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The Journal of Physical Chemistry, Vol. 82, No. 6, 1978
where 1 = z / 6 and A/ro is the flow rate ( E according to ref 7). The orientation and possible deformation and degradation of the polymer is governed by the shear force field. The shear stress can be approximated (neglecting radial components) by Pzx = P(au,/az), P z y = P(au,/W
(3) where p is the viscosity. Table I shows roughly how the shear varies within a swirl of the geometry used. The shear forces near the orifice are clearly large enough to disintegrate polymer strands (cf. the observation* of a degradation a t velocity gradients less than lo3s-l, i.e., 1 m-l kg s-2).
The observed circular dichroism in a number of experiments (Figure 3) does not suggest any correlation between the sense of swirl and the optical activity. The natural optical activity is in the present performance small compared to linear dichroism arising from accidental orientations of aggregates in the optical cell. An extensive study of how linear and circular dichroism affect the signals
G. Laustriat
and
D.Gerard
in a circular dichroism spectrometer has been performed in our l a b o r a t ~ r y(technique ~?~ of measuring circular dichroism on oriented films;1° general optical formalismll). The present results are in accord with our previous concept of macroscopic linear dichroism as the only significant source of the observed “circular dichroism”. However an explanation, which cannot definitely be dismissed, of the difference between these results and those of Honda and Hada, could be a greater turbulence in the boundary layer and the present apparatus, designed to promote laminar flow, may have suppressed some “micro~orticity~’ responsible of their observations.
References and Notes (1) (2) (3) (4)
C. Honda and H. Hada, Tetrahedron Lett., 3 , 177 (1976). 9.NordBn, J . Phys. Chem., 81, 151 (1977). F. D. Saeva and G. R. Olin, J. Am. Chem. Soc., 99 4848 (1977). C. Honda and H. Hada, private communication. (5) J. S.Nagie, J. Sediment. Petrol., 37, 1124 (1967). (6) D. W.Howard, E. N. Lightfoot, and J. 0. Hirschfelder, APChEJ., 44, 794 (1976). (7) L. F. Crabtree, D. Kuchemann, and L. Sowerby in “Laminar Boundary Layers”, L. Rosenheard, Ed., Clarendon Press, Oxford, 1963, p 432. (8) A. Davidsson and 9.NordBn, Spectrochim. Acta, 32, 717 (1976). (9) A. Davidsson and B. NordBn, Chem. Scr., 9, 49 (1976) (10) B. NordBn, Acta Chem. Scand., 26, 1763 (1972). (11) H. P. Jensen, Spectrosc. Left., 10, 471 (1977).
Influence of Dynamic Quenching on the Thermal Dependence of Fluorescence in Solution. Study of Indole and Phenol in Water and Dioxane Gllbert Laustriat* and Dominique Gerard Laboratoire de Physique, Facult6 de Pharmacie de I’ Universit6 Louis Pasteur, Equipe Assocle au CNRS (ERA 55 I), 67083 Strasbourg Cedex, France (Received November 21, 1977) Publication costs assisted by Institut National de la Seut6 et de la Recherche Medicale
The thermal dependence of fluorescence quantum yield 4 and lifetime T is modified in the presence of diffusion-controlledquenching because of temperature effects on the fluorophore lifetime and on molecular mobilities. This phenomenon can be evaluated and studied by means of the temperature coefficient C (relative variation of 4 and 7 per degree). Expressions of C in the absence and the presence of quencher show that C is temperature dependent, may increase or decrease upon addition of quencher, and tends at high quencher concentration to a limiting value which essentially depends on the activation energy for diffusion in the solvent. These properties were experimentally studied on solutions cf indole and phenol in water and dioxane that are model systems of protein residues.
Introduction It is well known that increased temperature reduces the fluorescence quantum yield and lifetime of excited molecules by increasing the efficiency of radiationless deactivati0n.l In solution, the magnitude of this effect generally depends on the solvent since solvent-solute interactions may modify the thermal dependence of radiationless transitions. For instance, the effect of temperature on indole fluorescence has been shown to be much greater in water than in nonpolar solvent^.^-^ In the presence of an external “dynamic” quencher, there is additional deactivation resulting from a diffusion-controlled bimolecular reaction. How this process influences the thermal dependence of fluorescence is not obvious. As a matter of fact, an increase in temperature induces opposite changes in two important parameters of the quenching mechanism: the fluorophore lifetime decreases, thus reducing the probability of an encounter with the quencher, but molecular mobilities increase, thus 0022-3654/78/2082-0746$01 .OO/O
enhancing this probability. According to which effect is predominent, the quenching efficiency, and therefore the fluorescence quantum yield, may be more temperature dependent or less so in the presence than in the absence of quencher . To our knowledge, such a phenomenon has not yet been analyzed. Besides its general interest for fluorescence studies, it is particularly important in the case of complex systems such as proteins, where it accounts for the variety of thermal variations of fluorescence ~ b s e r v e d . ~We therefore studied it in some detail in solutions that are model systems for aromatic residues of proteins: phenol and indole in water and dioxane.6 These solutions had the additional advantage that the spectroscopic behaviors of the solutes and the molecular properties of the solvents were quite different. In this study, the magnitude of the temperature effect was evaluated by means of the “temperature coefficient”, giving the relative change in quantum yield and lifetime 0 1978 American Chemical Society
The Journal of Physical Chemistry, Vol. 82, No.
Thermal Dependence of Fluorescence In Solution
6, 1978 747
per unit temperature increment. This parameter has the double advantage of being a convenient index in comparative studies and, as we shall see, of being related to molecular parameters, about which it may give interesting information. In the following, we shall establish the expressions of this coefficient in the absence and the presence of quencher, and show that its predicted properties are experimentally verified, thus giving a consistent interpretation of the observed phenomena.
Experimental Section Solutions were prepared in twice-distilled water or spectroquality dioxane. They were used in equilibrium with air since fluorescence quenching by oxygen is nil in water and very small (-5% a t ambient temperature) in dioxane. Indole (Prolabo or Sigma) was twice recrystallized in twice-distilled water. Phenol and carbon tetrachloride (Merck) and L-histidine (Sigma, I; grade) were used without further purification. Absorption spectra were recorded with a Cary 15 spectrophotometer and fluorescence spectra with an absolute spectrofluorimeter (Fica 55 M KII). Indole derivatives were excited at 295 nm and phenol derivatives a t 275 nm (band width 2.5 nm). Relative fluorescence q u a n t u m yields were determined from the areas under corrected emission spectra of solutions of equal optical densities; absolute yields were obtained using the reported value of 0.14 for L-tryptophan in water a t 25 "C.'** Lifetimes were measured by the single photoelectron technique with a laboratory-built apparatus previously de~cribed.~ Quartz cells (1 cm X 1 cm) containing solutions were placed in a metal sample holder whose temperature was regulated by circulation of liquid. The temperature of solutions was measured by a thermocouple and maintained within 0.5 "C during measurements. The ranges investigated were 10-75 "C in water, and 10-60 "C in dioxane. The temperature coefficient ~(7') at a given temperature T (eq 1) was determined from plots of quantum yield 4
or lifetime 7 vs. temperature. Such plots often being linear or only slightly curved (Figure l),we did not attempt to draw the tangent to the curve; we evaluated c from the changes in 4 (or 7) for a temperature increment of 15" around T: 1 #(Tf 7.5) - # ( T - 7.5) c ( T ) =-15 @(TI In most cases we used for convenience (ambient temperatures) the value of c corresponding to T = 30 "C.
Results and Discussion I. Temperature Coefficient in the Absence of Quencher. (1)Expression. In a solution containing only one solute, the fluorescence quantum yield and lifetime are given by 90
= kfro
(2)
( h , + kn,)-' (3) where kfand k,, are the rate constants of emission and of nonradiative deactivation, respectively. Extensive studies, recently reviewed by Birks,l have shown that temperature has practically no influence on the emission rate but affects the efficiencies of intersystem crossing to the triplet state and/or internal conversion to the ground state. Since one 70
=
C -D----[3----A- *
d
20
0
40
60
T "C
Figure 1. Thermal dependence of the temperature coefficient (C,) of fluorescence in the absence of dynamic quenching for (a) indole/water; (b) phenoVwater; (c) indole/dioxane; (d) phenol/dioxane.
of these thermal effects is generally predominant, the rate constant of radiationless transitions may be expressed as1 where kn: is a constant, k,,' and W,, are respectively the frequency factor and the activation energy of the main temperature-dependent process, and k is the Boltzmann constant. Using this expression of k,, in eq 3 and differentiating the latter with respect to temperature leads to (see eq 1)
[*
c
c o = -ro
-.I
exp(-Wnr/kT)i
(4)
The temperature coefficient is negative; in the following we shall consider its absolute (positive) value, which will be denoted by Co. (2) Properties. Equation 4 shows that co is temperature dependent, but in a nonobvious manner as the terms ( T ~ and T~ exp(-W,,/hT) ) display opposite thermal variations. Differentiation of (4) shows that Co increases with temperature (dco/dT C 0, Le., dCo/dT > 0) if
Wnr > 2kT
+ CokT2
(5) Figure 1,where experimental values of Co for indole and phenol in water and dioxane are plotted, shows that Co does increase with temperature for both solutes in water (curves a and b). This is in agreement with (5) since for both systems reported values of W, are greater than values w of the right-hand side of (5) in the temperature range explwed (20-60 "C): (indole/water) W,, = 0.52 eV,40.53 eV,l0 0.12 C w C 0.48 eV; (phenol/water) W,, = 0.27 eV,ll 0.11 C w C 0.17 eV. In dioxane, however, both coefficients are almost invariant (Figure 1,curves c and d), indicating that dCo/dT N 0, Le., W,, w. Since W,, is a constant, this condition first implies that w varies only slightly, in the temperature range considered, which is effectively the case, because of the low values of Co: 0.075 C w < 0.095 for indole; 0.08 < w < 0.11 for phenol. Furthermore, the predicted proximity of W,, to w is verified for indole, whose the activation energy in dioxane has been reported to be 0.065
740
The Journal of Physical Chemistry, Vol. 82, No. 6, 1978
TABLE I: Absolute Values ( X l o 2) of Fluorescence Temperature Coefficients (Relative Variation per Degree of Quantum Yield at 30 C)
c, = - r q
O
Solute Indole Phenol
Water
Dioxane
3.0 i 0.2 0.85 i 0.1
0.45 ? 0.1 0.55 ?: 0.1
eVa4For phenol the value of W , is not known; our results indicate that it should be about 0.09 eV. The thermal dependence of the temperature coefficient in the absence of quencher is thus consistently explained and may be useful in fluorescence studies. However, when this parameter is used in comparative studies of different systems, this phenomenon requires that coefficients be determined a t the same temperature. As already mentioned, we choose 30 f 7.5 OC. Values of Co (30 "C) are indicated in Table I for the four systems studied. For indole they agree with those deduced from data in the literature: 2.8 X and 3.2 X in ~ a t e r ,and ~ ? 0.45 ~ X in d i ~ x a n e . ~ For phenol in water our value is somewhat higher than that calculated from Turoverov's results1' (0.7 X no literature data are available for this compound in dioxane. 11. Temperature Coefficient i n t h e Presence o f Quencher. (1) Expression. A quencher Q a t molar concentration [Q]deactivates the excited fluorophore with a probability h,[Q] per unit time. The rate constant h, of the bimolecular reaction may be expressed as12
rA
kT2
G. Laustriat and D. Gerard
exp
(- %)
t k,[Q]
$1
and may be rewritten as
where K = h , is~the~ Stern-Volmer constant, and using absolute values C of temperature coefficients, one finally obtains
(2) Properties. Equation 6 , which reduces to C, = Co if [Q]= 0, shows that addition of a quencher to a fluorescent solution may increase or decrease the temperature coefficient according to the respective values of Coand W& As a matter of fact, differentiation of (6) with respect to [Q]a t constant temperature leads to ($$)T
=
( 1 tCKo [KQ ] 2 ( ) CokT2 I L -
which indicates that C , is an increasing function of the quencher concentration (Le., C, > C,) if where N is the Avogadro number, DF and DQ are the diffusion constants of the two molecules, RFQ is their interaction distance, and p is the probability of deactivation per encounter. In the present study, the "transient term" A,, = RFQ[(DF D Q ) T ~ ] - can ~ / ' be neglected; its value is small (
