Solubility measurement of verapamil for the preparation of developed nanomedicines using supercritical fluid

A static method is employed to determine the solubilities of verapamil in supercritical carbon dioxide (SC-CO2) at temperatures between 308 and 338 K and pressures between 12 and 30 MPa. The solubility of verapamil in SC-CO2 expressed as mole fraction are in the range of 3.6 × 10–6 to 7.14 × 10–5. Using four semi-empirical density-based models, the solubility data are correlated: Chrastil, Bartle, Kumar–Johnston (K–J), and Mendez-Santiago and Teja (MST), two equations of state (SRK and PC-SAFT EoS), expanded liquid models (modified Wilson's models), and regular solution model. The obtained results indicated that the regular solution and PC-SAFT models showed the most noteworthy exactness with AARD% of 1.68 and 7.45, respectively. The total heat, vaporization heat, and solvation heat of verapamil are calculated at 39.62, 60.03, and − 20.41 kJ/mol, respectively. Regarding the poor solubility of verapamil in SC-CO2, supercritical anti-solvent methods can be an appropriate choice to produce fine particles of this drug.


Experimental apparatus
The solubility measurement setup of verapamil is shown in Fig. 1.The equipment list includes a chamber of CO 2 (N-1), Needle valve (N-2), Filter (N-3), Refrigerator (N-4), Pump (N-5), Air compressor (N-6), Oven (N-7), Stirrer (N-8), Coil (N-9), Cell (N-10), 3-position valve (N-11), Back pressure (N-12), Micrometer valve (N-13), Syringe (N-14), Gathering vial (N-15), and Panel (N- 16).A molecular sieve as filter is used to separate the impurities of CO 2 .A refrigeration unit at -10 °C is used to liquefy CO 2 .A high-pressure pump is used to modify the pressure of the liquid CO 2 and an oven is used to change the temperature of the liquid CO 2 .2000 mg of verapamil is loaded in the equilibrium cell (300 mL).Subsequently, the pressure in the equilibrium cell is increased with the addition of CO 2 .To achieve the equilibrium condition, the cell is preserved at the desired temperature and pressure for 140 min.The 3-position valve is used to upload a saturated SC-CO 2 sample into the sample assemble (500 µL ± 0.6% volume).Then, the saturated SC-CO 2 sample is depressurized into a specific methanol volume.A valve is used to control the pressure drop to prevent the solvent dispersion.Finally, methanol is used to clean the line.A UV-V spectrophotometer is used to measure the verapamil concentration in the methanol solutions utilizing a calibration curve made using a 25 µg/mL primary solution.When the main solution is diluted, solutions with various concentrations are constructed.The following equations are used to calculate the number of verapamil (n solute ) and CO 2 moles (n CO2 ) in the taste loop: where V l (L) and V s (L) are the volumes of the sampling loop and the gather vial, respectively, and C s is the vera- pamil concentration (g/L) in the collection vial.

Modeling
To modeling the solubility of verapamil in scCO 2 are employed the semi-empirical density-based models (Chrastil, K-J, MST, and Bartle et al.), (ii) EoS-based SRK and PC-SAFT, (iii) expanded liquid theory (modified Wilson's model), and (iv) regular solution models.The adjustable parameters of the models are optimized through the simulated annealing (SA) algorithm in MATLAB software.The AARD% (Eq.( 6)) and R adj (Eq.( 7)) are utilized to optimize the adjustable parameters of semi-empirical models 22,23 :

Semi-empirical density-based models
(3) Table 2.The formula of semi-empirical model a .a a 0 − a 2 , adjustable parameters of models.

Name Formula
Chrastil 47 lnS = a 0 lnlnρ + a 1 + a2 T Bartle et al. 48 Here N t and N f are the number of report points in each series and the number of fitted parameters for each model.The report data in each series and the number of self-reliant variables in any equation are denoted by the letters N and Q, respectively.

Equation of state-based (EoS) models
When two phases are in equilibrium, the temperature, pressure, and fugacity of the two phases must be equal to each other.Equation ( 8) can be used to demonstrate that verapamil and SC-CO 2 have equal fugacity as follows: In this model, it is assumed that the solid phase is pure, CO 2 is insoluble in the solid phase, and pressure does not affect the solute's molar volume.verapamil's solubility in SC-CO 2 is found using the following formula: where P sub 2 is the sublimation pressure of solute (verapamil), as determined by the Ambrose-Walton method 24 , ∅ 2 is the verapamil fugacity coefficient in the supercritical carbon dioxide, v s 2 is the molar volume of the verapamil, as calculated by Immirzi-Perini method 25 , ∅ 2 is the verapamil fugacity coefficient in SC-CO 2 is defined by EoS as Eq. ( 10): Here, the fugacity coefficient is calculated using the SRK and PC-SAFT EoS.The Marrero and Gani method is used to compute the critical properties, and normal boiling point 26 , the acentric factor ( ω ) is calculated using the equivalent state approach of Ambros-Walton 27 , solid molar volume (v s ) 25 , and sublimation pressure 27 of solids in different temperature are shown in Table 3.

Material
Here, a ij and b ij are calculated as follows 28 :

PC-SAFT equation of state
The PC-SAFT can be explained by Eq. ( 20) 29 : Here, a id , a hc , anda disp are the contribution of ideal gas contribution, hard-sphere chain, and dispersion forces.In this study, the contribution of molecular association resulting from hydrogen bonding in the system is not considered in Eq. ( 20).This is because the solubility of Verapamil in SC-CO 2 is minimal (less than 0.001 in mole fraction), as described the result section.Accordingly, the effect of the self-association between API molecules is considered as small.Therefore, only the following three pure-component parameters of PC-SAFT are used in this study.In several articles, authors applied this equation for calculating APIs solubility in SC-CO 2 [30][31][32] .The value of Helmholtz energy for the N-component of non-associating chains is obtained in Eq. ( 21): The hard-chain reference contribution is written as: m is the mean segment number in the combination is calculated by Eq. ( 23): Dispersion contribution.The dispersion force contribution is defined by Eq. ( 24) 33 .
The mixing rule for segment diameter σ ij and energy ε ij are defined as: The ρ Å −3 , is equal to: The compressibility factor is defined as: The pressure can be calculated as: The fugacity coefficient is defined by Eq. ( 30): www.nature.com/scientificreports/ The chemical potential can be calculated via Eq.( 31): The amount of the segment number, energy, and diameter of CO 2 and verapamil are obtained in Table 4.

Expanded liquid theory
Since the supercritical fluid density is close to that of a liquid, the supercritical fluid phase can be assumed to be an expanded liquid 34 .The pure solid and the supercritical phase have equilibrium 35 : where f ScF 2 and f S 2 is the fugacity of verapamil in the supercritical phase and fugacity of the verapamil in the solid phase.The f L 2 is defined as follows: Rewriting Eq. ( 31) will give the following result: Here γ 2 and f 0L 2 are the activity coefficient and fugacity of the verapamil in the expanded liquid phase.The ratio f 0S 2 to f 0L 2 is calculated by Eq. ( 35) 36 : It can be written with Eqs. ( 33) and ( 34): Due to the very small value of verapamil in the supercritical fluid, the mole fraction is computed via Eq.( 37):

Modified Wilson model
The Excess Gibbs energy G E can be calculated by Eq. ( 38) 28 : where v 1 and v 2 are the molar volume of SC-CO 2 and verapamil.The activity coefficient of dilute verapamil in supercritical carbon dioxide is defined as 28 : (31)

Regular solution model
The fugacity of each element in the two phases must be equal to be in equilibrium.The solubility of carbon dioxide in the solid phase is considered negligible.The activity of the verapamil in the liquid phase is equal to the fugacity of the pure solute in the liquid phase in solid-liquid equilibrium.Fugacity can be calculated by knowing the solid substance's enthalpy and melting point.With the use of a solution model and the Flory-Huggins based, the activity coefficient is calculated.So, the solubility of solute (verapamil) in SC-CO 2 is calculated using the Eq. ( 47).
The solubility parameter of the solid solute is defined as: ρ r,1 is the reduced density of the supercritical fluid.

Experimental data
In order to demonstrate the reliability of the solubility measurement equipment, the solubility of capecitabine and naphthalene at different temperatures and pressures are measured using the device used in this study and compared with the data reported for Ardestani et al. 39 , Iwai et al. 40 , Yamini et al. 41 , Sodeifian et al. 42 .Experimental data of capecitabine and naphthalene in SC-CO 2 are compared in Figs. 2 and 3. Table 5 provides information on verapamil's solubility in SC-CO 2 .At temperatures between 308 and 338 K and pressures between 12 and 30 MPa, the SC-CO 2 density, mole fraction, and verapamil solubility are all tested in triplicate.The density of SC-CO 2 is determined by Span-Wanger EoS 43 .Based on the NIST recommendation, combined and extended uncertainties are presented in Table 5. Figure 4 depicts how SC-CO 2 pressure and density affect the solubility of verapamil.Verapamil's solubility in SC-CO 2 , as seen in Table 5 and Fig. 4, increased as pressure increased because verapamil's solvent density and vapor pressure rose as temperature and pressure rise.The crossover zone for verapamil's solubility is between 12 and 15 MPa.In this zone, the solubility of verapamil in SC-CO 2 is reduced with temperature increase in this range.On the contrary, the solubility of verapamil increased when the temperature is over this range.The struggle between the impacts of verapamil vapor pressure and CO 2 density on temperature led to the crossover.The sublimation pressure and enthalpy, critical characteristics, and solute molar volume are only a few of the variables that might affect the cross-over point 44,45 .The solubility of verapamil in SC-CO 2 expressed as mole fraction is in the border of 3.6 × 10 -6 to 7.14 × 10 -5 , which are collected at the temperature of 338 K and pressures of 12 and 30 MPa, respectively.

Solubility data with semi-empirical models
To correlate the experimental data of verapamil solubility in SC-CO 2 , semi-empirical density-based models (Chrastil, Bartle et al., MST, and K-J) are proposed in this study.The adjustable parameters of the semi-empirical model (a 0 , a 1 , a 2 ), AARD%, and R adj are reported in Table 6.The empirical and theoretical solubility data of verapamil obtained by the semi-empirical models are shown in Fig. 5.As indicated in AARD% in Table 6, the best models are K-J, MST, Chrastil et al., and Bartle, respectively.The review of other studies regarding the solubility of pharmaceutical substances shows that model K-J is reported to be the best in many cases such as salsalate 46 , Favipiravir 18 , and Lacosamide 19 .MST models also presented acceptable capability to describe the solubility of verapamil in SC-CO 2 .Total, vaporization solvation enthalpy is calculated with the tuning parameter of the Chrastil ( a 1 ) and Bartle et al. ( a 2 ) model.The values of these enthalpy are listed in Table 7.

Solubility correlation with the equation of state model
A simulated annealing method is used to improve the interaction parameters of the SRK EoS and PC-SAFT.
The adjustable parameters of PR-EoS ( k ij , l ij ) and PC-SAT ( k ij ) are dependent temperature and represented in Table 8. Figure 6 depicts how temperature affects the interaction parameters for the binary system verapamil-SC-CO 2 by SRK and PC-SAFT EoS models.The relation between interaction parameters and temperature is defined as follows: Figure 6 illustrates how this relationship's slope and intercept are identified using linear regression analysis.Figure 7 displays the empirical and predicted solubility data by the SRK and PC-SAFT EoS model at 308, 318, 328, and 338 K. SRK and PC-SAFT both had total AARD% of 20.68 and 7.45, respectively.As indicated by the AARD% in Table 8, while determining the solubility of verapamil in SC-CO 2 , PC-SAFT showed a higher verification of the SRK EoS. and SD y = S(y k ) √ n respectively.The relative combined standard uncertainty is earned by U combined /y = N i=1 (P i U(x i )/x i ) 2 .The expanded uncertainty U is k × U combined .b Standard uncertainty u are (T) = 0.1 K; u(p) = 0.1 MPa.The relative standard uncertainties are computed below 0.05 for solubilities and mole fractions.www.nature.com/scientificreports/

Expanded liquid theory-modified Wilson model
The model parameters for the solubility of verapamil in SC-CO 2 are optimized using the modified Wilson model.Table 9 lists the parameters of the modified Wilson model ( α , β , ′ 12 , and ′ 21 ).The modified Wilson model's ability to forecast the solubility of verapamil in SC-CO 2 is demonstrated by the value of AARD%, which is 9.89.The value of ′ 12 (− 2.0196) is smaller than ′ 21 (17.0059).So, according to Eqs. ( 39) and ( 40) the value of 21     www.nature.com/scientificreports/ is calculated to be smaller than 12 .The testing data and calculated solubility of verapamil in SC-CO 2 with a modified Wilson model are seen in Fig. 8.

Regular solution model
Table 10 contains the results of the correlation for the solubility of verapamil in SC-CO 2 .The A, B, and C are adjustable parameters of Eqs. ( 49)- (51).The values of tuning parameters (A, B, and C) are calculated with higher veracity at low temperatures (Table 10).The AARD% and R adj for Eqs. ( 49)-( 51) are determined and obtained in Table 10.As indicated by AARD%, Eq. ( 51

Figure 4 .
Figure 4.The effect of (a) pressure and (b) density of SC-CO 2 on verapamil solubility at several temperatures.

Figure 5 .
Figure 5.The experimental and model values of verapamil solubility according to the (a) Chrastil, (b) Bartle et al., (c) MST, and (d) K-J., models at different temperatures.

Figure 6 .
Figure 6.The effect of temperature on the interaction parameters for the verapamil-CO 2 system; (a) SRK, (b) PC-SAFT.

Figure 7 .
Figure 7.The experimental and model values solubility of verapamil according to (a) SRK and (b) PC-SAT at several temperatures.

Figure 8 .
Figure 8.The experimental data and model solubility of verapamil in SC-CO 2 according to modified Wilson.

Figure 9 .
Figure 9.The experimental data and model solubility of verapamil in SC-CO 2 according to the regular solution.

Figure 10 .Figure 11 .
Figure 10.Comparison of the AARD% calculated for all models (semi-empirical density-based, equations of state, expanded liquid, and regular solution).

Table 1 .
The properties of substances.
a High-performance liquid chromatography.b Gas chromatography.c Molecular weight.d Melting temperature.e Maximum wavelength.c,d http:// www.chems pider.com.b www.nature.com/scientificreports/The verapamil solubility in SC-CO 2 is calculated by Eqs. (

Table 2
displays the semi-empirical density-based models.These models have three variables that can be estimated using empirical data, y is the verapamil mole fraction and ρ is the density of SC-CO 2 in semi-empirical models.P ref and ρ ref in the Bartle et al. model are equivalent to 700 kg/m 3 and 0.1 MPa, respectively.

Table 6 .
The semi-empirical model's results of the verapamil-CO 2 system.a a a 0 − a 2 , adjustable parameters of models.

Table 7 .
Enthalpy for verapamil.a Chrastil's procedure.b Bartle et al., procedure c difference between the ΔH vap and ΔH total .

Table 8 .
Solidarity outcomes for solubility of verapamil in SC-CO 2 , by SRK and PC-SAFT.

Table 9 .
Modified Wilson parameters for solubility of verapamil in SC-CO 2 .

Table 10 .
Regular solution models outcomes for solubility of verapamil in Sc-CO 2 .