Photoacoustic phase study on the frequency dependence of phase angle and triplet state lifetime of Nd(III)-acetylacetonate

Article abstract of DOI:10.1016/j.saa.2005.04.028

The amplitude and phase of the photoacoustic (PA) signal generated in the rare earth complex powder of Nd(III)-acetylacetonate (Nd(AA)₃) were examined. By using the reasonably simplified formula about phase angle at the wavelengths assigned to π-π^* transition of ligand and f-f transitions of Nd³⁺, the instrumental contribution to phase angle at different chopping frequency was calculated. The frequency dependence of sample phase angle, the relative phase angle shift caused by instrumental factors and the calculation of triplet state lifetime of sample under study were also discussed. Being independent of sample, the instrumental contribution to phase angle was regarded as a parameter representing the situations of instruments and measurement and it became an approach to calculate the relaxation time of ligand in rare earth complex.

Full text of DOI:10.1016/j.saa.2005.04.028

Spectrochimica Acta Part A 63 (2006) 55–59
Photoacoustic phase study on the frequency dependence of phase angle
and triplet state lifetime of Nd(III)-acetylacetonate
Bin Hu, Da Chen, Qingde Su∗
Department of Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
Received 27 January 2005; accepted 21 April 2005
Abstract
The amplitude and phase of the photoacoustic (PA) signal generated in the rare earth complex powder of Nd(III)-acetylacetonate (Nd(AA)3)
were examined. By using the reasonably simplified formula about phase angle at the wavelengths assigned to ␲–␲* transition of ligand and f–f
transitions of Nd3+, the instrumental contribution to phase angle at different chopping frequency was calculated. The frequency dependence
of sample phase angle, the relative phase angle shift caused by instrumental factors and the calculation of triplet state lifetime of sample
under study were also discussed. Being independent of sample, the instrumental contribution to phase angle was regarded as a parameter
representing the situations of instruments and measurement and it became an approach to calculate the relaxation time of ligand in rare earth
complex.
© 2005 Elsevier B.V. All rights reserved.
Keywords: Photoacoustic angle; Frequency dependence; Instrumental contribution; Rare earth complex
1. Introduction
under study, the geometry of the photoacoustic cell, the
response of the detecting system, etc. In actual measure-
ments, many of the non-sample related parameters are always
regarded constant. In this paper the influence from the chop-
ping frequency to the instrumental contribution of phase
angle and the relaxation time of ligand are discussed. Then a
method to calculate the triplet state lifetime of Nd(AA)3 by
instrumental contribution at different chopping frequencies
is presented.
Photoacoustic spectroscopy (PAS) is a technique used in
the study of optical absorption. The PA response is gener-
ated when optical absorption causes a rapid local heating
in the sample under investigation. The subsequent thermal
expansion generates a pressure wave that is detected acousti-
cally [1]. From the analysis of the PA signal, the information
about the absorption of the sample is obtained. PAS is being
used extensively in the optical and thermal characterization of
wide spectrum of materials [2]. For instance, some researches
about rare earth complexes were reported [3–5]. The great
interest in the study of rare earth complexes is mainly due
to their close relationship to rare earth structure chemistry,
rare earth functional materials, environmental chemistry and
biochemistry [6–8].
2. Theory
In the Rosencwaig–Gersho’s model of PA, the nonradia-
tive relaxation processwassupposed to occur instantaneously
[9]. The first use of PA phase signal to measure the nonra-
diative relaxation time was employed by Merkle and Powell
[10]. Then Mandelies presented a phase formula for optically
opaque and thermally thick samples [11]:
One of the important characteristics of PAS is that it
provides information about both amplitude and phase of
response of a sample. Phase information contains contribu-
tions from a number of sources associated with the sample
ꢀ
ꢁ
−1
φ = tan−1(−ωτβ) + tan−1(ωτ) − tan−1
1 − (2ωτβ)1/2
∗
Corresponding author. Tel.: +86 551 3606642; fax: +86 551 3606642.
E-mail address: qdsu@ustc.edu.cn (Q. Su).
(1)
1386-1425/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.saa.2005.04.028

56
B. Hu et al. / Spectrochimica Acta Part A 63 (2006) 55–59
where τ is the lifetime of the excited states, ω = 2πf and f is the
chopping frequency of the light,τβ = 1/β2αs is a characteristic
relaxation time for the system corresponding to the thermal
transit time from a depth µβ (=1/β) within the solid.
In the PAS investigation of rare earth complexes, both
R–G model and Mandelies model are used. Since the triplet
state lifetime of ligand is not low enough to neglected while
the absorption coefficient β of ligand is very high, Eq. (1)
is simplified to Eq. (2). While the relaxation process of rare
earth ion is essentially fast, the R–G model, Eq. (3) is used
[12].
4. Results and discussion
4.1. Photoacoustic spectra and phase information
The amplitude spectrum of Nd(AA)3 (Fig. 1) shows
that there exists a very strong absorption in the wave-
length around 330 nm, which is assigned as the ␲–␲
*
electronic transition of AA. The peaks at 530 nm and
584 nm are assigned correspondingly to the f–f transitions
(4I9/2 → G7/2, 4I9/2 → G5/2 + 2G7/2) [10,15].
To learn about the frequency dependence of phase angle
and instrumental contribution, the PA amplitude and phase
information were obtained at different chopping frequency,
from 9 to 470 Hz. The phase angles at 330 nm, 530 nm and
584 nm versus different chopping frequencies are shown in
Fig. 2.
4
4
π
φ = tan−1(ωτ) +
(2)
(3)
4
ꢂ
ꢃ
2
φ = tan−1 1 +
βµs
µs is the thermal diffusion length. In fact, the experimental
value of phase angle includes a relative phase angle shift due
to the instrumental parameters. Eq. (2) and (3) are rewritten
as
π
φE(ligand) = φ0 + tan−1(ωτ) +
(4)
(5)
4
ꢂ
ꢃ
2
φE(central ion) = φ0 + tan−1 1 +
βµs
where ϕE is the experimental phase angle and ϕ0 is the instru-
mental contribution, which includes phase shifts due to cell
resonance, the positioning of the sample with respect to the
light beam, and the positioning of the monochromator slits
with respect to the chopper slots [13].
3. Experimental
3.1. Synthesis of rare earth complex
Fig. 1. PA amplitude spectra of Nd(AA)3.
The complex was synthesized according to the procedure
given in Ref. [14]. Nd2O3 was converted to NdCl3 by treat-
ment with concentrated HCl. A solution of the chloride in
absolute ethanol was added to a solution of acetylacetone
(AA) in the same solvent. The precipitation was accom-
plished by addition of ammonia. The element analyses and
infrared spectra were indicative of the structure formulae.
3.2. PA measurement
The PA spectra were obtained on a single-beam spectrom-
eter. A 500 W Xenon lamp, a CT-30F monochromator and a
PA cell fitted with an ERM10 electret microphone were used.
The output signal of the microphone was fed to a lock-in
amplifier (LI-574A) and was collected on an A/D converter
and dealt with by computer. The PA amplitude and phase
spectra were recorded in the region of 300–800 nm, and the
amplitude spectra were normalized against the carbon black
to account for the variation due to the light source and spec-
trometer.
Fig. 2. PA phase shift vs. chopping frequency.

B. Hu et al. / Spectrochimica Acta Part A 63 (2006) 55–59
57
The phase angles change irregularly with the increase of
chopping frequency. At the low frequency region, the rela-
tionship between ΦE and f is nearly linear. When f increases
to high value, the phase shift becomes saturated.
4.2. Calculations of instrumental contribution and
relaxation time
First, considering that the optical absorption coefficient
β of AA around 330 nm is high enough, τβ in Eq. (1)
was neglected reasonably and tan−1(−1/(1−(2ωτβ)1/2)) was
regarded as a constant. Based on Eq. (4), ϕE(330 nm) was given
as:
π
φE(330 nm) = φ0 + + tan−1(ωτ(AA)
)
(6)
4
Second, because the energy levels of Nd3+ are often inter-
mixed and the relaxation process undergoes a nonradiative
channel most readily. The relaxation process of Nd3+ is
very fast, τ → 0, which means that the Eq. (5) is available.
When the chopping frequency is chosen, µs keeps constant,
and β varies directly with the PA amplitude (A), so βµs
can be written as the form of KA. Eq. (5) were rewritten
as
Fig. 3. tan−1(ωτ) of a series τ vs. chopping frequency.
4.2.2. Method of plot-comparing
Since the lifetime of triplet state is about 10−3 s, it is logi-
cal to evaluate τ to be from 10−3 to 20 × 10−3 s. Fig. 3 is the
plot of tan−1(ωτ) versus chopping frequency at eight values
of τ. The value of tan−1(ωτ) closes to π/2 along with the
increase of frequency. The same trend is presented in the plot
of ϕ0 versus frequency at different τ (Fig. 4). ϕ0 can be also
acquired from Eq. (6) instead of calculating from Eq. (7) as
mentioned before. ϕ0 obtained in this way is defined as ϕ0∗
ꢂ
ꢃ
2
φE(λ) = φ0 + tan−1 1 +
(7)
KA(λ)
with λ, the wavelength of PAS peaks of central ion. Based on
Eq. (7), PA information about Nd3+ at 530 nm and 584 nm
were collected to calculate ϕ0 in different chopping fre-
quency. The results of ϕ0 were shown in Table 1 and Fig. 5.
There are two methods to acquire the τ(AA). One is method
of calculating, and the other is method of plot-comparing, as
described below.
π
φ0∗ = φE(330 nm)
−
− tan−1(ωτ(AA)
)
(8)
4
When f = 12 Hz, ϕ0∗ covers from −343.6◦ to −291.5◦ corre-
sponding to different τ, with the shift extent of 52◦. While
f = 470 Hz, φ0∗ is from 70.9◦ to 88.3◦, with the shift being
only 17.4◦. It is difficult to distinguish the dots from each
other in high frequency region for they gather tightly, while
in the low frequency region, they can be resolved clearly.
4.2.1. Method of calculating
Because ϕE(330 nm) is obtained directly from experiment,
τ(AA) can be acquired based upon Eq. (6) and the value of ϕ0
in Table 1.
Table 1
ϕ0, the instrumental contribution to phase angle in different chopping
frequency
f (Hz)
ϕ0 (◦)
f (Hz)
ϕ0 (◦)
12
22
31
39
55
59
69
70
80
−141.1
−64
−29
−7.7
15.5
33.4
42.9
47.1
71.4
112
180
200
220
240
260
280
310
370
420
470
190.3
228.5
221.2
237.7
244
245.3
254.7
266.7
270.9
269.4
100
160
181.0
Fig. 4. ϕ0 at a series of τ vs. chopping frequency.

58
B. Hu et al. / Spectrochimica Acta Part A 63 (2006) 55–59
Fig. 5. Method of curve-comparing to obtain τ(AA)
.
Fig. 6. Method of calculating to obtain τ(AA)
.
It is explained that the contributions from different triplet
state lifetime to the value of phase angle become closer and
closer to each other along with the increase of chopping
frequency.
Compare the ϕ0 in Table 1 with the data in Fig. 4. The dots
in Fig. 4 who match the curve of ϕ0 best should be regarded
as compatible theoretical results, and the τ described by those
dots is regarded as the value of triplet lifetime of AA. There
is one point should be noticed that the values of PA angle
during the processes of different calculations may shift with
one period, which is 180◦.
Table 2
ϕ0 and τ(AA) in different chopping frequency
f (Hz)
ϕ0 (◦)
τ
(s)
(AA)
9
12
15
18
21
24
−178.8
−140.1
−102.0
−73.3
−51.3
−29.5
0.0070
0.0083
0.0075
0.0067
0.0083
0.0055
results of τ(AA) keep consistent very well. It explains that
only in a limited region the frequency has hardly any influ-
encetothecalculationoftripletstatelifetime. Andinthesame
region, ϕ0 is linear with chopping frequency, which makes
ϕ0 the parameter representing the instrumental measurement
conditions.
4.3. Discussion and application of the method
It is clear that the curve representing τ(AA) matches those
dots corresponding to τ = 0.009 s and 0.007 s well in low fre-
quency region while is much closer to dots corresponding
to τ = 0.001 s in high frequency (Fig. 5). It is believed that
the simplifying method of Eq. (1) to (2) and (4) has no good
adaptability in high frequency region. Although the τβ in Eq.
(1) is a small value, the section of tan−1(−ωτβ) is neglected
reasonably only when ω is not high. With the increase of
ω, tan−1(−ωτβ) begins to show its influence to the process
of calculating ϕ0, and further more to that of τ(AA). Being
lacking one positive section, ϕ0∗ gotten from Eq. (8) becomes
smaller than should be, especially in high frequency region.
It is also proved by the τ(AA) acquired from method of
calculating.
Fig. 6 shows that τ(AA) decreases with the increase of fre-
quency. When the frequency is in the region below 30 Hz,
τ(AA) gathers around 0.007–0.009 s. When the frequency is
enhanced above 200 Hz, τ(AA) begins to close to 0.001 s,
which accords with the method of plot-comparing.
To obtain the value of τ(AA), chopping frequency was con-
trolled in low region and measurements were done again. The
results are shown in Table 2. In this frequency region, ϕ0 has
a good linear relationship with f. It is also evident that the
5. Conclusions
Instrumental contribution to PA phase angle is not always
the constant and has an irregular relationship with chop-
ping frequency, which is linear in the low frequency region.
For optically opaque and thermally thick samples, instru-
mental contribution is independent of samples and is one
of parameters representing the situations of instruments and
measurement. Instrumental contribution can be applied to
acquired the triplet state lifetime of ligand in complex, and
thelifetimeisalsoinfluencedbychoppingfrequency, because
the simplified model of PA is not always available in whole
frequency region. It is helpful to select proper chopping
frequency region to study the lifetime by PAS. When the
chopping frequency is in the region where the triplet state
lifetime keeps constant, it is efficient to investigate the instru-
mental contribution to phase angle, the relaxation process of
complex and calculate the lifetime of ligand.

B. Hu et al. / Spectrochimica Acta Part A 63 (2006) 55–59
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