Journal of Luminescence 37 (1987) 61-72 North-Holland, Amsterdam
FLUORESCENCE BEHAVIOUR OF HIGHLY CONCENTRATED RHODAMINE 6G SOLUTIONS
A. PENZKOFER and W. LEUPACHER Naturwissenschaftliche Fakultdt II - Physik, Universitat Regensburg, D-8400 Regensburg, Fed. Rep. Germany
Received 7 October 1986 Revised 23 January 1987 Accepted 27 January 1987
The fluorescence quantum distributions E(X) and fluorescence quantum efficiencies qF of rhodamine 6G in methanol and in water are measured for various concentrations up to the solubility limit. The fluorescence spectra are separated in monomer and dimer (ground-state dimer and closely spaced pair) contributions. The stimulated emission cross sections for the monomers and the dimers are resolved.
1. Introduction measured in [17] and found to be approximately equal to the fluorescence lifetime. The short fluo•
The fluorescence spectra of highly concentrated rescence lifetimes (e.g. rF — 2 ps, at 0.4 mol/1) and dye solutions are scarcely investigated [1-3] since the equal values of fluorescence lifetime and the fluorescence quantum efficiency reduces ground-state absorption recovery time exclude tri• drastically [1-9] and reabsorption of fluorescence plet fluorescence and delayed singlet fluorescence light distorts the frequency distribution [10,11]. caused by Srstate repopulation from triplet states. The formation af aggregates as dimers [12], closely For rhodamine 6G in water no dimer fluores• spaced pairs [13] and higher oligomers [12,14,15] is cence has been reported so far, since the monomer mainly studied by analyzing absorption changes. fluorescence dominates still at the highest possible
For rhodamine 6G in methanol and water the dye concentration (Cmax = 0.027 mol/1, rF = 150 absorption behaviour of highly concentrated solu• ps, see below). tions was studied in [13,16]. Rhodamine 6G in In this paper the fluorescence spectra of water forms stable ground-state dimers [16]. rhodamine 6G in methanol and water are investi• Rhodamine 6G in methanol has low tendency to gated at room temperature. The dye concentration form stable ground-state dimers [13]. At high con• is varied from very low values up to the solubility centrations the dye molecules come near together limit (methanol: 0.66 mol/1; water: 0.027 mol/1). by random motion and they interact with one From the measured fluorescence spectra the fluo• another (closely spaced pair formation [13]). For rescence quantum distributions E(X), the fluores• both stable ground-state dimers and closely spaced cence quantum efficiencies qF [jemE(X)d\ = qF] pairs the generic name dimers is used here. and the monomer and dimer stimulated emission For rhodamine 6G in methanol the dependence cross sections are determined. The resolved ab• of the fluorescence quantum efficiency and the sorption and emission cross-section spectra of the fluorescence lifetime on concentration was studied closely spaced pairs of rhodamine 6G in methanol in [9]. Closely spaced pair fluorescence was re• and of the stable ground-state dimers of rhoda• solved at high concentrations. The ground-state mine 6G in water are interpreted in terms of a absorption recovery time versus concentration was dimer model that assumes different Franck-Con-
0022-2313/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) don shifts between the S0 and ST states of mono• width close to the S0-S1 absorption peak (slightly mers, closely spaced pairs, and stable ground-state shifted to short-wavelength side). The pump light dimers. is focused to the sample S with lens L2. The fluorescence emission in backward direction is gathered by lens L2 and directed to the spec• 2. Experimental arrangement trometer SP by a broad-band 50 percent beam splitting cube (BSC) and lens L3. The dispersed The fluorescence spectra are measured with the fluorescence spectrum is registered by a diode experimental setup shown in fig. la. A tungsten array system (Tracor DARRS system) and the lamp (LS) is used as excitation source. The stabi• data are transfered to a computer for analysis. For lized power supply of the tungsten lamp guaran• fluorescence depolarization analysis two polarizer tees constant excitation of the sample. An inter• sheets PI and P2, are inserted in the experimental ference filter (IF) restricts the excitation band- system, one in the excitation path between IF and BSC and one in the detection path between BSC and L3. The fluorescence signal is independent of molecular reorientation if the polarizer sheets are Li . IF BSC L2 S oriented under an angle of
3. Fluorescence parameter extraction
The diode array detection system measures the
spectral photon distribution Sm(X) behind the spectrometer within a time duration A/ (unit:
counts nm_1, proportional to photons nm"1). The
fluorescence signal SE(X) emitted from the sam• ple S within the acceptance angle of lens L2 is calculated by taking care of the spectral transmis•
sion rBSC of the beam splitter cube BSC, of the
spectral transmission TSP of the spectrometer SP
and of the spectral sensitivity SnA (counts/pho- ton) of the diode array DA. The relation between
SE (A) and Sm(X) is
EK V ; (b) L_i I ' TBSC(X)TSP(X)S»A(X)-
0 xc I x
The intrinsic signal St(X) inside the sample is
Fig. 1. (a) Experimental setup. LS, tungsten lamp; L1-L3, different from the external signal SE(X) outside lenses; IF, interference filter; BSC, 50% beam splitting cube; S, the sample because of reabsorption of fluores• sample; SP, spectrograph; DA, diode array system. PI and P2, cence light along the path from the position of polarizer sheets (included in fluorescence depolarization analy• sis), (b) Pump light attenuation and fluorescence signal at• generation towards the exit window. The situation tenuation (generated at x0) in sample. Drawings illustrate is illustrated in fig. lb. At depth x0 inside the
derivation of eq. (2). sample the pump power P is reduced to P(x0) = P(0) exp(-JVaL.x0) (N = NAC is the number den• signal integrated over the full solid angle 477
23 -1 sity of dye molecules, iVA = 6.022045 X 10 mol [^Sj t(X) = *SI(\)47r/AI2I] to the absorbed pump
Avogadro's constant, C concentration, aL absorp• photons [n&hs = P(0)bt(l--TL)/hvL, A/ is the tion cross section of dye molecules at pump light integration time of the diode array system] leading wavelength AL). At position x0 the contribution to to the intrinsic fluorescence signal is
2 4T7T] F Sl(X)hpL dSl(X)/dx = -const(A) dP/dx E(X) = (3) Aft P(0)[l-rL] At'
= const(A) P(0) exp( — NoLx0)NoL
The fluorescence quantum efficiency qF (the and the contribution to the external signal is ratio of total number of intrinsic fluorescence photons to absorbed pump light photons) is given dSE(X)/dx = (l-R) exp[-Na(X)x0] by = (1-/*) const(A)P(0)
qF= f E(X) dX. (4) Xexp{-N[oL + o(X)]x0}NoL. J p.m R is the reflectivity of fluorescence light at the The integration extends over the SJ-SQ fluores• window. The total intrinsic fluorescence signal is cence band. Often a normalized fluorescence
l quantum distribution E(X) is used which is de• Si(X) = f dS,(A) = const(A) P(0)(1 - TL).
fined by E(X) = E(\)/qF9 i.e., femE(X) dX = 1.
TL = exp( — NoLl) is the pump pulse transmission. In the experiments E(X) and qF are de• The total external fluorescence signal is termined by calibration to the fluorescence signal of a reference substance of known quantum ef•
SE(X) = fdSE(X) ficiency qR in order to get rid of geometrical factors and absolute energy measurements. In our = (1 - R) const(A) case 10 ~5 molar rhodamine 6G in methanol is
XP(0){l-exp[-7V(aL + a(\))/]}aL used as reference (qR — 0.9 [6]). The quantum efficiency is found by use of relation (4)
1 x[aL + a(A)]"
= (1 -R) const(A) <7FAR = J E{X)d\/( ER(\)d\ 47 em •/em L + o(X)1/ffL XP(0) {l - ri° }aL and eq. (3):
x[aL + a(A)]-\
The relation between internal and external fluo• r,U 5,(X)dX rescence signal becomes ;em 1 1 L,R (5) l-T, "<7R- oL + o(X) l-rL
SI(X) = SE(X). (2) + W1/»L ffL(l -R) 1 - Tl°L °
In the analysis reemission of absorbed fluores• The fluorescence quantum distribution is given by cence light within the acceptance angle AJ2j = 2 ij Fs,(x) i-rLjR A p (T]f is the refractive index of the solution E(X) = at fluorescence wavelength A) is neglected since T=tTq*' (6) Vlf SUR(X)dX AJ2j is small compared to 477 and at high con• centration the fluorescence quantum efficiency is low. SY(X) and SlR(X) are related to the measured
The fluorescence quantum distribution ^(A) is quantities Sm(X) and SmR(X) by eqs. (1) and (2). defined as the ratio of total intrinsic fluorescence The fluorescence anisotropy r(X) is defined by [18,19] i—i—i—|—i—i—i—i—|—i—i—i—i—|—r
m_ £"(*)-£x(*) n 1 £„(X) + 2£±(X)
i; 5I,n(^) + 25I,,(X)'
Eu and • are the fluorescence quantum distri• butions for parallel and perpendicular oriented polarizers, respectively. SM is the intrinsic fluo• rescence signal for parallel oriented polarizers and
Sj ± is the intrinsic fluorescence signal for per• pendicular oriented polarizers. If no molecular reorientation of the excited molecules occurs within the fluorescence lifetime rF, then the ani- sotropy is r = 0.4 for parallel orientation of the absorption and emission transition dipole mo• ment, and r = — 0.2 for perpendicular orientation of the absorption and emission dipole moment [19,20]. In case of fast reorientation of the excited molecules within the fluorescence lifetime, Tf, it is r = 0. At high dye concentration fast energy trans• fer [14,12,9] depolarizes the fluorescence emission (r —> 0) even in highly viscous solvents. If fluo• rescence anisotropy is present, it is necessary to use two polarizers under an angle of 54.74° (see WAVELENGTH X [nm] above) in order to get rid of orientationai effects Fig. 2. Fluorescence quantum distribution E(\) of rhodamine (otherwise eq. (3) is inexact, since SY(X) becomes 6G in methanol. Solid curves, measured E(\) distributions for dependent on observation direction). various concentrations. Dashed curves, calculated monomelic
contributions EM(X, C).
4. Results tion region (C> 0.1 mol/1). The short-wavelength The measured fluorescence quantum distribu• part of the spectra continues to decrease with tions E(X) of rhodamine 6G in methanol and of concentration while the long-wavelength part re• rhodamine 6G in water are shown by the solid mains practically unchanged. The concentration curves in figs. 2 and 3, respectively. The fluo• dependence of the fluorescence lifetime rF of rescence quantum efficiencies qF are shown in fig. rhodamine 6G in methanol was measured recently 4 for rhodamine 6G in methanol and in fig. 5 for with a streak-camera [9] and the results are in• rhodamine 6G in water (triangles). cluded in fig. 4 (open circles, dashed curve gives In case of rhodamine 6G in methanol, E(X) least-square fit). In [9] it was shown that the and qF are independent of concentration up to decrease of Tf and qF is due to Forster-type about 5 X 10 ~3 mol/1. At higher concentration excitation transfer from monomers to weakly fluo•
E(X) and qF decrease strongly with increasing rescing closely spaced pairs [13] which are formed concentration. For C > 0.1 mol/1 the quantum randomly at high concentration. efficiency levels off to a limiting value of about In case of rhodamine 6G in water the fluo•
4 qF — 6.5x10" at 0.62 mol/1. The fluorescence rescence quantum distribution E(X) and the fluo•
spectra change their shape in the high-concentra- rescence quantum efficiency qF . are practically i i i | i i i i | i i i i | r T 1—i—q 1 1—i—rj 1 1—r
\
CONCENTRATION C [mol/l]
WAVELENGTH X [ nm ] Fig. 4. Fluorescence quantum efficiency q¥ versus concentra• tion C for rhodamine 6G in methanol (triangles are experimen• Fig. 3. Fluorescence quantum distribution E(X) of rhodamine tal values, the solid curve is calculated by use of eq. (10)).
Fluorescence lifetimes Tf (open circles and dashed line) are 6G in H20. Solid curves, measured E(X) distributions for various concentrations. Dashed curves, calculated monomelic included (from [9]).
contributions EM(\,C). Dashed-dotted curve, extracted
dimer fluorescence quantum distribution ED(X) = ED(X,
xD->l). rhodamine 6G in methanol. Complete fluo• rescence depolarization r(C) = 0 is observed for
all concentrations (10 ~5 mol/1 < C < 0.62 mol/1) constant for C<5xl0"5 mol/1. Above 10"3 within the experimental accuracy. At low con•
-3 mol/1 qF decreases strongly and E(X) decreases centrations C<5xl0 mol/1 the fluorescence more severely at short wavelengths than at long lifetime (TF = 3.9 ns) is long compared to the wavelengths. At the solubility limit of 0.027 mol/1 molecular reorientation time (ror « 100 ps [20-22])
the fluorescence quantum efficiency is q¥ ^ 4.5 X leading to an anisotropy factor of r = 0. In a
10 ~3. The fluorescence lifetime was measured with medium concentration region (2 X 10"2 mol/1 <
a streak camera and found to be Tf = 150 ps at C<0.2 mol/1) Tf becomes comparable to ror or
Cmax = 0.027 mol/1 (arrangement similar to fig. 1 shorter than ror. The Forster-type excitation en•
of ref. [9]). The decrease of qF and E(X) is ergy transfer from monomer to monomer de• thought to be due to Forster-type transfer of polarizes the fluorescence signal. At high con• excitation energy from monomers to weakly fluo• centrations (C > 0.2 mol/1) the closely-spaced pair rescing stable ground-state dimers [9,13]. The short fluorescence dominates (rF « Td < ror). In this re• fluorescence lifetime excludes triplet contributions gion the average distance between closely spaced to the fluorescence signal. pairs becomes less than the Forster-transfer radius
The fluorescence anisotropy is analyzed for R0 (see [9]) and the excitation energy transfer rate aqueous rhodamine 6G (monomers and ground-
state dimers) solutions. The mole fraction xD of molecules forming these dimers was determined as a function of concentration by analyzing the ab• sorption changes with concentration [13] and the result is depicted in fig. 6. The fluorescence quantum distribution E(X) id 10 and the fluorescence quantum efficiency qF may be separated into monomelic and dimeric parts:
E(\9 C) = EM(\, C) + £D(A, C), (8)
< qAC)=qM{C) + q»(C), (9) ZD O EM(X, C) and qM(C) represent the fluorescence
part emitted from monomers, while EU(X) and qu describe the fluorescence part emitted from dimers (ground-state dimers or closely-spaced pairs). O ZD The decrease of monomer fluorescence quan•
tum efficiency qM(C) and fluorescence quantum
distribution EM(X, C) is caused by Forster-type energy transfer (electric dipole-electric dipole in• CONCENTRATION C [mol/l] teraction) to dimers (quenching centers, see [9]) and is given by [9] Fig. 5. Fluorescence quantum efficiency q¥ of rhodamine 6G in H20. Triangles are experimental values. The curve is calcu• lated by use of eq. (10). The structure formula of rhodamine ?F(0) C (10) 6G is inserted. <7M( ) = (1 -*D)" 2 ' l+xD(C/C0) between closely spaced pairs is faster than the (11) fluorescence decay rate resulting in depolarized
emission. where C0 is the critical transfer concentration. In In case of rhodamine 6G in water the fluo• eq. (10) energy back-transfer from dimers to rescence lifetime at the highest possible concentra• monomers is neglected since the relaxed excited tion (C = 0.027 mol/1) is about 150 ps. The dimer states lie below the relaxed excited mono• molecular reorientation time is ror = 170 ps [22]. mer states (overlap integral between dimer fluo• At low concentrations fluorescence depolarization rescence spectrum and monomer absorption spec•
occurs because of Tf > ror. Towards the solubility trum is reduced as is seen in figs. 2, 3, 7 and 8, for limit the depolarization is enhanced by excitation inclusion of energy back-transfer see [9]).
energy migration. The C0-values of rhodamine 6G in methanol and in water are found by fitting eq. (10) to the
experimental #F-values at C = 0.1 mol/1 and C =
5. Monomelic and dimeric contributions to E(X) 0.02 mol/1, respectively. The results are C0 =
3 and qv 4.5 X 10" mol/1 (transfer radius R0 =
1/3 [3/47r7VAC0] = 4.45 nm) in case of solvent
3 In the following E(X) and qF are separated methanol and C0 = 5.6 X 10" mol/1 (JR0 = 4.14 into monomelic and dimeric contributions. As nm) for the aqueous solution. analyzed in [13] two components are formed at The solid curves in figs. 4 and 5 present the
elevated concentrations in methanolic rhodamine theoretical qM(C) curves of eq. (10). In case of
6G (monomers and closely spaced pairs) and rhodamine 6G in methanol, qM(C) continues to I I I | 1 1 I I | 1 1 I I |
10"5 10"A 10'3 10'2 10~1 CONCENTRATION C [mol/l]
6. Fraction xD of molecules in dimer state (from [13]). Curve 1: rhodamine 6G in water (xu/2 is mole fraction of stable
ground-state dimers). Curve 2: rhodamine 6G in methanol (xD/2 is mole fraction of closely spaced pairs).
i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—| i i i r
WAVELENGTH X [ nm ]
7. Absorption and stimulated emission cross-section spectra a of monomers and closely spaced pairs of rhodamine 6G in
methanol. Curve 1, aabsM(X); curve 2, aabsD(A); curve 3, oemM(\); curve 4, cremD(X). decrease strongly for C> 0.2 mol/1 while the ex• tribution represents the closely spaced pair fluo• perimental #F-values level off to a slight decrease. rescence quantum distribution £D(A) = 2sD(A,
The difference between the experimental qF-val• xD -> 1). This dimer fluorescence distribution is
1 ues and the theoretical qM curve indicates the spectrally broader (A£D — 3500 cm" FWHM) dimer contribution q^ = qF — qM (eq. (9)). For than the monomer fluorescence distribution (A£M rhodamine 6G in water no difference between the ^ 1700 cm-1). The maximum position of the di•
-1 experimental qF points and the theoretical qM mer distribution is shifted about 1000 cm to curve is resolvable within experimental accuracy. lower frequencies. The closely spaced pair fluores•
This fact indicates that up to the solubility limit cence quantum efficiency is qu = JemEr>(X)dX = the fluorescence emitted from dimers is small 8.5 X 10-4. compared to the fluorescence emitted from mono• For the 0.027 molar aqueous rhodamine 6G mers. solution (maximum concentration Cmax, solubility The monomelic contribution to the fluo• limit at room temperature) the monomer fluores• rescence quantum distribution (eq. (11)) is de• cence quantum distribution EM(X) still dominates picted by the dashed curves in figs. 2 and 3 for E(X% especially at short wavelengths. But the rhodamine 6G in methanol and water, respec• dimer contribution ED(X, Cm2LX) = E(X, Cmax) - tively. The differences £D(A,C) = E(X,C) - EM(X, Cmax) is clearly resolved. £D(A, Cmax) is
EM(X, C) represent the fluorescence emission from practically identical to EU(X) = EU(X, xu -> 1) excited dimer states (states are excited either di• since nearly all monomer excitation is transferred rectly by light absorption or indirectly by energy to dimers [qF(Cmax) - qM(Cmax) - 0.0045]. £D(A) transfer from excited monomers). is depicted by the dashed-dotted curve in fig. 3.
For 0.62 molar rhodamine 6G in methanol the The accuracy of EU(X) is somewhat reduced at monomer fluorescence contribution is negligibly the wavelength region of maximum emission be• small and the measured fluorescence quantum dis• cause the difference between two nearly equal quantities has to be formed. EU(X) represents the mine 6G in methanol and of the stable ground- fluorescence emission from excited stable ground- state dimers of rhodamine 6G in water are strongly state dimers. The spectral width of Eu is A£D ^ broadened and shifted to longer wavelengths com•
-1 -1 2500 cm (monomer: Ai>M — 1400 cm ) and the pared to the monomer spectra. The ^emD(X) spec• peak position is shifted about 700 cm-1 to the trum of rhodamine 6G in water is not very accu• long-wavelength side. The dimer fluorescence ef• rate because of the inaccurate determination of
-4 ficiency is qD = JemEu(X)dX — 6X 10 . ED(X) around the emission peak. The total in• tegrated emission cross sections of the monomers and the molecules in dimers are of similar strength 6. Monomelic and dimeric stimulated emission [rhodamine 6G in methanol: cross sections
/ 13 xD -»1) and the monomer and dimer absorption f aem,D(?)d? = 4.2xlO- cm; an( a tne •'em cross-section spectra aabs,M(^) * abs,D(^)> stimulated emission cross-section spectra oemM(X) rhodamine 6G in water: and aemD(X) of the monomers (i = M) and dimers (i = D) may be calculated by use of the formulae -13 / aem,M(?)d* = 4.4xlO cm; [23] •'em \%(\) X%(X) 13 f aem,D(?)d? = 5xl0- cm]. i(X) = (12) 2 8irij|c0TRAD jtf; 8wrj Fc0TRAD i and [24,25] 7. Dimer fluorescence lifetime XdX 8 Jem WTJFC0 The dimer fluorescence lifetimes may be esti• 'rad.i mated from the radiative lifetimes TRADD (eq. (13)) Va f Ei(X) X4d\ and the quantum efficiencies qu by use of the em relation X (13) ^D = ^rad,D- (14) •'abs <*abs,i(M The experimental results give rD = 3.9 ps for 4 c0 is the vacuum hght velocity and rjA the average rhodamine 6G in methanol (qD = 8.5 X 10 ~ , T = refractive index in the S0-S1 absorption band. The rad,D 4.6 ns) and Td = 2.2 ps for rhodamine 6G -4 integrations extend over the S^—S0 fluorescence in water (qu = 6 X 10 , rradD = 3.6 ns). In case band [^(X)] and the S0-S1 absorption band of rhodamine 6G in methanol the measured fluo• [aabsi(\)]. The relation between the cross section a rescence lifetime Tf at 0.4 mol/1 (fig. 4, [9]) agrees and the often used molar decadic coefficient c is within the error bars with Td. In case of rhoda• 3 -1 e = aJVA/[1000 cm ln(10)] (dimension: mole mine 6G in water the monomer fluorescence still cm-1). dominates at the solubility limit (C = 0.027 mol/1, The a TF — 150 ps) and Tf remains considerably longer *abs,M(*)> abs,D(*)> proportional to the mole fraction xM = 1 — [13] and [16]. The stimulated emission cross-sec• JCD tion spectra of the closely spaced pairs of rhoda• (eq. (10)) while Tm is independent of this factor. 8. Interpretation of dimer spectra between both molecules. The Srstate lowering is shown a little bit larger than the S0-state lowering The absorption and emission cross-section to account for the long-wavelength shift of the spectra may be qualitatively interpreted with the dimer absorption cross-section spectra. The en• aid of the configuration diagrams of fig. 9. Figure ergy levels of both molecules in the dimer are 9a represents the potential energy surface diagram somewhat different (exciton splitting [26-28]) due (energy versus intra-molecular configuration coor• to mutual interaction (Pauli exclusion principle). dinate) for a monomer. The S0 and the S: band is The Franck-Condon shifts, Am and ^D2, of both shown. The dominant vibrational breathing mode molecules are assumed to be larger than the in the S0 (v" = l) and the Sl band (i/ = l) is Franck-Condon shift AM of an undisturbed indicated (vibrational energy — 1500 cm-1). The monomer. hatched areas mark the regions of Franck-Con• The enlarged Franck-Condon shifts allow to don overlap for the absorption and the emission. explain the observed shape of the dimer absorp• The Franck-Condon shift AM is responsible for tion and emission cross-section spectra of figs. 7 the vibronic structure of the monomer absorption and 8 [13,26,29,30]: (i) In the absorption process and emission spectrum [12,14,16]. In the absorp• the S0(v" = 0) -> S^v' = 1) transition gains im• tion process the S0(i>" = 0) -> S^i/ = 0) portance (enlarged Franck-Condon overlap in• Franck-Condon factor dominates over the S0(v" tegral, see hatched regions ////) compared to = 0) -> S1(y' = 1) Franck-Condon factor. For the the S0(*/' = 0) -» S^v' = 0) transition which emission the S^v' = 0) -> S0(v" = 0) transition dominates for the monomers. In case of rhoda• / dominates over the S1(u = 0) S0(i/' = 1) transi• mine 6G in water (stable ground-state dimer) the tion. S0(v" = 0) -> Si(v' = 1) absorption becomes larger The configuration diagrams of the two dye than the S0(v" = 0) -» S^v' = 0) absorption (ab• molecules in a dimer (stable ground-state dimer or sorption peaks at 500 nm, fig. 8). For rhodamine closely spaced pair) are illustrated in fig. 9b. Com• 6G in methanol (closely spaced pairs) the pared to the monomer the potential energy surfaces Franck-condon overlap integrals are approxi• // are somewhat lowered to indicate the binding mately equal for the S0(t; = 0) -> S^v' = 1) and (a) (b) Fig. 9. Schematic configuration coordinate diagrams for a monomer (a), and for the two dye molecules forming a dimer (b). The vertical coordinate is energy, the horizontal coordinate is an intra-molecular distance. Parameters are explained in the text. the S0(v" = 0) -> SX(V = 0) transition resulting in water stable ground-state dimers are formed (EB the double peaked absorption spectrum of fig. 7. >kT). The solubility is limited to C < 0.027 (ii) For the emission process the enlarged mol/1. In both solvents the fluorescence quantum Franck-Condon shift (Am, AU2) leads to an ex• efficiency is quenched by Forster-type energy tended long-wavelength Franck-Condon overlap transfer to weakly fluorescing dimers (closely (see hatched regions \\\\). Consequently the spaced pairs in case of methanol, ground-state stable ground-state dimer stimulated emission dimers in case of water). From the measured cross-section spectrum (fig. 8, rhodamine 6G in fluorescence spectra the monomeric and dimeric water) and the closely spaced pair stimulated contributions to the fluorescence quantum distri• emission cross-section spectrum (fig. 7, rhodamine bution and to the fluorescence quantum efficiency 6G in methanol) extend further to the long-wave• were resolved and the stimulated emission cross- length region than the monomer spectra. section spectra of the dimers were determined. The absorption and emission spectra of figs. 7 The difference between the monomeric and di• and 8 give the overall behaviour of both molecules meric absorption and stimulated emission cross- in the dimer (average over both molecules in di• section spectra indicates an enlarged mers). Different Franck-Condon shifts for mono• Franck-Condon shift of the dimers compared to mers and dimers were previously assumed for the the monomers. interpretation of dimer spectra in [13,26,29,30]. The applied qualitative dimer model of fig. 9b is consistent with (i) the approximately constant en• Acknowledgements ergy separation between absorption peak and vibronic shoulder of the monomer, between the The authors thank the Deutsche Forschungs- two absorption peaks in the closely spaced pairs, gemeinschaft for financial support and the Rech- and between the long-wavelength absorption enzentrum of the University for computer time shoulder and the short-wavelength absorption peak put at their disposal. of the stable ground-state dimers, (ii) the long- wavelength extension of the dimer fluorescence compared to the monomer fluorescence, (hi) the References strong total integrated dimer emission cross sec• tion, and (iv) the possibility to observe fluores• [1] Th. Forster and E. Konig, Zeitschrift fiir Elektrochemie cence emission despite the short dimer fluores• 61 (1957) 344. cence lifetime (electric dipole allowed transition [2] G.S. Levinson, W.T. Simpson and W. Curtis, J. 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