D. IC MUSIMITSU, A. Y . WOODY,E. R.STIMSON, AXD H. A. SCHERAGA
856
Thermodynamic Data from Fluorescence Spectra. 11. Hydrophobic Bond Formation in Binary Complexes' by Donald K. Kunimitsu,2A. Young Woody, Evelyn R. Stimson, and Harold A. Scheraga3 Department of Chemistru, Cornell UniversiEu, Ithaca, New York
14860
(Received J u l y 19, 1967)
Association constants for the formation of complexes between some phenolic compounds and sodium nionocarboxylic acid salts have been determined at several temperatures by the method of fluorescence quenching. Some discussion is provided to support the validity of attributing deviations from Stern-Volmer kinetics, in these systems, to association, Assuming that complexes involving formate contain only a hydrogen bond, but that complexes involving higher homologs of formate contain both a hydrogen and a hydrophobic bond, subtraction of the thermodynamic parameters for hydrogen bonding from those for association in the higher homologs yields the thermodynamic parameters for the formation of pairwise hydrophobic bonds. These experimental values agree with those predicted from theory.
Introduction This is a continuation of previous tvork4 designed to provide experimental verification5-' of theoretically predicted values5 of the thermodynamic parameters for the formation of pairwise hydrophobic bonds. As used p r e v i ~ u s l y ,the ~ method of fluorescence quenching is applied here to determine the equilibrium constants for the association of phenolic compounds with carboxylate compounds. The complex is assumed to involve both a hydrogen bond between the phenolic OH group and the carboxylate ion group and also a pairwise hydrophobic bond between the nonpolar parts of the phenolic and carboxylate compounds. As the nonpolar parts vary in a homologous series, the hydrogen bond is assumed to be identical in all of the complexes studied. Thus, a subtraction of the free energy of hydrogen-bond formation from the free energy of association should provide a measure of the free energy of formation of the pairn-ise hydrophobic bond; in a similar manner, the enthalpy and entropy of formation of the hydrophobic bonds may be determined. The experimental quantities are then compared with theoretical values.8 Some of the problems involved in the interpretation of fluorescence quenching data, and the calculation of association constants from them, are discussed.
Experimental Section Xaterials. Phenol, 3,5xylenol, butyric acid, and isobutyric acid were Baker grade products from J. T. Baker and Co., New York, N. Y . , p-cresol (redistilled) was purchased from the Matheson Co., East Rutherford, K. J., and used without further purification. T h e Journal of Physical Chemistru
4-n-Propyl phenol was a product of Aldrich Co., Milwaukee, Wis., and was redistilled once under vacuum immediately before use. The sodium salts of all the compounds used were the best grades available commercially. Sodium butyrate and sodium isobutyrate were prepared from the corresponding acids; the acids were redistilled twice in the presence of potassium permanganate and their concentrations were determined by titration. DzO (99.7%) was acquired from the U. S. Atomic Energy Commission, Aiken, S. C., and was bottled by the Cornel1 University department of chemistry. Deionized water was used throughout. Fluorescence and Cltraviolet Difference Spectra 2Keasureinents. Fluorescence quenching data and ullraviolet difference spectra were obtained by the methods described p r e v i ~ u s l y . ~The concentration of fluorescent solute (e.g., phenol) employed in the fluorescence quenching studies was 2.0 X M . The difference (1) This work was supported by a research grant (HE-01662) from the Xational Heart Institute, National Institutes of Health, Public Health Service, and by a research grant (GB-4766) from the Kational Science Foundation. (2) Postdoctoral Fellow of the National Institute of General Medical Sciences, National Institutes of Health, 1965-1966. (3) To whom requests for reprints should be addressed. (4) A. Y. Moon, D. C. Poland, and H. A. Scheraga, J . Phys.
Chem., 69, 2960 (1965). (5) E . E. Schrier, &Pottle, !I. and H. 4.Scheraga, J. Am. Chem. Soc., 86, 3444 (1964). (6) H. Schneider, G. C. Kresheck, and H. A. Scheraga, J . Phys. Chem., 69, 1310 (1965). (7) IM. E. Friedman and H. A. Scheraga, ibid., 69, 3795 (1965). (8) G. Nemethy and H. A. Scheraga, ibid., 66, 1773 (1962); 67, 2888 (1963).
THERMODYNAMIC DATAFROM FLUORESCENCE SPECTRA
857 assumed to differ from Ic2 because of repulsion between the carboxylate ion groups of Q and of the Q . (MOH)" complex. Also, we make the reasonable approximation that the excited species, Q (MOH) *, is in equilibrium as follows
spectra studies were carried out at a higher concentraM). tion of phenol (6.4 X Viscosity Measurements. Viscosity measurements were made with a Cannon-Ubbelohde semimicro dilution viscosimeter, with flow times for water in excess of 200 see. Kinetic-energy corrections were not made, and viscosities mere computed simply as products of flow time and density, relative to the same product measured with water. The temperature was controlled to better than =kO.lo. Densities of the mixed electrolytes were calculated from the densities of the individual electrolyte^,^ essentially by a method outlined by Kawahara and 7ranford.lo The ratio of the density of a given solution to that of water was calculated at either 20 or 25" and was assumed to hold over the temperature range of 10-45".
-
It should be emphasized that KHd is very small compared to K,,,,,; hence, the concentration of Q .MOH will be much smaller than that of M0H.Q. Equation 6 is nevertheless introduced here, since the concentration of Q.MOH, though small, is not negligible. Thus, the K H b of eq 6 represents a small correction to be made in the experimental data and is not the quantity to be determined in this investigation. Instead, the equilibrium constant for pairwise hydrophobic bond formation, to be determined here by the fluorescence quenching method, is a component of K,,,,,; it is, therefore, K,,,,, which will be obtained from the experimental data. For steady illumination and no irreversible photochemical reactions, and assuming (a) that steady-state concentrations of (MOH)* and Q (IVIOH)* are achieved, and (b) that S is large and constant so that it appears in Ici, eq 11 may be derived.
Treatment of Fluorescence Data Mechanism of Fluorescence Quenching. If MOH refers to a fluorescent phenolic solute in a solvent s, and Q to the various added fluorescence quenchers, then, using parentheses to represent concentrations, we may write Scheme I for excitation by light of frequency v (with an asterisk to denote excited species), for fluorescence at a frequency Y', and for fluorescence quenching; the definitions of the rate constants are apparent from their use in eq 1-10.
-
Scheme I Prooess
Absorption Emission Quenching Deactivation by solvent and by internal conversion processes Association :involving phenolic-OH group Association not involving phenolic-OH group Absorption Emission Quenching Deactivation by solvent and by internal conversion processes
Rate or equilibrium expression
MOH
+ hv + +
-+
(MOH)*
-
+
(MOH)* 3 h'IOH kv' (MOH)* Q + MOH (NIOH)* S MOH
+ Q eM0H.Q MOH + Q e Q-MOH MOH
--
+ hv Q*(MOH)* Q*(MOH) + hv' Q.(PVIOH)* + Q Q.(MOH) 4Q + heat Q.(MOH)* + S Q.(MOH) + S + heat Q*MOH
4
Q*(MOH)*
-+
In the previous treatment,4 we allowed only for the species ATOH.&, which is postulated to involve an OH . -0OC hydrogen bond, with an additional hydrophobic bond between the nonpolar parts of MOH and Q; the hydrogen bond of such a complex accounts for the instantaneous de-excitation of excited phenol. l1 The above scheme differs from the previous one4 in that we have allowed for the species Q .MOH, a complex involving only hydrophobic bonding between the nonpolar parts of MOH and Q, but no hydrogen bonding of the phenolic OH group; this complex is postulated to be capable of being excited and fluorescing. Here, kl is 9
+ Q + heat + S + heat
~A(MOH) kf(MOH)* ki( MOH)*(Q) ki(MOH)*(S)
-
where I oand 40are the intensity of fluorescent light and (9) International Critical Tables, Vol. 3, McGraw-Hill Book Co., New York, N. Y., 1928, p 51 ff. (10) K. Kawahara and C. Tanford, J . Biol. Chem., 241, 3228 (1966). (11) The quenching of phenol fluorescence is assumed t o occur by a base-catidyzed dissociation of the proton of the aromatic hydroxyl group. For the experimental basis of this mechanism, see (a) A. White, Biochem. J . , 71, 217 (1960); (b) G. Weber and K. Rosenheck, Biopolymers, Svmposia, 1, 333 (1964); and (c) J. Feitelson, J . Phys. Chem., 68, 391 (1964). Volume 78. Number 3 March 1968
D. K. KUNIMITSU, A. Y . WOODY,E. R. STIMSON, ASD H. A. SCHERAGA
868
quantum yield, respectively, of emission from (MOH)* in the absence of Q, i.e.
and I and 4 are the intensity of fluorescent light and the quantum yield, respectively, of emission from (MOH)* and &.(XIOH)*, i.e., in the presence of Q, The expression for q5 can be obtained by dividing 4o of eq l l a by 40/$of eq 11. The constants of eq 11 are defined as foll0vc.s
+ ~ K H ++ K,8soc kq'KE+ + KH+' + kqKH+ + KassocK~o+ kqKassoc C ~ Q ' K H+ ~ 'kq'KassocKH+ k, kl/(kf + k1,o) = k2/(kf + k1,o) A = kq
B
=
=
Jcq'
Wb) (1lC) (1W
(IW (1lf)
k , ,O is the rate constant for solvent quenching and other internal conversion processes which result in the deexcitation of (NOH)* in the absence of &. I n general, k,,o = k , only if the viscosity (among other things) of the solution of R90H is the same as that of the solution of N O H Q. It is possible to determine the various parameters of eq 11 from the ratio Io/I in a manner to be discussed below. However, it is of interest at this point to note two limiting cases of eq 11, if k,,o = k,. These are: (1) for KH+ = 0, eq 11 reduces to eq S of our previous paper,4 which was used to account for positive deviations from the Stern-Volmer equation; and ( 2 ) for KH+ = K,,so, = 0 , eq 11 reduces t o the Stern-Volmer equation. Problems in Interpreting Fluorescence Quenching Data. Since K,,,,, < 1 for the systems studied here, it was necessary to use relatively high concentrations of kquencher(0.4-1.0 M ) in order to obtain precise values of K,,,,,. This introduced three problems: (1) the addition of quencher increased the viscosity of the solution; hence, had to be corrected (by a method outlined in the next section) to the viscosity of the solution containing quencher ; ( 2 ) the addition of quencher affects the activity coefficients; nevertheless, concentrations have been used here instead of activities for reasons stated in the paragraph following eq 3 of our previous paper;4 and (3) in attributing positive it is deviations from Stern-Volmer kinetics to KBBSOD, necessary to rule out an alternative mechanism, l 2 vix., if the possibility of (fast) diff usion-controlled rates exists, there may be deviations from the stationary concentrations assumed in the derivation of eq 11; these deviations can become important a t short excited-state lifetimes or, equivalently, at higher quencher concentrations. The theory for such a mechanism involving
+
The Journal of Physical Chemistry
diffusion-controlled reactions has been devel0ped;~3,'4 there exists, at present, a t least one application of this theory,I5 providing a satisfactory explanation of departures from Stern-Volmer kinetics which had originally been attributed to association.'o We will show that this effect is negligible in our systems; hence, eq 11 may be applied directly to interpret our data. Viscosity Correction,. I n order to correct k,,o to the viscosity, 7, of the solution containing quencher, we assume that k f is independent of viscosity and temperature. Hence, according to eq l l a , the dependence of k,,o on viscosity is given by the dependence of 4o on viscosity. Thus, we require the dependence of I o (which is proportional to 40)on viscosity in the absence of quencher. From the dependence of I o on 7, we can then compute k i , ~a t the value of 7, for the solution containing quencher, when using eq 11. The value of k i , o for phenol in water at 26' was obtained as follows. The value of do is 0.22 for phenol ki,o), under these conditions,llb and the value of (Icf which is the reciprocal of the lifetime of the excited state, was taken as 1.33 X lo*, as calculated by Feitelson for tyrosine from its absorption spectrum.llcf Hence, both kf and k,,o could be obtained, from eq l l a , for phenol in water a t 25". With kf assumed constant, I o (and hence ki,J was measured for phenol as a function of viscosity a t 25". The viscosity was varied over the required range by adding D 2 0 t o the phenol solution, assuming no additional quenching by DzO, to obtain Io at low viscosities.I8 Ethanol (EtOH) was added to HzO to attain higher viscosities. However, since there is a small amount of quenching by ethanol, it was corrected for by assuming that the ratio
+
I o (in DzO-H20) -1 I (in EtOH-H,O) (EtOH) is the same a t all viscosities. I n order to evaluate k i , ~for phenol as a function of viscosity a t temperatures other than 25', we require values of doof phenol at these other temperatures and viscosities. Similarly, we require $0 for 3,5-xylenol,
(12) We are indebted to R. M. Noyes for pointing this out to us. (13) R. M. Noyes, Progr. Reaction Kinetics, 1, 129 (1961). (14) A. Weller, ibid., 1, 187 (1961). (15) W. R. Ware and J. S. Novros, J . Phys. Chem., 70, 3246 (1966). (16) E. J. Bowen and W. S. Metcalf, Proc. Roy. SOC. (London), A206, 437 (1951). (17) While the use of (kr k,,o) for tyrosine may introduce some error in kl and kz for the other phenolic compounds (since k, and k,' are experimental quantities, yielding ki and kz from eq l l e and l l f ) , it will not affect the calculated value of IC,,,,o very much, since the viscosity corrections appear in the ratios of the quantum yields (see
+
eq 11).
(18) The viscosities of Hz0-Dz0 mixtures at various temperatures are given by 11. C. Hardy and R. L. Cottington, J . Res. Natl. Bur. Std., 42, 573 (1949).
THERMODYXAMIC DATAFROM FLUORESCENCE SPECTRA
859
p-cresol, and 4-n-propyl phenol as a function of viscosity at various temperatures in order to obtain k , , ~for these phenolic compounds as a function of viscosity and temperature. Since there are no significant differences in the wavelengths of absorption (270 f 5 mp) and emission (305 5 mp) at 25" for all of the phenolic compounds used in this study, and since these wavelengths do not shift by more than 5 mp over the temperature range 10-45", the quantum yields of interest were obtained by the comparative method described by Parker and Rees.19 In this method, it is assumed that, for a given spectrofluorimeter, the integrated area, A , under the fluorescence emission curve is proportional to the total intensity of fluorescent light, lo, emitted by the fluorescer. Xow, I o is proportional to the product I,,+oEcd, where J,, is the intensity of the exciting light, E is the molar extinction coefficient, c is the concentration, and d is the optical path length. Therefore, assuming the proportionality constants to be equal, it can be seen that, for a comparison of fluorescence from two solutions at the same intensity of the exciting light, l o / A is the same for the two solutions. Hence, using subscripts 1 and 2 to represent the two solutions, (40)1/(40)z = (AI/AZ) (Ezcz/Elcl). I n order to avoid the necessity of correcting the observed emission spectra for variation in the intensity of the xenon lamp with the wavelength of excitation, the wavelength of the exciting light was maintained constant at 270 mp for all of the phenolic compounds used in this study. While the sensitivity of the photomultipler tube varies with the wavelength of light, the similarity in the emission spectrum of the reference cornpound (phenol) to all the other phenolic compounds allowed us to compare the integrated areas directly without the necessity of first correcting the observed emission curves. The reference value'lb of @o = 0.22 for phenol in water at 25" was adopted. In order to obtain the dependence of 40 on r for 3,5-xylenol, p-cresol, and 4-n-propyl phenol, the same method used for phenol was employed. With the approximation that lcf is independent of 7 and T , and the assumption that (kf k,,o) = 1.33 X lo8for all the phenolic compounds at 25", it was possible to evaluate ki,o as a function of 7 and T from the corresponding data for the depisndence of doon 7 and T . Departure f r o m Stationary Concentrations. Consider next the possibility that the alternative mechanism of diffusion-controlled rates may be the cause of the deviations from Stern-Volmer kinetics or, at least, may be making a significant contribution, along with KaSsoD, t o such deviations. Since we do not have data on the lifetimes of the excited states, we must consider other factors to decide on this question. First of all, the fact that similar values of K,,,,, for and acetate were Obtained by both the cence quenching technique (neglecting this alternative mechanism) and the method of ultraviolet difference
spectra4 suggests that association is the main origin of the departures from Stern-Volmer kinetics. Secondly, in using the fluorescence quenching data t o evaluate K,,,,, (assuming that the alternative mechanism is not operative), we carry out a subtraction of free energies, Le., we subtract out the free energy of hydrogen-bond formation to obtain the free energy of hydrophobic-bond formation. This subtraction will largely eliminate effects from this alternative mechanism. n'evertheless, we shall not rely on this subtraction, but will estimate the effect of the alternative mechanism and show that it is negligible. For this estimation, we use Noyes' theoryz0for the case where the quenching reaction is intermediate between a diff usion-controlled and an activation-controlled one; we assume that this may be the situation for the reaction between phenol and acetate.'lC Defining [(10/0- (h kJ/(kr k,,o)I/(&) as kex (with the viscosity correction already introduced) , Noyes writes the following equation to express the departure from Stern-Volmer kineticszoa
*
+
+
kex
=
+
kexo
+ U(Q)
(12)
where
I: = T"*KJ K = [1000(kr
+ 4(n - 1) K z
(13)
+ k i ) / 4 ~ D N ] " ~ ( h r / 1 0 0 0 )J"22 (14)
and keXois the value of k,, at (Q) = 0. The quantity K describes the competition of fluorescence with the rate of the establishment of the steady-state concentration gradient and is related to fundamental parameters of collision theory; D is the coefficient of relative diffusion, N is Avogadro's number, and J is the collisional quenching constant when an equilibrium distribution is applicable. According to eq 28 of ref 20a
keXo= J
+ 2n"'K
(15) In order to show that this alternative mechanism is not applicable here, we shall compute U of eq 13 and show that it is too small to account for the large deviations from Stern-Volmer kinetics in our systems. For the phenol-acetate system at 25" (kf IC,) was taken as 1.33 X lo8. The intercept, kexo from our experimental plot of k,, vs. (Q) is 5.70 LW-l. Seglecting K in eq 15 (see below for justification), J = k,O = 5.70. Using this value of J , and D = 2.0 X cmz/ sec, K is found to be 0.02 from eq 14 (justifying the neglect of K in eq 15). With these values of J and K , eq 13 yields a value of 0.21 for U . As will be shown in the Results, the observed value of U for this system is 2.5 (the product of k, and K,,,,, of Table I). Hence, we conclude that this alternative mechanism is
+
(19) A. Parker and W. T. Rees, Analyst, 8 5 , 587 (1960). (20) (a) R. M. Noyes, J . Am. Chem. Soc., 79, 551 (1957); (b) R. &I. x'oyes, J. p h y s . Chem., 6 5 , 7 6 3 (1961).
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D. I
