A piezoelectric crystal microbalance (resonance frequency of 10 MHz) has been used to monitor the transition phase (solid → gas) of some dicarboxylic acids in a controlled environment in order to obtain their enthalpy of sublimation.

The microbalance is composed of a quartz crystal with a diameter of 14 mm and a thickness of 0.2 mm. The electrode, the sensible area of the crystal, is located in the central part and has a diameter of 4 mm (Fig. 1). The microbalance is connected to its proximity electronics (PE), including a frequency counter and an oscillation circuit, powered by USB-PC input.

In order to use the microbalance as an efficient mass attractor, the quartz crystal should be cooled with respect to the surrounding environment and in addition, the VOC molecular flux should be focused on the crystal. The PCM cooling is performed by means of a conductive connection to a copper plate in thermal contact with a coil containing liquid nitrogen. Finally, the PCM is enclosed in a metal case, acting as a thermal shield and avoiding the PCM heating by irradiation of the internal wall of the vacuum chamber, which is at ambient temperature (see Fig. 2).

In order to maximize the VOC flux, the microbalance has been placed in front of the effusion cell. This configuration strongly improves the flux collimation, increasing the amount of the collected molecules. The metal case has a temperature similar or even slightly smaller than the crystal and if the effusion cell is too far away from the PCM, the molecular flux could more likely condense on the metal case rather than the crystal, lowering the deposition rate too much (Fig. 2, left). Moreover, reaching lower PCM temperatures (i.e. -72 ∘C instead of -25 ∘C of the first attempt) by improving the thermal contact with PCM and cold sink, we were able to increase the incident flow of molecules on the microbalance (avoiding molecules dispersion in the surrounding environment). A previous calibration performed with the adipic acid sample has been performed at TPCM=-72 ∘C and at 10-6 mbar. The effusion cell has been heated from 30 to 75 ∘C. This first test has experimentally determined that the distance between the PCM and the effusion cell allowing the larger flux onto the PCM crystal is 2 cm. At higher distances, the fluxes are too low and the monitoring of the sublimation process is not reliable.

Then the PCM and effusion cell are placed in a sublimation micro-chamber, i.e. a controlled environment of cylindrical form (located inside the vacuum chamber) made of insulating material (Teflon), which further minimizes thermal dispersion and avoids the VOC's loss into the microbalance surrounding area (Fig. 2, right). The effusion cell is inserted into a hole in the cylinder's base.

In this experiment the PCM is cooled down to -72 ∘C, while the acid sample is placed in a small cylinder case (effusion cell) 6 mm wide and 10 mm deep. This configuration allows the VOC's deposition rates to be monitored from about 10-13 mol cm-2 s-1 up to 10-10 mol cm-2 s-1, 2 orders of magnitude better than the first set-up version discussed in Dirri et al. (2012). The sample is heated from room temperature (i.e. 25–30 ∘C) up to high temperatures (i.e. 75–80 ∘C) by means a heater of 20 Ω (resistance) in thermal contact with the effusion cell. In Fig. 3 a schematic representation of the set-up is shown.

The whole set-up is placed in a vacuum chamber in order to facilitate the transition phase, to avoid the simultaneous condensation on the PCM of other molecules present in the atmosphere at ambient pressure (mainly H2O) and to avoid convective heat exchange with the atmosphere, which would affect PCM and effusion cell temperature. The vacuum system (Fig. 4) is composed of a rotative pump (CF29PR-Alcatel Society), a turbo pump (1602450-Elettrorava Society), and a chamber (90 L), all of them assembled by the Vacuum Centre Representative (CRV S.r.l., Rome, Italy). A rotative pump can drive the system down to 10-2 mbar, whereas the turbo pump can lower the pressure down to 10-6–10-7 mbar. Pressure is measured using the TC1 sensor (Varian) up to 10-2 mbar and the ionization gauge (IG) sensor (Varian) up to 10-6–10-7 mbar. During data acquisition the pressure of the system is maintained constant during each experiment (fixed values between 3.5×10-6 mbar and 8×10-7 mbar).

The temperatures of the copper plate, metal case, resistance, and effusion cell have been continuously monitored with platinum sensors (PT100, dimensions of 7.6×7.6×0.7 mm), whose resistance changes linearly with temperature. Temperature controls of the effusion cell (heating system from 25 to 110 ∘C) and of the copper plate (cooling system, set to -90 ∘C and stable within 0.2 ∘C) have been driven by a proportional–integral–derivative system (PID), which allows a temperature stability of typically ±0.5 ∘C and is managed by means of LabVIEW 2010 software (PC1). The frequencies have been acquired by means of the Eureka electronic box powered by a USB of PC2, controlled by the software provided by Bioelectronics and Advanced Genomic Engineering (BioAge S.r.l., Lamezia Terme, Italy).

The dicarboxylic acid chemical formula is HOOC(CH2)n-2 COOH where n is the number of carbon atoms. The considered samples are acids in small grains in white crystalline form (odourless solid) with a purity degree of 99 %. Considering the sublimation point of these acids and the temperature range available by our set-up (from 25 to 80 ∘C), the studies were focused on acids with n between 2 and 9 carbon number: oxalic (n= 2), succinic (n= 4), adipic (n= 6), and azelaic (n= 9) acids. Adipic acid was provided by Sigma Aldrich S.r.l., succinic acid by Institute of Translational Pharmacology (ITF-CNR, Rome, Italy), while azelaic and oxalic acids were kindly provided by the University of Rome, La Sapienza (Department of Chemistry). Some structural and thermodynamic characteristics of the acids utilized in this work are shown in Table 1.

In order to measure the enthalpy of sublimation, a PCM has been used as a mass attractor for the volatile molecules inside the Teflon micro-chamber. Firstly, the crystal in thermal contact with a copper plate was cooled down to -72 ∘C (constant temperature during the heating cycle).

Then, each sample (13–20 mg) was placed in an effusion cell and at a later stage was heated by a resistance in a range of temperature from 25–30 to 75–80 ∘C. The stabilization of the VOC's molecular flow at each heating temperature was obtained by keeping the temperature constant for 30 min, while a good distinction between two successive flows at two different temperatures was possible by adopting temperature steps of 5 ∘C. The PCM frequency and temperature were measured every 2 s. Then, deposition rates were measured at each temperature set point in mol cm-2 s-1.

Finally, in order to infer the enthalpy of sublimation in a well-defined temperature range (from 25–30 to 75–80 ∘C), different couples of temperatures (T1 and T2) were considered for data analysis. By applying the Van 't Hoff relation (Eq. 5) to each couple of T1 and T2 and considering the related deposition rates k1 and k2, measured in Hz s-1, ΔHsub was inferred. The parameters of heating cycles of different acids, i.e. initial mass, pressure, expected enthalpy of sublimation, temperature range, stabilization time at each temperature, are listed in Table 2.

Our set-up and measurement procedure is similar to Albyn (2001). Thus similarly to him, we can predict that a temperature stability of ±0.5 ∘C (temperature control on effusion cell) should produce an error on the enthalpy of sublimation of about ±7 %. This value would be a good starting point for the organic compounds analysed in this work. This value is mainly related to the temperature instability of the sample heating and the efficiency of the deposition process (Albyn, 2001).

At 30 ∘C with the PCM at -72 ∘C, the succinic and oxalic acids already show higher sublimation rates than adipic and azelaic acids. Thus, the enthalpy of sublimation has been calculated considering a maximum temperature of 55 ∘C for oxalic and succinic, lower than those used for adipic acid, i.e. 70 ∘C, and azelaic, i.e. 60 ∘C (see Table 3). Besides, the retrieval of the enthalpy of sublimation can be considered reliable as long as T2 is quite distinct (≥ 5 ∘C) from the temperature limit, TL (Table 2), where the flows of molecules are not reliable. Choosing T2∼TL, a slope change of deposition curve is expected due to the phase transition or due to the introduction of a new physical–chemical process.

A total frequency variation of 13 kHz has been observed for the oxalic acid in the whole temperature range monitored (Fig. 5, blue curve): from 25 to 65 ∘C, corresponding to a mass deposition of 9.3 µg. This compound (with short carbon chain, C2) showed a high volatility even at low temperatures, confirmed by the moderately high deposition rate measured already at 25 ∘C. The deposition rate curve shows a continuous increase up to 60 ∘C, with a constant slope (Fig. 5, blue curve). The enthalpy of sublimation has been obtained in the temperature range from 25 up to 55 ∘C (Table 3), due to the instability of the sublimation flows at temperatures larger than 60 ∘C. Moreover, a best agreement is obtained when the difference between T1 and T2 is between 15 and 25 ∘C (within 9 % compared with the literature values, Table 3).

The oxalic acid presents in its molecular structure two water molecules (dihydrate, monocline structure) which are lost at about 100 ∘C and 1 bar. In this dehydration reaction, its molecular structure changes from monocline to rhombic crystals and becomes anhydrous (Bahl and Bahl, 2010). In our experiment, we considered a monocline dehydrate oxalic acid and the obtained enthalpy results (Table 4) differ to previous works, relative to the anhydrous form (Booth et al., 2009). On the contrary, our results, i.e. 62.5 ± 3.5 kJmol-1 (Table 4), agree within 5.5 % with values, relative to dehydrate oxalic acid (de Wit et al., 1983; Granovskaya, 1948), as it should be. Indeed, as verified by de Wit et al. (1983), a difference for the sublimation enthalpy values between the two anhydrous forms (beta and alpha, obtained by means vacuum sublimation) and the dehydrate state (this work) happens due to the two water molecules' desorption from oxalic acid structure.

In the succinic acid case, the frequency decreases by 10.6 kHz in the whole temperature range monitored (i.e. from 30 to 75 ∘C), corresponding to 5.9 µg. The measured deposition rates are shown in Fig. 5 (orange curve). During the sublimation process, at temperature larger than 60 ∘C, the deposition rate oscillates around a medium value (Fig. 5, orange curve). The enthalpy of sublimation has been obtained in the temperature range from 30 to 55 ∘C (Table 3) because of the instability of the flow of molecules from 60 ∘C. Probably, a new chemical–physical process occurred at these temperatures. The results at 75 ∘C have been excluded due to the high temperature oscillations occurred.

Succinic acid (with a short carbon chain, C4) shows a smaller deposition rate than the oxalic acid, even if it already strongly sublimates at 25 ∘C. The deposition rate curve shows an increase up to 60 ∘C and a slope change beyond this temperature. The succinic acid tends to lose one water molecule easily, becoming succinic anhydride. A good temperature range to monitor enthalpy variation is 30–55 ∘C, far away from the point where succinic acid changes its structure (∼ 137 ∘C) (Vanderzee and Westrum, 1970). In this range, the average enthalpy of sublimation measured is 113.3 ± 1.3 kJ mol-1, in agreement within 5 % with the previous works (Chattopadhyay and Ziemann, 2007; Davies and Thomas, 1960; Table 4). Considering the vacuum environment and an upper temperature larger than 55 ∘C, the retrieved enthalpy may not be reliable for the transformation (initial phase) of succinic acid crystalline form (monocline/triclinic prisms) into cyclic anhydride, a ring structure (pyramidal crystal), losing one water molecule (Orchin et al., 2005; Vanderzee and Westrum, 1970).

In the case of adipic acid (long carbon chain, C6), a total frequency decrease of 28 kHz in the whole temperature range monitored (i.e. from 30 to 75 ∘C, Fig. 6, black curve) corresponding to 15.5 µg has been observed. A considerable frequency variation is observed above 50 ∘C, due to the high volatility of the acid at these temperatures. This acid sublimates at low pressure without a decomposition and only at 230–250 ∘C changes its molecular structure, becoming cyclopentanone plus H2O and CO2. As a matter of fact, at temperatures lower than 50 ∘C, the variation of deposition rates of adipic acids is only 1.5 and 27 % of that measured for oxalic and succinic acid, respectively; this is due to the better stability of its carbon chain at these temperatures. The enthalpy of sublimation of adipic acid has been obtained in the temperature range from 40 to 70 ∘C. The data acquired at 75 ∘C have been excluded from the analysis due to the high temperature oscillations which produce unstable deposition rates. The deposition rates at 30 and 35 ∘C have been also excluded because of the low flows of molecules. At these temperatures, the adipic acid flows are 2 orders of magnitude lower than the oxalic and succinic acids.

Azelaic acid shows a larger frequency variation than succinic and oxalic acid, with a total frequency decrease in the whole temperature range monitored (from 35 to 80 ∘C, Fig. 6, red curve) of 21 kHz corresponding to 11.6 µg. Azelaic acid presents a very slow sublimation up to 35 ∘C and reaches the maximum deposition rate at 75 ∘C (whereas at 80 ∘C, the deposition rate begins to decrease). The enthalpy of sublimation has been obtained in the temperature range from 35 to 60 ∘C (Table 3). The enthalpies of sublimation at temperatures higher than 60 ∘C have not been considered reliable due to a decrease of the deposition rates.

This compound starts to decay at 360 ∘C (at atmospheric pressure) but in our experiment, the deposition curve shows a slope variation at 80 ∘C and a instability of the deposition flow from 65 to 80 ∘C (not used for the analysis). The reasons for that should be studied in more detail and the temperature range should be increased in order to monitor enthalpy variation at larger temperatures. Probably, monitoring a wider temperature range for the two other acids (oxalic and adipic) we could observe the same trend.

As listed in Table 3, when the temperature oscillations are within ±0.5 ∘C, the errors do not exceed 5 kJ mol-1, whereas when the temperatures oscillations are larger than ±0.5 ∘C, the errors on the enthalpy of sublimation are larger than 8 kJ mol-1 (adipic and succinic acids). In Table 4, the temperature range used is listed, as well as enthalpy results obtained in this study. A high accuracy has been obtained for succinic, adipic, and azelaic acid, i.e. within 1 % and within 5 % for oxalic acid. Thus, in order to demonstrate the high quality of our method and the validity of our results, the enthalpies of sublimation have been compared with the results obtained by previous works. In the comparison, we will take into account the different boundary conditions (initial temperatures and working pressures) of the different procedures (Table 4): TDMA (Bilde et al., 2003), Knudsen mass loss (Ribeiro da Silva et al., 1999), KEMS (Booth et al., 2009), TDPBMS (Chattopadhyay and Ziemann, 2007), the effusion method, EM (Davies and Thomas, 1960; Granovskaya, 1948), and E-1559 Method B (Albyn, 2001).

The values of enthalpy of sublimation obtained in our experiments for succinic and adipic acids are within 5 % of the enthalpy values reported by Chattopadhyay and Ziemann (2007), who present a temperature programmed thermal desorption method (TDPBMS) where the particles were collected at -50 ∘C in a vacuum chamber. Successively, by means of a heating process (2 ∘C min-1), the vapour pressure and evaporation rates of submicron particles were measured. This method use a modified Langmuir equation and the Clausius–Clapeyron equation, similar to our theoretical approach.

Our results are quite low compared to those measured by Bilde et al. (2003) (within 9 % for the adipic acid), who demonstrate the capability of the tandem differential mobility analyser (TDMA) technique to measure the vapour pressures of submicron aerosol particles at solid-state structure. The results of evaporation rates were measured over the temperature range 17–41 ∘C. In the TDMA technique, the major source of error was based on the sensitivity analysis (a conservative uncertainty and systematic errors were considered on vapour pressures). A different method was used by Booth et al. (2009), who directly measured the steady-state vapour pressure using the Knudsen effusion mass spectrometry (KEMS) method with a solid sample. In Booth et al. (2009), the working pressure and heating method of the sample was similar to ours: there was a temperature step of 5 ∘C considering 10 min of stabilization time. The enthalpy obtained for adipic and succinic acids is smaller than that measured in this work and is larger than that for the oxalic acid. However, it should be noted that their measurements are affected by a large uncertainty; in particular, the errors obtained for oxalic acid (19 kJ mol-1) are the result of the variation in the three calibration compounds used for that determination, whereas the high error on the adipic acid (26 kJ mol-1) is the result of low pressures, resulting in decreased signal-to-noise ratio. Regarding the oxalic acid, as discussed above, it is highlighted that these authors measured the value of the α-orthorhombic anhydrous form and a difference from our results is expected. This difference is evident in de Wit et al. (1983) results, where the analysis of the dehydrate and anhydrous form (prepared by a prolonged evacuation of the hydrate substance and vacuum sublimation) of the oxalic acid has been performed. The enthalpy of sublimation of oxalic acid, as listed in Table 4, agrees within 5.5 % of the average value obtained from the dehydrated results (de Wit et al., 1983; Granovskaya, 1948). Instead, Ribeiro da Silva et al. (1999, 2001) present Knudsen mass-loss effusion, a method similar to Booth et al. (2009) in order to study the vapour pressures of crystalline dicarboxylic acids at much higher temperatures. The vapour pressures were calculated with a Langmuir equation, whereas the enthalpy of sublimation at the mean temperature was derived by the Clausius–Clapeyron equation. Ribeiro da Silva et al. (1999) results show larger values than ours (Table 4): 32 kJ mol-1 for azelaic acid (Ribeiro da Silva et al., 1999) and 10 kJ mol-1 for succinic acid (Ribeiro da Silva et al., 2001). As stated by Bilde et al. (2015) the enthalpy of sublimation values between the different experimental methods can differ by tens of kilojoules per mole. The results of Davies and Thomas (1960), who measured heat and entropy of sublimation by means of the effusion method at 1.013 bar pressure, are in agreement with our values (within 9.5 % for adipic acid and within 4 % for succinic acid). Albyn (2001) used two different 15 MHz microbalances cooled at -42 ∘C in a vacuum chamber to measure the deposition rates of adipic acid from 25 to 60 ∘C. The enthalpy of sublimation measured by Albyn is 121 ± 8 kJ mol-1 and shows a difference of 20 kJ mol-1 compared to our result (Table 4). This is probably due to the different set-up and measurement procedure, i.e. the microbalance's temperature of -42 ∘C instead of -72 ∘C (this work) and the distance between the sensing crystal and the sample of 20 cm instead of 2 cm (this work). The constant error of 8 kJ mol-1, obtained with a temperature stability of ±0.5 ∘C on the effusion cell (Albyn, 2001), could be due to the re-evaporation of a minor portion of the deposited material. In this work, when the temperature stability is within ±0.5 ∘C, the error does not exceed 5 kJ mol-1 (Table 3, oxalic, succinic, and adipic acid). This improvement in the accuracy could be due to our increased gas flow of adipic molecules.

Thus, main differences observed among the various examined works and enthalpy results are probably due to different temperature and pressures considered in the experiments and different forms of the sample (e.g. solid or aerosol), which produced different evaporation rates and different vapour pressures at each monitored temperature.

In our procedure the efficiency of the deposition process was improved when the difference between PCM surface's and effusion cell's temperature increased, and molecule flux was focused directly on the PCM crystal (Dirri et al., 2012). In this way, we were able to discern the deposition rate at different temperatures. Data analysis has been performed excluding the set point with high temperature oscillations (adipic and succinic acids) which affects the deposition rates trend and the low flows of molecules at lower temperatures (e.g. 30–35 ∘C, adipic acid case). As listed in Table 3, a temperature stability of ±0.5 ∘C on the effusion cell causes errors on the enthalpies of sublimation lower than 4 % for oxalic, adipic, and succinic acids (a better accuracy compared with Albyn, 2001), whereas when the temperature stability is larger than ±0.5 ∘C, the corresponding errors are larger than 10 %. Thus, for each compound, we obtained several measurements of the enthalpy of sublimation (individually having a worse accuracy, Table 3) that allows the weight average value to be retrieved for the enthalpy of sublimation where the weight function, ωi=(1/σi2), has been used. The weight average values show a better accuracy compared with the single enthalpy measurement, i.e. an accuracy of within 1 % for succinic, adipic, and azelaic acids and within 5 % for oxalic acid (Table 4). In Fig. 7 the enthalpy of sublimation of four dicarboxylic acids analysed in this work is compared with previous studies. The behaviours of the enthalpies of sublimation are very similar and increase as the carbon chain number of the substance increases. Indeed, the substances with a short carbon chain (oxalic and succinic acid) show a lower enthalpy of sublimation compared with the substances with a higher carbon chain (adipic and azelaic acids), which require a higher temperature to reach complete sublimation (larger than 60 ∘C). Furthermore, as reported by other studies (Booth et al., 2009; Bilde et al., 2003, 2015), the dicarboxylic acid, with an odd number of carbon atoms, has a lower sublimation enthalpy compared with dicarboxylic acids that have an even number of atoms. This behaviour is based principally on the solid-state crystalline structure of the acids. In this work, the enthalpy alternation between the odd and even carbon chain dicarboxylic acid (> C5) has been confirmed for two compounds: the enthalpy of sublimation of adipic acid (C6) is higher than the sublimation enthalpy of azelaic acid (C9) of 17 kJ mol-1 (Fig. 7). The alternation in the enthalpy of sublimation has also been confirmed by the results of Bilde et al. (2003), which included the adipic and azelaic acids. As explained by Booth et al. (2009), the behaviour of the enthalpy alternation is not always clear and it is not possible to say firmly that this effect was observed in their work.