Preferential Solvation of Some Sulfonamidesin Propylene Glycol + Water Solvent MixturesAccording to the IKBI and QLQC Methods

Daniel Ricardo Delgado • Marıa Angeles Pena • Fleming Martınez

Received: 4 August 2013 / Accepted: 14 October 2013 / Published online: 30 January 2014� Springer Science+Business Media New York 2014

Abstract The preferential solvation parameters, which represent differences between the

local and bulk mole fractions of the solvents near to the solute, in solutions of some

sulfonamides in propylene glycol ? water binary mixtures are derived from their ther-

modynamic properties by means of the inverse Kirkwood-Buff integrals (IKBI) and the

Quasi-Lattice Quasi-Chemical (QLQC) method. From solvent effect studies, it is found

that sulfonamides are sensitive to solvation effects; the preferential solvation parameter,

dxPG,S, is negative in water-rich mixtures but positive in compositions from 0.20 to 1.00 in

mole fraction of propylene glycol according to IKBI method and positive in all co-solvent

compositions if the QLQC method is considered. It is conjecturable that in water-rich

mixtures, hydrophobic hydration around the aromatic ring and/or other non-polar groups

plays a relevant role in the solvation. The greater solvation by propylene glycol mixtures of

similar solvent compositions and in co-solvent-rich mixtures could be due mainly to

polarity effects and acidic behavior of the sulfonamides, in contrast to the more basic

solvent propylene glycol.

Keywords Sulfonamides � Solubility � Inverse Kirkwood-Buff integrals � IKBI �QLQC � Preferential solvation

List of symbols

Latin lettersE Pair-wise interactions energy

G Molar Gibbs energy; Kirkwood-Buff integral

IKBI Inverse Kirkwood-Buff integral

D. R. Delgado � F. Martınez (&)Grupo de Investigaciones Farmaceutico Fisicoquımicas, Departamento de Farmacia, Facultad deCiencias, Universidad Nacional de Colombia, 14490 Bogota D.C., Colombiae-mail: fmartinezr@unal.edu.co

M. A. PenaDepartamento de Ciencias Biomedicas, Facultad de Farmacia, Universidad de Alcala, Alcala deHenares, Madrid, Spain

123

J Solution Chem (2014) 43:360–374DOI 10.1007/s10953-014-0130-2

N Number of molecules or of neighboring molecule pairs

NA Avogadro’s constant

QLQC Quasi-Lattice Quasi-Chemical

R Gas constant

S Molar entropy

SA Sulfanilamide

SP Sulfapyridine

SMZ Sulfamethizole

T Absolute temperature

U Internal energy

V Molar volume

V Partial molar volume

x Mole fraction

Z Quasi-lattice parameter

Greek lettersb Kamlet-Taft hydrogen bond acceptor parameter

D Change on transformation

dx Preferential solvation parameter

jT Isothermal compressibility

Superscripts� Standard molar

ex Excess thermodynamic function

L Local

Subscripts0.5 Equimolar composition

? Transfer

Cor Correlation, where preferential solvation occurs

i Solvent i

p Constant pressure

PG Propylene glycol

S Solute

T Constant absolute temperature

W Water

1 Introduction

Knowledge of the solubility of drugs in co-solvent mixtures is very important for phar-

maceutical scientists involved in several development stages such as drug purification and

design of liquid medicines [1]. Although co-solvency has been employed in pharmacy for

centuries, it is only recently that study of the mechanisms that increase or decrease the

drug’s solubility have been approached from a physicochemical point of view [2].

Sulfonamides are drugs extensively used for the treatment of certain infections caused

by gram-positive and gram-negative microorganisms, some fungi, and certain protozoa.

Although the advent of antibiotics has diminished the usefulness of the sulfonamides, these

drugs still occupy an important place in the therapeutic resources of physicians and vet-

erinarians [3, 4].

J Solution Chem (2014) 43:360–374 361

123

Several thermodynamic works have been published based on the enthalpic and entropic

contributions to the Gibbs energy of solution of some sulfonamides in binary solvent

mixtures formed by propylene glycol and water [5–7]. Nevertheless, preferential solvation

of the drug, i.e. the co-solvent specific composition around the drug molecules, has not

been studied for sulfonamides. Therefore, the main goal of this paper is to evaluate the

preferential solvation of some sulfonamides in propylene glycol ? water co-solvent

mixtures, based on well-established thermodynamic definitions. The sulfonamides under

study are sulfanilamide, sulfapyridine, and sulfamethizole (Table 1). Thus, this work is

similar to the ones presented previously in the literature for some analgesic drugs in

co-solvent mixtures [8–11].

The inverse Kirkwood-Buff integrals (IKBI) method is a powerful tool for evaluating

the preferential solvation of nonelectrolytes in co-solvent mixtures, describing the local

compositions around a solute with respect to the different components present in the

solvent mixture [12–14].

In the present case, this treatment depends on the values of the standard molar Gibbs

energies of transfer of the sulfonamides from neat water to the propylene glycol ? water

solvent mixtures and the excess molar Gibbs energy of mixing for the co-solvent binary

mixtures. As has been indicated previously, this treatment is very important in pharma-

ceutical sciences to understand solute-solvent molecular interactions because most of the

solubility studies reported have been directed towards correlating or modeling the solu-

bilities and possibly predicting them from the individual solubilities in the neat solvents,

but not to analyzing the local environment around the drug molecules describing the local

fraction of the solvent components (PG or W) in the surrounding solute (S) [14–16].

A second method for obtaining local mole fractions around drug molecules in binary

solvent mixtures is the one proposed by Marcus [17], the so-called Quasi-Lattice Quasi-

Chemical (QLQC) method. This method supposes that the number of nearest neighbors a

molecule has (the lattice parameter Z) is the weighted mean of the lattice parameters of the

pure components. It also assumes that the interaction energy of a molecule of any com-

ponent with another molecule is independent of the nature of the other neighbors. The

model also assumes ideal volumes and entropies of mixing (i.e., Vex = 0 and Sex = 0). The

Table 1 Molecular structure of the considered sulfonamides

Sulfonamide Abbreviation CAS number Substituenta

Sulfanilamide SA 63-74-1 -H

Sulfapyridine SP 144-83-2 N

Sulfamethizole SMZ 144-82-1

NN

S CH3

a Substituent group on the basic structure of sulfanilamide

SO2NH2 NHR

362 J Solution Chem (2014) 43:360–374

123

main advantage of this method is that no derivative functions are required as in the case of

the IKBI method [17].

In this paper the IKBI and QLQC approaches are applied to evaluate the preferential

solvation of the some structurally related sulfonamides in the binary mixtures formed by

propylene glycol (PG) and water (W). The results are expressed in terms of the preferential

solvation parameter dxPG,S of the solute by the two solvent components.

2 Theoretical Background

The KBIs (Kirkwood-Buff integrals, Gi,S) are given by the following expression:

Gi;S ¼Zrcor

0

ðgi;S � 1Þ4pr2dr: ð1Þ

Here gi,S is the pair correlation function for the molecules of the solvent i around the

sulfonamide in the propylene glycol ? water mixtures, r the distance between the centers

of the molecules of sulfonamide and propylene glycol or water, and rcor is a correlation

distance for which gi,S (r [ rcor) &1. Thus, for all distances r [ rcor up to infinity, the

value of the integral is essentially zero. Therefore, the results are expressed in terms of the

preferential solvation parameter dxi,S for the solute in solution by the component solvents,

here propylene glycol and water [18]. For propylene glycol (PG) this parameter is defined

as:

dxPG;S ¼ xLPG;S � xPG ¼ �dxW;S ð2Þ

where xPG is the mole fraction of propylene glycol in the bulk solvent mixture and xLPG;S is

the local mole fraction of propylene glycol in the environment near to the drug. If

dxPG;S [ 0 then the sulfonamide is preferentially solvated by propylene glycol; on the

contrary, if \0 then the drug is preferentially solvated by water within the correlation

volume, Vcor ¼ 4p=3ð Þr3cor, and the bulk mole fraction of propylene glycol is xPG. Values of

dxPG;S are obtainable from those of GPG,S, and these, in turn, are obtained from thermo-

dynamic data of the co-solvent mixtures with the solute dissolved in it, as shown below

[15].

Algebraic manipulation of the basic expressions presented by Newman [18] leads to

expressions for the Kirkwood-Buff integrals (in cm3�mol-1) for the individual solvent

components in terms of some thermodynamic quantities as shown in Eqs. 3 and 4 [15–19]:

GPG;S ¼ RTjT � �VS þ xW�VWD=Q ð3Þ

GW;S ¼ RTjT � �VS þ xPG�VPGD=Q ð4Þ

where jT is the isothermal compressibility of the propylene glycol ? water solvent mix-

tures (in GPa-1), VPG and VW are the partial molar volumes of the solvents in the mixtures

(in cm3�mol-1), and similarly VS is the partial molar volume of the solute in these mixtures

(in cm3�mol-1). The function D is the derivative of the standard molar Gibbs energies of

transfer of the drug (from neat water to propylene glycol ? water mixtures) with respect to

the solvent composition (in kJ�mol-1, as also is RT), and the function Q involves the

second derivative of the excess molar Gibbs energy of mixing of the two solvents (GexPGþW)

with respect to the water proportion in the mixtures (also in kJ�mol-1) [15–19]:

J Solution Chem (2014) 43:360–374 363

123

D ¼oDtrG

0ðS;W!PGþWÞoxPG

!

T ;p

ð5Þ

Q ¼ RT � xPGxW

o2GexPG;W

ox2W

!

T ;p

ð6Þ

Because the dependence of jT on composition is not known for many investigated systems,

and because of the small contribution of RT jT to the IKBI, the dependence of jT on com-

position can be approximated by considering additive behavior according to Eq. 7 [19]:

jT ;mix ¼Xn

i¼1

xij0T ;i ð7Þ

where xi is the mole fraction of component i in the mixture and jT,i0 is the isothermal

compressibility of the pure component i.

Ben-Naim [12] showed that the preferential solvation parameter can be calculated from

the Kirkwood-Buff integrals as follows:

dxPG;S ¼xPGxW GPG;S � GW;S

� �xPGGPG;S þ xWGW;S þ Vcor

ð8Þ

The correlation volume, Vcor, is obtained by means of the following expression proposed

by Marcus [8, 16]:

Vcor ¼ 2522:5 rS þ 0:1363 xLPG;S

�VPG þ xLW;S

�VW

� �1=3

�0:085

� �3

ð9Þ

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

rS ¼3 � 1021VS

4pNAv

� �1=3

ð10Þ

where, NAv is Avogadro’s number. However, evaluation of the definitive correlation

volume requires iteration, because it depends on the local mole fractions. This iteration is

done by replacing dxPG;S in Eq. 2 to calculate xLPG;S, until a non-varying value of Vcor is

obtained.

For the QLQC method, the local mole fraction of the solvent component propylene

glycol around the sulfonamide molecules is defined as [16, 17]:

xLS ¼ 1= 1þ NPGPG=NWWð Þ0:5exp DEPGW;S=2RT

� �h ið11Þ

NPGPG=NWW ¼ xPG � NPGW=Z NPG þ NWð Þ½ �= xW � NPGW=Z NPG þ NWð Þ½ � ð12Þ

NPGW

Z NPG þ NWð Þ ¼1� 1� 4xPGxW 1� exp �DEPGW=RTf gð Þ½ �0:5

2 1� exp �DEPGW=RTð Þ½ � ð13Þ

DEPGW;S ¼ DtrG0ðS;W!PGÞ=Z ð14Þ

exp DEPGW=RTð Þ ¼ 2 exp �GexPGWðx¼0:5Þ=ZRT

n o� �� 1

h i2

ð15Þ

364 J Solution Chem (2014) 43:360–374

123

In these equations, the lattice parameter Z is usually assumed to be 10. NPG and NW are

the number of molecules of both components in the bulk liquid, whereas NPGPG, NWW, and

NPGW are the number of neighboring pairs of these molecules in the quasi lattice. Equa-

tion 14 expresses the difference in the molar neighbor interaction energies of sulfonamide

with the solvents propylene glycol and water, DEPGW,S, by the molar Gibbs energy of

transfer from water to propylene glycol per the neighboring lattice. DEPGW denotes the

molar energy of interaction of solvent on neighboring quasi-lattice sites. It is important to

note that only the Gibbs energy of drug transfer between the neat solvents and the excess

Gibbs energy of mixing at equimolar composition of both solvents are required for this

method.

3 Results and Discussion

The solubilities of sulfonamides in propylene glycol ? water mixtures (Table 2) were

taken from Delgado et al. [5–7]. Experimental uncertainties in the solubility are lower than

2.0 %. The standard molar Gibbs energy of transfer of these drugs from neat water to

propylene glycol ? water mixtures was calculated and correlated to polynomials from the

drug solubility data by using Eq. 16. Figure 1 shows the Gibbs energy of transfer behavior

at 303.15 K. According to the literature, Fig. 1 shows Gibbs energy profiles that are

consistent with preferential solvation [20]. In addition, Table 3 shows the behavior at all

the temperatures studied. Polynomials coefficients are reported in Table 4.

DtrG0S;W!PGþW ¼ RT ln

xS;W

xS;PGþW

� �¼ aþ bxPG þ cx1:5

PG þ dx2PG ð16Þ

Thus D values were calculated from the first derivative of the polynomial models

(Eq. 17) solved according to the composition of the co-solvent mixtures. This procedure

was done varying by 0.05 in mole fraction of propylene glycol, but in the following tables

the respective values are reported varying only by 0.10. D values are reported in Table 5.

D ¼ bþ 1:5cx0:5PG þ 2dxPG ð17Þ

In order to calculate the Q values, the excess molar Gibbs energies of mixing GexPG;W are

required at all the temperatures considered. These values were calculated by means of

Eq. 18 with the coefficients d, e, f and g at 293.15, 303.15 and 313.15 K reported in

Table 5 of Ref. [11].

GexPG;W ¼ dxPG þ ex2

PG þ fx3PG þ gx4

PG ð18Þ

The Q values at all temperatures are shown in Table 6. On the other hand, the same

table also shows the RT jT values calculated by assuming additive behavior of jT (Eq. 7)

using the values 0.487 and 0.457 GPa-1 for propylene glycol and water at 298.15 K,

respectively [21]. It is important to note that no values are available at other temperatures

and therefore these values were used at all temperatures considered.

The partial molar volumes of propylene glycol and water (Table 7) were calculated by

means of Eqs. 19 and 20 from the density (q) values of propylene glycol ? water mixtures

reported by Jimenez et al. [22] at all of the temperatures under study. V is the molar volume

of the mixtures and it is calculated as V = (xPG�MPG ? xW�MW)/q. The values of MPG and

MW are 76.09 and 18.02 g�mol-1, respectively.

J Solution Chem (2014) 43:360–374 365

123

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366 J Solution Chem (2014) 43:360–374

123

Fig. 1 Gibbs energy of transfer of the sulfonamides from neat water to propylene glycol ? water binaryco-solvent mixtures at 303.15 K: circles SA, squares SP, triangles SMZ

Table 4 Coefficients (kJ�mol-1) of the Eq. 16 applied to Gibbs energy of transfer for the consideredsulfonamides at three temperatures

Coefficient SA SP SMZ

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

a 0.22 0.16 0.07 0.65 0.47 0.22 0.37 0.28 0.20

b -49.37 -50.60 -50.89 -49.08 -57.65 -68.07 -73.73 -77.96 -84.59

c 64.61 71.21 75.14 54.57 74.59 99.96 98.66 107.94 122.30

d -24.95 -29.68 -32.63 -16.61 -27.90 -42.70 -38.09 -43.10 -51.06

Table 3 Gibbs energy of transfer (kJ�mol-1) of the sulfonamides from neat water to propyleneglycol ? water co-solvent mixtures at three temperatures

xPG SA SP SMZ

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

0.0000 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.0256 -0.81 -0.83 -0.90 -0.06 -0.54 -0.94 -1.04 -1.23 -1.44

0.0559 -1.49 -1.66 -1.77 -0.90 -1.43 -2.20 -2.21 -2.50 -2.87

0.0921 -2.50 -2.64 -2.79 -2.14 -2.66 -3.58 -3.68 -4.07 -4.45

0.1364 -3.75 -3.68 -3.80 -3.71 -4.21 -4.98 -5.40 -5.64 -6.18

0.1915 -4.93 -4.75 -4.67 -5.00 -5.58 -6.05 -7.12 -7.41 -7.78

0.2621 -5.90 -5.73 -5.41 -6.35 -6.79 -7.19 -8.64 -8.87 -9.23

0.3559 -6.87 -6.56 -6.18 -7.51 -7.85 -8.20 -9.73 -9.96 -10.33

0.4865 -7.67 -7.19 -6.83 -8.51 -8.77 -8.96 -10.95 -11.18 -11.49

0.6807 -8.60 -8.03 -7.58 -9.57 -9.63 -9.79 -11.92 -12.03 -12.34

1.0000 -9.52 -8.93 -8.30 -10.57 -10.56 -10.59 -12.83 -12.88 -13.17

J Solution Chem (2014) 43:360–374 367

123

VPG ¼ V þ xW

dV

dxPG

ð19Þ

VW ¼ V � xPG

dV

dxPG

ð20Þ

Partial molar volumes of nonelectrolyte drugs are not frequently reported in the liter-

ature. This is because of the large uncertainties in their determination due to their low

solubilities, in particular in aqueous media. For this reason, as a first approach, the molar

volumes of these sulfonamides are considered here as being independent of the co-solvent

composition and temperature, just as they are calculated according to the groups contri-

bution method proposed by Fedors [23, 24]. Thus, Table 8 shows the number of functional

Table 5 D values (kJ�mol-1) for the sulfonamides in propylene glycol ? water co-solvent mixtures atthree temperatures

xPG SA SP SMZ

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 -49.37 -50.60 -50.89 -49.08 -57.65 -68.07 -73.73 -77.96 -84.59

0.10 -23.71 -22.76 -21.78 -26.52 -27.85 -29.20 -34.55 -35.38 -36.79

0.20 -16.01 -14.71 -13.54 -19.12 -18.78 -18.10 -22.78 -22.79 -22.97

0.30 -11.25 -9.91 -8.74 -14.22 -13.11 -11.57 -15.52 -15.14 -14.74

0.40 -8.03 -6.79 -5.72 -10.61 -9.21 -7.40 -10.60 -10.04 -9.41

0.50 -5.79 -4.76 -3.83 -7.82 -6.44 -4.75 -7.17 -6.57 -5.93

0.60 -4.23 -3.48 -2.75 -5.62 -4.47 -3.17 -4.80 -4.27 -3.76

0.70 -3.21 -2.79 -2.28 -3.86 -3.10 -2.41 -3.23 -2.84 -2.58

0.80 -2.60 -2.56 -2.30 -2.45 -2.22 -2.28 -2.30 -2.11 -2.20

0.90 -2.33 -2.70 -2.71 -1.33 -1.73 -2.69 -1.89 -1.94 -2.46

1.00 -2.35 -3.15 -3.45 -0.46 -1.57 -3.54 -1.91 -2.26 -3.26

Table 6 Physicochemical properties of the propylene glycol ? water co-solvent mixtures at threetemperatures

xPG Q (kJ�mol-1) RT jT (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 1.190

0.10 2.492 2.430 2.367 1.121 1.159 1.198

0.20 2.509 2.428 2.340 1.128 1.167 1.205

0.30 2.514 2.481 2.433 1.136 1.175 1.213

0.40 2.521 2.559 2.574 1.143 1.182 1.221

0.50 2.540 2.638 2.707 1.150 1.190 1.229

0.60 2.568 2.697 2.797 1.158 1.197 1.237

0.70 2.595 2.723 2.823 1.165 1.205 1.244

0.80 2.602 2.704 2.786 1.172 1.212 1.252

0.90 2.562 2.637 2.701 1.180 1.220 1.260

1.00 2.437 2.520 2.604 1.187 1.227 1.268

368 J Solution Chem (2014) 43:360–374

123

groups present in all the sulfonamides as well as the respective individual contributions to

internal energy (U/kJ�mol-1) and molar volume (V/cm3�mol-1). In this way, Table 9 shows

the U and V values for every sulfonamide calculated as additive properties. From volume

values the radii of the drug molecules (required for Eq. 9) were calculated by using Eq. 10

and the values are also reported in Table 9.

Tables 10 and 11 show that the GPG,S and GW,S values are negative for all compositions

at all temperatures considered. In some cases these values change slightly with the tem-

perature and clearly they are proportional to the molar volume of the sulfonamides, just as

defined by Eqs. 3 and 4.

In order to use the IKBI method, the correlation volume was obtained by iteration, by

using Eqs. 2, 8 and 9 to obtain the values reported in Table 12. It is interesting to note that

this value is almost independent of temperature in water-rich mixtures but it increases to

some extent in propylene glycol-rich mixtures.

Table 7 Partial molar volumes of components in propylene glycol ? water co-solvent mixtures at threetemperatures

xPG VPG (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 69.09 69.91 70.70 18.07 18.11 18.17

0.10 70.45 71.18 71.89 18.00 18.05 18.11

0.20 71.50 72.16 72.81 17.81 17.87 17.95

0.30 72.27 72.88 73.49 17.56 17.63 17.73

0.40 72.82 73.39 73.97 17.27 17.36 17.47

0.50 73.17 73.72 74.27 16.98 17.10 17.22

0.60 73.37 73.90 74.45 16.74 16.88 17.02

0.70 73.45 73.98 74.52 16.59 16.74 16.88

0.80 73.46 73.99 74.53 16.57 16.72 16.86

0.90 73.44 73.97 74.51 16.70 16.85 16.99

1.00 73.42 73.95 74.49 17.05 17.18 17.29

Table 8 Contribution to internal energy and molar volume by every functional group and number of groupspresent in the sulfonamides according to the Fedors method [23, 24]

Group U (kJ�mol-1) V (cm3�mol-1) SA SP SMZ

-NH2 12.6 19.2 2 1 1

-NH- 8.4 4.5 – 1 1

=N- 11.7 5.0 – 1 2

-S- 14.2 12.0 – – 1

-SO2- 25.6 19.5 1 1 1

[C= 4.3 -5.5 – 1 2

-CH= 4.3 13.5 – 4 –

-CH3 4.7 33.5 – – 1

Phenylene 31.9 52.4 1 1 1

Ring closure 1.1 16.0 – 1 1

Conj. bond 1.7 -2.2 – 3 2

J Solution Chem (2014) 43:360–374 369

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According to the IKBI method the values of dxPG,S vary non-linearly with the propylene

glycol concentration in the aqueous mixtures (Table 13; Fig. 2). Addition of propylene

glycol to water tends to make the dxPG,S values of sulfonamides negative from pure water

up to the mixture with mole fraction 0.20 of propylene glycol, reaching minimum values

near xPG = 0.10. Possibly the structuring of water molecules around the non-polar groups

of this drug (Table 1), i.e. hydrophobic hydration, contributes to the lowering of the net

dxPG,S to negative values in these water-rich mixtures. These minimum values are

dependent on temperature to some extent for sulfanilamide and sulfamethizole (Table 13).

In the mixtures with composition 0.20 \ xPG \ 1.00, the local mole fraction of pro-

pylene glycol is greater than that in the bulk phase and it decreases as the temperature

increases. In this way, the co-solvent action may be related to the breaking of the ordered

structure of water (hydrogen bonds) around the non-polar moieties of the drugs which, in

turn, increases the solvation of the sulfonamides resulting in maximum values near

xPG = 0.40.

Table 9 Some physicochemical properties of the sulfonamides

Property SA SP SMZ

VSa (cm3�mol-1) 110.3 158.5 151.7

Ua (kJ�mol-1) 82.7 117.8 133.8

dSb (MPa1/2) 27.4 27.3 29.7

rSc (nm) 0.352 0.398 0.392

Acidic sitesd 4 3 3

Basic sitese 5 6 9

a VS and U are total molar volume and internal energy calculated according to Fedors [23] and Barton [24]b dS is the Hildebrand solubility parameter calculated as (1,000 U/VS)1/2

c rS is the molecular radius calculated with Eq. 10d Acidic sites were assigned as two for H2N- and one for -NH-e Basic sites were assigned as one for H2N-, four for -SO2-, one for = N-, and two for -S-

Table 10 GPG,S values (cm3�mol-1) for the sulfonamides in propylene glycol ? water co-solvent mixturesat three temperatures

xPG SA SP SMZ

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 -475 -473 -464 -521 -572 -632 -697 -711 -741

0.10 -263 -261 -259 -330 -344 -358 -375 -387 -404

0.20 -200 -196 -192 -266 -268 -268 -280 -285 -291

0.30 -164 -158 -154 -227 -223 -216 -226 -226 -226

0.40 -142 -137 -132 -201 -195 -187 -194 -191 -189

0.50 -128 -125 -121 -183 -178 -172 -175 -172 -169

0.60 -120 -118 -116 -172 -168 -165 -163 -161 -160

0.70 -115 -114 -113 -165 -163 -162 -157 -156 -155

0.80 -112 -112 -112 -160 -160 -160 -153 -153 -153

0.90 -111 -111 -111 -158 -158 -159 -152 -152 -152

1.00 -109 -109 -109 -157 -157 -157 -151 -150 -150

370 J Solution Chem (2014) 43:360–374

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According to the IKBI preferential solvation results, it is conjecturable that in inter-

mediate composition mixtures and propylene glycol-rich mixtures, the sulfonamides are

acting as Lewis acids towards propylene glycol molecules because this co-solvent is more

basic than water, i.e. the Kamlet-Taft hydrogen bond acceptor parameters are b = 0.75

for propylene glycol and 0.47 for water [25]. Apparently, there is no clear relationship

between the Hildebrand solubility parameter (dS, Table 9) of the sulfonamides and the

magnitude of the values obtained for dxPG,S. Thus, solvation is not strongly dependent on

the drug’s polarity for these compounds.

Sulfonamides in solution act as Lewis acids due to the hydrogen atoms in their -NH2

and -NH- groups (Table 1) in order to establish hydrogen bonds with proton-acceptor

functional groups in the solvents (oxygen atoms in -OH groups). In addition, these drugs

Table 11 GW,S values (cm3�mol-1) for the sulfonamides in propylene glycol ? water co-solvent mixturesat three temperatures

xPG SA SP SMZ

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 -109 -109 -109 -157 -157 -157 -151 -151 -151

0.10 -176 -176 -175 -232 -239 -246 -248 -254 -262

0.20 -200 -197 -193 -266 -269 -270 -280 -286 -293

0.30 -206 -196 -188 -280 -273 -262 -284 -284 -284

0.40 -202 -187 -175 -280 -263 -242 -273 -266 -259

0.50 -192 -176 -162 -270 -247 -222 -254 -242 -232

0.60 -182 -166 -153 -254 -231 -208 -233 -221 -210

0.70 -173 -162 -151 -234 -216 -202 -215 -205 -198

0.80 -168 -165 -158 -213 -206 -206 -202 -197 -198

0.90 -169 -177 -176 -192 -201 -224 -199 -200 -211

1.00 -180 -202 -208 -171 -203 -258 -208 -217 -244

Table 12 Correlation volume (cm3�mol-1) of the sulfonamides in propylene glycol ? water co-solventmixtures at three temperatures

xPG SA SP SMZ

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

0.00 616 617 618 759 760 762 740 741 742

0.10 699 701 704 856 857 858 829 830 830

0.20 807 810 814 978 982 985 955 959 962

0.30 909 912 915 1,095 1,099 1,102 1,072 1,076 1,081

0.40 1,003 1,005 1,007 1,202 1,204 1,206 1,176 1,180 1,184

0.50 1,089 1,091 1,094 1,300 1,302 1,303 1,271 1,274 1,278

0.60 1,172 1,175 1,178 1,392 1,394 1,397 1,361 1,365 1,369

0.70 1,253 1,257 1,262 1,480 1,485 1,489 1,448 1,454 1,459

0.80 1,332 1,338 1,344 1,567 1,573 1,581 1,535 1,542 1,549

0.90 1,409 1,417 1,424 1,653 1,661 1,670 1,621 1,628 1,637

1.00 1,485 1,492 1,499 1,738 1,746 1,755 1,705 1,713 1,721

J Solution Chem (2014) 43:360–374 371

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can act as Lewis bases due to free electron pairs in either (1) oxygen atoms of a -SO2-

group, (2) nitrogen atoms of -NH2 and =N- groups, or (3) sulfur atom of -S- groups, to

interact with hydrogen atoms in water. In this regard, Table 9 shows the respective

numbers of acidic and basic sites in the sulfonamides considered.

On the other hand, in order to use the QLQC method, the excess Gibbs energy of mixing

of the equimolar mixture of the solvents were used as: -70.31, -48.06 and

-13.50 J�mol-1 at 293.15, 303.15 and 313.15 K, respectively [11]. According to the

QLQC method (Table 14; Fig. 2), the sulfonamides are preferentially solvated by pro-

pylene glycol in all of the mixtures and the positive dxPG,S values are much bigger than

those obtained by using the IKBI method. Therefore, as has been indicated in the literature,

the IKBI method is more indicative than QLQC in discriminating the effect of co-solvent

composition on the local mole fraction around the drug molecules [10, 11]. Nevertheless, it

is important to keep in mind here that the classical QLQC method, as described by Marcus

Table 13 IKBI dxPG,S values for the sulfonamides in propylene glycol ? water co-solvent mixtures atthree temperatures

xPG SA SP SMZ

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 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.10 -0.0152 -0.0149 -0.0145 -0.0143 -0.0155 -0.0168 -0.0201 -0.0213 -0.0230

0.20 0.0001 0.0002 0.0003 0.0001 0.0002 0.0003 0.0001 0.0003 0.0005

0.30 0.0123 0.0110 0.0099 0.0134 0.0126 0.0113 0.0151 0.0151 0.0151

0.40 0.0174 0.0144 0.0120 0.0199 0.0169 0.0134 0.0203 0.0189 0.0176

0.50 0.0172 0.0136 0.0106 0.0201 0.0159 0.0113 0.0188 0.0165 0.0145

0.60 0.0144 0.0112 0.0085 0.0165 0.0124 0.0085 0.0143 0.0121 0.0103

0.70 0.0108 0.0089 0.0070 0.0112 0.0086 0.0064 0.0095 0.0080 0.0070

0.80 0.0073 0.0070 0.0061 0.0060 0.0052 0.0052 0.0057 0.0050 0.0051

0.90 0.0041 0.0046 0.0045 0.0020 0.0026 0.0039 0.0029 0.0029 0.0036

1.00 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Fig. 2 IKBI (empty symbols) and QLQC (filled symbols) dxPG,S values for the sulfonamides in propyleneglycol ? water co-solvent mixtures at 303.15 K: circles SA, squares SP, triangles SMZ

372 J Solution Chem (2014) 43:360–374

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[15], has been used. This method only requires two specific experimental values, i.e. the

Gibbs energy of transfer of the drugs from neat water to neat propylene glycol and the

excess Gibbs energy of mixing at xPG = 0.50; thus, this method is easier to use than the

IKBI method although the results are not completely reliable, in particular in water-rich

mixtures.

4 Conclusions

Explicit expressions for local mole factions of propylene glycol and water around sul-

fonamides were derived on the basis of the IKBI method applied to equilibrium solubility

values of these drugs in propylene glycol ? water mixtures. Thus, these drugs are pref-

erentially solvated by water in water-rich mixtures (until 0.20 in mole fraction of co-

solvent) but are preferentially solvated by propylene glycol in all the other mixtures at all

temperatures considered. In a different approach, according to the QLQC method, these

compounds will be preferentially solvated by propylene glycol in all the mixtures con-

sidered; nevertheless, it is important to keep in mind that IKBI method is more acceptable

because it involves the use of more detailed thermodynamic information about the overall

system, whereas QLQC method results are easier to calculate from a practical point of

view but are not as exact as those from the former method.

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