Thermal characterization of Glucose- Water mixtures by
photopyroelectric techniques
G Lara-Hernandez1,2, J J A Flores-Cuautle3,4,5, L M Cervantes-Espinosa6, A
Cruz-Orea1* and E Suaste-Gomez2
1
Physics Department, CINVESTAV-IPN, Av. IPN No. 2508, Col. San Pedro
Zacatenco, C. P. 07360,México D. F. México.
2
Electrical Engineering Department, CINVESTAV-IPN, Av. IPN No. 2508, Col. San
Pedro Zacatenco, C. P. 07360,México D. F. México.
3
Laboratorium voor Akoestiek en ThermischeFysica, KU Leuven, Celestijnelaan
200D, Leuven, Belgium
4
Present address: Cátedras CONACyT, Consejo Nacional de Ciencia y Tecnología,
Av. Insurgentes Sur 1582, Crédito Constructor, Benito Juárez C.P. 03940, México/
5
Present address: Maestría en Ingeniería Electrónica, División de Estudios de
Posgrado e Investigación, Instituto Tecnológico de Orizaba, Orizaba, Ver. México
6
ESCOM-IPN, Av. Juan de Dios Bátiz s/n esquina Miguel Othón de Mendizabal, U.
P. A. L. M., Col. Lindavista, 07738 México, D. F. México
* Corresponding author e-mail: orea@fis.cinvestav.mx
Abstract. The increasing levels of diabetes mellitus, points out the necessity to develop new
methods to get accurate values of the glucose level as a way to reduce the risk of major
hypoglycaemia, this level also provides the information necessary to make small changes in
insulin treatment and allows us to understand the effects of some foods, exercise or different
doses of insulin. As first step to develop an accurate system of glucose determination,
measurement of thermal properties of glucose on solutions were obtained by means of
Photopyroelectric (PPE) technique, which has proved to be a suitable method to measure
thermal parameters of liquid samples, then by using the back and inverse Photopyroelectric
configurations, the thermal diffusivity and effusivity of glucose-water mixtures were obtained,
at room temperature, as a function of glucose concentration.
1. Introduction
Nine out of ten adults, aged 25 years old and older, had blood glucose over the recommended limits
[1]. Raised blood glucose is an indicator of diabetes mellitus, since diabetes can lead to several health
risks like: strokes, renal failure, lower limb amputations, visual impairment, blindness, there is also a
disease which medical care cost up to 15% of national healthcare budgets in developed countries. As
part of prevention and early diagnosis of this disease, it is necessary to carry on research on effective
ways to measure small variations in glucose concentration in solutions, as first step, to develop a
measurement system to determine glucose concentration in blood, in this sense several methods to
measure glucose concentrations have been developed [2-4].
Most of those methods involve expensive equipment, on the other hand photothermal (PT)
techniques have been used to detect small concentrations of some compound in solution and, are
cheaper than other techniques with the same or even less resolution [5-8]. PT techniques are based in
the analysis of thermal waves, induced by a frequency modulated light source, traveling through a
layered system in which a thermal wave detector and sample under analysis are slabs, when thermal
wave detector is a pyroelectric material then it is so-call photopyroelectric (PPE) technique.
Depending on selected configuration PPE methods are able to provide several sample features as
optical absorption spectra [9], nonradiative relaxation process [10] and, thermal properties [11, 12]. In
the present study the so-called back (BPPE) and inverse (IPPE) photopyroelectric configurations, both
based on PPE detection, are used to determine thermal diffusivity and thermal effusivity of glucosewater mixtures.
In the IPPE configuration the thermal effusivity (e) of samples can be obtained, in this case
frequency modulated light impinges on one side of a pyroelectric detector which has the liquid sample
on the other side, in such a way that sample acts as heat dissipater for thermal waves originated at
pyroelectric detector. By other hand, to obtain the sample thermal diffusivities the BPPE configuration
was used, in this configuration the sample is enclosure between the pyroelectric detector and a metal
sheet acting as thermal wave generator due to absorbed light. The liquid sample allows conducting the
thermal waves to the pyroelectric sensor where a PPE signal is generated and processed by the lock-in
amplifier.
2. Experimental
2.1. Samples preparation
Aqueous solutions were prepared by mixing glucose and bi-distilled water, different concentrations
were prepared. Adequate glucose quantities (x% w/v) were diluted into 90 ml of bi-distilled water, in
order to obtain complete dissolution samples were magnetically stirred during 10 minutes at room
temperature.
2.2. Experimental setups
Experimental setup used to obtain sample thermal effusivity (es), can be seen in figure 1. In this setup
the sample is placed in a container, over the pyroelectric detector, while modulated light strikes on the
bottom side of the detector. The PPE signal, of the PVDF 9 µm thick pyroelectric detector, was
amplified by a lock-in amplifier and its amplitude and phase were measured as a function of the laser
beam modulation frequency (f).
Figure 1 IPPE experimental setup for thermal effusivity measurements
For frequencies that leads to a thermally thick sample (i.e. ls >> µs, where ls is the sample thickness
and µs= (αs/(πf))1/2, with αs is the sample thermal diffusivity) and, having optically opaque pyroelectric
sensor, the theoretical expression of pyroelectric sensor output is expressed by [7, 13]:
V ( ) 
(1  e
 plp
( g  1)e
)(1  b)  (e
 p l p
 p l p
 1)(1  b)
(1  b)  (1  g )e
 plp
(1  b)
(1)
where σp is the complex thermal diffusion coefficient (σp= (1+j)/µp, j=(-1)1/2 and µp= (αp/(πf))1/2), with
αp the pyroelectric thermal diffusivity), lp is the pyroelectric thickness, b = es/ep, g = eg/ep and es, eg and
ep, are the thermal effusivities for sample, surrounding gas and pyroelectric detector, respectively.
By fitting the Equation 1 to the experimental data, for the IPPE geometry, it is possible to obtain the
sample thermal effusivity. Furthermore, in order to avoid the pyroelectric sensor signal dependence on
the frequency, the obtained V(ω) signal was normalized with the empty PPE cell signal.
BPPE configuration is formed by a chamber of variable length (l) containing the liquid sample;
cavity is formed by a circular Cu foil 100 𝜇m thick and, Lanthanum modified lead zirconate (PLZT)
756 micron thick as pyroelectric sensor. A laser diode beam, modulated by the internal oscillator of a
lock-in amplifier, impinges on the black painted inner surface of the metallic foil, which acts as light
absorber. As the modulated light strikes on the metallic foil, its temperature fluctuates periodically at
the same modulation frequency of the incident beam; temperature oscillations at 𝑥 = 𝑙 can be measured
with the pyroelectric sensor as showed in figure 2.
Figure 2 BPPE experimental setup for thermal diffusivity measurements
Thermal diffusivity (αs) was obtained by performing frequency scans at x and x + Δx, where Δx is a
well controlled distance then, using Δx as sample thickness (ls), the PPE signal, for thermally thick
sample, is expressed by equation 2.
V ( f )  Beasls e
 j  2  asls 
(2)
where as= ((πf)/ αs)1/2
3. Results and discussion
Amplitude and phase, as a function of the light modulation frequency, obtained by IPPE technique are
depicted in figure 3 for 0.7% glucose concentration sample, solid line represents the result of carefully
fitting using Equation 1, having es as fitting parameter, ep was determined a priori, by using glycerol
and water as reference samples.
Figure 3 IPPE amplitude and phase as function of frequency
Figure 4 shows the frequency dependence of the phase signal for 0.7% glucose concentration sample,
obtained by BPPE technique. Solid line represents the best fitting of phase of Equation 2 to the
experimental data, using αs as fitting parameter, with ls well controlled as mentioned.
Figure 4 BPPE normalized phase as function of square root of the light modulation frequency
Figure 5 summarizes the obtained thermal effusivities and diffusivities as a function of glucose
concentration, solid lines are used for eye guide to show tendency values. In the case of the thermal
effusivity there is a slightly decrease of this parameter when is increased the glucose concentration.
For thermal diffusivity values it is possible to see a decrease of this thermal parameter when the
concentration of glucose is increased.
Figure 5 Thermal diffusivity and effusivity as function of glucose concentration
4. Conclusions
In the present study the back (BPPE) and inverse (IPPE) photopyroelectric configurations were used to
determine the thermal diffusivity and thermal effusivity of glucose-water mixtures. The experimental
results show a decrease of the thermal diffusivity with increasing amount of glucose. In the case of
thermal effusivity, the concentration dependence is roughly within the statistical uncertainty, even
though this gives us a first sight on the behavior of glucose thermal properties as function of
concentration.
Acknowledgments
This work was partially supported by CONACyT and COFAA-IPN. We are also grateful to Ing. E.
Ayala from Physics Department - CINVESTAV-IPN, for their technical assistance.
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