Meloxicam Solubility in Ethanol+Water MixturesAccording to the Extended Hildebrand SolubilityApproach

Diana M. Cristancho • Daniel R. Delgado • Fleming Martınez

Received: 12 October 2012 / Accepted: 29 March 2013 / Published online: 20 August 2013� Springer Science+Business Media New York 2013

Abstract In this work the extended Hildebrand solubility approach (EHSA) was applied

to evaluate the solubility of the analgesic drug meloxicam in ethanol?water mixtures at

298.15 K. An acceptable correlative capacity of EHSA was found using a regular poly-

nomial model in fifth order (overall deviation 0.52 %), where the W interaction parameter

is related to the solubility parameter of the co-solvent mixtures. Nevertheless, the devia-

tions obtained in the estimated solubility with respect to experimental solubility were

similar to those obtained directly by means of an empirical regression of the logarithm of

the experimental solubility as a function of the same polarity index (near to 0.51 %).

Keywords Meloxicam � Binary mixtures � Extended Hildebrand solubility

approach � Solubility parameter

1 Introduction

Meloxicam (MEL, Fig. 1) is an analgesic drug whose physicochemical properties have not

yet been completely studied [1]. In particular, it is known than its solubility in aqueous

media is very low [2]. Thus, it is important to note that cosolvency is the best technique

used in pharmacy for increasing drug solubility [3]. On the other hand, it is clear that

predictive methods of physicochemical properties of drugs, in particular to estimate sol-

ubilities, are very important for industrial pharmacists because they allow optimizing

several design processes [4].

For this reason, this work presents a physicochemical study of the solubility prediction

of MEL in binary mixtures conformed by ethanol (EtOH) and water. The study is based on

the extended Hildebrand solubility approach (EHSA) [5] by using the experimental

D. M. Cristancho � D. R. Delgado � F. Martınez (&)Grupo de Investigaciones Farmaceutico-Fisicoquımicas, Departamento de Farmacia, UniversidadNacional de Colombia, A.A. 14490 Bogota, D. C., Colombiae-mail: fmartinezr@unal.edu.co

123

J Solution Chem (2013) 42:1706–1716DOI 10.1007/s10953-013-0058-y

solubility values and some properties relative to the fusion of this drug. All this physi-

cochemical information has been reported previously in the literature [2]. Thus, this work

expands the previous description about this system which was based on some classical

thermodynamics and preferential solvation procedures [2]. Moreover, it is a continuation of

similar studies developed previously for other analgesic drugs in the same co-solvent

mixtures [6–8]. It is important to keep in mind that the EHSA method has been widely used

to study the solubility of many pharmaceutical compounds as has been recently described

[9]. It is to be remarked that EtOH is the most employed co-solvent to develop liquid

pharmaceutical dosage forms [10].

2 Theoretical

The ideal solubility (Xid2 ) of a solid solute is calculated adequately by means of the

expression:

� log10 Xid2 ¼

DfusH Tfus � Tð Þ2:303RTfusT

ð1Þ

where, DfusH is the fusion enthalpy of the solute, R is the gas constant, Tfus is the melting

point of the solute, and T is the absolute temperature of the solution. On the other hand, the

real solubility (X2) of a solid solute in a liquid solution is calculated adequately by means

of the expression:

� log10 X2 ¼DfusH Tfus � Tð Þ

2:303RTfusTþ log10 c2 ð2Þ

where, log10 c2 is the non-ideality term. The c2 term is the solute activity coefficient and it

is determined experimentally. One method of calculating c2 is in reference to the regular

solutions model proposed by Hildebrand and Scatchard as exposed by Prausnitz et al. [11],

according with:

log10 c2 ¼V2u2

1

2:303RTd1 � d2ð Þ2 ð3Þ

where V2 is the partial molar volume of the solute, u1 is the volume fraction of the solvent

in the saturated solution, and d1 and d2 are the solubility parameters of solvent and solute,

respectively. u1 is calculated as:

u1 ¼V1ð1� X2Þ

V1ð1� X2Þ þ V2X2

ð4Þ

Nevertheless, all the pharmaceutical dissolutions deviate from those predicted by the

regular solution theory which was developed for systems where only London dispersion

NS CH3

OH O

OO

NH

N

SCH3

Fig. 1 Molecular structure ofmeloxicam

J Solution Chem (2013) 42:1706–1716 1707

123

forces are involved. This is because pharmaceutical polar systems can involve self-asso-

ciation of solute or solvent, a solute’s solvation by the solvent molecules, or even com-

plexation between different solute species. The intermolecular attractions can consist of

hydrogen bonding, charge transfer complexes and other types of Lewis acid–base inter-

actions [5]. In this way, Martin et al. developed the EHSA method [12–18]. If the A term,

defined as, V2u21=ð2:303RTÞ, is introduced in the Eq. 2, then the real solubility of drugs can

be calculated from the expression:

� log10 X2 ¼ � log10 Xid2 þ A d2

1 þ d22 � 2W

� �ð5Þ

where the W term is equal to 2Kd1d2 (where, K is the Walker parameter [19]), which

replaces the w12 solvent–solute interaction term in the classical regular solution theory,

which is based exclusively on dispersion forces [5, 11]. The W factor considers all the

possible solvent–solute interactions present in real solutions and it can be calculated from

experimental data by means of:

W ¼ 0:5� d21 þ d2

2 �log10 c2

A

� �ð6Þ

where, c2 is the activity coefficient of the solute in the saturated solution, and it is cal-

culated as Xid2 =X2. The experimental values of the W parameter can be correlated by means

of regression analysis by using regular polynomials as a function of d1, as follows:

W ¼ C0 þ C1d1 þ C2d21 þ C3d

31. . .::þ Cnd

n1 ð7Þ

These empirical models can be used to estimate the drug solubility by means of back-

calculation resolving this property from the specific W value obtained in the respective

polynomial regression.

3 Results and Discussion

The information about polarity and volumetric behavior of EtOH?water mixtures, as a

function of the composition, is shown in Table 1. Volume fractions and Hildebrand sol-

ubility parameters were calculated assuming additive behavior [19, 20]. On the other hand,

the properties of fusion of MEL are as follows: Tfus = 536.7 K and DfusH = 43.9 kJ�mol-1

[2]. Thus, the ideal solubility obtained by using Eq. 1 for this drug at 298.15 K is

3.817 9 10-4, expressed in mole fraction. Table 1 also summarizes the experimental

solubility of MEL expressed in molarity and mole fraction [2]. Figure 2 shows the

experimental solubilities and the calculated solubilities by using the regular solution model

as a function of the solubility parameter of solvent mixtures.

According to Eq. 4, the u1 values are almost equal to 1.000 because the drug

solubility is extremely low in all the solvent systems considered (the molar volume of

MEL calculated according to Fedors and other authors [21, 22] is 189.1 cm3�mol-1,

Table 2). It is important to keep in mind that ethanol?water mixtures exhibit highly

non-ideal behavior, which implies non-additive volumes. For this reason, the experi-

mental V1 values used in Eq. 4 were taken from the literature [23]. Ultimately, the

activity coefficients of MEL as decimal logarithms are presented in Table 1. These

values were calculated from experimental solubility values and ideal solubilities at

298.15 K.

1708 J Solution Chem (2013) 42:1706–1716

123

In order to calculate the W parameter, the solubility parameter of MEL (d2) is required and

for this reason it was considered as the one of the mixtures with maximum drug solubility in

mole fraction, i.e. 28.2 MPa1/2. On the other hand, the additive method of Fedors and other

authors [21, 22] was also used obtaining the d2 value 30.95 MPa1/2 as shown in Table 2. It is

important to note that these values are different from those reported by Satesh Babu et al. [24]

that vary from 21 to 25 MPa1/2 for this drug. These results demonstrate that the maximum

solubility is not always obtained in mixtures where the solubility parameters of drug and

Table 1 Ethanol?water solvent mixtures composition, Hildebrand solubility parameter of mixtures, me-loxicam solubility expressed in molarity and in mole fraction, and activity coefficient of meloxicam asdecimal logarithm, at 298.15 K

wEtOH u EtOH d1/MPa1/2 MELa log10 c2

mol�L-1 X2 %CVb

0.0000 0.0000 47.80 6.29 9 10-5 1.14 9 10-6 0.98 2.526

0.1000 0.1236 45.17 8.36 9 10-5 1.63 9 10-6 0.52 2.368

0.2000 0.2409 42.67 1.03 9 10-4 2.18 9 10-6 2.64 2.244

0.3000 0.3524 40.29 1.38 9 10-4 3.19 9 10-6 1.44 2.078

0.4000 0.4584 38.04 2.07 9 10-4 5.29 9 10-6 2.23 1.859

0.5000 0.5594 35.89 3.38 9 10-4 9.62 9 10-6 0.44 1.599

0.6000 0.6557 33.83 5.22 9 10-4 1.66 9 10-5 0.71 1.361

0.7000 0.7476 31.88 7.10 9 10-4 2.57 9 10-5 0.84 1.172

0.8000 0.8355 30.00 8.30 9 10-4 3.44 9 10-5 1.45 1.046

0.9000 0.9195 28.21 7.25 9 10-4 3.51 9 10-5 1.35 1.036

1.0000 1.0000 26.50 4.68 9 10-4 2.72 9 10-5 1.54 1.148

a From Delgado et al. [2]b %CV is percentage coefficient of variation in the reported solubility

Fig. 2 Experimental solubility (circle) and calculated solubility according to the regular solutions model ofHildebrand (square) of meloxicam as a function of the solubility parameter in ethanol?water mixtures at298.15 K

J Solution Chem (2013) 42:1706–1716 1709

123

solvent are coincident. Nevertheless, in the next calculations the used value was the one

obtained experimentally from the solubilities (28.2 MPa1/2).

Table 3 summarizes the parameters A, K, and W for MEL in EtOH?water mixtures,

whereas Fig. 3 shows that the variation of the W parameter with respect to the solubility

parameter of solvent mixtures and presents deviations from linear behavior.

The W values were adjusted to regular polynomials in orders from 1 to 5 (Eq. 7).

Table 4 summarizes the coefficients obtained in all the regular polynomials from degrees

one to five. The significant figures in the coefficients and uncertainties are defined

according to the criterion 3–30 [25]. On the other hand, the W values back-calculated by

using the respective polynomials are presented in Table 5. It is quite clear that these values

Table 2 Application of the Fedors method to estimate internal energy, molar volume, and Hildebrandsolubility parameter of meloxicam

Group Group number E/kJ�mol-1 V/cm3�mol-1

–CH3 2 2 9 4.71 = 9.42 2 9 33.5 = 67.0

[C= 4 4 9 4.31 = 17.24 4 9 - 5.5 = - 22.0

–CH= 1 4.31 13.5

Phenylene ring 1 31.9 52.4

–OH 1 29.8 10.0

[C = O 1 17.4 10.8

[N– 1 4.2 -9.0

–NH– 1 8.4 4.5

–N= 1 11.7 5.0

–S– 1 14.15 12.0

–SO2– 1 25.6 19.5

Ring closure 2 2 9 1.05 = 2.1 2 9 16.0 = 32.0

Conjugate bonds 3 3 9 1.67 = 5.01 3 9 - 2.2 = - 6.6

Etotal = 181.18 kJ�mol-1 Vtotal = 189.1 cm3�mol-1

d2 = (181,180/189.1)1/2 = 30.95 MPa1/2

Table 3 A, K, and W experimental parameters of meloxicam in ethanol?water mixtures at 298.15 K

d1/MPa1/2 100 A/cm3�J-1 K/J�cm-3 a Wexpt/J�cm-3 a

47.80 6.58204 0.564130 1520.851

45.17 6.58199 0.549440 1399.648

42.67 6.58194 0.536411 1290.867

40.29 6.58186 0.525236 1193.654

38.04 6.58168 0.515967 1106.871

35.89 6.58136 0.508590 1029.342

33.83 6.58090 0.502897 959.642

31.88 6.58043 0.498803 896.739

30.00 6.58013 0.496267 839.804

28.21 6.58040 0.495051 787.763

26.50 6.58104 0.495132 740.025

a 1 J�cm-3 = 1 MPa

1710 J Solution Chem (2013) 42:1706–1716

123

depend on the model used in the W back-calculation. Similar behaviors have been reported

in the literature for several other compounds in different solvent mixtures [6–9, 12–20].

Table 6 summarizes the solubility values obtained by using the W values obtained by

back-calculation from the polynomial models (Table 4) that are presented in Table 5. In

the same way as was done previously [7–9], because we are searching for the best pro-

cedure, the first criterion used to define the polynomial order of the W term as a function of

d1 is the fitting standard uncertainties obtained, whose values are as follows, 21.89, 0.9407,

0.3888, 0.0805, and 0.0361 (Table 4), for orders one to five, respectively. As another

comparison criterion, Table 6 also summarizes the percentage differences between the

MEL experimental solubility and those calculated by using EHSA.

It is found that the more complex the polynomial used is, the better is the agreement

found between experimental and calculated solubility. Accordingly, the most important

increment in concordance is obtained passing from order 1 to order 2 (From 19.455 to

Fig. 3 W parameter of meloxicam in ethanol?water mixtures as a function of the solubility parameter ofthe solvent mixtures at 298.15 K

Table 4 Coefficients and statistical parameters of regular polynomials in several orders of W as a functionof solubility parameters of cosolvent mixtures free of meloxicam (Eq. 7) in ethanol?water mixtures

Coefficientor parameter

Polynomial order

1 2 3 4 5

C0 -255 (36) 398 (9) 243 (25) -180 (34) 344 (106)

C1 36.4 (1.0) -0.1 (0.5) 13.0 (2.1) 61 (4) -13 (15)

C2 – 0.494 (0.007) 0.13 (0.06) -1.85 (0.16) 2.3 (0.8)

C3 – – 3.2 (0.5) 9 10-3 3.93 (0.29) 9 10-2 -7.4 (2.3) 9 10-2

C4 – – – -2.43 (0.19) 9 10-4 1.3 (0.3) 9 10-3

C5 – – – – -8.3 (1.7) 9 10-6

Adj. r2 0.9919 1.0000 1.0000 1.0000 1.0000

Fit. Error 21.89 0.9407 0.3888 0.0805 0.0361

Values in parentheses are the respective uncertainties

J Solution Chem (2013) 42:1706–1716 1711

123

21.4 %). The concordances also increase in a good way from order 2 to 3 (21.4 to 8.5 %)

and from order 3 to 4 (8.5 to 1.59 %). It is important to note that for pharmaceutical

purposes uncertainties lower than 5 % are useful for practical purposes but for academic

purposes the best agreement is required. In this way, the best improvement is obtained on

passing from order 4 to 5, i.e. from 1.59 to 0.52 %. Thereby, in the following calculations

the model in order 5 was used. Nevertheless, it is interesting to note that the mean

deviation using polynomial of order 5 (0.52 %, Table 6) is lower than that obtained as the

mean in the uncertainties of experimental solubilities (1.28 %, Table 1).

As has been described previously, an important consideration about the usefulness of

the EHSA method is the one referent to justify the complex calculations involving any

other variables, instead of a simple empirical regression of the experimental solubility as

a function of the solubility parameters of solvent mixtures (Table 1; Fig. 4). For this

reason, in Table 7 the experimental solubilities are compared to those calculated directly

by using a regular polynomial of log10 X2 in order 5 as a function of the d1 values

(Eq. 8, with adjusted determination coefficient r2 = 0.9999 and fitting standard uncer-

tainty = 0.0047), and also to those calculated involving the W parameters obtained from

Eq. 7 adjusted to order 5 (Tables 4, 5). The respective difference percentages are also

presented in Table 7.

log10 X2 ¼� 10ð14Þ � 1:8ð2:0Þd1 þ 0:23ð0:11Þ � 10�2d21 � 1:0ð0:3Þ � 10�3d3

1

þ 1:7ð0:4Þ � 10�4d41 � 1:10ð0:22Þ � 10�6d5

1ð8Þ

Based on mean deviation percentages presented in Table 7 (0.51 and 0.52 % for direct

calculation and the EHSA method, respectively), it follows that no significant difference is

found between the values obtained by using both methods. It is notable that similar

uncertainties are obtained when polynomial in orders 3 and 4 of log10 X2 versus d1 are

used, i.e. 8.5(± 4.1) and 1.59(± 0.88) %, respectively. These results show a non-signifi-

cant usefulness of the EHSA method for practical and academic purposes. Nevertheless, it

is necessary to keep in mind that this method considers the drug solubility from a

Table 5 W parameters (J�cm-3) of meloxicam back-calculated by using several polynomial models formeloxicam in ethanol?water mixtures at 298.15 K

d1/MPa1/2 Polynomial order

1 2 3 4 5

47.80 1484.823 1520.099 1521.211 1520.887 1520.854

45.17 1388.998 1399.570 1399.106 1399.555 1399.648

42.67 1298.075 1291.538 1290.587 1290.877 1290.861

40.29 1211.688 1194.606 1193.824 1193.735 1193.665

38.04 1129.504 1107.557 1107.264 1106.931 1106.897

35.89 1051.226 1029.328 1029.590 1029.264 1029.296

33.83 976.580 958.985 959.680 959.570 959.636

31.88 905.320 895.710 896.571 896.758 896.792

30.00 837.220 838.780 839.439 839.818 839.779

28.21 772.075 787.557 787.574 787.833 787.757

26.50 709.697 741.475 740.361 739.980 740.030

1 J�cm-3 = 1 MPa

1712 J Solution Chem (2013) 42:1706–1716

123

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J Solution Chem (2013) 42:1706–1716 1713

123

systematic physicochemical point of view. Moreover, it is necessary to find an effective

method to calculate the Walker K parameter in order to calculate the W term according to

the expression 2Kd1d2, because then the d1 and d2 terms should be known, and thus, the

drug experimental solubility could be calculated in any mixture.

On the other hand, it is very interesting to note that this drug exhibits positive and

negative deviations with respect to the ideal log–linear additive model proposed by Yal-

kowsky and Roseman [3] according to the mixture’s polarity (dotted line in Fig. 4). This

Fig. 4 Logarithmic solubility (base 10) of meloxicam in ethanol?water mixtures as a function of thesolubility parameter of the solvent mixtures at 298.15 K. Dotted line is the additive solubility behavior

Table 7 Comparison of the meloxicam solubility values in ethanol?water mixtures calculated directly andby using the EHSA at 298.15 K

d1/MPa1/2 X2 % Dev.d

Expt. Calc. direct.a Calc. Wc Calc. direct. Calc. W

47.80 1.14 9 10-6 1.14 9 10-6 1.14 9 10-6 0.04 0.10

45.17 1.63 9 10-6 1.63 9 10-6 1.63 9 10-6 0.04 0.00

42.67 2.18 9 10-6 2.17 9 10-6 2.17 9 10-6 0.21 0.18

40.29 3.19 9 10-6 3.20 9 10-6 3.20 9 10-6 0.29 0.31

38.04 5.29 9 10-6 5.33 9 10-6 5.33 9 10-6 0.78 0.80

35.89 9.62 9 10-6 9.49 9 10-6 9.49 9 10-6 1.39 1.39

33.83 1.66 9 10-5 1.66 9 10-5 1.66 9 10-5 0.18 0.18

31.88 2.57 9 10-5 2.61 9 10-5 2.61 9 10-5 1.61 1.61

30.00 3.44 9 10-5 3.41 9 10-5 3.41 9 10-5 0.76 0.76

28.21 3.51 9 10-5 3.50 9 10-5 3.50 9 10-5 0.19 0.19

26.50 2.72 9 10-5 2.72 9 10-5 2.72 9 10-5 0.16 0.16

Mean valueb 0.51 0.52

Standard deviationb 0.55 0.55

a Calculated using Eq. 8b Calculated considering the obtained values in the neat solvents and the nine binary mixturesc Calculated using Eq. 7 adjusted to order 5 (Tables 4 and 5)d Calculated as 100 9 jX2 (expt.) - X2 (calc.)j/X2 (expt.)

1714 J Solution Chem (2013) 42:1706–1716

123

behavior is similar with respect to the one observed for Rubino and Obeng [26] who found

negative deviations in water-rich mixtures and positive deviations in propylene glycol-rich

mixtures by studying the solubility of a homologous series of alkyl p-hydroxybenzoates

and p-aminobenzoates. It is also similar with respect to the ones reported for ibuprofen,

naproxen, ketoprofen, indomethacin, and piroxicam, in EtOH?water mixtures [27–30]

where negative and positive deviations were also found in water-rich and cosolvent-rich

mixtures, respectively.

A possible explanation for negative deviations observed in the drug solubility at low

cosolvent proportions can be found in the research reported by Kimura et al. [31], where

similar behavior was found for the dissolution enthalpies of 1-methyl-2-pyrrolidinone in

EtOH?water mixtures. According to these investigators, at low cosolvent concentrations

the water retains its ability to form ordered structures.

Although alcohols of low molar masses have been considered as polar compounds,

Matsumoto et al. [32], based on excess molar enthalpy values, have presented some evidence

about the influence of the ending methyl group on the water structure formation. The inter-

actions present between alcohols and water could diminish the interactions between water

and the drug leading to lower solubility values as expected according to the log-linear model.

On the other hand, at high cosolvent concentrations in the mixtures, the tridimensional

structure of water is lost and therefore the water molecules should be available to interact

with the drug molecules. This would lead to larger solubilities than those expected

according to the log–linear model. According to the literature another plausible explana-

tion to positive deviations to the log–linear equation could be due to possible drug asso-

ciation in the saturated solution [26]. Nevertheless, to verify this it would be necessary to

dispose of any other kind of experimental evidence, such as organic solvent/water drug

distribution coefficients at several concentrations and temperatures [33].

4 Conclusion

In this investigation the EHSA method has been adequately used to study the solubility of

meloxicam in ethanol?water mixtures. In particular, a good predictive character has been

found by using a regular polynomial of order five for the interaction parameter W as a

function of the solubility parameter of solvent mixtures free of solute. Nevertheless, the

predictive character of EHSA is the same as the one obtained by direct correlation between

solubility and mixtures composition.

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