3.1. Experimental Results
Thermodynamic properties such as density, speed of sound and refractive index of binary mixtures furfural + furfuryl alcohol, were measured at 0.1 MPa over the temperature range
T = (293.15–343.15) K. The dynamic viscosity of the mentioned mixtures was studied at somewhat wider temperature range of (288.15–373.15) K and the same pressure, 0.1 MPa. The results of the measurements are listed in
Table 2.
The results of the measurements are compared to the data found in literature for pure furfural and furfuryl alcohol [
12,
13,
14,
15,
16,
17,
18,
19,
20] and good agreements were noted (
Figure 1).
In the case of furfural, the measured densities differ slightly from the values reported by Almeida et al. [
15], Lomba et al. [
12] and Bendiaf et al. [
13], average absolute deviation (AAD) was about 0.02%, 0.03% and 0.08% (0.3 kg·m
−3, 0.4 kg·m
−3 and 0.9 kg·m
−3), respectively. A somewhat better agreement was observed between the measured furfural density and the data of Qureshi et al. [
17] and Belhadj et al. [
20] with AAD ≈ 0.02% (0.2 kg·m
−3), and in the case of Nduli and Deenadayalu [
18] AAD was about 0.05% (0.6 kg·m
−3). Furfural viscosities given here deviate from the data reported by Lomba et al. [
12] with AAD ≈ 5.25% (0.07 mPa·s) and from the data reported by Qureshi et al. [
17] with AAD ≈ 4.67% (0.07 mPa·s). Speed of sound measurements for furfural were in good accordance with the literature data; the deviation from the data of Bendiaf et al. [
13], Lomba et al. [
12] and Belhadj et al. [
20] was AAD ≈ 0.02% (0.3 m·s
−1), and for the data of Nduli and Deenadayalu [
18] AAD was slightly higher, 0.03% (0.4 m·s
−1). Almeida et al. [
15] and Lomba et al. [
12] also reported refractive indices of furfural that deviate from the data presented here with AAD of 0.07% (0.001) and 0.11% (0.002), respectively. The comparison of the measured values with the refractive index reported by Nduli and Deenadayalu [
18] and Belhadj et al. [
20] resulted in AAD of 0.08% (0.001) and 0.12% (0.002), respectively.
As for furfuryl alcohol, the measured density data differ from those obtained by Hough et al. [
16], Lomba et al. [
12] and Zaoui-Djelloul-Daouadji et al. [
14] with AAD of 0.11%, 0.06% and 0.17% (1.2 kg·m
−3, 0.7 kg·m
−3 and 1.9 kg·m
−3), respectively. The deviation between the measured data and the densities reported by Mahi et al. [
19] was about 0.11% (1.3 kg·m
−3), but it was significantly higher for the results of Nduli and Deenadayalu [
18], AAD ≈ 0.24% (2.7 kg·m
−3). In the case of the viscosity of furfuryl alcohol, AAD between the data given here and those of Lomba et al. [
12] was about 1.11% (0.05 mPa·s). The measured speed of sound of furfuryl alcohol deviates from data of Lomba et al. [
12] and Zaoui-Djelloul-Daouadji et al. [
14] with AAD of 0.03% and 0.16% (0.4 m·s
−1 and 2.3 m·s
−1), respectively. The comparison of speed of sound data with the values reported by Mahi et al. [
19] gave similar results, AAD ≈ 0.11% (0.6 m·s
−1) but for the results of Nduli and Deenadayalu [
18] AAD was about 0.44% (6.2 m·s
−1). Finally, Lomba et al. [
12], Nduli and Deenadayalu [
18] and Mahi et al. [
19] also reported the refractive indices of furfuryl alcohol, which agree well with the experimental values presented here; the AAD was about 0.09%, 0.02% and 0.04% (0.001, 0.0003 and 0.0006), respectively.
The measurement uncertainties reported by Zaoui-Djelloul-Daouadji et al. [
14], Qureshi et al. [
17] and Baird et al. [
23] are of the same order of magnitude as the uncertainties estimated for the results given in this work. Mahi et al. [
19] and Belhadj et al. [
20] assessed higher uncertainties while the uncertainties of the other compared data [
12,
13,
15,
16,
18,
22] were lower than those reported here. The agreement of the results presented in this paper with the literature data [
12,
13,
14,
15,
16,
17,
18,
19,
20] is very good and falls mostly within the reported uncertainties. The unsatisfactory results were obtained only when the density and speed of sound of furfuryl alcohol were compared with the data of Zaoui-Djelloul-Daouadji et al. [
14] and Nduli and Deenadayalu [
18]. The comparison of experimental results with literature data performed by the mentioned authors in their papers [
14,
18] gave deviations similar to those obtained comparing the data presented here with their results [
14,
18]. Therefore, the poor agreement of the measured density and speed of sound of furfuryl alcohol with the data published in two mentioned papers [
14,
18] should not cast doubt on the reliability of the presented results.
Density, speed of sound and refractive index decrease linearly as a function of temperature (
Figure 2). Density and refractive index increase for increasing concentration of furfural in the mixture because these thermodynamic properties of pure furfural are higher than of furfuryl alcohol. The dependence of the mentioned properties on the furfural fraction in the mixtures is given at
Figure S1. The density, speed of sound and refractive index measured for the studied mixtures are higher than the values that would be expected for ideal mixture (based on Kay’s rule). Deviation of the mixture’s properties from ideal behaviour indicates the specific interactions between components and in this case the increase in
ρ,
u and
nD implies the presence of attractive forces, assumingly hydrogen bonds, between furfural and furfuryl alcohol. The influence of the composition of the mixture on speed of sound is weaker than on the other studied properties. Furthermore, the addition of small amount of furfural (up to 40%) caused the increase in speed of sound while further increase in furfural fraction led to decrease in speed of sound of binary mixture.
As for the dependence of viscosity on temperature, it decreases exponentially with temperature elevation, as expected (
Figure 2b). The obtained results showed that the increase in the molar fraction of furfural in mixture led to lower viscosity due to lower viscosity of furfural than of furfuryl alcohol. Additionally, the measured viscosities of the studied mixtures are lower than the values expected for ideal mixture (Grunberg–Nissan rule) indicating the heteromolecular interactions (
Figure S1b). Furfural and furfuryl alcohol are both derivatives of furan, where hydrogen at position 2 is substituted with formyl or hydroxymethyl group, respectively (see
Table 1). Both compounds have similar densities, higher than water. However, furfuryl alcohol is more viscous comparing to furfural presumably due to hydrogen bonding, especially at lower temperatures. The difference in viscosities diminishes at higher temperatures which might be attributed to the rupture of hydrogen bonding in furfuryl alcohol.
The experimentally obtained viscosity data were fitted to the Vogel–Fulcher–Tammann (VFT) Equation (1) [
30,
31,
32] leading to the optimized parameters given in
Table 3.
The obtained good agreement between calculated and measured viscosities (AAD ≈ 0.2%) confirmed the suitability of VFT equation for viscosity correlation (
Figure 2b).
Density measurements for pure compounds were also carried out at pressures up to 60 MPa and at temperatures ranging (293.15–413.15) K for furfural and (293.15–373.15) K for furfuryl alcohol (
Table 4).
Densities of the studied compounds at 0.1 MPa pressure determined using DMA HP device were compared with the values measured by means of DSA 5000 M and the average absolute deviations were 0.01% for furfural and 0.04% for furfuryl alcohol. Guerrero et al. [
22] measured densities of furfural and furfuryl alcohol at temperatures (283.15–338.15) K and pressures up to 60 MPa and their results differ from the data presented in this paper for about 0.02% (0.3 kg·m
−3) and 0.03% (0.4 kg·m
−3), respectively. Baird et al. [
23] determined the density and vapour pressure of 11 biocompounds in the temperature interval (293.15–423.15) K at pressures up to 10 MPa and one of them was furfural; the agreement between their and the data given here was very good with AAD ≈ 0.03% (0.4 kg·m
−3).
The experimentally determined densities of the pure compounds as a function of temperature and pressure are presented at
Figure 3 showing that the density depends on temperature almost linearly. As expected, an increase in density with pressure rise and decrease in density as a function of increasing temperature was noted for both of the studied compounds.
3.2. High Pressure Density Correlation
The correlation of the experimentally determined high-pressure densities was performed applying the modified Tammann–Tait equation [
24] (Equation (2)). That further enabled the calculation of various derived properties.
where
ρref represents the density of sample at the reference pressure,
pref = 0.1 MPa,
B(
T) is temperature dependent, while
C is temperature independent parameter.
ρref and
B(
T) are expressed in a form of second-order polynomial:
where
ai and
bi, in addition to
C, are adjustable parameters.
Firstly, for each individual compound, the density data obtained at reference pressure (0.1 MPa) were fitted to Equation (3) which resulted in the determination of parameters
ai. The parameter optimisation was conducted by applying the Levenberg–Marquardt algorithm [
33] aiming to minimize the absolute average deviation between the measured and correlated values. The second step was to adjust parameters
bi and
C of Equations (2) and (4) by applying the same optimization procedure to the whole density data set, excluding densities at 0.1 MPa. The optimized parameters of the modified Tammann–Tait equation (Equations (2)–(4)) are given in
Table 5. The average absolute percentage deviation (AAD), the maximum percentage deviation (MD), the average percentage deviation (Bias) and the standard deviation (σ) of the experimental data from those calculated using the modified Tammann–Tait equation are also given in
Table 5. The low values of AAD (about 0.006%) achieved for both studied pure compounds indicate the good quality of density data modelling.
3.3. Derived Thermodynamic Properties
The knowledge of the density at wide ranges of temperature and pressure enables calculation of various derived volumetric properties. These properties are calculated by differentiating density with respect to pressure or temperature.
The change of density as a response to pressure change is described by the isothermal compressibility,
κT: [
34]
The incorporation of Equation (2) into (5) gives: [
34]
The influence of temperature on density, i.e., the change of density when temperature is changed under constant pressure, is described by the isobaric thermal expansivity,
αp: [
34]
The following expression is derived from the modified Tammann–Tait Equations (2) and (7): [
34]
where
ρref’(
T,
pref) and
B’(
T) are derivatives of the parameters
ρref(
T,
pref) and
B(
T) with respect to
T, respectively:
The thermal pressure coefficient,
γ, which represents the ratio between
κT and
αp, can be calculated as follows: [
34]
The internal pressure,
pint, which gives insight into intermolecular interaction of the sample can be determined using Equation (12): [
34]
where
U stands for an internal energy and
V is volume of the sample.
Another important thermodynamic property is the difference between the specific heat capacity at constant pressure,
cp, and the specific heat capacity at constant volume,
cv: [
34]
The coupling of Equations (5) and (7) with (13) leads to the following expression of the mentioned property:
Knowledge on the isothermal and isentropic compressibility enables the calculation of the isobaric specific heat capacity: [
35]
which is significant for the determination of the isochoric heat capacity using Equation (14).
The calculation of isentropic compressibility,
κS, requires the knowledge on density and speed of sound: [
35]
The calculated isothermal compressibility, the isobaric thermal expansivity, the internal pressure and the difference between the isobaric and isochoric specific heat capacities for both examined pure compounds, in the temperature interval (293.15–413.15) K for furfural and (293.15–437.15) K for furfuryl alcohol at pressures up to 60 MPa, are given in the
Supplementary Material to the paper (
Tables S1 and S2). The isothermal compressibility and the isobaric thermal expansivity calculated for furfural and furfuryl alcohol are presented in
Figure 4 and
Figure 5.
The isothermal compressibility and the isobaric thermal expansivity of both studied pure compounds increase as temperature rises at constant pressure and decrease with increasing pressure along the isotherms (
Figure 4 and
Figure 5). The obtained values of
κT are slightly higher for furfural than for furfuryl alcohol so the change of pressure will affect densities of both compounds similarly. The isothermal compressibility is inversely proportional to the ability of molecules to create hydrogen bonds [
22], which could explain the lower values of
κT obtained for furfuryl alcohol. As for
αp, the calculated values are somewhat higher for furfural than for furfuryl alcohol, meaning that the increase in temperature will cause greater expansion, i.e., a density decrease in the case of furfural than of furfuryl alcohol. This indicates that furfuryl alcohol has a better packed structure than furfural, likely because of stronger intermolecular interactions due to hydrogen bonds that are also known to limit the movement of molecules and that way disable the expansion [
12,
36]. The isobaric thermal expansivity shows the typical behaviour where its dependence on temperature becomes weaker with the increase in pressure resulting in the intersection of the isotherms. The intersection point where
αp is temperature independent
was not observed at the studied range of pressure for furfural, while for furfuryl alcohol, it is expected to occur at pressure slightly above 60 MPa.
In addition to this, the isobaric thermal expansivities of both studied compounds were calculated using a pseudo-experimental technique where the measured densities at constant pressure were fitted using polynomial function:
The values obtained this way agreed very well with the
αp calculated by differentiating the modified Tammann–Tait equation (
Tables S1 and S2); the average absolute percentage deviations for
αp of furfural was less than 0.2% and for furfuryl alcohol it was about 0.5%.
The dependence of the internal pressure on pressure is given in
Figure S2. The
pint represents the change in internal energy as a result of a very small change in volume at constant temperature and gives insight mainly into weak intermolecular forces such as dispersive, repulsive and dipolar [
36]. The internal pressures of the studied compounds are positive implicating the dominant attractive intermolecular forces. The internal pressure decreases with the increase in temperature while pressure does not affect it considerably, especially at lower temperatures, for both studied compounds. The increase in pressure leads to lower values of
pint of furfural at temperatures under 343.15 K while at temperatures above 343.15 K
pint increases when pressure rises. In the case of furfuryl alcohol, the internal pressure decreases when pressure increases in the whole studied range of temperature indicating that the higher pressure restricts the change of internal energy as a respond to expansion. The
pint values calculated for furfural are higher than those obtained for furfuryl alcohol, which is more noticeable at lower temperatures, possibly due to stronger dipole–dipole interactions within more polar furfural when compared with furfuryl alcohol [
12]. Although molecules of furfuryl alcohol are linked by hydrogen bonds that are stronger than dipole–dipole interactions between molecules of furfural, hydrogen bonds do not have significant effect on the internal pressure [
36].
The isentropic compressibility,
κS, of furfural and furfuryl alcohol (
Table 6) increases with the increase in temperature. A comparison of isothermal (
Tables S1 and S2) and isentropic compressibility (
Table 6) showed that the values determined for
κT are for about 25% higher than those calculated for
κS, for both studied compounds. In general, the ratio
κT/
κs is equal to the ratio between isobaric and isochoric heat capacities,
Cp/
CV. While isentropic compressibility of furfural at 0.1 MPa is higher than of furfuryl alcohol (for about 6%), the isentropic compressibilities of the examined samples are almost the same. The
κS of furfuryl alcohol is slightly higher than
κS of furfural at temperatures up to 313.15 K and at higher temperatures, the relation is reversed.
The calculated values of the specific heat capacities at constant pressure and at constant volume are given in
Table 6. The obtained values for both,
cp and
cV, are higher for furfuryl alcohol than furfural. The increase in temperature resulted in the increase in the isobaric and isochoric specific heat capacities and the temperature influence was stronger in the case of furfuryl alcohol.