Solubilization and thermodynamic properties of simvastatin in various micellar solutions of different non-ionic surfactants: Computational modeling and solubilization capacity

The aim of this work was to solubilize simvastatin (SIM) using different micellar solutions of various non-ionic surfactants such as Tween-80 (T80), Tween-20 (T20), Myrj-52 (M52), Myrj-59 (M59), Brij-35 (B35) and Brij-58 (B58). The solubility of SIM in water (H2O) and different micellar concentrations of T80, T20, M52, M59, B35 and B58 was determined at temperatures T = 300.2 K to 320.2 K under atmospheric pressure p = 0.1 MPa using saturation shake flask method. The experimental solubility data of SIM was regressed using van’t Hoff and Apelblat models. The solubility of SIM (mole fraction) was recorded highest in M59 (1.54 x 10−2) followed by M52 (6.56 x 10−3), B58 (5.52 x 10−3), B35 (3.97 x 10−3), T80 (1.68 x 10−3), T20 (1.16 x 10−3) [the concentration of surfactants was 20 mM in H2O in all cases] and H2O (1.94 x 10−6) at T = 320.2 K. The same results were also recorded at each temperature and each micellar concentration of T80, T20, M52, M59, B35 and B58. “Apparent thermodynamic analysis” showed endothermic and entropy-driven dissolution/solubilization of SIM in H2O and various micellar solutions of T80, T20, M52, M59, B35 and B58.

There is lack of temperature dependent solubility data of statins in literature. The solubilities (mole fraction) of statin drugs like lovastatin in some organic solvents such as acetone, methanol, ethanol, ethyl acetate and butyl acetate at temperature T = 283 K to 323 K under atmospheric pressure p = 0.1 MPa are reported elsewhere [28]. The solubilities of SIM (mole fraction) in various alcohols such as ethanol, 1-propanol, 1-butanol, 1-pentanol, 1-hexanol and 1-octanol at T = 286.15 K to 310.15 K are also available [1]. The micellar solubilization of drugs is one of the useful techniques which is being applied in solubility enhancement of weakly aqueous-soluble drug compounds [11,29,30]. Micellar solubilization of several poorly water-soluble drugs such as SIM, itraconazole, danazol, fenofibrate and androstane has been studied [12,31,32]. Temperature dependent solubilities of SIM in micellar solutions of various non-ionic surfactants such as Tween-80 (T80), Tween-20 (T20), Myrj-52 (M52), Myrj-59 (M59), Brij-35 (B35) and Brij-58 (B58) are not reported elsewhere. Therefore, the aim of this work was to determine the solubility of SIM in various molar concentrations of T80, T20, M52, M59, B35 and B58 in comparison with its solubility in water (H 2 O) at T = 300.2 K to 320.2 K and p = 0.1 MPa. The dissolution/solubilization behavior of SIM in different molar concentrations of T80, T20, M52, M59, B35 and B58 was investigated by apparent thermodynamic analysis. All studied surfactants are non-ionic surfactants which are safe for human use.
They have potential for enhancing the solubility of poorly soluble drugs via micelle formation. Hence, the studied surfactants were selected for the solubilization of SIM in this work.

Quantification of SIM by UPLC-UV analysis
"Waters Acquity 1 H-class Ultra-Performance Liquid Chromatography (UPLC)" apparatus connected with a "Waters diode-array-ultra-violet detector (DAD-UV) (Waters, MA, USA)" was applied for quantification of SIM at 237 nm. The quantification was carried out at reversephase isocratic elution mode using "Acquity 1 UPLC BEH C 18 column (2.1 x 50 mm, 1.7 μm)" which was acquired from "Waters (Waters Inc., Bedford, MA, USA)". The binary mixture of 0.1% formic acid and acetonitrile (25:75, v/v) was used as mobile phase which was delivered with a flow rate of 0.3 mL min -1 . The volume of injection was 1 μL. The quantification of SIM was performed at 237 nm. The column temperature was maintained at "T = 313.2 K". The UPLC response of SIM was obtained at retention time of 1.12 min with a total run time of 1.5 min. The "Masslynx software" was utilized for data analysis.

Calibration and regression
The measured UPLC response of SIM was plotted against its concentrations in order to obtain calibration and regression. The calibration plot of SIM was observed linear in the range of (10 to 500.0) ng g -1 . The coefficient of determination (R 2 ) and equation for regression line were recorded as 0.9990 and UPLC area = 225.43 � concentration-502.98. The proposed UPLC-UV method was validated in terms of "linearity, accuracy, precision, robustness, sensitivity, reproducibility and specificity". The results of validation parameters were obtained within the recommended limits of International Council for Harmonization guidelines [33].

Solid state characterization of pure and SIM equilibrated with water
The solid phases of SIM in pure and equilibrated samples (equilibrated with water) were characterized by differential scanning calorimetry (DSC) and powder X-ray diffraction (PXRD) studies. The pure SIM was original SIM powder which was used before solubility studies. The equilibrated SIM was recovered from water after solubility studies. The equilibrated SIM was recovered by slow evaporation of water and stored at an ambient temperature till further use. The characterization of solid phases was performed for the investigation of physical form and probable transformation of SIM into polymorphs/solvates/hydrates after equilibrium. DSC thermogram of SIM in pure and equilibrated forms was obtained using "DSC-8000 Instrument (Perkin Elmer, MA, USA)". The whole DSC assembly was connected with chiller and autosampler. Before DSC experiments, the calibration of instrument was performed using pure indium. Accurately weighed 5.40 mg of pure SIM and 5.20 mg of equilibrated SIM were taken and transferred into an aluminium pan which was sealed hermetically. DSC spectra for SIM in both samples was recorded in the temperature range of T = 303.2 K to 573.2 K with heating rate of 10.0 K min -1 . The flow for nitrogen for this analysis was set at 20 mL min -1 .
PXRD spectra of SIM in both samples were obtained with the help of "Ultima IV Diffractometer (Rigaku Inc. Tokyo, Japan)" in the 2θ range of 3−60˚at a scan speed of 0.5˚min -1 . The tube anode utilized for PXRD measurements was "Cu with Ka = 0.1540562 nm mono chromatized with a graphite crystal (Rigaku Inc., Tokyo, Japan)". PXRD spectra of SIM in both samples were recorded at tube voltage and tube current of 40 kV and 40 mA, respectively.

Measurement of SIM solubility in H 2 O and various micellar solutions of different non-ionic surfactants
The solubilities of SIM (mole fraction) in H 2 O and different micellar solutions of T80, T20, M52, M59, B35 and B58 were measured using a saturation shake flask technique propose by Higuchi and Connors [34]. The solubility of SIM was measured at T = 300.2 K to 320.2 K under atmospheric pressure. The excess quantity of pure SIM was added into known quantities of H 2 O and various micellar solutions (1, 5, 10 and 20 mM) of T80, T20, M52, M59, B35 and B58. Each experiment was performed in triplicates manner. Each drug-surfactant/drug-H 2 O mixture was vortexed using a Vortex mixer (Thermo Fisher Scientific, Waltham, MA, USA) for about 5 min. The samples were then kept in the WiseBath 1 WSB Shaking Water Bath (Model WSB-18/30/-45, Daihan Scientific Co. Ltd., Seoul, Korea). The speed of shaker was maintained at 100 rpm and temperature was varied from 300.2 K to 320.2 K. The equilibrium time was optimized as 72 h by preliminary investigations. After 72 h, each drug-surfactant/drug-H 2 O mixture was taken out from the WSB shaking Water bath. The samples were centrifuged using a Remi Centrifuge (Remi Sales & Eng. Ltd., Mumbai, India) at 5000 rpm for about 20 min at ambient temperature i.e. T = 298.2 K. The supernatants were withdrawn, filtered using Whatman filter paper (Sigma Aldrich, St. Louis, MO, USA), diluted (wherever applicable) and subjected for the quantification of SIM by UPLC-UV technique at 237 nm. The experimental mole fraction solubility (x e ) values of SIM were obtained using Eq (1) [35,36]: In which, m 1 and m 2 represent the amounts of SIM (g) and H 2 O/surfactant (g), respectively. M 1 and M 2 represent the molecular weights of SIM (g mol -1 ) and H 2 O/surfactant (g mol -1 ), respectively.

Solid state characterization of pure and equilibrated SIM
The solid phases of SIM in both samples were characterized for the investigation their physical form and possible transformation of SIM into polymorphs/solvates/hydrates after equilibrium. DSC thermograms of SIM in pure and equilibrated samples are shown in Fig 2A and 2B, respectively. DSC thermogram of SIM in pure form presented a crystalline endothermic peak at melting/fusion temperature (T fus ) of 412.95 K. The values of fusion enthalpy (ΔH fus ) and fusion entropy (ΔS fus ) for pure SIM were obtained as 28.38 kJ mol -1 and 68.72 J mol -1 K -1 , respectively (Fig 2A). The equilibrated SIM was recovered from slow evaporation of water. DSC thermogram of SIM in equilibrated form (the SIM equilibrated with water) also presented a crystalline endothermic peak at T fus of 413.18 K. The values of ΔH fus and ΔS fus for equilibrated SIM were obtained as 28.58 kJ mol -1 and 69.19 J mol -1 K -1 , respectively ( Fig 2B). The DSC spectra and various thermal parameters such as T fus , ΔH fus and ΔS fus of pure SIM very closed with those of equilibrated SIM. The results of DSC analysis indicated crystalline nature of SIM in both samples. Although, the peak intensities of pure and equilibrated SIM were slightly different, but their thermal parameters were almost closed to each other. The difference in peak intensity might be due to the fact that different amounts of pure and equilibrated SIM were taken for DSC analysis. Similar DSC spectra for pure and equilibrated SIM suggested no transformation of SIM into amorphous/polymorphic/solvate form after equilibrium. The T fus and ΔH fus values of pure SIM have been reported as 410.92 K and 24.46 kJ mol -1 , respectively [1]. The T fus and ΔH fus values of pure SIM were obtained as 412.95 K and 28.38 kJ mol -1 , respectively in the present study. These thermal parameters of present work were found to be closed with literature values [1].
The PXRD spectra of pure and equilibrated SIM are shown in Fig 3A and 3B, respectively. PXRD spectra of SIM in pure sample presented different crystalline peaks at various 2 θ values,  also suggesting crystalline nature of SIM ( Fig 3A). PXRD spectra of SIM in equilibrated form also presented different crystalline peaks at similar 2 θ values ( Fig 3B). Similar PXRD spectra of pure and equilibrated SIM again suggested crystalline nature of SIM in both samples and no transformation of SIM into amorphous/polymorphic/solvate form after equilibrium. Based on DSC and PXRD results, we can say that the crystal form of SIM was similar in water and most probably on studied surfactants as no transformation of SIM was recorded after equilibrium.

Experimental solubilities of SIM in H 2 O and various micellar solutions of different non-ionic surfactants
The experimental solubility (x e ) values of SIM in H 2 O and various micellar solutions (1, 5, 10 and 20 mM) of T80, T20, M52, M59, B35 and B58 at three different temperatures T = 300.2 K, 310.2 K and 320.2 K and p = 0.1 MPa are presented in Table 1. Saturated solubility of SIM in H 2 O at ambient temperature i.e. T = 298.2 K has been reported elsewhere [19,27]. Micellar solubilization of SIM in polyglycerol diisostearate ethoxylates surfactants has also been reported [12]. However, temperature-dependent solubilities of SIM in H 2 O and various micellar solutions of T80, T20, M52, M59, B35 and B58 are not reported so far. Murtaza reported   [27]. However, it was much deviated from solubility of SIM reported by Craye et al. [19]. The influence of temperature on logarithmic solubilities of SIM is presented in Fig 4. It was observed from experimental data that the logarithmic solubility values of SIM were increasing linearly with increase in temperature in H 2 O and four different micellar solutions of T80, T20, M52, M59, B35 and B58 (Fig 4). The results of influence of temperature on solubility of SIM were accordance with those reported for several weakly water soluble drugs [35][36][37][38][39].
The influence of molar concentrations of various non-ionic surfactants on logarithmic solubilities of SIM at three different temperatures is presented in Fig 5. It was found that the logarithmic solubility values of SIM were increasing non-linearly with increase in the molar concentrations of T80, T20, M52, M59, B35 and B58 at each temperature studied. The  to the highest solubility of SIM in 20 mM M59, it can be used as a solubilizer in liquid formulation design of SIM.

Solubility parameter for SIM, H 2 O and different surfactants
In this work, Hansen solubility parameter (δ) for SIM, H 2 O, T80, T20, M52, M59, B35 and B58 was obtained using Eq (2) [40][41][42]: In which, the symbol δ is the total Hansen solubility parameter for solute/solvent. However, the symbols δ d , δ p and δ h represent dispersion, polar and hydrogen-bonded Hansen solubility parameters, respectively. The δ, δ d , δ p and δ h values were obtained by putting "simplified molecular-input line-entry system (SMILES)" of each component using "HSPiP software (version 4.1.07)" The SMILES of each compound is easily available in the compound database.
The calculated values of δ, δ d , δ p and δ h are presented in Table 2

Determination of drug solubilization efficiency
The drug solubilization efficiency for different micellar solutions of various non-ionic surfactants was determined as the molar solubilization capacity (S c ) using Eq (3) [31,32]: In which, S t is the measured SIM solubility in the presence of surfactants, S w is the intrinsic water solubility of SIM, C s is the molar surfactant concentration and CMC is the critical micelle concentration of surfactant. The values of solubilization capacity for SIM in different micellar solutions of various non-ionic surfactants were determined at "T = 300.2 K" and results are presented in Table 3. The solubilization capacity for SIM was found to be lower in all micellar solutions of T80, T20, B35 and B58 compared to various micellar solutions of M52

Theoretical/ideal solubilities
Theoretical/ideal solubility of solute/SIM (x idl ) was obtained using Eq (4) [43,44]: In which, R represents the universal gas constant and ΔC p represents the differential molar heat capacity of solute/SIM [43][44][45]. Other symbols in Eq (4) were defined previously in the article.
The values of T fus , ΔH fus and ΔC p for solute/SIM were obtained as 412.95 K, 28.38 kJ mol -1 and 68.72 J mol -1 K -1 , respectively from DSC/thermal analysis of SIM. The x idl values for solute/SIM were obtained using Eq (4) and these values at three different temperatures are presented in Table 1. Theoretical/ideal solubilities of SIM were compared with experimental solubilities at each temperature. It was noticed that theoretical/ideal solubility of SIM was significantly higher than SIM solubility in H 2 O and various micellar solutions (1, 5, 10 and 20 mM) of T80, T20, M52, M59, B35 and B58 at each temperature investigated. Theoretical/ideal solubility of SIM was also recorded as increasing significantly with increase in temperature, suggesting the dissolution behavior of SIM was endothermic process [1].

Model solubilities and curve fitting
The experimental solubilities of SIM were modelled/curve fitted with the help of van't Hoff and Apelblat models [38,46,47]. Apelblat model solubility (x Apl ) of SIM in H 2 O and various micellar solutions (1, 5, 10 and 20 mM) of T80, T20, M52, M59, B35 and B58 was calculated using of Eq (5) [46,47]: In which, A, B and C represent the coefficients/parameters of Apelblat model which were obtained by applying "nonlinear multivariate regression analysis" of experimental solubilities of SIM listed in Table 1 [48]. The x e of SIM were modelled/curve fitted with Apelblat solubilities of SIM using root mean square deviations (RMSD) and R 2 . RMSD values between experimental and Apelblat solubilities of SIM were obtained using Eq (6) [35]: In which, N represents the number of experimental data points used in the study. The graphical correlation/curve fitting between logarithmic experimental solubilities (ln x e ) and logarithmic Apelblat solubilities (ln x Apl ) of SIM in H 2 O and 1 mM and 5 mM micellar solution of T80, T20, M52, M59, B35 and B58 against reciprocal of absolute temperature (1/T) is presented in Fig 6A and 6B, respectively. However, the curve fitting between ln x e and ln x Apl of SIM in H 2 O and 10 mM and 20 mM micellar solution of T80, T20, M52, M59, B35 and B58 against 1/T is presented in Fig 6C and  6D, respectively. The results showed in Fig 6A-6D suggested good correlation/curve fitting between ln x e and ln x Apl values of SIM in H 2 O and different micellar solutions of T80, T20, M52, M59, B35 and B58. The resulting data of this correlation/fitting are listed in Table 4. RMSD values for SIM in H 2 O and various micellar solutions of T80, T20, M52, M59, B35 and B58 were obtained as (0.16 to 5.84) %. An average RMSD for this correlation was found to be 0.60%. The R 2 values for SIM in H 2 O and various micellar solutions of T80, T20, M52, M59, B35 and B58 were obtained in the range of 0.9957 to 0.9999. The results presented in Table 4 in terms of RMSD and R 2 suggested good correlation of experimental data of SIM with Apelblat model.
The van't Hoff model solubility (x van't ) of SIM in H 2 O and various micellar solutions (1, 5, 10 and 20 mM) of T80, T20, M52, M59, B35 and B58 was obtained using Eq (7) [38]: In which, a and b represent the coefficients/parameters of van't Hoff model which were obtained by least square method.
The experimental solubilities of SIM were modelled/curve fitted with van't Hoff solubilities of SIM using RMSD and R 2 . The curve fitting between logarithmic experimental solubilities and logarithmic van't Hoff solubilities of SIM in H 2 O and 1 mM and 5 mM micellar solution of T80, T20, M52, M59, B35 and B58 against 1/T is shown in S1 and S2 Figs, respectively. However, the curve fitting between logarithmic experimental solubilities and logarithmic van't Hoff solubilities of SIM in H 2 O and 10 mM and 20 mM micellar solution of T80, T20, M52, M59, B35 and B58 against 1/T is presented in S3 and S4 Figs, respectively. The data presented in S1-S4 Figs also showed good correlation/curve fitting between experimental and model solubilities of SIM in H 2 O and different micellar solutions of T80, T20, M52, M59, B35 and B58. The resulting data of this correlation are presented in Table 5. The RMSD values for SIM in H 2 O and various micellar solutions of T80, T20, M52, M59, B35 and B58 were obtained as (0.23 to 1.74) %. An average RMSD for this correlation was predicted as 0.78%. The R 2 values for SIM in H 2 O and various micellar solutions of T80, T20, M52, M59, B35 and B58 were recorded as 0.9944 to 1.0000. The results presented in Table 5 in terms of RMSD and R 2 again suggested good correlation of experimental data of SIM with van't Hoff model.

Apparent thermodynamics
Apparent thermodynamics is helpful in evaluation of various thermodynamic parameters, which could ultimately determine the dissolution behavior in case of real solutions and solubilization in case of non-ideal solutions [49]. Hence, the dissolution/solubilization behavior of SIM in H 2 O and various micellar solutions of T80, T20, M52, M59, B35 and B58 were determined by applying "apparent thermodynamic analysis" on solubilities (mole fraction) of SIM. Accordingly, three different thermodynamic parameters including "apparent standard dissolution enthalpy (Δ sol H 0 ), apparent standard Gibbs free energy (Δ sol G 0 ) and apparent standard dissolution entropy (Δ sol S 0 )" for SIM dissolution/solubilization were determined using this analysis. The Δ sol H 0 values for SIM dissolution/solubilization in H 2 O and various micellar solutions of T80, T20, M52, M59, B35 and B58 were determined at mean harmonic temperature (T hm ) by applying van't Hoff analysis using Eq (8) [43,49]: The value of T hm was calculated as 309.98 K using its reported formula [41]. The Δ sol H 0 values for SIM dissolution/solubilization in H 2 O and various micellar solutions of T80, T20, M52, M59, B35 and B58 were obtained by van't Hoff plots plotted between ln x e values of SIM and 1 = T À 1 = T hm .
The Δ sol G 0 values for dissolution/solubilization behavior of SIM in H 2 O and various micellar solutions of T80, T20, M52, M59, B35 and B58 were also obtained at T hm of 309.98 K by Table 4

Samples
In which, the intercept value for SIM in H 2 O and various micellar solutions of T80, T20, M52, M59, B35 and B58 was calculated from van't Hoff plot discussed under van't Hoff analysis.
Finally, the Δ sol S 0 values for dissolution/solubilization behavior of SIM were obtained using the combined approaches of van't Hoff and Krug et al. analysis with the help of Eq (10) [43,49,50]: The calculated values of these thermodynamic parameters for dissolution/solubilization behavior of SIM in H 2 O and different micellar solutions of T80, T20, M52, M59, B35 and B58 at T hm of 309.98 K are presented in Table 6.
The Δ sol H 0 values for SIM dissolution/solubilization in H 2 O and various micellar solutions of T80, T20, M52, M59, B35 and B58 were recorded as (11.62 to 36.64) kJ mol -1 . The Δ sol H 0 value for SIM dissolution was recorded highest in H 2 O (36.64 kJ mol -1 ). However, the lowest Δ sol H 0 value (11.62 kJ mol -1 ) for SIM solubilization was obtained in 20 mM micellar   [38,51]. The positive values of Δ sol H 0 and Δ sol G 0 might be due to the formation of new bond energy of attraction between the drug and solvent molecules [49]. The Δ sol S 0 values for SIM dissolution/solubilization in H 2 O and different micellar solutions of T80, T20, M52, M59, B35 and B58 were also recorded as positive values in the range of (0.39 to 48.55) J mol -1 K -1 . The average Δ sol S 0 value for SIM dissolution/solubilization was recorded as 7.28 J mol -1 K -1 with uncertainty of 1.40. The positive Δ sol S 0 values for SIM showed an entropy-driven dissolution/solubilization behavior of SIM in H 2 O and various micellar solutions of T80, T20, M52, M59, B35 and B58 [51]. Finally, the dissolution/solubilization behavior of SIM was found to be endothermic and entropy-driven in H 2 O and various micellar solutions of T80, T20, M52, M59, B35 and B58 [36,38,51].

Conclusions
The objective of this work was to solubilize SIM using different micellar solutions of various non-ionic surfactants including T80, T20