# Solubility Data of the Bioactive Compound Piperine in (Transcutol + Water) Mixtures: Computational Modeling, Hansen Solubility Parameters and Mixing Thermodynamic Parameters

^{*}

## Abstract

**:**

_{e}) of PPN in THP + water combinations were recorded at T = 298.2–318.2 K and p = 0.1 MPa by the shake flask method. Hansen solubility parameters (HSPs) of PPN, pure THP, pure water and THP + water mixtures free of PPN were also computed. The x

_{e}values of PPN were correlated well with “Apelblat, Van’t Hoff, Yalkowsky–Roseman, Jouyban–Acree and Jouyban–Acree–Van’t Hoff” models with root mean square deviations of < 2.0%. The maximum and minimum x

_{e}value of PPN was found in pure THP (9.10 × 10

^{−2}at T = 318.2 K) and pure water (1.03 × 10

^{−5}at T = 298.2 K), respectively. In addition, HSP of PPN was observed more closed with that of pure THP. The thermodynamic parameters of PPN were obtained using the activity coefficient model. The results showed an endothermic dissolution of PPN at m = 0.6–1.0 in comparison to other THP + water combinations studied. In addition, PPN dissolution was recorded as entropy-driven at m = 0.8–1.0 compared with other THP + water mixtures evaluated.

## 1. Introduction

_{2}) and near critical CO

_{2}at different temperatures has also been reported elsewhere [42]. So far, there is no report on PPN solubilization in “THP + water” mixtures at “T = 298.2–318.2 K” and “p = 0.1 MPa”. Therefore, in this research, the solubility profile of PPN in various “THP + water” mixtures, including pure water and pure THP at “T = 298.2–318.2 K” and “p = 0.1 MPa” is studied and reported. Mixing thermodynamic parameters of PPN are also computed and reported using an activity coefficient model. The solubility values of PPN reported in this research could be beneficial in “isolation, extraction, purification, recrystallization, drug discovery, pre-formulation studies and dosage form design” of PPN.

## 2. Results and Discussion

#### 2.1. Experimental Solubility Values of PPN and Literature Comparison

_{e})” values of PPN in various “THP + water” combinations including pure water and pure THP at “T = 298.2–318.2 K’ and “p = 0.1 MPa” are summarized in Table 1. The solubility values of PPN in pure water and pure THP have been reported [38]. However, its solubility values in “THP + water” mixtures have not been reported elsewhere so far.

^{−1}(equivalent to x

_{e}= 1.04 × 10

^{−5}) and 10 µg g

^{−1}(equivalent to x

_{e}= 6.31 × 10

^{−7}) by Shao et al. and Veerareddy et al., respectively [30,31]. In addition, the solubility of PPN in water at “T = 291.2 K” was obtained as 40 µg g

^{−1}(equivalent to x

_{e}= 2.53 × 10

^{−6}) by another report [1]. The x

_{e}value of PPN in pure water at “T = 298.2 K” was calculated as 1.03 × 10

^{−5}in the current research (Table 1). The solubility of PPN in pure THP at “T = 298.2 K” was obtained as 185.29 mg g

^{−1}(equivalent to x

_{e}= 8.01 × 10

^{−2}) [31]. The x

_{e}value of PPN in pure THP at “T = 298.2 K” was calculated as 7.88 × 10

^{−2}in the current research (Table 1). The x

_{e}values of PPN in pure water and pure THP obtained in the current research were found to be very close to those reported by Shao et al. [31]. However, the x

_{e}value of PPN in pure water obtained in the current research was found to have deviated much from those reported by Veerareddy et al. and Vasavirama and Upender [1,30]. This deviation could be due to the variation in shaking speed, equilibrium time and analysis method of PPN [1,30,38]. The solubility values of PPN in pure water and pure THP at five different temperatures, i.e., “T = 298.2–318.2 K” have also been reported [38]. The graphical comparison between x

_{e}and literature solubility values of PPN in pure water and pure THP at “T = 298.2–318.2 K” are summarized in Figure 2A,B, respectively. The data summarized in Figure 2A,B suggested an excellent correlation of x

_{e}values of PPN with the literature solubility data of PPN in pure water and pure THP at “T = 298.2–318.2 K”. Overall, the experimental solubility values of PPN obtained in the current research were found in good agreement with those reported in the literature. The reliability of the proposed method of solubility measurement was verified by obtaining the x

_{e}values of another phytomedicine/nutraceutical apigenin in pure THP at T = 298.2 K and T = 318.2 K. The x

_{e}value of apigenin in pure THP at T = 298.2 K and T = 318.2 K was found as 3.36 × 10

^{−1}and 3.82 × 10

^{−1}, respectively, in the literature [27]. The x

_{e}value of apigenin in pure THP at T = 298.2 K and T = 318.2 K was determined as 3.33 × 10

^{−1}and 3.84 × 10

^{−1}, respectively, in the current research. These results suggested that the x

_{e}value of apigenin in pure THP obtained using the current technique was very close to those reported in the literature [27]. Therefore, the present technique of solubility measurement was reliable for the solubility determination of PPN.

_{e}values of PPN were found to increase with increases in both THP mass fraction (m) in various “THP + water” combinations and temperature, and therefore the minimum x

_{e}value of PPN was obtained in pure water (x

_{e}= 1.03 × 10

^{−5}) at “T = 298.2 K”, and the maximum x

_{e}value of PPN was observed in pure THP (x

_{e}= 9.10 × 10

^{−2}) at “T = 318.2 K”. The maximum x

_{e}value of PPN in pure THP could be due to the lower polarity and low Hansen solubility parameter (HSP) of THP in comparison to high polarity and higher HSP of water [25,26]. The impact of m value of THP on PPN solubility at “T = 298.15–318.15 K” is summarized in Figure 3.

_{e}values of PPN were significantly enhanced from pure water to pure THP, and therefore THP could be utilized as an excellent co-solvent in PPN solubility enhancement.

#### 2.2. Hansen Solubility Parameters (HSPs)

^{1/2}. The HSP value for pure THP (δ

_{1}) and pure water (δ

_{2}) were computed as 21.40 and 47.80 MPa

^{1/2}, respectively. The HSP values for various “THP + water” mixtures free of PPN (δ

_{mix}) were computed as 24.04–45.16 MPa

^{1/2}. As per the data recorded, the HSP value of pure THP (δ

_{2}= 21.40 MPa

^{1/2}) and “THP + water” mixtures (at m = 0.9; δ

_{mix}= 24.04 MPa

^{1/2}) were found to close to that of PPN (δ = 22.30 MPa

^{1/2}). The x

_{e}values of PPN were also obtained at the maximum in pure THP and at m = 0.9 of THP in “THP + water” mixtures. Hence, the obtained solubility data of PPN in various “THP + water” mixtures was in good agreement with their HSPs

#### 2.3. Mixing Thermodynamic Parameters of PPN Solution

_{mix}G), mixing enthalpy (Δ

_{mix}H) and mixing entropy (Δ

_{mix}S)” along with activity coefficients (γ

_{i}) for PPN in different “THP + water” combinations including pure water and pure THP are given in Supplementary Materials Table S2. The Δ

_{mix}G values for PPN at m = 0.6–1.0 were found as negative values, which decreased with the increase in temperature. Hence, PPN dissolution was proposed as endothermic at m = 0.6–1.0. The Δ

_{mix}S values for PPN at m = 0.8–1.0 were found as positive values, which also decreased with increases in temperature. Therefore, PPN dissolution was proposed as entropy-driven at m = 0.8–1.0. The Δ

_{mix}H values for PPN were found as negative values in most of the “THP + water” combinations studied.

#### 2.4. Solute–Solvent Molecular Interactions

_{i}for PPN in different “THP + water” combinations including pure water and pure THP at “T = 298.2–318.2 K” is summarized in Table 2. The γ

_{i}value obtained for PPN was highest in pure water at all five temperatures studied. However, the γ

_{i}value obtained for PPN was lowest in pure THP at all five temperatures. The highest γ

_{i}value for PPN in pure water could be possible due to the lowest x

_{e}value of PPN in pure water. As per these results, the γ

_{i}value for PPN was found to increase with increases in temperature in all “THP + water” mixtures studied. Based on these results, the maximum solute–solvent interactions were considered in PPN–THP compared with PPN–water.

#### 2.5. Modeling of PPN Solubility

_{e}and “Van’t Hoff model solubility (x

^{Van’t})” of PPN is presented in Supplementary Materials Figure S1, which shows good graphical correlation. The root mean square deviations (RMSDs) for PPN in various “THP + water” combinations including pure water and pure THP were recorded as 0.31–1.11% with an average RMSD of 0.65%. In addition, the determination coefficients (R

^{2}) were obtained as 0.9935–0.9985.

_{e}and “Alelblat model solubility (x

^{Apl})” values of PPN are presented in Figure 4, which expressed good graphical correlation.

^{2}values were estimated as 0.9978–0.9999.

## 3. Experimental

#### 3.1. Materials

#### 3.2. PPN Solubility Measurement

_{e}values of PPN were calculated using Equations (1) and (2) [26,27]:

_{1}= PPN mass; m

_{2}= THP mass; m

_{3}= water mass; M

_{1}= PPN molar mass; M

_{2}= THP molar mass and M

_{3}= water molar mass. PPN solubility in pure water and pure THP was computed by applying Equation (1). PPN solubility in “THP + water” mixtures was calculated using Equation (2).

#### 3.3. Computation of HSPs

_{d}= dispersion HSP; δ

_{p}= polar HSP and δ

_{h}= hydrogen-bonded HSP”. The HSPs for PPN, pure THP and pure water were estimated using “HSPiP software (version 4.1.07, Louisville, KY, USA)” [51]. The HSPs of various “THP + water” mixtures free of PPN (δ

_{mix}) were calculated using Equation (4) [26,53] as follows:

_{1}= HSP of pure THP and δ

_{2}= HSP of pure water.

#### 3.4. Mixing Thermodynamics Parameters of PPN Solution

_{mix}G

^{id}), mixing entropy (Δ

_{mix}S

^{id}) and mixing enthalpy (Δ

_{mix}H

^{id})” in different “THP + water” mixtures including pure water and pure THP can be calculated using Equations (5)–(7) [54,55] as follows:

_{1}= PPN mole fraction; x

_{2}= THP mole fraction and x

_{3}= water mole fraction.

_{mix}G, Δ

_{mix}H and Δ

_{mix}S in different “THP + water” mixtures including pure water and pure THP can be calculated using Equations (8)–(10) [54,55,56] as follows:

^{E}= excess Gibbs energy and H

^{E}= excess enthalpy. The G

^{E}and H

^{E}values were computed using the activity coefficient-based Wilson model by applying Equations (11) and (12) [56,57] as follows:

_{i}value for PPN in different THP + water combinations including pure water and pure THP was calculated by applying Equation (13) [58,59,60] as follows:

^{idl}= ideal solubility of PPN which was computed using Equation (14) [58] as follows:

_{p}= difference between the molar heat capacity of solid state and liquid state; T

_{fus}= fusion temperature of PPN and ∆H

_{fus}= fusion enthalpy of PPN [59,61]. The values of T

_{fus}, ∆H

_{fus}and ∆C

_{p}for PPN were taken as 404.88 K, 32.69 kJ mol

^{−1}and 80.74 J mol

^{−1}K

^{−1}, respectively, from reference [38].

#### 3.5. Solute–Solvent Molecular Interactions

_{i}values for PPN in different “THP + water” mixtures and pure solvents at “T = 298.2–318.2 K” were calculated by applying Equation (13) listed above.

#### 3.6. Thermodynamics-Based Computational Models

^{Van’t}value of PPN in different “THP + water” mixtures including pure water and pure THP was calculated by applying Equation (15) [26] as follows:

_{e}of PPN and 1/T. The correlation between x

_{e}and x

^{Van’t}values of PPN was carried out using RMSD and R

^{2}. The RMSDs of for PPN were calculated using its formula reported previously in the literature [27]. The x

^{Apl}value of PPN in various “THP + water” combinations including pure water and pure THP was calculated using Equation (16) [43,44].

_{e}values of PPN summarized in Table 1 [26]. The correlation between x

_{e}and x

^{Apl}values of PPN was again performed using RMSD and R

^{2}. The logarithmic solubility of “Yalkowsky–Roseman model (log x

^{Yal})” for PPN in various “THP + water” mixtures was calculated by applying Equation (17) [45] as follows:

_{1}= mole fraction solubility of PPN in THP; x

_{2}= mole fraction solubility of PPN in water; m

_{1}= THP mass fraction and m

_{2}= water mass fraction.

_{m,T})” of PPN in different “THP + water” combinations was calculated by applying Equation (18) [62,63,64] as follows:

_{i}= model coefficient of Equation (18) which was obtained using “no-intercept regression analysis” [65,66]. Based on the current data set, the trained version of Equation (18) can be expressed using Equation (19).

_{e}and x

_{m,T}of PPN was conducted using RMSD. The “Jouyban–Acree–Van’t Hoff model solubility of PPN (x

_{m,T})” in different “THP + water” combinations was calculated by applying Equation (20) [26,66] as follows:

_{1}, B

_{1}, A

_{2}, B

_{2}and J

_{i}= the model coefficient of Equation (20). Based on the current data set, the trained version of Equation (20) can be expressed using Equation (21).

## 4. Conclusions

## Supplementary Materials

_{mix}/MPa

^{1/2}) for various THP + water mixtures free of PPN at “T = 298.2 K”, Table S2: The values of mixing enthalpy (Δ

_{mix}H/J mol

^{−1}), mixing entropy (Δ

_{mix}S/J mol

^{−1}K

^{−1}), mixing Gibbs energy (Δ

_{mix}G/J mol

^{−1}) and activity coefficient (γ

_{i}) for PPN dissolution in different “THP + water” mixtures.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Sample Availability: Samples of the compound PPN are available from the authors. |

**Figure 2.**Comparison of mole fraction solubility of PPN in (

**A**) pure water and (

**B**) pure Transcutol-HP (THP) with reported solubilities at “T = 298.2 K to 318.2 K”; the symbol shows the experimental mole fraction solubility of PPN in (

**A**) pure water and (

**B**) pure THP, and the symbol shows the reported solubilities of PPN in (

**A**) pure water and (

**B**) pure THP taken from reference [38].

**Figure 4.**Correlation of experimental solubility values of PPN with “Apelblat model” in different “THP + water” mixtures at “T = 298.2–318.2 K”; Apelblat model solubility values of PPN are represented by solid lines, and experimental solubility values of PPN are represented by the symbols.

**Table 1.**Experimental solubilities (x

_{e}) of piperine (PPN) in mole fraction in different “Transcutol-HP (THP) + water” mixtures (m) at “T = 298.2–318.2 K” and “p = 0.1 MPa”

^{a}.

m | x_{e} | ||||
---|---|---|---|---|---|

T = 298.2 K | T = 303.2 K | T = 308.2 K | T = 313.2 K | T = 318.2 K | |

0.0 | 1.03 × 10^{−5} | 1.17 × 10^{−5} | 1.31 × 10^{−5} | 1.47 × 10^{−5} | 1.59 × 10^{−5} |

0.1 | 2.57 × 10^{−5} | 2.85 × 10^{−5} | 3.19 × 10^{−5} | 3.55 × 10^{−5} | 3.80 × 10^{−5} |

0.2 | 6.20 × 10^{−5} | 6.88 × 10^{−5} | 7.61 × 10^{−5} | 8.40 × 10^{−5} | 9.01 × 10^{−5} |

0.3 | 1.59 × 10^{−4} | 1.71 × 10^{−4} | 1.86 × 10^{−4} | 1.99 × 10^{−4} | 2.15 × 10^{−4} |

0.4 | 3.71 × 10^{−4} | 4.07 × 10^{−4} | 4.42 × 10^{−4} | 4.79 × 10^{−4} | 5.09 × 10^{−4} |

0.5 | 9.06 × 10^{−4} | 9.80 × 10^{−4} | 1.08 × 10^{−3} | 1.16 × 10^{−3} | 1.25 × 10^{−3} |

0.6 | 2.23 × 10^{−3} | 2.39 × 10^{−3} | 2.56 × 10^{−3} | 2.74 × 10^{−3} | 2.88 × 10^{−3} |

0.7 | 5.40 × 10^{−3} | 5.74 × 10^{−3} | 6.10 × 10^{−3} | 6.51 × 10^{−3} | 6.80 × 10^{−3} |

0.8 | 1.35 × 10^{−2} | 1.40 × 10^{−2} | 1.47 × 10^{−2} | 1.55 × 10^{−2} | 1.63 × 10^{−2} |

0.9 | 3.26 × 10^{−2} | 3.37 × 10^{−2} | 3.53 × 10^{−2} | 3.70 × 10^{−2} | 3.87 × 10^{−2} |

1.0 | 7.88 × 10^{−2} | 8.12 × 10^{−2} | 8.44 × 10^{−2} | 8.79 × 10^{−2} | 9.10 × 10^{−2} |

x^{idl} | 5.13 × 10^{−2} | 6.02 × 10^{−2} | 7.06 × 10^{−2} | 8.26 × 10^{−2} | 9.63 × 10^{−2} |

^{a}The relative uncertainties u

_{r}are u

_{r}(T) = 0.010, u

_{r}(m) = 0.001%, u(p) = 0.003 and u

_{r}(x

_{e}) = 0.11.

**Table 2.**Activity coefficients (γ

_{i}) of PPN in different “THP + water” mixtures (m) at “T = 298.2–318.2 K”.

m | γ_{i} | ||||
---|---|---|---|---|---|

T = 298.2 K | T = 303.2 K | T = 308.2 K | T = 313.2 K | T = 318.2 K | |

0.0 | 4980.00 | 5150.00 | 5380.00 | 5620.00 | 6050.00 |

0.1 | 1995.20 | 2108.92 | 2215.74 | 2339.59 | 2533.27 |

0.2 | 827.00 | 875.00 | 927.00 | 984.00 | 1070.00 |

0.3 | 322.00 | 353.00 | 380.00 | 416.00 | 448.00 |

0.4 | 138.00 | 148.00 | 160.00 | 173.00 | 189.00 |

0.5 | 56.60 | 61.40 | 65.50 | 71.40 | 77.30 |

0.6 | 23.00 | 25.20 | 27.60 | 30.20 | 33.40 |

0.7 | 5.40 | 5.74 | 6.10 | 6.51 | 6.80 |

0.8 | 3.81 | 4.31 | 4.82 | 5.33 | 5.92 |

0.9 | 1.57 | 1.79 | 2.00 | 2.23 | 2.49 |

1.0 | 0.65 | 0.74 | 0.83 | 0.94 | 1.06 |

m | a | b | R^{2} | RMSD (%) | Overall RMSD (%) |
---|---|---|---|---|---|

0.0 | −4.45 | −2093.60 | 0.9960 | 1.11 | |

0.1 | −4.20 | −1897.30 | 0.9963 | 0.91 | |

0.2 | −3.65 | −1799.00 | 0.9973 | 0.70 | |

0.3 | −3.98 | −1421.50 | 0.9982 | 0.33 | |

0.4 | −2.83 | −1509.30 | 0.9968 | 0.62 | |

0.5 | −1.90 | −1520.50 | 0.9981 | 0.77 | 0.65 |

0.6 | −1.95 | −1238.70 | 0.9985 | 0.42 | |

0.7 | −1.49 | −1112.00 | 0.9973 | 0.42 | |

0.8 | −1.24 | −916.75 | 0.9935 | 0.56 | |

0.9 | −0.64 | −829.34 | 0.9932 | 1.01 | |

1.0 | −0.21 | −696.21 | 0.9960 | 0.31 |

^{b}The average relative uncertainties are u(a) = 0.30 and u(b) = 0.07.

m | A | B | C | R^{2} | RMSD (%) | Overall RMSD (%) |
---|---|---|---|---|---|---|

0.0 | 331.19 | −17,505.00 | −49.84 | 0.9995 | 0.78 | |

0.1 | 224.66 | −12,407.50 | −33.98 | 0.9982 | 0.73 | |

0.2 | 217.93 | −11,974.50 | −32.90 | 0.9993 | 0.58 | |

0.3 | −105.09 | 3214.87 | 15.01 | 0.9988 | 0.57 | |

0.4 | 228.14 | −12,114.70 | −34.29 | 0.9999 | 0.60 | |

0.5 | 45.42 | −3697.43 | −7.02 | 0.9981 | 0.45 | 0.54 |

0.6 | 87.58 | −5351.77 | −13.29 | 0.9991 | 0.34 | |

0.7 | 84.34 | −5054.78 | −12.74 | 0.9981 | 0.44 | |

0.8 | −157.86 | 6268.79 | 23.26 | 0.9978 | 0.61 | |

0.9 | −157.97 | 6388.73 | 23.36 | 0.9985 | 0.45 | |

1.0 | −84.70 | 3179.61 | 12.54 | 0.9982 | 0.47 |

^{c}The average relative uncertainties are u(A) = 0.92, u(B) = 1.54 and u(C) = 0.90.

**Table 5.**Results of “Yalkowsky–Roseman model” for PPN in different “THP + water” mixtures (m) at “T = 298.2–318.2 K”.

m | Log x^{Yal} | RMSD (%) | Overall RMSD (%) | ||||
---|---|---|---|---|---|---|---|

T = 298.2 K | T = 303.2 K | T = 308.2 K | T = 313.2 K | T = 318.2 K | |||

0.1 | −4.59 | −4.54 | −4.50 | −4.45 | −4.42 | 1.21 | |

0.2 | −4.21 | −4.16 | −4.12 | −4.07 | −4.04 | 0.46 | |

0.3 | −3.82 | −3.77 | −3.74 | −3.69 | −3.67 | 2.81 | |

0.4 | −3.43 | −3.39 | −3.35 | −3.32 | −2.29 | 0.91 | |

0.5 | −3.04 | −3.01 | −2.97 | −2.94 | −2.91 | 2.27 | 1.24 |

0.6 | −2.65 | −2.62 | −2.59 | −2.56 | −2.54 | 1.11 | |

0.7 | −2.26 | −2.24 | −2.21 | −2.18 | −2.16 | 0.38 | |

0.8 | −1.88 | −1.85 | −1.83 | −1.81 | −1.79 | 1.31 | |

0.9 | −1.49 | −1.47 | −1.45 | −1.43 | −1.41 | 0.78 |

**Table 6.**Results of “Jouyban–Acree” and “Jouyban–Acree–Van’t Hoff” models for PPN in “THP + water” combinations.

System | Jouyban–Acree | Jouyban–Acree–Van’t Hoff |
---|---|---|

A_{1}–0.21 | ||

PEG-400 + water | J_{i}–14.43 | B_{1}–696.21 |

A_{2}–4.45 | ||

B_{2}–2093.60 | ||

RMSD (%) | 0.42 | J_{i}–16.42 |

0.54 |

Material | Molecular Formula | Molar Mass (g mol^{−1}) | CAS Registry No. | Purification Method | Mass Fraction Purity | Analysis Method | Analysis Method | Source |
---|---|---|---|---|---|---|---|---|

PPN | C_{17}H_{19}NO_{3} | 285.34 | 94-62-2 | None | >0.99 | HPLC | HPLC | Sigma Aldrich |

THP | C_{6}H_{14}O_{3} | 134.17 | 111-90-0 | None | >0.99 | GC | GC | Gattefosse |

Water | H_{2}O | 18.07 | 7732-18-5 | None | - | - | - | Milli-Q |

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**MDPI and ACS Style**

Shakeel, F.; Haq, N.; Alshehri, S. Solubility Data of the Bioactive Compound Piperine in (Transcutol + Water) Mixtures: Computational Modeling, Hansen Solubility Parameters and Mixing Thermodynamic Parameters. *Molecules* **2020**, *25*, 2743.
https://doi.org/10.3390/molecules25122743

**AMA Style**

Shakeel F, Haq N, Alshehri S. Solubility Data of the Bioactive Compound Piperine in (Transcutol + Water) Mixtures: Computational Modeling, Hansen Solubility Parameters and Mixing Thermodynamic Parameters. *Molecules*. 2020; 25(12):2743.
https://doi.org/10.3390/molecules25122743

**Chicago/Turabian Style**

Shakeel, Faiyaz, Nazrul Haq, and Sultan Alshehri. 2020. "Solubility Data of the Bioactive Compound Piperine in (Transcutol + Water) Mixtures: Computational Modeling, Hansen Solubility Parameters and Mixing Thermodynamic Parameters" *Molecules* 25, no. 12: 2743.
https://doi.org/10.3390/molecules25122743