key: cord-0716130-82d1s1oi
authors: Sajadian, Seyed Ali; Ardestani, Nedasadat Saadati; Esfandiari, Nadia; Askarizadeh, Mahshid; Jouyban, Abolghasem
title: Solubility of favipiravir (as an anti-COVID-19) in supercritical carbon dioxide: An experimental analysis and thermodynamic modeling
date: 2022-02-04
journal: J Supercrit Fluids
DOI: 10.1016/j.supflu.2022.105539
sha: a0df82d4c2515a8826f3e6e97f8c18e0bd1f369a
doc_id: 716130
cord_uid: 82d1s1oi

Favipiravir is one of the most commonly prescribed drugs in the treatment of COVID-19 in the early stages of the disease. In this work, the solubility of favipiravir was measured in supercritical CO(2) at temperatures ranging from 308 to 338 K and pressures ranging from 12 to 30 MPa. The mole fraction solubility of favipiravir was in the range of 3.0 × 10(-6) to 9.05 × 10(-4). The solubility data were correlated with three types of methods including; (a) density-based models (Chrastil, Garlapati and Madras, Sparks et al., Sodeifian et al., K-J and Keshmiri et al.), (b) Equations of states SRK with quadratic mixing rules) and (c) expanded liquid theory (modified Wilson model). According to the results, modified Wilson and K-J models are generally capable of providing good correlation of solubility. Finally, the approximate values of total ([Formula: see text]), vaporization ([Formula: see text]), and solvation ([Formula: see text]) enthalpies were computed.

solubility of solid at different pressures and temperatures in SC-CO 2 . Prediction and correlation via EoS and expanded liquid require the calculation of the physicochemical properties of solid (pharmaceutical components) such as acentric factor, critical pressure, temperature, and sublimation pressure. These properties are not in literature and are usually determined by different group contribution (GC) methods. In return, the empirical models (densitybased model), only require pressure, temperature, and SC-CO 2 density. The correlative model has indicated the best fitting with the experimental data [8, 9, 13, 19 ].

In the current research, the solubility of favipiravir was measured in the temperature range of 308−338 K and the pressure range of 12−30 MPa. For this purpose, solubility data were correlated with three types of methods including (1) Empirical density-based models (Chrastil, Garlapati (3) expanded liquid theory (modified Wilson model). The mentioned models were evaluated based on mean absolute deviation (AARD%) and adjusted correlation coefficient (R adj ).

Favipiravir (CAS No. 259793-96-9) has been procured through the Tofigh Darou pharmaceutical corporation (Tehran, Iran), at the minimum purity of 99%. Carbon dioxide (CO 2 ) was prepared by Oxygen Novin Company (Shiraz, Iran) with a purity of 99.99%. Analytical-grade methanol was supplied by Merck (Darmstadt, Germany).

The structure of favipiravir (drug) and the information of all components are presented in Table 1 .

The applied laboratory setup with a spectrophotometer is presented in Fig. 1 which encompassed a CO 2 cylinder (E-1), a needle valve (E-2), a molecular sieve filter (E-3), a refrigerator unit (E-4), a high-pressure pump (E-5, air driven liquid pump, type-M64, Shineeast Co., Shandong, China), an air compressor (E-6), an incubator (E-7, shimaz), magnetic stirrer (100 rpm) (E-8, Alfa, D-500 180,), a high-pressure equilibrium cell (E-9), a back-pressure valve (E-10, Xi'an Shelok Instrument Technology Co., Shaanxi, China), a micrometer valve (E-11), a collection vial (E-12), a Syringe (E-13). In this high-pressure system, all equipment, piping and connections were made from stainless steel 316 at 1/8″ in size. The CO 2 flow from the cylinder first enters the molecular sieve filter (pore size of 1 μm) to prevent impurities. It then flows to the refrigerator. The temperature inside the refrigerator is about -15 °C, liquifying the CO 2 flow. The liquid CO 2 at the pressure in the CO 2 tank (about 60 bar) entered the high-pressure J o u r n a l P r e -p r o o f reciprocating pump. Using the pressure gauge and transmitter, measurements were performed at a precision of ± 1bar.

In the next step, 3000 mg favipiravir was mixed in SC-CO 2 using a magnetic stirrer to establish an equilibrium phase into a cell with a capacity of 300 mL. The temperature was maintained at the desired level by an oven equipped with a digital display with temperature measurements at an accuracy of ±0.1 K. A sintered filter (1 μm) was used on both sides of the cell to hold the drug. Carbon dioxide was pressurized and then transferred to the cell at the appropriate pressure. The static time, i.e. the time to reach equilibrium, was considered 120 min based on the preliminary experiments. After 120 min, 600 μL of saturated SC-CO 2 was introduced into the injection loop using a three-valve two-position device. By redirecting the injection valve, the loop was depressurized into the collection vial containing a certain volume of methanol (solvent). In this part, the micrometer valve was used for controlling the flow.

In the final step, about 1 mL of solvent was injected through an external needle valve for washing the loop and the solution is collected in the vial. The final volume of the solution was 5 mL. Each experiment was repeated three times (triplicates). The favipiravir solubility values were determined by measuring the absorbance at λ max on a Shimadzu UV-Vis spectrophotometer with a 1 cm long quartz cell. The solubility was calculated from the concentration of solute using the calibration curve (with regression coefficient 0.998) and the UV-absorbance.

At different sets of temperature and pressure, the equilibrium mole fraction, y 2 , and solubility, S (g/L), in SC- CO 2 were computed as follows [20] :

where: 

where n solute and n CO2 are moles of solute (favipiravir) and CO 2 in the sampling loop, respectively, C s denotes the solute concentration (g/L) in the collection vial as obtained from the calibration curves. The volumes of the collection vial and sampling loop are Vs(L)=5×10 -3 and V l (L)=600×10 -6 respectively. M s also represents the molecular weight of the solute while M CO2 is the molecular weight of CO 2 . The accuracy of the mentioned volumes (500 µL and 5 mL) was 0.5 and 0.2 % respectively.

The equilibrium solubility, S (g/L), of the solute in the SC-CO 2 can be obtained by Eq. (4):

In this research, three types of models were considered to correlate the experimental solubility data of Favipiravir in Table 2 reports the critical and other physicochemical properties of favipiravir. Selection of the proper mixing and combining rules to calculate the thermodynamic characteristics of the mixtures and parameters of the EoS is of crucial importance. In the current work, the quadratic mixing rules was applied for EoS.

The reduced residual Helmholtz energy of the SRK model can be expressed as follows [21] :

Where R , T , and v are the universal gas constant, absolute temperature, and molar volume, respectively.

The parameters of a and b depend on the critical and physical properties of pure components and can be determined by the following equation (for a single-component system):

The quadratic mixing rules in mole fraction for   aT and b are used as follows: can be calculated by:

The density of the supercritical fluid is very close to the typical liquid and its phase can be considered as an expanded liquid [22] . As a result, the thermodynamic phase equilibrium of solid and supercritical fluid can be defined by solid-liquid equilibrium and activity coefficients. The activity coefficients are required to calculate the solid solubility in the supercritical phases. In this regard, the equilibrium between the pure solid and the supercritical phase is expressed as follows [23, 24] : (15) Where and are the fugacity of the solid solute in the solid phase and the supercritical phase, respectively.

The fugacity of solute in the supercritical phase can be expressed by: (16) and (17) Where is the activity coefficient, is the mole fraction of solid solubility and is and the fugacity of the pure solid solute in the expanded liquid phase.

According to Prausnitz et al. [25] :

The heat capacity terms can be neglected [25] , so :

Where is the enthalpy of fusion and shows the melting point of the solid (drug). The solid solubility in the supercritical fluid is very low (~ infinite dilution). Therefore, the activity coefficient of the solid solute is one at infinite dilution. Thus, Eq. (19) becomes:

Wilson equation can be utilized for determining the activity coefficient of the solid solute at infinite dilution. This equation consists of two parts, a combinatorial contribution based on Flory's theory, and a term based on the Gibbs excess energy, which can be written as follows [23] :

Where G E is the excess Gibbs energy, and and represent adjustable parameters.

According to the theory proposed by Assael et al., [26] , Eq. (22) can be rewritten to the following form:

where and are defined at infinite dilution conditions:

Where is the critical density of SCF, ( ) represents the reduced density of the SCF, denotes the molar volume of the solid solute. The dimensionless energies of interaction are as follows: RT    (27) To address the effect of high pressures and simplify the prediction process, Wilson model was introduced by an empirical expression that linearly correlates the molar volume and the reduced density [23] : (28) where , , and are the regressed parameters of the model.

Density-based correlations are common techniques for modeling solid solubility in SCFs. Empirical models do not require estimation of the physicochemical properties of solid as they only depend on temperature, pressure, and density of SCF (independent variables) as well as several adjustable parameters (constants). In the current work, The constants in the empirical models were determined by regression of experimental data. The adjustable parameters were optimized by simulated annealing (MATLAB software). The average absolute relative deviation ( ) was used to compare the precision of the model with experimental data which can be defined by:

Where Z and are the number of fitted parameters for each model and the number of data points in each set, respectively. As another criterion for comparing different models, R adj has the following expression [27, 28] :

Where N shows the number of data points in each set, Q is the number of independent variables in each equation.

Solubility of favipiravir in SC-CO 2 was experimentally measured at the temperature range of 308-338 K and pressure range of 10-30 MPa. Solubility data of favipiravir is collected in Table 3 . The SC-CO 2 density was J o u r n a l P r e -p r o o f calculated by Span-Wanger EoS [29] . Furthermore, each data point was repeated three times to increase the reliability of the measurements; relative standard uncertainties were lower than 5%. The expanded uncertainty with the mole fractions is also reported in Table 3 . Figure 2 shows the mole fraction solubility of favipiravir vs. pressure and density at different temperatures. In general, the density of SC-CO 2 and its solvating power increased with increasing the pressure. Therefore, favipiravir solubility in SC-CO 2 rose with increasing pressure (Table 3 and Fig. 2 ). As indicated in Fig. 2 , at the pressure range of 12 to 18 MPa, the solubility of favipiravir in SC-CO 2 decreased with increasing the temperature. At pressures below 18 MPa, favipiravir solubility showed a decremental trend with increasing temperature. Above this pressure (18 MPa) , the solubility increased with elevating the temperature. The mentioned trend can be also observed in Fig.   2 , where the solubility curve showed the crossover region between 15 to 18 MPa. At pressures lower than the crossover region, the density effect is predominant and as a result, the solubility increases with decreasing temperature. However, at pressures above the crossover point, the vapor pressure of the solution was the main factor and the solubility increased at higher temperatures. The crossover point of various pharmaceutical compounds in SC-CO 2 have been investigated by some other researchers, that crossover point of some of these compounds was reported in Table 4 .

The crossover pressure was investigated by several articles which proposed some methods to predict the crossover pressure region [58] [59] [60] [61] . Investigation of these methods showed the crossover region depends on the critical properties of solutes, sublimation pressure, enthalpy of sublimation, partial molar enthalpy, and molar volume of the solute. Minimum and maximum favipiravir solubility were seen at the temperature of 338 K and pressures of 12 and 30, respectively. As indicated in Table 3 , the mole fraction of favipiravir in the binary system (favipiravir-SC-CO 2 ) ranged in 3.0×10 -6 -9.05×10 -4 . The mole fraction of drugs in Table 4 shows a wide range of values. These values were reported between 10 -3 and 10 -7 according to the experimental conditions. The mole fraction of favipiravir also was in this range. The results present that high mole fraction values were obtained in the order of 10 -4 . As above mentioned some researchers reported that the solubility of solutes in SC-CO 2 can be dependent on the critical properties of solutes, sublimation pressure values, enthalpy of sublimation, partial molar enthalpy, and molar volume of solute. This experimental data can be used to develop the method for the production of favipiravir J o u r n a l P r e -p r o o f nanoparticles using SCF. This information can be also employed for the incorporation of polar co-solvent to increase the solubility.

The modified Wilson model was studied to model the favipiravir solubility in SC-CO 2 . The modified Wilson model parameters ( , , and ) were optimized for binary system favipiravir-SC-CO 2 . The results on the solubility of favipiravir in SC-CO 2 are listed in Table 5 . Figure 3 shows the experimental data and model of solubility of favipiravir in SC-CO 2 . As indicated in Fig. 3 , the model exhibited a proper agreement with experimental solubility data of favipiravir in SC-CO 2 . According to Table 5 , the values of AARD% and R adj were 10.09% and 0.9658.

Therefore, the modified Wilson model can correlate the solubility of favipiravir at proper accuracy.

As presented in Table 6 Table 7 .

The equation developed by K-J (AARD = 10.55%) presented the best fit compared to the other equation with three parameters namely Chrastil (AARD = 18.61%). K-J provided a relationship between the logarithm of the mole fraction of a solute has a linear dependence on the density of the SCF phase. On the other hand, Chrastil described one of the first density-based models, based on the solvato complex formed between the solute and solvent molecules at equilibrium. However, it has some limitations in high solubility [62] . Therefore, the model described Table 7 showed that Sparks et al. (AARD = 11.10 %) was more adequate than Chrastil model. presented. Both of them included more combined terms than K-J, but the AARDs obtained with these models were 13.45 and 11.31% respectively. The main conclusion obtained from Table 7 is that the best models for correlating favipiravir solubility were the equation developed by K-J and Sparks et al."

Furthermore, experimental data and favipiravir solubility calculated by empirical models are compared in Fig. 4 . As seen, the models showed satisfactory agreement with experimental data. Using the model, total heat (ΔHtotal = 70.09 KJ mol -1 ), vaporization heat (ΔHvap = 90.12 KJ mol -1 ), and solvation heat (ΔHsol = 20.04 KJ mol -1 ) can be calculated for binary system.

In this study, the SRK EoS with quadratic mixing rules was employed. Interaction parameters (k ij , l ij ) are used to calculate the parameters of the SRK equation for the binary system. As previously mentioned, different group contribution (GC) methods are used to calculate the physico-chemical and critical properties of solids (drug), which can affect the correlation results (AARD) for solubility data in SC-CO 2 by EoS, but in many cases the results were not significantly different [65] . In the current research, the Ambrose-Walton equation [66] , Immirzi and Perini [67] , Edmister [66] and Marrero and Gani [68] , methods were applied to determine the sublimation pressure, solid molar volume, acentric factor, critical temperature and pressure, respectively. The results of estimating of drug properties are presented in Table 2 .

Moreover, interaction parameters can be written as a function of temperature :

The corresponding values of interaction parameters were optimized by the simulated annealing (SA) method. The correlation results obtained with the SRK-EoS and quadratic mixing rules at four temperatures are reported in Table   8 . According to AARD% values in Table 8 , the interaction parameters were calculated with acceptable accuracy.

However, it can be said that the accuracy of the data obtained at low temperatures (308 K) is higher than those determined at high temperatures (338 K). Figure 5 shows the experimental solubility of favipiravir in SC-CO 2 at four temperatures (308, 318, 328, and 338 K) and those predicted by SRK-EoS. As indicated in Fig. 5 , the SRK EoS (34)) were calculated via linear regression analysis (Fig. 6 ).

Proper knowledge of drug's solubility in a supercritical fluid is essential in the production of pharmaceutical micro and nanoparticles using supercritical fluids. In this study, the solubility of favipiravir in SC-CO 2 was explored at the temperature range 308 -338 K and pressure range 12 J o u r n a l P r e -p r o o f 

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