of B coefficients is not much developed after the achievement of Gurney.2 TOimprove this situation, we Carry Out here a systematic study on the viscosity B coefficients for a variety ( I ) Ibuki, K.; Nakahara. M . J . Chem. Phys. 1988, 89, 5015. ( 2 ) Gurney, R. W . Ionic Processes in Solurion: Dover: Yew York, 1962.
C 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 21, 1990 8371
Viscosity B Coefficients TABLE I: Phvsical ProDerties of Acetonitrile properties 15 "C 25 "C ~
.D . e- cm-' ?lo3 CP f0 lD.
Ps
RHO,' A
0.7873 0.377 37.55 4.3 1.91
0.7765 0.341 35.96 3.9 1.93
35 "C 0.7656 0.310 34.45 3.5 1.95
OThe Hubbard-Onsager radius RHOis a solvent parameter used in the dielectric friction theory and defined by the following equation:
RHO= [e2(to- t , ) ~ , / 1 6 ~ q " t 0 * ] ' / ~ where e is the ionic charge and t, the high-frequency dielectric constant. The values for monovalent ions are tabulated here with the assumption that c, = 2 for each temperature.
of monovalent ions in acetonitrile at 15, 25, and 35 "C and compare them with the B values in other solvents available in the literature. Simple aprotic solvents can be regarded as a reference solvent in the study of electrolyte solutions, and a systematic measurement of B coefficients in such a solvent is necessary for progress in our understanding of the physical significance of the B coefficient, which is widely used in solution chemistry. The main purposes of the present work are (1 ) to elucidate the general trends of the B behavior in the simple polar aprotic solvent and (2) to confirm the role of the long-range effect of ionic charge in determining the B coefficient. Recently,' we have derived a dielectric friction theory of the viscosity B coefficient starting with the Hubbard-Onsager electrohydrodynamic equation of motion to see the nonequilibrium polarization effect due to the ion in motion. Our dielectric friction theory of electrolyte viscosity relies on the sphere-in-continuum model, which can be regarded as a primitive reference system where the solvent structure and granularity are completely ignored but where long-range hydrodynamic effects of ionic charge is taken into account in a proper manner. For a comparison of theory and experiment, we want experiment in such a polar aprotic solvent as acetonitrile and acetone. Since the use of a reference solvent has been successful in our previous comparative study on the electric conductances for ions in different solvent^,^ the same approach is expected to be meaningful also in the study of electrolyte viscosity. The choice of acetonitrile as a reference solvent has been motivated by ( I ) the high enough solubilities of simple electrolytes of our interest and (2) the negligibly low probability of the ion-pair formation. Experimental Section
Acetonitrile (guaranteed reagent grade, Nakaai Tesque) was distilled with P2OSand then redistilled with CaH2.5 The density at 25 "C (0.7765 g cm-') was in excellent agreement with the literature value (0.7765 g ~ m - ~ The ) . ~water content was 0.1 mol % according to the Karl-Fisher titration. The physical properties of acetonitrile used in the present work are listed in Table I. The dielectric constant to at each temperature,' the density p and viscosity 7" at 25 oC,6and the dielectric relaxation time rD at 35 "c8are taken from the literature. To estimate the 7 D values at 15 and 25 "C, we assumed that q , / r ) O is independent of temperature. Commercially available salts were used without further purification. Lil (Aldrich, 99%) was vacuum dried for 1 day at 130 "C. N a l and K I (Merck, Sprapur) were dried in the atmosphere for several hours at 150 "C. Sodium tetraphenylborate (NaBPh4, Nakaai, colorimetric quantitative analysis grade) and tetra(3) Ibuki, K.; Nakahara, M. J. Chem. Phys. 1986, 85, 7312; 1987, 86, 5734. (4) Ibuki, K.; Nakahara, M. J . Phys. Chem. 1987,9/, 1864,441 I , 4414. ( 5 ) The Chemical Society of Japan, Shin-Jickenkagaku-Kohza (New Leclures on Experimental Chemistry); Maruzen: Tokyo, 1975; Vol. 1. (6) Riddick, J. A.; Bunger, W. B.; Sakano, T. K . Organic Soluenrs, 4th ed.; Wiley: New York, 1986. (7) Barthel. J.; Watcher, R.; Gores, H.-J. Mod. Aspects Electrochem. 1979, 13, I . (8) Mansingh, K.; Mansingh. A . J . Chem. Phys. 1964, 4 1 , 827.
butylammonium tetraphenylborate (Bu4NBPh4,Aldrich, 99%) were vacuum dried for several days at room temperature. All the solutions were prepared by weight and vacuum corrected; the molarity concentration c was calculated from the density independently measured. Densities ( p ) of solutions were measured to 0.0001 g cm-3 by a vibrating densimeter (Kyoto Electronics, DA-200). Kinematic viscosities of the dilute solutions were measured by an automatic viscometer (Shibayama Scientific Instrument, SS290S), the glass part of which is of the Ubbelohde-type; the viscometer is equipped with an optical detection system. The flow time of water in the viscometer was about 570 s at 25 "C, and its uncertainty was 0.03 s. The kinematic viscosity u and the dynamic viscosity r) are given by the following equations: v = Ct - K / t (1)
(2)
7 = "P
where t is the flow time and C and K are the cell constants. The cell constants were assumed to be independent of temperature and calibrated at 25 "C using water, methanol, acetonitrile, and cm2 acetone.6 Typical values for C and K are 1.582 X and 0.2730 cm2, respectively. The temperature of the water bath was controlled within 0.01 "C in every case. The viscosity of each solution was determined within an error of 0.1%. Results and Discussion Determination ofB Coefficients. Table I1 shows the densities
and relative viscosities qr of electrolyte solutions in acetonitrile at 15, 25, and 35 "C. For all the electrolyte solutions studied here, we can neglect the effect of the ion pairing as shown by Gill et aL9 by the conductance method. The viscosity B coefficient is defined by the following JonesDole equationlo as long as ion pairs are negligible:
vr = q / q o =
1
+
+ BC
(3)
where 7 and r)" are the viscosities of the solution and solvent, respectively, c is the molarity concentration of the solution, and A and B are the constants to be determined experimentally. We plotted ( q , - l)c-'l2 against c1I2and got good straight lines in all the cases; A and B were given as the intercept and slope of the line, respectively. The B coefficients thus obtained are summarized in Table 111. The A coefficient has been expressed theoretically by Falkenhagen et aI.'l in view of the relaxation of the ionic atmosphere; it can be calculated from the dielectric constant and viscosity of solvent and the electrical conductance of each ion. Our experimental results at 25 "C agree with the theoretical ones within 25%; this error in the small A coefficient corresponds to the experimental uncertainty of 0.1% in the viscosity. The B coefficients are determined with a precision of 2 ~ 0 . 0 3 and given in Table 111. Our results for the alkali-metal iodides at 25 "C agree with those by Gill et aL9.l2within experimental error. For the case of Bu4NBPh4and NaBPh,, our results are slightly larger than those by Gill et al. The B coefficient for electrolyte is determined by dynamic interactions between ions and solvent, so that it can be divided into contributions of the individual ions. We need an assumption for the division, and the method proposed by Gill et a1.I2 is taken here at each temperature. In their method, Bu4NBPh4, which is composed of the bulky, nearly spherical cation and anion, is used a reference electrolyte, and the following relations are assumed: B(Bu4NBPh4) = B(Bu4N+)
+ B(BPh4-)
B( Bu4N+)/ B ( BPh4-) = (5.00/ 5.35)3 (9) Gill, D. S.; Cheema, J . S. Z . Phys. Chem. 1983. 134, 205. (10) Jones, G.; Dole, M. J . A m . Chem. Soc. 1929, 51, 2951. ( I I ) Falkenhagen, H.; Vernon, E. L. Philos. Mag. 1932, 14, 537. (12) Gill, D. S.; Chauhan, M. S. 2. Phys. Chem. 1984, 140, 149.
(4)
8372 The Journal of Physical Chemistry, Vol. 94, No. 21, 1990 TABLE 11: Densities and Relative Viscosities for Electrolyte Solutions in Acetonitrile at 15. 25. and 35 OC
0.7876 0.7882 0.7891
Lil, 15 1.002 1.007 1.013
0.1977 0.6670 1.311
0.7768 0.7774 0.7783
Lil, 25 "C 1.002 2.137 1.007 4.239 1.012
0.7794 0.7821
1.019 1.036
0.1950 0.6578 1.293
0.7659 0.7666 0.7674
Lil, 35 "C 1.002 2.137 1.006 4. I80 1.012
0.7685 0.7712
1.018
0.2005 0.6763 1.330
O C
2.197 4.297
0.7902 0.7928
1.020 1.037
1.035
electrolvtes
15 OC
Lil Nal KI NaBPh,
0.77 0.8 i 0.73 1.35
Bu4NBPh4
1.50
0 2633 0 6805 1.437
0.7769 0.7775 0.7786
NaI, 25 "C 1.003 2.368 1.007 4.605 1.014
0.7799 0.7831
1.021
0.2596 0.6710 1.417
0.7660 0.7666 0.7677
Nal, 35 "C 1.003 2.336 1.007 4.541 1.013
0.7691 0.7722
1.020 1.038
0.2319 0.4575 1.368
0.7877 0.788 I 0.7894
K I , 15 "C 1.002 2.591 1.005 4.585 1.012
0.7913 0.7943
1.022 1.037
0.2287 0.45 I 2 1.349
0.7769 0.7772 0.7786
KI, 25 "C 1.002 2.555 1.004 4.522 1.012
0.7804 0.7833
1.021 1.036
0.2255 0.4449 1.330
0.7661 0.7664 0.7677
K1, 35 OC 1.002 2.519 1.004 4.459 1.011
0.7695 0.7725
1.020 1.035
0.3079 0.5338 1.201
0.7877 0.7880 0.7890
NaBPh,, 15 "C 1.005 1.995 1.008 3.804 1.018
0.7900 0.7925
I .029
0.3037 0.5266 1.185
0.7770 0.7773 0.7782
1.005 1.008 1.018
NaBPh4, 25 "C 1.968 3.753
0.7793 0.78 18
1.028 1.053
0.2994 0.5192
1.005
0.7684 0.7710
1.027 1.051
1.168
0.7660 0.7664 0.7673
0. I633 0.3284 0.9762
0.7876 0.7878 0.7887
1.770 2.777
0.7897 0.791 1
1.028 1.044
0.161 I 0.3239 0.9629
0.7769 0.7771 0.7780
Bu,NBPh,, 25 "C 1.003 1.746 1.006 2.739
0.7790 0.7804
1.027 1.043
0.7681 0.7696
1.025 1.040
0.7908 0.7939
1.022 1.042
35 o c
25 OC 0.75 0.77 0.7 I 1.29 I .43
0.75 0.75 0.73 1.28 1.41
TABLE 1V: Viscosity B Coefficients for Monovalent Ions in Acetonitrile at 15, 25, and 35 O C 25 "C 0.48 0.50 0.44 0.27 0.64 0.79
15 "C
Li+ Na+ K+ 1-
N a l , 15 O C 1.003 2.402 1.007 4.669 1.014
1.457
TABLE 111: Viscosity B Coefficients for Electrolytes in Acetonitrile at 15, 25, and 35 "C
ions
0.7877 0.7883 0.7894
0.2670 0.6900
Ibuki and Nakahara
Bu4Nt
BPh,-
0.48 0.52 0.44 0.29 0.67 0.83
35 O C 0.50 0.50 0.48 0.25 0.63 0.78 I
NaBPh,, 35 1.008 1.017
0. I588
0.3193 0.9493
0.7659 0.7661 0.7670
-' _
E"
0
-E 0 4 D
m
02
00
1.055
1.015
Bu4NBPh4,35 "C 1.003 1.722 1.005 2.701 1.014
06 h
Bu4NBPh4,I S "C 1.003 1.006 1.016
0
1.040
O C
1.941 3.701
08
I n eq 5 , the B values are assumed to be proportional to the ionic volume. The resultant ionic B coefficients are listed in Table IV. Temperature Dependence. Figure 1 shows the temperature dependence of the viscosity B coefficients for monovalent ions in acetonitrile. For all the ions studied, the B values are positive, and their temperature coefficients are small; although positive cciefficients are exhibited by some ions, they are negligibly small
, 15
I
25 Temp ('C)
I
35
Figure 1 . Temperature dependence of the viscosity B coefficients for monovalent ions in acetonitrile. The solid and broken lines indicate the experimental results and the predicted values by the dielectric friction theory with the slip boundary condition. The vertical bar in the right middle indicates the magnitude of the experimental uncertainty for the B coefficients.
compared with the exerimental uncertainty. The temperature dependence of the B coefficients for the monovalent ions in methanol, formamide, and N-methylacetamide are small also,' and we here find the same behavior in this simple aprotic solvent. This finding is in sharp contrast to the abnormally large tem, ' ~the perature dependence of the B coefficients in ~ a t e r , ' ~and remarkable difference can be ascribed to the hydrogen-bonded structure of water. The prediction of the dielectric friction theory for the temperature dependence of B coefficients is also indicated in Figure 1 . The predicted values for the Li+, Na+, K+,and I- ions are identical on the scale of this figure. The dielectric friction t h e ~ r y , ~ which takes account of the long-range effect of the ionic charge within the framework of the continuum model, predicts almost constant positive B coefficients for all the ions indicated. Such behavior of the theoretical B values are in qualitative agreement with the experimental results. However, we are skeptical about the general validity of the continuum theory because of the large quantitative discrepancies, in particular for the small ions. We have reached a similar conclusion in the comparison of theory and (13) Kaminsky, M . Discuss. Faraday Soc. 1957, 24, 133. (14) Out. D. J.: Los. J. M . J . Solut. Chem. 1980, 9. 19.
The Journal of Physical Chemistry, Vol. 94, No. 21, 1990 8373
Viscosity B Coefficients
w 1 2345 6
0.8
E
m
0.0
i
0
80
LO
120
EO
Figure 2. Solvent dielectric constant dependence of the viscosity B coefficients for Kt (0). 1- (A), and Bu4N+ (0) at 25 OC. Solvents included are ( I ) acetone, (2) hexamethylphosphoric triamide, (3) methanol, (4) acetonitrile, (5) N,N-dimethylformamide, (6) dimethyl sulfoxide, ( 7 ) water, and (8) formamide. indicates the prediction of the dielectric friction theory (slip) for the Kt ion. The solid line is there as a guide to see the correlation between the solvent dielectric constant and the B value for the Kt ion.
+
experiment in methanol, formamide, and N-methylacetamide.' Solvent Dielectric Constant Dependence. Solvent effects on the B coefficient have never been thoroughly discussed, probably because the exclusion volume theory of the B coefficient by Einstein gives no but they are important to confirm the long-range polarization effect on the B value. Figure 2 exhibits the solvent dielectric constant dependences of the B coefficients for the K+, I-, and Bu4N+ ions in various solvents at 25 O C for which the experimental values are available. Solvents included are acetone,ls hexamethylphosphoric triamide,I6 methanol,'* dimethyl sulfoxide," acetonitrile, N,N-dimethylformamide,Is and f ~ r m a m i d e . ~The ~ , ~static ~ dielectric constants and other physical properties of these solvents are tabulated elsehere.^.^^ The prediction of the dielectric friction theory for the K+ ion is also exhibited in Figure 2. A close look at Figure 2 shows the following trends: (1) the smaller the dielectric constant, the larger the B coefficient for the (15) Gill, D. S.; Sharma, A. N. J . Chem. SOC.,Faraday Trans. 1 1982, 78. 475. (16) Sacco, A.; Monica, M. D.; De Giglio, A,; Lawrence, K. J . Chem. Soc., Faraday Trans. 1 1983, 79, 2631. (17) Lawrence, K. G.; Sacco, A. J . Chem. SOC.,Faraday Trans. 1 1983,
79, 615. (18) Kay, R. L.; Vituccio, T.; Evans, D. F. J . Phys. Chem. 1966, 70,2336. (19) Martinus, N.; Vincent, C. A. J . Chem. Soc., Faraday Trans. 1 1981, 77. 141. (21) Evans, D. F.; Toi Chem. 1979, 83, 3669.
-
K+ and Bu4N+ ions except for water, (2) the dielectric constant (to) dependences of the K+ and Bu4N+ ions are similar except for water, (3) the observed todependence of B for the K+ ion is much larger than predicted by the dielectric friction theory, (4) the B value for the Bu4N+ ion is exceptionally large in water, and ( 5 ) for the I- ion, the correlation between to and B is poor. We can explain the dependence of B for the K+ ion on the solvent dielectric constant qualitatively in terms of the effect of the ionic charge or dielectric friction. In the solvents with a dielectric constant lower than that for water, the solvent screening effect on the ionic charge is weaker, so that the B coefficient becomes larger. However, only a part of the observed increments of the B values can be explained by the dielectric friction theory. While the effect of the long-range Coulombic interaction between an ion and solvent dipoles is properly taken into account in the dielectric friction theory, any kind of short-range effects of the molecular nature are neglected in the continuum theory. Therefore, no quantitative agreement is expected. The remaining difference may be attributed to the solvent-berg effect due to the ion solvation in the short range. When the dielectric constant becomes lower, an ion is solvated more tightly and the effective radius becomes larger. For the case of the hydrophobic ion, Bu4N+,however, the eo dependence of B cannot be simply related to the effect of the ionic charge because of the low surface charge density of the large ion. For an unknown reason, however, the large hydrophobic ion is similar to simple ions with respect to the solvent polarity dependence. For the I- ion, the effect of the ionic charge on the B coefficient does not play an important role even in solvents with a low dielectric constant; note that the surface charge density of this ion is relatively small. This suggests that a rather short-range factor controls the B value. Such a short-range interaction as charge transfer from the ion to solvent may play an important role in this case. In a series of studies on electrolyte conductance, we have shown that the dielectric friction theory is more successful in polar aprotic solvents than in polar protic solvents4 and expected a parallel result for electrolyte viscosity. However, it turns out here that although the continuum model is fairly successful for the ionic mobility, it is not so for the ionic B coefficient; the dominant factor, measured solvent viscosity, is just used in the former, but there is no such factor incorporated in the case of the viscosity B Coefficient. The pre5ent study tells us that the B coefficient is very sensitive to solvent, say, solvent structure as have long been supposed without a basic study.
Acknowledgment. We are grateful to Professor M. Ueno of Doshisha University for allowing us to determine the water content in acetonitrile by the Karl-Fisher titration. This work was supported by a Research Grant-in-Aid from the Ministry of Education, Science, and Culture (No. 63790199 and 01540370). K.I. thanks JSPS (the Japan Society for the Promotion of Science) for the Fellowship for Japanese Junior Scientists. Registry No. LiI, 10377-51-2; N a l , 7681-82-5; KI, 7681-1 1-0; NaBPh,, 143-66-8; Bu4NBPh4, 15522-59-5; Lit, 17341-24-1; Na', 17341-25-2; K', 24203-36-9; I-, 20461-54-5; B u ~ N * ,10549-76-5; BPhd-, 4358-26-3; CH,CN, 75-05-8.
