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Study on photoacoustic phase spectrum of rare earth complex: Pr(HFA)3·2H2O
SPECTROCHIMICA ACTA PART A ELSEVIER
Spectrochimica Acta Part A 52 (1996) 675 681
Study on photoacoustic phase spectrum of rare earth complex: Pr(HFA)3" 2H=O Mao Qinglu*, Su Qingde, Zhao Guiwen Department qf Applied Chemistry, UniversiO' q/' Science and Technology of China, HeJei, Anhui 230036, People's Republic qf C7tina
Received 10 July 1995; revision accepted 10 October 1995
Abstract
The /,~-diketone rare earth complex: Pr(HFA)3.2HzO was synthesized and its amplitude and phase photoacoustic spectra in the range of 300-700 nm were reported. It was observed that the phase angle depends variously on the relaxation time ~ and the optical absorption coefficient ~ with the incident light wavelength 2. A model of a homogeneous powder sample containing multiple optical absorption bands based on the Mandelis work was introduced to interpret the phase spectrum. It is shown that this model is very suitable for explaining the phase data associated with the ~z ~r* transition and./~-f transitions of the title complex. The phase angle ~, is mainly related to r for the ~r ~r* transition while it is determined by fl for the f_)c transition at relatively low chopping frequencies. Furthermore, the dependence of amplitude and phase information on the chopping frequency was also investigated. Ke)'words: Optical absorption coefficient; Phase spectrum: Photoacoustic spectroscopy: Rare earth complex (Pr (HFA) 3"2HzO); Relaxation time
I. Introduction
Photoscoustic spectroscopy (PAS) has come of age simultaneously inspiring both fundamental and technical developments and been widely used in physics [1], biology [2], chemistry [3], agriculture and environment [4], and other fields [5]. Unlike conventional transmission spectroscopy, it provides both amplitude and phase information on the response of a photoacoustic system to an
* Corresponding author.
optical excitation process [6,7]. The PAS phase measurements have been used with gaseous samples to obtain information about relaxation rates and photochemical processes [8]. For the case of solids, various contributions to the phase of the PAS signal have been considered by several authors. The phase data contain contributions from a number of sources associated with the sample under study: the geometry of the photoacoustic cell [9], the response of the detecting system [10], the interaction between the sample and its backing [8], the optical absorption coefficient [11], the nonradiative decay paths [12], etc. In an actual
0584-8539/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0584-8539(95)01593-0
676
Q. Mao et al. / Spectroch#nica Acta Part A 52 (1996) 675-681
photoacoustic measurement, many of the nonsample related parameters may be maintained constant and the phase data may therefore be used to provide information about the optical and thermal properties of the solid under study as well as the relaxation times associated with the non-radiative de-excitation processes that give rise to the PAS signal [13]. One of the uses of phase information is to provide a measurement of the absorption coefficient of a material. Roark et al. [14] made use of photoacoustic phase data to obtain an estimate of the absolute absorption coefficient. Teng and Royce [15] proposed a method for determining the absolute absorption coefficient of an aqueous solution using only PAS data including both amplitude and phase information. On the other hand, the phase data may be used to provide information about the relaxation time associated with the non-radiative paths [12]. PAS measurements have received a great deal of interest as a method for characterizing radiationless relaxation processes of ions in solids [16]. Merkle and Powell [17,18] have employed the PAS phase to measure the lifetime associated with the non-radiative deexcitation paths. Mandelis et al. [13] presented a theoretical model of photoscoustic processes in the frequency domain including the relaxation time of the radiationless de-excitations and a twolayer absorbing system. The phase shifts for a layered sample or doped materials are always under consideration [1,19]. Recently, PAS could prove very beneficial to investigations of the rare earth complexes [20-22]. However, those reports concentrate on the amplitude PA spectrum rather than the phase data. According to our work, the phase angle ~ for the fl-diketone rare earth complexes [23] has a special dependence on the wavelength due to different lifetimes and intensities of the st-st* transition and the f - f transitions. The phase data can be well explained by the wavelength domain mode on the basis of Mandelis' work [13,24] which study a sample in a wide wavelength range. In this paper, the PA spectra of the title complex as powder or crystal, are reported. Emphasis is placed on the interpretation of the phase spectrum by using a model based on Mandelis theory.
2. Theoretical model
A simple configuration of our photoacoustic system is shown in Fig. 1. It is similar to that discussed by Mandalis [13] in which a finite relaxation time is associated with the non-radiative decay processes. Mandelis derived an expression to evaluate the phase angle for a single-layer sample model with a finite non-radiative relaxation rate. The solid sample, of thickness l, contains a two-level optical absorption band which has an excited-state lifetime r and a wavelengthdependent optical absorption coefficient ft. The sample is supported by a large thickness of quartz and is in thermal contact with a transparent gas. Heat transfer between the solid and the gas results in pressure fluctuations which constitute the PAS signal. The cell is closed by quartz (a non-absorbing thick window). By choosing both the transparent cell window and sample backing to be infinitely thick, the growing exponential solutions for the thermal transport equations in these components can be eliminated by application of the boundary conditions. The PAS signal for this model then has the form
= {P°4'q]3 "~R [-{'
exp[i(~o0t-~/4)]
eLt,2','%(1 + [(r-
(
l)(b+ 1) exp(o-,.l)- (r + 1)(b- 1)
\]
× exp(-<,il)+Z(b-.)exp(-m)ll (1) x
Light Window (w) Gas (8) Sample (s) Backing (b)
Fig. 1. Schematicdiagram of the photoacousticsystem.
Q. Mao et al. i Spectrochimica Acta Part A 52 (1996) 675 681
where the symbols have their conventional meanings and are defined in Refs. [6,13]. Eq. (1) includes the effects of a noninstaneous deexcitation process. For an optically opaque and thermally thick sample both the optical absorption depth,/~/j, and the thermal diffusion length, /~,, are much less than the sample thickness. Under these conditions exp( - [71) ~ 0 and exp( - a,l) = 0, Eq. (1) can be rewritten as
(px(t; ,Oo))
=
\ ~
exp[i(~oot- rr/'4)] (2)
x (,-- 1)i
Following Rosencwaig and Gersho [6], the amplitude and the phase of the PA signal can be separated conveniently
(p=(t; "o)) = Re{ Q exp[i({oot - ~r/4)]} = Re{q exp[i(~oot - 1r/4) - ig,]} such that Q = Q l + i Q e = q e x p ( - i ~ , ) and the phase lag of the signal with respect to the source modulation is given by 05 = 7r/4+ ~b with g,= tan ' [ - (Qz/Q,)]. By writing the components of Q in the polar notation for the complex quantities,
1 + i(oor = [1 +
((Oor)2] 1'2
/]2 __ O'~ = /]211
q-((DOT/])2]1'2 exp(i05 2)
1 = (eJor/:)
exp(i051)
ol
¢
¢1
Z 6o el J:
o.
( - #, - 05~ + 050
~(~Oor)+ tan
tan
.s¢(X)
1(1/(1 --
i(_
((OOT/>,)I"2))
'~,
.
500 Wavelength (nm)
600
Fig, 2. Phase angle 7, as a function of wavelength while/~l'] is a Gaussian shaped peak ( ) with I~// ...... equalling to 1, 10 and 100 respectively.
the phase ~b, for an optically opaque and thermally thick sample, depends mainly upon the optical absorption coefficient of the solid, the relaxation time of the nonradiative processes, the modulation frequency of the light, and the thermal properties of the solid. The third term 053 in Eq. (3) is not a simple decreasing function of /] and has an additional constraint for ~oor/¢¢ 1. For this reason, we derive another form for
(/]~ -
o-~)i(,-- 1)
= [(fl/It,) e + (~]~It, + 2///~)2] l ? exp(i052)
so that ~(/], r, ,Oo) = - ( - 051 - 052)
~(~Oor)+ tan
~[(/]ll, + 2)//]IL,] (4)
~ + 1 - (2/(oorfl)12] 1'2 exp(i053)
= tan
_o
= tan
the expression for the phase can take on a particular simple form ~,(/], r, co()) =
-~oo
46 400
eLt, z, 2a=(l + io,,:)(/]
r-
= 75
)
x R V[
677
~oor/~) (3)
where r/,= 1//]2~ is a characteristic relaxation time for the system corresponding to the thermal transit time from a depth/~/~ within the solid. It can be seen that the variable contribution to
At a chosen chopping frequency, IL= remains constant and the phase g, is only related to fl and r. For an instantaneous relaxation process, the phase ~, in the wavelength-domain photoacoustic spectroscopy will then depend on fl(2). Assuming that a Gaussian-shaped absorption is centered at 500 nm and with a full width at a half-maximum (FWHM) of 40 nm, the phase response is illustrated in Fig. 2. The two quantities fl and ¢, anticorrelate as a function of 2. In addition, it is observed that phase saturation occurs for samples having high optical absorption coefficients.
678
Q. Mao et at. / Spectrochimica Acta Part A 52 (1996) 675 681
The complex of Pr(I-IFA)3-2H20 covers multiple absorption bands through a wavelength region. A parallel scheme for the energy levels of both ligand and center ion in the rare earth fl-diketone complex sample is satisfactory [25]. Therefore, the model discussed by Mandelis can be employed to interpret the PAS spectra of Pr(HFA)3'2H20 with multiple energy levels.
3. Experimental
3. I. Synthesis' of the rare earth fl-diketone complex: Pr(HFA )3 "2H20 A procedure [22] was introduced to synthesize the complex. Pr60~l was dissolved in 6 N HCI and Pr(OH)3 was then formed by dropping 6 N aqueous ammonia slowly. After washing thoroughly, the precipitate was dissolved by dropping HHFA and with vigorous stirring. On the colloid formed, 2 N aqueous ammonia was dropped to adjust to pH 7. The crystal obtained was filtrated and washed. When the remaining water was removed, the crystal was dissolved in the HHFA and acetone (1:30) and reflused for 1 h. Acetone was evaporated and the complex was washed by hexane. The elemental analysis of the crystal corre-
o[
!
0" 4 .
i
'30 ~. ~. ,jivr~, P
1 D2
'60 ® o
soo
460
soo
~o
Wavc~length (nm)
700
Fig. 3. Amplitude ( ) and phase (-~ ) spectra of Pr(HFA)3.2H20 in the range 300-700 nm at a chopping frequency of 12 Hz.
sponds to Pr(HFA)3.2H20 and the IR spectrum is indicative of its structure formulae.
3.2. PA measurement The PA spectra containing both amplitude and phase information were measured on a single-beam spectrometer constructed in our lab. A 500 W Xenon lamp, a CT-30F monochromator and a PA cell fitted with an ERM 10 electret microphone were used. The chopping frequencies were 8 80 Hz. After the preamplification, the output of the microphone was fed to a lock-in-amplifier (LI-574A) to which a reference signal was normalized for changes in lamp intensity using a carbon-black reference.
4. Results and discussion
4.1. Amplitude and phase spectra The PA spectra including both amplitude and phase data of Pr(HFA)3.2H20 in the range 300 700 nm at a frequency of 12 Hz, are shown in Fig. 3. The amplitude spectrum shows that there exists a very strong and moderately broad absorption in the wavelength less than 380 nm. The bond was then assigned as the rr-~* electronic transition of the ligand. On the other hand, due to the special electronic structure and the shield effect of the 5 S 2 5 p 6 electrons, the Ln 3+ ions are characterized by large spin-orbit coupling constants and small crystalfield effects. Hence, the f - f transitions appear as sharp lines in the UV-Vis region. The f f transitions of different J energy levels are also illustrated in Fig. 3. The phase spectrum reveals that the phase angle varies corresponding to each absorption band. For the rr-~r* transition, the phase angle decreases in a short wavelength region less than 400 nm. The f f transitions of the Pr 3+ ion show reverse peaks (antipeaks) to those in the amplitude spectrum. This phase change of Pr(HFA)3.2H20 can be explained qualitatively by the above model of a homogeneous powder sample containing multiple absorption bands.
679
Q. Mao et al./ Spectrochimica Acta Part A 52 (1996) 675 681
4.2. Interpretation on the phase data of the complex: Pr(HFA)," 2HeO Adjusting to this wavelength domain photoacoustic system, the expression of the phase angle g, can be recast in a new form. The previous model can be adopted to the complex system in which multiple energy levels are parallel. The phase data can be discussed separately with respect to the two different transitions. The ~r-rt* transition has a lifetime r of the order of milliseconds whose modulation of the triplet will be delayed and lag in phase with respect to that of other rapidly relaxing states [26]. On the other hand, the optical absorption fl of the rr-Tr* transition absorption is higher than that of f f transition absorption as displayed in the amplitude spectrum. In such a case of less than 380 nm range, with iz~ > p/~ and/~,fl--+ ac, ~b in Eq. (4) can be simplified as ~,(2) -- ~r/4 + tan
-I[(L/~(.,~.)]
l(l +2/fl/~,)
"o
Hz
\
2, 36"z/ 72
3oo
i
/,,, /,,____.4oo
so0
700
s60
7oo
Wavelength(nm)
l 30
(b)
(5)
Here, r is dependent on wavelength 2 because of the population on the single excited-state (~E) and lowest triplet state (3T) varied with the incident light wavelength 2. Then, r decreases with an increase of 2 and ~ decreases with the disappearance of the 7r ~* transition. As the wavelength increases up to the absorption bands corresponding to the f - f transitions, the factors affecting the phase angle (/ change. The lifetimes of the excited-states for Pr 3 + ion involving non-radiative relaxation processes are less than l0 4 s [27]. Assuming ~o= 12 Hz and r = 0 . 1 ms, tan I[~,)r(2)] is 0.43 ° which can be neglected. Therefore, Eq. (4) can be revised in the following form ~,(,i) = zr/4+tan
o" 4, / 2 4 @
(6)
This means that the phase ~ is mainly dependent on the optical absorption coefficient fl of the complex sample in the case that the relaxation time is essentially instantaneous. As /~ is varied at a given chopping frequency, both the amplitude q and phase ¢ of the photoacoustic response change. They anticorrelate as a function of/Jsfl. Fig. 3 shows the expected anticorrelation between the amplitude and the phase as a func-
300
46o
56o
Wavelength(nm)
Fig. 4. Amplitude (a) and phase (b) spectra Pr(HFA)~2H:O at different chopping frequencies.
of
tion of wavelength at the range of 400-700 nm. It is shown that the phase data can replicate the shape of an optical absorption band. Just the same as we have recorded, for the carbon black, having p/; < p~ and IL,fl--+ ~oc, the phase angle is saturated and remains constant with the wavelength 2.
4.3. Influence of the frequency on the amplitude and phase spectra The amplitude and phase spectra of Pr(HFA))'2H20 at different frequencies in the region of 300-700 nm are shown in Fig. 4. It is observed that the amplitude of the photoacoustic response decreases with an increase of frequencies and high modulation frequencies have good phase resolution. This result is in good agreement with the expression in Eq. (1) for the photoacoustic signal [24]. As illustrated in Fig. 4, the amplitude spectrum was impossible to measure for the transition while the phase spectrum has a
680
Q. Mao et al. / Spectrochimica Acta Part A 52 (1996) 675-681
high resolution in high chopping frequency. This suggests that the phase spectrum can provide very useful information about the energy levels as a complement of amplitude in most cases. The dependence of the thermal diffusion length, /L~, upon the chopping frequency means that for a sample with instant de-excitation processes, the amplitude of the PAS signal has an co ] dependence at low chopping frequencies and an co 3..2 dependence at high frequencies [13]. For the same limited case, the phase change also depends on the co. Eq. (4) gives an expression, ~ = ~(co), and the phase changes increase expectedly in the wavelength less than 380 nm. Though the overall shape of phase spectrum remains similar, the phase change does not continue to increase with an increase of co. A sharp valley associated with the Jr-~r* transition results from an increase of co. A probable explanation is that an additional factor such as fl may have a contribution to the phase angle of the 7r lr* transition in relatively high frequencies. To check the PAS response of different energy levels on the frequency, the amplitude and phase data related to the zr-~r* transition (/~max = 345 nm) and the energy levels 3P2 (2 .... = 451 nm) and ]De (Amax = 591 nm) of Pr 3+ ion at different frequencies were recorded. As plotted in Fig. 5, the amplitude of 3P2 has a relationship with the frequencies a s qpas-----kco ~.2. The phase decreases with an increase of co. The dependence of the two 100
1.6!
0
I
-t
o" Q
~
0.8,
-200
o
~. O. o
E
~[ 0 . 4 '
-300
&
~
o o
,
t
m
...
2o 40 eo Frequency (Hz)
Acknowledgements The authors thank Dr. Xianzhi Xu for his useful discussions on the theoretical part in this work. This work was supported by the National Natural Science Foundation of PR China.
"o
w o •1 O 0 w
¢~ t . 2 .
quantities on the frequency deviate a little from the PAS existing theory [28]. Similar dependence of the PAS signals on the frequency for the 7r-z* transition and the ]D 2 level was observed. In addition, the carbon black has a similar decrease for the phase angle with an increase of co. The model presented for interpreting results qualitatively provides a consistent way for reconciling the apparent discrepancies between optical and photoacoustic data. The discrepancy between the calculated phase data and the experimental results can be eliminated by the estimated additional contribution from the instrument with a form of ~xp = g'th + ///app [14]. In summary, the model based on Mandelis' work is very suitable for interpreting the amplitude and phase spectrum of the complex Pr(HFA)3"2H20. The phase of the PAS response depends on either the optical absorption fl or the excited-state lifetime r at different wavelength regions. The phase angle reflects not only the relaxation properties of energy levels but also the intensities of the transitions. On the other hand, since g, is closely related to the optical absorption coefficient, the phase angle can be used to determine the fl of the solids.
-4OO
8O
Fig. 5. Dependence of the PAS amplitude (e) and phase ( A ) of 3P2 (,~.... = 451 nm) on the chopping frequency.
References [1] C.S. Sunandana, Phys. Stat. Solidi., A 105 (1988) I I. [21 A. Lachaine, R. Pottier and D.A. Russell, Spectrochim. Acta Rev., 15(3) (1993) 125. [3] M.J. Adams and G.F. Kirkbright, Analyst, 102 (1977) 678. [4] D. Bicanic, M. Chirtoo et al., Acta Chim. Sloven., 40(2) (1993) 175. [5] S. Rai, S.N. Thakur and L. Mishira, Spectrochim. Acta Part A, 46(3) (1990) 429. [6] A. Rosencwaig and A. Gersho, J. Appl. Phys., 47 (1976) 64.
Q. Mao et al. / Spectrochimica Acta Part A 52 (1996) 675 681
[7] M.J. Adams, A.A. King and G.F. Kirkbright, Analyst, 101 (1976) 73. [8] M.B. Robin, in Yoh-Han Pao (Ed.), Optoacoustic Spectroscopy and Detection, Academic Press, New York, 1977, p. 167. [9] L.C. Aamodt. J.C. Murphy and J.G. Parker, J. Appt. Phys., 48 (1977) 927. [10] A. Rosencwaig, Photoacoustic and Photoacoustic Spectroscopy, Wiley, New York, 1980. [11] P. Poulet, J. Chamboron and R. Unterreiner, J. Appl. Phys., 51(3) (1980) 1738. [12] A. Mandelis and B.S.H. Royce, J. Opt. Soc. Am., 70(5) (1980) 474. [13] A. Mandelis, Y.C. Teng and B.S.H. Royce, J. Appl. Phys. 50(11) (1980) 7138. [14] J.C. Roark, R.A. Palmer and J.S. Hutchinson, Chem. Phys. Lett., 60 (1978) 112. [15] Y.C. Teng and B.S.H. Royce, J. Opt. Soc. Am., 70(5) (1980) 557. [16] R.C. Powell, D.P. Neikirk and D. Sardar, J. Opt. Soc. Am., 70(5) (1980) 486. [17] L.D. Merkle and R.C. Powell, Chem. Phys. Lett., 46 (1977) 303.
68l
[18] L.D. Merkle and R.C. Powell, J. Phys. C, 11 (1978) 3103. [19] J. Fresquet, B. Girault et al., Appl. Optics, 23 (1984) 2784 [20] Zhang Yugeng, Su Qingde and Zhao Guiwen. CrystalIogr. Res. Yech., 28(7) (1993) 995. [21] Su Qingde, Zhao Guiwen and T. Kuwamoto, Rare Earths (Japan), 3 (1989) 68. [22] Su Qingde, Mao Qinglu and Zhao Guiwen, Spectrochim. Acta Part A., 51 (1995) 2459. [23] N. Sabbatatini and M. Guardigli, Coord. Chem. Rev., 123 11993) 201. [24] A. Mandelis and B.S.H. Royce, J. Appl. Phys., 50(6) (1970) 4330. [25] F. Halverson, J.S. Brinen and J.R. Leto, J. Chem. Phys., 40 (1964) 2790. [26] T.A. Moore, D. Benin and R. Tom, J. Am. Chem. Soc., 104 c 1982) 7356. [27] W.T Carnall, in K.A. Gschneidner, Jr. and L.R. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, Vol. 3, North-Holland, Amsterdam, 1979, p. 197. [28] G.J. Papadopoulos and G.L.R. Mair, J. Phys. D Appl. Phys., 25(4) (1992) 722.
Spectrochimica Acta Part A 52 (1996) 675 681
Study on photoacoustic phase spectrum of rare earth complex: Pr(HFA)3" 2H=O Mao Qinglu*, Su Qingde, Zhao Guiwen Department qf Applied Chemistry, UniversiO' q/' Science and Technology of China, HeJei, Anhui 230036, People's Republic qf C7tina
Received 10 July 1995; revision accepted 10 October 1995
Abstract
The /,~-diketone rare earth complex: Pr(HFA)3.2HzO was synthesized and its amplitude and phase photoacoustic spectra in the range of 300-700 nm were reported. It was observed that the phase angle depends variously on the relaxation time ~ and the optical absorption coefficient ~ with the incident light wavelength 2. A model of a homogeneous powder sample containing multiple optical absorption bands based on the Mandelis work was introduced to interpret the phase spectrum. It is shown that this model is very suitable for explaining the phase data associated with the ~z ~r* transition and./~-f transitions of the title complex. The phase angle ~, is mainly related to r for the ~r ~r* transition while it is determined by fl for the f_)c transition at relatively low chopping frequencies. Furthermore, the dependence of amplitude and phase information on the chopping frequency was also investigated. Ke)'words: Optical absorption coefficient; Phase spectrum: Photoacoustic spectroscopy: Rare earth complex (Pr (HFA) 3"2HzO); Relaxation time
I. Introduction
Photoscoustic spectroscopy (PAS) has come of age simultaneously inspiring both fundamental and technical developments and been widely used in physics [1], biology [2], chemistry [3], agriculture and environment [4], and other fields [5]. Unlike conventional transmission spectroscopy, it provides both amplitude and phase information on the response of a photoacoustic system to an
* Corresponding author.
optical excitation process [6,7]. The PAS phase measurements have been used with gaseous samples to obtain information about relaxation rates and photochemical processes [8]. For the case of solids, various contributions to the phase of the PAS signal have been considered by several authors. The phase data contain contributions from a number of sources associated with the sample under study: the geometry of the photoacoustic cell [9], the response of the detecting system [10], the interaction between the sample and its backing [8], the optical absorption coefficient [11], the nonradiative decay paths [12], etc. In an actual
0584-8539/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0584-8539(95)01593-0
676
Q. Mao et al. / Spectroch#nica Acta Part A 52 (1996) 675-681
photoacoustic measurement, many of the nonsample related parameters may be maintained constant and the phase data may therefore be used to provide information about the optical and thermal properties of the solid under study as well as the relaxation times associated with the non-radiative de-excitation processes that give rise to the PAS signal [13]. One of the uses of phase information is to provide a measurement of the absorption coefficient of a material. Roark et al. [14] made use of photoacoustic phase data to obtain an estimate of the absolute absorption coefficient. Teng and Royce [15] proposed a method for determining the absolute absorption coefficient of an aqueous solution using only PAS data including both amplitude and phase information. On the other hand, the phase data may be used to provide information about the relaxation time associated with the non-radiative paths [12]. PAS measurements have received a great deal of interest as a method for characterizing radiationless relaxation processes of ions in solids [16]. Merkle and Powell [17,18] have employed the PAS phase to measure the lifetime associated with the non-radiative deexcitation paths. Mandelis et al. [13] presented a theoretical model of photoscoustic processes in the frequency domain including the relaxation time of the radiationless de-excitations and a twolayer absorbing system. The phase shifts for a layered sample or doped materials are always under consideration [1,19]. Recently, PAS could prove very beneficial to investigations of the rare earth complexes [20-22]. However, those reports concentrate on the amplitude PA spectrum rather than the phase data. According to our work, the phase angle ~ for the fl-diketone rare earth complexes [23] has a special dependence on the wavelength due to different lifetimes and intensities of the st-st* transition and the f - f transitions. The phase data can be well explained by the wavelength domain mode on the basis of Mandelis' work [13,24] which study a sample in a wide wavelength range. In this paper, the PA spectra of the title complex as powder or crystal, are reported. Emphasis is placed on the interpretation of the phase spectrum by using a model based on Mandelis theory.
2. Theoretical model
A simple configuration of our photoacoustic system is shown in Fig. 1. It is similar to that discussed by Mandalis [13] in which a finite relaxation time is associated with the non-radiative decay processes. Mandelis derived an expression to evaluate the phase angle for a single-layer sample model with a finite non-radiative relaxation rate. The solid sample, of thickness l, contains a two-level optical absorption band which has an excited-state lifetime r and a wavelengthdependent optical absorption coefficient ft. The sample is supported by a large thickness of quartz and is in thermal contact with a transparent gas. Heat transfer between the solid and the gas results in pressure fluctuations which constitute the PAS signal. The cell is closed by quartz (a non-absorbing thick window). By choosing both the transparent cell window and sample backing to be infinitely thick, the growing exponential solutions for the thermal transport equations in these components can be eliminated by application of the boundary conditions. The PAS signal for this model then has the form
= {P°4'q]3 "~R [-{'
exp[i(~o0t-~/4)]
eLt,2','%(1 + [(r-
(
l)(b+ 1) exp(o-,.l)- (r + 1)(b- 1)
\]
× exp(-<,il)+Z(b-.)exp(-m)ll (1) x
Light Window (w) Gas (8) Sample (s) Backing (b)
Fig. 1. Schematicdiagram of the photoacousticsystem.
Q. Mao et al. i Spectrochimica Acta Part A 52 (1996) 675 681
where the symbols have their conventional meanings and are defined in Refs. [6,13]. Eq. (1) includes the effects of a noninstaneous deexcitation process. For an optically opaque and thermally thick sample both the optical absorption depth,/~/j, and the thermal diffusion length, /~,, are much less than the sample thickness. Under these conditions exp( - [71) ~ 0 and exp( - a,l) = 0, Eq. (1) can be rewritten as
(px(t; ,Oo))
=
\ ~
exp[i(~oot- rr/'4)] (2)
x (,-- 1)i
Following Rosencwaig and Gersho [6], the amplitude and the phase of the PA signal can be separated conveniently
(p=(t; "o)) = Re{ Q exp[i({oot - ~r/4)]} = Re{q exp[i(~oot - 1r/4) - ig,]} such that Q = Q l + i Q e = q e x p ( - i ~ , ) and the phase lag of the signal with respect to the source modulation is given by 05 = 7r/4+ ~b with g,= tan ' [ - (Qz/Q,)]. By writing the components of Q in the polar notation for the complex quantities,
1 + i(oor = [1 +
((Oor)2] 1'2
/]2 __ O'~ = /]211
q-((DOT/])2]1'2 exp(i05 2)
1 = (eJor/:)
exp(i051)
ol
¢
¢1
Z 6o el J:
o.
( - #, - 05~ + 050
~(~Oor)+ tan
tan
.s¢(X)
1(1/(1 --
i(_
((OOT/>,)I"2))
'~,
.
500 Wavelength (nm)
600
Fig, 2. Phase angle 7, as a function of wavelength while/~l'] is a Gaussian shaped peak ( ) with I~// ...... equalling to 1, 10 and 100 respectively.
the phase ~b, for an optically opaque and thermally thick sample, depends mainly upon the optical absorption coefficient of the solid, the relaxation time of the nonradiative processes, the modulation frequency of the light, and the thermal properties of the solid. The third term 053 in Eq. (3) is not a simple decreasing function of /] and has an additional constraint for ~oor/¢¢ 1. For this reason, we derive another form for
(/]~ -
o-~)i(,-- 1)
= [(fl/It,) e + (~]~It, + 2///~)2] l ? exp(i052)
so that ~(/], r, ,Oo) = - ( - 051 - 052)
~(~Oor)+ tan
~[(/]ll, + 2)//]IL,] (4)
~ + 1 - (2/(oorfl)12] 1'2 exp(i053)
= tan
_o
= tan
the expression for the phase can take on a particular simple form ~,(/], r, co()) =
-~oo
46 400
eLt, z, 2a=(l + io,,:)(/]
r-
= 75
)
x R V[
677
~oor/~) (3)
where r/,= 1//]2~ is a characteristic relaxation time for the system corresponding to the thermal transit time from a depth/~/~ within the solid. It can be seen that the variable contribution to
At a chosen chopping frequency, IL= remains constant and the phase g, is only related to fl and r. For an instantaneous relaxation process, the phase ~, in the wavelength-domain photoacoustic spectroscopy will then depend on fl(2). Assuming that a Gaussian-shaped absorption is centered at 500 nm and with a full width at a half-maximum (FWHM) of 40 nm, the phase response is illustrated in Fig. 2. The two quantities fl and ¢, anticorrelate as a function of 2. In addition, it is observed that phase saturation occurs for samples having high optical absorption coefficients.
678
Q. Mao et at. / Spectrochimica Acta Part A 52 (1996) 675 681
The complex of Pr(I-IFA)3-2H20 covers multiple absorption bands through a wavelength region. A parallel scheme for the energy levels of both ligand and center ion in the rare earth fl-diketone complex sample is satisfactory [25]. Therefore, the model discussed by Mandelis can be employed to interpret the PAS spectra of Pr(HFA)3'2H20 with multiple energy levels.
3. Experimental
3. I. Synthesis' of the rare earth fl-diketone complex: Pr(HFA )3 "2H20 A procedure [22] was introduced to synthesize the complex. Pr60~l was dissolved in 6 N HCI and Pr(OH)3 was then formed by dropping 6 N aqueous ammonia slowly. After washing thoroughly, the precipitate was dissolved by dropping HHFA and with vigorous stirring. On the colloid formed, 2 N aqueous ammonia was dropped to adjust to pH 7. The crystal obtained was filtrated and washed. When the remaining water was removed, the crystal was dissolved in the HHFA and acetone (1:30) and reflused for 1 h. Acetone was evaporated and the complex was washed by hexane. The elemental analysis of the crystal corre-
o[
!
0" 4 .
i
'30 ~. ~. ,jivr~, P
1 D2
'60 ® o
soo
460
soo
~o
Wavc~length (nm)
700
Fig. 3. Amplitude ( ) and phase (-~ ) spectra of Pr(HFA)3.2H20 in the range 300-700 nm at a chopping frequency of 12 Hz.
sponds to Pr(HFA)3.2H20 and the IR spectrum is indicative of its structure formulae.
3.2. PA measurement The PA spectra containing both amplitude and phase information were measured on a single-beam spectrometer constructed in our lab. A 500 W Xenon lamp, a CT-30F monochromator and a PA cell fitted with an ERM 10 electret microphone were used. The chopping frequencies were 8 80 Hz. After the preamplification, the output of the microphone was fed to a lock-in-amplifier (LI-574A) to which a reference signal was normalized for changes in lamp intensity using a carbon-black reference.
4. Results and discussion
4.1. Amplitude and phase spectra The PA spectra including both amplitude and phase data of Pr(HFA)3.2H20 in the range 300 700 nm at a frequency of 12 Hz, are shown in Fig. 3. The amplitude spectrum shows that there exists a very strong and moderately broad absorption in the wavelength less than 380 nm. The bond was then assigned as the rr-~* electronic transition of the ligand. On the other hand, due to the special electronic structure and the shield effect of the 5 S 2 5 p 6 electrons, the Ln 3+ ions are characterized by large spin-orbit coupling constants and small crystalfield effects. Hence, the f - f transitions appear as sharp lines in the UV-Vis region. The f f transitions of different J energy levels are also illustrated in Fig. 3. The phase spectrum reveals that the phase angle varies corresponding to each absorption band. For the rr-~r* transition, the phase angle decreases in a short wavelength region less than 400 nm. The f f transitions of the Pr 3+ ion show reverse peaks (antipeaks) to those in the amplitude spectrum. This phase change of Pr(HFA)3.2H20 can be explained qualitatively by the above model of a homogeneous powder sample containing multiple absorption bands.
679
Q. Mao et al./ Spectrochimica Acta Part A 52 (1996) 675 681
4.2. Interpretation on the phase data of the complex: Pr(HFA)," 2HeO Adjusting to this wavelength domain photoacoustic system, the expression of the phase angle g, can be recast in a new form. The previous model can be adopted to the complex system in which multiple energy levels are parallel. The phase data can be discussed separately with respect to the two different transitions. The ~r-rt* transition has a lifetime r of the order of milliseconds whose modulation of the triplet will be delayed and lag in phase with respect to that of other rapidly relaxing states [26]. On the other hand, the optical absorption fl of the rr-Tr* transition absorption is higher than that of f f transition absorption as displayed in the amplitude spectrum. In such a case of less than 380 nm range, with iz~ > p/~ and/~,fl--+ ac, ~b in Eq. (4) can be simplified as ~,(2) -- ~r/4 + tan
-I[(L/~(.,~.)]
l(l +2/fl/~,)
"o
Hz
\
2, 36"z/ 72
3oo
i
/,,, /,,____.4oo
so0
700
s60
7oo
Wavelength(nm)
l 30
(b)
(5)
Here, r is dependent on wavelength 2 because of the population on the single excited-state (~E) and lowest triplet state (3T) varied with the incident light wavelength 2. Then, r decreases with an increase of 2 and ~ decreases with the disappearance of the 7r ~* transition. As the wavelength increases up to the absorption bands corresponding to the f - f transitions, the factors affecting the phase angle (/ change. The lifetimes of the excited-states for Pr 3 + ion involving non-radiative relaxation processes are less than l0 4 s [27]. Assuming ~o= 12 Hz and r = 0 . 1 ms, tan I[~,)r(2)] is 0.43 ° which can be neglected. Therefore, Eq. (4) can be revised in the following form ~,(,i) = zr/4+tan
o" 4, / 2 4 @
(6)
This means that the phase ~ is mainly dependent on the optical absorption coefficient fl of the complex sample in the case that the relaxation time is essentially instantaneous. As /~ is varied at a given chopping frequency, both the amplitude q and phase ¢ of the photoacoustic response change. They anticorrelate as a function of/Jsfl. Fig. 3 shows the expected anticorrelation between the amplitude and the phase as a func-
300
46o
56o
Wavelength(nm)
Fig. 4. Amplitude (a) and phase (b) spectra Pr(HFA)~2H:O at different chopping frequencies.
of
tion of wavelength at the range of 400-700 nm. It is shown that the phase data can replicate the shape of an optical absorption band. Just the same as we have recorded, for the carbon black, having p/; < p~ and IL,fl--+ ~oc, the phase angle is saturated and remains constant with the wavelength 2.
4.3. Influence of the frequency on the amplitude and phase spectra The amplitude and phase spectra of Pr(HFA))'2H20 at different frequencies in the region of 300-700 nm are shown in Fig. 4. It is observed that the amplitude of the photoacoustic response decreases with an increase of frequencies and high modulation frequencies have good phase resolution. This result is in good agreement with the expression in Eq. (1) for the photoacoustic signal [24]. As illustrated in Fig. 4, the amplitude spectrum was impossible to measure for the transition while the phase spectrum has a
680
Q. Mao et al. / Spectrochimica Acta Part A 52 (1996) 675-681
high resolution in high chopping frequency. This suggests that the phase spectrum can provide very useful information about the energy levels as a complement of amplitude in most cases. The dependence of the thermal diffusion length, /L~, upon the chopping frequency means that for a sample with instant de-excitation processes, the amplitude of the PAS signal has an co ] dependence at low chopping frequencies and an co 3..2 dependence at high frequencies [13]. For the same limited case, the phase change also depends on the co. Eq. (4) gives an expression, ~ = ~(co), and the phase changes increase expectedly in the wavelength less than 380 nm. Though the overall shape of phase spectrum remains similar, the phase change does not continue to increase with an increase of co. A sharp valley associated with the Jr-~r* transition results from an increase of co. A probable explanation is that an additional factor such as fl may have a contribution to the phase angle of the 7r lr* transition in relatively high frequencies. To check the PAS response of different energy levels on the frequency, the amplitude and phase data related to the zr-~r* transition (/~max = 345 nm) and the energy levels 3P2 (2 .... = 451 nm) and ]De (Amax = 591 nm) of Pr 3+ ion at different frequencies were recorded. As plotted in Fig. 5, the amplitude of 3P2 has a relationship with the frequencies a s qpas-----kco ~.2. The phase decreases with an increase of co. The dependence of the two 100
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0
I
-t
o" Q
~
0.8,
-200
o
~. O. o
E
~[ 0 . 4 '
-300
&
~
o o
,
t
m
...
2o 40 eo Frequency (Hz)
Acknowledgements The authors thank Dr. Xianzhi Xu for his useful discussions on the theoretical part in this work. This work was supported by the National Natural Science Foundation of PR China.
"o
w o •1 O 0 w
¢~ t . 2 .
quantities on the frequency deviate a little from the PAS existing theory [28]. Similar dependence of the PAS signals on the frequency for the 7r-z* transition and the ]D 2 level was observed. In addition, the carbon black has a similar decrease for the phase angle with an increase of co. The model presented for interpreting results qualitatively provides a consistent way for reconciling the apparent discrepancies between optical and photoacoustic data. The discrepancy between the calculated phase data and the experimental results can be eliminated by the estimated additional contribution from the instrument with a form of ~xp = g'th + ///app [14]. In summary, the model based on Mandelis' work is very suitable for interpreting the amplitude and phase spectrum of the complex Pr(HFA)3"2H20. The phase of the PAS response depends on either the optical absorption fl or the excited-state lifetime r at different wavelength regions. The phase angle reflects not only the relaxation properties of energy levels but also the intensities of the transitions. On the other hand, since g, is closely related to the optical absorption coefficient, the phase angle can be used to determine the fl of the solids.
-4OO
8O
Fig. 5. Dependence of the PAS amplitude (e) and phase ( A ) of 3P2 (,~.... = 451 nm) on the chopping frequency.
References [1] C.S. Sunandana, Phys. Stat. Solidi., A 105 (1988) I I. [21 A. Lachaine, R. Pottier and D.A. Russell, Spectrochim. Acta Rev., 15(3) (1993) 125. [3] M.J. Adams and G.F. Kirkbright, Analyst, 102 (1977) 678. [4] D. Bicanic, M. Chirtoo et al., Acta Chim. Sloven., 40(2) (1993) 175. [5] S. Rai, S.N. Thakur and L. Mishira, Spectrochim. Acta Part A, 46(3) (1990) 429. [6] A. Rosencwaig and A. Gersho, J. Appl. Phys., 47 (1976) 64.
Q. Mao et al. / Spectrochimica Acta Part A 52 (1996) 675 681
[7] M.J. Adams, A.A. King and G.F. Kirkbright, Analyst, 101 (1976) 73. [8] M.B. Robin, in Yoh-Han Pao (Ed.), Optoacoustic Spectroscopy and Detection, Academic Press, New York, 1977, p. 167. [9] L.C. Aamodt. J.C. Murphy and J.G. Parker, J. Appt. Phys., 48 (1977) 927. [10] A. Rosencwaig, Photoacoustic and Photoacoustic Spectroscopy, Wiley, New York, 1980. [11] P. Poulet, J. Chamboron and R. Unterreiner, J. Appl. Phys., 51(3) (1980) 1738. [12] A. Mandelis and B.S.H. Royce, J. Opt. Soc. Am., 70(5) (1980) 474. [13] A. Mandelis, Y.C. Teng and B.S.H. Royce, J. Appl. Phys. 50(11) (1980) 7138. [14] J.C. Roark, R.A. Palmer and J.S. Hutchinson, Chem. Phys. Lett., 60 (1978) 112. [15] Y.C. Teng and B.S.H. Royce, J. Opt. Soc. Am., 70(5) (1980) 557. [16] R.C. Powell, D.P. Neikirk and D. Sardar, J. Opt. Soc. Am., 70(5) (1980) 486. [17] L.D. Merkle and R.C. Powell, Chem. Phys. Lett., 46 (1977) 303.
68l
[18] L.D. Merkle and R.C. Powell, J. Phys. C, 11 (1978) 3103. [19] J. Fresquet, B. Girault et al., Appl. Optics, 23 (1984) 2784 [20] Zhang Yugeng, Su Qingde and Zhao Guiwen. CrystalIogr. Res. Yech., 28(7) (1993) 995. [21] Su Qingde, Zhao Guiwen and T. Kuwamoto, Rare Earths (Japan), 3 (1989) 68. [22] Su Qingde, Mao Qinglu and Zhao Guiwen, Spectrochim. Acta Part A., 51 (1995) 2459. [23] N. Sabbatatini and M. Guardigli, Coord. Chem. Rev., 123 11993) 201. [24] A. Mandelis and B.S.H. Royce, J. Appl. Phys., 50(6) (1970) 4330. [25] F. Halverson, J.S. Brinen and J.R. Leto, J. Chem. Phys., 40 (1964) 2790. [26] T.A. Moore, D. Benin and R. Tom, J. Am. Chem. Soc., 104 c 1982) 7356. [27] W.T Carnall, in K.A. Gschneidner, Jr. and L.R. Eyring (Eds.), Handbook on the Physics and Chemistry of Rare Earths, Vol. 3, North-Holland, Amsterdam, 1979, p. 197. [28] G.J. Papadopoulos and G.L.R. Mair, J. Phys. D Appl. Phys., 25(4) (1992) 722.