Scientific paper
Accurate Photopyroelectric Calorimetry Applied to Isotopic Liquid Mixtures
D. Dadarlat, C. Neamtu, V. Tosa, M. Streza
National R&D Institute for Isotopic and Molecular Technologies, 65-103 Donath Street, POB 700, 400293 Cluj-Napoca, Romania. Tel.: +40 264 584037, Fax: +40 264 420042, E-mail: dadarlat@s3.itim-cj.ro.
Submitted: 06-11-2006
Abstract
The suitability of the photopyroelectric (PPE) calorimetry for detection of molecular associations in binary liquid mixtures was investigated. Accurate PPE measurements in two detection configurations (using the information contained only in the phase of the PPE signal) were performed to obtain the values of thermal diffusivity and effusivity. The limits of the method were tested by detecting isotopic effects in H2O-D2O and DMSO(6H)-DMSO(6D) mixtures. The composition behaviour of the above mentioned thermal parameters for DMSO(6H)-H2O mixtures was presented for comparison. Small isotopic effects in thermal diffusivity were observed for H2O-D2O and DMSO(6H)-DMSO(6D) mixtures (about 4% and 8%, respectively).
Keywords: photopyroelectric calorimetry, thermal diffusivity, thermal effusivity, molecular associations, isotopic mixtures
1. Introduction
In the photopyroelectric (PPE) technique, the temperature variation of a sample, exposed to a modulated radiation, is measured with a pyroelectric sensor. In the last years, the two PPE calorimetric configurations (i.e. "back" and "front", respectively) have been applied for investigating the behaviour of static (specific heat) and dynamic (thermal conductivity, diffusivity, effusivity) thermal parameters of condensed matter samples.1-3
In the most general case, the complex PPE signal depends on all optical and thermal parameters of the layers of the detection cell. After some mathematical approximations, one can obtain results in which the amplitude or the phase of the signal depend on one or, in a simple way, on two of the sample's related thermal parameters.1,3 In these special cases of experimental interest, the information is usually contained in the amplitude of the signal, the phase being often constant.2 However, sometimes, the phase of the PPE signal also contains information, and it refers either to thermal diffusivity or effusivity of the sample.2,4,5
It is very convenient to measure the phase of the signal, because the phase represents only a time delay of the signal, as compared to a reference one, and it is not dependent on the power fluctuations of the incident radiation and on the quality of the incident surface (as is the case of the amplitude).
In the back (standard) configuration, the most convenient PPE particular case, largely used in order to find
the values of the thermal diffusivity, requests thermally thick sample and sensor and optically opaque sample. In this configuration, a modulated light impinges on the front surface of a sample, and a pyroelectric sensor, situated in good thermal contact with the sample's rear side, measures the heat developed in the sample due to the absorption of radiation. In order to find the thermal diffusivity of a given sample, the phase of the PPE signal can be measured, by performing either a frequency or a thickness scan.4
Recently, it has been demonstrated that the methodology based on sample's thickness scan leads to very accurate and reproducible values for the thermal diffusivity, due to the possibility of precisely controlling the sample's thickness variation.4,6
Concerning the front (inverse) configuration (the radiation impinges on the front surface of the sensor, and the sample, in good thermal contact with its rear side, acts as a heat sink), two main detection schemes were proposed until now: (i) with thermally thin and optically opaque sensor, and (ii) with thermally thick and semitransparent sensor.7, 8 In both cases, the sample must be thermally thick, and the information is contained in the amplitude of the signal.
Recently, this front configuration, but with opaque sensor and thermally thick sensor and sample, was used to measure the thermal effusivity of some (semi)liquids. The experimental conditions (chopping frequency, number and geometrical thickness of the layers of the detection cell) were set up in such a way that the information (the
value of the thermal effusivity) is contained in the phase of the signal.910
Both back and front configurations were independently used by the authors in order to detect molecular associations in some water-based binary mixtures (as water-ethanol, methanol, ethylene glycol, acetic acid, glyce-rol).4,11 It has been demonstrated that both thermal diffusi-vity and effusivity are thermal parameters suitable for molecular association studies, the expected excess value11 being larger for the thermal diffusivity.
In principle, concerning molecular association processes in binary mixtures, the liquids were divided in two classes: "interacting" and "non-interacting" liquids.4,11 When interacting liquids are involved in a binary mixture (water-ethanol, for example), large deviations from additi-vity for thermal parameters (thermal diffusivity and effu-sivity) were found. In the case of non-interacting liquids (water- ethylene glycol, for example), the excess values (deviation from linearity) of thermal parameters are small (few percents), or zero. In such a context, a PPE calori-metry applied to isotopic liquid mixtures represents a challenge; small deviations from linearity of the thermal parameters as a function of composition is expected and, consequently, accurate investigations are necessary.
In this paper we intend to test the limits of the two particular PPE detection cases mentioned above and, using the information contained only in the phase of the PPE signal, to detect isotopic effects in H2O - D2O and DM-SO(6H) -DMSO(6D) liquid mixtures. Due to the fact that thermal effusivity is less sensitive to association processes (than thermal diffusivity), a special attention was paid to mathematical fits of the measured data for this parameter.
2. Theory
The theory of the two configurations (including the approximations for each particular case), together with the schematic diagrams of the detection cells, were largely presented elsewhere.1,3,5,7,12 We will present here only the results.
the phase.
Front Configuration
In the front configuration, with opaque sensor and thermally thick sensor and sample, the phase of the PPE signal is given by9, 10:
tan 6 =
(l + /?y)exp(- IJ^)sm(L/MP) ] - (l + ff p)exp(-Lp/fjp)co$(Lp/fj^)
(2)
From Eq.2, for a given frequency, one can calculate Rsp and then derive the sample's effusivity es according to the following relationship:
In Eqs.2 and 3,

(3)
(4)
represents the reflection coefficient of the thermal waves at the interface of two media, where b„ = ei/ej The symbols
j 1 J.
"p" and "s" refer to the pyroelectric sensor and substrate (sample), respectively. The thermal diffusion length is:
a

(5)
where f is the modulation chopping frequency and a is the thermal diffusivity, related to the other thermal parameters (the volume specific heat C, thermal conductivity k and thermal effusivity e) by:

• = (Ckfi,
(6)
3. Experimental
Back Configuration
In the particular case when the sample and the sensor are thermally thick and, additionally, the sample is optically opaque, the phase 8 of the PPE signal is given by:2
0 = eo-Lt{m/2ay*,	(l)
where 80 is an instrumental, frequency independent, phase offset, Ls and as are the sample's thickness and thermal diffusivity, respectively, and ra is the angular modulation frequency of the incident radiation.
As mentioned before, an inspection of Eq.1 leads to the conclusion that, in order to find the thermal diffusivity, one can perform either a frequency or a thickness scan of
A standard PPE calorimetric line was used for investigations.2 The radiation source was a 30 mW HeNe laser, chopped by an acousto-optical modulator. The signal from a 500 pm thick LiTaO3 pyroelectric sensor was processed with a SR 830 lock-in amplifier.
The detection cell in the front configuration was presented elsewhere.12 The liquid sample accomodates the space between the sensor and a glass window, its thickness (5 mm) being delimitated by two glass spacers. It is to point out that the cell can be filled and the sample removed without moving the sensor. The frequency scan was performed in the 1 - 46 Hz frequency range, with a step of 0.75 Hz. In this frequency range, both the sensor and the sample are thermally thick. The optical opacity of
the sensor was ensured by its front (Cr-Au) electrode. In order to eliminate parameters difficult to be estimated experimentally (e.g. incident radiation power density, radiation to heat conversion efficiency, thermal and electrical time constants of the electrical circuit), the PPE phase was normalized to the one obtained with air instead of sample;10 the obtained normalized phase satisfies Eq.2.
The detection cell, in the back configuration, was largely described before.4 The radiation source was modulated at 1 Hz by an acousto-optical modulator, driven from the internal oscillator of the lock-in amplifier, used also for signal processing. The value of the frequency was kept constant with a precision better than 0.1 mHz. The thickness scan was performed between 600 and 1100 pm (incremental step 50 pm) with a precision of 1 pm.
In both configurations, a computer was used for data acquisitions. The signal/noise ratio was better than 1000.
For each investigated concentration, 10 mL solution was prepared starting from 99% pure solvents, by adding x volume parts of solute (s) to (1-x) parts of solvent (w). Since such a binary mixture does not obey the simple volume additivity law, the mass concentration cs (% mass) = 100 x (ps x Vs)/(ps x Vs + pw x Vw) was used for the graphical representation of the obtained results. The necessary sample quantity was 200-300 pl. The two isotopic di-methylsulfoxid species C2H6OS and C2D6OS (denoted in the paper DMSO(6H) and DMSO(6D)) were selected for investigations due to their large use in drugs industry.
Figure 2. Typical frequency scans of the phase of the PPE signal, in the "front" configuration, for the pure components of the investigated mixtures. The frequency for which all curves cross the zero value is used for the calculation of the sensor's thermal diffusivity.10
In the back configuration, the precision of the fits performed with Eq.1, and expressed by percent of residuals about mean explained, is 100%.
A special attention was paid to the fits of the experimental data obtained in the front configuration. The parameters of the LiTaO3 sensor were: ap = 1.56 x 10-6m2/s and ep = 3823 Ws1/2/m2K. The sample's thermal effusivity was considered as a parameter, and the best fit was selected by minimizing the root mean square. An example is presented in Figure 3.
4. Results and Discussion
Typical thickness scans of the phase of the PPE signal, in the back configuration, for pure H2O, D2O, DM-SO(6H) and DMSO(6D) are presented in Figure 1, and the corresponding frequency scans of the normalized phase, in the front configuration, are displayed in Figure 2.
Figure 1. Typical thickness scans of the phase of the PPE signal, in the "back" configuration, for the pure components of the investigated mixtures.
Figure 3. The root mean square obtained with experimental points and different fits, having as fitting parameter the sample's effusi-vity. DMSO(6H) was selected as an example.
The obtained relative deviations from additivity for the thermal diffusivity and effusivity for H2O-D2O, DM-SO(6H)-DMSO(6D) and H2O-DMSO(6H)2 are p2resented in Figure 4 and Figure 5, respectively.
The maximum relative deviation from additivity of the thermal diffusivity for H2O-DMSO(6H) mixtures is about -18% and indicates association processes taking place in this system. In fact, DMSO is well known for its
0.0 0.2 0.4 0.6 0.8 1.0 weight fractionx
Figure 4. Relative deviations from additivity of the thermal diffusi-vity for H2O-D2O and DMSO(6H)-DMSO(6D), together with a mixture (H2O-DMSO(6H)) known for its "aggressivity" in forming molecular associations.
0.0 0.2 0.4 0.6 0.8 1,0 weight fraction x
Figure 5. Relative deviations from additivity of the thermal effusi-vity for H2O-D2O and DMSO(6H)-DMSO(6D), together with a mixture (H2O-DMSO(6H)) known for its "aggressivity" in forming molecular associations.
hygroscopicity; this is the reason why this mixture was selected as comparison system. On the other hand, the maximum relative deviations from additivity of the thermal dif-fusivity for H2O-D2O and DMSO(6H)-DMSO(6D) are about -4% and -8%, respectively. This fact can be explained only as an isotopic effect because, from chemical point of view, H2O and D2O, and DMSO(6H) and DM-SO(6D) molecules, respectively, are almost equivalent. The larger effect observed in the case of DMSO mixtures is due to an increased number of possibilities of interchanging H-D ions and creating DMSO(1D) ... DMSO(5D) species. In the case of H2O-D2O mixtures, there is only one posibility of creating a HDO intermediate molecule. We want to stress also on the fact that, in the case of DM-SO mixtures, the (accidental) presence of OH- radicals accelerates the H-D change.
Concerning the relative deviations of the thermal ef-fusivity (Figure 5) for H2O-D2O and DMSO(6H)-DM-SO(6D) mixtures, they are about -1% —2%, at the reso-
lution limit of our method. The same deviation for H2O-DMSO(6H) mixtures is about -7% - -8%, respecting the (about)3 reduction factor for the sensitivity (in detecting molecular associations) of thermal effusivity, as compared to thermal diffusivity, observed for water-etha-nol mixtures.11
5. Conclusions
Two PPE detection configurations, (i) the back one, with thermally thick sample and sensor, and optically opaque sample (for thermal diffusivity measurements), and (ii) the front configuration, with opaque sensor and thermally thick sensor and sample (for thermal effusivity measurements), were used to detect isotopic effects in H2O-D2O and DMSO(6H)-DMSO(6D) binary liquid mixtures. In both cases the information was contained in the phase of the PPE signal, and was obtained via a sample thickness and frequency scan, respectively. High accurate investigations were necessary in order to detect isoto-pic effects; the sensitivity of both methods is about 1%, and, consequently, small isotopic effects were observed in the behaviour of the thermal diffusivity of the two isotopic mixtures. No clear isotopic effects were detected in the composition behaviour of the thermal effusivity.
Work is in progress with increasing the accuracy of thermal diffusivity measurements, by increasing the quality of thickness variation control.
6. Acknowledgement
Work supported in part by Romanian Ministry of Education and Research through the projects 39N/2005 and CEEX 65/2006. The authors acknowledge useful conversation about isotopic effects with Dr. V. Almasan.
7. References
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Povzetek
Proučevali smo primernost uporabe fotopiroelektrične kalorimetrije za raziskave asociativnih procesov v binarnih tekočih mešanicah.. Z natančnimi meritvami z dvema možnostima detekcije smo dobili vrednosti termične difuzivnosti in efuzivnosti. Omejitve metode smo testirali z detekcijo izotopskega efekta v mešanicah H2O-D2O in DMSO(6H)-DM-SO(6D). Opazili smo relativno majhne izotopske efekte in termično difuzivnost: približno 4 % za mešanico H2O-D2O in 8 % za DMSO(6H)-DMSO(6D).