COMMUNICATIONS TO THE EDITOR
4172 ( 1 - x “ )
0
p”
.2.
- 4
5: 3
0
0.2
0.4
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tissues. Dye aggregation, rather than interaction between the ionic site and the dye, has been shown to be the major driving force in such interactions.2 Changes in the fluorescence properties of the dye have also been noted, but this aspect has received little detailed study. A limitation of the dye-binding technique in quantitative study is the tendency of the emission to fade rapidlyra I n emission studies attention has been mainly devoted to DNA-acridine orange complexes, in an attempt to understand the powerful mutagenic activity of acridine dyes.4 Little is known about the mechanism of fluorescence quenching of cationic dyes by polyanions, and this is the objective of our investigation. When acridine orange is added to dilute aqueous solutions of dextran sulfate or heparin the absorption and emission spectra depend on the ratio P / D where P is the number of available anionic sites and D is the number of dye molecules in solution. When P / D 1 the dye has an absorption spectrum very similar to the aggregated dye in polymer free solution. When P I D >> 1 the absorption spectrum is similar to that of the free monomeric dye. Unlike the spectral shift t o the blue observed in absorption, increase of acridine orange concentration results in the buildup of a new emission band at longer wavelengths arising from excited dimer molecules. There is no detectable emission from excited states of larger aggregates. The main features of both the emission and absorption spectra can be explained by the theory of exciton splitting.6v6 An upper singlet state of a monomer splits on N-fold aggregation into an N-fold band of levels with a band width depending on the intensity of monomer absorption as well as the relative orientations and separation of the dye molecules. The behavior of acridine orange molecules on interaction with the polyanions mentioned above is consistent with this theory and with the dye molecules forming laminar or card-pack aggregates. Apart from the strong exciton coupling which results in the blue shift in absorption, weak coupling is to be expected and should lead to rapid excitation energy transfer effects. Experiments have been carried out on the quenching of fluorescence from acridine orange bound to polyanions by very low concentrations (lo-* t o 10-71!f) of methylene blue or thionine. I n Figure 1 the SternVolmer plots for the quenching of acridine orange on dextran sulfate fluorescence are shown. F is the
, -
- 1
- 2
- 3
Figure 1. Excess isentropic compressibilities for the systems: (a) tert-butyl alcohol-water a t 27”. Data are scaled from graph in ref 4. Density data are extrapolated from the data of A. Doroshevski, J . Russ. Phys. Chem. Soe., 43,66 (1911); listed in J. Timmermans, “Physico-chemical Constants of Binary Systems in Concentrated Solutions,” Vol. 4,Interscience, New York, N. Y . 1960; (b) acetone-water a t 20’ (ref 2); (c) n-propyl alcohol-water a t 20’ (ref 2); (d) ethanol-water at 20” (ref 2); (e) methanol-water at 20” (ref 2). Thevertical hash marks on the curves indicate the composition at which the maximum ultrasonic absorption occurs (PSAC, ref 4).
(Dr. Blandamer has indicated to the editors that he concurs with the authors’ comments on ref 1 of this communication.)
* To whom correspondenceshould be addressed. DEPARTMENT O F CHEMISTRY
UNIVERSITY OF MISSOURI, ROLLA, MISSOURI65401 ROLLA,
GARY L. BERTRAND* LARRY E. SMITH
RECEIVED JUNE 29, 1970
Electronic Excitation Energy Transfer in Dye-Polyanion Complexes
Sir: The shift in the absorption spectra of cationic dyes upon interaction with polyanions (metachromasia) is the basis of a wide range of cytological and histochemical methods for identifying these materials in cells and The Journal of Physical Chemistry, Vol. 74, No. 29, 1970
(1) For an evaluation see J . W. Kelly, Acta Histochcm., Suppl., IS, 66 (1958). (2) J. S. Moore, G. 0. Phillips, D. M. Power, and J. V . Davies, J . Chem. SOC.A , 1155 (1970). (3) P. J. Stoward, “Luminescence in Chemistry,” E. J. Bowen, Ed, Van Nostrand, London, 1968, pp 222. (4) 1. Isenberg, It. B. Leslie, S. L. Baird, R. Rosenbluth, and R. Bersohn, Proc. Nat. Acad. Sci. U.S., 52,374 (1964). (5) A . S. Davydov, “Theory of Molecular Excitons (trans. by M . Kasha and M. Oppenheimer),” MoGraw-Hill, New YorB, N. Y., 1962. (6) M. Kash:b, Radiat. Res., 20,55, (1963).
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COMMUNICATIONS TO THE EDITOR
I
/O
Table I
Polyanion
Dextran sulfatea Dextran sulfate Dextran sulfate Dextran sulfate Heparin Heparin
”
1
‘ 2 3 4 5 6 7 8 Concentration of methylene blue (xlO*MVI)
3
1
I
1.0
I
2.0
I
3.0
I
4.0
I
5.0
5.3 5.5 2.4 2.3 3.9 3.6
10 4 10 5 10 5
K,” (mole ratio
units)
Acceptor
Methylene Blueb Methylene Blue Thionine Thionine Methylene Blue Methylene Blue
x
10-a
2.97 3.03 2.24 2.59 2.77 2.84
0
Figure 1. Stern-Volmer relationships for the quenching of the fluorescence of dextran sulfate-acridine orange complexesby methylene blue at various acridine orange concentrations. Dextran sulfate concentration 2 X 10-4 equivalent anionic sites per liter.
1
Acridine orange ooncentration X 106M P/D
I
6.0
Concentration of acridine orange (x105M)
Figure 2. Variation of the Stern-Volmer constants, K,,, with concentration of acridine orange for dextran sulfate-acridine orange complexes.
fluorescence intensity in the preserice of quencher and F o the value in the absence of quencher. The values of K,, (mole ratio units) which are given by the slopes of the plots multiplied by the acridine orange concentration do not depend significantly on the P / D ratio in the range 4-20, but increase with acridine orange conM (Figure 2). centration in the range 0.8-7 X Table I summarizes K,, values obtained with both methylene blue and thionine on two polyanions. The exciting wavelength was chosen so that predominantly acridine orange dye aggregates were excited and the aggregation was unchanged by the small amounts of methylene blue or thionine present. I n addition no evidence for the formation of mixed aggregates between acridine orange and quenching dye could be found. K,, measures the effectiveness of the methylene blue and thionine in the deactivation of excited states which give rise to dimer emission relative to the specific rate of decay in the absence of quenching dye. The values of K,, are high and approach the maximum value of
a Temperatures: 24’ (dextran sulfate); 20’ (heparin). Acceptor concentrations varied between lo-* and lO-’M.
about 4 X lo4 found for quenching of anthracene fluorescence by naphthacene in anthracene crystal^.'^^ ((Energy hopping” between dye aggregates, similar to that postulated for organic crystals, must occur until, among other possibilities, trapping occurs at a dimer aggregate and fluorescence from the lower level of the first excited singlet state occurs. Analysis of the results of the quenching experiments with heparin shows that energy migration from one polyanion-dye complex to another occurs. A typical heparin molecule used in these experiments had a molecular weight of about lo4 and about 70 anion sites per molecule. From results given in Table I an acridine orange concentration of 3.9 X lop5M and a mole ratio of 1.9 X 10-3 for methylene blue t o acridine orange gives a 30% quenching. At P / D = 10 there is one methylene blue molecule for each 5200 sites and therefore at least 22 heparin molecules must, on average, be involved in each quenching act. If methylene blue molecules were only able to quench excited states of acridine orange on the same molecule as it was located there would only be 1.5% quenching. It can be shown by calculation that both diff usive and long-range Forster type energy transfer are not sufficiently effective to explain the observations under the experimental conditions. There must be a weak or intermediate exciton coupling between dye molecules on different polyanions in clusters formed under the conditions of solution. This interpretation is consistent with the lack of significant change in the effectiveness of energy transfer between aggregates when the P / D ratio is changed. The effect of increasing acridine orange concentration on the value of K,, is probably due t o quenching of the fluorescent dimer state by transfer to lower excited levels of higher aggregate. The demonstration of rapid electronic energy transfer, apart from improving understanding of the behavior of (7) 5. B. Birks, “The Theory and Practice of Scintillation Counting,” Pergamon, Oxford, 1964, p 259. (8) D. C. Northrop and 0. Simpson, Proc. Roy. Soc. Ser A . , 234, 136, (1950).
The Journal of Physical Chemistry, Vol. 74, N o . 83,1970
COMMUNICATIONS TO THE EDITOR
4174
dyes used in fluorescence microscopy and histochemistry, provides a valid model for energy transfer under biological conditions. The extremely facile intermolecular energy transfer between aggregates, in particular, raises interesting possibilities about such processes being operative in the connective tissue matrix, where the polyanions are in similar association with a range of polycations. It has also been found possible to render dye-polyanion systems resistant to fading under conditions of illumination. The small amounts of methylene blue or thionine added do not affect the absorption spectra, but seem to decrease the photodecomposition or photoxidation reactions of acridine orange in the presence of air. The decrease in fading brought about by methylene blue is much more marked than the quenching of dimer fluorescence. This useful finding is consistent with very rapid energy transfer involving a number of excited states. The high efficiency of transfer makes it possible for energy transfer from higher excited states to occur. Acknowledgment. This work was supported in part by a grant from the Medical Research Council and the United States Department of Agriculture PL 480 Grant FG-UK- 147.
E ( { v))
Z({ej)niePp*ei
=
(1)
le1
where v, is the chemical potential of the i t h atomic species and p is the statistical temperature. The function E ( { v is essentially the Laplace transform of Inverting the transform, we have Z({ e
1)
1).
where v f f can be conveniently chosen (within the convergence limit) on the real axis of vj. We can evaluate X by making use of the fact that the only important contributions to X come from energy levels which result from the atoms being associated jn stable species. Let vii (i = 1 to n) be the number of molecules of the ith stable compound and write the stoichiometric relations for the decomposition of molecules to atoms in the form i=l
niail = el ( j = 1 to m )
where aij are stoichiometric coefficients. Then
* To whom correspondence should be addressed. DEPARTMENT OF CHEMISTRY THEUNIVERSITY, NOTTINGHAM, ENGLAND
canonical partition function for the set of atomic components { e ). The atomic composition of the system is, of course, unchanged by chemical reaction. The grand partition function X ( [ v )) is then given by
R. B. CUNDALL C.LEWIS
~ ( v= ) CZ({e})ir,epuiei = le1
C ~ ( { n } ) r ~ ~(3)( ~ i
in1
where At = irjePyJasJis the activity of the ith moleaular DEPARTMENT OF CHEMISTRY AND P. J. LLEWELLYN G. 0. PHILLIPS* species. In the last equality we have made use of the APPLIEDCHEMISTRY fact that only atomic configurations corresponding to THEUNIVERSITY SALFORD, M5 4WT, ENGLAND RECEIVED JULY 25, 1970
Chemical Equilibrium and the Anti-Helmholtz Function.
A Statistical Interpretation
Sir: Recently Duffin and Zener have discussed the problem of chemical equilibrium as formulated in the language of geometric programming. They establish that the usual method of minimizing the Helmholtz free energy with respect to concentration of products and reactants is equivalent to maximizing an “anti-Helmholtz” function with respect to the activities of the atomic species present in the system. They also give a statistical mechanical interpretation of this approach in terms of the method of Darwin and Fowler. The well known relation between the “selector variables” of the Darwin-Fowler method and chemical activities suggests an alternate statistical interpretation of their results which clearly reveals the relationship between the atomic activities and the anti-Helmholtz function. Let e, (i = 1 to m) be the number of atoms of the ith atomic component in the system and Z({e]) be the The Journal of Physical Chemistry, Vol. 74, N o . $9,1970
stable compounds give an important contribution to the sum. If we substitute eq 3 into eq 2 and evaluate the resulting integrals by the method of steepest descents, we obtain an expression for Z in terms of the minimum of the function Z*({ v)) = E / r t e P ~ with ~ e ~ respect to the atomic chemical potentials { v) , This is equivalent to the maxiniization of the anti-Helmholtz function F* = - 1 / p In Z* = Ziv,ei - PV where PV is the pressurevolume product. As an example, in the case considered by Duffin and Zener, when all the species are ideal gases, then
E
= C i r i ( x i ~ J n z / n= a ! exp(Ctx,njeP~~a~~) in!
where x i is the molecular partition function of the ith stable species. From eq 3 we have
which when computed by the method of steepest descents yields the result of Duffin and Zener
(1) R. J. Duffin and C. Zener, J.Physc. Chem., 74,2419 (1970).
