Measurement and Thermodynamic Modeling of the

Article pubs.acs.org/jced

Measurement and Thermodynamic Modeling of the Solubility of Lamotrigine, Deferiprone, Cefixime Trihydrate, and Cephalexin Monohydrate in Different Pure Solvents from 283.1 to 323.1 K Jaber Yousefi Seyf and Ali Haghtalab* Department of Chemical Engineering, Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran ABSTRACT: The solubility of lamotrigine, deferiprone, cefixime trihydrate, and cephalexin monohydrate (pharmaceutical solutes) were measured in water, methanol, acetonitrile, and ethyl acetate from 283.1 to 323.1 K at atmospheric pressure. Cephalexin monohydrate was unstable and decomposed in ethyl acetate (even at 283.1 K), acetonitrile (at 303.1 K), and methanol (at 313.1 K). The experimental solubility data were correlated using the local composition models such as Wilson, nonrandom two-liquid theory (NRTL), universal quasichemical (UNIQUAC), and segment-based UNIQUAC (UNIQUAC-SAC). Moreover, the two temperature-dependent Buchowski-Ksiazaczak λh and modified Apelblat equations were applied to correlate the present data. The predicted solubility of the present studies using UNIQUAC-SAC model are compared with those have been given for the other solvents, so that one can conclude lamotrigine, deferiprone, cefixime trihydrate, and cephalexin monohydrate presented the highest solubility in acetic acid, acetic acid, formic acid, and acetic acid, respectively.

1. INTRODUCTION From a standpoint of thermodynamics, solubility is as a key parameter for the selection of solvents in the pharmaceutical industry.1 Solubility directly impacts the reaction rates, extraction efficiency, crystallization, and so forth. On the other hand, most of the chemical reactions, particularly in pharmaceutical industry, are taking place in solvent media. The production of pharmaceuticals/fine chemicals is known for its high consumption of raw materials; particularly solvents which are between 80 and 90 mass percent utilization in batch chemical reactions.2,3 From environmental point of view, solvents are the source of 40% of the anthropogenic volatile organic compounds.4 A proper solvent selection in a pharmaceutical process leads to faster product separation and purification, less solvent emission, higher yield, lower total cost, and better material production. In addition, it is imperative that the solubility of drugs remains one of the most challenging aspects in the pharmaceutical industry.5 Considering the importance of the solubility of drugs, in the present study the solubility of the four pharmaceutical solutes which include lamotrigine, deferiprone, cefixime, and cephalexin monohydrate were measured in the selected pure solvents of water, methanol, acetonitrile, and ethyl acetate from 283.1 to 323.1 K at atmospheric pressure. Methanol and acetonitrile presented less severe toxicity solvent (Class 2), and ethyl acetate is as the less toxic solvent (Class 3).6 Although the solubility of lamotrigine and deferiprone in some binary mixtures,7−11 and the cefixime trihydrate in some pure solvents have been reported,12 to the best of our knowledge, the solubility of the present solutes has not been given in water, methanol, acetonitrile, and ethyl acetate so far. These drugs have been widely used in treatment of the various sicknesses so that © XXXX American Chemical Society

lamotrigine as an anticonvulsant drug has been used in the treatment of epilepsy and bipolar disorder, deferiprone as a drug that chelates iron and is used to treat iron overload in thalassemia major, cefixime as a third generation cephalosporin which has been used for the treatment of a number of bacterial infections, and cephalexin monohydrate as an antibiotic that can treat a certain bacterial infection.13 The chemical formula of these drug compounds are shown in Figure 1.

Figure 1. Chemical structure formulas of lamotrigine, deferiprone, cefixime trihydrate, and cephalexin monohydrate.

Activity coefficient parameter is a thermodynamic factor that is used to present the nonideality of a liquid mixture, and activity Received: February 23, 2016 Accepted: May 18, 2016

A

DOI: 10.1021/acs.jced.6b00163 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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and saturated solutions were filtered at isothermal conditions through membrane filters (SIMPLEPURE PTFE/L 0.22 μm) to ensure that the solution is free from fine undissolved crystals. The concentration of solution was measured using double beam spectrophotometers model T80+ UV/vis spectrometer, so that the λmax (wavelength of maximum absorption) were for lamotrigine at 307 nm, deferiprone at 283 nm, cefixime trihydrate at 289 nm, and cephalexin monohydrate at 266 nm following dilution with a certain amount of methanol. All experiments were repeated three times so that the average of solubility is given in this study. To prepare the calibration curve for deferiprone, a sample of 0.025 g of deferiprone was dissolved in 100 mL of methanol. Then, the samples of 25 μL, 50 μL, 100 μL, 200 μL, 300 μL, and 400 μL were taken from the prepared solution and diluted with pure methanol to prepare a 10 mL solution. The absorbance of the standard solutions was measured by UV spectrometer as shown in Figure 2.

shows the effective concentration of a solute in a mixture. This parameter is usually used to take into account the nonideality of pharmaceutical solubility in the different types of the solvents. The Buchowski−Ksiazaczak λh14 and modified Apelblat15 equations are the empirical temperature-dependent solubility relations that have been applied to correlate the solubility of a solute in a liquid mixture. Moreover, the local composition activity coefficient models such as Wilson,16 Non-Randomness Two Liquid theory (NRTL),17 UNIversal QUAsiChemical (UNIQUAC)18 have been widely used in chemical and pharmaceutical industries to compute the phase equilibrium systems such as liquid−liquid equilibria and solid−liquid equilibria. On the other hand, the segmental activity coefficient (SAC) models such as NRTL-SAC and UNIQUAC-SAC19 have been developed to calculation the solubility of pharmaceutical solutes in the different solvents. Using these segmental activity coefficient models allow one to use the conceptual segment numbers so that one can easily predict the solubility of solutes in the approved solvents based on International Conference on Harmonization (ICH)6 of technical requirements for registration of pharmaceuticals for human use. In this work, the UNIQUACSAC model as a practical and predictive model was used to correlate and predict the solubility of the pharmaceutical solutes in the different solvents.

2. EXPERIMENTAL SECTION 2.1. Materials. Methanol, acetonitrile, ethyl acetate, and benzoic acid were supplied from Merck Millipore Company. Cefixime trihydrate and cephalexin monohydrate were purchased from Cosar Company, Iran. Lamotrigine and deferiprone were obtained from Arastoo Company, Iran. All of these reagents were in analytical grade and used without further purification. The specifications of these chemicals together with the lab-made water are presented in Table 1.

Figure 2. (a) The calibration curve and (b) ultraviolet (UV) spectra of deferiprone standard solutions.

3. RESULTS AND DISCUSSION 3.1. Experimental Results. First, to verify the experimental results, the solubility of benzoic acid in water was measured (λmax = 227 nm) as presented in Table 2 and Figure 3 along with

Table 1. Specifications the Chemicals Used in This Work (Samples Were Used without Further Purification and That the Reported Purities Were Stated by the Suppliers) chemical

CAS registry number

water benzoic acid methanol acetonitrile ethyl acetate lamotrigine

7732-18-5 65-85-0 67-56-1 75-05-8 141-78-6 84057-84-1

deferiprone

30652-11-0

cefixime trihydrate

125110-14-7

cephalexin monohydrate

23325-78-2

manufacturer lab-made Merck Millipore Merck Millipore Merck Millipore Merck Millipore Arastoo Company, Iran Arastoo Company, Iran Cosar Company, Iran Cosar Company, Iran

Table 2. Experimental Solubility of Benzoic Acid in Water at Different Temperatures at 101.3 kPaa

analytical mass fraction purity

T (K)

S (g/100 g)

99.9% 99.5% 99.9% 99.9% 99.8% 99.6%

293.1 298.1 303.1 308.1 313.1 318.1

0.253 0.300 0.364 0.419 0.525 0.621

a

The standard uncertainty of T is u(T) = 0.1 K, ur(p) = 0.06, and ur(S) = 0.05. The confidence interval of experimental solubility were calculated at p-value = 0.05.

99.6% 99.6%

the literature data.20−24 As one can see the experimental data deviate significantly from those results were given by Oliveira,21 particularly at temperature above 320 K. However, at the whole temperature range, there are fairly good agreement between the present experimental data and those reported in the literature. The experimental solubility of lamotrigine, deferiprone, and cefixime trihydrate were measured in water, methanol, acetonitrile, and ethyl acetate from 283.1 to 323.1 K. It is worthwhile to mention that the unit operations in the pharmaceutical industry such as extraction, crystallization, and so forth, are carried out at or near room temperature. Marrero and Abildskov have analyzed the distribution of the solubility data points with

99.6%

2.2. Apparatus and Procedures. A 15 mL double jacket vessel coupled with a thermostatic oil bath (Paar Physica VISCOTHERM VT 2) and a magnetic agitator was used to carry out the solubility measurement. The standard uncertainty of temperature was 0.1 K. To carry out solubility measurement, an excess amount of solute with 5 mL of solvent was added to a glass testing tube. The mass standard uncertainty was 0.001 g. Consequently, the solution was heated to the set temperature and held constant for 24 h. Thereafter, the stirring was stopped, B



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tested with unfavorable results. Amoxicillin and penicillin V sodium were not stable in these solvents even at 283.1 K so that they were decomposed. On the other hand, montelukast sodium in ethyl acetate and water were formed as a honey-like solution so that these mixtures become so viscous that the magnetic stirring bars were stopped. Thus, the solubility of these solutes was not determined. The experimental data of the solubility of lamotrigine, deferiprone, cefixime trihydrate, and cephalexin monohydrate in the different pure solvents are presented in Table 3 at 283.1−323.1 K and 0.1 MPa. Also the uncertainties of the solubility data and temperature are shown in this table. The present experimental solubility of deferiprone and lamotrigine were compared with the available data in the literature. The literature solubility of lamotrigine in methanol, ethyl acetate, and water are 8.10 × 10−4, 1.04 × 10−3, and 1.31 × 10−5, respectively.26−29 Our experimental solubility data of lamotrigine in methanol, ethyl acetate, and water are 9.51 × 10−4, 1.78 × 10−3, 0.96 × 10−5, respectively. Results show that there is consistency between the literature and our experimental data. It is worthwhile to note that determination of very low solubilities of solutes may be hampered by problems such as slow equilibration during measurement. The experimental solubility data of deferiprone in water were compared with the literature data30,31 which has been given in Figure 4 and Table 4. As it is shown, there is a close agreement between the present experimental data and those reported in the

Figure 3. Present experimental solubility of benzoic acid in water versus temperature and comparison with those reported in the literature. ▼, literature data;20 ▲, literature data;21 ◀, literature data;22 ▶, literature data;23 ■, literature data;24 ●, the present experiment.

respect to temperature. The important feature is that the half of the experimental solubility data points have been measured at temperature between 290 and 300 K.25 It should be noted that the solubility of cephalexin monohydrate is measured only in water (283.1−323.1 K), methanol (283.1−303.1 K), acetonitrile (283.1 K), and its solubility in ethyl acetate was not accessible, because of decomposition of cephalexin monohydrate in these solvents (decomposition was confirmed by extra peaks in the ultraviolet spectrometer). In addition to the mentioned solutes, amoxicillin, penicillin V sodium, and montelukast sodium solubility were

Table 3. Experimental Data of the Solubility of the Four Drugs in the Four Selected Solvents at 0.1 MPa and the Various Temperatures xexp × 105a T/K

water

283.1 293.1 303.1 313.1 323.1

0.56 ± 0.002 0.80 ± 0.007 1.16 ± 0.007 2.04 ± 0.008 3.01 ± 0.034

283.1 293.1 303.1 313.1 323.1

183.88 ± 0.091 226.76 ± 1.729 310.01 ± 0.091 413.93 ± 8.224 532.22 ± 8.332

283.1 293.1 303.1 313.1 323.1

0.97 ± 0.015 1.45 ± 0.020 2.02 ± 0.005 3.18 ± 0.013 5.09 ± 0.025

283.1 293.1 303.1 313.1 323.1 278.1b 280.1

53.30 ± 0.182 72.10 ± 0.154 82.62 ± 0.209 96.03 ± 0.307 125.33 ± 0.177

methanol Lamotrigine 19.43 ± 0.041 53.48 ± 0.091 143.57 ± 0.367 283.16 ± 0.042 459.17 ± 2.380 Deferiprone 194.25 ± 0.201 347.66 ± 2.633 520.03 ± 4.904 774.66 ± 6.423 1136.12 ± 2.280 Cefixime Trihydrate 635.12 ± 16.202 891.69 ± 7.600 1319.91 ± 31.275 2085.58 ± 33.501 3086.04 ± 38.206 Cephalexin Monohydrate 35.36 ± 0.406 60.55 ± 0.587 95.11 ± 0.281 dc d 23.54 ± 0.281 28.11 ± 0.307

acetonitrile

ethyl acetate

57.03 ± 0.069 68.26 ± 0.354 142.76 ± 1.734 207.41 ± 2.282 304.23 ± 1.277

129.00 ± 1.670 160.74 ± 0.100 205.19 ± 0.101 277.51 ± 1.228 381.33 ± 0.684

18.73 ± 0.189 32.43 ± 0.093 59.90 ± 0.725 90.95 ± 0.353 137.50 ± 1.432

6.77 ± 0.039 10.38 ± 0.020 15.52 ± 0.351 21.81 ± 0.747 31.77 ± 1.403

8.28 ± 0.113 10.48 ± 0.135 12.65 ± 0.084 18.31 ± 0.084 29.24 ± 0.137

5.08 ± 0.097 7.12 ± 0.026 12.87 ± 0.050 17.53 ± 0.097 24.99 ± 0.041

2.37 ± 0.015 d d d d 0.95 ± 0.021 1.52 ± 0.025

d d d d d d d

a exp x = experimental solubility; the standard uncertainty of T is u(T) = 0.1 K, and ur(p) = 0.06. The confidence interval of experimental solubility were calculated at p-value = 0.05. bThe solubility of cephalexin monohydrate was measured at these two low temperatures so that this drug is not stable at high temperatures for the given solvents. cd = decomposed.

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solubility experimental data using the following objective function (OF): N

%ARD = OF =

Table 4. Comparing Experimental Data with Existing Literature Data Sources30,31 (Based on Mole Fraction) literature data30

T (K)

xexp × 105

283.1 293.1

184 227

303.1

310

313.1 323.1

414 532

T (K)

xexp × 105

293.2 298.2 303.2 308.2 313.2

180 190 230 270 320

literature data31 T (K)

xexp × 105

298.15

180

literature.30,31 It should be noted that a slight difference may be due to the influence of impurities and inherent heterogeneity in the energetic content of the crystalline solid.25 3.2. Correlation of the Solubility Data. The solubility of a solute in a solution at a given temperature is calculated through the equality of the activity of the solute in the saturated solution (aeq) and its activity in the pure solid state (as). Thus, through a solid−liquid equilibrium (SLE) framework, the following equation is obtained as32 −ln(xiγi) =

Figure 5. X-ray powder diffraction pattern of cefixime trihydrate.

compare this figure with that is given in the literature.33 Thus, the experimental X-ray diffraction pattern is in good agreement with the reported pattern for cefixime trihydrate. 3.2.1. Correlation the Solubility Data Using Modified Apelblat and Buchowski−Ksią zċ zak λh Equations. The solubility data are correlated using the two empirical temperature-dependent relations. The modified Apelblat equation15 is presented as B ln(x) = A + + C ln(T /K) (T /K) (4)

ΔHt ⎛ 1 1 ⎞ ΔCp ⎛ Tt ⎞ ln⎜ ⎟ ⎜ − ⎟+ R ⎝T Tt ⎠ R ⎝T ⎠ −

⎞ − 1⎟ ⎠ R ⎝T

ΔCp ⎛ Tt ⎜

(1)

where xi stands for the mole fraction of the solute in liquid phase; γi denotes the activity coefficient of the solute; ΔHt, Tt, and ΔCp stand for the molar enthalpy of fusion at the triple point temperature, the triple point temperature, and the difference in solute heat capacity between liquid and solid at the melting point, respectively. Generally, the contributions of ΔCp in eq 1 are negligible, and the triple point can be replaced by the melting point temperature. Therefore, eq 1 can be simplified as ln(xiγi) =

ΔHfus ⎛ 1 B 1⎞ − ⎟=A+ ; ⎜ R ⎝ Tm T⎠ T

A=

(3)

where ARD denotes the percent average relative deviation and N is the number of experimental points. The superscript “cal” and “exp” stand for calculated and experiment, respectively. It should be noted that it may improbable that the crystal hydrate such as cefixime trihydrate and cephalexin monohydrate will be an equilibrium solid phase in nonaqueous solvents. To confirm that the solid phase in equilibrium with the acetonitrile is cefixime trihydrate, the solid−liquid equilibrium of cefixime trihydrate was attained in 60 mL of acetonitrile. 50 mL of upper clear solution was sampled by filtration through a 0.22 μm pore size syringe filter and evaporated in a vacuum drying oven at 45 °C for 48 h. The obtained solid was analyzed by powder X-ray diffraction which is shown in the below figure (Figure 5 in the text). As on can

Figure 4. Present experimental solubility of deferiprone in water versus temperature and comparison with those reported in the literature. ▲, literature data;30 ●, literature data;31 ▼, the present experiment.

present exp. data

xiexp − xical ⎛ 100 ⎞ ⎜ ⎟ ∑ ⎝ N ⎠ xiexp i=1

where A, B, and C are the model parameters. Using this correlation, the values of A, B, and C together with the %ARD for the four drugs soluble in the selected solvents are presented in Table 5. As it is seen, using modified Apelblat correlation the overall deviation is 4.32%. The Buchowski−Ksiaz̨ ċ zak λh relation which is originally proposed by Buchowski14 is an expression which is known as the λh equation. This correlation is written as

ΔSfus , R

⎛1 ⎛ λ(1 − x) ⎞ 1 ⎞ ln⎜1 + ⎟ = λh⎜ − ⎟ ⎝ ⎠ x Tm ⎠ ⎝T

ΔHfus (2) R where the Tm and ΔHfus are not available and the constants of A and B can be regressed by using activity coefficient models through adjusting the interaction energy parameters. For all of the investigated solutes with known melting point of the drugs, simultaneously ΔHfus and the energy parameters for each activity coefficient model are calculated through the optimization of the B=−

(5)

where the parameters λ and h are adjustable parameters which are correlated through the experimental solubility data of the solutes. The parameters of the λ and h together with the %ARD are shown in Table 6. As is seen, the overall percent of the average relative deviation of the calculated solubility for the four solutes in the different solvents is 4.16. Thus, this shows that the λh equation D



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NRTL model:

Table 5. % ARD and the Adjustable Parameters of Modified Apelblat Equation for the Pharmaceutical Solutes in the Different Solvents A water methanol acetonitrile ethyl acetate water methanol acetonitrile ethyl acetate water methanol acetonitrile ethyl acetate water methanol overall

B

C

Lamotrigine −5228.24 −3.40 −5634.84 4.59 −297.47 2.81 −2343.36 0.54 Deferiprone −21.08 −1514.49 3.55 116.13 −8915.82 −16.10 −19.28 −33397.30 4.02 75.01 −6719.86 −10.78 Cefixime Trihydrate 8.66 −3941.98 −1.12 11.18 −4015.79 −0.39 1.60 −2651.61 −0.30 23.82 −4609.24 −3.09 Cephalexin Monohydrate 1.28 −1974.89 −0.33 9.86 −4585.43 −0.30 25.41 −14.38 −12.81 −1.48

m

ln(γi) =

102 ARD

water methanol acetonitrile ethyl acetate water methanol acetonitrile ethyl acetate water methanol acetonitrile ethyl acetate water methanol overall

h

Lamotrigine 0.00 1721221.70 20.03 382.29 0.17 22712.98 0.01 215366.50 Deferiprone 0.13 19940.06 1.53 2537.81 0.08 57736.72 0.03 133049.61 Cefixime Trihydrate 0.00 1743210.61 2.11 1864.34 0.00 803813.50 0.01 299023.78 Cephalexin Monohydrate 0.01 121845.76 1.47 3051.41

m j=1

−αijτij

(7)

(8)

⎛Φ ⎞ Z ⎛θ ⎞ Φ ln γiC = ln⎜ i ⎟ + qi ln⎜ i ⎟ + li − i xi 2 ⎝ xi ⎠ ⎝ Φi ⎠

1.2821 1.8816 2.8134 1.1644

lj =

4.4125 3.5597 7.4004 3.6435

m

∑ xjlj ; j=1

Z (ri − qi) − (ri − 1) 2

m m ⎞ ⎛ θτ j ij ⎟; ln γi R = −qi⎜⎜1 + ln(∑ θτ ) − ∑ j ji m ⎟ ∑ θ τ k kj j=1 j=1 k=1 ⎠ ⎝ qixi rx θi = m ; Φi = m i i ∑ j = 1 qjxj ∑ j = 1 rjxj

3.0452 3.4875 4.3204

The adjustable interaction parameters for these three models are written as ln(Λij) = −

λij − λjj RT

=−

bij Δλ = aij + T RT

(Wilson) (9)

102 ARD

τij = aij +

5.2746 10.4665 7.0605 2.7956

bij T

ln(τij) = aij +

1.3788 2.5137 2.7181 0.7286

(NRTL)

bij

(10)

(UNIQUAC)

T

(11)

where for each local composition model, these adjustable parameters are temperature dependence that can be expressed by the parameter coefficients of aij and bij as presented in eqs 9−11). These parameter coefficients were obtained through regression of the experimental solubility data. In the NRTL model, the constants α and τ are the nonrandomness and interaction parameters, respectively. In this work, a value of 0.2 was used for nonrandomness. In the UNIQUAC model, the variables ϕi, θi, and τij are the volume fraction, area fraction, and interaction parameter between molecule i and j, respectively. The coordination number “Z”, i.e., the number of molecules surrounding the central molecule, is set to 10. The volume and surface area parameters for the present drugs and solvents were calculated by the Bondi method as given in Table 7.

4.2218 3.6219 7.1642 3.8057 2.9548 3.4946 4.1571

Table 7. Volume and Surface Parameters of UNIQUAC Model for the Pharmaceutical Solutes and the Four Solvents solute lamotrigine deferiperone cefixime trihydrate cephalexin monohydrate

m

xi Λik m ∑ j = 1 xj Λij i=1

j=1

m ⎛ ∑r = 1 xrτrjGrj ⎞ ⎜ ⎟ τ − ij m m ∑l = 1 Gljxl ⎟⎠ ∑l = 1 Gljxl ⎜⎝

xjGij

ln γi = ln γiC + ln γi R

could well correlate the experimental data rather better than the modified Apelblat equation. 3.2.2. Correlation the Solubility Using the Local Composition Activity Coefficient Models. To correlate the solubility data of the present drugs in the solvents, one needs to take into account the nonideality of the liquid solution through an accurate activity coefficient function. In this work, the three activity coefficient models such as Wilson,16 NRTL,17 and UNIQUAC18 are used that are presented as Wilson model: ln(γk) = 1 − ln(∑ xj Λkj) −

m

∑

UNIQUAC model:

Table 6. % ARD and the Adjustable Parameters of Buchowski−Ksiaz̨ ċ zak λh Equation for the Pharmaceutical Solutes in the Different Solvents λ

+

∑i = 1 Glixl

Gij = e

5.4630 11.6675 7.0018 3.6636

m

∑ j = 1 τjiGjixj

r

q

solvent

r

q

7.469 5.104 16.501 12.455

4.544 4.364 14.900 10.288

water methanol acetonitrile ethyl acetate

0.920 1.431 1.870 3.479

1.400 1.432 1.724 3.116

Having the melting temperature for each drug, these parameters together with enthalpy of fusion for each solvent were obtained through the regression of the solubility data. It should be noted

∑

(6) E



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Table 8. % ARD and the Adjustable Parameters of Wilson Activity Coefficient Model for the Pharmaceutical Solutes in the Different Solvents b21

ΔHm (kJ/mol)

102 ARD

Lamotrigine −2305.51 208.84 244.03 640.27

−2269.32 −82.33 1446.26 474.58

7.2061 63.7047 54.1976 28.0958 38.3011

4.3765 8.9264 7.7421 3.4635

−3.19 −0.41 −22.54 −25.80

Deferiprone 232.53 213.87 −1779.32 2433.61

241.40 149.86 1648.67 −1249.21

23.6284 35.6668 22.5382 49.6364 32.8674

1.4021 2.4913 2.7943 0.6994

−15.68 −1.75 −7.28 −2.44

9.78 1.44 −0.42 −7.50

Cefixime Trihydrate 3627.93 31.97 398.58 −483.19

−3088.30 −63.38 463.15 23.85

44.05752 36.6060 32.8222 26.1810 34.9167

1.6402 4.1634 6.4146 3.8063

−5.01 0.69

2.77 −0.61

Cephalexin Monohydrate 518.96 50.86

−1157.45 80.32

16.2632 38.3191 27.2912

2.7740 3.4952

a12

a21

water methanol acetonitrile ethyl acetate overall

−2.09 −1.74 0.14 −3.61

5.56 1.90 −4.29 −2.08


−1.48 0.23 2.29 −7.06

water methanol acetonitrile ethyl acetate overall water methanol overall overall

b12

3.8707

Table 9. % ARD and the Adjustable Parameters of NRTL Activity Coefficient Model for the Pharmaceutical Solutes in the Different Solvents b21

ΔHm (kJ/mol)

102 ARD

Lamotrigine 293.98 220.99 132.99 262.16

−120.33 258.74 131.58 28.93

34.3801 58.9203 29.9522 19.2613 35.6285

5.2987 10.0845 7.0679 3.6093

0.83 −0.86 1.32 2.82

Deferiprone 122.82 476.18 86.62 195.76

93.19 119.17 69.33 −67.54

20.1361 28.3591 36.8675 29.0372 28.6000

0.3983 2.5840 2.6807 0.7123

4.51 0.68 0.52 −1.26

4.46 −1.67 5.12 7.25

Cefixime Trihydrate 72.75 −144.88 196.62 −648.40

−80.81 252.76 −137.96 555.76

30.6056 31.9028 21.3668 43.5478 31.8558

4.3257 3.7060 7.3532 3.9617

−1.40 2.72

4.22 −2.60

Cephalexin Monohydrate 528.98 209.23

176.04 321.50

10.1793 34.4719 22.3256

2.9665 3.4956

a12

a21


0.37 −2.04 0.95 0.90

5.41 −1.44 0.55 1.91


1.08 −0.69 1.21 0.76


b12

4.1603

results for these three models are 3.87, 4.16, and 4.02, for Wilson, NRTL, and UNIQUAC models, respectively. As one can see the Wilson model presents better results in respect to the other local composition models, even this model is more accurate than the modified Apelblat and λh correlations. Thus, the performance of these models in correlation of the experimental solubility data can be ordered as Wilson > UNIQUAC > λh > NRTL > modified Apelblat. Figure 6 presents the calculated and experimental solubility

that the enthalpy of fusion for each solute was obtained by optimization in each solvent so that the different enthalpy of fusion is calculated for each solute in the different solvents. Using the Wilson, NRTL, and UNIQUAC activity coefficient models, Tables 8−10 present %ARD, the adjustable parameter coefficients (a12, a21, b12, b21) and the fusion enthalpy for the lamotrigine, deferiprone, cefixime trihydrate, and cephalexin monohydrate in the different solvents. As shown in these tables, the overall %ARD F



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Table 10. % ARD and the Adjustable Parameters of UNIQUAC Activity Coefficient Model for the Pharmaceutical Solutes in the Different Solvents b21

ΔHm (kJ/mol)

102 ARD

Lamotrigine −191.09 134.71 247.16 105.40

182.72 80.04 121.96 167.48

40.9510 70.2687 41.0917 28.4986 45.2025

5.2954 10.4655 7.0552 3.6075

0.00 −0.74 −0.03 −0.38

Deferiprone 244.30 −260.24 115.46 101.55

44.88 657.98 75.10 102.69

31.4744 55.7799 41.2185 36.6241 41.2742

1.1302 2.5160 2.6762 0.7132

−1.27 −0.55 −1.20 −1.38

0.03 −0.41 −0.28 0.07

Cefixime Trihydrate 96.73 14.86 131.78 120.80

45.26 90.22 69.09 87.03

40.0822 31.4819 37.2212 46.9233 38.9271

4.2476 1.3693 7.2354 3.7840

−0.88 −1.29

0.05 0.14

Cephalexin Monohydrate 168.18 −23.93

121.88 122.47

35.6772 48.0749 41.8760

2.7876 3.3891

a12

a21


−1.76 −0.81 −0.77 −1.24

1.01 1.10 −0.21 −0.02


−0.66 −0.06 −2.25 −1.22


b12

4.0194

Figure 6. Calculated and experimental solubility of lamotrigine in (a) water, (b) methanol, (c) acetonitrile, and (d) ethyl acetate using the two correlations, local composition models and the UNIQUAC-SAC.

the present solvents have been already given.19 The results of the %ARD, enthalpy of fusion, and the values of the segments for the solutes are presented in Table 11. As one can see the overall ARD is 29.20% using UNIQUAC-SAC model that shows a more deviation respect to the other models. However, one should pay attention that this model is a semi predictive model so that it can be used for prediction of the solubility of the same solutes in the other different solvents by using only the obtained enthalpy of fusion, X, Y−, Y+, and Z which have been once already calculated without optimization of the new parameters, while the other models need the new experimental data to obtain the interaction parameters for these new solvents. Therefore, using the data of Table 11, the solubility of the present solutes was predicted in the 62 solvents which are common in the pharmaceutical industry. The prediction results are shown in Figure 7. It should be noted that the provided data are the predicted solubility so that they should be checked by the experimental data to verify the performance of the present segment model. On the other hand, each of the conceptual segments represents the nature of the given segments in the both solute and solvent. In this case,

of lamotrigine in water, methanol, acetonitrile, and ethyl acetate using the two correlations, local composition models and the UNIQUAC-SAC. 3.2.3. Correlation and Prediction Solubility Using the UNIQUAC-SAC Equation. Chen and Song developed a segment-based activity coefficient model as NRTL-SAC for calculation and prediction solubility of the nonelectrolyte solutes.5 Following the segment-based approach with the modification of the reference pure segments of NRTL-SAC, Haghtalab and Yousefi Seyf developed UNIQUAC-SAC which has been used for calculation and prediction of many solutes in the various solvents.19 In these segmental models the parameters of X, Y−, Y+, and Z are used as the conceptual values for the pure hydrophobic, polar attractive, polar repulsive, and hydrophilic segments, respectively. The values of these segments are determined through the optimization of experimental solubility data. In this work, the UNIQUAC-SAC segment model was applied to calculate simultaneously enthalpy of fusion, and the conceptual segments, through optimization of the present solubility data. One should be noted that the conceptual segments for G



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Table 11. Segment Parameters and the Deviation in the Solubility between the Regressed and Experimental Values Using the UNIQUAC-SAC Model solute 34

lamotrigine deferiprone25 cefixime trihydrate33 cephalexin monohydrate35 overall a

Deviation =

1 N

Tm (K)

ΔHm (kJ/mol)

X

Y−

Y+

Z

deviationa

102 ARD

491.00 545.15 494.65 599.95

39.031 33.048 45.315 42.328

0.4661 0.1176 0.9222 0.0622

0.1556 0.5289 0.9703 1.0366

0.2237 0 0 0

0.1784 0.9456 1.5972 0.6610

0.3158 0.1353 0.6153 0.2803 0.3367

28.1252 9.9813 57.5127 21.1640 29.1958

⎡ ⎛ xiexp. ⎞⎤2 ⎟ ∑i ⎢ln⎜ pred. ⎥ ⎣ ⎝ xi ⎠⎦

Figure 8. Predicted solubility (UNIQUAC-SAC) and experimental solubility of cefixime trihydrate in (a) ethanol, (b) 2-propanol, (c) 1-butanol, (d) 2-butanol, (e) 1-pentanol, and (f) acetone from 278.15 to ⎡ ⎛ xiexp. ⎞⎤2 1 ⎟ . 323.15 K. dev = N ∑i ⎢ln⎜ pred. ⎥ ⎣ ⎝ xi ⎠⎦

Figure 7. Predicted solubility of (a) lamotrigine, (b) deferiprone, (c) cefixime trihydrate, and (d) cephalexin monohydrate in food and drug administration (FDA)6 approved solvents.

Figure 9. Predicted solubility (UNIQUAC-SAC) versus the experimental solubility of deferiprone in the different solvents.

lamotrigine presents the considerable contributions from the all four conceptual segments, i.e., X, Y−, Y+, and Z, so that as shown in Figure 7, the predicted results demonstrate that this drug can dissolves in the wide range of the solvents. However, as one can see from Figure 7b,c,d, the deferiprone, cefixime trihydrate, and cephalexin monohydrate present a limited contribution of the segments so that the values of some conceptual segments are negligible in these drugs that lead to the limited solubility of these solutes in the certain solvents. As a result, the UNIQUAC-SAC model can be used as a practical thermodynamic model so that it could be easily applied in the conceptual design of the pharmaceutical processes.

To evaluate the prediction ability of the UNIQUAC-SAC model, the solubility of cefixime trihydrate was predicted in ethanol, 2-propanol, 1-butanol, 2-butanol, 1-pentanol, and acetone and were compared with those data have been given in literature data as shown in Figure 8.12 As one can observe, from engineering and practical point of view, the predicted values are in good agreement with the experimental data. Figure 9 presents the predicted solubility (UNIQUAC-SAC) versus the experimental solubility of deferiprone in the different solvents. As it is seen, the calculated values are in very good agreement with the experiment. H



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(13) Sweetman, S. C. Martindale: the complete drug reference; Pharmaceutical Press: London, 2009. (14) Buchowski, H.; Ksiazczak, A.; Pietrzyk, S. Solvent activity along a saturation line and solubility of hydrogen-bonding solids. J. Phys. Chem. 1980, 84, 975−979. (15) Apelblat, A.; Manzurola, E. Solubilities ofo-acetylsalicylic, 4aminosalicylic, 3,5-dinitrosalicylic, andp-toluic acid, and magnesiumDL-aspartate in water from T = (278 to 348) K. J. Chem. Thermodyn. 1999, 31, 85−91. (16) Wilson, G. M. Vapor-Liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127− 130. (17) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135−144. (18) Abrams, D. S.; Prausnitz, J. M. Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems. AIChE J. 1975, 21, 116−128. (19) Haghtalab, A.; Yousefi Seyf, J. Vapor-Liquid and Solid-Liquid Modeling with a Universal Quasichemical Segment-Based Activity Coefficient Model. Ind. Eng. Chem. Res. 2015, 54, 8611−8623. (20) Wang, H.; Wang, Q.; Xiong, Z.; Chen, C.; Shen, B. Solubilities of benzoic acid in binary (benzyl alcohol+benzaldehyde) solvent mixtures. J. Chem. Thermodyn. 2015, 83, 61−66. (21) Oliveira, A. C.; Coelho, M. G.; Pires, R. F.; Franco, M. R. Solubility of Benzoic Acid in Mixed Solvents. J. Chem. Eng. Data 2007, 52, 298−300. (22) Kong, M.-Z.; Shi, X.-H.; Cao, Y.-C.; Zhou, C.-R. Solubility of Imidacloprid in Different Solvents. J. Chem. Eng. Data 2008, 53, 615− 618. (23) Apelblat, A.; Manzurola, E.; Abo Balal, N. The solubilities of benzene polycarboxylic acids in water. J. Chem. Thermodyn. 2006, 38, 565−571. (24) Strong, L.; Neff, R.; Whitesel, I. Thermodynamics of dissolving and solvation processes for benzoic acid and the toluic acids in aqueous solution. J. Solution Chem. 1989, 18, 101−114. (25) Dechema, Gesellschaft für Chemische Technik und Biotechnologie. Solubility and related properties of large complex chemicals. Dechema: Frankfurt am Main; 2003. (26) Farjami, A.; Jouyban, A. Lamotrigine Solubility in Some Nonaqueous Solvent Mixtures at 298.2 K. J. Chem. Eng. Data 2015, 60, 2490−2494. (27) Shayanfar, A.; Acree, W. E.; Jouyban, A. Solubility of Clonazepam, Diazepam, Lamotrigine, and Phenobarbital in N-Methyl-2-pyrrolidone +Water Mixtures at 298.2 K. J. Chem. Eng. Data 2009, 54, 2964−2966. (28) Shayanfar, A.; Acree, W. E.; Jouyban, A. Solubility of Lamotrigine, Diazepam, Clonazepam, and Phenobarbital in Propylene Glycol+Water Mixtures at 298.15 K. J. Chem. Eng. Data 2009, 54, 1153−1157. (29) Shayanfar, A.; Fakhree, M. A. A.; Acree, W. E.; Jouyban, A. Solubility of Lamotrigine, Diazepam, and Clonazepam in Ethanol +Water Mixtures at 298.15 K. J. Chem. Eng. Data 2009, 54, 1107−1109. (30) Fathi-Azarbayjani, A.; Abbasi, M.; Vaez-Gharamaleki, J.; Jouyban, A. Measurement and correlation of deferiprone solubility: Investigation of solubility parameter and application of van’t Hoff equation and Jouyban-Acree model. J. Mol. Liq. 2016, 215, 339−344. (31) Bretti, C.; Cigala, R. M.; Crea, F.; Lando, G.; Sammartano, S. Thermodynamics of proton binding and weak (Cl−, Na+ and K+) species formation, and activity coefficients of 1,2-dimethyl-3-hydroxypyridin-4one (deferiprone). J. Chem. Thermodyn. 2014, 77, 98−106. (32) Prausnitz, J. M., Lichtenthaler, R. N., de Azevedo, E. G. Molecular thermodynamics of fluid-phase equilibria, 3rd ed.; Prentice Hall: New York, 1999. (33) Okeke, C. C.; Srinivasan, V. S.; Brittain, H. G. Cefixime. In Analytical Profiles of Drug Substances and Excipients, Vol. 25; Brittain, H., Ed.; Academic Press: New York,, 1998; pp 39−83. (34) Beattie, K; Phadke, G; Novakovic, J. Chapter 6Lamotrigine. In: Profiles of Drug Substances, Excipients and Related Methodology, Vol. 37; Harry, G. B., Ed.; Academic Press: Waltham, 2012; pp 245−285. (35) http://www.drugbank.ca/drugs/DB00567, June 13, 2005. Updated on November 30, 2015.

4. CONCLUSION The solubility of the four drugs which include lamotrigine, deferiprone, cefixime trihydrate, and cephalexin monohydrate in four pure solvents, namely, water, methanol, acetonitrile, and ethyl acetate were determined experimentally in an equilibrium glass tube at different temperatures using an ultraviolet spectrometer. The two empirical correlations such as the modified Apelblat and λh were used to obtain a solubility−temperature relation. Moreover, to take into account the nonideality of the liquid mixture, the local composition activity coefficient models such as Wilson, NRTL, and UNIQUAC were applied to determine the solubility data. Also the UNIQUAC-SAC was used to correlate and predict the experimental solubility. It turned out that the Wilson model could give a better satisfactory correlation results than those obtained by the other models. Using the obtained conceptual segment numbers of the present solutes, the solubility of the present drugs were predicted in 62 FDA approved solvents through the UNIQUAC-SAC model. It was shown that the lamotrigine could dissolve in wide range of solvents.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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