Measurement and modeling of metoclopramide hydrochloride (anti-emetic drug) solubility in supercritical carbon dioxide

2.1 Materials

Metoclopramide hydrochloride, MCP, (CAS Number 7232–21-5) was provided by Aminpharma Company (Isfahan, Iran) with a minimum purity of 99.0%. The molecular structure and thermodynamic properties of MCP are summarized in Table 1. The carbon dioxide (CAS Number 124–38-9) with a purity of 99.99% was supplied by Fadak Company (Kashan, Iran). Methanol (CAS Number 67–56-1) was produced by Merck (Darmstadt, Germany) with a purity exceeding 99.9%.

Table 1 Moleuclar structure and thermodynamic properties of metoclopramide hydrochloride.

Compound	metoclopramide hydrochloride
Structure
Formula	C14H22ClN3O2•HCl
CAS number	7232–21-5
λmax (nm)	270
Minimum purity	99%
MW (g∙mol−1)	336.26
Tm (K)	455.30 (Pabón et al., 1996)
ΔHm (kJ∙mol−1)	25.72 (Pabón et al., 1996)
Tc (K)a	1321.25
Pc (MPa) a	2.3958
ω (-) a	0.3471
Vs (cm3∙mol−1) b	233.51

a The critical properties and acentric factor were calculated from the PR + COSMOSAC EoS and Lee-Kesler equation.

b Solid molar volume was retrieved from the molecular volume in the COSMO calculation. In this work, we have calculated hf=6146.4 cal/mol.

2.2 Experimental apparatus and procedure

In this work, an experimental setup with the schematic shown in Fig. 1 along with a UV–vis spectrophotometer was employed to measure the drug solubility statically. Originated from a high-pressure storage cylinder (about 6 MPa), CO₂ passed through a filter with a pore size of 1-μm and then was liquefied via cooling down from ambient temperature to about 253 K in a refrigeration unit. A reciprocating pump powered by an air compressor was used to pressurize CO₂ to the desired value. The pressure was monitored and controlled by a pressure gauge (WIKA, Germany, Code EN 837–1) and a digital pressure transmitter (WIKA, Germany, Code IS-0–3-2111, pressure range 1–6000 psi) within ± 0.1 MPa of accuracy throughout the experiment. After passing through a preheater, carbon dioxide entered a 70-mL equilibrium cell where the temperature was carefully adjusted and controlled by an oven with an accuracy of ± 0.1 K. The equilibrium cell was preloaded with 500 mg of MCP along with 2-mm glass beads uniformly (for particle distribution and complete saturation). The undissolved drug was retained by putting two stainless-steel sintered filters on both ends of the equilibrium cell, and thus any solids carryover was prevented. The system (cell) was maintained at the desired experimental condition for 120 min to achieve the thermodynamic equilibrium (according to preliminary experiments). Then, the saturated SC-CO₂ was transferred into a 600 μL ± 0.6% of volume collection loop through a six-port, two-position valve. Then this valve was turned over to evacuate the loop into an organic solvent (methanol) vial with a given volume. The depressurization (evacuation) process was controlled utilizing a micrometer valve to avoid solvent (methanol) dispersion. Eventually, the loop was rinsed with the collection vial solution followed by pure methanol, and the final sample volume was adjusted to 5 mL ± 0.6%.

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Fig. 1

Experimental setup for solubility measurement.

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Utilizing a spectrophotometer (Cintra 101 UV–Vis), MCP solubility in different thermodynamic conditions was measured (λ_max = 270 nm). A stock methanol solution of 100 μg∙mL⁻¹ was prepared, using an appropriate mass of solid MCP. Subsequently, different standard solutions were fabricated by diluting the stock solution, and a calibration curve (regression coefficient = 0.989) was formulated for determining the MCP concentration in the collection vial. While MCP was denoted as 2 in the binary supercritical system, its solubility was quantitatively analyzed through UV absorption data. The equilibrium mole fraction in SC-CO₂, y₂, was computed as follows:

where $n_{\mathit{solute}}$ , $n_{{\mathit{co}}_2}$ , $M_{\mathit{solute}}$ and $M_{{\mathit{co}}_2}$ indicate moles of solute and CO₂ in the sampling loop and molecular weights of the solute and CO₂, respectively. Solute concentration (in unit of g∙L⁻¹) in the collection vial, volumes (in unit of L) of the collection vial and sampling loop were denoted by $C_s$ , $V_s$ and $V_l$ , respectively. The equilibrium solute solubility in SC-CO₂ (in unit of g∙L⁻¹) is then calculated from the following equations:

The collection vial and sampling loop (V_s and V_l) volumes were measured carefully by microliter pipette (transferpette® S). The accuracy of volumes was calculated by Eq. (6):

A = accuracy.

V₀ = nominal value.

V = mean value.

These values for 600 µL and 5 mL were 2% and 0.6%, respectively.

To make sure the obtained absorption numbers by UV–Vis spectrophotometer (Cintra-101) are confident, absorption of number of samples were measured by other UV–Vis spectrophotometer like Unico, SQ-4802 and Shimadzu, model UV-3101 UV–Vis spectrophotometers. The obtained results indicate that uncertainty of UV–Vis spectrophotometer (Cintra) is less than 1%.

Due to the uncertainties values of different parameters (P, T and standard deviation of mole fraction), uncertainties of solubility data were calculated and presented in Table 2.

The experimental standard deviation and the experimental standard deviation of the mean (SD) were obtained by $S(y_k)=\sqrt{\frac{{\sum }_{j=1}^n{(y_j-\overline{y})}^2}{n-1}}$ .

and $\mathit{SD}(\overline{y})=\frac{S(y_k)}{\sqrt{n}}$ , respectively.

Expanded uncertainty and the relative combined standard uncertainty were defined (U) = k*u_combined and u_combined/y= $\sqrt{{\sum }_{i=1}^N{(P_{i}u(x_i)/x_i)}^2}$ , respectively.

3.1 Experimental data

It is worth mentioning that in our previous work (Sodeifian et al., 2017), the validity and reliability of the experimental apparatus and the applied procedure were approved by SC-CO₂ solubility determination of naphthalene and alpha-tocopherol at several temperatures and pressures. Also, before solubility measurement, equipment was calibrated with the mentioned materials to validate the setup.

Experimental measurements were performed at least in triplicate for each data point. By computing the average, SC-CO₂ solubility values of MCP were reported in Table 2. As the solubilities were low, the system density values presented in Table 2 were approximated by the density of pure carbon dioxide. The CO₂ density was specified according to NIST chemistry database ( https://webbook.nist.gov/chemistry) (National Institute of Standards, xxxx). The MCP solubility in terms of mole fraction (y) and g∙L⁻¹ (S) ranges from 0.15 × 10^-5 to 5.56 × 10^-5 and 0.0044 to 0.3329, respectively. The magnitude of MCP solubility in SC-CO₂ in mole fraction ranges from 10^-6 to 10^-5. The minimum and maximum values of MCP solubility in SC-CO₂ among all experimental conditions were observed at 338 K under pressures of 12 MPa and 27 MPa, respectively. Fig. 2 depicts solubility isotherms and shows that pressure increment results in MCP solubility enhancement, indicating solvating power increasing. This phenomenon is due to higher SC-CO₂ density, which is equivalent to the reduced mean distance of system molecules and improved solvent–solute interactions (Sodeifian et al., 2017; Iwai et al., 1991).

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Fig. 2

Solubility versus (a) pressure and (b) density from experiment and three semi-empirical models for solubility of metoclopramide hydrochloride in SC-CO₂.

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As shown in Fig. 2, isothermal lines intersect around 22 MPa, the cross-over point of the investigated system. Generally, the temperature has two antithetical effects on solid solute solubility in SC-CO₂ due to its effect on SC-CO₂ density and solute vapor pressure. The cross-over phenomenon indicates that the dominant effect of temperature on solubility changes from its effect via SC-CO₂ density at the low-pressure region to solute vapor pressure at the high-pressure region. At lower pressures, the solubility diminishes on temperature increase due to density reduction. In contrast, the solubility increases with increasing temperature at higher pressures because of an excess elevation in solute vapor pressure. This behavior, i.e., the presence of a cross-over pressure, has been observed in many other SC-CO₂ systems that could confirm the results of this work (Khimeche et al., 2007; Tamura et al., 2017; Pitchaiah et al., 2017; Kazemi et al., 2012; Sodeifian et al., 2017; Sodeifian et al., 2019; Sodeifian and Sajadian, 2019; Sodeifian et al., 2019).

3.2 Data correlation using semi-empirical models

The newly measured solubility data were correlated by six semi-empirical models, which were proposed by Chrastil (Chrastil, 1982), Méndez-Santiago and Teja (Méndez-Santiago and Teja, 1999), Kumar and Johnston (Kumar and Johnston, 1988), Bartle et al. (Bartle et al., 1991), Sodeifian et al. (Sodeifian et al., 2019) and Gordillo et al. (Gordillo et al., 1999). The expressions for these semi-empirical models, as well as their abbreviations, are summarized in Table 3. The values of adjustable parameters in these models were determined by minimizing the percentage average absolute relative deviation (AARD%) for solubility in mole fraction:

where N is the number of data; the superscripts exp and cal indicate results from experiment and correlation models, respectively.

Table 4 summarizes the optimized parameter values for these six semi-empirical models, as well as their corresponding AARD%. The overall deviations for solubility data correlation are from 11.41% (Gordillo model) to 22.82% (Chrastil model). The Gordillo and Sodeifian models contain more terms, i.e., more adjustable parameters, than the other four models to consider possibly complex relations between solubility and independent variables of pressure, temperature and CO₂ density, resulting in better representations of solubility. Fig. 2 illustrates the correlation results from three employed models: Chrastil, Sodeifian and Gordillo models. As can be seen, all these three models can approximately capture the tendency of solubility obtained from experiments. The correlation results from all six studied models are plotted separately in Figures S1 and S2 of the supplementary material. Gordillo and Sodeifian models contain more terms, i.e., more adjustable parameters, than the other four models to consider possibly complex relations between solubility and independent variables of pressure, temperature and CO₂ density, resulting in better representations of solubility. In addition, the studied semi-empirical models, except for the Sodeifian and Gordillo models, could also be used to perform simple self-consistency tests for experimentally obtained solubility data to confirm their reliability. As shown in Fig. 3, the experimental solubility data are considered self-consistent since most of them were aligned to a single correlation line.

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Fig. 3

Experimental data self-consistency test for solubility of metoclopramide hydrochloride in SC-CO₂ using (a) K-J, (b) MST, (c) Chrastil and (d) Bartle models.

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The total enthalpy for solid solute dissolution in SC-CO₂ was proposed to be determined from the model parameter a₁ of the Chrastil model (Chrastil, 1982): $\mathrm{\Delta }{H}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}={-a}_{1}R.$ While the sublimation enthalpy of a solute molecule was estimated from the model parameter a₂ of the Bartle model (Bartle et al., 1991): $\mathrm{\Delta }{H}_{\mathrm{s}\mathrm{u}\mathrm{b}}=-a_{2}R$ . If the process of a solute molecule dissolution in SC-CO₂ consists of two steps: sublimation and solvation in SC-CO₂; the solvation enthalpy ( $\mathrm{\Delta }{H}_{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{v}}$ ) can then be calculated from $\mathrm{\Delta }{H}_{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{v}}=\mathrm{\Delta }{H}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}-\mathrm{\Delta }{H}_{\mathrm{v}\mathrm{a}\mathrm{p}}$ . The calculated total enthalpy, sublimation enthalpy, and solvation enthalpy for MCP are 36.87 kJ∙mol⁻¹, 55.30 kJ∙mol⁻¹ and −18.43 kJ∙mol⁻¹, respectively.

3.3 Solubility from Peng-Robinson equation of state

The standard formula for solving the solubility in SC-CO₂ of the studied solute i using a cubic EoS is the equifugacity condition for the solute in its pure solid phase (S) and supercritical fluid phase (SF) at a given temperature (T) and pressure (P) (Sandler, 2006):

Following the approach proposed by Kikic et al. (Kikic et al., 1997); fugacity of a solid solute i is obtained from its melting temperature ( $T_{m,i}$ ) and fusion enthalpy ( ${\mathrm{\Delta }\underline{H}}_i^m$ ):

where $P_{\mathit{atm}}$ is atmospheric pressure and set to 101325 Pa in this study; $f_i^L$ and ${\underline{V}}_i^L$ are the fugacity and molar volume in a hypothetical liquid state determined from the studied equation of state as well; ${\underline{V}}_i^S$ is the solid molar volume and its value was retrieved from the molecular volume in COSMO solvation calculation (Ting and Hsieh, 2017; Chen et al., 2018; Cai et al., 2020; Cai and Hsieh, 2020; Wang et al., 2021).

The Peng-Robinson (PR) EoS (Peng and Robinson, 1976) was used to model the solubility of MCP in SC-CO₂:

where a and b are energy and volume parameters of the investigated fluid. For pure fluid i, they are calculated from critical pressure (P_c,i), critical temperature (T_c,i) and acentric factor (ω_c,i):

with $\kappa =0.37464+1.54226{\omega }_i-0.26992{\omega }_i^2$ . In the case of a mixture, the composition has to be considered via a mixing rule, such as van der Waals (VDW) one-fluid mixing rule (Sandler, 2006):

where k_ij is the binary interaction parameter and × is the mole fraction. This approach is referred to as PR + VDW in the underlying context. In this study, the critical properties and acentric factor for MCP were estimated from PR + COSMOSAC EoS (Liang et al., 2019) and Lee-Kesler equation (Lee and Kesler, 1975), respectively, as described in previous works (Cai and Hsieh, 2020; Wang et al., 2021). The normal boiling temperature and critical temperature from PR + COSMOSAC EoS were rescaled with a factor of 0.91 in order to provide satisfactory correlation results, which was determined via regressing experimental solubility data together with k_ij. Their values are summarized in Table 1.

Two other approaches using ${\underline{G}}^{\mathit{ex}}$ -based mixing rules with activity coefficient models to determine the energy and volume parameters were investigated in this study. One is the combination of the Wong-Sandler mixing rule (Wong and Sandler, 1992) and Wilson model (Wilson, 1964):

where $C_{\mathrm{W}\mathrm{S}}=\mathrm{l}\mathrm{n}\left(\sqrt{2}-1\right)/\sqrt{2}$ , ${\underline{G}}^{\mathit{ex}}$ is the molar excess Gibbs energy and two binary interaction parameters ${\mathrm{\Lambda }}_{12}$ and ${\mathrm{\Lambda }}_{21}$ are adjustable parameters. This approach, denoted as PR + WS + Wilson, was taken into account to understand the capability of PR EoS in correlating the solubility data with two adjustable parameters. The other approach is to combine the MHV1 mixing rule (Michelsen, 1990) with COSMO-SAC model (Chen et al., 2016; Hsieh et al., 2010; Bell et al., 2020):

where $C_{\mathrm{M}\mathrm{H}\mathrm{V}1}=-0.53$ and ${\underline{G}}^{\mathit{ex}}$ is determined from the COSMO-SAC model (Hsieh et al., 2010) without any adjustable species-specific binary interaction parameters. This approach, denoted as PR + MHV1 + COSMOSAC, was used to demonstrate the capability of PR EoS in predicting solubility with limited information. The quantum mechanical and COSMO solvation calculations were performed to generate molecular information for the COSMO-SAC model following the “b3lyp/6-31G(d.p)-cosmo” method in the literature (Chen et al., 2016).

In the above approaches, the binary interaction parameters were obtained by minimizing the AARD% described in Eq. (7). Table 5 summarizes overall deviations in AARD% and the corresponding values of binary interaction parameters. The AARD% for MCP from two correlation approaches PR + VDW and PR + WS + Wilson are 24.0% and 26.2%, respectively, similar to those from the semi-empirical models. The advantage of using an EoS is that these optimal parameter values could be further applied to describe the phase behavior of multicomponent mixtures containing the studied solutes and CO₂ (Li et al., 2004). The AARD% for MCP from the predictive approach PR + MHV1 + COSMOSAC is 28.9%, similar to those from the above correlation methods. This result demonstrates that the predictive models based on COSMO-SAC model can provide good solubility estimation with sufficient information for the investigated chemicals.

Fig. 4 compares the solubility of MCP in SC-CO₂ from experimentation and the three studied thermodynamic models (the calculation results are plotted separately in Figure S3 of the supplementary material). In general, all three approaches provide satisfactory solubility results, but PR + MHV1 + COSMOSAC overestimates the isotherm cross-over pressure, which was experimentally determined around 22 MPa. It is worth mentioning that PR + MHV1 + COSMOSAC has been proved to provide reasonable predictions for binary vapor–liquid equilibria of CO₂ and low molecular weight alcohols (Hsieh et al., 2013), indicating that this predictive approach has the potential to predict the solubility of MCP in CO₂ + alcohol binary mixtures.

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Fig. 4

Solubility of metoclopramide hydrochloride in SC-CO₂ from experimental measurement and three thermodynamic models based on PR EoS.

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