Experimental and thermodynamic analyses of supercritical CO₂-Solubility of minoxidil as an antihypertensive drug

Highlights

• For the first time, the solubility of Minoxidil in SC-CO₂ was measured.

• Experiments were performed at different temperatures (308–338 K) and pressures (120–270 bar).

• Several equations of state, density-based models and activity coefficient equations were examined.

• Estimations of thermodynamic enthalpy were performed for Minoxidil.

• The consistency analysis was applied to test the thermodynamic consistency.

Abstract

A major challenge in the production of micro/nano-sized drug particulates is to understand the solubility behavior of the drug in a supercritical fluid (SCF). In the present study, solubility of Minoxidil, an antihypertensive drug, in SC-CO₂ was measured statically under various sets of operating conditions in terms of temperature (308–338 K) and pressure (120–270 bar), leading to solubilities in the range of 0.24 × 10⁻⁶ to 3.39 × 10⁻⁶. Next, three different approaches were followed to estimate, rather than actually measure, the solubility, where models based on two equations of state (i.e., Soave–Redlich–Kwong (SRK) and Peng-Robinson (PR)) combined with either Wong-Sandler (WS) or van der Waals (vdW2) mixing rules, semi-empirical equations (Méndez-Santiago and Teja (MST), Bartle et al., Chrastil, Kumar and Johnston (K-J)), and the activity coefficient (UNIQUAC and modified Wilson models) were adopted to model the experimental data. The semi-empirical models were proved to be self-consistent upon performing the respective self-consistency tests. Eventually, results were devised to calculate estimates of the vaporization ($\Delta H_{vap}$), solvation ($\Delta H_{sol}$) and total enthalpies ($\Delta H_{total}$).

Introduction

Minoxidil (2,4-pyrimidinediamine, 6-(1-piperidinyl)-,3-oxide; C₉H₁₅N₅O) is among the most widely used medicaments worldwide. Minoxidil is a crystalline powder that is soluble in methanol but rather insoluble in water, acetone and alkaline solutions [1]. Minoxidil is an antihypertensive drug which has a positive effect on treating hypertension by primarily making the arteriolar vascular smooth musculature relaxed. In addition, Minoxidil is effective in the treatment of androgenic alopecia by enlarging the hair follicles while strengthening the hair cycle anagen phase [[2], [3], [4], [5], [6]].

Investigation and determination of solubility of medicines under different operating conditions determine the medicine bioavailability, thereby taking significant parts in the development of a drug product. The design and optimization of the drug crystallization process (to obtained the desired micro/nano particle size (PS), particle size distribution (PSD), and particle morphology) and the scale-up of this process requires a thorough understanding of the drug solubility in the different solvents [7]. In fact, the solubility of medications in the aquatic matrix and the rate of solubility of these drugs are of paramount importance for determining the bioavailability of the pharmaceutical ingredients [8,9]. The Noyes–Whitney equation implies that the extent of solubility and its rate can be increased by decreasing the particle size to extend the particle surface area. Generally, the PS and PSD are major determinants of the solubility of drug compounds [[10], [11], [12]].

Nowadays, drug-dependent processes using supercritical fluid (SCF) techniques have replaced the traditional methods for improving the performance of drug processes without degradation or contamination of the product. Also, experimental data of solubility in SCFs represent the first step and provide the most important data for designing pharmaceutical processes [[13], [14], [15]]. Advantages of the supercritical carbon dioxide (SC–CO₂), such as non-explosiveness, non-combustibility, no residual substance, widespread availability, and inexpensiveness, have made the fluid widely used in pharmaceutical-related processes. Additionally, it is a green solvent (environment-friendly) exhibiting high solvating power, small surface tension, high selectivity, non-flammability, recyclability, high purity and low and moderate critical temperature and pressure, respectively ($P_C$ = 73.8 bar and $T_C$ = 31.4 °C) [[15], [16], [17], [18], [19], [20], [21], [22], [23]].

Due to the limitations of the experiments such as difficulty working in the lab and the time- and cost-intensiveness of experimentally measuring the solubility in SC-CO₂, obtaining laboratory data is very difficult. Hence, mathematical modeling and predictive methods are necessary for studying the solubility and equilibrium phase behaviors [20,21,24,25]. Information on nanoparticles and supercritical technologies adopted in the pharmaceutical industry can be rather generated by modeling the data on solubility in the SCF [24]. Such models include thermodynamic models (equation of state; (EoS)), computer-assisted modeling, neural networks, and density-based methods (semi-empirical and empirical approaches). In some of these models, the SCF has been simulated as a gas at a high pressure, while others have approached the SCF as a liquid [24,25]. The models derived from the EoSs need physicochemical and critical properties of the considered medicinal compounds (solid), which are frequently not readily available and rather group contribution methods must be applied to estimate them [[26], [27], [28]]. Also, EoSs call for extremely complex processing tasks that require special tools, rather than conventional software utilities, to address them adequately [29,30]. The empirical models, on the other hand, cannot be utilized unless the SCF temperature, pressure and density are known; these parameters are, in many cases, roughly approximated through an error minimization approach based on the so-called least squares technique [31].

Since the density of the SCF is in the range of liquids (i.e. relatively high), the SCF can be adequately described by modeling it as an expanded liquid [32]. The solid–liquid equilibrium and activity coefficients (ACs) can be devised to scrutinize the solute-SCF phase equilibria thermodynamically. Universal quasi-chemical (UNIQUAC) and modified Wilson's models have been used to explain different phase equilibria (i.e. liquid–solid/liquid/vapor equilibria) [33].

A review of the relevant literature shows that the SC–CO₂–solubility of Minoxidil has not been addressed so far. In this regard, the present research attempts to investigate it at various temperatures and pressures. This was done by three groups of models, namely empirical models (the density-based models proposed by Méndez-Santiago and Teja (MST), Kumar and Johnston (K-J), Chrastil, and Bartle et al.), EoSs (Peng-Robinson (PR) and Soave–Redlich– Kwong (SRK)), and expanded liquid models (UNIQUAC and modified Wilson's models). Noteworthy though, the PR and SRK were applied with two types of mixing rules, namely the vdW2¹) and the WS² rules. For the WS, the excess Helmholtz free energy was evaluated through the NRTL³ model [34]. The PSO⁴ algorithm was used to obtain optimal solutions. Accuracy of the proposed models was assessed through evaluating the deviation of their results from the observed solubility values represented by statistical criteria such as $AARD\%$⁵, $R_{adj}$⁶ and $F-value$. Further performed were self-consistency assessments of the experimental models. Estimation of the vaporization ($\Delta H_{vap}$), total ($\Delta H_{total}$), and solvation enthalpies ($\Delta H_{sol}$) was further conducted.