# The 2,2,4-trimethylpentane + ethyl propanoate binary system: density, Bancroft point and vapor-liquid equilibrium at 30, 60 and 101.3 kPa

Stéphane Vitu, Kaoutar Berkalou, Jean-Louis Havet, Vincent Caqueret

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Stéphane Vitu, Kaoutar Berkalou, Jean-Louis Havet, Vincent Caqueret. The 2,2,4-trimethylpentane + ethyl propanoate binary system: density, Bancroft point and vapor-liquid equilibrium at 30, 60 and 101.3 kPa. Journal of Chemical Thermodynamics, 2025, 207, pp.107486. 10.1016/j.jct.2025.107486. hal-05014978

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# The 2,2,4-trimethylpentane + ethyl propanoate binary system: density, Bancroft point and vapor-liquid equilibrium at 30, 60 and 101.3 kPa

Stéphane Vitu<sup>a,b,*</sup>, Kaoutar Berkalou<sup>a,b</sup>, Jean-Louis Havet<sup>a,b</sup>, Vincent Caqueret<sup>a,b</sup>

## ARTICLE INFO

### Keywords:

VLE

Vapor pressure

Density

Binary mixture

Azeotrope

Bancroft point

Isooctane

## ABSTRACT

The 2,2,4-trimethylpentane (isooctane) – ethyl ethanoate binary system was experimentally investigated. The density of the mixture was measured using a vibrating-tube apparatus and is reported at temperatures T = (288.15, 298.15, 308.15 and 318.15) K. The mixture exhibits positive excess molar volumes. Isobaric vapor-liquid equilibrium (VLE) of the system were obtained at three pressures P = (30, 60 and 101.3) kPa. Pure components vapor pressures were also acquired over a range of P = (20 to 160) kPa. Equilibrium data were measured using a recirculation ebulliometer (Gillespie-type VLE cell).

The 2,2,4-trimethylpentane – ethyl ethanoate presents a Bancroft point within the investigated pressure range and, consequently, an azeotropic behavior at each studied pressure. The azeotropic coordinates, derived from the measured VLE data, are reported. A notable dependence of the azeotropic composition on pressure was observed.

The NRTL and Wilson activity coefficient models were used to correlate the VLE data. Temperature-dependent interaction parameters were determined, enabling precise correlation of the reported VLE data. The predictive UNIFAC (Dortmund) model was also tested. While it produced accurate results at 30 kPa, significant deviations were noted at higher pressures.

## 1. Introduction

Phase equilibria and thermophysical properties of mixtures containing alkanes and esters are well-documented in the literature. Because of their relevance in several industrial sectors and their significant deviations from ideality, many studies have been dedicated to these mixtures [1–14]. However, despite these efforts, some basic binary systems have not yet been experimentally described. For example, although the VLE of binary mixtures of linear alkanes (from n-pentane to n-nonane) with ethyl propanoate (EP) has been reported at 101.3 kPa [2,5,12], to our knowledge, the phase behavior of branched alkanes + ethyl propanoate systems remains unstudied.

To offset this lack of data, the phase equilibria of the 2,2,4-trimethylpentane (isooctane, 224m5) + EP binary system was measured. 224m5 was chosen for two main reasons. Firstly, 224 m5 contains all the elementary groups (CH and C) found in branched alkanes which is important for increasing the available experimental data to consolidate or reassess interaction parameters in group contribution methods. Secondly, the binary system 224m5 + EP presents a Bancroft point near atmospheric pressure. As a reminder, for a binary system, a Bancroft

point is the intersection point of the saturation curves of the pure components [15–22]. Therefore, the 224m5 + EP necessarily exhibits an azeotropic behavior, at least in the vicinity of the Bancroft point.

Binary systems that exhibit a Bancroft point are very common [16], but the existence of the Bancroft point is often omitted or not discussed by authors reporting VLE data of azeotropic binary systems. However, the presence of a Bancroft point is an important information because in such mixtures, the azeotropic composition can substantially vary as a function of pressure (or temperature) [16,19]. The azeotropic phenomenon may also exists only over a limited range around the Bancroft point [15]. If a separation by distillation is considered, clear information about the existence, or not, of a Bancroft point is crucial.

The present study reports, for the first time, the VLE of the binary system 224m5 (1) + EP (2). Isobaric experimental data (T, x₁, y₁) were measured at 30, 60 and 101.3 kPa using a dynamic equilibrium device. The vapor pressures of the pure components were measured with the same apparatus beforehand and are provided herein from 20 to 160 kPa. The density of the liquid binary mixture at atmospheric pressure was also measured from 288.15 to 318.15 K. To achieve this, 17 synthetic mixtures were prepared to cover the entire composition range.

<footnote><sup>a</sup>Conservatoire National des Arts et Métiers, 2 rue Conté, 75003 Paris, France</footnote>

<footnote><sup>b</sup>Université Paris-Saclay, INRAE, AgroParisTech, UMR SayFood, 91120 Palaiseau, France</footnote>

<footnote>* Corresponding author at: Conservatoire National des Arts et Métiers, 2 rue Conté, 75003 Paris, France.</footnote>

<footnote>E-mail address: stephane.vitu@lecnam.net (S. Vitu).</footnote>
The NRTL and Wilson activity coefficient models were employed to correlate the VLE data. A comparison between the experimental results and predictions from the UNIFAC (Dortmund) model was also performed.

## 2. Experimental section

### 2.1. Materials

The suppliers and purities of the compounds used in this study are listed in Table 1. The purities provided by the manufacturers were verified by using a gas chromatograph equipped with a flame ionization detector. In addition, the water content of the components was measured by Karl-Fischer titrations. The chemicals were used without any additional purification. They were stored with molecular sieves and degassed prior to use.

### 2.2. Density measurements

Pure components and mixture density measurements were performed under atmospheric pressure (P = 101 ± 2 kPa), at four temperatures (T) ranging from (288.15 to 318.15) K, using a vibrating tube densimeter (DMA 4500 M, Anton Paar). More details about the experimental method employed can be found in a previous work [23].

17 binary mixtures of known compositions were prepared to accurately describe the entire composition range. The binary mixtures were carefully prepared using glass vials and an analytical lab balance (Mettler Toledo, model ML204, capacity: 220 g, weighing error: 0.0002 g). Chemicals were maintained at low temperature during the weighing process to minimize evaporation whereas the glassware used (vials, petettes) were at room temperature to prevent water vapor condensation on the glassware. A very short time was needed to prepare a binary mixture since the total mass of each prepared mixture did not exceed 9 g.

Uncertainties relating to the measurements performed in this study were evaluated following the method fully described in [23,24]. The maximum combined expanded uncertainty in mole fraction was found to be $U(x_1) = 0.0001$, corresponding to the combined standard uncertainty (maximum value of $u(x_1) = 3.1 \times 10^{-5}$) multiplied by a coverage factor of $k = 2$ for a 95 % level of confidence.

The density meter was calibrated daily with dry air and ultrapure water. The thermometer included in the measurement device was calibrated against a Pt-100 probe (MKT 10, Anton Paar GmbH). The expanded uncertainty of the temperature ($U(T)$) measured by the device was 0.02 K ($k = 2$). The density was measured with a standard uncertainty ($u(\rho)$) of 0.0003 g·cm⁻³ and the impurities of the chemicals were taken into account [25,26] through the following expression

$$u(\rho_i) = \sqrt{\left(\frac{u(\rho)}{\sqrt{3}}\right)^2 + \left(\rho_i \xi \left(1 - x_{\text{purity},i}\right)\right)^2} \quad (1)$$

In which $u(\rho_i)$ is the density uncertainty of the pure component i, $x_{\text{purity},224m5} = x_{\text{purity},EP} = 0.999$ and $\xi = 0.1$, the expected density difference between the pure component and its impurities.

The combined relative standard uncertainties are $u_r(\rho_i) = 0.0003$ for pure 224m5 and pure EP and $u_r(\rho_m) = 0.0004$ for the binary mixture 224m5 + EP.

The combined standard uncertainty of the excess molar volume ($V_m^E$)

was calculated by propagating the standard uncertainties related to the mole fractions and the mixture densities. The maximum combined standard uncertainty obtained is $u(V_m^E) = 0.05 \text{ cm}^3\text{·mol}^{-1}$.

### 2.3. VLE measurements

A dynamic equilibrium apparatus (Labodest VLE 602, ILUDEST, Germany) was used to measure isobaric VLE data at 30, 60 and 101.3 kPa. This commercial equipment has been described in previous works [9,23,27] and is widely used by others research groups [5,10,28–30].

In brief, the ebulliometer consists of a mixing chamber, a boiling chamber, an equilibrium cell (Cottrell pump) and a separation chamber surrounded by a heating mantle.

The pressure is regulated by a vacuum pump and injections of pure gaseous nitrogen and is measured by a P-30 (WIKA, Germany) pressure sensor. A buffer vessel is located between the vacuum pump and the VLE device to limit the pressure variations in the equilibrium cell. Figure S1 schematically depicts the pressure control system. A combined standard uncertainty of $u(P) = 0.2$ kPa was evaluated.

A Pt-100 resistance sensor (Temperaturmeßtechnik Geraberg, Germany) was used to measure the equilibrium temperatures. Taking into account the standard uncertainty of the sensor (0.06 K) and the inevitable temperature variations (0.05 K) observed at the equilibrium, the combined standard uncertainty is $u(T) = 0.07$ K.

Equilibrium was typically reached within 30 to 60 min. Samples (~1.5 mL) from both the liquid and condensed vapor phases were then collected. The collected samples were poured in small glass vials. Immediately after sampling, the glass vial containing the liquid phase was hermetically sealed whereas the condensed vapor phase sample was injected in the density meter for measurement. The liquid phase density was measured shortly after the condensed vapor phase analysis. The equilibrium compositions of the phases were thus indirectly determined through density measurements conducted at 298.15 K, using the previously described density meter. For this purpose, density data obtained from synthetic mixtures at 298.15 K were used to generate a fourth-order polynomial correlating the density with the molar composition of the binary system:

$$x_1 = A \rho_m^4 + B \rho_m^3 + C \rho_m^2 + D \rho_m + E \quad (2)$$

The coefficients of the polynomial function are listed in Table S1 in the Supporting Information, along with the calibration curve analysis in Figure S2. Average deviation between calculated and experimental molar fractions is 0.0001, with a maximum deviation of 0.0003.

Using this indirect determination method, the maximum combined uncertainty of the liquid and vapor phase mole fractions were $u(x_1) = u(y_1) = 0.002$.

## 3. Experimental results

### 3.1. Pure component densities and vapor pressures

Table 2 compares densities of the pure components measured in this study with literature data.

The densities measured in this work, as presented in Table 2, are consistent with numerous published values, underscoring the accuracy of the experimental method and the quality of the pure compounds employed.

<table><caption>**Table 1**

Description of the chemicals involved in this work.</caption><thead><tr><th>Compound</th><th>Abbreviation</th><th>CAS Number</th><th>Supplier</th><th>purity<sup>b</sup><br>g·g<sup>-1</sup></th><th>Water content<sup>c</sup><br>g·g<sup>-1</sup></th></tr></thead><tbody><tr><td>2,2,4-trimethylpentane</td><td>224m5</td><td>540–84–1</td><td>Sigma Aldrich</td><td>0.999</td><td>Non-detecable</td></tr><tr><td>Ethyl propanoate</td><td>EP</td><td>105–37–3</td><td>Alfa Aesar<sup>a</sup></td><td>0.999</td><td>0.0004</td></tr></tbody></table>

<footnote>a ThermoFisher Scientific. b information provided by the manufacturers and confirmed by GC analyses. c determined by Karl-Fischer titrations.</footnote>
<caption>**Table 2**</caption>

Measured densities (ρ) of 2,2,4-trimethylpentane and ethyl propanoate with literature values at temperatures T and pressure P = 101 kPa <sup>a</sup>.

<table><thead><tr><th rowspan="2">T/K</th><th colspan="2">ρ/g·cm<sup>-3</sup></th><th colspan="2">ethyl propanoate</th></tr><tr><th>This work</th><th></th><th>This work</th><th></th></tr></thead><tbody><tr><td rowspan="6">288.15</td><td rowspan="6">0.69594</td><td>Literature</td><td></td><td></td></tr><tr><td>0.69598 [31]</td><td></td><td>0.89558 [5]</td></tr><tr><td>0.695948 [32]</td><td></td><td>0.895707 [39]</td></tr><tr><td>0.68774 [7]</td><td></td><td></td></tr><tr><td>0.68777 [31]</td><td></td><td>0.88415 [5]</td></tr><tr><td>0.687749 [32]</td><td></td><td>0.88409 [7]</td></tr><tr><td rowspan="6">298.15</td><td rowspan="6">0.68776</td><td>Literature</td><td></td><td></td></tr><tr><td>0.68770 [33]</td><td></td><td>0.884359 [39]</td></tr><tr><td>0.68782 [34]</td><td></td><td>0.88438 [40]</td></tr><tr><td>0.6878 [35]</td><td></td><td>0.88430 [41]</td></tr><tr><td>0.68773 [36,37]</td><td></td><td>0.88418 [42]</td></tr><tr><td>0.687735 [38]</td><td></td><td></td></tr><tr><td rowspan="6">308.15</td><td rowspan="6">0.67946</td><td>Literature</td><td></td><td></td></tr><tr><td>0.67948 [31]</td><td></td><td></td></tr><tr><td>0.679459 [32]</td><td></td><td>0.87262 [5,40]</td></tr><tr><td>0.67940 [33]</td><td></td><td>0.87270 [41]</td></tr><tr><td>0.67951 [34]</td><td></td><td>0.87248 [42]</td></tr><tr><td>0.67946 [37]</td><td></td><td></td></tr><tr><td rowspan="6">318.15</td><td rowspan="6">0.67105</td><td>Literature</td><td></td><td></td></tr><tr><td>0.679470 [38]</td><td></td><td></td></tr><tr><td>0.67107 [31]</td><td></td><td></td></tr><tr><td>0.671069 [32]</td><td></td><td>0.86108 [5]</td></tr><tr><td>0.67098 [33]</td><td></td><td>0.86087 [40]</td></tr><tr><td>0.67105 [34]</td><td></td><td>0.86090 [41]</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

<sup>a</sup> Standard uncertainties: u(T) = 0.01 K, u(P) = 1 kPa. Relative standard uncertainty: u<sub>r</sub>(ρ) = 0.0003.

As mentioned previously, the binary system under study presents a Bancroft point near the atmospheric pressure, indicating that the pure components vapor pressures remain very close at low pressures. Vapor pressures were thus measured between 20 and 160 kPa to locate the Bancroft point and to characterize the saturation curves. The experimental vapor pressure data are reported in Table 3 and depicted in Fig. 1 as deviation plots and in Fig. 2.

A modified version of the Riedel equation was employed

$$ \ln P_i^{\text{vap}} = A_i + B_i/T + C_i \ln T + D_i T^{E_i} \quad (3) $$

In which $P_i^{\text{vap}}$ is expressed in Pa and T in K. Considering the proximity of the vapor pressure curves, the parameters of eq. 3 were fitted against the measured vapor pressures. It was mandatory for the latter treatment of the binary VLE data and the adjustment of the activity coefficient models parameters. The coefficients of the modified Riedel expression

<caption>**Table 3**</caption>

Measured vapor pressures for pure 2,2,4-trimethylpentane and ethyl propanoate <sup>a</sup>.

<table><thead><tr><th colspan="2">2,2,4-trimethylpentane</th><th colspan="2">ethyl propanoate</th></tr><tr><th>T/K</th><th>P/kPa</th><th>T/K</th><th>P/kPa</th></tr></thead><tbody><tr><td>323.83</td><td>20.0</td><td>327.26</td><td>20.0</td></tr><tr><td>334.48</td><td>30.0</td><td>337.19</td><td>30.0</td></tr><tr><td>342.56</td><td>40.0</td><td>344.71</td><td>40.0</td></tr><tr><td>349.17</td><td>50.0</td><td>350.83</td><td>50.0</td></tr><tr><td>354.80</td><td>60.0</td><td>356.03</td><td>60.0</td></tr><tr><td>359.74</td><td>70.0</td><td>360.57</td><td>70.0</td></tr><tr><td>364.13</td><td>80.0</td><td>364.65</td><td>80.0</td></tr><tr><td>368.13</td><td>90.0</td><td>368.30</td><td>90.0</td></tr><tr><td>372.20</td><td>101.3</td><td>372.10</td><td>101.3</td></tr><tr><td>375.14</td><td>110.0</td><td>374.79</td><td>110.0</td></tr><tr><td>378.30</td><td>120.0</td><td>377.66</td><td>120.0</td></tr><tr><td>381.27</td><td>130.0</td><td>380.36</td><td>130.0</td></tr><tr><td>384.05</td><td>140.0</td><td>382.90</td><td>140.0</td></tr><tr><td>386.69</td><td>150.0</td><td>385.30</td><td>150.0</td></tr><tr><td>389.19</td><td>160.0</td><td>387.58</td><td>160.0</td></tr><tr><td></td><td></td><td>389.75</td><td>170.0</td></tr></tbody></table>

<sup>a</sup> Maximum combined standard uncertainties u are u(T) = 0.07 K, u(P) = 0.2 kPa.

<figure><img src="image_2.png" /></figure>

**Fig. 1.** Deviation plots of vapor pressures reported in this work from the Riedel equation and parameters listed in Table 4. ●: experimental data from this work. (a) 2,2,4-trimethylpentane. □: Benecke et al. [36], ×: Wisniak et al. [43], ○: Sapei et al. [44], +: Willingham et al. [45], ◦: Gardeler et al. [46], ▲: Smith [47], △: Bernatova et al. [48], ■: Funk et al. [49]. (b) ethyl propanoate. •: Rios et al. [5], ×: Hernandez and Ortega [50], ○: Polak and Mertl [51], ◦: [49] Blanco and Ortega [52], ◦: Macedo and Rasmussen [53], △: Agafonova et al. [54].

<figure><img src="image_3.png" /></figure>

**Fig. 2.** Vaporization curves of the pure compounds calculated with eq. 3 and parameters provided in Table 4 and experimental vapor pressures from this work. Continuous curve: 2,2,4-trimethylpentane. Dashed curve: ethyl propanoate. ▲: Position of the Bancroft point.
<table><caption>**Table 4**
Riedel equation parameters used in this work.</caption><thead><tr><th>Compound</th><th>A<sub>i</sub></th><th>B<sub>i</sub></th><th>C<sub>i</sub></th><th>D<sub>i</sub></th><th>E<sub>i</sub></th><th>T<sub>min</sub>/K</th><th>T<sub>max</sub>/K</th><th>σ<sub>p</sub>/kPa<sup>a</sup></th></tr></thead><tbody><tr><td>2,2,4-trimethylpentane</td><td>-39.589</td><td>-2101.29</td><td>10.0184</td><td>-1.83571 × 10<sup>-5</sup></td><td>2</td><td>323.8</td><td>389.2</td><td>0.10</td></tr><tr><td>ethyl propanoate</td><td>214.909</td><td>-12056.60</td><td>-29.6232</td><td>3.15096 × 10<sup>-5</sup></td><td>2</td><td>327.3</td><td>389.8</td><td>0.06</td></tr></tbody></table>

a Standard deviation between experimental vapor pressures (Table 3) and calculated values using the Riedel equation.

determined in this study are given in Table 4.

Fig. 1 illustrates the good agreement between the vapor pressures measured with many experimental data previously published while Fig. 2 illustrates the intersection of the vapor pressure curves.

The coordinates of the Bancroft point can be estimated to be $T_{Ba} = 370.89$ K and $P_{Ba} = 97.5$ kPa. For temperatures lower than $T_{Ba}$, 224m5 is the most volatile compound of the system while EP becomes the most volatile compound for temperatures higher than $T_{Ba}$. EP is thus the component whose vapor pressure increases the more quickly with temperature.

## 3.2. Density and excess molar volume of the binary liquid mixture

Pintos-Barral et al. [7] published excess molar volumes at 298.15 K for the binary system 224m5 + EP but, in their paper, density values were not reported and only excess molar volumes were given. The density of the 224m5 (1) + EP (2) liquid mixture is thus disseminated for the first time in this work. The density of the mixture ($\rho_m$) was measured at 288.15, 298.15, 308.15 and 318.15 K for 17 mixtures ranging from $x_1 = \{0.0237$ to $0.9728\}$ (mole fraction of component 1). Excess molar volumes were calculated using eq. 4

$$V_m^E = \frac{x_1 M_1 + x_2 M_2}{\rho_m} - \left( \frac{x_1 M_1}{\rho_1} + \frac{x_2 M_2}{\rho_2} \right) \quad (4)$$

$x_1$ and $x_2$ are the mole fractions of the mixture whereas $M_1$, $M_2$ and $\rho_1$, $\rho_2$ are the pure component molar masses and densities, respectively.

Experimental densities and excess molar volumes for the system 224m5 (1) + EP (2) measured in this work are compiled in Table 5 and plotted in Fig. 3.

Excess molar volumes were correlated with the following Redlich-Kister [55] expression

$$\frac{V_m^E}{x_1(1 - x_1)} = a_0 + a_1(2x_1 - 1) + a_2(2x_1 - 1)^2 \quad (5)$$

Table S2 provides the regressed parameters $a_0$, $a_1$ and $a_2$.

The studied binary system exhibits positive excess molar volumes, reflecting the repulsion forces occurring in the liquid mixture. Excess molar volumes are significantly affected by the mixture temperature, as illustrated by Fig. 3(b), with a maximum value of $V^E$ found around $x_1 = 0.55$. These results align with previously published volumetric properties relating to EP + alkane binary systems. Fig. 4 presents the excess molar volume (for $x_1 = 0.5$) at 298.15 K for all the EP + alkane (normal and branched) binary mixtures studied to date.

The previously investigated EP + alkane mixtures systematically present positive excess molar volumes. Moreover, Fig. 4 highlights that, for the same number of carbon atoms, mixtures containing a branched alkane always present lower excess molar volumes than mixture containing the corresponding linear alkane. For example, the excess molar volume of the EP + 224m5 system measured in this work lies between those of the EP + n-pentane and EP + n-hexane mixtures. It can also be underlined that EP + 224m5 presents $V^E$ value noticeably lower than EP + basic C8 branched alkane (2-methylheptane, 3-methylheptane...). This difference can be attributed to marked steric effects that partially counterbalance dispersive interactions.

## 3.3. VLE of the binary system 224m5 (1) + EP (2)

The isobaric phase equilibrium of the mixture was investigated at 30, 60 and 101.3 kPa. To our knowledge, it was measured for the first time in this work. Phase compositions were determined by density measurements as described in Section 2.3. The measured density values of the liquid and condensed vapor phases are listed in Table S3.

<caption>**Table 5**</caption>

Experimental densities ($\rho$) and calculated excess molar volumes ($V_m^E$) of 2,2,4-trimethylpentane (1) + ethyl propanoate (2) binary mixtures at mole fraction $x_1$ in 224m5 at temperature $T$ and $P = 101$ kPa$^a$.

<table><thead><tr><th rowspan="2">x<sub>1</sub><br>/mol·mol<sup>-1</sup></th><th colspan="2">T = 288.15 K</th><th colspan="2">T = 298.15 K</th><th colspan="2">T = 308.15 K</th><th colspan="2">T = 318.15 K</th></tr><tr><th>ρ<br>/g·cm<sup>-3</sup></th><th>V<sub>m</sub><sup>E</sup><br>/cm<sup>3</sup>·mol<sup>-1</sup></th><th>ρ<br>/g·cm<sup>-3</sup></th><th>V<sub>m</sub><sup>E</sup><br>/cm<sup>3</sup>·mol<sup>-1</sup></th><th>ρ<br>/g·cm<sup>-3</sup></th><th>V<sub>m</sub><sup>E</sup><br>/cm<sup>3</sup>·mol<sup>-1</sup></th><th>ρ<br>/g·cm<sup>-3</sup></th><th>V<sub>m</sub><sup>E</sup><br>/cm<sup>3</sup>·mol<sup>-1</sup></th></tr></thead><tbody><tr><td>0.0000</td><td>0.89570</td><td>0.00</td><td>0.88435</td><td>0.00</td><td>0.87285</td><td>0.00</td><td>0.86125</td><td>0.00</td></tr><tr><td>0.0237</td><td>0.88866</td><td>0.04</td><td>0.87741</td><td>0.04</td><td>0.86601</td><td>0.04</td><td>0.85450</td><td>0.05</td></tr><tr><td>0.0547</td><td>0.87973</td><td>0.08</td><td>0.86858</td><td>0.09</td><td>0.85730</td><td>0.10</td><td>0.84592</td><td>0.11</td></tr><tr><td>0.0912</td><td>0.86951</td><td>0.13</td><td>0.85850</td><td>0.15</td><td>0.84737</td><td>0.16</td><td>0.83612</td><td>0.17</td></tr><tr><td>0.1449</td><td>0.85507</td><td>0.21</td><td>0.84427</td><td>0.23</td><td>0.83334</td><td>0.25</td><td>0.82229</td><td>0.27</td></tr><tr><td>0.2067</td><td>0.83936</td><td>0.27</td><td>0.82878</td><td>0.30</td><td>0.81807</td><td>0.33</td><td>0.80724</td><td>0.36</td></tr><tr><td>0.2773</td><td>0.82238</td><td>0.35</td><td>0.81205</td><td>0.38</td><td>0.80160</td><td>0.41</td><td>0.79102</td><td>0.45</td></tr><tr><td>0.3496</td><td>0.80609</td><td>0.40</td><td>0.79601</td><td>0.44</td><td>0.78580</td><td>0.48</td><td>0.77546</td><td>0.52</td></tr><tr><td>0.4221</td><td>0.79070</td><td>0.45</td><td>0.78086</td><td>0.49</td><td>0.77088</td><td>0.53</td><td>0.76078</td><td>0.58</td></tr><tr><td>0.4974</td><td>0.77571</td><td>0.47</td><td>0.76610</td><td>0.51</td><td>0.75636</td><td>0.56</td><td>0.74650</td><td>0.60</td></tr><tr><td>0.5724</td><td>0.76166</td><td>0.47</td><td>0.75229</td><td>0.51</td><td>0.74277</td><td>0.56</td><td>0.73314</td><td>0.61</td></tr><tr><td>0.6501</td><td>0.74798</td><td>0.46</td><td>0.73884</td><td>0.49</td><td>0.72956</td><td>0.54</td><td>0.72017</td><td>0.58</td></tr><tr><td>0.7283</td><td>0.73506</td><td>0.41</td><td>0.72614</td><td>0.44</td><td>0.71709</td><td>0.48</td><td>0.70793</td><td>0.52</td></tr><tr><td>0.7809</td><td>0.72680</td><td>0.36</td><td>0.71804</td><td>0.39</td><td>0.70914</td><td>0.42</td><td>0.70012</td><td>0.46</td></tr><tr><td>0.8332</td><td>0.71895</td><td>0.30</td><td>0.71033</td><td>0.32</td><td>0.70157</td><td>0.35</td><td>0.69271</td><td>0.38</td></tr><tr><td>0.8879</td><td>0.71105</td><td>0.22</td><td>0.70257</td><td>0.24</td><td>0.69396</td><td>0.26</td><td>0.68525</td><td>0.28</td></tr><tr><td>0.9326</td><td>0.70487</td><td>0.14</td><td>0.69650</td><td>0.16</td><td>0.68802</td><td>0.17</td><td>0.67943</td><td>0.18</td></tr><tr><td>0.9728</td><td>0.69949</td><td>0.06</td><td>0.69124</td><td>0.06</td><td>0.68286</td><td>0.07</td><td>0.67438</td><td>0.08</td></tr><tr><td>1.0000</td><td>0.69594</td><td>0.00</td><td>0.68776</td><td>0.00</td><td>0.67946</td><td>0.00</td><td>0.67105</td><td>0.00</td></tr></tbody></table>

a Expanded uncertainties are $U(T) = 0.02$ K, $U(P) = 2$ kPa, $U(x_1) = 0.0001$ mol·mol⁻¹ and $U(V_m^E) = 0.10$ cm³·mol⁻¹ (k = 2, level of confidence ≈ 0.95). Relative standard uncertainty is $u_r(\rho_m) = 0.0004$.
<figure><img src="image_4.png" /><figcaption>Fig. 3. Densities (a) and excess molar volumes (b) of the binary system 224m5 (1) + EP (2). ●: 288.15 K, ▲: 298.15 K, □: 308.15 K, ◆: 318.15 K. △: Pintos-Barral et al. at 298.15 K [7]. Dashed lines: Redlich-Kister equation (eq. 5) with parameters reported in the Supporting Information (Table S2).</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. Comparison of excess molar volumes ($V^E$) at 298.15 K of equimolar mixtures of EP + alkane. ●: EP + linear alkane, values derived from [5,56,57]. ▲: EP + basic branched alkane (substituted by a single methyl group: 2-methylpentane, 3-methylpentane, 2-methylhexane...), values derived from [6]. △: EP + 2,2,4,4,6,8,8-heptamethylnonane, value derived from [7]. ▲: EP + 224m5, this work.</figcaption></figure>

Experimental VLE data and activity coefficients are presented in Table 6. The truncated virial EOS was used to calculate the activity coefficients ($\gamma_i$)

$$ \gamma_i = \frac{y_i P}{x_i P_i^{\text{vap}}} \exp \left[ \frac{(B_{ii} - V_i^{\text{liq}})(P - P_i^{\text{vap}}) + P(1 - y_i)^2 (2B_{ij} - B_{ii} - B_{jj})}{RT} \right] \quad (6) $$

In which P is the pressure, $x_i$ is the liquid-phase mole fraction and $y_i$ is

the vapor-phase mole fraction. $V_i^{\text{liq}}$ is the molar volume of the pure component i at the equilibrium temperature, T. The second virial coefficients $B_{ii}$, $B_{ij}$ and $B_{ij}$ were calculated using the Tsonopoulos approach [58].

The excess Gibbs energy ($G^E$) was calculated by

$$ G^E = RT \sum_i x_i \ln \gamma_i \quad (7) $$

Fig. 5 illustrates the experimental VLE data acquired in this study while activity coefficients are plotted in Fig. S3 of the supplementary material.

Three widely used consistency tests were performed to verify the thermodynamic consistency of the VLE data: the Fredenslund test, the Wisniak L-W test and the Kojima area test. They are described in detail elsewhere [59–62]. Table 7 summarizes the results obtained from the measured VLE data for these tests.

The datasets validate the consistency tests though, for the Fredenslund test, a lack of randomness in the distribution of the residuals may be observed at 60 and 101.3 kPa. A probable explanation is the closeness of the pure component boiling temperatures and the resulting typical shape of the phase diagram near the Bancroft point.

# 4. VLE modeling and discussion

## 4.1. VLE data modeling

The experimental VLE data were modeled by the NRTL and Wilson activity coefficient models [63,64]. The interaction parameters were regressed against experimental data using the following objective function (OF)

$$ \text{OF} = \sum_{i=1}^{N} \left[ \left( \frac{x_i^{\text{exp}} - x_i^{\text{calc}}}{\sigma_x} \right)^2 + \left( \frac{y_i^{\text{exp}} - y_i^{\text{calc}}}{\sigma_y} \right)^2 + \left( \frac{T^{\text{exp}} - T^{\text{calc}}}{\sigma_T} \right)^2 \right] \quad (8) $$

In which N is the number of data points included in the data set and σ is the standard deviation of the data set.

The expression of the temperature dependent NRTL binary interaction parameters can be written as follows

$$ \tau_{ij} = \frac{g_{ij} - g_{ji}}{RT} = \frac{A_{ij}^0 + A_{ij}^T (T - 273.15)}{RT} \quad (9) $$
<caption>**Table 6**</caption>

Experimental isobaric vapor-liquid equilibrium data for the 2,2,4-trimethylpentane (1) – ethyl propanoate (2) system at pressures *P* = 30, 60 and 101.3 kPa, temperature *T*, liquid mole fraction *x*₁ and vapor mole fraction *y*₁ᵃ.

<table><thead><tr><th><i>T</i><br>/K</th><th><i>x</i><sub>1</sub><br>/mol·mol<sup>-1</sup></th><th><i>y</i><sub>1</sub><br>/mol·mol<sup>-1</sup></th><th><i>γ</i><sub>1</sub></th><th><i>γ</i><sub>2</sub></th><th><i>G</i><sup>E</sup>/<i>RT</i></th></tr></thead><tbody><tr><td colspan="6"><b><i>P</i> = 30.0 kPa</b></td></tr><tr><td>337.19</td><td>0.000</td><td>0.000</td><td></td><td>1.000</td><td>0.000</td></tr><tr><td>335.15</td><td>0.071</td><td>0.147</td><td>2.044</td><td>0.994</td><td>0.045</td></tr><tr><td>334.65</td><td>0.094</td><td>0.184</td><td>1.966</td><td>0.994</td><td>0.059</td></tr><tr><td>333.77</td><td>0.140</td><td>0.250</td><td>1.848</td><td>0.997</td><td>0.084</td></tr><tr><td>333.31</td><td>0.175</td><td>0.288</td><td>1.730</td><td>1.006</td><td>0.100</td></tr><tr><td>333.02</td><td>0.197</td><td>0.312</td><td>1.682</td><td>1.010</td><td>0.110</td></tr><tr><td>332.45</td><td>0.236</td><td>0.348</td><td>1.597</td><td>1.030</td><td>0.133</td></tr><tr><td>332.07</td><td>0.279</td><td>0.384</td><td>1.510</td><td>1.047</td><td>0.148</td></tr><tr><td>331.84</td><td>0.317</td><td>0.414</td><td>1.444</td><td>1.062</td><td>0.157</td></tr><tr><td>331.59</td><td>0.364</td><td>0.445</td><td>1.364</td><td>1.091</td><td>0.168</td></tr><tr><td>331.51</td><td>0.384</td><td>0.457</td><td>1.331</td><td>1.106</td><td>0.172</td></tr><tr><td>331.33</td><td>0.428</td><td>0.486</td><td>1.278</td><td>1.136</td><td>0.178</td></tr><tr><td>331.15</td><td>0.492</td><td>0.526</td><td>1.210</td><td>1.189</td><td>0.182</td></tr><tr><td>331.11</td><td>0.524</td><td>0.545</td><td>1.179</td><td>1.220</td><td>0.181</td></tr><tr><td>331.04</td><td>0.576</td><td>0.577</td><td>1.138</td><td>1.278</td><td>0.178</td></tr><tr><td>331.08</td><td>0.629</td><td>0.612</td><td>1.103</td><td>1.338</td><td>0.170</td></tr><tr><td>331.16</td><td>0.686</td><td>0.650</td><td>1.071</td><td>1.423</td><td>0.158</td></tr><tr><td>331.26</td><td>0.726</td><td>0.680</td><td>1.054</td><td>1.486</td><td>0.147</td></tr><tr><td>331.51</td><td>0.782</td><td>0.724</td><td>1.032</td><td>1.596</td><td>0.127</td></tr><tr><td>331.92</td><td>0.842</td><td>0.780</td><td>1.017</td><td>1.728</td><td>0.101</td></tr><tr><td>332.70</td><td>0.904</td><td>0.852</td><td>1.006</td><td>1.857</td><td>0.065</td></tr><tr><td>333.31</td><td>0.943</td><td>0.906</td><td>1.003</td><td>1.941</td><td>0.041</td></tr><tr><td>334.48</td><td>1.000</td><td>1.000</td><td>1.000</td><td></td><td>0.000</td></tr><tr><td colspan="6"><b><i>P</i> = 60.0 kPa</b></td></tr><tr><td>356.03</td><td>0.000</td><td>0.000</td><td></td><td>1.000</td><td>0.000</td></tr><tr><td>354.09</td><td>0.058</td><td>0.119</td><td>2.132</td><td>0.998</td><td>0.042</td></tr><tr><td>353.70</td><td>0.078</td><td>0.150</td><td>2.020</td><td>0.997</td><td>0.052</td></tr><tr><td>353.23</td><td>0.103</td><td>0.186</td><td>1.923</td><td>0.997</td><td>0.065</td></tr><tr><td>352.30</td><td>0.170</td><td>0.264</td><td>1.698</td><td>1.006</td><td>0.095</td></tr><tr><td>351.65</td><td>0.225</td><td>0.318</td><td>1.575</td><td>1.022</td><td>0.119</td></tr><tr><td>351.09</td><td>0.300</td><td>0.378</td><td>1.426</td><td>1.053</td><td>0.142</td></tr><tr><td>350.67</td><td>0.349</td><td>0.415</td><td>1.363</td><td>1.081</td><td>0.159</td></tr><tr><td>350.61</td><td>0.390</td><td>0.443</td><td>1.303</td><td>1.101</td><td>0.162</td></tr><tr><td>350.33</td><td>0.442</td><td>0.477</td><td>1.248</td><td>1.142</td><td>0.172</td></tr><tr><td>350.29</td><td>0.519</td><td>0.526</td><td>1.173</td><td>1.204</td><td>0.172</td></tr><tr><td>350.33</td><td>0.585</td><td>0.564</td><td>1.113</td><td>1.283</td><td>0.166</td></tr><tr><td>350.40</td><td>0.624</td><td>0.588</td><td>1.085</td><td>1.335</td><td>0.160</td></tr><tr><td>350.57</td><td>0.680</td><td>0.629</td><td>1.059</td><td>1.406</td><td>0.148</td></tr><tr><td>350.77</td><td>0.729</td><td>0.667</td><td>1.040</td><td>1.481</td><td>0.135</td></tr><tr><td>350.92</td><td>0.765</td><td>0.695</td><td>1.028</td><td>1.558</td><td>0.125</td></tr><tr><td>351.22</td><td>0.803</td><td>0.730</td><td>1.018</td><td>1.630</td><td>0.111</td></tr><tr><td>352.24</td><td>0.888</td><td>0.828</td><td>1.011</td><td>1.769</td><td>0.073</td></tr><tr><td>353.60</td><td>0.950</td><td>0.913</td><td>0.998</td><td>1.919</td><td>0.031</td></tr><tr><td>354.80</td><td>1.000</td><td>1.000</td><td>1.000</td><td></td><td>0.000</td></tr><tr><td colspan="6"><b><i>P</i> = 101.3 kPa</b></td></tr><tr><td>372.10</td><td>0.000</td><td>0.000</td><td></td><td>1.000</td><td>0.000</td></tr><tr><td>369.83</td><td>0.070</td><td>0.123</td><td>1.914</td><td>1.009</td><td>0.054</td></tr><tr><td>369.40</td><td>0.092</td><td>0.153</td><td>1.831</td><td>1.011</td><td>0.066</td></tr><tr><td>368.86</td><td>0.118</td><td>0.189</td><td>1.787</td><td>1.013</td><td>0.080</td></tr><tr><td>368.19</td><td>0.153</td><td>0.231</td><td>1.713</td><td>1.022</td><td>0.100</td></tr><tr><td>367.89</td><td>0.181</td><td>0.262</td><td>1.653</td><td>1.024</td><td>0.110</td></tr><tr><td>367.42</td><td>0.240</td><td>0.311</td><td>1.497</td><td>1.045</td><td>0.131</td></tr><tr><td>367.14</td><td>0.279</td><td>0.345</td><td>1.438</td><td>1.057</td><td>0.141</td></tr><tr><td>366.93</td><td>0.329</td><td>0.382</td><td>1.356</td><td>1.079</td><td>0.152</td></tr><tr><td>366.85</td><td>0.375</td><td>0.415</td><td>1.294</td><td>1.101</td><td>0.156</td></tr><tr><td>366.79</td><td>0.460</td><td>0.471</td><td>1.197</td><td>1.156</td><td>0.161</td></tr><tr><td>366.79</td><td>0.495</td><td>0.494</td><td>1.166</td><td>1.183</td><td>0.161</td></tr><tr><td>366.84</td><td>0.590</td><td>0.554</td><td>1.094</td><td>1.284</td><td>0.155</td></tr><tr><td>366.93</td><td>0.626</td><td>0.576</td><td>1.068</td><td>1.336</td><td>0.150</td></tr><tr><td>367.18</td><td>0.687</td><td>0.621</td><td>1.041</td><td>1.418</td><td>0.137</td></tr><tr><td>367.58</td><td>0.747</td><td>0.669</td><td>1.019</td><td>1.516</td><td>0.119</td></tr><tr><td>367.98</td><td>0.798</td><td>0.713</td><td>1.005</td><td>1.630</td><td>0.102</td></tr><tr><td>368.73</td><td>0.858</td><td>0.780</td><td>1.000</td><td>1.742</td><td>0.079</td></tr><tr><td>369.44</td><td>0.900</td><td>0.833</td><td>0.998</td><td>1.843</td><td>0.060</td></tr><tr><td>369.95</td><td>0.923</td><td>0.865</td><td>0.997</td><td>1.908</td><td>0.047</td></tr><tr><td>372.20</td><td>1.000</td><td>1.000</td><td>1.000</td><td></td><td>0.000</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Isobaric phase diagrams of the binary system 224m5 (1) + EP (2). Symbols: experimental data. Solid lines: bubble and dew curves calculated using the NRTL model. Dashed lines: curves predicted using UNIFAC.</figcaption></figure>

<footnote>ᵃ Maximum standard uncertainties *u* are *u*(*P*) = 0.2 kPa, *u*(*T*) = 0.07 K, *u*(*x*) = *u*(*y*) = 0.002 mol·mol⁻¹. *T*, equilibrium temperature, *x*₁ and *y*₁, liquid and vapor-phase 2,2,4-trimethylpentane mole fraction, respectively. *γ*₁, activity coefficient, *G*⁵/RT, dimensionless Gibbs function.</footnote>
<table><caption>**Table 7**

Results of the consistency tests.</caption><thead><tr><th>Pressure dataset</th><th>Fredenslund test<br>100·Δy ≤ 1</th><th>L-W point test<br>0.92 &lt; L<sub>l</sub>/W<sub>l</sub> &lt; 1.08</th><th>L-W area test<br>D &lt; 3</th><th>Kojima area test<br>|A*| &lt; 3</th></tr></thead><tbody><tr><td>30.0 kPa</td><td>0.65</td><td>0.96 &lt; L<sub>l</sub>/W<sub>l</sub> &lt; 0.98</td><td>1.2</td><td>1.9</td></tr><tr><td>60.0 kPa</td><td>0.99</td><td>0.95 &lt; L<sub>l</sub>/W<sub>l</sub> &lt; 0.99</td><td>1.8</td><td>1.3</td></tr><tr><td>101.3 kPa</td><td>0.96</td><td>0.95 &lt; L<sub>l</sub>/W<sub>l</sub> &lt; 0.97</td><td>2.5</td><td>2.1</td></tr></tbody></table>

Whereas adjustable parameters of the Wilson equation are

$$ \Lambda_{ij} = \frac{V_j}{V_i} \exp \left( - \frac{\lambda_{ij} - \lambda_{ii}}{RT} \right) = \frac{V_j}{V_i} \exp \left( - \frac{A_{ij}^0 + A_{ij}^T T}{RT} \right) \quad (10) $$

The interaction parameters obtained are given in Table 8.

Both models provide an accurate description of the phase equilibrium of the studied mixture. Results obtained are very similar. Calculated bubble and dew curves are almost superimposed. For clarity, only the curves calculated by the NRTL model are shown in Fig. 5. Deviations between experimental and calculated values are summarized in Table 9.

With the parameters proposed in Table 8 for the Wilson and the NRTL model, the deviations do not exceed 0.005 for Δy and 0.12 K for ΔT. Even though these results are very good, they could have been better. To this end, a set of interaction parameters could have been determined for each set of isobaric VLE data (30, 60 and 101.3 kPa). This would have improved the correlation, notably at 101.3 kPa. Yet, in this work, we chose to determine a single set of parameters covering the entire range studied, which seems a more useful approach for practical applications.

The predictive UNIFAC (Dortmund) model [65–67] was also tested. The corresponding curves are drawn in Fig. 5 (dashed curves) and the deviations are reported in Table 9.

## 4.2. Discussion

The pressure dependence of azeotropic composition is a crucial information if a pressure-swing distillation is envisaged to separate an azeotropic mixture [68]. In this work, azeotropic temperature and composition were inferred from the experimental measurements and are presented in Table 10. This table also reports azeotropic points predicted by the UNIFAC model.

As expected, within the studied pressure range, the proximity of the pure components boiling temperatures lead to a significant variation in the azeotropic composition. It decreases from 0.579 at 30 kPa to 0.492 at 101.3 kPa. Increasing the pressure, the composition of the azeotrope logically shifts toward the EP-rich side of the diagram, the most volatile compound above the Bancroft point. These observations are in agreement with previous descriptions of positive azeotropic mixtures with a Bancroft point [15,16,69]. The shape of the phase behavior illustrated in Fig. 5 is typical of a binary system approaching its Bancroft point. At 101.3 kPa, the phase diagram is nearly symmetrical.

The UNIFAC predictive model performs very well at 30 kPa (Δy = 0.008 and ΔT = 0.08 K) whereas poorer results are observed when the

<table><caption>**Table 8**

Temperature dependent NRTL and Wilson binary interaction parameters for the 224m5 (1) + EP (2) system regressed against data at P = 30, 60 and 101.3 kPa.</caption><thead><tr><th>Activity coefficient model</th><th>A<sup>0</sup><sub>12</sub>/J·mol<sup>-1</sup></th><th>A<sup>0</sup><sub>21</sub>/J·mol<sup>-1</sup></th><th>A<sup>T</sup><sub>12</sub>/J·mol<sup>-1</sup>·K<sup>-1</sup></th><th>A<sup>T</sup><sub>21</sub>/J·mol<sup>-1</sup>·K<sup>-1</sup></th><th>α<sup>NRTL</sup><sub>12</sub></th></tr></thead><tbody><tr><td>NRTL</td><td>2030.79</td><td>25.96</td><td>-15.477</td><td>18.677</td><td>0.47</td></tr><tr><td>Wilson</td><td>-5217.87</td><td>6368.63</td><td>16.153</td><td>-12.821</td><td>-</td></tr></tbody></table>

<table><caption>**Table 9**

Average deviations in vapor phase mole fraction and equilibrium temperature between experimental data and NRTL, Wilson and UNIFAC model predictions.</caption><thead><tr><th>Model</th><th>Δy<br>/mol·mol<sup>-1</sup></th><th>ΔT<br>/K</th></tr></thead><tbody><tr><td>NRTL</td><td>0.005</td><td>0.12</td></tr><tr><td>Wilson</td><td>0.005</td><td>0.11</td></tr><tr><td>UNIFAC (Dortmund)</td><td>0.011</td><td>0.40</td></tr></tbody></table>

<table><caption>**Table 10**

Experimental and estimated with UNIFAC azeotropic temperature, T<sub>az</sub>, and azeotropic composition, x<sub>1,az</sub>, for the 224m5 (1) + EP (2) system at P = 30, 60 and 101.3 kPa.</caption><thead><tr><th rowspan="2">P<br>/kPa</th><th colspan="2">Experimental</th><th colspan="2">UNIFAC</th></tr><tr><th>T<sub>az</sub><br>/K</th><th>x<sub>1,az</sub><br>/mol·mol<sup>-1</sup></th><th>T<sub>az</sub><br>/K</th><th>x<sub>1,az</sub><br>/mol·mol<sup>-1</sup></th></tr></thead><tbody><tr><td>30</td><td>331.04</td><td>0.579</td><td>331.10</td><td>0.570</td></tr><tr><td>60</td><td>350.29</td><td>0.536</td><td>350.66</td><td>0.526</td></tr><tr><td>101.3</td><td>366.79</td><td>0.492</td><td>367.36</td><td>0.490</td></tr></tbody></table>

pressure increases (for P = 101.3 kPa, Δy = 0.014 and ΔT = 0.76 K). The overall shape of the phase diagram is nevertheless well reproduced by UNIFAC.

## 5. Conclusion

From the experiments conducted in this work, it can be concluded that (i) the binary mixture 224m5 + EP exhibits positive excess molar volumes induced by the molecular interactions within the mixture; (ii) the binary system displays a Bancroft point and, consequently, a positive homogeneous azeotrope over the investigated pressure range; (iii) the azeotropic composition varies significantly with pressure.

The excess molar volumes obtained in this work were well described using a classical Redlich-Kister expansion. Three thermodynamic consistency tests were employed to evidence the quality of the experimental VLE data. These data were finally correlated by the NRTL and Wilson models with binary interaction parameters regressed against the reported experimental data. Temperature-dependent interaction parameters were chosen to cover the full pressure range studied.

In the future, to complement this study, it would be interesting to perform high-pressure phase behavior measurements to further characterize the 224m5 + EP binary system. Indeed, at this stage, it remains uncertain whether the system presents an absolute azeotropy (i.e. the azeotropic line intersects the liquid-vapor critical locus at a critical azeotropic end point) or a limited azeotropy (the azeotropic line intersects the EP vapor pressure curve, forming a pure azeotropic end point).

### CRediT authorship contribution statement

Stéphane Vitu: Writing – review & editing, Validation, Supervision, Methodology, Investigation, Formal analysis. Kaoutar Berkalou: Validation, Methodology, Investigation. Jean-Louis Havet: Resources. Vincent Caqueret: Writing – original draft, Validation, Methodology, Investigation.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
# Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jct.2025.107486.

## Data availability

The data measured in this study are available within the article. Other data used in this work will be made available on request.

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