1695
NATUREOF BONDING IN DYEAGGREGATES
Nature of Bonding in Dye Aggregates
by K. K. Rohatgi and G . S. Singhal Jadavpur Universitg, CaZcutta-39, India
(Received March SO, 1966)
Dye aggregation has been studied in aqueous solutions of sodium fluorescein and rhodamine B by means of their absorption and emission characteristics and the effect of temperature on these. The thermodynamic functions, AF, AH,and Ah‘,have been calculated for the dimer stage, 2M ~2 D. The values obtained are, for sodium fluorescein, - 1.0 kcal, -7.6 i 0.7 kcal, and -21.7 eu, respectively, and for rhodamine B, -4.4 kcal, -2.8 kcal, and +5.3 eu, respectively. Positive entropy change and low enthalpy change for the latter dye suggest that in this case, aggregation is an entropy-determined phenomenon, brought about by “hydrophobic” bonding, whereas in the first case, hydrogen bonding may be responsible for aggregation. Complete absorption curves of the dimer are obtained for both dyes. A splitting of the excited energy level is observed. The ratio of intensities E ~ / B X of the two band components is 0.77 for fluorescein and 0.24 for rhodamine B, where e2 and €1 are the respective molar extinction coefficients for the long-wave and the shortwave peaks of the dimer spectra. These values, governed by the mutual orientation of the transition moment vectors of the two molecules in the dimer, support the nature of bonding postulated for the two dyes.
The problem of dye aggregation has been studied to the influence of the dielectric constant on mutual in relation to concentration quenching of energy of two charges. However, this factor is not and action spectrum of fluorescence?J In case of chlorophyll, stacking of molecules has been discussed (1) B. Walter, Ann. Physik., 36, 502, 518 (1889). as factor in energy migration in photosynthe~is.~ (2) B. Soderborg, ibid.,41, 381 (1913). Aggregation has been in general deduced from non(3) V. L. Levschin, Acta Physicochim. URSS, 1, 685 (1935). conformity with Beer’s la~.~*’O-’~ (4) E. Rabinowitch and L. F. Epstein, J . Am. Chem. SOC., 63, 69 (1941). Various mechanisms have been advanced for aggre(5) 5. I. Vavilov, J. Phys. U S S R , 7, 141 (1943). gation of dyes in aqueous ~olutions.~-7~1~-17 Rabino(6) V. L. Levschin and L. V. Krotova, Opt. Spectry. (U.S.S.R.),13, witch and Epstein4 determined the thermodynamic 457 (1962); V. L. Levschin and E. G. Baranova, J . Chim. Phys., 55, 869 (1958). functions for the dimer formation in thionine and meth(7) Th. Forster, “Fluoreszenz Organischer Verbindungen,” Vanden ylene blue. Since association does not stop at the dimer Hoek and Ruprecht, Gottingen, 1951, p 245. stage, they considered the additive forces of van der (8) J. Lavorel, J . Phys. Chem., 61, 1600 (1957). Waals type4s12p16as responsible for the phenomenon. (9) 9. S.Brody and M. Brody, Nature, 189, 547 (1961). London’s dispersion forces could cause the stacking of (10) V. Zanker, 2. Physik. Chem. (Liepzig), 200, 250 (1952). dye molecules in parallel orientation in a polymer unit. (11) H. Zimmerman and G. Scheibe, 2.Elektrochem., 60,566 (1956). (12) Th. Forster and E. Konig, ibid., 61, 344 (1957). From a study of the heat of association of dyes, it has (13) P.Mukerjee and A. K. Ghosh, J. Phys. Chem., 67, 193 (1963). been concluded that intermolecular hydrogen bond(14) Kh. L. Arvan and N. E. Zaitseva, Opt. Spectry. (U.S.S.R.), 10, ing,6J6 or bonding by sandwiched water molecules,6?l6 137 (1961). may be involved in this phenomenon. (15) V. L. Levschin and I. 8. Lonskaya, ibid., 11, 148 (1961). It has been further observed that in alcohol or glyc(16) S. E. Sheppard, Proc. Roy. SOC. (London), A82, 256 (1909); S. E. Sheppard and A. L. Geddes, J . Am. Chem. Soc., 66, 2003 erol solution aggregation is very weak.4~6 Addition of (1944). alcohol or glycerol to concentrated aqueous solution (17) V. L. Levschin and V. K. Gorshkov, Opt. Spectry. (U.S.S.R.), may cause disaggregation. This has been ascribed 10, 401 (1961). Volume 70.Number 6 June 1966
K. K. ROHATGI AND G. S.SINGHAL
1696
very important, as shown by Arvan and ZaitsevaI4 for a number of dyes in simple and mixed solvents of identical dielectric constants. I n the absence of any knowledge of the microscopic dielectric constant around the dye ion, correlation with the macroscopic dielectric constant may not be significant. Arvan and Zaitseva ascribe a substantial role in dye aggregation to hydroxyl groups of the solvent molecules. Thus, no single mechanism can be put forward to explain the forces holding the dye molecules together. We have made an attempt to interpret the nature of bonding in two dyes, sodium fluorescein and rhodamine B, by determining the thermodynamic functions, AF, AH, and AS, for their dimerization.
Experimental Section The dyes were purified as reported earlier.l* Absorption spectra were measured in a Beckman DU spectrophotometer (Model 4700) by placing a drop of concentrated solution on a glass slide and sandwiching it under another glass slide. The slides were cut to fit the Beckman cell holder. The edges of the cell were greased to prevent evaporation. The desired temperature of the spectrophotometer was maintained by circulating water from a thermostat through thermospacer coils. For higher temperature the slides and the solution were preheated to the desired temperature. Adsorption of the dyes on the glass slides was found to be small and hence neglected. The difference in transmittance between a clean slide and a slide treated for 45 min with a concentrat,ed solution M ) was about 3% of rhodamine B (C 1 X . . (Tz?2a, . -~ .. . 89%, Tf:&,d 86% against air). Fluorescence was measured in a Brice-Phoenix light-scattering instrument (Model 1OOO). Temperature was controlled by circulating water through zigzag coils, made of thin-glass narrow-diameter tubing, constructed so as to fit the measuring cell without obstructing the light path. I n some experiments the solution was heated to a high temperature and readings were taken during progressive cooling. The temperature as recorded on a thermometer dipped in the solution was noted before and after each reading. The temperature was varied from 20 to 55". The fluorescence measurements were made a t an angle of 135" to the incident beam. The 436-mp radiation from a H.P. mercury lamp was used for excitation of fluorescein solution. An appropriate filter was used in front of the photomultiplier to cut off stray incident light. Absorption by dilute solutions was measured in the same experimental setup by positioning the photomultiplier in line with the incident beam. A geometric Correction factor Was needed for Comparison Of dilute
_.
-
5
x
#n
+--aI x IZ'M A-4-
I
x/2M
&.a5.3x d'n
N
I9
20
PI
22
23
21
25
F x /6J cm-'
Figure 1. Fluorescein absorption spectra at pH 12.
and concentrated solutions, which took into account the depth viewed by the photomultiplier. This was obtained by using quinine sulfate solution in 1 M H2SO4,in which the effect of secondary fluorescence is absent. Details of correction factors necessary for obtaining true quantum yield (4) will be the subject matter of separate communicati~n.~~
~~
The Journul of Physical Chemistry
Results and Discussion Sodium Fluorescein. Normalized absorption spectra of fluorescein in alkaline aqueous solution (pH 12) are given in Figure 1 for four different concentrations. M soluThe spectrum is only slightly distorted a t tion; but at 5 X lo-' M , it is strongly deformed. A second prominent peak appears a t 470 mp, where only a vibrational shoulder is present in dilute solutions. Because of the high extinction coefficients of the dye, thin layers must be used in the determination of absorption in concentrated solutions. Since the thickness of these layers is not exactly known, absolute determination of extinction coefficientsis impossible. We assume that only dimers are formed in the concentrations used. The fraction X of the molecules in the monomeric form at a certain concentration can be obtained from the relation (18) K. K. Rohatgi and G. S. Singhal, J. Phys. Chem., 67, 2844 (1963).
(19) G. s. Singhal, Ph.D. Thesis, Jadavpur University, 1965.
NATURE OF BONDING IN DYEAGGREGATES
e, =
evmz
1697
+ eyd(1 - z)
Here, 1 - z is the fraction of the total number of molecules present in the dimeric form, and eyd is the corresponding molar extinction coefficient per single molecule in the dimer. In absence of exact knowledge of the path length, the ratios of the optical densities (OD) at the peaks V d and V, at different concentrations can be considered. If
D = - -OD - at Vd - Q m X m OD at Y, evm x
+
Eydd(l d
e,
- 2)
(1 - z)
(1)
dividing throughout by evmm'2,the expression simplifies to
D=
Do 1
Table I: The Fraction of Monomer (z)and the Equilibrium Constant Kd for Fluorescein Solution (pH 12) at 30"
5 . 0 X lo6 2.5 X 5 . 0 x lo-* 1 . 0 x 10-2 5.0 x 7 . 0 X 10+ 1 . 0 x 10-1 5 . 3 x 10-1
0.455(Do) 0.470 0.475 0.496 0.631 0.668 0.727 0.889
1.0 0.968 0.958 0.917 0.721 0.681 0.626 0.512
1.0 ... 0.968 0.15 0.958 0.22 0.909 0.20 0.714 0.18 0.673 0.19 0.613 0.19 0.413 0.31 Av0.19i0.015
+ AZ
+ BZ
where A = e,dd/eVmm, B = evmd/eVmm,and 2 = (1 x ) / x . At low concentrations, where is unity, D = Do. This expression can be rearranged to the final form 1_ -- A - B D o -B
Z
D-Do
which predicts a linear relationship between 1/Z and
1/(D - Do). Our problem is to calculate Z [= (1 - z)/z]. This is not easily determinable due to unknown thickness of the absorbing solution. Therefore, we have taken recourse to the method of successive approximation. A clue to the first approximation is obtained from the Lavorel's* data on the variation of the ratio of optical densities for concentrated and dilute solutions of fluorescein with wavelength. He observes that (a) emm >> eymd and (b) %dm = evdd. With these approximations, we obtain from expression I
The so calculated values of z are given in Table I, column 3, and are utilized for plotting 1/Z us. 1/(D Do) according to expression I1 (Figure 2). Using the values of A and B obtained from the slope and the intercept of the plot, better values of 2 can be calculated. These values of Z can again be plotted as before. This is repeated until the successives values of Z do not vary. We found that only two plots are necessary to obtain concordant values of 2, from which z can be recalculated. These refined values of z are recorded in column 4 of Table I. The data have been plotted up to a concentration of 1 X 10-1 M , as it is very likely that in this range of concentrations aggregation does not proceed much beyond the dimer stage. There are two justifications
.
a0
10
70
0-DO
Figure 2. Plot of l / Z vs. 1/(D
- DO)for fluorescein.
for this conclusion: (1) the values of the equilibrium constant (Ka) calculated for the dissociation of dimers according to the expression, D e 2M, are nearly constant up to this concentration; and (2) a systematic study'g of the concentration quenching of fluorescence of fluorescein solution showed that in this range the Volume 70, Nuder 6 Jum 1966
K. K. ROHATGI AND G. S. SINGHAL
1698
relative quantum yield can be expressed as function of concentration of the dye by a quadratic equation. At concentrations higher than 1.0 X 10-l M , the value of K d tends to increase, probably due to the formation of higher polymers. The average value of K d below 0.1 M is 0.19. This compares with Lavorel’s8 value of 0.14 and Levschin and Krotova’se value of 0.17. From this we calculate the free energy change, A F , for dimerization at 30”. AF = -RT In 1/0.19 = -1.0 kcal/mole Enthalpy, A H . Since dimerization of sodium fluorescein starts at fairly high concentration, and experiments on the effect of temperature on the absorption spectra are therefore difficult, the enthalpy of dimerization has been calculated from the effect of temperature on the fluorescence yield of the dye. Because of the high yield of fluorescence, I$ = 0.85,20this is a very convenient method in this case. I n general, if several temperature-dependent phenomena are superimposed, the effect of temperature on a concentrated solution of fluorescing dyes may not be very simple.21 A study of the concentration quenching of fluorescence of fluorescein s o l ~ t i o n ’ ~ (at pH 12) has revealed that the concentration quenching begins at a concentration of 6 X lo-* M . The M; Stern-Volmer equation is obeyed up to 3 X beyond that, deviations are observed which can be represented by adding another term, containing the square of the concentration. The plot of log (+/& - l)Tvs. 1/T at three different CZ = 5 X concentrations, CI = 1.63 X and Cs = 1 X M is shown in Figure 3, where C#J is the absolute fluorescence yield for 1 X M solution at the temperature T and & the yield at any other concentration. All C#J values are corrected for secondary fluorescence and geometrical effects.l9 The concentration C1 corresponds to the Stern-Volmer region and Cz and C3 correspond to the region where the quadratic form becomes significant. Two opposite temperature effects are observed in the two regions: at C1, the temperature coefficient of quenching is positive, while at Cz and Ca this coefficient is negative. The slopes for Cz and C3 give the same value for the heat of quenching (4.6 kcal). They probably represent the combined effect of the heat of dissociation of the dimers and the activation energy for Stern-Volmer quenching. A detailed study of the effect of temperature on the quenching of sodium fluorescein is in progress. The data for CI are susceptible to error owing to the smallness of the temperature effect. Since an Arrhenius plot in this region gives a straight line, and a value The Journal of Physical Chemistry
32
3’1
+
XI03
3’3
Figure 3. Plot of log (quenching constant) us. 1 / T for three different concentrations of fluorescein solution (pH 12): ( A ) Ct = 1.63 X M; (B) Cz = 5 X 10-aM; and (C) C3 = 1 X 10-2M.
for heat of activation equal to 3.0 f 0.7 kcal, it seems that the increase in quenching due to increased frequency of collisions is less important than that due to the need for an energy of activation. From these data, the heat of dimerization is calculated as A H = -4.6 - (3.0 f 0.7) = -7.6 + 0.7 kcal. Entropy, A S . Now we have all the data needed to calculate the entropy of aggregation of sodium fluorescein at 30”
D
2M 1
AF = - RT In - = - 1.0 kcal/mole K d
AH = -7.6
f
0.7 kcal/mole
therefore A S = -21.7eu
The values of heat and entropy of dimerization for fluorescein suggest that probably hydrogen bonding between the two dinegative FP- ions is responsible for dimerization. The influence of polarization forces may also be present. Levschin and Krotovae obtained a very low value, A H = 2.2 kcal, and explained it as due to strong repelling action between the two ions which the bond has to overcome; it therefore cannot be taken as a reliable indicator of the character of the bond. Their low value may have been due to the (20) C. A. Parker and W. T. Rees, A d y s t , 8S, 587 (1960). (21) E. J. Bowen and F. Wokes, “Fluorescence in Solution,” Long-
mans, Green and Co., London, 1953,p 40.
NATUREOF BONDING IN DYEAGGREGATES
1699
1'0
0.D
OD
0.6
-2.91
05
31
,
I
1
3'2
3'3
5'4
+XIS
Figure 5. Arrhenius plot of log Kd for 2M equilibrium. rhodamine B, D
0.4
Table 11: The Fraction of Monomer (2)and the Equilibrium Constant, Kd, for Rhodamine B a t 30"
0.2
D 0.1
0
ni
t?
H
PO
PI
t x 1 6 3 CY-!
Figure 4. Rhodamine B, absorption spectra in water.
fact that they did not take into account the possible temperature dependence of other quenching reactions in the system. Rhodamine B . Rhodamine B is a strongly aggregating dye. The absorption spectrum is very much distorted even in a 1 X M solution (Figure 4). The equilibrium constant was calculated in the same manner as in the case of sodium fluorescein anion. The data are presented in Table 11. Since the intercept for the plot of 1/Z us. 1/(D- Do)was very small, it was evaluated analytically from the best points on the straight line. The recalculated values of 2 are given in column 4, Table 11. The value for the highest concentration again has been omitted from calculation of the average value of the equilibrium constant. Enthalpy, A H . Since the changes in the absorpM solution spectrum were considerable in 1 X tion of rhodamine B, the variation in the spectrum with temperature was utilized for the calculation of the enthalpy of aggregation, by the relationship
1 X lo-' 8X 6X 4x 1 x 10-8
0.4000 (Do) 0.4100 0.4558 0.6521 0,8181
1.00 0.976 0.878 0.613 0.489
...
...
0.976 0.878 0.613 0.485
6.4 7.6 7.8 9.1 Av 7.3 j=0.57
the value of AH is calculated to be +2.8 kcal for the dissociation of the dimer. The values of log Kd plotted are those obtained at 1 X M, which are slightly greater than those for lower concentrations, utilized for calculation of Kd (av), Therefore, this value for the enthalpy of dissociation can be taken as the upper limit for the dissociation of the dimer. The thermodynamic functions for the association process at 30" are AF = -4.4 kcal/mole, AH = - 2.8 kcal/mole, and A S = +5.3 eu. This small energy of dye association, together with a positive entropy value, is noteworthy. Similar examples are known in the thermodynamics of protein stabilization, where "hydrophobic bonds" have been suggested as an important factor in stabilization of natural protein.22 An analogy to this behavior is found in the thermodynamic changes involved in the transfer of hydrocarbons from a nonpolar solvent t o water, as discussed by Frank and EvansnZ3The process is invariably exo-
AH
log K = log A - 2.3RT The data are plotted in Figure 5. From the slope,
~~
~
(22) W. Kauzman, Advan. Protein Chem., 14, 1 (1969). (23) H. S. Frank and M. W. Evans, J . C h m . Phys., 13, 607 (1945).
Volume 70.Number 6 June 1966
K. K. ROHATGI AND G. S. SINGHAL
1700
thermic or athermal, with a large negative entropy change. This entropy effect is also observed in molecules containing nonpolar groups and has been made responsible for micelle formation by long-chain molecules like soaps and detergent^.^^-*^ The origin of these large entropy effects is found in the breaking of "icebergs," in the terminology of Frank and Evans, around the polar molecules, when they leave the aqueous environment. Recently Mukerjee and Ghoshls have used urea as a probe t o investigate the contribution of water structure to dye association. They have shown that metachromatic behavior of methylene blue dyes and their tendency for aggregation can be ascribed to the same cause, the gain in entropy when nonpolar groups leave the aqueous environment and crowd in their own nonpolar region to form intermolecular hydrophobic bonds. A similar behavior is observed here for rhodamine B; it may be concluded that the association of rhodamine B also is an entropy-governed and not an enthalpy-governed phenomenon. Effect of urea on fluorescence yield and degree of associationla confirm the hydrophobic nature of bonding. Nature of Dimer Spectra. The complete absorption curves for the dimers of fluorescein and rhodamine B are given in Figures 6 and 7. They have been obtained from the values of x or the fraction of the monomer as given before. The molar extinction coefficient for the dimer has been obtained from the slope and inter-
*
)'O
-
a-
E Imp Figure 7. Rhodamine B, absorption spectra of monomer (0) and dimer ( 0 ) .
cept of the figure (2) plotted according to expression 11. Thus knowing the value of A and B, evmd and evdd can be calculated. These values can then be utilized for the calculation of E, and thence the value of I , the solution thickness, from the observed optical density a t the frequency under consideration. Generally, the frequency of the apparent dimer peak in the solution spectrum is utilized for calculation. After that it is simple to obtain the molar extinction coefficients at other frequencies from the observed optical densities for concentrated solutions and construct the complete absorption curve for the dimer from the expression Ev
E,d
I
400
=
- €,mx 1-x
where :E is the extinction coefficient per molecule in the dimer; these values should be doubled t o obtain the extinction coefficient of dimer as such. The spectra are observed to have two peaks, situated on either side of the monomer peak. Similar observations have been made by earlier workers2ss'12,16 and have
" I
I
453
WAVELENGTH
t40
X
IN
mp
Figure 6. Fluorescein, absorption spectra of monomer (0)and dimer ( 0 ) .
The Journal of Physical Chemistry
$5
(24) P. Mukerjee and A. Roy, J . Phys. Chem., 67, 190 (1963). (25) G. Stainby and A. E. Alexander, Trans. Faraday Sac., 46, 587 (1950). (26)W.Bruning and A. Holzer, J . Am. Chem. SOC.,83, 4865 (1961).
NATURE OF BONDING IN DYEAGGREGATES
1701
been suggested as the simplest case of the “Davydov splitting” known to occur in solids. The wavelength and molar extinction coefficients for the two peaks in the two dyes are given in Table 111.
Table 111: Wavelength and Molar Extinction Coefficient for the Two Peaks of the Spectra of Fluorescein and Rhodamine B Dimers
x
x
XI,
(1
X2,
e2
Compd
mp
10-4
ma
10 -4
Fluorescein Rhodamine B
468 522
4.08 3.95
508 568
3.16 0.96
Recently, the quantum mechanical approach to this phenomenon has attracted great interest.26-m Following the treatment of Levinson, Curtis, and Simpson2’-30 on dimerization of pseudoisocyanine, electronic energy levels of the ground state and the excited state of the +a’$*b, molecule can be represented as ‘$a& and ‘$*ahJ respectively, where the asterisk represents the excited molecule. These degenerate excited-state wave functions will suitably combine to destroy the degeneracy, giving rise to two electronic energy levels, W+ and W- . For the monomer, the dipole moment of transition will lie in the plane of the molecule. I n the dimer, these dipole moments must have proper orientation with respect to each other, to produce a positive transition probability. Calculations show that transition to W+ will be zero for parallel orientation of the transition moments in the two molecules of the dimer, and transition strength will be double for the W- energy state.
If the dipole transition moments deviate from parallel orientation, then a low-energy transition to W+ may become allowed. Therefore, the ratio of the intensities of the two peaks gives an idea of the orientation of the molecules in dye aggregate.9,s1J2 For fluorescein anion, e2/q = 0.77 where e2 and e1 are molar extinction coefficients for the long-wave and the short-wave peaks. For rhodamine B the ratio is much smaller, e2/e1 = 0.24. The molecules are distorted from parallel orientation to a much greater extent for fluorescein. Such a behavior may be partly due to coulombic repulsion between the two doubly charged negative ions.6s12 However, hydrogen bonding between the two dye molecules appears to be a more likely factor responsible for a definite geometrical arrangement in the dimer, which would not have been possible if only polarization forces were present. For rhodamine B, hydrogenbonding assistance is not available and the molecules are oriented according to their mutual polarizability and thermal fluctuations in the system. Acknowledgment. The authors wish to thank the Council of Scientific and Industrial Research for the award of Senior Research Fellowship to G. S. S. Thanks are also due to Dr. P. iLIukerjee for many helpful discussions on hydrophobic bonding.
(27) G. S. Levinson, W. T. Simpson, and W. Curtis, J . Am. Chem. Soc., 79, 4314 (1957). (28) A. Witkowski and W. Moffitt, J. Chem. Phys., 33, 842 (1960). (29) E. G. McRae, Australian J . Chem., 14, 344 (1961). (30) G. J. Hoijtink, 2.Elektrochem., 64, 156 (1960). (31) H. De Voe, J . Chem. Phys., 37, 1534 (1962). (32) E. G. McRae and M. Kasha, ibid., 28, 721 (1958).
Volume 70, Number 6 June 1966
