Photopyroelectric spectroscopy and calorimetry

The development of photothermal (PT) methods began in the 1980s due to the emerging opportunities being offered by laser and radiation detection techniques. Since then, the main discussion forum of the international scientific community in this field has been the “International Conference on Photothermal and Photoacoustic Phenomena,” organized each second year. Often, Gordon type research conferences were organized on this topic and held on alternate years. Since 1981, there have been 21 international conferences on photoacoustic and photothermal phenomena and eight Gordon research conferences. The most recent of which was the ICPPP21.

Concerning the development of this field of research, after passing through the stages of experimental demonstration and fundamental theory, efforts are now placed on optimizing experimental configurations of PT techniques toward quantitative analysis of the thermo-optical properties of materials. The compatibility of PT techniques with a large class of materials has been proved. This includes homogeneous materials with well-defined properties, as well as inhomogeneous materials with complex structures, such as composite materials, foodstuffs, agricultural and biological products, drugs, building materials, etc.

All PT techniques are based on the same principle: a sample is irradiated with optical light and part of this radiation is absorbed by the sample and transformed into heat. If the heat absorbed into the sample and its propagation are measured, then optical or thermal information about the sample is obtained. The main information obtained with PT techniques are thermal properties (specific heat, thermal conductivity, diffusivity and effusivity, coefficients of thermal exchange, etc.), optical properties (surface and volume optical absorption coefficient, reflection and diffusion coefficients, etc.), and quantum properties (fluorescence and radiation to heat conversion efficiency). Each way of measuring the heat developed in the sample is practically associated with a PT method. The main photothermal techniques comprise the photopyroelectric method, thermal lensing, infrared radiometry, the photothermal displacement method, photothermal beam deflection, and several others.¹ Among these methods, the photopyroelectric (PPE) technique is probably the simplest because the temperature variation of the sample is directly measured with a pyroelectric sensor. The first PPE experiments were performed in 1984.^2–4 The targets of the investigations were very different: to detect a phase transition, to study a chemical reaction, or to find the optical absorption bands of certain solids. This wide range of applications has demonstrated early on that the PPE method is suitable for both spectroscopic and calorimetric investigations.

The PPE method is practically based on the pyroelectric effect, i.e., the induction of spontaneous polarization in a non-centrosymmetric piezoelectric crystal, as a result of a temperature change in the crystal. The pyroelectric effect was discovered in antiquity, but the physical processes behind pyroelectricity were only studied at the end of 18th century by William Thomson (Lord Kelvin), Woldemar Voigt, and the Curie brothers.^5,6 Nowadays, single crystals such as LiTaO₃ and TGS, ceramics such as PZT, or polymers such as PVDF are used as pyroelectric sensors.

Essentially, the PPE method is based on the following principle: temperature variation in a sample exposed to modulated radiation is measured with a pyroelectric sensor, situated in close thermal contact with the sample.^7,8 The main advantages of this technique include its simplicity, high sensitivity, non-destructive character, and adaptability to practical restrictions imposed by the experimental requirements.

From a theoretical point of view, in the most general case, the complex PPE signal depends on all optical and thermal parameters of the layers of the detection cell (of which there are usually six: air, the window, the sample, the pyroelectric sensor, the substrate, and the backing) and on several instrumental parameters (the modulation frequency of radiation, the power of the laser beam, the electrical capacity and permittivity of the sensor, etc.). Unfortunately, the mathematical expression of the PPE signal is very complicated, rendering it impractical for most applications. As a result, over the last few decades, a large effort was dedicated to simplifying it, with the focus on the number of components of the detection cell and on the thermal and optical thickness of each layer. As a final result, several specific modes were obtained, in which information is contained in both the amplitude and phase of the complex PPE signal.^7–9 

If the wavelength of the radiation source is scanned in a PPE experiment, spectroscopic information (mainly optical absorption coefficients) can be obtained. If the wavelength of the radiation source is constant, the PPE technique practically becomes calorimetric and experimental investigation yields thermal information (static and dynamic thermal parameters). The thermal parameters directly obtained from PPE measurements are usually the “fundamental” ones, namely, the thermal diffusivity and effusivity (which are also present in the thermal diffusion equation and its solution). It is well known that the four thermal parameters, the static volume specific heat (C), the dynamic thermal diffusivity (α), conductivity (k), and effusivity (e), are connected by two relationships, k = C ⋅ α and e = (C ⋅ k)^1/2. Thus, only two parameters are independent.

Recently, it was demonstrated that PPE spectroscopy is able, in certain detection modes, to offer both spectroscopic and calorimetric information.¹⁰ Concerning PPE detection configurations, two of them, “back” and “front,” have mostly been applied to spectroscopic/calorimetric studies, respectively. Some spectroscopic information has also been obtained from a so-called “reflection mode” PPE configuration. In the back (standard) 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.^9,11 In the front (inverse) configuration, 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.^12,13 The reflection mode PPE configuration is in fact a back configuration with a (semi)transparent sample and a very reflective sensor.¹⁴ 

Concerning the types of samples that can be investigated, in general, the PPE method can be successfully applied to condensed matter (liquids and solids). Liquids are the most suitable materials for PPE investigation because the sample-sensor thermal contact is perfect in most cases, leading to accurate, quantitative results. For solid samples, the method can be readily applied but the sample-sensor coupling fluid (that is almost always necessary) may introduce uncontrolled errors. PPE calorimetry can also be used for gases but only under very special conditions due to their low optical absorption coefficients and large thermal diffusion lengths.

Historically speaking, in PPE calorimetry, many different approaches have been developed to obtain values of thermal parameters. Some of them are based on the measurement of single values;^13,15 while other alternatives make use of scanning procedures.^9,11,15 The second approach proves to be more precise. When liquid samples are under investigation, two parameters are available to be scanned: the chopping frequency of radiation and the sample's thickness.

In principle, several combinations can be selected by researchers in order to obtain at least one of the dynamic thermal parameters related to a sample (thermal diffusivity or effusivity). The combinations refer to the detection configuration (back or front), the source of information (PPE amplitude or phase), and the scanning parameter (chopping frequency or a sample thickness scan).

To conclude this introduction, we must highlight that optical and thermal parameters are markers in many physical/chemical processes. Consequently, the PPE method is a very suitable technique to not only determine values of optical and thermal parameters but also study processes such as compositional changes (chemical reactions, mixtures of liquids, molecular and/or isotopic association, food adulteration, etc.), structural/magnetic/electric changes induced by temperature variation (phase transitions), and more.

In this Tutorial, we intend to present an overall view of the development of the PPE technique starting from 1984 until now. This review is organized into three main sections to explore both theoretical and experimental aspects of PPE detection as well as provide important examples of spectroscopic and calorimetric applications. In the theoretical section, we describe some specific detection cases of experimental interest, in both back and front configurations. The experimental section contains examples of setups, detection cells' configurations, and various sensor/sample assemblies that are used in both spectroscopic and calorimetric experiments. The section dedicated to applications contains a selection of case studies that cover a wide variety of scientific disciplines and research fields. We intend to show that the PPE technique is not only useful to investigate optical and thermal properties of various solids (homogeneous and porous, magnets, ferroelectrics, thermoelectrics, etc.) and liquids (binary and isotopic mixtures, volatile liquids, liquid foodstuffs, magnetic nanofluids, etc.), but simultaneously provides a good method to study physical processes (such as molecular associations, food adulteration, or phase transitions).

The reader should be made aware that it is impossible to encompass the whole activity in this field, which extends over more than 35 years, within a single paper; this review, therefore, often focuses on the activity of the author's group and co-workers. However, the extended list of references represents a wealth of important results that have been obtained by other groups that are active in this field.

The starting point in developing the theory of the PPE method is the relationship between the PPE voltage V and the temperature variation ΔT across the pyroelectric sensor. It was demonstrated^7,8 that for low levels of irradiation, the two quantities are proportional, V = p⋅ΔT, with p being the pyroelectric coefficient of the sensor. From a theoretical point of view, the target is to calculate ΔT by solving a system of heat diffusion equations through the layered detection cell with boundary conditions of temperature and flux continuity at interfaces. On the other hand, it is now well known that the general expression for the PPE signal is analytically exact^7,8 but, as mentioned in the introduction, it is too complicated for experimental applications. This is why, in this theoretical section, we will not describe the development of the general PPE theory; we will limit our presentation to mathematical equations of the complex PPE signal used in several specific detection cases of the two most commonly applied detection configurations (back and front).

One-directional heat propagation is based on the concept of thermal waves and several parameters characterizing light propagation have corresponding parameters in heat propagation. As with the case of optics and light, thermal waves are attenuated when propagating into a given material. In analogy with the optical penetration depth, in heat propagation, the thermal diffusion length, μ, is defined as the heat penetration distance for which the thermal wave is attenuated with a factor of “e.” In frequency dependent experiments, the thermal diffusion length depends on the material's thermal diffusivity and on the modulation frequency of incident radiation [see Eq. (4)]. When the frequency of modulated light increases, the thermal diffusion length decreases, which is in fact a method of manipulating the thermal thickness of a given layer of the detection cell. Often, in real experiments, we are obliged to assign various layers of the detection cell as either “thermally thin” or “thermally thick.” This means that sometimes we like to let the heat to pass through a given layer of the detection cell almost non-attenuated (a thermally thin layer) or we want all (or most) of the heat to be absorbed in the layer (a thermally thick layer). From a theoretical point of view the critical frequency at which a layer passes from a thermally thin to a thick regimen is obtained when the geometrical thickness of the layer, L, is equal with the thermal diffusion length, μ. Thermally, thin/thick concepts are in fact connected with approximations that are required in the development of theoretical aspects. Approximations that are made when $1≪ L/μ$ or $L/μ≫1$ lead to simplified theoretical results that are of experimental interest.

Several assumptions (restrictions) must be made from the beginning for the sake of simplification. These assumptions are general in nature, and it is easy to set them up experimentally. They are (i) a one-dimensional propagation of heat is considered and (ii) heat transport is due only to conduction (heat transport by radiation and convection is neglected). However, under special experimental conditions, these latter two heat transfer mechanisms can be also considered.^16–18 In Secs. II A–II C, we will describe, from a theoretical point of view, some specific PPE detection cases of experimental interest. Additional restrictions will be imposed in each particular case.

As described in Sec. II, the general expression for the PPE signal is analytically rather complicated. It depends on the optical and thermal parameters of all layers of the detection cell, together with others parameters that characterize the setup. For practical reasons, many of these parameters are eliminated by performing various approximations or normalization procedures. The main difference between spectroscopic and calorimetric applications is the sample transparency. In calorimetric applications (which will be presented later in Sec. IV), the sample (or the sensor, in front configuration) is opaque and all radiation is absorbed by the irradiated surface. In spectroscopic applications, the sample is (semi)transparent and the PPE signal depends on the optical absorption coefficient of the sample. There are many analytical expressions of the PPE signal used in spectroscopic applications. We will not list them here, but interested readers can find more information in Refs. 7 and 8.

A typical geometry of the back PPE configuration is presented in Fig. 1.^7,8,19,20

In Eq. (2), the term (1 – R) represents the quantity of the light intensity absorbed at the (w, m) interface and H₀ is the incident light intensity.

In order to eliminate V₀, normalization of the signal is necessary; it is the best reference signal being obtained by direct irradiation of the empty sensor.

For practical applications, a frequency scan of the phase of the signal is performed and the thermal effusivity is, hence, obtained by optimizing the fit performed on the experimental data with Eq. (17), considering e_s as a fitting parameter.

In this configuration, the amplitude has also been used (in the thermally thin regime for the sensor) to obtain single values of the sample's thermal effusivity.³⁴ However, in recent years, it was mainly used to obtain information about the thermal properties of pyroelectric sensors.^35–37 

Special detection configurations are usually related to the analysis of solid (especially porous) samples. When investigating solids, a coupling fluid (liquid or paste) is used between the sensor and sample, in order to ensure a good thermal contact. Often, especially when the target of the investigation refers to qualitative data, the influence that the coupling fluid may have on the results was neglected: experimental parameters (such as the sample and sensor thickness, modulation frequency of incident radiation, etc.) were designed in such a way that the coupling fluid layer was considered to be thermally very thin. Unfortunately, when accurate quantitative data are required, the influence of the coupling fluid cannot be neglected and much work was dedicated to reduce its influence. Several authors tried select the most appropriate coupling fluids and attempted to find mechanical methods to reduce their thickness.³⁸ Others elaborated mathematical models in which they included a layer of coupling fluid in a detection sandwich (i.e., sample/coupling fluid/sensor). In this case, the main problem is the unknown thickness of the coupling fluid, which is treated as a fitting parameter.^39,40 Another method to eliminate the influence of the coupling fluid was to use the aforementioned thermal-wave resonator cavity (TWRC) method^20–31 in which a frequency scanning procedure is replaced by a coupling fluid thickness scan.

Even if the influence of the coupling fluid were reduced, the methods described above are only suitable for the investigation of non-porous solids. For porous solids, any type of liquid or pasty coupling fluid can infiltrate the sample and make the results less accurate. The only other option available for thermal studies of porous samples with PPE is to replace the liquid/pasty coupling fluid between the sensor and sample with a layer of air. Unfortunately, if one decides to use air as a coupling fluid between the two solids (the sensor and the porous solid sample), the following additional problems must be dealt with (i) air is a bad thermal conductor, acting as a low pass filter in frequency dependent measurements and as a consequence an adequate experimental frequency range must be selected; (ii) the thickness of the air gap is unknown—meaning that it must be considered to be a fitting parameter or, if possible, it must be eliminated from the final result by some self-normalization method; (iii) sometimes, due to rather poor heat conduction in the layered detection cell, heat losses by convection and radiation at the heat-absorbent surface are indicated to be included in the model.

Now that we have described the challenges associated with the thermal investigation of porous solids, we will now describe two methods that can be used for such a purpose. The first, proposed by Salazar et al.¹⁸ is based on a frequency scan of the phase of the FPPE signal. This method uses a front detection configuration that takes into account heat losses from convection and radiation at the irradiated surface. It uses thin opaque pyroelectric sensors and leads to the direct measurement of the sample thermal effusivity by performing a fit of the experimental data (FPPE phase vs modulation frequency) with three fitting parameters: the sample thermal effusivity, heat losses from convection and radiation, and the air gap thickness between the sensor and sample. The second method, proposed by Zammit et al.⁴¹ is in fact a combined BPPE/FPPE configuration. It is based on two successive measurements (frequency scans), one in back and one in front configuration, followed by a self-normalization of the phase vs modulation frequency behavior. The method uses transparent pyroelectric sensors, and the self-normalized PPE phase depends only on the sample thermal effusivity and diffusivity and on the thermal effusivity of the backing material (the phase of the signal is independent of the thermal and geometrical parameters of the sensor and coupling fluid between sensor and sample). This method allows the direct measurement of the sample thermal effusivity in the low frequency regime provided the thermal diffusivity has already been measured in the high frequency region.

PPE detection cells used in the two methods are schematically depicted in Fig. 2.

Equation (27) shows that in using air as a backing material with this configuration, one can only measure the sample's thermal diffusivity, both in low and high frequency range.

Combining both previously described methods,^18,41 we can obtain both the thermal diffusivity and effusivity of a porous sample and, subsequently, calculate the remaining thermal parameters, the thermal conductivity and the volume specific heat, for complete thermal characterization of the material.

The PPE method can be combined with other PT techniques in order to obtain a complete thermal characterization (i.e., the measurement of all thermal parameters) of condensed matter samples. Practically, when we combine two methods, we try to utilize the particular advantages of each technique while simultaneously trying to eliminate their limitations. The PPE method has been combined with photothermal radiometry (PTR),^43–45 the photothermoelectric (PTE) method,^46–53 the thermography (IRT), etc.^54–57 

To describe of all these mixed methodologies would take too much space and so we will limit our description to the theoretical aspects of the PPE-PTR approach only. Readers interested in other combinations are directed toward the references described above.

The PTR technique has mostly been used for calorimetric investigations of solid samples,^58,59 with the frequency scan method. In such types of investigation, the irradiated layer is a thermally thin and opaque solid, and normalization of the PTR signal involves a thermally thick backing with known thermal properties.

The layout of the PPE-PTR detection configuration is presented in Fig. 3.

We can conclude that both normalized FPPE and PTR signals depend on the thermal diffusivity and effusivity of the pyroelectric sensor and the liquid layer respectively, and on the thermal effusivity of the backing material. Performing a thickness scan of the amplitude and/or phase of the FPPE and PTR signals (at constant chopping frequency), one can get information about one or eventually two layers of the detection cell.

The theoretical equations deduced here represent a small selection that describe particular cases of experimental interest. They will be used later in the section dedicated to Applications.

A classical experimental setup for PPE spectroscopy is presented in Fig. 4.

In PPE spectroscopy, radiation is emitted by a black-body radiation source at a temperature appropriate for the spectral range of interest. For the visible-infrared spectral range, the most common radiation source is the Globar (GS), which is a silicone-carbide bar at a temperature of about 1600 K, capable of covering the spectral range from 0.5 up to about 20 μm. Radiation is collimated (lens L) and modulated with an electro-mechanical chopper (CH) before it passes through a prism monochromator (M). The radiation that exits the monochromator impinges on the sample's (S) incident surface. The rear side of the sample is in thermal contact with the pyroelectric sensor (PY). The PPE signal from the sensor is amplified (PA) and then processed with a selective or a lock-in nanovoltmeter (LI). The reference signal for the lock-in amplifier is obtained with an opto-coupler (OC) photodiode–phototransistor. With such a setup, one can usually obtain the optical absorption bands of the samples in the spectral range of interest.

If additional information is needed (for example, one is also interested in the reflection coefficient of the sample), another detection line can be added to the setup from Fig. 4 (see Fig. 5). The reflected radiation from the sample can be collected with a second pyroelectric sensor (RD) and the signal processed with a second lock-in.⁶¹ 

Other experimental solutions can be found in Refs. 10 and 62.

A typical experimental setup for the PPE measurement of thermal parameters for liquid samples at room temperature is displayed in Fig. 6.

In this setup, a pyroelectric sensor, usually a 100–500 μm thick LiTaO₃ single crystal provided with Cr-Au electrodes on both faces, is glued to a rotating stage. The backing material of the detection cell is situated on a micrometric stage. The modulated radiation (provided by a 30–200 mW laser) is partially absorbed by the front electrode of the sensor. The space between the sensor and the backing material accommodates a liquid layer. Variation in the thickness of the liquid is achieved with a step in the range 30 nm–1 μm with a nano-motor and data acquisition is taken each 10th–30th step. The “rough” control of the liquid's thickness and the parallelism between the backing and the sensor are assured by 3- and 6-axis micrometric stages. During the scanning procedure, the sample's thickness variation is rigorously controlled but the absolute sample thickness is not precisely known. The PPE signal is processed with a lock-in amplifier. The internal oscillator of the lock-in gives the reference signal and assures the modulation of the incident radiation. The data acquisition, processing, and analysis are performed with appropriate software.

The setup presented in Fig. 6 was specially designed for investigations of thermal parameters (mainly, thermal effusivity) of liquids, and it is based on the TWRC method.^20–31 With minor changes in the design of the detection cell (see the section dedicated to Detection cells), the very same experimental setup can be used for PPE measurements of thermal diffusivity and can be applied to solid samples. In such a case, the TWRC method must be replaced by a classical frequency scanning procedure.

Figure 7 presents an extended experimental setup in which the PPE method is coupled with the PTR technique. In this improved setup, a second lock-in amplifier is added, which processes the signal provided by an IR detector. During such an experiment, a second IR signal is generated by the pyroelectric sensor itself. The IR radiation emitted by the pyroelectric sensor is collected with parabolic mirrors and diverted to the surface of a cooled HgCdTe IR detector. The internal oscillator of the lock-in used in PPE measurements also gives the reference signal for the second lock-in. The two PPE and PTR signals are processed with a computer.

The experimental setups described so far are useful for studies at room temperature. When temperature dependent processes must be studied, certain components must be added to allow temperature variation and control. A schematic view of such a setup is presented in Fig. 8.

In Fig. 8, a radiation source, usually a laser, is modulated by an acoustic-optical modulator and the PPE signal is processed with a lock-in amplifier. When performing temperature scans (phase transition investigations, for example), a thermostat, provided with Peltier elements⁶³ with additional equipment (programmable power supply, electronic thermometer, etc.) for temperature control, is included in the setup. A computer with appropriate software is used for data acquisition.

During the past 35 years of PPE technique development, many detection cells have been designed. They have been operated in both back and front configurations, making use of frequency or thickness scanning procedures. It is impossible to review all of these detection cells; therefore, we will limit our presentation to several cells that were designed by our group, together with our co-workers. Alternative detection cells and setups can be found in Refs. 63–71.

One of the first detection cells to be developed, used by the authors for thermal inspection of liquid samples, is described in Fig. 9. It is based on the TWRC method.

The cell is based on two micrometer systems. One (with a precision of 5 μm) performs the sample thickness scan, by modifying the distance between the sensor and an irradiated (50 μm thick) Be foil; the second one (with a precision of 1 μm) ensures rigorous control of the thickness variation. The liquid sample fills the space between the sensor, the Be foil, and a plastic ring and glued onto the sensor with silicone rubber. As stated above, precision in the thickness variation control offered by this cell is of about 1 μm. For high resolution measurements (required, for example, by molecular and/or isotopic association studies in liquid mixtures), this resolution may not be sufficient.^20,30 As a result, new detection cells, based on motors with nano-meter resolution, have been developed.

Figures 10 and 11 (Ref. 20) present the evolution of the detection cells (nano-meter resolution) used in PPE calorimetry of liquids, based on the TWRC method.

The cells described above have been used for the PPE calorimetry of liquids at room temperature. They can be easily adapted for measurements on solid samples if the TWRC method is replaced by a frequency scanning procedure.

In Sec. IV, we will describe two concepts for detection cells used for temperature dependent PPE calorimetry.

The first cell is based on a cold-finger refrigerator system.⁹ The cold-finger concept (Fig. 12) allows investigations at temperatures both below and above ambient conditions. The cell has two windows for investigations in both BPPE and FPPE configurations. In principle, the copper bar transmits the temperature to the sample—one extremity of the bar can be cooled using liquid nitrogen, or heated electrically with a resistive coil. The role of the 0.1 mm thick steel cylinder is to keep the cell (except the copper bar) at room temperature. Depending on the operating temperature, one can make a vacuum inside the cell or introduce a dry atmosphere. The temperature of the sample is measured with a diode that is glued with silicon grease to the cold finger in the vicinity of the sample.

The second cell concept is based on a system that has Peltier elements for temperature scans.⁷² The design of a PPE detection cell equipped with Peltier elements is presented in Fig. 13. One face of one of the two Peltier elements (electrically connected in parallel) is thermally connected to a thermostat (liquid flux from a thermostatic bath). The opposite face of the second Peltier element is in thermal contact with an inside-chamber that accommodates the sample-sensor assembly. Temperature feed-back is achieved with a thermistor placed close to the sensor. Computer-controlled temperature scans with positive/negative rates (heating/cooling) are possible.

When investigating solid samples, the sensor–sample assembly is composed of the sensor and sample which is in thermal contact. A coupling fluid (silicone grease, ethylene glycol, water, etc.) is usually used at the sensor–sample interface (Fig. 14).

The back detection configuration is used both for spectroscopic and calorimetric applications. It requires a flat sample of a reasonable thickness (10–500 μm). The front detection configuration is used only for calorimetric measurements and is dedicated to thermal effusivity measurements. This configuration requires only a flat surface in contact with the sensor and a geometrical thickness that can be considered “thermally thick” for the modulation frequencies used in the experiment.

When liquid samples are under investigation, the design of the detection cell is more complicated. Even if the contact between a liquid sample and a solid sensor is perfect and thus no coupling fluid is necessary, it is rather difficult to control exactly the liquid's (i.e., the sample) thickness. For thermal effusivity investigations, as in the case of solid samples, the liquid is in a back position (front detection configuration) and knowledge of its thickness is not necessary. Therefore, liquid sample can fill the space inside a ring such as in Fig. 15. The only requirement in order to obtain the value of the thermal effusivity is that the sample is “thermally thick.”

For the analysis of solids using the back detection configuration, we can perform spectroscopic investigations or, just as in calorimetry, we can directly measure thermal diffusivity. However, for this purpose we need to know the precise sample thickness or its variation. This can be accomplished using a calibrated cell⁷³ or using the TWRC technique.

Figure 16 displays a PPE detection cell for liquids that is used for spectroscopy in the “reflection mode.” This mode, with on a calibrated cell, has been successfully applied to the analysis of the optical absorption bands of water in the near IR.¹⁴ 

Figure 9 presents the sensor–sample assembly in back detection configuration for the TWRC method. As previously described, the distance between the sensor and the irradiated absorbent metallic layer (Be foil) is modified in a controlled way by using a nano-motor. The thermal diffusivity of the liquid sample is obtained from the slope of the phase of the PPE signal as a function of sample thickness [Eq. (9)]. We will now describe a more complex sensor–sample assembly used for the investigation of volatile liquids (Fig. 17).

When volatile liquids are under study, we must somehow prevent their evaporation during the measurement process. One option is to encapsulate the liquid in a closed box fitted with two glass windows. A thin window (50–100 μm) acts as a separator between the liquid to be investigated (backing liquid in Fig. 16) and second liquid layer which acts as a coupling fluid between the separator and the pyroelectric sensor. Using a sensor–sample assembly such as this, one can directly measure the thermal effusivity of volatile liquids, however, for accurate results, the separator window must be considered as a layer in the theoretical assumption (it cannot be ignored).

In order to conduct experiments, one can combine the setups, detection cells and sensor/sample assemblies described above, in a convenient way, in order to measure both the thermal diffusivity and the effusivity of condensed matter samples.

As mentioned in the Introduction, the first PPE spectroscopic experiment was reported in 1984³ and described experiments on solid samples. Using the experimental setup from Fig. 4, the optical absorption bands of anodized Al (anodized in H₂SO₄ and H₂C₂O₄) in the near infrared (IR) (0.7–20 μm) were detected. The experiment used a Globar source of radiation, a single prism monochromator, and a TGS single crystal as pyroelectric sensor. This combination offered enough light intensity and spectral resolution to allow good quality measurements in the near (IR). No absolute values of absorption coefficients of the investigated materials were obtained, but the method proved to be useful in comparing the optical absorption of different non-transparent materials used as potential absorbent layers for IR detectors or laser energy meters (see Fig. 18).

Figure 18 shows that graphite has a uniform optical absorption in the 0.7–20 μm spectral range. Al samples were anodized in H₂SO₄ and H₂C₂SO₄ and have selective optical absorption with strong absorption bands in the 2.5–4 and 6–15 μm spectral range.

A more sophisticated study could be performed by using thermally coupled and conventional PPE spectroscopy. The reader can find an example of such an experiment in Ref. 72, which is performed on hydrogen uranyl phosphate (HUP). The absorption bands found at about 1.25, 1.5, and 2 μm can be correlated with higher protonic conductivity of HUP, suggesting polaronic effects on the conduction mechanism in this solid electrolyte.

When irradiating a liquid sample in contact with a pyroelectric sensor, the overall PPE signal is produced by the vector sum of two periodic heat sources. The first source, generated upon the absorption in the opaque pyroelectric, is proportional with the fraction of radiation transmitted through the sample. In this case, the radiation sensor acts as a radiation detector and produces a signal analogous to conventional transmission spectra. A second source arises due to radiation absorption within the partially transparent sample. For this signal component, the pyroelectric sensor is a true thermal wave sensor, yielding a combined transmission-absorption spectrum. In the standard PPE configuration, the signal is often saturated due to the dominance of the first heat source, especially for transparent samples. This is why it is useful to suppress it. The remaining PPE signal is expected to be richer in spectroscopic information. Experimentally, one can achieve this by using a pyroelectric sensor equipped with a highly reflected front electrode. This PPE configuration is termed “reflection mode pyroelectric” (RPPE) spectroscopy, and it has been successfully used for the investigation of the optical properties of strongly absorbing liquids.¹⁴ 

Using the sensor–sample assembly in Fig. 16, the optical absorption bands of water in the near IR region have been detected.

In the near IR spectral region, H₂O and D₂O have three optical absorption bands at approximately 1.5, 1.9, and 3 μm (H₂O) and 1.9, 2.6, and 4 μm (D₂O). It can, therefore, be expected that the PPE spectrum in the 2–5 μm spectral range will be resolved with respect to peaks from 3 and 4 μm, respectively. We can, therefore, conclude that RPPE spectroscopy in the 2–5 μm spectral range is able to detect the presence of both H₂O and D₂O in H₂O–D₂O mixtures. Two examples of results obtained by RPPE spectroscopic investigations on H₂O–D₂O mixtures are presented in Figs. 19 and 20.⁷³ 

The amplitude of the absorption peaks is proportional to the component concentration, allowing a compositional analysis of these mixtures. In Ref. 73, several solutions allowing compositional analyses such as this are described.

When investigating solid samples, it is not easy to obtain accurate quantitative results due to the influence of the coupling fluid placed between sample and sensor. PPE calorimetry is a contact technique and so coupling fluids, always necessary when investigating solids, lead to uncontrolled errors. Over the last two decades, a lot of effort has been dedicated finding a way of eliminating the influence of the coupling fluid on results. Some researchers have tried to identify the most suitable coupling fluids and find mechanical methods that reduce their thickness.³⁸ Others have elaborated mathematical models in which they included the layer of coupling fluid in the detection sandwich (sample/coupling fluid/sensor).^39,40 Another method to eliminate the influence of the coupling fluid was to use the aforementioned TWRC method.^20–31 

We can focus our attention on the front photopyroelectric (FPPE) configuration as in the past, this was most commonly applied to obtain the thermal parameters of solid samples.^{9,12,16,74,75} In most cases, the FPPE detection cell contained three layers: air, a directly irradiated sensor, and a solid semi-infinite sample. The value of thermal effusivity could be obtained by performing frequency scans of the amplitude or phase of the FPPE signal. Pittois et al.⁷⁶ designed for the first time a four layer FPPE cell with a thermally thin solid sample and a semi-infinite backing material. With the restriction of “very good thermal conductor backing,” they were able to derive both the thermal conductivity and the effusivity of the sample by performing a frequency scan of the PPE signal over a large frequency range.

As mentioned above, Mandelis and co-workers proposed the TWRC method, as an alternative to frequency scanning procedures.^21,29 It was demonstrated using a technique that combined the FPPE configuration with the TWRC method. During the experiment, the thickness of the coupling fluid was monitored and a solid material was used as a backing, which lead to the direct measurement of the solid sample's thermal effusivity. In doing this, the coupling fluid was no longer a disturbing factor and instead its properties could be used to obtain the value of the thermal effusivity.

The results of this application for a detection cell with ethylene glycol as a coupling fluid and different solids as backing materials are presented in Fig. 21: typical behaviors of the normalized phase of the FPPE signal can be seen.

As mentioned in the Theoretical section, FPPE can be coupled with PTR in order to obtain calorimetric information. Using the experimental setup from Fig. 7 together with the theoretical assumptions described previously [Eq. (34)], one can simultaneously obtain values of the thermal effusivity samples (see Fig. 22).

Figure 23 illustrates some results obtained on dental polymers with different values of thermal effusivity. The results indicate that the thermal parameters for these dental materials are composition dependent. The values of the thermal effusivity of the dental polymers are important parameters in establishing their thermal biocompatibility.^77–82 

Results obtained at room temperature for the thermal effusivity of the solids under study are presented in Tables I and II, together with some available literature data.

The front photopyroelectric (FPPE) configuration, together with the TWRC method, has also been applied to the measurement of thermal diffusivity in thin solids. The methodology is based on an FPPE detection cell in which a thin solid layer is inserted between two layers of identical liquids—one layer in contact with the pyroelectric sensor acting as a coupling fluid and a second one acting as a backing layer.⁸⁴ The value of the thermal diffusivity is obtained as a result of a scan of the phase of the FPPE signal as a function of the coupling fluid's thickness (i.e., the TWRC method). The applicability of this method was demonstrated with experiments on solids of different thicknesses (50–200 μm) and values of thermal diffusivity (glass, steel, aluminum, and copper).⁸⁴  Figure 24 displays the behavior of the normalized FPPE phase as a function of coupling fluid thickness for a detection cell with 150 μm thick Al foil as a separator, and Table II summarizes the results obtained for several foils. For the thicknesses reported in Table II, it seems that the results are in rather good agreement with data obtained for bulk materials.

It should be noted that the very same method (same experimental measurement and same theoretical analysis) can be used to obtain the thermal effusivity of a thin solid layer, if its thermal diffusivity is known.

Another important application of the PPE technique is in the investigation of the thermal parameters of the pyroelectric sensors themselves.^{35,36,86–88} For most applications concerning pyroelectric materials, knowledge of their thermal parameters is necessary because they are relevant for evaluating the figure of merit of an IR sensor⁸⁹ or a pyroelectric accelerator,⁹⁰ for instance. When used as a sensor in a PPE experiment, knowledge of these parameters is crucial because all other measured properties depend of these values.⁸⁸ Moreover, it has been shown that these parameters have slightly different values as a function of the composition/purity of the pyroelectric material.⁹¹ 

In principle, in order to obtain the thermal parameters of a pyroelectric sensor, it must be inserted in a simple front PPE detection cell composed of three layers [air/pyroelectric sensor/substrate (backing), see Fig. 14]. Performing a frequency scan of the FPPE signal, one can obtain the sensor's thermal parameters, based on information of both amplitude and the phase of the signal, provided that the thermal parameters of the backing material are known.^92,93

In the following paragraph, we will describe the results obtained on a frequently used pyroelectric sensor LiTaO₃ single crystal.

The behavior of the normalized phase and amplitude of the PPE signal, as a function of frequency, obtained for a 510 μm thick LiTaO₃ single crystal is plotted in Fig. 25.

A plot of the modulus of the complex quantity (1− V_n) as a function of the square root of frequency should display a line with a slope equal to the value of the thermal diffusivity of the sample; an extrapolation of the curve to zero frequency leads to the value of the thermal effusivity. Such a calculation has been performed for the experimental data shown in Fig. 27, and the result is presented in Fig. 26.

A linear fit of the data yields values of thermal parameters in agreement with previous calculated ones, as reported in Table III.

The theoretical results we present here have been obtained without any hypothesis on the nature of the pyroelectric sensor. While the experimental results were obtained on LiTaO₃ crystals, a similar procedure can be carried out for any type of pyroelectric material, such as PZT ceramics, polymer films (PVDF), etc.

One of the most challenging applications of PPE calorimetry is in the thermal characterization of porous solids. As mentioned above, for porous solids, any type of liquid or pasty coupling fluid penetrates into the sample and the obtained results are not accurate. The only alternative for PPE analysis of porous samples, is to replace the liquid/pasty coupling fluid between sensor and sample with a layer of air. A good example of this is in the analysis of building materials. For example, bricks collected from old buildings. It is well known that accurate estimation of thermophysical parameters of building materials is critical for the evaluation and improvement of energy efficiency in the building sector and the development of new materials. In this respect, the science of building materials has mainly focused on maximizing or minimizing thermal conductivity, while thermal effusivity and diffusivity have received relatively limited attention, despite their importance when considering thermal energy exchange with the environment. The thermal regime of a building can be considered for a limited time interval as stationary, but during 24 h, with significant temperature variations in a day/night cycle, the conditions are non-stationary. This is why correct and accurate measurement of thermal effusivity and diffusivity is very important in heat conduction studies for building materials.

Figure 27 displays the frequency behavior of the normalized FPPE phase for three bricks collected from old buildings (denoted by samples 1–3), together with the best-fit performed with Eq. (19).⁴² 

Table IV shows the results obtained for the thermal effusivity of the investigated samples, together with the values obtained for the other two fitting parameters, h and L_a.

Figure 28 displays the behavior of the self-normalized PPE phase as a function of sqrt.(f) for the investigated samples (in the samples thermally thick regime), and Table V contains the values obtained for the thermal diffusivity, conductivity, and volume specific heat.

The results obtained for the thermal parameters are in good agreement with those already reported for new and old bricks. This type of information becomes vital for many old buildings given their continued degradation over time.

In this section, we will select some applications of PPE calorimetry for liquids of great interest: liquid foodstuffs and magnetic nanofluids. These applications place emphasis on high resolution measurements for room temperature values of dynamic thermal parameters.

Studies of the thermo-physical properties of foodstuffs represent an intensive research effort that has been carried out both in industry and academic institutions.^93–98 Once known and their behavior understood, such properties can be used to benefit industrial manufacturers by improving applications, as well as control the stability and the shelf life of the product. In this section, we will present some applications in which accurate measurements of thermal parameters can lead to structural information.

The first example application is presented in Fig. 29. The thermal diffusivity of several commercially available margarines was measured in front configuration, using the thickness-scan method of the phase of the PPE signal. The value of the thermal diffusivity was obtained from the slope of the graph. A clear correlation between the values of thermal diffusivity and fat content was found.

When accurate measurements are performed, thermal diffusivity can be correlated with the fatty acid composition of various types of fats. An example is presented in Fig. 30 for vegetable oils.

A clear correlation can be observed between the values of the thermal diffusivity and the percentage of total (linoleic + linolenic) unsaturated fatty acids; the total amount of fatty acids slightly decreases with decreasing thermal diffusivity.

Ferrofluids represent a special category of smart nanomaterials, consisting of stable dispersions of magnetic nanoparticles in different liquid carriers. While magnetic properties of magnetic nanofluids are the subject of intensive study, there are far fewer data in literature concerning their thermal properties. Normally, thermal properties of magnetic nanofluids must depend on the composition of the nanofluid: the type of nanoparticles, the surfactant and carrier fluid, the concentration, nanoparticle size, etc. Furthermore, values of the static and dynamic thermal parameters and their temperature behavior are correlated with structural changes and/or the dynamics of various processes occurring inside the nanofluid.

Conversely, the little calorimetric data available indicate sometimes drastic changes in the thermal conductivity of nanofluids as a function of nanoparticle size. This is the case for Cu nanoparticles and carbon nanotubes immersed in ethylene glycol, for example.^100,101

Due to the correlation between thermal parameters and the compositional parameters of nanofluids, PPE calorimetric studies of magnetic nanofluids can provide a lot of information.^51,102,103

In Sec. IV B 2 c, we will present results (obtained with the PPE technique) describing the correlation between the thermal and compositional parameters of nanofluids.

Figure 31 presents a thickness scan of thermal diffusivity, obtained for nanofluids based on Fe₃O₄ nanoparticles stabilized by a double layer of oleic acid but with different carrier fluids: water and decahydronaphtalene (DHNA).

Figure 32 displays thickness scans of thermal diffusivity for water-based nanofluids with different concentrations of CoFe₂O₄ nanoparticles.

Figures 31 and 32 indicate that thermal diffusivity is a sensitive to changes of other important nanofluid parameters such as the type of carrier liquid and the concentration of nanoparticles.

In the next example, thermal effusivity was measured in the front configuration by making use of a frequency scan (i.e., based on the method proposed in Ref. 33).

Figures 33 and 34 present the results obtained for thermal effusivity. The same nanofluid samples were used for these experiments.

As is apparent on inspection on Figs. 33 and 34, thermal effusivity also depends on the main parameters of the nanofluid, but it is less sensitive than the thermal diffusivity. The changes in thermal effusivity as a function of liquid carrier are clearly detected, but the changes as a function of nanoparticle type and concentration lie somewhere within the precision of the measurement at approximately ±1%.

In order to obtain this information, five types of magnetic nanofluids, based on Fe₃O₄ nanoparticles with water as a carrier liquid, were investigated using both PPE detection configurations (back and front) together with the TWRC technique as a scanning procedure. The type of surfactant varied between the nanofluids including: double layers of lauric (LA–LA), oleic (OA–OA), and miristic (MA–MA) acids and also double layers of lauric–miristic (LA–MA) and palmitic–oleic (PA–OA) fatty acids. In both detection configurations, the information was contained in the phase of the PPE signal. The thermal diffusivity of nanofluids was obtained in the BPPE configuration, from the scan of the phase of the signal as a function of the liquid thickness. Using the same scanning procedure in the FPPE configuration, the thermal effusivity was measured directly.

Typical plots of the relative phase of the BPPE signal at room temperature as a function of nanofluid thickness are shown for the linear region of the graph in Fig. 35.¹⁰² Room temperature thermal diffusivity can be calculated from the slope of the curves [Eq. (7)].

Having obtained the values of thermal diffusivity, the thermal effusivity can be obtained in front detection configuration using the method proposed in Ref. 102. Figure 36 presents the behavior of the phase of the FPPE signal as a function of the relative thickness of the coupling fluid.

The results obtained for the values of the thermal diffusivity and effusivity are listed in Table VI. The table also contains the values of the remaining thermal parameters: thermal conductivity and volume specific heat (obtained from calculation).

In conclusion, it was found that different types of surfactants changed the thermal effusivity for the nanofluids under study by up to approximately 16%. The value of thermal diffusivity is practically unmodified by the type of surfactant.

For this investigation, two types of carrier liquids (transformer oil and polypropylene glycol) were combined with two types of iron based magnetic nanoparticles (Fe₃O₄ and MnFe₂O₄). Different sizes (10–80 nm) and shapes (spherical, octahedral, or cubic) of nanoparticles were obtained, depending on the oleic acid/oleylamine molar ratio.¹⁰³ 

The results obtained for the values of the thermal diffusivity for the various combinations of polypropylene glycol/transformer oil and MnFe₂O₄/Fe₃O₄ are displayed in Fig. 37.

The corresponding results obtained for the thermal effusivity for all combinations of polypropylene glycol/transformer oil and MnFe₂O₄/Fe₃O₄ are displayed in Fig. 38.

The results obtained by the PPE technique indicate that the presence of the nanoparticles decreases the value of the thermal parameters of pure carrier liquids and both thermal diffusivity and effusivity decrease with increasing nanoparticle size, independent of the carrier liquid. The influence of nanoparticle size is more pronounced for the thermal effusivity (relative change 24%) compared with the thermal diffusivity (relative change 7%).

As mentioned in the Introduction, optical and thermal properties are important parameters in many physical/chemical processes. The PPE method, therefore, provides a suitable technique to investigate processes associated with compositional changes (molecular associations and food adulteration) and structural/magnetic/electric changes induced by temperature variation (phase transitions). In this section, we present examples of several such applications.

Assume that we mix two liquids. There are two possibilities: the liquids can mix in a non-associative way (non-interacting liquids) or they are able to form molecular associations. If one intends to investigate the associative character of a liquid mixture, they must study the behavior of the thermal parameters of the mixture as a function of composition. For non-associative liquids, the additivity law is respected and, as a consequence, a linear dependence of thermal parameters as a function of % mass composition is found. If molecular associations are present, thermal parameters depart from the linear additive law.

As an example, the excess value curves for the thermal diffusivity for various water–solvent mixtures as a function of solvent concentration are displayed in Fig. 39. Thermal diffusivity was measured in the back configuration using the sample thickness-scan method, as proposed in Ref. 98. The excess value curves presented in Fig. 39 demonstrate the associative character of water-based binary liquid mixtures.^20,23,99

Figure 40 presents the composition behavior of all thermal parameters for various water–ethanol mixtures. It is clear that the sensitivity to molecular associations in liquid mixtures is higher for the thermal diffusivity compared to other thermal parameters. Some deviations are observed for thermal effusivity, though they are not specific. Small deviations from additivity may occasionally be observed for non-associative mixing.²⁴ 

When considering the applications presented above, PPE calorimetry applied to isotopic liquid mixtures represents a challenge; small deviations from linearity are expected for thermal parameters as a function of composition. Let us consider the case of mixtures of H₂O–D₂O and two isotopic dimethylsulfoxide species, C₂H₆OS and C₂D₆OS [denoted by DMSO(6H) and DMSO(6D)]. In this example, the thermal diffusivity was measured in the back configuration using the sample thickness-scan method,⁹⁸ and the thermal effusivity was measured in the front configuration with a frequency scan of the phase of the signal.⁸⁴ 

The obtained relative deviations from additivity for the thermal diffusivity and effusivity for H₂O–D₂O, DMSO(6H)–DMSO(6D), and H₂O–DMSO(6H) are presented in Figs. 41 and 42, 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 hygroscopic character. Conversely, the maximum relative deviations from additivity of the thermal diffusivity for H₂O–D₂O and DMSO(6H)–DMSO(6D) are about −4% and −8%, respectively. This can only be explained by an isotopic effect because, from a chemical point of view, H₂O and D₂O, and DMSO(6H) and DMSO(6D) molecules, are almost equivalent.

In order to study such a process, accurate PPE investigation with the TWRC method must be combined with another conventional technique for compositional analysis [gas chromatography (GC), for example]. In Figs. 43 and 44, two methods were combined in order to detect adulteration of flax oil with sunflower oil.⁹⁰ The behavior of the thermal diffusivity as a function of sample thickness for flax–sunflower oil mixtures is presented in Fig. 43. Figure 44 describes the correlation of thermal diffusivity with the content of relevant fatty acids [stearic, α-linolenic, and the total amount of polyunsaturated fatty acids (PUFAs)]

The plots indicate that the thermal diffusivity of the mixtures ranges from 8.07 × 10⁸ (pure sunflower oil) to 10.03 × 10⁸ m²/s (pure flax oil) and is directly correlated with the total amount of the polyunsaturated fatty acids in oils.¹⁰⁴ 

The correlation between the PPE signal and the composition of unadulterated and adulterated vegetable oils confirms the data obtained previously on fresh and spoiled vegetable oils¹⁰⁵ and suggests that thermal diffusivity may be a suitable parameter to determine the quality of oils and their early spoilage and adulteration. Another parameter that can be used detect oil adulteration is the freezing point, which can also be detected by the PPE method (see the section dedicated to Phase transitions).

A phase transition is a phenomenon associated with a break in the system's symmetry.^45,106 Usually, at the transition temperature, the system passes from an ordered to a disordered phase. The transition is always associated with fluctuations of the order parameter. As a consequence of these fluctuations, the derivatives of the thermodynamic potential present anomalies in the critical region. If the first derivatives of the thermodynamic potential are discontinuous, the phase transition is of first order. If the first derivatives of the thermodynamic potential are continuous and the second derivatives are discontinuous, the phase transition is of second order. The most common first order phase transitions are associated with melting, vaporization, etc. The most common second order phase transitions are magnetic and ferro-paraelectric. If one intends to detect and study a phase transition, they must be able to measure a quantity (parameter) that presents an anomaly at the critical point. These parameters can be specific for different classes of materials (magnetization for magnets, polarization for ferroelectrics, etc.), but they can also characterize all types of materials; among this last type of parameters are the thermal parameters. As calorimetry is able to directly measure thermal parameters it is particularly suitable for phase transition studies. As presented in the Theoretical section, the amplitude and phase of the complex PPE signal depend on two (or sometimes one) thermal parameters related to the sample. Theory dictates that the PPE technique is suitable to detect both first and second order phase transitions, by measuring critical anomalies of thermal parameters.

One of the most important factors in making high-temperature-resolution measurements of thermal parameters in the critical region of a phase transition is that the thermal gradients in the sample under investigation must be as small as possible. Often, at a phase transition the thermal parameters have a strong temperature dependence when approaching the critical temperature. Thermal gradients tend to smooth-out this temperature dependence and, sometimes, the phase transition is difficult to detect. To avoid this effect, it is important to keep the sample in quasi-thermal equilibrium. In most cases, measuring techniques are based on detection of a rise in sample temperature as a response to a heat input but are themselves additional sources of temperature gradients. This is especially true of ac techniques. Accordingly, techniques that involving periodic sample heating are preferred, and the PPE technique is among them.

Over time, the PPE technique became increasingly applied to detect second^{11,73,92,107–114,120,127} or first^{2,9,115–117} order phase transitions. For second order phase transitions, PPE results were used to calculate the critical exponents of thermal parameters and to validate existing theories. Due to the fact that the PPE technique uses thermal parameters for phase transition investigations, a wide range of condensed matter specimens have been investigated: ordinary liquids and liquid mixtures; liquid crystals; liquid, pasty, or solid foodstuffs; ferroelectric, thermoelectric and magnetic materials; high T_c superconductors; plastics; and more.

The PPE study of phase transitions essentially developed over the last few decades due to the suitability of this technique toward this type of investigation. For readers who are interested in this topic, we recommend Ref. 73 and references therein.

From an experimental point of view, in order to study a phase transition by PPE, one has to use a detection cell that allows a sample temperature scan (see Figs. 12 and 13). Both back and front PPE configurations can be used in order to detect a phase transition.⁹ The critical temperature can be easily detected through the critical anomalies of the amplitude and phase of the PPE signal. However, if the critical behavior of the thermal parameters is the target of the investigation, things become more complex. One has to use the back detection configuration together with the information contained in both the amplitude and phase of the signal,¹¹ or use a combination of back/front detection.⁴¹ Additionally, calibration of the measurement at the given temperature (usually room temperature) is necessary.

In the following, we will select only specific applications that concern both first and second order phase transitions, developed by the authors and co-workers.

As an example of PPE detection of first order phase transitions, we present results obtained on four samples of commercial Royal Jelly (RJ), provided by different producers.¹¹⁸ Measurements were conducted in the front PPE configuration, in the −15–5 ˚C temperature range. Figures 45 and 46 display the amplitude of the PPE signal as a function of temperature for the samples, in a temperature range that includes the transition (solid/liquid) point (heating–cooling cycles).

Figure 45 shows that during the heating procedure the amplitude of the PPE signal displays critical anomalies typical for melting processes. Concerning the specific temperature of these anomalies, for sample 1, the anomaly appears at 0 °C and for sample 2, it appears at a lower temperature (around −2 °C). During the cooling procedure the phase transition anomalies appear at much lower temperatures due to the well-known undercooling phenomenon. All four samples present anomalies at around −13 °C, but sample 1 is involved in a second phase transition at a higher temperature (around −10 °C). Chemical analysis indicates that both samples have a similar composition (similar water and sugar content). The only explanation is that for the samples involved in two phase transitions, a coexistence of two different phases (probably free and water-bound) is present. In conclusion, the PPE method, used in a temperature scan arrangement, offers structural information simply by detecting first order phase transitions.

Mandelis et al. were the first to apply the PPE method to ferromagnetic materials, in the detection of a ferro-paraelectric phase transition in Seignette salt.² We present an application of the PPE technique to detect ferroelectric–paraelectric phase transitions in another very well-known and intensively studied ferroelectric crystal: triglycine sulfate (TGS). TGS is a ferroelectric crystal with a Curie temperature at about 49 °C.¹¹⁹ The interest in its thermal properties is connected to its pyroelectric properties: in the ferroelectric phase, TGS has often been used as a pyroelectric sensor.¹⁰⁷ 

Typical temperature scans of the amplitude and phase of the PPE signal in a temperature range including the Curie point of TGS are displayed in Figs. 47 and 48.

Using Eqs. (7) and (9), and the well-known relationship between the thermal parameters, one gets the critical behavior of all four thermal parameters (Fig. 49).

One of the most important features concerning the use of the PPE technique for phase transitions investigations is the possibility of enhancing the critical anomaly of the PPE signal, by appropriate handling of the chopping frequency and sample's thickness.

Results from an experiment on a TGS crystal with two different thicknesses (230 and 500 μm), investigated at different frequencies (6 and 25 Hz) is displayed in Fig. 50. In this experiment, a 1 mm thick PZT ceramic pyroelectric sensor was used.

Figure 50 indicates that the critical anomaly of the PPE amplitude, ΔV/V, increases from 0.14 up to 1.22 with increasing a_mL_m for the same critical anomaly (a jump of about 0.2 in the specific heat). This conveys the suitability of the method toward studies of phase transitions with small critical anomalies of thermal parameters.

Magnetic phase transitions were most commonly studied with the purpose of calculating the critical exponents of thermal parameters and to validate existing theories concerning critical phenomena. One of the most studied systems has been Cr₂O₃ involved in an antiferromagnetic-paramagnetic phase transition at about 35 °C..¹¹ Reference 11 describes in detail the procedure of PPE investigations and how to correctly calculate critical exponents. In this Tutorial, we will present only some general results obtained on this subject: the temperature behavior of the static and dynamic thermal parameters in a temperature region including the Néel temperature (Fig. 51). The system used in this example was in back configuration, and the pyroelectric sensor was a LiTaO₃ single crystal.

As expected, all thermal parameters present anomalies at the Néel point, typical for second order phase transitions.

Figure 52 presents results obtained in the critical region of the ferro-paramagnetic phase transition of the Ni₇₀Cu₃₀ alloy.

This application demonstrates a similar principle to the case of ferroelectric materials by proper selection of the experimental parameters (sample thickness and chopping frequency), one can amplify the critical anomaly of the signal.

To conclude this section, we want to make some remarks concerning the temperature behavior of the pyroelectric sensor's properties. Investigations of phase transitions are based on temperature scans, and during a phase transition, the measurements of properties of both the sample and sensor change. Figure 50 contains as an example (inset) where the PPE signal was obtained with an empty sensor over the investigated temperature range. It is clear that the pyroelectric properties of the sensor change monotonically and very little as a function of temperature. For example, for a LiTaO₃ sensor, if the investigation is performed far enough from the Curie point of the sensor (about 300 °C), the PPE signal increases by about 1% as a function of temperature. Conversely, in the critical region of a phase transition, the sample's properties (i.e., thermal parameters) display sharp anomalies and the critical region is usually rather narrow (a few degrees). Consequently, a small, monotonic change in sensor properties does not significantly influence the results (the critical behavior of the sample's thermal parameters), and usually no normalization procedures are required. It is important that studies are conducted far enough from the Curie temperature of the sensor.

In this Tutorial, we have attempted to create a picture of how the PPE technique has developed over the past 35 years. In order to remain practical and educational, this paper is organized into three main sections (preceded by an Introduction and followed by a Conclusion sections). The first two main sections describe the development of the theoretical assumptions and experimental setups of the PPE method. The third section is devoted to applications, where of the hundreds of applications available, we selected only a small set that we consider most relevant to convey the breadth of potential that PPE techniques offer.

From a theoretical point of view, it is well-known that the general expression of the complex PPE signal can be calculated exactly (independent of the composition of the detection cell including the number of layers, the thermal and optical thickness of the layers, etc.) by solving a system of thermal diffusion equations with boundary conditions of flux and temperature continuity at the interfaces of the layered detection cell. However, the mathematical expression of the PPE signal is very complicated and practically useless for most applications. This is why a large effort was dedicated to simplifying it, focusing on the number of components of the detection cell and on the thermal and optical thickness of each layer. In this Tutorial, we described several specific cases of experimental interest. The cases reflect the available combinations of the detection configuration, the source of information, scanning parameters, and the goal of the measurement.

It should be noted that the theory presented in this Tutorial assumes 1D heat propagation through the layers of the detection cell. This restriction seems to be easily satisfied from an experimental point of view. However, theories involving 2D and 3D heat propagation have also been developed.

The main PPE detection configurations used in PPE experiments were originally termed “back” and “front” depending on the relative position of the sensor-incident radiation. For spectroscopic applications, a so-called “reflection mode” configuration has also been used. Concerning the detection configuration, the back mode has been more exploited because it can result in complete thermal characterization (measurement of the thermal diffusivity and effusivity and calculation of the remaining thermal conductivity and volume specific heat) of the sample. The front configuration allows the direct measurement of only the thermal effusivity.

Concerning the source of information, both amplitude and phase of the complex PPE signal can be used. However, the “competition” of PPE amplitude vs phase as a source of information seems to be won by the latter, even if both often result in the same accuracy of results. It is more 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 power fluctuations of the incident radiation or on the quality of the incident surface (as is the case with the amplitude).

Many detection schemes have been proposed for investigating the thermal parameters of condensed matter samples. Some of them are based on measurements of single values (fixed chopping frequency and sample thickness) and others on scanning procedures. This latter type of investigation is clearly more accurate. Two scanning parameters can be used: the chopping frequency of incident radiation and/or the thickness of one of the liquid layers (the sample or coupling fluid) of the detection cell. Each scanning procedure has its advantages and limitations. Frequency scanning is very simple as a procedure, but for accurate results, one must know the thickness of all layers of the detection cell. If the scanning procedure is developed over a large frequency range, various layers of the detection cell can pass from a thermally thin to a thick regime in an uncontrolled way, and consequently, theoretical restrictions may be violated. The thickness scanning procedure (performed at constant chopping frequency) does not have the problems mentioned above. Exact knowledge of the liquid layer is not needed because thickness variation can be controlled. However, for the TWRC method, the experimental setup is rather complicated: it must contain 6-axis micrometric stages, nano-motors, etc.

Concerning the “targets” of the measurements, both thermal diffusivity and effusivity can be obtained using the PPE amplitude and phase as the source of information. If in a thermal effusivity measurement at least one calibration procedure is involved, a normalization technique is not always necessary when thermal diffusivity measurements are performed. When the thermal diffusivity is deduced from the slope of the amplitude or phase as a function of sample thickness, no calibration is required. In many cases, the measurement of thermal effusivity is conditional upon knowledge of thermal diffusivity. The final resolution is always better for thermal diffusivity. It is known that the four thermal parameters are connected by two relationships. Consequently, the direct measurement of two of them leads automatically to the possibility of calculating the remaining two (thermal conductivity and volume specific heat). In order to achieve this complete thermal characterization of a sample, one must use the back detection configuration, collecting information from both amplitude and phase, or they must combine two specific cases in back and front configuration.

When considering experimental aspects, the setups, detection cells and sensor/sample assemblies described in this Tutorial are only examples. The reader can find other experimental solutions in the extended list of references. From the experimental point of view, it is important to select experimental parameters in such a way that the constraints of the theory are respected during the whole measurement.

At this stage, it is probably useful to recommend some of the most suitable parts of a PPE setup in light of the available technologies. Concerning radiation sources, for PPE spectroscopy, the best sources depend on the wavelength of interest. The source can be a Globar or Nernst source, a UV lamp, or a tunable diode laser, depending on what wavelength you want to obtain the information. For PPE calorimetry, lasers with power in the range 5–200 mW are recommended. It is well-known that the intensity of the absorbed radiation must be rather low, in order to keep valid the linear dependence of the PPE voltage as a function of the pyroelectric coefficient (if the intensity of irradiation is too high, non-linear effects can appear). Concerning the modulation of the incident radiation, PPE spectroscopy is usually performed with electro-mechanical choppers, which introduces a limitation to the frequency range, especially in the low regime (f ≤ 2 Hz). For PPE calorimetry, the best modulation is performed electronically, directly from the power supply of the laser. In such a way, the frequency range can be extended from 10⁻³ to 10⁵ Hz. Opto-acoustical modulators may also be a solution (they can be used together with lasers for large frequency ranges), but the user must be aware that such a modulator cuts about 25%–50% from the incident power of the laser. Concerning pyroelectric sensors, the best available, in our opinion, is the z-cut LiTaO₃ single crystal; it has a good pyroelectric coefficient, a high Curie temperature, very stable and reproducible thermal and electrical properties, and can be obtained from producers as slices of 50–500 μm thickness. Occasionally, PVDF foils (10–50 μm thickness) can be used as pyroelectric sensors, especially when thermally thin sensors are required by the experiment, but the user must be aware that the Curie point of such a sensor is rather low (around 100 °C). PZT ceramics constitute another class of pyroelectric sensors, with a rather good pyroelectric coefficient and a rather high Curie temperature, but, unfortunately, their thermal and electrical properties are not stable over time. In the past, some authors have also used triglycine sulfate (TGS) as a pyroelectric sensor due to its large pyroelectric coefficient but, unfortunately, the applications for which TGS is suitable are limited due to its low Curie point (around 49 °C) and its hygroscopicity.

PPE signal processing is always performed with lock-in amplifiers. In principle, any type of double-phase lock-in amplifier is suitable for signal processing. Such amplifiers have in-built preamplifiers of 10⁶ or 10⁸ Ω. When necessary, additional preamplifiers of larger electrical resistivity can be used. Current or voltage mode types of measurement can be selected experimentally, depending on the application. For PPE spectroscopy, an important part of the setup is the monochromator. Though their resolution can be limited, we suggest that the most suitable option for PPE experiments are prism monochromators; our main reason is that they let enough energy reach the detection cell. Due to the fact that PPE spectroscopy is usually one-channel spectroscopy, a degree of normalization is always necessary; blackened LiTaO₃ can be used as the sensor for normalization.

Selecting the applications to present in this Tutorial was a significant challenge. As already mentioned, in over 35 years of development, the PPE technique has proven itself to be useful in many types of applications. We stress the idea that the PPE method can be applied for the thermal characterization of practically all types of condensed matter materials: liquids [simple and volatile liquids, binary and isotopic mixtures, magnetic nanofluids, (semi)liquid foodstuffs -oils, margarine, juices, honey, meat, cheese, starch, blood, etc.] and solids (thermal and electrical good or bad conductors, ferroelectrics, pyroelectrics, thermoelectrics, magnets, composites as dental or building materials, etc.). To the best of our knowledge, the only types of samples that cannot be investigated by PPE are chemically aggressive (acids, for example). Liquids are the best samples for investigation as the thermal contact liquid sample/solid pyroelectric sensor is ideal. As mentioned, when investigating solids, a coupling fluid between the solid sample and the solid pyroelectric sensor can influence quantitative data. However, due to the effort of several groups, during the last decade the influence of the coupling fluid on results has been reduced or in certain cases eliminated. A recent success story in the development of this technique is the ability to investigate, with high accuracy, porous solids. It is important to note that, for all types of PPE investigation, a small quantity of material (μl or mg) is required. The possibility of using a small quantity of samples is of great importance when investigating rare and/or expensive samples such as isotopic liquid mixtures, magnetic nanofluids, itinerant electron antiferromagnetic materials, high Tc superconductors, etc.

One of the purposes of presenting the applications described in this Tutorial is to demonstrate that physical and chemical processes, such as molecular and isotopic associations, vegetable oils spoilage, and adulteration or phase transitions, can be studied by PPE calorimetry, provided accurate measurements are performed. In fact, high-alorimetry is able to investigate any process associated with small changes in static and dynamic thermal parameters. Of all of the applications to which PPE is suited, in our opinion special attention should be placed on phase transition detection. PPE is one of the most powerful techniques for phase transition investigations. Both first and second order phase transitions have been investigated by PPE, and the behavior of all static and dynamic thermal parameters in the phase transition region has been obtained. Concerning first order phase transitions, melting (vaporization and freezing) points have been detected and the hysteresis of heating–cooling cycles has been observed. This information has been used to study various processes such as oil adulteration and honey hygroscopicity. Concerning second order phase transitions (due to the possibility offered by advanced PPE experimental setups, which allow very slow temperature variation rates), the behavior of thermal parameters in very narrow critical regions (antiferromagnetic—paramagnetic, ferroelectric—paraelectric, phase transitions taking place in liquid crystals or liquid thermoelectrics) has been obtained. Even more, critical exponents for thermal parameters have been measured proving the suitability of the PPE method in fundamental physics research (critical exponents are universal numbers).

The PPE method is an example of absorption spectroscopy, and consequently, it appears to be useful in the investigation of strongly absorbing materials (solids and liquids). For such types of materials, classical two-channel transmission spectroscopy is useless. As a recent result, PPE spectroscopy was successfully used to obtain both spectroscopic and calorimetric information on strongly absorbing solids (semiconductors). A weakness to this is that it is a one-channel method, so it needs normalization procedures and for classical (semi-transparent) samples, classical two-channel differential spectroscopies are more often performed.

Finally, we would like to point out that almost all of the results described in this Tutorial belong to our group, together with our co-workers. We hope that the readers and the members of other groups active in this field understand the reason behind this limitation (i.e., there would be too much information to be included in a single paper). However, we are confident that the extended list of references will provide access to the results of other groups.

This work is funded by the Romanian Ministry of Research, Innovation and Digitalisation through Programme NUCLEU, Contract No. PN19 35 02 01 and by Slovenian