5118
J. Phys. Chem. 1984,88, 5 1 18-5 121
maximum is 5-10 nm above its value in aqueous solution, while the emission maximum is 5-20 nm below its aqueous solution value. The quantum yield of emission is independent of the loading, up to 30% of the 2 3 CEC, ~ ~except for BS, where a reorganization of the molecules occurs around 15% loading. The Fe(II1) levels of BS and H are too small to quench the emission. For the other clay minerals the quenching by structural Fe(II1) follows Perrin's law of quenching in absence of diffusion. The
radius of the quenching sphere is 1.4 f 0.1 nm.
Acknowledgment. Acknowledgment is made to the National Fund of Scientific Research (Belgium) for support of this research and for the research tenure to R.A.S. as Senior Research ASSOciate. Registry No. R~(2,2'-bpy),~+, 15158-62-0; Fe(III), 20074-52-6; montmorillonite, 1318-93-0.
Diffusion of Crown Ethers In Alcohols HangChang Chen and Shaw-Horng Chen* Department of Chemical Engineering, University of Rochester, Rochester, New York 14627 (Received: January 31, 1984; In Final Form: April 6, 1984)
Tracer diffusivities of s-trioxane, 12-crown-4,15-crown-5,18-crown-6, dicyclohexano-18-crown-6, and dicyclohexano-24-crown-8 in methanol, ethanol, and 1-butanol are reported as a function of temperature. Microfriction correction to the Stokes-Einstein equation successfully accounts for the diffusion behavior of crown ethers in methanol with the idea of moving units serving as the basis for evaluating the effective size of the solvent molecule. The failure of this approach in ethanol and 1-butanol is attributable to the noncompact nature of the associated entities.
Introduction Crown ethers have been extensively employed to achieve phase transfer catalysis' and liquid membrane separation,2 where the rates of the involv+ transport processes may largely be determined by the diffusion mfficients of crown ethers. A recent investigation by Lassegues et ale.3on liquid 18-crown-6 using the quasielastic neufron-scattering technique has resolved the intricacy of its thermal motion: translational and rotational diffusion as well as molecular flexibility. However, current advances in computer simulation on model fluids have not yet been able to generate useful information on transport properties for such complex systems. We have thus been prompted-to carry out tracer diffusion measurements in the hope of providing reliable experimental data based on which to further our understanding of the transport processes involving hydrogen-bonded species. Solvents used ih the present study include methanol, ethanol, and 1-butanol, all having a tendency to interact via hydrogen bonding either with each other or with solute crown ethers. To this effect t h e idea of moving units proposed by Thomas4 is employed to estimate the effective site of solvent molecules. In addition, from viscosity and self-diffusivity measurements Vogel and Weiss5 concluded that the extensiveness of solutesolvent interactions are rather limited. This observation allows us to examine the tracer diffusion of crown ethers in view of the microfriction theory of molecular The applicability and limitation of this approach are also discussed. Experimental Section The Taylor dispersion apparatus and experimental procedures for diffusion measurements were described p r e v i o ~ s l y .Methanol ~~ (99.5+%, Mallinckrodt), ethanol (99%, University of Rochester Medical Center), and 1-butanol (99%, Aldrich) were filtered before use with 0.5-pm Teflon membrane on an all-glass filtration apparatus (Millipore). The solutes s-trioxane (98%), 12-crown-4 (99+%), 15-crown-5 (99%), 18-crown-6 (99%), dicyclohexano(1) C. M. Starks and C. Liotta, "Phase Transfer Catalysis: Principles and Techniques", Academic Press, New York, 1978. (2) C. F. Reusch and E. L. Cussler, AIChE J., 19, 736 (1973). (3) J. C. Lassegues, M. Fouassier, and J. L. Viovy, Mol. Phys., 50, 417 (1983). (4) L. H. Thomas, Trans. Faraday SOC.,62, 328 (1966). ( 5 ) H. Vogel and A. Weiss, Ber. Bunsenges. Phys. Chem., 86, 6 i 5 (1982). (6) A. Gierer and K. Wirtz, Z . Naturforsch. A , 8, 532 (1953). (7) A. H. Alwattar, M. D. Lumb, and J. B. Birks, "Organic Molecular Photophysics", Vol. 1, J. B. Birks, Ed., Wiley, New York, 1973, Chapter 8.
0022-3654/84/2088-5 118$01.50/0
18-crown-6 (99%), and dicyclohexano-24-crown-8(97%) were all used as received from Aldrich Chemical Co. The bath temperatures were controlled to within fO.l K. The concentration of injected solution is never higher than 1 mol %. Each reported diffusivity is the result from at least three measurements, the standard deviations being normally f 1%. Results and Discussion Presented in Table I are the tracer diffusivities measured with the Taylor dispersion method for s-trioxane, 12-crown-4, 15crown-5, 18-crown-6, dicyclohexano- 18-crown-6, and dicyclohexano-24-crown-8 (molecular structures are shown in Table 11) in methanol, ethanol, and 1-butanol as a function of temperature. Although Hildebrand's free-volume equation* is found inadequate, the Arrhenius equation correlates quite well the experimental data reported ip this work as shown in Figure 1. The parameters given in Table I11 are capable of reproducing the experimental results to within h l % . This is indicative of the versatility of the activation-energy approach, as opposed to the free-volume approach, in dealing with transport processes in liquids, although Hildebrandg expressed his qualms over the former. Molecular diffusion in liquids has traditionally been discussed in terms of the Stokes-Einstein equation. Its failure has been well documented over the years, and tremendous effort has also been devoted to its modification from a theoretical or empirical standpoint. The latter has resulted in a number of engineering correlations compiled by Reid et a1.I0 Gierer and Wirtz's6 microfriction theory represents the only theoretical modification but, due to the lack of quantitative agreement between theory and experiment, as indicated by Spernol and Wirtz" for translational diffusion, its application has been limited to rotational diffusion12 and self-diff~siod:'~In a recent paper,14we have revived the spirit of the microfriction theory in the interpretation of tracer diffusion in binary systems. (8) J. H. Hildebrand, Science, 174, 490 (1971). (9) J H. Hildebrand, Ind. Eng. Chem. Fundam., 12, 387 (1973) (10) R. C. Reid., J. M. Prausnitz, and T. K. Sherwood, "The Properties of Gases and Liquids", 3rd ed, McGraw-Hill, New York, 1977. (11) A. Spernol and K. Wirtz, Z . Naturforsch. A , 8, 522 (1953). (1 2) Z. Pajak, L. Latanowicz, and K. Jurga, Ber. Bunsenges. Phys. Chem., 87, 143 (1983). (13) H. Vogel and A. Weiss, Ber. Bunsenges. Phys. Chem.,85,539 (1981). (14) E. Yumet, H. C. Chen, and S. H. Chen, AIChE J., in press.
0 1984 American Chemical Society
Diffusion of Crown Ethers in Alcohols
The Journal of Physical Chemistry, Vol. 88, No. 21, 1984 5119
TABLE I: Tracer Diffusivities of s -Trioxane, 12-Crown-4, 15-Crown-5, 18-Crown-6, Dicyclohexano-18-crown-6, and Dicyclohexano-24-crown-8 in Methanol, Ethanol, and 1-Butanol“ dicyclohexanodkyclohexanoT. K s-trioxane 12-crown-4 15-crown-5 18-crown-6 18-crown-6 24-crown-8 MeOH 297.0 2.55 f 0.02 1.43 f 0.01 1.29 f 0.01 1.14 f 0.01 0.933 f 0.015 0.825 f 0.008 308.2 3.03 f 0.04 1.72 f 0.03 1.57 f 0.01 1.39 f 0.01 1.14 f 0.01 0.985 f 0.008 318.2 3.51 f 0.04 1.98 f 0.01 1.82 f 0.01 1.63 f 0.01 1.31 f 0.01 1.17 f 0.01 328.2 4.04 f 0.03 2.32 f 0.01 2.10 f 0.02 1.91 f 0.02 1.53 f 0.01 1.38 f 0.01 338.2* 4.51 f 0.04 2.68 f 0.03 2.44 f 0.01 2.17 i 0.01 1.80 f 0.01 1.62 f 0.01 ~
298.2 308.2 323.2 338.2 353.lC
1.72 f 0.01 2.04 f 0.01 2.58 f 0.01 3.21 f 0.03 3.98 f 0.04
298.3 323.1 348.2 372.8
0.861 f 0.006 1.05 f 0.01 1.36 f 0.01 1.76 f 0.02 2.25 f 0.03
EtOH 0.761 f 0.01 0.929 i 0.003 1.22 f 0.01 1.58 f 0.01 2.03 f 0.03
0.671 f 0.001 0.823 f 0.015 1.08 f 0.01 1.43 f 0.01 1.85 f 0.01
0.515 f 0.002 0.639 f 0.005 0.853 i 0.012 1.12 f 0.01 1.47 f 0.02
0.459 f 0.003 0.568 f 0.002 0.763 f 0.007 1.01 f 0.01 1.27 f 0.01
0.407 f 0.002 0.727 f 0.004 1.24 f 0.01 1.94 f 0.01
1-BuOH 0.363 f 0.001 0.656 f 0.001 1.12 f 0.01 1.72 f 0.01
0.311 f 0.001 0.572 f 0.006 0.973 f 0.002 1.52 f 0.01
0.241 f 0.001 0.436 f 0.001 0.766 f 0.010 1.24 f 0.01
0.207 f 0.001 0.389 f 0.001 0.675 f 0.004 1.06 f 0.01
‘Diffusivities reported in 105D,cm2/s. ”System pressure: -6 psig. cSystem pressure:
N
16 psig.
TABLE 11: Structures of the Crown Ethers Studied
n
GI
CJ-
12 -crown- 4
s t r ioxanr
15-crown-5
18-crown-6
P ?
r0”r
ao COY O
X
>
a
dicyclohexano- 18-crown-6
0
O D
Lu0J
dicyclohexano- 24-crown-8
I-
The microfriction correction to the Stokes-Einstein equation
0 31CYCLOHEXANO-24-CROWN-8
- 12.0
is
100O/T(K-’) 32
3.0
3.4
Figure 1. Arrhenius plot of tracer diffusion of crown ethers in niethanol.
where k is Boltzmann’s constant, T the absolute temperature, rl the solute molecular radius, kL2the solvent viscosity, and ft the
microfriction factor accounting for the failure of continuum hydrodynamics at molecular dimensions. Presuming that both sblute and solvent molecules are spheres of radius rl and rz, respectively, and taking account of the finite thickness of the solvent layers
TABLE 111: Values of E , and A in the Arrhenius equationR
ED, cal/g-mol
i03A, cm2/s ED, cal/g-mol
10’4 cm2/s
ED,cal/g-mol 1 0 3 ~cm2/s ,
“D = A exp(-E,/RT).
18-crown-6
dicyclohexano18-crown-6
dicyclohexano24-crown-8
3126 2.284
3141 1.906
3292 2.159
Ethanol 3722 4.046
3861 4.494
3968 4.149
3902 3.326
Butanol 4624 8.862
4717 8.880
4862 8.678
4857 7.499
s-trioxane
12-crown-4
2194 2.903
3046 2.486
15-crown-5 Methanol 3064 2.316
3175 3.646
3650 4.046 4647 10.25
5120 The Journal of Physical Chemistry, Vol. 88, No. 21, 1984
Chen and Chen ~
5-TRIOXANE 12-CROWN-4 o 15-CROWN-5 0 18-CROWN-6 v DICYCLOHEXANO18-CROWN-6 o DICYCLOHEXANO24 -CROWN - 8 A
10
'
'YEORET I CAL
8\ in
N
6
I
A MeqSn rn O CB u C q4S n
1
I
/ /
/
/-
/
0
rl/ r 2
/
/
283-383K
6 % n m
I
297-338 K
0
/
A
/
4 I
0.0 0.5 1.o 1.5 Figure 2. The dependence of microfriction factorf, on solute-to-solvent size ratio r l / r 2 . In cyclohexane solvent: Ar, 0; CH4, 6 ;Kr, 0 ;Xe, 0; c-C6HI2,0;CCI4,0 ; Me4Sn,@; Et4Sn, 0 ;Pr4Sn,0;Bu4Sn,Q; in carbon tetrachloridesolvent: Ar, A;CH,, A; Kr, A; Xe, A;CC14,r;Me4Sn,v; Et4Sn,V; Pr4Sn, V; Bu4Sn,8 ; c-C6HI2,0 ; CBr,, 0 .
flowing around a moving solute molecule, Gierer and Wirtz6 arrived at the following expression for ft:
-
I
I
I
8 I
Figure 3. Stokes-Einstein prediction of tracer diffusivities in methanol
compared to experimental results.
5-TRIOXANE 12-CROWN-4 o \5-CROWN-5 o 18-CROWN-6 v DICYCLOHEXANO18-CROWN-6 Q DICYCLOHEXANO24-CROWN-8 A
In place of eq 2, which is good only for order-of-magnitude estimation," the following formula was generatedL4using the observed tracer diffusivities for systems where both solute and solvent molecules are spherical or quasispherical in shape:
ft = [l + 0.695(r,/r,)2.234]-'
10
(3)
The difference between eq 2 and 3, as shown in Figure 2, is believed to arise from the simplistic geometric consideration intrinsic to the microfriction theory. The relationship between these two formulas is further discussed in Appendix A. Bondi's group contribution method was followed to evaluate both r, and r, in developing eq 3, which reproduces to within *8% of theft values calculated from experimentally determined diffusivity and viscosity by using eq 1. In what follows eq 1 and 3 shall be tested for the experimental data reported in Table 1. Specifically, we will examine the effects on tracer diffusion of hydrogen bonding and molecular compactness. Conditions for the applicability of eq 1 and 3 shall then emerge from testing additional systems selected from open literature. To test the microfriction approach outlined above, we have calculated the van der Waals radiils for the crown ethers: 2.64 A, s-trioxane; 3.44 A, 12-crown-4; 3.71 A, 15-crown-5; 3.94 A, 18-crown-6; 4.43 A, dicyclohexano- 18-crown-6; 4.76 A, dicyclohexano-24-crown-8. Plotted in Figure 3 is a comparison between predicted (with the Stokes-Einstein equation, i.e.,ft = 1 in eq 1) and observed tracer diffusivities in methanol of crown ethers in addition to carbon tetrachloride, tetramethyltin, and tetrabutyltin reported by Chen et a1.16 from 283 to 383 K. The dashed line in Figure 3 represents perfect agreement between theory and experiment. The qualitative behavior reflects the anticipation that the deviation from the Stokes-Einstein relationship increases with a decrease in solute size. If the solute/solvent size discrepancy is corrected by eq 3 all the predicted diffusivities, D,,, scatter around experimental results with an absolute average deviation of 8% (see Figure 4). Note that in calculating r2, the effective (15) A. Bondi, J . Phys. Chem., 68, 441 (1964). (16) S. H. Chen, D.F. Evans, and H. T. Davis, AZChE J., 29,640 (1983).
)
297-338K
J
/
/
6 3 in
n
m
0
Figure 4. Stokes-Wirtz prediction of tracer diffusivities in methanol compared to experimental results.
radius of solvent methanol, the idea of moving units is adopted. The van der Waals volume of a methanol molecule15is scaled with the association number 1.44 obtained from viscosity data in the temperature range 273-333 K." The effective radius is then calculated from the resultant volume. The agreement shown in Figure 4 leads one to conclude that with the microfriction correction, eq 3, to the Stokes-Einstein relationship the molecular shape, polarity,'* and flexibility of crown ethers play no significant (17) L. H. Thomas, J. Chem. Soc., 1345 (1948).
The Journal of Physical Chemistry, Vol. 88, No. 21, 1984 5121
Diffusion of Crown Ethers in Alcohols TABLE I V A Comparison of D,., to Dcxpt solute/solvent T, K CCl,/acetone Et,Sn/acetone Bu,Sn/acetone CCI4/acetonitrile Et,Sn/acetonitrile CCI4/benzene Et,Sn/ benzene Bu,Sn/ benzene CCI4/MeOH Et4Sn/MeOH Bu4Sn/MeOH MeOH/ benzene benzene/MeOH acetone/CC14 CCl,/acetone acetone/benzene benzene/acetone biphenyl/MeOH triphenylmethane/MeOH ethyl bromide/MeOH ethyl iodide/MeOH bromobenzene/MeOH p-dibromobenzene/MeOH toluene/cyclohexane cyclohexane/ toluene
298.2 298.2 298.2 298.2 298.2 298.2 298.2 298.2 298.2 298.2 298.2 313.2 313.2 298.3 298.3 298.3 298.3 298.2 298.2 288.2 288.2 288.2 288.2 298.2 298.2
ft
10sD,,p,, cm2/s 3.63 2.92 2.00 3.32 2.42 1.95 1.58 1.03 2.25 1.66 1.18 4.67 3.15 1.70 3.57 2.75 4.17 1.89 1.16 2.40 2.16 1.75 1.55 1.569 2.420
0.642 0.761 0.827 0.695 0.801 0.604 0.729 0.802 0.672 0.787 0.847 0.5 13 0.662 0.536 0.641 0.551 0.628 0.760 0.816 0.622 0.643 0.700 0.725 0.588 0.592
1OO(Dw - Dcxpt)/Dexpt 13 -8 2 0 -8 9 -13 0 -4 -14 -7 -17 -8 9 9 -3 -1 -16 9 -10 -7 -6 -4 -8 -3
ref (Dexpt) a a
a a a a a
a a
a a b
b b
b b b C
c d d d d
e e
"D. F. Evans, T. Tominaga, and H. T. Davis, J . Chem. Phys., 74, 1298 (1981). bD. K. Anderson, J. R. Hall, and A. L. Babb, .I Phys. . Chem., 62, 404 (1958). C M .A. Lusis and G. A. Ratcliff, AIChEJ., 17, 1493 (1971). d"International Critical Tables", McGraw-Hill, New York, 1926-30. 'S. A. Sanni and P. Hutchinson, J. Chem. Eng. Data, 18, 317 (1973).
role in affecting their diffusion behavior in comparison to quasispherical carbon tetrachloride and the two tetraalkyltins. The presence of solute/solvent hydrogen bonding is neither significant, as also understood from viscosity and diffusion measurements on 18-crown-6/methanol solution^.^ This result is quite encouraging in view of the yet unsuccessful effort to relate transport to thermodynamic properties in nonideal solutions. However, recent effort by Ito et al.I9 to identify the moving units in mutual diffusion in alcohol/water systems using the light scattering technique appears to lead in the right direction. In the solvents ethanol and 1-butanol the performance of eq 1 and 3 is erratic, leading one to suspect that hydrogen-bonded ethanol and 1-butanol with an association number of 1.91 (273-343 K) and 2.21 (273-373 K),I7 respectively, might be casual. To verify this speculation, tracer diffusivities in binary solutions involving long-chain hydrocarbons are also tested. The performance of the present theory, eq 1 and 3, is found to be equally erractic. In order to establish conditions for the applicability of eq 1 and 3 we have collected experimental results for additional systems from the literature. From the comparison made in Table IV it is clear that the performance of eq 1 and 3 is satisfactory for relatively compact solute and solvent molecules; the effects of molecular interactions seem to be insignificant. Conclusions The following points emerge from the present study on the diffusion of crown ethers in aliphatic alcohols as a function of temperature: (1) The Arrhenius equation is more versatile than the Hildebrand free-volume model in correlating the temperature dependence of tracer diffusivities in liquids. The linear relationship is ubiquitous with the former, while it normally breaks down with the latter for hydrogen-bonded systems. (2) The tracer diffusion in methanol of crown ethers, caron tetrachloride, tetramethyltin, and tetrabutyltin can be successfully (18) R. Perrin, C. Doceret, G . Bertholon, and R. Lamartine, C.R. Hebd. Seances Acad. Sci., Ser. 11, 294, 7 5 (1982). (19) N. Ito, K.Saito, T. Kato, and T. Fugiyama, Bull. Chem. SOC.Jpn., 54, 991 (1981).
interpreted when the idea of moving units involved in viscous flow is incorporated with the microfriction correction to the StokesEinstein equation. (3) The Stokes-Wirtz equation is also shown to work satisfactorily for tracer diffusion in binary systems where both solute and solvent molecules are relatively compact. The failure in correlating diffusion data involving ethanol and higher alcohols is attributed to the noncompact nature of the associated moving units. Acknowledgment. The authors are grateful for the financial support of this work by the National Science Foundation under Grant CPE-8305649. Appendix A Equation 3 is entirely based on curve fitting, but it will be. shown in the following how it is related eq 2 and under what condition eq 2 is applicable. Let rl/r2= x and expand eq 2 about y x - 1 = 0. This yields ft-1
x+3 1.5 + -= ==1+ 1+ X 1 2x(x + 1') 1+X
y+4
1
+ [ l + '/4y +
=
20, + 1)0, + 2) 0(y2)]-' E 1 (1 y)-5/4 = 1
+ +
+ x-5/4 ( A l )
Equation 3 is then rewritten as
Comparing eq A1 and A2, one would anticipate that eq 2 can describe experimental data equally well as 7'1/r2
-.
4/3(ri/rd2
('43)
which is in accord with what is shown in Figure 2. Registry No. s-Trioxane, 110-88-3; 12-crown-4, 294-93-9; 15-crown-5, 33100-27-5; 18-crown-6, 17455-13-9; dicyclohexano-18-crown-6, 16069-36-6; dicyclohexano-24-crown-8,17455-23-1; methanol, 67-56-1; ethanol, 64-17-5; 1-butanol, 71-36-3.
