Measurement and modeling of clemastine fumarate (antihistamine drug) solubility in supercritical carbon dioxide

The solubilities of clemastine fumarate in supercritical carbon dioxide (ScCO2) were measured for the first time at temperature (308 to 338 K) and pressure (12 to 27 MPa). The measured solubilities were reported in terms of mole faction (mol/mol total) and it had a range from 1.61 × 10–6 to 9.41 × 10–6. Various models were used to correlate the data. The efficacy of the models was quantified with corrected Akaike’s information criterion (AICc). A new cluster salvation model was derived to correlate the solubility data. The new model was able to correlate the data and deviation was 10.3% in terms of average absolute relative deviation (AARD). Furthermore, the measured solubilities were also correlated with existing K.-W. Chen et al., model, equation of state model and a few other density models. Among density models, Reddy and Garlapati model was observed to be the best model and corresponding AARD was 7.57% (corresponding AICc was − 678.88). The temperature independent Peng–Robinson equation of state was able to correlate the data and AARD was 8.25% (corresponding AICc was − 674.88). Thermodynamic parameters like heats of reaction, sublimation and solvation of clemastine fumarate were calculated and reported.

The clemastine fumarate is a special drug and it has specific uses. It is an antihistamine with antimuscarinic and partial sedative properties. One of its forms also acts an antileishmanial drug. It also stimulates a macrophage response to leishmaniainfection 1 . For all the medical studies (for both in vivo and in vitro) a proper dosage is very essential and this may be achieved through proper particle size 1 . The usage of supercritical fluid technology in particle micronisation has gained significant importance in the recent times, wherein, carbon dioxide as a supercritical fluid has been used widely in practice 2 . The application of carbon dioxide as supercritical fluid solvent has several advantages over conventional solvents 2 and it is designated as ScCO 2 . It possesses attractive physical properties such as, gas like diffusivity and liquid like density with low viscosity and surface tension 2,3 . By adjusting pressures and temperatures, one can tune the density of ScCO 2 as desired and it is exploited in various applications. Due to this tunable nature, it has been used as a solvent in various process applications. ScCO 2 's major applications include drug particle micronization, extraction, reactions, food processing, textile dyeing, ceramic coating, and many more [4][5][6][7][8] . To implement SFT, one needs to have exact phase equilibrium information such as saturation solubility. Solubility is one of the basic information that is essential for the design and development of SFT. Drug particle micronization requires precise solubility information and in literature, solubility of many solid drugs 9,10 in ScCO 2 is readily available, however, the solubility of clemastine fumarate is not reported. Therefore, for the first time, the solubility of clemastine fumarate in ScCO 2 is reported in this work. We believe that this study may be useful in particle micronization using ScCO 2 .
The main objectives of the present work are in two stages; in the first stage we determine solubility of clemastine fumarate. Since, measuring experimental solubility data at each pressure and temperature is very difficult, we need a proper model to generate the solubility data 11 Figure 2 shows the line diagram of the equipment used in the study. More details about the solubility measuring device have been presented in our earlier studies [12][13][14][15][16][17][18][19][20] . However, a brief outline of the same has been presented in this section. This measuring methodology may be classified as an isobaricisothermal method 21 . Each reading has been reported by controlling temperature and pressure at desired values within ± 0.1 K and ± 0.1 MPa precision, respectively. For each experiment about 1 g of clemastine fumarate drug has been used in the static cell. The saturation samples have been collected from the static cell after equilibrating for 60 min. Our earlier studies indicated that 60 min is enough for equilibrium. After equilibrium, saturated ScCO 2 samples (600 µL) have been collected via 2-status 6-way port valve in a methanol preloaded vial. Once a sample was collected, the port valve was washed with 1 mL methanol. Thus, the total saturation solution obtained was 5 mL. Each measurement has been repeated thrice and average readings were reported. For calculations, the following formulas have been used [12][13][14][15][16][17][18][19][20] .
(1) y 2 = n drug n drug + n CO 2   www.nature.com/scientificreports/ where n drug denotes the quantity of the drug, and n CO 2 denotes the quantity of CO 2 in the sampling loop. Further, we quantify moles of drug and moles of CO 2 as where C s denotes the drug concentration in saturated sample vial in g/L. The volume of sampling loop, V s = 5 × 10 -3 m 3 and vial collection, V 1 = 600 × 10 -6 m 3 . The M s and M CO 2 denote the molecular weight of drug and CO 2 , respectively. Solubility is also described as The relation between S and y 2 is explained as To ensure equilibrium solubility, the experiments were performed with fresh samples at various time intervals. For a specified temperature and pressure in each experiment, the drug sample was contacted with ScCO 2 and stirred thoroughly in an equilibrium cell until a specific time (5 min, 10 min, 20 min, 30 min, 40 min, 50 min and 60 min) and the solubility readings were recorded. It was observed that the solubility was independent of time after 30 min. This experimental setup has already been validated in our previous works with alpha-tocopherol and naphthalene 17 .
A UV-visible (UNICO-4802) spectrophotometer has been used for the measurements of clemastine fumarate solubility. Samples collected for analysis in methanol solvent were analyzed at 270 nm.

Models
In this section, a brief note about the existing density models and their mathematical form were presented.
Existing empirical and semi-empirical models. Alwi-Garlapati model 22 . It is a semi-empirical model. It has three parameters. According to this, solubility is represented as a function of reduced temperature and reduced density and it is mathematically stated as where A 1 − A 3 are model constants. Bartle et al., model 23 . It is based on enhancement factor concept and it has three parameters. According to this, solubility is represented as a function of pressure, temperature and density and it is mathematically stated as Chrastil model 25 . It is a three parameter model. It is a semi empirical model and it is mathematically stated as where κ, E 1 and E 2 are model constants.
In terms of mole fraction it is mathematically stated as  26,27 . It is also a three parameter model. It is a semi-empirical model and it is mathematically stated as where κ ′ , F 1 and F 2 are model constants. Reference fugacity ( f * ) is 0.1 MPa.
Garlapati-Madras model 28 . It is a five parameter model. It is a mathematical model and it is mathematically stated as where G 1 − G 5 are model constants. 29 . It is a semi-empirical model and it has three parameters. It is mathematically stated as
Equation (12) is used in checking self-consistency of the measured solubility data. Accordingly, all the data points lie on a line when they are plotted T ln y 2 P − H 3 T versus ρ 1 . 30 . It is a mathematical model and it has six parameters and it is mathematically stated as where I 1 − I 9 are model constants. 9 . It is based on degree of freedom. It is a six parameter model. It is an empirical model and it is mathematically stated as where J 1 − J 6 are model constants. 11 . It is based on degree of freedom. It is a three parameter model. It is an empirical model and it is mathematically stated as Equation of state (EoS) model. The solubility of clemastine fumarate drug, i (solute), in a supercritical carbon dioxide, j(solvent), is expressed as 31 where p s i is solute sublimation pressure;v i is solute molar volume; The fugacity coefficient of the pure solute at saturation ( φ S i ) is usually taken to be unity. In this work, φ ScCO 2 i is the fugacity coefficient of the solute in the solvent phase. φ ScCO 2 i is calculated using Peng-Robinson (PR) EoS along with two parameter van der Waals mixing rule (vdW2) 32 . The expression used for calculation of φ ScCO 2 is obtained from the following basic thermodynamic relation 33 .

The general PREoS form 32 is
The pure component parameters a and b are (10) The expressions for VdW2 The PR EoS regression may be carried out either temperature independent or temperature dependent. For temperature independent regression suitable sublimation expression is used. The general form 34,35 used for the regression purpose is The regression directly results in binary interaction parameters along with sublimation pressure expression coefficients ( β/R , γ /R and � sub δ/R ) and from parameters γ and � sub δ we can estimate sublimation pressure. The expression for sublimation enthalpy is It is an equilibrium reaction and at equilibrium the following condition is satisfied.
where is summation; ν and F are stoichiometric coefficient and partial molar Gibbs energy, respectively.
In general the partial molar Gibbs energy for species is written as where P o and z o i are reference state pressure and composition of species "i". The reference pressure is taken as critical pressure of the supercritical fluid and finally the expression for the equilibrium in terms of fugacity coefficients is where F rxn T, P c,scf is the change in Gibbs energy as a result of formation of solvate complex.
The model has two parameters κ ′′ and F rxn T, P c,scf . K.-W. Chen et al. 35 , used the following temperature dependent general form 36 in place of F rxn T, P c,scf Thus the final model has κ ′′ , a ′ and b ′ (three adjustable parameters). The Eq. (31) is further simplified with the help of Taylor series on left hand side The fugacity coefficient of the components and mixtures are evaluated with PR EoS. For fugacity coefficient calculations we need mixture properties and they are calculated with the help of solute, solvent and cluster volume and energy parameter. More details about these can be seen elsewhere [36][37][38] .
The cluster obeys the following mixing rules for volume and energy parameters More details about PR EoS, fugacity coefficient of pure component and mixture can be seen in section "Equation of state (EoS) model" and literature 37,38 .
The final expression for the solubility is Regression results are represented in terms of average absolute relative deviation percentage (AARD %) (33) ln z ABκ 1 − κ ′′ z ABκ = k ln φ B (T, P, z B )P φ B T, P c,Scf P c,scf + V s P − P c,scf RT −ln φ ABκ T, P, z ABκ P φ ABκ T, P c,scf P c,scf − �F rxn T, P c,scf RT where N is number of experimental data points; N p is model parameters; SSE is error sum of squares.
When N is less than 40 corrected AIC is used and it is stated as follows Table 1 indicates some properties of the used materials. Table 2 shows clemastine fumarate solubility in ScCO 2 . The density indicated in Table 2 is obtained from the NIST data base 50 . Computed properties of clemastine fumarate are shown in Table 3. Figure 3 indicates the effect of pressure on various isotherms and no cross over region observed, such solubility behavior is observed for some other pharmaceutical compounds in our earlier studies 14 . From Table 3, it is clear that the vapor pressure of clemastine fumarate increases from 0.0114 Pa to 0.1277 Pa, when the temperature is increased from 308 to 338 K, it is a 11.2 fold jump. Due to this, solubility increases from 0.0161 × 10 -4 to 0.0359 × 10 -4 (in mole/mole total) at 12 MPa (it is a 2.23 fold jump) and 0.051 × 10 -4 to 0.0941 × 10 -4 (in mole/mole total) at 27 MPa (it is a 1.845 fold jump). At the same time, densities have changed from 769 kg m -3 (corresponding to 308 K and 12 MPa) to 338 kg m -3 (corresponding to 338 K and 12 MPa) and 914 kg m -3 (corresponding to 308 K and 27 MPa) to 783 kg m -3 (corresponding to 338 K and 27 MPa),which clearly indicates that density decreases at 12 MPa (i.e., 338/769 = 0.4395) and somewhat increases at 27 MPa (i.e., 783/914 = 0.8567). From preceding arguments we say that the pressure effect is less pronounced with respect to density than the temperature effect. This kind of nonlinearity is well captured with models having more parameters compared to less number of parameter 14 . Therefore, models proposed by Sodeifian et al.    Figure 4 indicates the self-consistency of the measured data with MT model. The regression analysis of experimental data is carried out easily with density model, but the regression analysis of EoS model and cluster model requires critical properties of the solute and solvent. The required critical temperature, critical pressure, acentric factor and molar volume of the solute and sublimation pressure of the solute are not readily available; due to this these properties are computed with standard group contribution methods [39][40][41][42] . The empirical and semi empirical models considered in this study have shown different degree of fitting in terms of AARD%. The regression results of various models are indicated in Tables 4, 5 and 6. Among the existing empirical and semi-empirical models, Reddy-Garlapati model is having lower AARD%. Chrastil model parameter ( E 2 ) and Reformulated Chrastil model parameter ( F 2 ) are used in calculating total enthalpy, from Bartel et al., model parameter ( B 2 ) we get sublimation enthalpy of the clemastine fumarate. Heat of solvation is obtained from the magnitude difference between total enthalpy and sublimation enthalpy. The more details about these calculations can be seen in literature 34 . All the computed results are reported in Table 7. EoS model is regressed in two different ways. In the first approach correlation parameter are treated as temperature dependent where as in second approach the correlation parameters are treated as temperature independent. From regression results (Table 5) temperature independent correlation is better than temperature dependent correlation. EoS model also provide sublimation enthalpy and it is reported in Table 7. From Table 6    The models used in correlation exercise, have a varying number of parameters and the best model is obtained with the help of Akaike's information criterion (AIC) [45][46][47][48][49] . The data used in this exercise is small (N < 40), hence