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Solution thermodynamics of nimodipinein some PEG 400 + ethanol mixturesJorge L. Gómez a , Gerson A. Rodríguez a , Diana M. Cristancho a ,Daniel R. Delgado a & Fleming Martínez aa Departamento de Farmacia, Grupo de InvestigacionesFarmacéutico-Fisicoquímicas , Universidad Nacional de Colombia ,A.A. 14490, Bogotá , D.C , ColombiaPublished online: 22 Apr 2013.

To cite this article: Jorge L. Gómez , Gerson A. Rodríguez , Diana M. Cristancho , Daniel R. Delgado& Fleming Martínez (2013) Solution thermodynamics of nimodipine in some PEG 400 + ethanolmixtures, Physics and Chemistry of Liquids: An International Journal, 51:5, 651-662, DOI:10.1080/00319104.2013.771262

To link to this article: http://dx.doi.org/10.1080/00319104.2013.771262

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Solution thermodynamics of nimodipine in some PEG 400 + ethanolmixtures

Jorge L. Gómez, Gerson A. Rodríguez, Diana M. Cristancho, Daniel R. Delgadoand Fleming Martínez*

Departamento de Farmacia, Grupo de Investigaciones Farmacéutico-Fisicoquímicas, UniversidadNacional de Colombia, A.A. 14490, Bogotá D.C., Colombia

(Received 16 March 2012; final version received 26 January 2013)

The solubility of nimodipine (NMD) in several PEG 400 + ethanol mixtures wasdetermined at five temperatures from 293.15 to 313.15 K. The thermodynamic functionsof Gibbs energy, enthalpy and entropy of solution and of mixing were obtained by usingthe van’t Hoff and Gibbs equations from these solubility data and drug properties offusion. The highest solubility value was obtained in PEG 400 and the lowest in ethanolat all temperatures. A non-linear enthalpy–entropy relationship was observed from aplot of enthalpy vs. Gibbs energy of solution. Accordingly, the driving mechanism forNMD solubility in ethanol-rich mixtures is the enthalpy, whereas in PEG 400-richmixtures the driving mechanism is the entropy, although the molecular events involvedare unclear.

Keywords: nimodipine; PEG 400; ethanol; solubility; solution thermodynamics

1. Introduction

Nimodipine (NMD, Figure 1, molar mass 418.44 g mol−1) is a calcium channel blockerthat prevents calcium-dependent smooth muscle contraction and therefore the subsequentvasoconstriction. It exhibits greater effects on cerebral circulation than on peripheralcirculation, and for this reason, it is specially used as an adjunct to improve the neuro-logical outcome following subarachnoid haemorrhage from ruptured intracranial aneur-ysm [1].

On the other hand, NMD aqueous solubility is too low to allow designing homo-geneous liquid dosage forms in solvents that are strictly aqueous [2]. For this reason,disperse and coarse dosage systems have been investigated and developed, which includeliposomes [3], solid dispersions [4,5], cyclodextrin inclusion complexes [6–8], hydrogelsand hydrophilic matrices [9,10], and some emulsions [11]. In each of these formulations,this drug is dispersed in a coarse way instead of a molecular way. Nevertheless, severalmixed solvents have been tested to improve the solubility of different kinds of drugs whenthese are poorly soluble in water as NMD is [12,13]. Keeping this in mind, it is importantto consider that the behaviour of drugs in solvent mixtures has been evaluated for thepurpose of purification of substances by pharmaceutical chemists and pre-formulationstudies and design of pharmaceutical dosage forms by product designers and developers[14]. Hence, it is very important to determine systematically their equilibrium solubilitiesin order to obtain complete physicochemical data about the relevant liquid pharmaceutical

*Corresponding author. Email: fmartinezr@unal.edu.co

Physics and Chemistry of Liquids, 2013Vol. 51, No. 5, 651–662, http://dx.doi.org/10.1080/00319104.2013.771262

© 2013 Taylor & Francis

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systems. One the other hand, the temperature dependence of the solubility allows athermodynamic analysis that permits insight into the molecular mechanisms involved inthe different drug dissolution processes [15].

It is important to note that the physicochemical information about the solubility of thisdrug in non-aqueous media is relatively scarce [2,16]. For this reason, the main objectiveof this study was to evaluate the effect of the solvent composition on the solubility andsolution thermodynamics of NMD in binary mixtures conformed by polyethylene glycol400 (PEG 400) and ethanol based on the van’t Hoff method, including the respectivecontributions by mixing of this compound towards the solution processes. The PEG400 + ethanol mixtures are commonly employed in the formulation of liquid dosageforms and other medicines. Some PEG 400 + ethanol mixtures have been studiedpreviously as possible solvents for some drugs [17,18].

2. Experimental

2.1. Reagents

Nimodipine (1,4-dihydro-2,6-dimethyl-4-(3-nitrophenyl)-3,5-pyridinedicarboxylic acid 2-methoxyethyl 1-methylethyl ester; CAS no. 66085-59-4; Haohua Ind. & Co., China),polyethylene glycol 400 (DOW Chemical Co., USA), and absolute ethanol A.R. (Merck,Darmstadt, Germany) used in this research were in agreement with the quality require-ments of the American Pharmacopeia, USP [19].

2.2. Solvent mixtures preparation

Both solvents were dried by using molecular sieve (3 Å, Merck) before preparing themixtures. All PEG 400 + ethanol mixtures were prepared by mass, using an OhausPioneer TM PA214 analytical balance with a sensitivity of ±0.1 mg, in quantities of50 g. The mass fractions of PEG 400, wPEG, of the nine binary mixtures prepared variedby 0.10 from 0.10 to 0.90.

2.3. Solubility determinations

An excess of NMD was added to approximately 10 g of each solvent mixture or neatsolvents in stoppered dark glass flasks. The flasks with the solid–liquid mixtures wereplaced in thermostatic mechanical shakers (Julabo SW23, Seelbach, Germany) kept at303.15, 308.15, or 313.15 (±0.05) K or placed in re-circulating thermostatic baths (NeslabRTE 10 Digital One Thermo Electron Company, Waltham, MA, USA) kept at 293.15 or

NH

CH3

CH3 O

OOCH3

NO2

OH3C

H3C

O

Figure 1. Molecular structure of nimodipine.

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298.15 (±0.05) K for at least 7 days to reach the equilibrium. After this time, thesupernatant solutions were filtered at isothermal conditions (Swinnex®-13, MilliporeCorp., Billerica, MA, USA) to ensure that they were free of particulate matter beforesampling for composition analysis. The NMD concentrations were determined by UV-spectrophotometric analysis at 236 nm after alcoholic dilution (UV/VIS BioMate 3Thermo Electron Company, Waltham, MA, USA). All the solubility experiments wererun at least in triplicates. In order to transform mole fractions into molar concentrations(mol dm−3), the density of the saturated solutions was determined with a digital densitymetre (DMA 45 Anton Paar, Graz, Austria) connected to the same re-circulating thermo-static baths [20].

2.4. Calorimetric study

The melting point and enthalpy of fusion of NMD were determined by DSC studies (DSC823E Mettler Toledo, Columbus, OH, USA). Thermal analyses were performed at aheating rate of 10 K min−1 in a dynamic nitrogen atmosphere (60 cm3 min−1). Nearly1.5 mg of drug was used. The equipment was calibrated using indium as standard [21].

3. Results and discussion

As has been made with other drugs in similar studies in non-aqueous solvent mixtures[22–24], it is important to consider that NMD has hydrogen donor but mainly acceptorgroups (Figure 1) and it could interact in solution as a Lewis acid and mainly as a Lewisbase, in order to establish hydrogen bonds with proton–acceptor or donor functionalgroups of the solvents (–OH and –O– groups) [25]. On the other side, this drug couldalso interact by means of weak London forces because of its aromatic group.

3.1. Experimental and ideal solubility

Table 1 shows the experimental solubilities of NMD expressed in mole fractions, x2. Inalmost all cases, the coefficients of variation of the solubility were smaller than 2.0%. Thesolubility values expressed in molarity are presented in Figure 2. The molarities (C) werecalculated from NMD mole fractions by using Equation (1), where ρ is the density of thesaturated solutions and M1 and M2 are the molar masses of solvents and solute, respec-tively [25]. Table 2 shows the density of the saturated solutions at all compositions andtemperatures studied.

C ¼ 1000ρx2M1ð1� x2Þ þM2x2

(1)

If the mole fraction is considered, it happens that in all cases the solubility increases withthe temperature and the PEG 400 proportion in the mixtures. The highest solubility ofNMD was obtained in PEG 400 at 313.15 K, whereas the lowest value was found inethanol at 293.15 K. Nevertheless, if the molarity scale is considered at temperatures from293.15 to 308.15 K, the maximum solubility is obtained in the mixtures of 0.80 or 0.90 inmass fraction of PEG 400 instead of pure ethanol. This apparent contradiction is just aconsequence of the definitions of each concentration scale and, in this particular case,because of the great difference in molar masses between both solvents (400.0 and46.07 g mol−1 for PEG 400 and ethanol, respectively). Our solubility values in neat

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solvents at 293.15 K are slightly higher than the values reported by Squillante et al. [16],i.e. 6.45 × 10−2 and 0.191 mol dm−3, in ethanol and PEG 400, respectively [16], comparedto 8.31 × 10−2 and 0.204 mol dm−3, in ethanol and PEG 400, respectively (this work).These little differences could be attributed to different equilibration times, polymorphicsolids or many other factors described in the literature. In contrast, no solubility values forthis drug in these mixed solvents are available in the literature and therefore no compar-ison is possible. On the other hand, the ideal solubility of a crystalline solute can becalculated by using Equation (2) [15]:

ln x2�id ¼ �ΔfusHðTfus � TÞRTfusT

þ ΔCp

R

� � ðTfus � TÞT

þ lnT

Tfus

� �� �(2)

0.80

0.80 1.00

0.70

0.60

0.60

0.50

0.40

0.40

0.30

0.20

0.20

0.10

0.000.00

Mass fraction of PEG 400

NM

D /

mol

dm

–3

Figure 2. Experimental solubility of nimodipine in PEG 400 + ethanol mixtures, expressed inmolarity, as a function of composition of solvent mixtures. (●): 293.15 K; (■): 298.15 K; (▲):303.15 K; (○): 308.15 K; (□): 313.15 K.

Table 1. Experimental solubility of nimodipine in PEG 400 + ethanol mixtures, expressed in molefraction, including ideal solubility at several temperatures (values in parentheses are the standarddeviations).

wPEGa

100 x2

293.15 K 298.15 K 303.15 K 308.15 K 313.15 K

0.00 0.495 (0.012) 0.693 (0.010) 0.947 (0.019) 1.35 (0.03) 1.80 (0.03)0.10 0.637 (0.014) 0.858 (0.022) 1.123 (0.016) 1.50 (0.03) 1.98 (0.03)0.20 0.901 (0.003) 1.125 (0.011) 1.412 (0.027) 1.81 (0.04) 2.21 (0.05)0.30 1.21 (0.03) 1.47 (0.03) 1.82 (0.05) 2.24 (0.03) 2.77 (0.08)0.40 1.51 (0.03) 1.891 (0.022) 2.26 (0.06) 2.82 (0.05) 3.36 (0.07)0.50 1.91 (0.04) 2.308 (0.002) 2.86 (0.03) 3.54 (0.10) 4.15 (0.08)0.60 2.274 (0.005) 2.77 (0.07) 3.40 (0.09) 4.34 (0.11) 5.23 (0.02)0.70 2.870 (0.029) 3.59 (0.07) 4.39 (0.05) 5.94 (0.10) 7.38 (0.11)0.80 3.57 (0.04) 4.64 (0.10) 5.77 (0.12) 7.84 (0.16) 10.04 (0.22)0.90 4.61 (0.04) 6.19 (0.10) 8.33 (0.17) 11.74 (0.20) 15.07 (0.26)1.00 7.24 (0.18) 9.52 (0.18) 12.75 (0.27) 18.43 (0.03) 26.51 (0.29)Ideal 2.17 (0.03) 2.68 (0.04) 3.31 (0.05) 4.07 (0.06) 4.98 (0.07)

Note: awPEG is the mass fraction of PEG 400 in the solvent mixtures free of nimodipine.

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where x2-id is the ideal solubility of the solute as mole fraction, ΔfusH is the molarenthalpy of fusion of the pure solute (at the melting point), Tfus is the absolute meltingpoint, T is the absolute solution temperature, R is the gas constant (8.314 J mol−1 K−1),and ΔCp is the difference between the molar heat capacity of the crystalline form and themolar heat capacity of the hypothetical supercooled liquid form, both at the solutiontemperature [15]. According to the literature, ΔCp is assumed to be approximately equal tothe entropy of fusion (ΔfusS) calculated as the quotient ΔfusH/Tfus [15]. The valuesobtained by means of DSC for NMD were 41.7 (±0.6) kJ mol−1 and 397.2 K for ΔfusHand Tfus, respectively. These values are similar to the values reported by Guo et al. [26].The ideal solubility values of NMD are also presented in Table 1. In ethanol-richmixtures, the ideal solubilities were greater than the experimental ones, but in PEG400-rich mixtures the behaviour was opposite, particularly in neat PEG 400.

3.2. Nimodipine activity coefficients

The solute activity coefficient in the solution (γ2) is calculated as x2-id/x2 from therespective ideal and experimental solubility values presented in Table 1, and it is anindication of the deviation presented by NMD from its ideal behaviour [24]. Table 3shows the NMD activity coefficients as a function of temperature. Accordingly, the γ2values vary from 0.2 to 4.0 and they diminish in ethanol-rich mixtures (γ2 values greaterthan 1.0) and in PEG 400-rich mixtures (γ2 values lower than 1.0) as the temperatureincreases. These results indicate more ideal solubility behaviour at high temperatures inthe former case and less ideal in the latter case.

From the γ2 values, a rough estimate of solute–solvent intermolecular interactions canbe made by considering the following expression [27]:

ln γ2 ¼ ðe11 þ e22 � 2e12ÞV2’21

RT(3)

Table 2. Density of saturated solutions at several temperatures.

wPEGa fPEG

b xPEGc M1

d/g mol−1

ρ/g cm−3e

293.15 K 298.15 K 303.15 K 308.15 K 313.15 K

0.00 0.0000 0.0000 46.07 0.8045 0.8067 0.8088 0.8115 0.81490.10 0.0721 0.0126 50.54 0.8309 0.8322 0.8341 0.8367 0.83990.20 0.1489 0.0280 55.97 0.8609 0.8624 0.8639 0.8658 0.86830.30 0.2307 0.0470 62.72 0.8915 0.8930 0.8945 0.8967 0.89850.40 0.3181 0.0713 71.31 0.9243 0.9255 0.9270 0.9292 0.93170.50 0.4116 0.1033 82.62 0.9591 0.9610 0.9636 0.9655 0.96710.60 0.5121 0.1473 98.21 0.9904 0.9883 0.9863 0.9848 0.98290.70 0.6201 0.2118 121.04 1.0247 1.0236 1.0224 1.0208 1.02010.80 0.7367 0.3154 157.69 1.0600 1.0569 1.0537 1.0510 1.04780.90 0.8630 0.5090 226.21 1.0954 1.0915 1.0877 1.0842 1.08031.00 1.0000 1.0000 400.00 1.1331 1.1282 1.1236 1.1201 1.1178

Notes: awPEG is the mass fraction of PEG 400 in the solvent mixtures free of nimodipine. bfPEG is the volumefraction of PEG 400 in the solvent mixtures free of nimodipine. cxPEG is the mole fraction of PEG 400 in thesolvent mixtures free of nimodipine. dM1 is the molar mass of the solvent mixtures free of nimodipine. eMeanuncertainty was near to 0.0004 g cm−3.

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where the subscript 1 stands for the solvent (i.e. the solvent mixture: PEG 400 + ethanol);e11, e22 and e12 represent the solvent–solvent, solute–solute, and solvent–solute interactionenergies, respectively; V2 is the molar volume of the supercooled liquid solute; and φ1 isthe volume fraction of the solvent in the saturated solution. As a first approximation, forrelatively low solubilities x2, the term V2φ1

2/RT may be considered constant; thus, γ2depends mainly on e11, e22 and e12 [27]. The terms e11 and e22 are unfavourable for drugsolubility, whereas the term e12 favours the solution process. This happens because energymust be supplied first against the cohesive forces of the solute in solid state to separatethem and then against the cohesive forces of the solvent to create the respective cavity (forsolute accommodation). These processes decrease drug solubility. On the other hand, thesolute–solvent interaction is exothermic and results mainly from the van der Waals andLewis acid–base interactions, which increase the drug solubility. If the calorimetricbehaviour of the solid phases in equilibrium with the saturated solutions was the sameas the original drug sample, it could affirm that the contribution of the term e22 is almostconstant in every solvent system.

As a qualitative approach, the following analysis could be made based on theenergetic quantities and magnitudes described in Equation (3): the term e11 is highest inneat ethanol (Hildebrand solubility parameter δ = 26.6 MPa1/2) and lowest in PEG 400(δ = 21.7 MPa1/2) [25,28]. The term e22 would be relatively high based on the propertiesof fusion of this drug. Thus, the low γ2 values exhibited by this drug in these solventmixtures could indicate a great contribution of the term e12 in the dissolution process ofthis drug, implying high solute–solvent interactions despite the solvent, although it is clearthat they are superior in the PEG 400-rich mixtures.

3.3. Thermodynamic functions of solution

Apparent standard enthalpy change of solution (ΔsolnH°) is obtained from the modifiedvan’t Hoff equation by using the mean harmonic temperature (Thm) [29], calculated as

Thm ¼ n=Xni¼1

ð1=TÞ (4)

Table 3. Nimodipine activity coefficients (γ2) in PEG 400 + ethanol mixtures at severaltemperatures.

wPEGa 293.15 K 298.15 K 303.15 K 308.15 K 313.15 K

0.00 4.38 (0.13) 3.87 (0.08) 3.49 (0.09) 3.01 (0.08) 2.78 (0.06)0.10 3.40 (0.09) 3.12 (0.09) 2.95 (0.06) 2.71 (0.07) 2.52 (0.05)0.20 2.41 (0.04) 2.38 (0.04) 2.34 (0.06) 2.25 (0.06) 2.25 (0.06)0.30 1.79 (0.05) 1.83 (0.05) 1.81 (0.06) 1.81 (0.04) 1.80 (0.06)0.40 1.43 (0.04) 1.418 (0.027) 1.46 (0.04) 1.44 (0.03) 1.48 (0.04)0.50 1.132 (0.029) 1.162 (0.017) 1.155 (0.022) 1.15 (0.04) 1.201 (0.029)0.60 0.953 (0.014) 0.969 (0.027) 0.97 (0.03) 0.937 (0.028) 0.953 (0.015)0.70 0.755 (0.014) 0.748 (0.018) 0.754 (0.015) 0.685 (0.015) 0.675 (0.014)0.80 0.607 (0.011) 0.578 (0.015) 0.573 (0.015) 0.518 (0.013) 0.496 (0.013)0.90 0.470 (0.008) 0.433 (0.010) 0.397 (0.010) 0.347 (0.008) 0.331 (0.008)1.00 0.299 (0.009) 0.282 (0.007) 0.259 (0.007) 0.221 (0.003) 0.188 (0.003)

Note: awPEG is the mass fraction of PEG 400 in the solvent mixtures free of nimodipine.

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where n is the number of temperatures studied. In the present case (from 293.15 to313.15 K), the Thm value obtained is 303.0 K. Thus, ΔsolnH° is obtained from [22–24]

@ ln x2@ 1=T � 1=303Kð Þ

� �P

¼ �ΔsolnH�

R(5)

The apparent standard Gibbs energy change for the solution process (ΔsolnG°), consider-ing the approach proposed by Krug et al. [29], is calculated at 303.0 K by means of

ΔsolnG� ¼ �R� 303 K � intercept (6)

in which the intercept used is the one obtained in the analysis by treatment of ln x2 as afunction of 1/T – 1/303 K. Finally, the apparent standard entropic change for a solutionprocess (ΔsolnS°) is obtained from the respective ΔsolnH° and ΔsolnG° values at 303.0 K byusing

ΔsolnS° ¼ ΔsolnH� � ΔsolnG�ð Þ

303K(7)

Table 4 presents the standard molar thermodynamic functions for the dissolution of NMDin all PEG 400 + ethanol solvent mixtures, including those for neat solvents and the idealsolution process. The propagation of uncertainties in the thermodynamic quantities calcu-lations was made according to the literature [30].

The standard Gibbs energy of solution is positive in every case as is also the enthalpyand entropy of solution; therefore, the respective processes are always endothermic andentropy-driven. The ΔsolnH° and ΔsolnS° values diminish from pure ethanol to the mixturewPEG = 0.60 and later they increase up to pure PEG 400.

The relative contributions by enthalpy (ζH) and entropy (ζTS) towards the solutionprocess are given by Equations (8) and (9) [31]:

Table 4. Thermodynamic quantities relative to solution process of nimodipine in PEG400 + ethanol mixtures including ideal process at 303.0 K (values in parentheses are the standarddeviations).

wPEGa ΔsolnG°/kJ mol−1 ΔsolnH°/kJ mol−1 ΔsolnS°/J mol−1 K−1 TΔsolnS°/kJ mol−1 ζH

b ζTSb

0.00 11.72 (0.23) 49.5 (1.2) 125 (4) 37.8 (1.2) 0.567 0.4330.10 11.30 (0.21) 43.1 (1.1) 105 (3) 31.8 (1.0) 0.575 0.4250.20 10.72 (0.17) 34.6 (1.0) 79 (3) 23.9 (0.8) 0.592 0.4080.30 10.09 (0.23) 31.7 (1.3) 71 (3) 21.6 (1.0) 0.595 0.4050.40 9.53 (0.18) 30.5 (1.1) 69 (3) 21.0 (0.9) 0.592 0.4080.50 8.97 (0.15) 30.2 (1.2) 70 (3) 21.2 (0.9) 0.587 0.4130.60 8.48 (0.14) 32.3 (1.3) 78 (3) 23.8 (1.0) 0.576 0.4240.70 7.78 (0.12) 36.5 (1.7) 95 (5) 28.7 (1.4) 0.560 0.4400.80 7.10 (0.14) 39.5 (1.6) 107 (5) 32.4 (1.4) 0.549 0.4510.90 6.24 (0.10) 45.9 (1.3) 131 (4) 39.7 (1.3) 0.536 0.4641.00 5.07 (0.08) 49.6 (2.6) 147 (8) 44.6 (2.4) 0.527 0.473Ideal 8.59 (0.13) 31.8 (0.5) 76.5 (1.6) 23.2 (0.5) 0.578 0.422

Notes: awPEG is the mass fraction of PEG 400 in the solvent mixtures free of nimodipine. bζH and ζTS are therelative contributions by enthalpy and entropy towards the Gibbs energy of solution. These values werecalculated by means of Equations (8) and (9), respectively.

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ζH ¼ ΔsolnH�j jΔsolnH�j j þ TΔsolnS�j j (8)

ζ TS ¼TΔsolnS�j j

ΔsolnH�j j þ TΔsolnS�j j (9)

The main contributor to the (positive) standard molar Gibbs energy of solution of NMD isthe (positive) enthalpy in all cases, although in some cases the contributions are similar,indicating energetic predominance on the dissolution processes. It is interesting to notethat ζH and ζTS for the ideal process are similar to the ones of the mixture wPEG = 0.60 in asimilar way as the thermodynamic quantities also are.

3.4. Thermodynamic functions of mixing

The solution process may be represented by the following hypothetic stages [32]:

SoluteðSolidÞ ! SoluteðLiquidÞ at Tfus ! SoluteðLiquidÞ at Thm ! SoluteðSolutionÞ

where the solution stages are solute fusion, cooling the liquid solute to the mean harmonictemperature Thm (303.0 K), and subsequent mixing of the hypothetical supercooled liquidsolute with the solvent at this temperature. This also allows the calculation of the partialthermodynamic contributions to the overall solution process by means of Equations (10)and (11), respectively:

ΔsolnH° ¼ ΔfusH

303 þ ΔmixH° (10)

ΔsolnS° ¼ ΔfusS

303 þ ΔmixS° (11)

where ΔfusH303 and ΔfusS

303 represent the thermodynamic functions of fusion of NMDand its cooling to the harmonic mean temperature, 303.0 K. However, in this research, theΔsolnH°

-id and ΔsolnS°-id values for the ideal solution processes were used instead of

ΔfusH303 and ΔfusS

303 as has been done previously [22–24]. Figure 3 summarises thethermodynamic quantities of mixing of supercooled liquid NMD with all solvent mix-tures. The Gibbs energy of mixing is positive from neat ethanol to the mixturewPEG = 0.50 and negative after this solvent composition. This is because the experimentalsolubilities are lower or greater than the ideal ones at all temperatures, according to thecomposition.

The ideal dissolution contributions (related to solute fusion process) to the enthalpyand entropy of dissolution of NMD, i.e. ΔsolnH°

-id and ΔsolnS°-id, are positive (Table 4), as

also are the quantities of mixing, except for the ones in the region 0.30 ≤ wPEG ≤ 0.50. Onthe other hand, it is clear that the contribution of the energetic and organisational aspectsof the mixing process towards the overall dissolution is almost proportional in the presentsolvent system despite the sign of positive or negative.

According to Figure 3, the ΔmixG° values diminish as the PEG 400 proportionincreases in the mixtures, whereas the ΔmixH° and ΔmixS° values decrease non-linearlyfrom pure ethanol up to the mixtures with wPEG = 0.40 and 0.50, where the lowest valuesare obtained and later increasing to reach the highest values in neat PEG 400.

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3.5. Thermodynamic functions of transfer

In order to verify the effect of co-solvent composition on the thermodynamic functiondriving the solution process, Table 5 summarises the thermodynamic functions of transferof NMD from the more polar solvents to the less polar ones. These new functions werecalculated as the differences between the thermodynamic quantities of solution obtained inthe more polar mixtures and in the less polar ones.

If the addition of PEG 400 to ethanol is considered (being the solvent mixture lesspolar as the PEG 400 proportion increases), as has been done earlier [22–24], thefollowing happens: From neat ethanol to 0.40 in mass fraction of PEG 400(ΔA→BG° < 0, ΔA→BH° < 0 and ΔA→BS° < 0), the solution process is driven by theenthalpy; whereas from this PEG 400 proportion to the mixture wPEG = 0.50(ΔA→BG° < 0, ΔA→BH° < 0 and ΔA→BS° > 0), the solution process is enthalpy- andentropy-driven. Finally, in the region 0.50 ≤ wPEG ≤ 1.00 (ΔA→BG° < 0, ΔA→BH° > 0 andΔA→BS° > 0), the process is entropy-driven. Nevertheless, the molecular events involvedremain unclear because of the lack of information about structural effects in those solventmixtures.

25.0

20.0

15.0

10.0

5.0

–5.0

0.0

0.00 0.20 0.40 0.60 0.80 1.00

Qua

ntity

/ kJ

mol

–1

Mass fraction of PEG 400

Figure 3. Thermodynamic quantities of mixing of nimodipine in PEG 400 + ethanol mixtures at303.0 K as function of composition of solvent mixtures. (■): ΔmixH°; (▲): TΔmixS°; (●): ΔmixG°.

Table 5. Thermodynamic quantities relative to transfer of nimodipine from more polar solvents toless polar solvents in PEG 400 + ethanol mixtures at 303.0 K (values in parentheses are the standarddeviations).

wPEGa,b ΔA→BG°/ ΔA→BH°/ ΔA→BS°/ TΔA→BS°/

A B kJ mol−1 kJ mol−1 J mol−1 K−1 kJ mol−1 ζHc ζTS

c

0.00 0.40 −2.19 (0.30) −19.0 (1.6) −55 (5) −16.8 (1.5) 0.531 0.4690.40 0.50 −0.56 (0.23) −0.4 (1.6) 1 (4) 0.2 (1.2) 0.659 0.3410.50 1.00 −3.90 (0.16) 19.5 (2.8) 77 (8) 23.4 (2.6) 0.454 0.546

Notes: awPEG is the mass fraction of PEG 400 in the solvent mixtures free of nimodipine. bA and B are the morepolar and less polar media, respectively. cζH and ζTS are the relative contributions by enthalpy and entropytowards the Gibbs energy of transfer. These values were calculated by means of equations analogous toEquations (8) and (9), respectively.

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3.6. Enthalpy–entropy compensation

There are some reports in the literature that have demonstrated the non-existence ofenthalpy–entropy compensation effects for the solubility of drugs in various non-aqueoussolvent mixtures [22–24,33]. This analysis has been used in order to identify the mechan-ism of the solvent action on the drug dissolution processes. Weighted graphs of ΔsolnH° asa function of ΔsolnG° at the harmonic mean temperature permit such an analysis [34].

Figure 4 shows that NMD in the PEG 400 + ethanol solvent system presents a non-linear ΔsolnH° vs. ΔsolnG° curve with a variable positive slope in the interval from pureethanol up to wPEG = 0.50, and beyond this PEG 400 proportion up to pure PEG 400 avariable but negative slope is obtained. Accordingly, the driving mechanism for solubilityis the enthalpy in the former case, probably due to better solvation of the drug because ofthe ethanol molecules, whereas in the latter case the driving mechanism is the entropy,involving probably the great flexibility of the PEG 400 molecules.

On the other hand, accordingly with the literature [35–37], another interesting com-pensation graph is obtained by plotting ΔsolnH° as a function of TΔsolnS°. Normally twolines are obtained according to the composition of the mixtures, and in this way, the linearequations with slopes lower than 1.0 correspond to the entropy-driven solution processes,whereas those with slopes higher than 1.0 correspond to the enthalpy-driven processes. Inthis way, Figure 5 shows that effectively two linear equations are obtained for NMD asfollows: for the region 0.00 ≤ wPEG ≤ 0.40, the equation ΔsolnH° = 1.113(±0.025) × TΔsolnS° + 7.6 (±0.7), with r2 adjusted: 0.998 and typical error: 0.371, wasobtained; whereas for the region 0.40 ≤ wPEG ≤ 1.00, the equation ΔsolnH° = 0.831(±0.011) × TΔsolnS° + 12.7 (±0.3), with r2 adjusted: 0.999 and typical error: 0.242, wasobtained.

4. Conclusions

From all the topics discussed here, it can be concluded that the solution process of NMDin the PEG 400 + ethanol mixtures depends on the solvent composition. Non-linear

55.0

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45.0

40.0

35.0

30.0

25.0

20.0

Δ sol

nH°/

kJ m

ol–1

ΔsolnG°/kJ mol–1

3.00 5.00 7.00 9.00 11.00 13.00

1.00

0.90

0.800.70

0.60

0.50 0.400.30

0.20

0.10

0.00

Figure 4. ΔsolnH° vs. ΔsolnG° enthalpy–entropy compensation plot for the dissolution process ofnimodipine in PEG 400 + ethanol mixtures at 303.0 K. The points represent the values obtained ateach mass fraction of PEG 400 in the solvent mixtures free of nimodipine.

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ΔsolnH° vs. ΔsolnG° compensation was found for this drug in this solvent system. In thiscontext, enthalpy-driving was found for the solution processes in compositions0.00 ≤ wPEG ≤ 0.40, whereas entropy-driving was obtained for the other region.Nevertheless, the molecular events present are unclear because of the lack of informationabout structural facts in these mixtures. Ultimately, it can be said that the data presented inthis report expand the physicochemical information about drugs in non-aqueous solventmixtures.

AcknowledgementsWe thank the Department of Pharmacy of the Universidad Nacional de Colombia for facilitating theequipment and laboratories used. We also thank the Laboratorio Procaps de Colombia for facilitatingthe DSC equipment.

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