- Email: [email protected]
Photoinduced dichroism and vibronic relaxation of rhodamine dyes
Volume 44, numbci 3
PHOTOINDUCED
CHEMICAL PHYSICS LETTERS
DICHROlSM
15 Dcccmber 1976
AND VIBRONIC RELAXATION OF RHODAMINE DYES
A. PENZKOFER and W. FALKENSTEIN Physik-Department der Technischen Munich, Germany
Univenitdt Munchen,
Received 2 September 1976
The absorption anisotropy of rhodaminc dye molecules h: various solvents is measured on a picosecond time SC&. The dye solutions are partially bleached with pump pulses and the dichroism is measured with detaycd perpcndicularIy polarized probe pulses. The cxpcrimcntal results are compared with the linear oscillator model.
The absorption spectra of dye solutions measured cules results that is monitored by observing the degree with convcntrcnal spectral photometers are indepenof polarization of the fluorescence light. OnIy dyes dent of the polarization of the incident light. The sohrdissolved in highly viscous solvents can be investigated tions show isotropic behavior since all molecular orienby this technique since otherwise rotational reorientatations have the same probability. Absorption anisotion within the fluorescence decay time disturbs the tropy is observed for dyes embedded in stretched foils induced anisotropy. The concentration of the dissolved 111 and for dye solutions that are subjected to hydrodyes has to be kept very low (5 low5 M/Q)to eliminate dynamic [2] or electric fields [3]. The acting forces energy transfer from the excited molecules to (differpartially orient the molecules. The dichroism indicates ently oriented) unexcited molecules within the fluorcsthat the dye molecules have different absorption cross cence lifetime. sections ul, and u1 for light polarized parallel and perThe hght absorption of the dyes is caused by elecpendicular to the molecular axis, respectively. Since tric dipole transitions. A classical description of the the orientation of the molecules is not complete [4] absorption process leads to the linear oscillator model the measured dichroism D = (cx,,-cu,)/(a, + CYJgives [S]. This model predicts a molecular dichroism of only a qualitative indication of the molecular dichroism Dm = 1 and a fluorescence polarization ofP=O.S for + uJ crUand CK~ indicate the abSO-St transitions in dyes. The measured dichroism Dm = (On-a,)/(~, sorption coefficients for light polarized parallel and for dyed films was found to be D 5 0.8. The molecules perpendicular to the orienting direction. The anisotropy are not completely aligned so that no conclusion about of dye molecules was studied extensively by measuring the true value of D, can be drawn. The limiting values the degree of polarization of fluorescence light 15-81. of fluorescence polarization (called fundamental polarIn most cases the molecules were excited by linear ization) in highly viscous sohents at very Iow concenpolarized light and the polarization P = (Is-l~)/(la+I~)trations are found to be PO 5 0.46. They do not reach of the fluorescence light emitted under 90” to the the theoretical value of PO = 0.5(for a discussion see propagation direction of the exciting light was measbelow). ured. I, and 1, are the components of the fluorescence In this letter we describe a new technique for the light polarized parallel and perpendicular to the polarinvestigation of moIccular dichroism. An intense picoization of the exciting light. The dye molecules with second light pulse bleaches the dye partially and gcntheir tpnsition moments parallel to the polarization erates an anisotropic orientation of the molecules. direction of the exciting light are preferentially exA weak probe beam polarized perpendicular to the cited. An anisotropic distribution of the excited molestrong exciting pulse monitors the absorption anisotropy I 547
Volume 44, number 3
15 December 1976
CIIEMICAL PHYSICS LETTERS
Additionally
to the determination
this method
allows within
a certain
of the drcflroism time range to
measure the vibronic relaxation r of the excited molecules by scanning the probe beam througfi a delay range of a few tens of picoscconds. The rotational redistribution lies in the range between 200 ps and several nanoseconds for our solutions [9] and does not disturb the determination of II,,, and 7. The molecular dichroism can be measured for dyes in any solvent. Higher dye concentrations can bc used in our experiments than for the fluorescence polarization technique, since the concentration dependent energy transfer to unexcited molecules is negligible on a picosecond time scale. We determined tire absorption anisotropy of rhodamine dyes in several solvents. WC restricted our measurements to the determinatron of the dichroism of the SO-St transition at a fixed frequency. The described technique can be cxtcnded to the measurcment of drchroitic spectra by applying an intense monochromatic picosecond pump pulse and a weak picosecond probing continuum [lo]. The absorption of polarized light by dye molecules depends on the angfc 0 between the direction of the electrical dipole transition moment and the dlrcctlon of the polarization vector of the light wave. The absorption cross section for an ideal linear oscillator 1s given by o(O) = u cos2f?. Tfre conventionally measured absorption cross section for dye solutions is obtained by integration over all orientations of the isotropically distributed molecufcs
cial case. A five-level system gives a rather realistic picture of our dyes (set ref. [I I]). The laser light excites the molccufes from the ground state So to a FranckCondon state in the first excited singlet state St. The mofeculcs decay from the Franck-Condon state to a temporary cqurfrbrium position in the St state with a trmc constant 7. From the first excited singlet state St absorption of laser fight to h&r lying singlet states is taken into account by an excited state absorption cross section uex. For tfre excited state absorption we assume the same brancfling ratio ulex/uIIcx as in the ground state (fluorescence polarization spectra indicate the same orientation of tfle transition moments [I])_ The fluorescence relaxation of molecules in St state to a Franck-Condon level in the SO state occurs m tfrc nanosecond range and does not affect the picosecond measurements. Light propagation tflrough the dye is determined by the following equations: a/,/a2
+ (r~/~) ar,iat
+A,,(0)[N-NI (O,@lI sin0de d@, ar,la2
(1)
+ (PZ/C) ar,pt
7’ u cos20 sin0 dO = u/3 . d For a linear oscillator
it is u,, = u, a1 = 0 and D,,, = 1.
In our measurements we want to determine 0,. We allow u1 # 0 in our calculations and use the ansatz u(0) = ull cos28 + u, sin28 (see below). For this situation the conventional transmission measurement leads to oM = 4 (us + 20,). For on # uI the pump pulse induces an anisotropy to the orientational distribution of the molecules remaining in the ground state. The absorption of the probe beam polarized perpendicular to the pump beam depends on the ratio a,/~,, and therefore on D,. To describe the absorption processes we have to introduce a model for the relevant transitions in our spc548
a~,(o,~))iar
x [Wo,44
=(I/~~vL)c[~(e)IL+B(o,~))Iri -N2(o,e4i
-[~,,(e)zL+g,(e,~)z~iN2(e,~)} - iv2(e,w7
- w20w
-N2ihor.
(4)
The initial conditions arc I&,r,z=
-(r/ro)*] ,
0) =10Lexi,[-(t/r0)2
(5)
I&. r, z =O) = IoP exp{-f(t-t~)/r~12-(‘/‘~)2)9
(6)
N, (t-m/c
(7)
= -*,
r, z, 8, Q) = iv)
Ni!(t-?fZ/C=-~,r,z,O,~)=O. The following abbreviations
(8) are used in eqs. (l)-(4):
A (0) = uII cos*O + u1 sin20 , A,(O)=
oll,cos20
+
= ul,cu sin*0 cos2@+ul,,(1
mitted intensities I&‘,r,z’ = r) and lp(t’,r,i = l) are obtained by numerical methods. The encrbn transmissions of the pump pulse TL and the probe pulse T, arc calculated by integrating the transmitted intensitics over space and time and by dividing through the input energies. The energy transmissions TL and ?‘, are determined by the system parameters N, all, uL, ulcx, uLcx, r and T,,~, the pulse parameters IoL, Ioop, and to and the delay time t,,. N is @en by the dye concentration. The absorption parameters erg, uJ1,u,,,__ and Us,,, can be expressed by the parameters ohI = (u,, C 20,)/3, )/3, and n, = (o~-oJ/(o, +oJ = (%x * %,hl = (uIIcx-~Lcx)/(uII,, + uLex). ohI is obtained by absorption measurements at the frequency uL with a spectral photometer. The 15, values were determined by energy transmission measurements of the pump beam at high intensities in ref. [I 1). D,, wil1 be determined in this letter by measuring the energy transmission ratio T,/TI_ and by comparison with calculated curves. T has been determined with two different techniques in ref. [ 111. In this letter an upper limit of T can be determined from the depcndcncl: of TLIT~ on the delay time tl, at fixed peak intensities foL and lop _ The experimental set-up is depicted in frg. I.
%cx
uLlcxsin2U,
B(O, @) = u,, sm20 cos*f#~+ u1 (1 - sin28 cos2G) , B,,(O,@)
15 December 1976
CXEMICAL PHYSICS LET-I-ERS
Volume 44. number 3
- sin20 cos*@),
0 IoL and IoF arc the peak Intensities of the incident picosecond pump pulse and the perpendicularly polar&d probe pulse, respcctivcly. The temporal and spatial shape of the pulses is assumed to be gaussian. 2to and r. arc the l/e values of the pulse duration and the beam radius. t, is the delay time between pump beam and probe beam. LJ~is the frequency of the laser pulses (both pulses have the same frequency). n is the refractive index of the dye solution. N is the total number density of dyo molecules. N, (O,@) and N2(0, @) describe the density of molecules in the ground state and the excited Franck-Condon state, respectively. 8 IS the angle between the transition moment of the molcculc and the polarization of the pump pulse. @IS the azimuthal angle of the transition moment relative to the polarization of the probe pulse. The orientational redistribution of the molecules by rotational brownian motion is taken into account in a phenomcnological manner by the last terms of eqs. (3) and (4). At !arge delay times the rotational rcdistnbution increases the transmission of the probe beam. The transformation z’ = z and t’ = t - nz/c brings the equation system to a simpler form. Solutions for the trans-
WP
m P
s
BS
BS
5+---+-q
Ci=H
-!-F
R
PO3
PO2
PO1
Fig. 1. Experimental set-up for the mcasuremznt of dichroirm. HI, ADP crystal for second harmonic generation; F. filters; BC, beam dividing cubes; WP, A/2 waveplate; DL. variable delay line; L, tenses, Uhf. 50% mirror; DC, two-photon fluorescing dye for puke duration measuremest; CA. cancra; OhlA, optical multichannel analyzer syQem; BS, beam splitters; R, rutile crystal for intensity determination; S. sample; P. polAzer; PD14. photodetectors. tight pokization is indicated by + and -c.
549
Volume 44, number
3
CHEMICAL
A mode-locked Nd-glass laser [ 121 was used for the generation of trains of picosecond light pulses. An electro-optical shutter selects a single pulse from the beginning of the pulse train and a subsequent Nd-glass amplifier increases the energy of the pulse to approximately 3 mJ. The light pulses (X = 1.06 pm) have a of duration of At = 5 ps (fwhm) and a bandwidth Ai3’= 3 cm- 1 (fwhm). Using an ADP crystal the pulses are frequency doubled w& a conversion efficicncy of = 20%. The fundamental light pulse is absorbed by the filter F following the ADP crystal. Two green light pulses are gcncratcd with the help of a 50% beam dividing cube. One pulse travels through a delay line and is reduced in intensity by a factor of 16 with an appropriate filter F. This puisc serves as the probe pulse. The other pulse acts as intense pump pulse. Its polarization is rotated by 90” with a X/2 wave plate. Part of the pulse energy is used for the determination of the pulse duration in a two-photon fluorescence system. 9, IO-dlphenylanthracene (!Om3 M/!2) acts as two-photon absorber. The two pulses are collimated in a second 50% beam dividing cube. The pump and probe beam are focused into the rhodaminc dye samples. The peak intensity of the pump pulse is determined by the energy transmission through a two-photon absorbing rutile crystal [ 131. The delayed probe pulse travels at exactly the same path through the dye sample as the pump pulse. Behind the sample, the pulses arc separated with a polarizer_ The energy transmission of the pump pulse and the perpendicularly polarized probe pulse is measured with photodetectors. Rhodamine 6G solutions in water, ethanol, cthylcne
glycol and glycerol and rhodamine B solutions in water, ethanol and glycerol were investigated at room temperature. The rhodamine 6G concentrations were 10m5 M/P. Dye cells of 2 cm length were used. For the rhodamine B solutions concentrations of 10S4 M/Q and cell length of 0.5 cm were applied. Energy transmission ratios T,,/T,_ versus the delay time tD were measured for all dye solutions. In fig. 2 the results for rhodamine 6G dissolved in water are shown as an example. The peak intensity of the pump beam was loL - 1 X log W/cm*. The pulse duration was tp a 3.7 ps (fwhm). In fig. 2 the curves are calculated for differer.t relaxation times T and for D, = 1, D, = 0.93, and D, = 0.85. For T 2 t,/3 a distinct peak in the curves occurs at tD * t,/2. The absorption 550
PHYSICS LETTCKS
15 Dcccmbcr
PROBE
PULSE
DELAY
llME
1976
tDCp53
Fig. 2. Normalized cncrgy transmission of pcrpcndicularly polarized probe pulws versus delay trme measured for rhodamine 6G dissolved in water. Dye concentration lOA5 M/Q, sample length 2 cm. The circles rcprcscnt cxpcrimcntal data. The input parameters arc pulse duration tp = 3.7 ps, peak mten\itics l,-,L = 10’ W/cm2 and lop = 6.3 X 10’ W/cm2. The curves arc calculated for D,, = 1, D, = 0.93. D, = 0.85, for T = 4 ps (a), 7 = 2 PF (b), 7 = 1 ps (c), T = 0.5 ps (d). 7 = 0 ps (c), and for 70r = 230 ps [9]. of the probe beam increases when the dye molecules relax from the excited Franck-Condon state. The shape of the curves allows the determination of 7 for T > t,/3. In our experiments no peak was found for T,/T,(t,). The relaxation time T is thcrcfore expected to be shorter than 1.5 ps. The absolute value of the transmission ratio is influenced by the relaxation time T and the molecular dichroism D,. The true value of T has to be determined by a method that IS insensitive ofD,. Two such methods were descrlbcd in ref. [ 111. Using the T values of ref. [ 111, the molecular dichroism values D, are determined from the absolute transmission ratio. For our example in fig. 2 it is T = 0.7 f 0.3 ps and we find D, = 0.93 + 0.03. The energy transmission ratio T,/TL depends on the peak intensities of the pump and probe beam as shown in fig. 3 for rhodamine GG dissolved in water (delay time tD = 7 ps). The curves are calculated for T = 0.7 ps and D, = 1,0.93, and 0.85. At low intcnsities the pump beam does not bleach the dye and pump and probe beam suffer the same linear absorption (T,/T + 1). In the intensity range around log W/cm li the dye solution is partially bleached by the intense pump beam. The transmission of the probe beam depends on the value of D,. For values of D,
Volume 44, number
CHEMICAL
3
PHYSICS LLXTERS
15 December
1976
high mtensities the pump pulse promotes a11dye molecules to an excited state and pump and probe beams pass through the sample with practicaIIy no absorption. The transmission T,/TL approaches the value of 1 for all ~1~2s of D ,,,. It is readily seen in fig. 3 that our experimental points are well accounted for by a calculated curve with D, = 0.93. In table 1 our experimental results for D, are
summarized together with the parameters ahf, o,,_ hi, 7Or,and T. The molecular dichroism is found to bi in
q
,
,
, ,
,
,
,
,] 10'0
109 PUMP
PULSE
PEAK
INTENSITY
I,LWk~l
Fig. 3. Intensity dcpcndent energy transmission of pcrpendicularly polaru.cd probe pukes through a rhodaminc 6G solution in water (lo-’ M/Q, I = 2 cm). The circles represent cxpcrimcntal data. The laser parameters arc ip - 3.7 ps and IoLjlop = 16. The curves .lrc calculated for 7 = 0.7 ps Ill ] and rol = 230 ps 191.
near one (uI < u,,) the pump pulse preferentially cxcites molecules onented under a small angle 0 to the pump pulse polarization. The perpendicularly oriented molecules remain in the ground state and absorb the delayed probe beam. The probe pulse is stronger absorbed than the pump pulse. For small values of D,, the pump pulses also excite molecules oriented pcrpendlcular to the pump polarization. The delayed probe beam suffers less absorption than the pump beam since the molecules are already excited when the probe beam pdsscs through Table 1 Solution
the sample.
At very
the range between 0.90 and 0.95. The theoretical value of Din = 1 for the Iincar oscillator model is not found experimentally. This result is in agreement with the fluoresccncc poIarization measurements for very diluted rhodaminc GG and rhodamine B solutions in glycerol [14I (PO = 0.44) and Plexiglas [ 151 (PO = 0.46). Deviations from the linear oscillator model are expected fur symmetric molecules [5], for overlapping absorption bands with differently oriented transition moments [6], for molecules that execute deformation [6] or torsional vibrations [16], and for transitions that involve magnetic dipole and electric quadrupole transitions [S]. The investigated rhodamine molecules are asymmetric (Cl), so the symmetry of the molecules cannot cxplain the reduced D, and P values. At the wavcIength of the laser pulses (P; = 18 910 cm-l) there is onIy one electronic absorption band expected. The studied transition is allowed for electric dipole transitions; contributions to the absorption from magnetic dipole and electric quadrupole transitions arc unlikely. Deformational and torsional vibrations seem to be the most likely process that causes the deviation from the linear oscillator model.
---_---_
-Cont. W/Q)
oM (cm2
rhodamine 6G in water ethanol ethylene glycol glycerol
1O-s 1o-5 lo-5 10-s
3.7 4.2 3.8 3.5
5.9 5.9 IO 4.8
rbodaminc B in Wilta ethanol glycerol
1o-4 1O-4 1o-4
1.5 1.6 1.0
5.7 5.3 4.4
X
‘F (PSI
Dill
230 270 2iloo > 2000
0.7 0.7 0.8 0.8
0.93 0.95 0.94 0.92
230 270 > 2000
0.9 0.9 0.8
0.90 k 0.03 0.93 * 0.03 0.93 r 0.05
Tar (es)
10r6)
,
-
r 0.03 :‘-0.03 k 0.03 k 0.03
551
Volume 44, number
CHEMICAL
3
The molecules in the ground state populate vibrational states wthin an energy range of Ah = kT * 200 cm-l. In the absorption process, transitions from various vlbrational levels in the So state to vibrational Franck-Condon levels in the S1 state are involved. The orientation of the transition moments for these various vibronic transitions seem to be different. Assumrng a spread A0 of the orientation angles 13around 3 mean value 0, and using the linear oscdlator model one calculates by use of a Taylor expansion (o(0)) = o(cos20) = a(cos2(&,
+ Ad)>
= u [( 1 - ((AfI)2)) cos20g + ((A0)*) sin2U0 ] . This formula is identical with the ansatx used in our calculations {u,, = ~(1 -<(A0)2>), u, = u<(AO)~>). The measured value ofD,,, = 0.93 is equal to uI = u( 1-D,,)/2 = 0.0357 and corresponds to an average angular spread of the transltion moments A0 = [<(A0)2>] -U2 = 0.19 = IO’. This value i.-,in agreement with results of fluorescence polarization measurements [5,151. In conclusion we want to emphasize that we have introduced a new technique to determmc the absorption amsotropy of dye solutions. In contrast to the common fluorescence polarlzrttion technique our method is not linnted to highly viscous solvents and low solute concentrations. The measured dichroism ~3s found to be lower than the theoretical value for a linear oscillator model. This behavior IS explamcd by 3ssu:ning differently oriented transition moments for the transitions from the thermal equilibrium states in the ground state to the respective S, states,
552
PIIYSICS
LETTERS
15 Deccmbcr 1976
The authors are very indebted to Professor W. Kaiser nnd to Drs. A. Laubercau and J-1’. Heritage for many valuable discussions.
‘References [I] 11. Jakobs and H. Kuhn, Z. Elcktrocbcm. 66 (1962) 46. [ 21 P.R. Callis and N. Davidson, Rlopolymcrr 7 (1969) 335. 131 E.D. Badly and 13.R. Jennings. Appl. Opt. 11 (1972) 527. [4 1 K.R. Popov. Opt. Spcctry. 39 (1975) 285. C.C. Rott snd T. Kurucsev. J. Chem. Sot. I~areday Trans. Ii 71 (1975) 749. [5 J P-1’. I’cofilov, The pl~ys~c,d basis of polnrizcd cmis\ion (Conwltants I%urcau, New York, 1961). [6] I‘. Dixr and M. Ileld, Angcw. Chcm. 72 (1960) 287. [ 7 ] G. Webrr, in. I’luorcscencc and phosphorcscencc analy& cd. D.hI. Ifcrculcs (Interscicncc, New York, 1966) p. 217. 181 AC. Albrccht, J. hlol. Spectry. 6 (1961) 84. [9[ T.J. Clwang and K.B. Ewznthal, Cilcm. Pbyr. Lcttcrs 11 (1971) 368; I1.E. Lcwng. A. von Jcna and hf. Reichcrt, Chem. Phys. Letters 36 (1976) 517; D.W. Plullion, D.J. Kuircnga, and A.E. Sicgman, Appl. P11yc. Lcttcrs 27 (1975) 85. IlO] A. Penlkofcr, A. Laubereau and W. Karscr, Pbys. Rev. Lcttcrs 31 (1973) 863. [ 11 j A. Penzkofcr, W. Palkcnstoin and W. Kaiser, Chcm. Phys. Lcrtcrs 44 (1976) 82. (I 21 A. Lwbercau and IV. Kaiser, Opto-Electronicc 6 (1974) 1. {13] A. Pcrwkofcr and W. Mkcnstcin, Opt. Commun. 17 (1976) 1. [14] G. Webcr. J. Opt. Sot. Am. 46 (1956) 962. [ 151 E. Lafittc. Ann. Phy\. (Paris) 10 (1955) 71. [ 161 A. Jablonskl, Acta Pbys. Polon. 10 (1950) 3.
PHOTOINDUCED
CHEMICAL PHYSICS LETTERS
DICHROlSM
15 Dcccmber 1976
AND VIBRONIC RELAXATION OF RHODAMINE DYES
A. PENZKOFER and W. FALKENSTEIN Physik-Department der Technischen Munich, Germany
Univenitdt Munchen,
Received 2 September 1976
The absorption anisotropy of rhodaminc dye molecules h: various solvents is measured on a picosecond time SC&. The dye solutions are partially bleached with pump pulses and the dichroism is measured with detaycd perpcndicularIy polarized probe pulses. The cxpcrimcntal results are compared with the linear oscillator model.
The absorption spectra of dye solutions measured cules results that is monitored by observing the degree with convcntrcnal spectral photometers are indepenof polarization of the fluorescence light. OnIy dyes dent of the polarization of the incident light. The sohrdissolved in highly viscous solvents can be investigated tions show isotropic behavior since all molecular orienby this technique since otherwise rotational reorientatations have the same probability. Absorption anisotion within the fluorescence decay time disturbs the tropy is observed for dyes embedded in stretched foils induced anisotropy. The concentration of the dissolved 111 and for dye solutions that are subjected to hydrodyes has to be kept very low (5 low5 M/Q)to eliminate dynamic [2] or electric fields [3]. The acting forces energy transfer from the excited molecules to (differpartially orient the molecules. The dichroism indicates ently oriented) unexcited molecules within the fluorcsthat the dye molecules have different absorption cross cence lifetime. sections ul, and u1 for light polarized parallel and perThe hght absorption of the dyes is caused by elecpendicular to the molecular axis, respectively. Since tric dipole transitions. A classical description of the the orientation of the molecules is not complete [4] absorption process leads to the linear oscillator model the measured dichroism D = (cx,,-cu,)/(a, + CYJgives [S]. This model predicts a molecular dichroism of only a qualitative indication of the molecular dichroism Dm = 1 and a fluorescence polarization ofP=O.S for + uJ crUand CK~ indicate the abSO-St transitions in dyes. The measured dichroism Dm = (On-a,)/(~, sorption coefficients for light polarized parallel and for dyed films was found to be D 5 0.8. The molecules perpendicular to the orienting direction. The anisotropy are not completely aligned so that no conclusion about of dye molecules was studied extensively by measuring the true value of D, can be drawn. The limiting values the degree of polarization of fluorescence light 15-81. of fluorescence polarization (called fundamental polarIn most cases the molecules were excited by linear ization) in highly viscous sohents at very Iow concenpolarized light and the polarization P = (Is-l~)/(la+I~)trations are found to be PO 5 0.46. They do not reach of the fluorescence light emitted under 90” to the the theoretical value of PO = 0.5(for a discussion see propagation direction of the exciting light was measbelow). ured. I, and 1, are the components of the fluorescence In this letter we describe a new technique for the light polarized parallel and perpendicular to the polarinvestigation of moIccular dichroism. An intense picoization of the exciting light. The dye molecules with second light pulse bleaches the dye partially and gcntheir tpnsition moments parallel to the polarization erates an anisotropic orientation of the molecules. direction of the exciting light are preferentially exA weak probe beam polarized perpendicular to the cited. An anisotropic distribution of the excited molestrong exciting pulse monitors the absorption anisotropy I 547
Volume 44, number 3
15 December 1976
CIIEMICAL PHYSICS LETTERS
Additionally
to the determination
this method
allows within
a certain
of the drcflroism time range to
measure the vibronic relaxation r of the excited molecules by scanning the probe beam througfi a delay range of a few tens of picoscconds. The rotational redistribution lies in the range between 200 ps and several nanoseconds for our solutions [9] and does not disturb the determination of II,,, and 7. The molecular dichroism can be measured for dyes in any solvent. Higher dye concentrations can bc used in our experiments than for the fluorescence polarization technique, since the concentration dependent energy transfer to unexcited molecules is negligible on a picosecond time scale. We determined tire absorption anisotropy of rhodamine dyes in several solvents. WC restricted our measurements to the determinatron of the dichroism of the SO-St transition at a fixed frequency. The described technique can be cxtcnded to the measurcment of drchroitic spectra by applying an intense monochromatic picosecond pump pulse and a weak picosecond probing continuum [lo]. The absorption of polarized light by dye molecules depends on the angfc 0 between the direction of the electrical dipole transition moment and the dlrcctlon of the polarization vector of the light wave. The absorption cross section for an ideal linear oscillator 1s given by o(O) = u cos2f?. Tfre conventionally measured absorption cross section for dye solutions is obtained by integration over all orientations of the isotropically distributed molecufcs
cial case. A five-level system gives a rather realistic picture of our dyes (set ref. [I I]). The laser light excites the molccufes from the ground state So to a FranckCondon state in the first excited singlet state St. The mofeculcs decay from the Franck-Condon state to a temporary cqurfrbrium position in the St state with a trmc constant 7. From the first excited singlet state St absorption of laser fight to h&r lying singlet states is taken into account by an excited state absorption cross section uex. For tfre excited state absorption we assume the same brancfling ratio ulex/uIIcx as in the ground state (fluorescence polarization spectra indicate the same orientation of tfle transition moments [I])_ The fluorescence relaxation of molecules in St state to a Franck-Condon level in the SO state occurs m tfrc nanosecond range and does not affect the picosecond measurements. Light propagation tflrough the dye is determined by the following equations: a/,/a2
+ (r~/~) ar,iat
+A,,(0)[N-NI (O,@lI sin0de d@, ar,la2
(1)
+ (PZ/C) ar,pt
7’ u cos20 sin0 dO = u/3 . d For a linear oscillator
it is u,, = u, a1 = 0 and D,,, = 1.
In our measurements we want to determine 0,. We allow u1 # 0 in our calculations and use the ansatz u(0) = ull cos28 + u, sin28 (see below). For this situation the conventional transmission measurement leads to oM = 4 (us + 20,). For on # uI the pump pulse induces an anisotropy to the orientational distribution of the molecules remaining in the ground state. The absorption of the probe beam polarized perpendicular to the pump beam depends on the ratio a,/~,, and therefore on D,. To describe the absorption processes we have to introduce a model for the relevant transitions in our spc548
a~,(o,~))iar
x [Wo,44
=(I/~~vL)c[~(e)IL+B(o,~))Iri -N2(o,e4i
-[~,,(e)zL+g,(e,~)z~iN2(e,~)} - iv2(e,w7
- w20w
-N2ihor.
(4)
The initial conditions arc I&,r,z=
-(r/ro)*] ,
0) =10Lexi,[-(t/r0)2
(5)
I&. r, z =O) = IoP exp{-f(t-t~)/r~12-(‘/‘~)2)9
(6)
N, (t-m/c
(7)
= -*,
r, z, 8, Q) = iv)
Ni!(t-?fZ/C=-~,r,z,O,~)=O. The following abbreviations
(8) are used in eqs. (l)-(4):
A (0) = uII cos*O + u1 sin20 , A,(O)=
oll,cos20
+
= ul,cu sin*0 cos2@+ul,,(1
mitted intensities I&‘,r,z’ = r) and lp(t’,r,i = l) are obtained by numerical methods. The encrbn transmissions of the pump pulse TL and the probe pulse T, arc calculated by integrating the transmitted intensitics over space and time and by dividing through the input energies. The energy transmissions TL and ?‘, are determined by the system parameters N, all, uL, ulcx, uLcx, r and T,,~, the pulse parameters IoL, Ioop, and to and the delay time t,,. N is @en by the dye concentration. The absorption parameters erg, uJ1,u,,,__ and Us,,, can be expressed by the parameters ohI = (u,, C 20,)/3, )/3, and n, = (o~-oJ/(o, +oJ = (%x * %,hl = (uIIcx-~Lcx)/(uII,, + uLex). ohI is obtained by absorption measurements at the frequency uL with a spectral photometer. The 15, values were determined by energy transmission measurements of the pump beam at high intensities in ref. [I 1). D,, wil1 be determined in this letter by measuring the energy transmission ratio T,/TI_ and by comparison with calculated curves. T has been determined with two different techniques in ref. [ 111. In this letter an upper limit of T can be determined from the depcndcncl: of TLIT~ on the delay time tl, at fixed peak intensities foL and lop _ The experimental set-up is depicted in frg. I.
%cx
uLlcxsin2U,
B(O, @) = u,, sm20 cos*f#~+ u1 (1 - sin28 cos2G) , B,,(O,@)
15 December 1976
CXEMICAL PHYSICS LET-I-ERS
Volume 44. number 3
- sin20 cos*@),
0 IoL and IoF arc the peak Intensities of the incident picosecond pump pulse and the perpendicularly polar&d probe pulse, respcctivcly. The temporal and spatial shape of the pulses is assumed to be gaussian. 2to and r. arc the l/e values of the pulse duration and the beam radius. t, is the delay time between pump beam and probe beam. LJ~is the frequency of the laser pulses (both pulses have the same frequency). n is the refractive index of the dye solution. N is the total number density of dyo molecules. N, (O,@) and N2(0, @) describe the density of molecules in the ground state and the excited Franck-Condon state, respectively. 8 IS the angle between the transition moment of the molcculc and the polarization of the pump pulse. @IS the azimuthal angle of the transition moment relative to the polarization of the probe pulse. The orientational redistribution of the molecules by rotational brownian motion is taken into account in a phenomcnological manner by the last terms of eqs. (3) and (4). At !arge delay times the rotational rcdistnbution increases the transmission of the probe beam. The transformation z’ = z and t’ = t - nz/c brings the equation system to a simpler form. Solutions for the trans-
WP
m P
s
BS
BS
5+---+-q
Ci=H
-!-F
R
PO3
PO2
PO1
Fig. 1. Experimental set-up for the mcasuremznt of dichroirm. HI, ADP crystal for second harmonic generation; F. filters; BC, beam dividing cubes; WP, A/2 waveplate; DL. variable delay line; L, tenses, Uhf. 50% mirror; DC, two-photon fluorescing dye for puke duration measuremest; CA. cancra; OhlA, optical multichannel analyzer syQem; BS, beam splitters; R, rutile crystal for intensity determination; S. sample; P. polAzer; PD14. photodetectors. tight pokization is indicated by + and -c.
549
Volume 44, number
3
CHEMICAL
A mode-locked Nd-glass laser [ 121 was used for the generation of trains of picosecond light pulses. An electro-optical shutter selects a single pulse from the beginning of the pulse train and a subsequent Nd-glass amplifier increases the energy of the pulse to approximately 3 mJ. The light pulses (X = 1.06 pm) have a of duration of At = 5 ps (fwhm) and a bandwidth Ai3’= 3 cm- 1 (fwhm). Using an ADP crystal the pulses are frequency doubled w& a conversion efficicncy of = 20%. The fundamental light pulse is absorbed by the filter F following the ADP crystal. Two green light pulses are gcncratcd with the help of a 50% beam dividing cube. One pulse travels through a delay line and is reduced in intensity by a factor of 16 with an appropriate filter F. This puisc serves as the probe pulse. The other pulse acts as intense pump pulse. Its polarization is rotated by 90” with a X/2 wave plate. Part of the pulse energy is used for the determination of the pulse duration in a two-photon fluorescence system. 9, IO-dlphenylanthracene (!Om3 M/!2) acts as two-photon absorber. The two pulses are collimated in a second 50% beam dividing cube. The pump and probe beam are focused into the rhodaminc dye samples. The peak intensity of the pump pulse is determined by the energy transmission through a two-photon absorbing rutile crystal [ 131. The delayed probe pulse travels at exactly the same path through the dye sample as the pump pulse. Behind the sample, the pulses arc separated with a polarizer_ The energy transmission of the pump pulse and the perpendicularly polarized probe pulse is measured with photodetectors. Rhodamine 6G solutions in water, ethanol, cthylcne
glycol and glycerol and rhodamine B solutions in water, ethanol and glycerol were investigated at room temperature. The rhodamine 6G concentrations were 10m5 M/P. Dye cells of 2 cm length were used. For the rhodamine B solutions concentrations of 10S4 M/Q and cell length of 0.5 cm were applied. Energy transmission ratios T,,/T,_ versus the delay time tD were measured for all dye solutions. In fig. 2 the results for rhodamine 6G dissolved in water are shown as an example. The peak intensity of the pump beam was loL - 1 X log W/cm*. The pulse duration was tp a 3.7 ps (fwhm). In fig. 2 the curves are calculated for differer.t relaxation times T and for D, = 1, D, = 0.93, and D, = 0.85. For T 2 t,/3 a distinct peak in the curves occurs at tD * t,/2. The absorption 550
PHYSICS LETTCKS
15 Dcccmbcr
PROBE
PULSE
DELAY
llME
1976
tDCp53
Fig. 2. Normalized cncrgy transmission of pcrpcndicularly polarized probe pulws versus delay trme measured for rhodamine 6G dissolved in water. Dye concentration lOA5 M/Q, sample length 2 cm. The circles rcprcscnt cxpcrimcntal data. The input parameters arc pulse duration tp = 3.7 ps, peak mten\itics l,-,L = 10’ W/cm2 and lop = 6.3 X 10’ W/cm2. The curves arc calculated for D,, = 1, D, = 0.93. D, = 0.85, for T = 4 ps (a), 7 = 2 PF (b), 7 = 1 ps (c), T = 0.5 ps (d). 7 = 0 ps (c), and for 70r = 230 ps [9]. of the probe beam increases when the dye molecules relax from the excited Franck-Condon state. The shape of the curves allows the determination of 7 for T > t,/3. In our experiments no peak was found for T,/T,(t,). The relaxation time T is thcrcfore expected to be shorter than 1.5 ps. The absolute value of the transmission ratio is influenced by the relaxation time T and the molecular dichroism D,. The true value of T has to be determined by a method that IS insensitive ofD,. Two such methods were descrlbcd in ref. [ 111. Using the T values of ref. [ 111, the molecular dichroism values D, are determined from the absolute transmission ratio. For our example in fig. 2 it is T = 0.7 f 0.3 ps and we find D, = 0.93 + 0.03. The energy transmission ratio T,/TL depends on the peak intensities of the pump and probe beam as shown in fig. 3 for rhodamine GG dissolved in water (delay time tD = 7 ps). The curves are calculated for T = 0.7 ps and D, = 1,0.93, and 0.85. At low intcnsities the pump beam does not bleach the dye and pump and probe beam suffer the same linear absorption (T,/T + 1). In the intensity range around log W/cm li the dye solution is partially bleached by the intense pump beam. The transmission of the probe beam depends on the value of D,. For values of D,
Volume 44, number
CHEMICAL
3
PHYSICS LLXTERS
15 December
1976
high mtensities the pump pulse promotes a11dye molecules to an excited state and pump and probe beams pass through the sample with practicaIIy no absorption. The transmission T,/TL approaches the value of 1 for all ~1~2s of D ,,,. It is readily seen in fig. 3 that our experimental points are well accounted for by a calculated curve with D, = 0.93. In table 1 our experimental results for D, are
summarized together with the parameters ahf, o,,_ hi, 7Or,and T. The molecular dichroism is found to bi in
q
,
,
, ,
,
,
,
,] 10'0
109 PUMP
PULSE
PEAK
INTENSITY
I,LWk~l
Fig. 3. Intensity dcpcndent energy transmission of pcrpendicularly polaru.cd probe pukes through a rhodaminc 6G solution in water (lo-’ M/Q, I = 2 cm). The circles represent cxpcrimcntal data. The laser parameters arc ip - 3.7 ps and IoLjlop = 16. The curves .lrc calculated for 7 = 0.7 ps Ill ] and rol = 230 ps 191.
near one (uI < u,,) the pump pulse preferentially cxcites molecules onented under a small angle 0 to the pump pulse polarization. The perpendicularly oriented molecules remain in the ground state and absorb the delayed probe beam. The probe pulse is stronger absorbed than the pump pulse. For small values of D,, the pump pulses also excite molecules oriented pcrpendlcular to the pump polarization. The delayed probe beam suffers less absorption than the pump beam since the molecules are already excited when the probe beam pdsscs through Table 1 Solution
the sample.
At very
the range between 0.90 and 0.95. The theoretical value of Din = 1 for the Iincar oscillator model is not found experimentally. This result is in agreement with the fluoresccncc poIarization measurements for very diluted rhodaminc GG and rhodamine B solutions in glycerol [14I (PO = 0.44) and Plexiglas [ 151 (PO = 0.46). Deviations from the linear oscillator model are expected fur symmetric molecules [5], for overlapping absorption bands with differently oriented transition moments [6], for molecules that execute deformation [6] or torsional vibrations [16], and for transitions that involve magnetic dipole and electric quadrupole transitions [S]. The investigated rhodamine molecules are asymmetric (Cl), so the symmetry of the molecules cannot cxplain the reduced D, and P values. At the wavcIength of the laser pulses (P; = 18 910 cm-l) there is onIy one electronic absorption band expected. The studied transition is allowed for electric dipole transitions; contributions to the absorption from magnetic dipole and electric quadrupole transitions arc unlikely. Deformational and torsional vibrations seem to be the most likely process that causes the deviation from the linear oscillator model.
---_---_
-Cont. W/Q)
oM (cm2
rhodamine 6G in water ethanol ethylene glycol glycerol
1O-s 1o-5 lo-5 10-s
3.7 4.2 3.8 3.5
5.9 5.9 IO 4.8
rbodaminc B in Wilta ethanol glycerol
1o-4 1O-4 1o-4
1.5 1.6 1.0
5.7 5.3 4.4
X
‘F (PSI
Dill
230 270 2iloo > 2000
0.7 0.7 0.8 0.8
0.93 0.95 0.94 0.92
230 270 > 2000
0.9 0.9 0.8
0.90 k 0.03 0.93 * 0.03 0.93 r 0.05
Tar (es)
10r6)
,
-
r 0.03 :‘-0.03 k 0.03 k 0.03
551
Volume 44, number
CHEMICAL
3
The molecules in the ground state populate vibrational states wthin an energy range of Ah = kT * 200 cm-l. In the absorption process, transitions from various vlbrational levels in the So state to vibrational Franck-Condon levels in the S1 state are involved. The orientation of the transition moments for these various vibronic transitions seem to be different. Assumrng a spread A0 of the orientation angles 13around 3 mean value 0, and using the linear oscdlator model one calculates by use of a Taylor expansion (o(0)) = o(cos20) = a(cos2(&,
+ Ad)>
= u [( 1 - ((AfI)2)) cos20g + ((A0)*) sin2U0 ] . This formula is identical with the ansatx used in our calculations {u,, = ~(1 -<(A0)2>), u, = u<(AO)~>). The measured value ofD,,, = 0.93 is equal to uI = u( 1-D,,)/2 = 0.0357 and corresponds to an average angular spread of the transltion moments A0 = [<(A0)2>] -U2 = 0.19 = IO’. This value i.-,in agreement with results of fluorescence polarization measurements [5,151. In conclusion we want to emphasize that we have introduced a new technique to determmc the absorption amsotropy of dye solutions. In contrast to the common fluorescence polarlzrttion technique our method is not linnted to highly viscous solvents and low solute concentrations. The measured dichroism ~3s found to be lower than the theoretical value for a linear oscillator model. This behavior IS explamcd by 3ssu:ning differently oriented transition moments for the transitions from the thermal equilibrium states in the ground state to the respective S, states,
552
PIIYSICS
LETTERS
15 Deccmbcr 1976
The authors are very indebted to Professor W. Kaiser nnd to Drs. A. Laubercau and J-1’. Heritage for many valuable discussions.
‘References [I] 11. Jakobs and H. Kuhn, Z. Elcktrocbcm. 66 (1962) 46. [ 21 P.R. Callis and N. Davidson, Rlopolymcrr 7 (1969) 335. 131 E.D. Badly and 13.R. Jennings. Appl. Opt. 11 (1972) 527. [4 1 K.R. Popov. Opt. Spcctry. 39 (1975) 285. C.C. Rott snd T. Kurucsev. J. Chem. Sot. I~areday Trans. Ii 71 (1975) 749. [5 J P-1’. I’cofilov, The pl~ys~c,d basis of polnrizcd cmis\ion (Conwltants I%urcau, New York, 1961). [6] I‘. Dixr and M. Ileld, Angcw. Chcm. 72 (1960) 287. [ 7 ] G. Webrr, in. I’luorcscencc and phosphorcscencc analy& cd. D.hI. Ifcrculcs (Interscicncc, New York, 1966) p. 217. 181 AC. Albrccht, J. hlol. Spectry. 6 (1961) 84. [9[ T.J. Clwang and K.B. Ewznthal, Cilcm. Pbyr. Lcttcrs 11 (1971) 368; I1.E. Lcwng. A. von Jcna and hf. Reichcrt, Chem. Phys. Letters 36 (1976) 517; D.W. Plullion, D.J. Kuircnga, and A.E. Sicgman, Appl. P11yc. Lcttcrs 27 (1975) 85. IlO] A. Penlkofcr, A. Laubereau and W. Karscr, Pbys. Rev. Lcttcrs 31 (1973) 863. [ 11 j A. Penzkofcr, W. Palkcnstoin and W. Kaiser, Chcm. Phys. Lcrtcrs 44 (1976) 82. (I 21 A. Lwbercau and IV. Kaiser, Opto-Electronicc 6 (1974) 1. {13] A. Pcrwkofcr and W. Mkcnstcin, Opt. Commun. 17 (1976) 1. [14] G. Webcr. J. Opt. Sot. Am. 46 (1956) 962. [ 151 E. Lafittc. Ann. Phy\. (Paris) 10 (1955) 71. [ 161 A. Jablonskl, Acta Pbys. Polon. 10 (1950) 3.