Correlation of Solubility and Prediction of the Mixing Properties of

Research Note pubs.acs.org/IECR

Correlation of Solubility and Prediction of the Mixing Properties of Capsaicin in Different Pure Solvents Hao Yan, Zhao Wang,* and Jingkang Wang State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, People’s Republic of China S Supporting Information *

ABSTRACT: Using a static analytical model, experimental solubility data were obtained for capsaicin in n-hexane, cyclohexane, carbon disulfide, butyl ether, and isopropyl ether at temperatures ranging from 278.15 to 323.15 K. The melting temperature and fusion enthalpy of capsaicin were measured using differential scanning calorimetry. The measured solubility data were well correlated by the van’t Hoff, modified Apelblat, λh (Buchowski), Wilson, and NRTL models, with the Wilson model showing the best agreement. The activity coefficients of capsaicin and the mixing Gibbs free energies, enthalpies, and entropies of the resulting solutions were predicted on the basis of the Wilson model parameters at measured solubility points. In addition, the infinite-dilution activity coefficients and excess enthalpies of capsaicin were estimated. Finally, the effects of solute−solvent intermolecular repulsive interactions on the solubility behavior and the values of mixing Gibbs free energy were discussed.

1. INTRODUCTION Capsaicin (C18H27NO3, CAS Registry No. 404-86-4) is the major pungent ingredient in Capsicum annuum;1 its chemical structure is shown in Figure 1. The compound has a bright future, owing to

temperature range from 278.15 to 323.15 K using a static analytical method to determine the proper dissolution/ crystallization solvent and obtain systematic thermodynamic information on the crystallization of capsaicin. The van’t Hoff, modified Apelblat, λh (Buchowski), Wilson, and NRTL models were chosen to correlate the experimental data based on the pure component thermophysical properties (including the mole volume, melting temperature, and enthalpy of fusion). The activity coefficients of capsaicin and the mixing Gibbs free energies, enthalpies, and entropies of solutions were estimated to understand its solubility behavior. Finally, the infinite-dilution activity coefficients and excess enthalpies of capsaicin were calculated.

Figure 1. Molecular structure of capsaicin.

2. EXPERIMENTAL SECTION 2.1. Materials. Capsaicin supplied by Tianjin Shennong Biotechnology Co., Ltd. of China was recrystallized from isopropyl ether several times for further purification. Its mass fraction purity was analyzed by HPLC (type Agilent 1100, Agilent Technologies, USA) and determined to be higher than 98.0%. All of the organic solvents used for the experiments, including n-hexane, cyclohexane, carbon disulfide, butyl ether, and isopropyl ether, were analytical grade reagents (volume fractions were higher than 99.5%) obtained from Tianjin Kewei Chemical Co. in China and used without any treatment. 2.2. Melting Properties Measurements. The melting temperature Tm1 and enthalpy of fusion ΔfusH1 of capsaicin were determined by differential scanning calorimetry (DSC 1/ 500, Metler Toledo, Switzerland) under a nitrogen atmosphere. Precalibration of the temperature and heat flow of the instrument was performed with a high purity indium standard before use. Approximately 5 mg of capsaicin was added to the DSC

its powerful pharmacological properties, for instance, as a topical analgesic against neurogenic pain and inflammation,2 an antimutagenic and antitumorigenic chemoprotector,3 an antioxidant,4 an antimicrobial,5 and a promoter for cardiovascular and respiratory systems.6 However, some impurities in capsaicin extracted from chili peppers have shown mutagenic activities in previous studies,7,8 limiting its clinical application. Thus, the purification process employed to obtain capsaicin of high purity is very significant. In industry, capsaicin goes through several purification and separation processes to purify it; in such processes, solution crystallization and further recrystallization are the key steps.9 The solubility of capsaicin in solvents is of overwhelming importance for the screening of solvents to develop optimized crystallization processes and operation conditions.10,11 Solubility information is also extremely valuable for estimating the crystal characteristics (polymorph and crystal size distribution), toxicity, bioavailability, delivery, metabolism, and drug excretion of the compound.12,13 Although some solubility data on capsaicin in supercritical carbon dioxide during extraction are available,14,15 experimental data in organic solvents are scarce reported. The solubility of capsaicin in n-hexane, cyclohexane, carbon disulfide, butyl ether, and isopropyl ether was measured in the © 2012 American Chemical Society

Received: Revised: Accepted: Published: 2808

December 12, 2011 January 19, 2012 January 20, 2012 January 20, 2012 dx.doi.org/10.1021/ie202917x | Ind. Eng.Chem. Res. 2012, 51, 2808−2813

Industrial & Engineering Chemistry Research

Research Note

same under constant temperature T and pressure P.

pan, which was then heated from 303.15 to 373.15 K at a heating rate of 2 K/min. The uncertainty of the measurement was estimated to be less than 2%. 2.3. Solubility Measurements. The solubility of capsaicin was measured using a static method that was described in a previous work.16 A sealed four-necked flask that contained an excess of capsaicin powder and pure solvent was equilibrated for 8 h at each temperature controlled by a thermostatical bath (type 501A, Shanghai Laboratory Instrument Works Co., Ltd., China) with an uncertainty of ±0.05 K. It was confirmed that 8 h of contact was sufficient to achieve equilibrium. After equilibrium was attained, the upper saturated solution was dried in vacuum over phosphorus pentoxide at 313.15 K for 5 h according to USP32,17 in which condition the solvent can completely evaporate and no solute molecules escaped. The concentration was determined by the gravimetric method using a balance (type AB204, Metler Toledo, Switzerland) with an uncertainty of ±0.0001 g. Samples were analyzed by HPLC to ensure that no thermal decomposition effect had occurred on capsaicin during the experiments. The solubility data obtained represent the average of at least five independent measurements. According to repeated trial and error analyses, the uncertainty of the experimental values was lower than 2%.

f11 (T , P , x1) = f1s (T , P) (4) 1 The fugacity of solute in the liquid phase f1 can be expressed with the help of the activity coefficient

x1γ1(T , P , x1)f11 (T , P) = f1s (T , P)

where γ1 is the activity coefficient of solute in the liquid phase. Further assumptions lead to the following simplified equation depending only on the melting point data of the solute.

ln x1 =

ΔfusH1 ⎛ 1 1⎞ − ⎟ − ln γ1 ⎜ R ⎝ Tm1 T⎠

(6)

Therefore, the thermodynamic equation for the calculation of solubility requires knowledge of the melting temperature, the enthalpy of fusion, and the activity coefficient in the liquid phase of solute considered. A more detailed derivation of eq 6 can be found in the literature.24 Two well-established activity coefficient models were employed to calculate the activity coefficient of solute in this work: the Wilson25 and NRTL26 models. 3.4.1. Wilson Model. In the binary system, the activity coefficient of this model can be expressed as ⎛ ⎞ Λ12 Λ21 ln γ1 = − ln(x1 + Λ12x2) + x2⎜ − ⎟ x2 + Λ21x1 ⎠ ⎝ x1 + Λ12x2

3. THERMODYNAMIC MODELS 3.1. van’t Hoff Equation. The van’t Hoff equation expresses the relationship between the mole fraction solubility of a solute and the temperature in a real solution by taking the solvent effect into account18

(7)

where

⎛ λ − λ11 ⎞ v2 ⎟ and exp⎜ − 12 ⎝ v1 RT ⎠ ⎛ λ − λ 22 ⎞ v ⎟ Λ21 = 1 exp⎜ − 21 ⎠ ⎝ v2 RT

Λ12 =

ΔH o ΔS o + (1) RT R where x1 is the mole fraction solubility of solute in the solvent, T is the corresponding absolute temperature, and R is the gas constant; ΔHo and ΔSo denote the standard enthalpy and entropy of crystallization, respectively.19 3.2. Modified Apelblat Equation. The modified Apelblat equation can also be used to correlate the solubility and the temperature as follows20 B ln x1 = A + + C ln T (2) T where A, B, and C are empirical constants. The values of A and B represent the variation in the solution activity coefficient, and the C value reflects the effect of temperature on the fusion enthalpy.21 3.3. λh (Buchowski) Equation. The measured solubility can be represented by the λh equation, which was originally developed by Buchowski et al.,22 and is given as ln x1 = −

⎛ ⎛1 1 − x1 ⎞ 1 ⎞ ln⎜1 + λ ⎟ = λ h⎜ − ⎟ x1 ⎠ Tm1 ⎠ ⎝ ⎝T

(5)

(8)

in which Δλ12 (= λ12 − λ11) and Δλ21 (= λ21 − λ22) are the cross interaction energy parameters, independent of temperature and composition, and v1 and v2 are the mole volumes of solute and solvent, respectively.27 3.4.2. NRTL Model. In the binary system, the activity coefficient of this model is calculated by 2 ⎤ ⎡ τ21G21 τ12G12 ⎥ ln γ1 = x22⎢ + 2⎥ ⎢⎣ (x1 + G21x2)2 (x2 + G12x1) ⎦

(9)

Here, G12 = exp( −α12τ12) τ12 = (g12 − g22)/RT

and and

G21 = exp(−α12τ21)

(10)

τ21 = (g21 − g11)/RT

(11)

where Δg12 (= g12 − g22) and Δg21 (= g21 − g11) are the cross interaction energy parameters, and parameter α12 is a measure of the nonrandomness of the mixture,28 which generally varies between 0.20 and 0.47.29 In the current study, the optimized α12 values were taken into account in the calculations for the data.

(3)

where λ and h are two model parameters and Tm1 is the melting temperature of capsaicin. The value of λ is identified as the approximate mean association number of solute molecules, which reflects the nonideality of the solution system, and h estimates the excess mixing enthalpy of solution. 23 3.4. Local Composition Models. At phase equilibrium, the calculation criteria require that the fugacity of the solute 1 in the liquid phase l and that in the pure solid phase s be the

4. RESULTS AND DISCUSSION 4.1. Property Evaluation of Pure Components. From the results obtained by DSC analysis, as presented in Figure 2, the melting temperature Tm1 and enthalpy of fusion ΔfusH1 of capsaicin are 338.62 ± 0.5 K and 19.82 kJ/mol, respectively. The entropy of fusion of capsaicin ΔfusS1 can be determined using the identity30

ΔfusS1 = ΔfusH1/Tm,1 2809

(12)

dx.doi.org/10.1021/ie202917x | Ind. Eng.Chem. Res. 2012, 51, 2808−2813


Research Note

Figure 2. DSC curve of capsaicin with a melting temperature of 338.62 K and a fusion enthalpy of 19.82 kJ/mol.

and the value of ΔfusS1 is 58.53 J/(mol·K). The mole volume of capsaicin was calculated from the density of capsaicin, 1.041 g/cm3, which was measured using a pycnometer method,31 and the mole volumes of solvents were the literature values32 listed in the Supporting Information. 4.2. Solubility Data of Capsaicin. The measured mole fraction solubility data of capsaicin in the above-mentioned solvents, which is determined by both temperature and the properties of solvents, are available in the Supporting Information and plotted in Figure 3. For each solvent studied, the solubility of capsaicin increases with temperature, but the systems behave differently. For a given temperature, as a result of the relatively strong polarity of capsaicin (Figure 1), the solubility order is n-hexane ≈ cyclohexane < carbon disulfide < butyl ether < isopropyl ether; that is, capsaicin solubility increases along with the polarities of the solvents.33 The solubility of capsaicin in more polar isopropyl ether is almost 2 orders of magnitude larger than that in n-hexane, while carbon disulfide shows intermediate dissolution, indicating that the solubility behavior of capsaicin is in accordance with the empirical rule “like dissolves like”. Because yield is a very important aspect of industrial profit, butyl ether and isopropyl ether appear to be more appropriate solvents for the crystallization of capsaicin. 4.3. Correlation of the Solubility Data. The van’t Hoff, modified Apelblat, λh, Wilson, and NRTL model parameters were obtained by fitting the experimental solubility data and minimizing the average absolute deviation (AAD). The results are given in the Supporting Information.

1 AAD = N

N

∑ i=1

Figure 3. (a and b) Experimental and modeling solubility of capsaicin in different pure solvents: □, n-hexane; ●, cyclohexane; Δ, carbon disulfide; ■, butyl ether; ○, isopropyl ether. The corresponding lines are calculated values based on the Wilson model.

highly nonideal. In addition, the determined λ, h, and α12 values have a dependence on the polarities of solvents, which indicate that the nonidealities of solutions increase along with the polarities of the solvents. The solute activity coefficients γ1 in a saturated solution can estimate the solute−solvent intermolecular interactions, which is mainly decided by temperature.34 The logarithms of the activity coefficients of capsaicin ln γ1 at measured solubility points are presented in Figure 4. Equation 6 used for these estimates ignores the effect on solubility of the heat capacities difference of the solid and its supercooled liquid form at the solution temperature. As a consequence, activity coefficients of capsaicin in these systems are slightly underestimated.35 The positive values of ln γ1 indicate that the solutions positively deviate from Raoult’s law and that repulsive interactions exist between capsaicin and the solvent molecules. The repulsive interactions decrease with increasing polarities of solvents, directly corresponding to changes in the solubility of capsaicin (Figure 4). 4.4. Prediction of Mixing Properties. For a nonideal solution, the mixing Gibbs free energy ΔG, mixing enthalpy ΔH, and mixing entropy ΔS can be predicted by36

x1, i − x1,cali x1, i

(13)

where N refers to the number of experimental points; x1,i and cal x1,i represent the experimental solubility and calculated solubility, respectively. The overall AADs of the five models are 12.08% (van’t Hoff), 8.73% (Apelblat), 4.42% (λh), 1.37% (Wilson), and 2.27% (NRTL). For the capsaicin systems, the Wilson model is better than the other models in describing the temperature dependence of solubility. The low values of λ and α12 are given in the Supporting Information. The results indicate that there is no obvious association in these weak polar systems, which are not

ΔM = ΔM id + ME 2810



Research Note

values are positive for all solutions studied, they are consistent with the endothermic dissolution and the solute−solvent intermolecular repulsive interactions. The ΔG value of a solution determines the degree of difficulty of dissolution and its inverse process crystallization.39 The ΔG values are negative for all capsaicin systems and plotted in Figure 5, illustrating that the

Figure 4. Logarithm of activity coefficient of capsaicin as a function of temperature at measured solubility points: □, n-hexane; ●, cyclohexane; Δ, carbon disulfide; ■, butyl ether; ○, isopropyl ether. The corresponding lines are calculated values based on the Wilson model.

for

M = G , H , and S

(14)

where ΔMid is the mixing property of an ideal solution and ME is the excess property. If the solution is an ideal system, the mixing enthalpy is equal to 0 (ΔHid = 0), and other mixing properties can be calculated using the relation36

ΔGid = RT (x1 ln x1 + x2 ln x2)

(15)

ΔS id = − R(x1 ln x1 + x2 ln x2) (16) in which x1 and x2 are the respective mole fractions of solute and solvent at a measured temperature. Based on the Wilson model, the expression for the excess properties of a binary mixture is37 G E = RT (x1 ln γ1 + x2 ln γ2) = − x1RT (x1 + x2 Λ12) − x2RT (x2 + x1Λ21)

(17)

⎡ ∂(GE /T ) ⎤ ⎛ Δλ1Λ12 Δλ 2Λ21 ⎞ ⎥ = x1x2⎜ + H E = − T 2⎢ ⎟ x2 + x1Λ21 ⎠ ⎝ x1 + x2 Λ12 ⎣ ∂T ⎦

(18)

S E = (HE − GE)/T

(19)

Figure 5. (a and b) Predicted mixing Gibbs free energy at measured solubility points based on the Wilson model: □, n-hexane; ●, cyclohexane; Δ, carbon disulfide; ■, butyl ether; ○, isopropyl ether.

dissolution of capsaicin in the solvents is a spontaneous process. Lower ΔG values correspond to higher solubility and more favorable dissolution. In addition, the appropriate ΔG values for all solutions indicate that capsaicin can be easily crystallized from the selected solvents. These results are very useful for optimizing the dissolution and crystallization of capsaicin.

Moreover, the logarithm of infinite-dilution activity coefficient ln γ1∞ and the infinite-dilution excess enthalpy H1E,∞ of capsaicin can be respectively obtained as38

ln γ1∞ = − ln Λ12 + 1 − Λ21

(20)

⎡ HE ⎤ ⎛ν ⎞ ⎛ Δλ ⎞ ⎥ H1E, ∞ = ⎢ = Δλ1 + Δλ 2⎜ 1 ⎟ exp⎜ − 2 ⎟ ⎝ RT ⎠ ⎝ ν2 ⎠ ⎣ x1x2 ⎦x → 0

(21)

1

5. CONCLUSIONS Experimental data on the solubility of capsaicin were obtained in n-hexane, cyclohexane, carbon disulfide, butyl ether, and isopropyl ether at temperatures ranging from 278.15 to 323.15 K. DSC was employed to determine the melting temperature Tm1 and enthalpy of fusion ΔfusH1 of the compound. The solubility of capsaicin is dependent on both temperature and the polarities of solvents in the order of n-hexane ≈ cyclohexane < carbon disulfide < butyl ether < isopropyl ether; this behavior is corroborated by solute−solvent intermolecular repulsive interactions and values of mixing Gibbs free energy ΔG.

Substituting the experimental solubility data and the Wilson model parameters into eqs 14−21, the values of ΔG, ΔH, ΔS, ln γ1∞ and H1E,∞ of capsaicin at measured solubility points were estimated and are shown in the Supporting Information. The difference between ln γ1 and ln γ1∞ is small, verifying that the capsaicin systems are not highly nonideal. Since the ΔH 2811



Research Note

γ = activity coefficient γ∞ = infinite-dilution activity coefficient λ = model parameter for the λh equation Δλ12 = cross interaction energy parameter for Wilson equation (λ12 − λ11) (J/mol) Δλ21 = cross interaction energy parameter for Wilson equation (λ21 − λ22) (J/mol)

The measured solubility data were well correlated by the van’t Hoff, modified Apelblat, λh, Wilson, and NRTL models, with the Wilson model showing the best agreement in general. The mixing properties of capsaicin in each solvent were predicted based on the Wilson model parameters. The results indicate that solutions of capsaicin are not highly nonideal, and the dissolution of capsaicin is a spontaneous endothermic process. Ultimately, the data presented in this contribution add to the physicochemical information about capsaicin in selected solvents and are very useful for optimization of the dissolution and purification of capsaicin.

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Subscripts

1 = solute (capsaicin) 2 = solvent (n-hexane, cyclohexane, carbon disulfide, butyl ether and isopropyl ether)

ASSOCIATED CONTENT

Superscripts

* Supporting Information S

Mole volumes of pure components, experimental solubility, optimized parameters for the models, and predicted values of the mixing properties. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

cal = calculated data id = ideal solution l = liquid s = solid

REFERENCES

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Corresponding Author

*Tel.: 86-22-27405754. Fax: 86-22-27374971. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Funding provided by China Ministry of Science and Technology for the key technology of the preparation of edible pigment and industrialization Project No. 2011BAD23B02 is acknowledged.

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NOTATIONS A = empirical constant for the modified Apelblat equation AAD = average absolute deviation B = empirical constant for the modified Apelblat equation C = empirical constant for the modified Apelblat equation f = fugacity Δg12 = cross interaction energy parameter for the NRTL model (g12 − g22) (J/mol) Δg21 = cross interaction energy parameter for the NRTL model (g21 − g11) (J/mol) ΔG = mixing Gibbs free energy (J/mol) GE = excess Gibbs free energy (J/mol) h = model parameter for the λh equation ΔH = mixing enthalpy (J/mol) HE = excess enthalpy (J/mol) HE,∞ = infinite-dilution reduced excess enthalpy (J/mol) ΔHo = standard enthalpy of crystallization (J/mol) ΔfusH = enthalpy of fusion at the melting point (J/mol) N = number of experimental data P = pressure (Pa) R = the gas constant (8.3145 J/mol·K) ΔS = mixing entropy (J/mol·K) SE = excess entropy (J/mol·K) ΔSo = standard entropy of crystallization (J/mol·K) ΔfusS = entropy of fusion at the melting point (J/mol·K) T = temperature (K) Tm = melting temperature (K) v = molar volume (cm3/mol) x = mole fraction in the solution

Greek Letters

α12 = nonrandomness parameter 2812



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Correlation of Solubility and Prediction of the Mixing Properties of

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