Journal of Molecular Liquids 193 (2014) 152–159

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Journal of Molecular Liquids

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Preferential solvation of sulfadiazine, sulfamerazine and sulfamethazinein ethanol + water solvent mixtures according to the IKBI method

Daniel Ricardo Delgado, Fleming Martínez ⁎Grupo de Investigaciones Farmacéutico-Fisicoquímicas, Departamento de Farmacia, Universidad Nacional de Colombia, A.A. 14490, Bogotá D.C. Colombia

⁎ Corresponding author. Tel.: +57 1 3165000x14608;E-mail address: fmartinezr@unal.edu.co (F. Martínez).

0167-7322/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.molliq.2013.12.021

a b s t r a c t

a r t i c l e i n f o

Article history:Received 14 September 2013Received in revised form 19 November 2013Accepted 14 December 2013Available online 27 December 2013

Keywords:SulfonamidesSolubilityEthanol +Water mixturesInverse Kirkwood–Buff integralsIKBIPreferential solvation

The preferential solvation parameters of sulfadiazine, sulfamerazine and sulfamethazine in ethanol + waterbinary mixtures were derived from their thermodynamic properties by means of the inverse Kirkwood–Buffintegrals (IKBI) method. From solvent effect studies, it is found that these sulfonamides are sensitive to solvationeffects, so the preferential solvation parameter by ethanol δxE,S, is negative in water-rich and ethanol-richmixtures but positive in compositions from 0.24 to 0.54–0.58 inmole fraction of ethanol according to the sulfon-amide. It is conjecturable that in water-rich mixtures the hydrophobic hydration around aromatic rings and/ormethyl groups plays a relevant role in the solvation. The more solvation by ethanol in mixtures of similar co-solvent compositions could be due mainly to polarity effects. Finally, the preference of these drugs for water inethanol-rich mixtures could be explained in terms of the bigger acidic behavior of water interacting withhydrogen-acceptor groups in the sulfonamides.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Solubility determination of drugs in all possible co-solvent mix-tures is very important for pharmaceutical and chemical scientistsinvolved in several development stages such as drug purificationand design of liquid medicines [1]. Although co-solvency has beenemployed in pharmacy for centuries it has been recently that themechanisms involved in the processes to increase or decreasedrugs solubility started to be approached from a physicochemicalpoint of view [2].

Sulfonamides are drugs extensively used for the treatment of severalinfections caused by gram-positive and gram-negativemicroorganisms,some fungi, and certain protozoa. Although the advent of the antibioticshas diminished the clinical use of sulfonamides, these drugs still occupyan important place in the therapeutic resources of physicians and veter-inarians [3,4].

Several thermodynamic works have been published about theenthalpic and entropic contributions to the Gibbs energy of solution ofsome sulfonamides in binarymixtures conformed by ethanol or propyl-ene glycol and water [5–9]. Nevertheless, the drug preferentialsolvation, i.e. the co-solvent specific composition around the drugmolecules has not been studied for sulfonamides. Therefore, the maingoal of this paper is to evaluate the preferential solvation of some struc-turally related sulfonamides in ethanol + water co-solvent mixtures,based on well-established thermodynamic definitions. Sulfonamidesunder study were sulfadiazine (SD, Fig. 1, CAS RN: [68-35-9], 4-

fax: +57 1 3165060.

ghts reserved.

amino-N-2-pyrimidinyl-benzenesulfonamide), sulfamerazine (SMR,Fig. 1, CAS RN: [127-79-7], 4-amino-N-(4-methylpyrimidin-2-yl)benzenesulfonamide), and sulfamethazine (SMT, Fig. 1, CAS RN [57-68-1], 4-amino-N-(4,6-dimethylpyrimidin-2-yl)benzenesulfonamide).Thus, this work is similar to the ones presented previously in the litera-ture for some analgesic drugs in co-solvent mixtures [10–13].

The use of inverse Kirkwood–Buff integral (IKBI) is a powerful toolfor evaluating the preferential solvation of non-electrolytes in solventmixtures, describing the local compositions around a solute with re-spect to the different components present in the solvent mixture[14–16].

In the present case, this treatment depends on the values of thestandard molar Gibbs energies of transfer of the sulfonamides fromneat water to the ethanol + water solvent mixtures and the excessmolar Gibbs energy of mixing for the co-solvent binary mixtures.As has been indicated previously, this treatment is very importantin pharmaceutical sciences to understand the molecular interactionsof solute–solvent because most of the solubility studies developedhave been directed towards correlating or modeling the solubilitiesand possibly predicting them from the solubilities in the neat sol-vents, but not to analyzing the local environment around the drugmolecules describing the local fraction of the solvent componentsin the surrounding of solute (S) [17]. As was indicated earlier, inthis paper the IKBI approach is applied to evaluate the preferentialsolvation of the structurally related sulfonamides sulfadiazine, sulfa-merazine and sulfamethazine in the binary mixtures conformed byethanol (E or EtOH) and water (W). The results are expressed interms of the preferential solvation parameter δxE,S of the solute bythe co-solvent ethanol.

Fig. 1.Molecular structure of the sulfonamides analyzed. Sulfadiazine: R1 andR2 = H. Sul-famerazine: R1 = H, R2 = CH3. Sulfamethazine: R1 and R2 = CH3.

153D.R. Delgado, F. Martínez / Journal of Molecular Liquids 193 (2014) 152–159

2. Theoretical

The KBIs (Kirkwood–Buff integrals, Gi,S) are given by the followingexpression:

Gi;S ¼Z rcor

0gi;S−1� �

4πr2dr ð1Þ

Here gi,S is the pair correlation function for the molecules of thesolvent i in the ethanol + water mixtures around the sulfonamide,r is the distance between the centers of themolecules of sulfonamideand ethanol or water, and rcor is the correlation distance for which gi,S(r N rcor) ≈ 1. Thus, for all distances r N rcor up to infinite, the valueof the integral is essentially zero. Therefore, the results are expressedin terms of the preferential solvation parameter δxi,S for the sulfon-amide in solution by the component solvents ethanol and water[17,18]. For ethanol (E) this parameter is defined as

δxE;S ¼ xLE;S−xE ¼ −δxW;S ð2Þ

where xE is themole fraction of ethanol in the bulk solventmixture andxE,SL is the local mole fraction of ethanol in the environment near to thedrug. If δxE,S N 0 then the sulfonamide is preferentially solvated byethanol; on the contrary, if it is b0 the drug is preferentially solvatedby water, within the correlation volume, Vcor = (4π/3)rcor3 , and thebulk mole fraction of ethanol, xE. Values of δxE,S are obtainable fromthose of GE,S, and these in turn, from thermodynamic data of the co-solvent mixtures with the solute dissolved on it, as shown below [16].

Algebraic manipulation of the basic expressions presented byNewman [19] leads to expressions for the Kirkwood–Buff integrals(in cm3 mol−1) for the individual solvent components in terms ofsome thermodynamic quantities as shown in Eqs. (3) and (4). Theseequations show whether S (sulfonamide) is surrounded preferentially

Table 1Gibbs energy of transfer (kJ mol−1) of the sulfonamides from neat water to ethanol + water c

xEtOHa Sulfadiazine Sulfamerazine

293.15 K 303.15 K 313.15 K 293.15 K

0.0000 0.00 0.00 0.00 0.000.0417 −1.09 −1.28 −1.25 −0.740.0891 −2.76 −2.86 −3.13 −2.290.1436 −4.46 −4.77 −4.96 −4.210.2068 −5.99 −6.03 −6.07 −5.730.2812 −7.13 −7.09 −7.04 −7.050.3698 −7.75 −7.76 −7.64 −7.840.4772 −8.22 −8.23 −8.08 −8.360.6101 −8.26 −8.28 −8.17 −8.530.7788 −7.74 −7.79 −7.54 −8.161.0000 −6.83 −6.75 −6.49 −7.36

a xEtOH is the mole fraction of ethanol in the ethanol + water co-solvent mixtures free of su

by molecules of the ethanol (if GE,S N GW,S) or by molecules of thewater (if GE,S b GW,S). Thus, the relative magnitudes of Kirkwood–Buffintegrals GE,S and GW,S, which are measurements of the affinities ofethanol and water for the sulfonamides, determines the preferentialsolvation of these solutes in the binary solvent mixtures of ethanoland water [10,12,17]:

GE;S ¼ RTκT−VS þ xWVWD=Q ð3Þ

GW;S ¼ RTκT−VS þ xEVED=Q ð4Þ

where κT is the isothermal compressibility of the ethanol + water sol-vent mixtures (in GPa−1), VE and VW are the partial molar volumes ofthe solvents in the mixtures (in cm3 mol−1), similarly, VS is the partialmolar volume of solute in these mixtures (in cm3 mol−1). The functionD is the derivative of the standard molar Gibbs energies of transfer ofthe sulfonamide (from neat water to ethanol + water mixtures) withrespect to the solvent composition (in kJ mol−1, as also is RT) and thefunction Q involves the second derivative of the excess molar Gibbsenergy of mixing of the two solvents (GE + W

Exc ) with respect to thewater proportion in the mixtures (also in kJ mol−1) [10]:

D ¼ ∂ΔtrG0S;W→EþWð Þ∂xE

!T;p

ð5Þ

Q ¼ RT−xExW∂2GExc

E;W

∂x2W

!T;p

ð6Þ

Because the dependence of κT on composition is not known for alot of the systems investigated and because of the small contributionof RT κT to the IKBI the dependence of κT on composition could be ap-proximated by considering additive behavior from individual iso-thermal compressibilities of components according to the followingequation [19,20]:

κT;mix ¼Xni¼1

xiκ0T;i ð7Þ

where xi is the mole fraction of component i in the mixture and κT,i0 isthe isothermal compressibility of the pure component i.

Ben-Naim [14] showed that the preferential solvation parameter canbe calculated from the Kirkwood–Buff integrals as follows:

δxE;S ¼xExW GE;S−GW;S

� �xEGE;S þ xWGW;S þ Vcor

ð8Þ

o-solvent mixtures at several temperatures.

Sulfamethazine

303.15 K 313.15 K 293.15 K 303.15 K 313.15 K

0.00 0.00 0.00 0.00 0.00−1.01 −1.19 −1.51 −1.38 −1.68−2.57 −3.00 −3.03 −2.98 −3.60−4.50 −4.89 −4.76 −5.01 −5.54−6.11 −6.37 −6.19 −6.50 −7.03−7.21 −7.60 −7.49 −7.70 −8.25−8.02 −8.30 −8.50 −8.67 −9.18−8.43 −8.80 −9.15 −9.30 −9.69−8.65 −8.84 −9.49 −9.61 −9.88−8.29 −8.45 −9.28 −9.21 −9.52−7.50 −7.82 −8.57 −8.54 −8.79

lfonamide.

-12.00

-10.00

-8.00

-6.00

-4.00

-2.00

0.00

0.00 0.20 0.40 0.60 0.80 1.00xEtOH

Δ trG

° / k

J m

ol -1

Fig. 2. Gibbs energy of transfer of the sulfonamides from neat water to ethanol + waterco-solvent mixtures at 303.15 K. Sulfadiazine: circles. Sulfamerazine: squares.Sulfamethazine: triangles.

154 D.R. Delgado, F. Martínez / Journal of Molecular Liquids 193 (2014) 152–159

The correlation volume, Vcor, is obtained by means of the followingexpression proposed by Marcus [10,17]:

Vcor ¼ 2522:5 rS þ 0:1363 xLE;SVE þ xLW;SVW

� �1=3−0:085� �3

ð9Þ

where rS is the radius of the solute (in nm), calculated as

rS ¼3 � Vm

4 � π� �1=3

ð10Þ

where Vm is themolecular volume of the sulfonamide. However, the de-finitive correlation volume requires iteration, because it depends on thelocal mole fractions. This iteration is done by replacing δxE,S in Eq. (2) tocalculate xE,S

L until an almost non-variant value of Vcor is obtained. Nor-mally, the last differences in the iterated Vcor values should be lowerthan 0.05%.

3. Results and discussion

The solubility of these three sulfonamides in ethanol + watermixtures (Table 1A in Appendix A) was taken from Delgado andMartínez [8,9]. Standard molar Gibbs energy of transfer of thesedrugs from neat water to ethanol + water mixtures is calculatedand correlated to regular quartic polynomials from the drug solubil-ity data by using Eq. (11). Fig. 2 shows the Gibbs energy of transferbehavior at 303.15 K whereas Table 1 shows the behavior at all thetemperatures studied. Polynomials coefficients with their uncer-tainties as well as some statistical parameters are shown in Table 2.

Table 2Coefficients a, b, c, d and e (kJ mol−1) and statistical parameters of Eq. (11) applied to Gibbs enerat several temperatures.

Coefficient Sulfadiazine Sulfamerazine

293.15 K 303.15 K 313.15 K 293.15 K

a 0.25 (0.17) 0.19 (0.15) 0.18 (0.17) 0.37 (0.25)b −41.4 (3.0) −43.2 (2.6) −45.3 (2.9) −37.6 (4.3)c 66.3 (13.7) 77.2 (11.9) 89.0 (13.4) 45.9 (20.1)d −39.8 (22.1) −58.3 (19.1) −76.0 (21.5) −10.4 (32.3)e 7.8 (11.2) 17.3 (9.7) 25.7 (10.9) −5.7 (16.4)r2 0.997 0.998 0.997 0.995Fit. std. err. 0.203 0.176 0.197 0.297

Values in parentheses are standard uncertainties.

The main criteria considered to choose the respective models werethe determination coefficients and the fitting standard uncertainties.

ΔtrG0A;W→EþW ¼ RT ln

xA;WxA;EþW

!¼ aþ bxE þ cx2E þ dx3E þ ex4E ð11Þ

Thus D values are calculated from the first derivative of polynomialmodels (Eq. (12)) solved according to the co-solventmixtures composi-tion. This procedure was done varying by 0.05 in mole fraction of etha-nol. D values are reported in Table A2 in Appendix A.

D ¼ bþ 2cxE þ 3dx2E þ 4ex3E ð12Þ

In order to calculate the Q values the excess molar Gibbs energies ofmixing GE,W

Exc at all the temperatures considered are required. Neverthe-less, normally these values are reported only at one temperature, i.e.298.15 K. For this reason, it is necessary to calculate it at other temper-atures. In this way, GE,W

Exc values were calculated at 298.15 K by usingEq. (13) as reported by Marcus [17]. On the other hand, the GE,W

Exc

values at the other temperatures were calculated by using Eq. (14),where, HE,W

Exc is the excess molar enthalpy of the co-solvent mixtures,T1 is 298.15 K and T2 is one of the other temperatures under consider-ation [15]. In turn, HE,W

Exc values were calculated by using Eq. (15) at298.15 K as also reported by Marcus [17].

GExcE;W ¼ xExW 2907−777 1−2xEð Þ þ 494 1−2xEð Þ2

� �ð13Þ

GExcE;W T2ð Þ ¼ GExc

E;W T1ð Þ−TZ T2

T1

HExcE;Wd

1T

� �≈ T2

T1GExcE;W T1ð Þ þ HExc

E;W 1− T2

T1

� �ð14Þ

HExcE;W ¼ xExW −1300−3567 1−2xEð Þ−4971 1−2xEð Þ2

� �ð15Þ

It is important to note that quartic regular polynomials of GE,WExc as a

function of themole fraction ofwaterwere obtained.Q values at all tem-peratures considered are shown in Table A3 in Appendix A. On the otherhand, this table also shows the RT κT values calculated by assuming ad-ditive behavior of κT (Eq. (7)) with the values 1.153 and 0.457 GPa−1,for ethanol and water, respectively [21].

The partial molar volumes of ethanol and water (Table A4 inAppendix A) were calculated by means of Eqs. (16) and (17) from thedensity (ρ) values of ethanol + water mixtures reported by Jiménezet al. at the temperatures under study [22]. V is the molar volume ofthe mixtures and it is calculated as V = (xE·ME + xW·MW)/ρ. ME andMW are 46.06 and 18.02 g mol−1, respectively.

VE ¼ V þ xWdVdxE

ð16Þ

gy of transfer of the sulfonamides fromneatwater to ethanol + water co-solventmixtures

Sulfamethazine

303.15 K 313.15 K 293.15 K 303.15 K 313.15 K

0.31 (0.22) 0.26 (0.17) 0.07 (0.06) 0.17 (0.14) 0.11 (0.09)−41.4 (3.8) −44.8 (3.0) −41.5 (1.1) −43.8 (2.5) −50.3 (1.5)63.0 (17.8) 74.4 (13.7) 62.6 (5.0) 67.0 (11.5) 91.5 (7.0)−35.2 (28.7) −48.0 (22.1) −38.9 (8.0) −39.9 (18.6) −72.2 (11.2)5.7 (14.6) 10.3 (11.2) 9.1 (4.1) 7.9 (9.4) 22.1 (5.7)0.996 0.998 1.000 0.999 0.9990.264 0.203 0.073 0.171 0.103

Table 3GE,S values (cm3 mol−1) for the sulfonamides in ethanol + water co-solvent mixtures at several temperatures.

xEtOHa Sulfadiazine Sulfamerazine Sulfamethazine

293.15 K 303.15 K 313.15 K 293.15 K 303.15 K 313.15 K 293.15 K 303.15 K 313.15 K

0.00 −455.1 −458.7 −464.4 −441.5 −460.1 −475.8 −484.9 −492.1 −528.00.05 −417.5 −427.4 −439.5 −417.0 −437.5 −460.2 −450.2 −468.1 −505.20.10 −376.5 −387.0 −399.5 −386.8 −404.6 −428.2 −411.8 −433.3 −465.30.15 −335.4 −342.6 −350.8 −353.9 −365.6 −384.4 −373.2 −392.4 −414.20.20 −296.8 −299.2 −301.2 −321.0 −325.4 −336.7 −336.7 −350.5 −360.70.25 −262.2 −260.5 −257.1 −289.7 −288.0 −291.9 −303.9 −311.5 −311.90.30 −232.4 −228.0 −221.4 −261.1 −255.3 −253.7 −275.4 −277.6 −271.60.35 −207.2 −202.0 −194.4 −235.8 −228.1 −223.3 −251.3 −249.3 −240.30.40 −186.3 −181.8 −174.7 −213.7 −206.0 −200.0 −231.1 −226.5 −217.00.45 −169.1 −166.3 −160.7 −194.6 −188.3 −182.6 −214.4 −208.4 −200.10.50 −155.0 −154.5 −150.9 −178.2 −174.4 −169.7 −200.5 −194.1 −188.00.55 −143.8 −145.6 −144.1 −164.4 −163.6 −160.3 −189.1 −182.9 −179.40.60 −135.3 −139.0 −139.3 −153.4 −155.4 −153.7 −179.9 −174.3 −173.40.65 −129.6 −134.5 −136.1 −145.6 −149.6 −149.5 −172.8 −168.2 −169.30.70 −127.4 −132.1 −134.2 −141.9 −146.7 −147.6 −168.2 −164.6 −167.00.75 −128.9 −132.0 −133.8 −142.9 −146.9 −148.3 −166.5 −163.9 −166.40.80 −133.2 −134.4 −135.2 −147.6 −150.0 −151.3 −167.5 −166.0 −167.50.85 −138.6 −138.2 −138.1 −153.6 −154.4 −155.4 −170.0 −169.5 −169.90.90 −143.0 −142.1 −141.6 −158.3 −158.2 −158.8 −172.8 −172.8 −172.50.95 −145.8 −145.1 −144.6 −161.0 −160.6 −160.8 −174.9 −175.0 −174.61.00 −147.2 −147.1 −147.0 −161.7 −161.6 −161.5 −176.2 −176.1 −176.0

a xEtOH is the mole fraction of ethanol in the ethanol + water co-solvent mixtures free of sulfonamide.

155D.R. Delgado, F. Martínez / Journal of Molecular Liquids 193 (2014) 152–159

VW ¼ V−xEdVdxE

ð17Þ

Partialmolar volumes of non-electrolyte drugs such as sulfonamidesare not frequently reported in the literature. This is because of the biguncertainty obtained in its determination due to the low solubilitiesexhibited in particular in aqueous media. For this reason, in a firstapproach the molar volume of these drugs is considered here as in-dependent of co-solvent composition and temperature, just as it iscalculated according to the groups contribution method proposedby Fedors [23] and exemplified by Barton [24]. Thus, these valueswere taken from the literature as follows: 150.0, 164.5, and 179.0cm3 mol−1, for SD, SMR and SMT respectively [8,9].

Table 4GW,S values (cm3 mol−1) for the sulfonamides in ethanol + water co-solvent mixtures at seve

xEtOHa Sulfadiazine Sulfamerazine

293.15 K 303.15 K 313.15 K 293.15 K

0.00 −148.9 −148.8 −148.8 −163.40.05 −190.6 −192.7 −195.2 −202.80.10 −224.8 −229.3 −234.5 −237.90.15 −249.5 −254.6 −260.2 −266.20.20 −264.0 −267.1 −269.8 −286.10.25 −268.8 −268.1 −265.4 −297.00.30 −264.6 −259.6 −251.2 −298.90.35 −252.6 −244.3 −231.2 −292.10.40 −233.2 −223.8 −208.3 −276.50.45 −206.5 −199.2 −183.9 −251.70.50 −172.4 −170.8 −158.4 −216.90.55 −130.2 −138.1 −131.5 −170.90.60 −80.1 −100.5 −101.9 −114.00.65 −24.9 −58.0 −68.6 −49.30.70 27.5 −13.0 −31.3 12.80.75 63.1 26.9 7.2 53.90.80 69.0 50.5 38.4 56.50.85 44.6 50.9 53.2 19.60.90 3.2 33.0 50.3 −39.80.95 −40.3 8.3 37.3 −102.11.00 −77.4 −14.9 22.2 −155.8

a xEtOH is the mole fraction of ethanol in the ethanol + water co-solvent mixtures free of su

Tables 3 and 4 show that the GE,S and GW,S values for all the sulfon-amides are negative with the exception of GW,S for sulfadiazine and sul-famerazine in some ethanol-rich mixtures and mainly in the lowtemperatures. These results show in a first approach that these com-pounds exhibit affinity for both solvents. If the addition of ethanol towater is considered (being the solventmixture less polar as the ethanolproportion increases) the following events happen: i) from neat waterto 0.20 in mole fraction of ethanol (GE,S b GW,S) the solutes SD, SMRand SMT, are surrounded preferentially by molecules of water; ii)from 0.20 to 0.50 in mole fractions of ethanol (GE,S N GW,S) the SD issurrounded preferentially by molecules of ethanol; however for SMRand SMT this composition range of preferential solvation by ethanol iswider (i.e. from 0.20 to 0.55 in mole fraction of ethanol); finally, iii)from this composition up to neat ethanol (GE,S b GW,S) the solutes SD,

ral temperatures.

Sulfamethazine

303.15 K 313.15 K 293.15 K 303.15 K 313.15 K

−163.3 −163.3 −177.9 −177.8 −177.8−206.5 −210.7 −220.2 −223.6 −230.0−244.9 −253.8 −256.0 −264.2 −276.1−273.7 −285.2 −283.3 −295.0 −308.2−290.9 −301.0 −301.5 −313.7 −323.0−296.5 −301.7 −311.1 −320.6 −322.2−292.0 −290.6 −313.1 −317.3 −309.9−279.3 −271.5 −308.3 −306.0 −290.6−260.0 −247.2 −297.5 −288.2 −267.4−234.9 −219.1 −281.1 −265.0 −242.2−204.2 −188.0 −258.6 −236.6 −215.8−167.6 −153.7 −229.6 −202.9 −188.0−124.8 −116.1 −193.2 −163.4 −158.5−77.0 −75.9 −149.8 −118.7 −126.7−29.0 −36.6 −103.3 −72.7 −93.3

7.9 −7.2 −62.7 −34.8 −62.419.6 −0.2 −39.0 −17.9 −41.40.8 −21.4 −37.2 −27.8 −36.5

−37.8 −60.3 −51.7 −56.7 −45.8−80.1 −100.3 −72.9 −90.8 −60.9

−116.1 −131.7 −93.9 −120.8 −74.9

lfonamide.

Table 5Correlation volume (cm3 mol−1) for the sulfonamides in ethanol + water co-solvent mixtures at several temperatures after three iterations.

xEtOHa Sulfadiazine Sulfamerazine Sulfamethazine

293.15 K 303.15 K 313.15 K 293.15 K 303.15 K 313.15 K 293.15 K 303.15 K 313.15 K

0.00 713 713 715 738 739 740 767 768 7690.05 735 735 736 762 762 762 790 791 7900.10 767 768 770 795 795 795 825 825 8240.15 808 811 813 836 838 839 867 869 8700.20 853 857 861 881 885 889 914 917 9210.25 898 902 907 927 932 937 961 966 9710.30 940 945 949 972 976 982 1006 1012 10170.35 979 984 988 1013 1017 1022 1048 1054 10580.40 1015 1020 1024 1051 1055 1059 1088 1093 10970.45 1049 1054 1059 1086 1090 1094 1125 1130 11330.50 1081 1087 1092 1118 1123 1128 1160 1164 11680.55 1111 1119 1125 1149 1155 1160 1194 1197 12020.60 1140 1150 1157 1177 1186 1192 1226 1229 12360.65 1169 1181 1190 1206 1217 1225 1257 1261 12700.70 1199 1212 1222 1236 1249 1258 1289 1293 13040.75 1233 1245 1256 1270 1283 1293 1322 1328 13390.80 1271 1281 1291 1308 1320 1331 1358 1365 13770.85 1311 1320 1329 1350 1361 1372 1397 1405 14160.90 1352 1360 1369 1392 1402 1413 1436 1446 14560.95 1391 1399 1409 1432 1441 1452 1476 1486 14961.00 1428 1438 1448 1468 1478 1489 1514 1524 1535

a xEtOH is the mole fraction of ethanol in the ethanol + water co-solvent mixtures free of sulfonamide.

156 D.R. Delgado, F. Martínez / Journal of Molecular Liquids 193 (2014) 152–159

SMR and SMT, are surrounded preferentially by molecules of water,again.

Solute radii (rS) values required to calculate the correlation vol-umes were calculated from the molecular volumes reported in theliterature as follows: 0.236, 0.251, and 0.268 nm3 for SD, SMR andSMT, respectively [25]. In order to use the IKBI method, the correla-tion volume was iterated three times by using the Eqs. (2), (8) and(9) to obtain the values reported in Table 5. It is important to notethat the last differences in the iterated Vcor values were lower than0.02% as mean. It is interesting to note that these values are almostindependent on temperature in water-rich mixtures but increasesin some extent in ethanol-rich mixtures which could be a conse-quence of the higher molar expansibility of ethanol in comparisonwith water [21].

Table 6δxE,S values of the sulfonamides in ethanol + water co-solvent mixtures at several temperatur

xEtOHa Sulfadiazine Sulfamerazine

293.15 K 303.15 K 313.15 K 293.15 K

0.00 0.0000 0.0000 0.0000 0.00000.05 −0.0202 −0.0210 −0.0219 −0.01860.10 −0.0259 −0.0271 −0.0286 −0.02470.15 −0.0201 −0.0207 −0.0214 −0.02010.20 −0.0090 −0.0088 −0.0086 −0.00950.25 0.0019 0.0022 0.0024 0.00220.30 0.0099 0.0096 0.0088 0.01160.35 0.0139 0.0127 0.0109 0.01730.40 0.0141 0.0124 0.0097 0.01890.45 0.0108 0.0094 0.0065 0.01650.50 0.0047 0.0044 0.0020 0.01050.55 −0.0035 −0.0019 −0.0032 0.00160.60 −0.0129 −0.0090 −0.0087 −0.00910.65 −0.0221 −0.0162 −0.0142 −0.02000.70 −0.0291 −0.0224 −0.0193 −0.02850.75 −0.0312 −0.0259 −0.0228 −0.03140.80 −0.0275 −0.0250 −0.0233 −0.02720.85 −0.0195 −0.0199 −0.0200 −0.01810.90 −0.0108 −0.0128 −0.0139 −0.00860.95 −0.0040 −0.0058 −0.0068 −0.00221.00 0.0000 0.0000 0.0000 0.0000

a xEtOH is the mole fraction of ethanol in the ethanol + water co-solvent mixtures free of su

Table 6 shows the δxE,S values for the sulfonamides at all the tem-peratures studied. It is important to note that these results are basi-cally related with the behavior of the solutes in solution and notwith the uncertainties propagated in the calculation methods. Thisis because the individual uncertainties associated with almost allthe physicochemical properties involved in the calculations arelower than 1.0 or 2.0% [8,9,17,21,22], and therefore, it is expectedthat the propagated uncertainties in δxE,S values do not be greaterthan 5.0%. The values of δxE,S vary non-linearly with the ethanol con-centration in the aqueous mixtures at 303.15 K (Fig. 3). Addition ofethanol to water tends to make negative the δxE,S values of thesulfonamides from the pure water up to the mixture 0.24 in molefraction of ethanol reaching minimum values (near to –0.027) inthe mixture with 0.10 in mole fraction of ethanol. Possibly the

es.

Sulfamethazine

303.15 K 313.15 K 293.15 K 303.15 K 313.15 K

0.0000 0.0000 0.0000 0.0000 0.0000−0.0202 −0.0220 −0.0196 −0.0209 −0.0239−0.0269 −0.0299 −0.0254 −0.0280 −0.0322−0.0213 −0.0234 −0.0201 −0.0222 −0.0248−0.0094 −0.0098 −0.0093 −0.0099 −0.0102

0.0025 0.0029 0.0021 0.0026 0.00290.0111 0.0110 0.0112 0.0118 0.01120.0154 0.0143 0.0171 0.0168 0.01460.0159 0.0136 0.0195 0.0178 0.01420.0132 0.0101 0.0189 0.0157 0.01150.0080 0.0048 0.0156 0.0112 0.00720.0010 −0.0016 0.0101 0.0049 0.0021

−0.0070 −0.0086 0.0031 −0.0025 −0.0033−0.0151 −0.0152 −0.0048 −0.0101 −0.0087−0.0217 −0.0204 −0.0119 −0.0167 −0.0133−0.0247 −0.0224 −0.0165 −0.0202 −0.0163−0.0225 −0.0200 −0.0169 −0.0193 −0.0164−0.0161 −0.0138 −0.0136 −0.0144 −0.0134−0.0086 −0.0070 −0.0085 −0.0081 −0.0088−0.0030 −0.0022 −0.0037 −0.0030 −0.0041

0.0000 0.0000 0.0000 0.0000 0.0000

lfonamide.

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

0.00 0.20 0.40 0.60 0.80 1.00xEtOH

100

δx E,

S

Fig. 3. δxE,S values for the sulfonamides in ethanol + water co-solvent mixtures at303.15 K. Sulfadiazine: circles. Sulfamerazine: squares. Sulfamethazine: triangles.

157D.R. Delgado, F. Martínez / Journal of Molecular Liquids 193 (2014) 152–159

structuring of water molecules around the non-polar groups of thesedrugs (aromatic ring and/or methyl groups, Fig. 1), i.e. hydrophobichydration, contributes to lowering of the net δxE,S to negative valuesin these water-rich mixtures [26,27]. These minimums increase as anegative magnitude with the temperature rising indicating bettersolvation (Table 6).

In the mixtures with composition 0.24 b xEtOH b 0.53–0.58 at303.15 K, the local mole fraction of ethanol is greater than the onein the bulk and it decreases with the temperature increasing. Inthis way, the co-solvent action may be related to the breaking ofthe ordered structure of water (hydrogen bonds) around the non-polar moieties of the drug which increases the solvation of thesulfonamides and has a maximum value near to xEtOH = 0.40, i.e.δxE,S = 0.0197. On the other hand, similitude in polarities betweensolutes and co-solvent mixtures could also be involved in these be-haviors. It is interesting to note that in these mixtures the order inpreferential solvation by ethanol increases with the drug polaritydiminishing as indicated by Hildebrand solubility parameterscalculated according to the Fedors method [23], i.e. sulfamethazine(δS =27.4 MPa1/2) N sulfamerazine (δS = 28.1 MPa1/2) N sulfadiazine(δS = 28.9 MPa1/2) [8,9]. Ultimately, from these ethanol proportionsup to neat ethanol, the local mole fraction of the ethanol decreases,the δxE,S values being negative, as they also are in water-rich mixtures.

Table A1Mole fraction solubility (xS) of the sulfonamides at several temperatures.

xEtOHa Sulfadiazineb Sulfamerazinec

293.15 K 303.15 K 313.15 K 293.15 K

0.0000 3.80E−6 6.49E−6 1.14E−5 1.34E−50.0417 5.94E−6 1.08E−5 1.85E−5 1.81E−50.0891 1.18E−5 2.02E−5 3.79E−5 3.43E−50.1436 2.37E−5 4.31E−5 7.65E−5 7.52E−50.2068 4.43E−5 7.09E−5 1.17E−4 1.40E−40.2812 7.08E−5 1.08E−4 1.70E−4 2.41E−40.3698 9.12E−5 1.41E−4 2.14E−4 3.34E−40.4772 1.11E−4 1.70E−4 2.54E−4 4.13E−40.6101 1.12E−4 1.73E−4 2.64E−4 4.43E−40.7788 9.11E−5 1.43E−4 2.07E−4 3.82E−41.0000 6.26E−5 9.46E−5 1.38E−4 2.74E−4

a xEtOH is the mole fraction of ethanol in the ethanol + water co-solvent mixtures free of sub Data from Ref. [8].c Data from Ref. [9].

These sulfonamides could act in solution as Lewis acids due to thehydrogen atoms present in their –NH2 and –NH– groups (Fig. 1) inorder to establish hydrogen bonds with proton-acceptor functionalgroups in the solvents (oxygen atoms in –OH groups). In addition,these drugs could act as Lewis bases due to free electron pairs in ei-ther i) oxygen atoms of –SO2– group or ii) nitrogen atoms of –NH2,and =N– groups, to interact with hydrogen atoms in water.

According to the preferential solvation results, it is conjecturablethat in intermediate composition mixtures, the sulfonamides areacting as Lewis acids with ethanol molecules because this co-solvent is more basic than water, i.e. the Kamlet–Taft hydrogenbond acceptor parameters are β = 0.75 for ethanol and 0.47 forwater [28]. On the other hand, in ethanol-rich mixtures, wherethese drugs are preferentially solvated by water, these compoundsare acting mainly as a Lewis base in front to water because theKamlet–Taft hydrogen bond donor parameters are, α = 1.17 forwater and 0.86 for ethanol, respectively [29]. Thus, water is moreacidic than ethanol. In this way, the specific and nonspecific interac-tions between these sulfonamide drugs and the co-solvent decreasein these mixtures [30].

On the other hand the effect of the ethyl group of ethanol couldalso be involved in the solvation effects described previously; in par-ticular because some extent of hydrophobic hydration around alkylgroups of alcohols in water-rich mixtures has been proposed in theliterature [31,32]; whereas, some organized structures based on hy-drogen bonding and van der Waals interactions of alcohol moleculesin alcohol-rich mixtures have also been proposed [21]. Nevertheless,the specific role of the ethyl groups of ethanol in the preferential sol-vation of these sulfonamides by ethanol molecules is not clear.

4. Conclusions

Some explicit expressions for the local mole fraction of ethanoland water around sulfadiazine, sulfamerazine and sulfamethazinewere derived on the basis of the IKBI method applied to equilibriumsolubility values of these drugs in ethanol + water mixtures. Thus,these compounds are preferentially solvated by water in water-richand ethanol-rich mixtures but preferentially solvated by ethanol inmixtures with intermediate composition at all temperatures consid-ered. This behavior is very similar for all these sulfonamides. Theseresults are in agreement with that described previously and basedon more classical thermodynamic treatments [8,9].

Appendix A

Sulfamethazinec

303.15 K 313.15 K 293.15 K 303.15 K 313.15 K

2.09E−5 3.16E−5 2.22E−5 3.67E−5 5.55E−53.12E−5 4.99E−5 4.13E−5 6.34E−5 1.06E−45.78E−5 9.98E−5 7.69E−5 1.20E−4 2.21E−41.24E−4 2.07E−4 1.57E−4 2.68E−4 4.66E−42.35E−4 3.64E−4 2.81E−4 4.84E−4 8.25E−43.64E−4 5.86E−4 4.80E−4 7.79E−4 1.32E−35.02E−4 7.67E−4 7.27E−4 1.15E−3 1.88E−35.92E−4 9.27E−4 9.49E−4 1.47E−3 2.29E−36.45E−4 9.43E−4 1.09E−3 1.66E−3 2.47E−35.59E−4 8.11E−4 1.00E−3 1.42E−3 2.15E−34.09E−4 6.36E−4 7.47E−4 1.09E−3 1.62E−3

lfonamide.

Table A2D values (kJ mol−1) of the sulfonamides in ethanol + water co-solvent mixtures at several temperatures.

xEtOHa Sulfadiazine Sulfamerazine Sulfamethazine

293.15 K 303.15 K 313.15 K 293.15 K 303.15 K 313.15 K 293.15 K 303.15 K 313.15 K

0.00 −41.35 −43.17 −45.29 −37.56 −41.35 −44.84 −41.46 −43.79 −50.250.05 −35.01 −35.88 −36.96 −33.05 −35.31 −37.75 −35.48 −37.38 −41.630.10 −29.25 −29.41 −29.68 −28.71 −29.79 −31.35 −30.07 −31.55 −34.030.15 −24.04 −23.72 −23.40 −24.56 −24.76 −25.61 −25.17 −26.27 −27.380.20 −19.36 −18.74 −18.02 −20.63 −20.20 −20.50 −20.79 −21.51 −21.620.25 −15.18 −14.43 −13.47 −16.91 −16.10 −15.98 −16.87 −17.26 −16.670.30 −11.48 −10.73 −9.68 −13.44 −12.45 −12.03 −13.40 −13.49 −12.470.35 −8.24 −7.59 −6.56 −10.22 −9.22 −8.61 −10.36 −10.17 −8.970.40 −5.44 −4.97 −4.05 −7.28 −6.39 −5.69 −7.70 −7.29 −6.070.45 −3.04 −2.80 −2.06 −4.64 −3.96 −3.25 −5.41 −4.81 −3.740.50 −1.03 −1.04 −0.51 −2.30 −1.90 −1.24 −3.46 −2.72 −1.890.55 0.61 0.37 0.67 −0.29 −0.20 0.35 −1.82 −0.98 −0.460.60 1.92 1.47 1.55 1.37 1.17 1.56 −0.46 0.42 0.620.65 2.91 2.33 2.22 2.67 2.21 2.43 0.64 1.50 1.410.70 3.60 2.98 2.75 3.60 2.95 2.97 1.51 2.30 1.970.75 4.03 3.49 3.23 4.13 3.40 3.23 2.18 2.84 2.380.80 4.21 3.90 3.72 4.25 3.58 3.23 2.67 3.13 2.700.85 4.16 4.27 4.30 3.93 3.51 3.01 3.02 3.20 3.000.90 3.91 4.65 5.05 3.17 3.20 2.59 3.24 3.09 3.340.95 3.49 5.10 6.06 1.95 2.67 2.01 3.37 2.80 3.791.00 2.92 5.65 7.39 0.24 1.95 1.30 3.44 2.37 4.41

a xEtOH is the mole fraction of ethanol in the ethanol + water co-solvent mixtures free of sulfonamide.

Table A3Physicochemical properties of the ethanol + water co-solvent mixtures at severaltemperatures.

xEtOHa Q (kJ mol−1) RT κT (cm3 mol−1)

293.15 K 303.15 K 313.15 K 293.15 K 303.15 K 313.15 K

0.00 2.437 2.520 2.604 1.114 1.152 1.1900.05 2.232 2.210 2.189 1.199 1.240 1.2800.10 2.077 2.000 1.924 1.283 1.327 1.3710.15 1.956 1.862 1.769 1.368 1.415 1.4620.20 1.855 1.771 1.687 1.453 1.503 1.5520.25 1.762 1.705 1.648 1.538 1.590 1.6430.30 1.668 1.648 1.627 1.623 1.678 1.7330.35 1.568 1.587 1.606 1.708 1.766 1.8240.40 1.460 1.515 1.570 1.792 1.853 1.9150.45 1.343 1.427 1.512 1.877 1.941 2.0050.50 1.220 1.324 1.429 1.962 2.029 2.0960.55 1.098 1.211 1.323 2.047 2.117 2.1860.60 0.985 1.095 1.204 2.132 2.204 2.2770.65 0.894 0.989 1.085 2.216 2.292 2.3680.70 0.838 0.912 0.986 2.301 2.380 2.4580.75 0.835 0.883 0.932 2.386 2.467 2.5490.80 0.906 0.930 0.953 2.471 2.555 2.6390.85 1.074 1.080 1.087 2.556 2.643 2.7300.90 1.365 1.370 1.374 2.641 2.731 2.8210.95 1.809 1.835 1.862 2.725 2.818 2.9111.00 2.437 2.520 2.604 2.810 2.906 3.002

a xEtOH is the mole fraction of ethanol in the ethanol + water co-solvent mixtures freeof sulfonamide.

Table A4Partial molar volumes of components in ethanol + water co-solvent mixtures at severaltemperatures.

xEtOHa VEtOH (cm3 mol−1) VW (cm3 mol−1)

293.15 K 303.15 K 313.15 K 293.15 K 303.15 K 313.15 K

0.00 52.49 53.38 54.30 18.05 18.09 18.140.05 53.31 54.16 55.02 18.03 18.07 18.120.10 54.05 54.86 55.68 17.97 18.01 18.070.15 54.71 55.49 56.27 17.88 17.92 17.990.20 55.31 56.06 56.79 17.75 17.80 17.880.25 55.83 56.56 57.27 17.60 17.66 17.740.30 56.29 56.99 57.68 17.42 17.49 17.580.35 56.69 57.38 58.05 17.23 17.31 17.410.40 57.03 57.70 58.37 17.03 17.11 17.210.45 57.33 57.98 58.64 16.81 16.90 17.010.50 57.57 58.22 58.87 16.59 16.69 16.800.55 57.77 58.41 59.07 16.37 16.48 16.590.60 57.94 58.57 59.23 16.15 16.27 16.370.65 58.06 58.69 59.35 15.93 16.06 16.160.70 58.16 58.79 59.45 15.73 15.86 15.950.75 58.23 58.86 59.53 15.55 15.68 15.750.80 58.28 58.91 59.58 15.38 15.52 15.560.85 58.31 58.94 59.62 15.24 15.37 15.390.90 58.33 58.95 59.64 15.12 15.25 15.240.95 58.33 58.96 59.65 15.04 15.17 15.111.00 58.34 58.96 59.66 14.99 15.11 15.00

a xEtOH is the mole fraction of ethanol in the ethanol + water co-solvent mixtures freeof sulfonamide.

158 D.R. Delgado, F. Martínez / Journal of Molecular Liquids 193 (2014) 152–159

159D.R. Delgado, F. Martínez / Journal of Molecular Liquids 193 (2014) 152–159

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