Thermodynamic and structural aspects of sulfonamide crystals and solutions

Thermodynamic and Structural Aspects of Sulfonamide Crystals and Solutions GERMAN L. PERLOVICH,1,2 VALERY V. TKACHEV,1,3 NADEZDA N. STRAKHOVA,1 VLADIMIR P. KAZACHENKO,1 ¨ RGEN SCHAPER,4 OLEG A. RAEVSKY1 TATYANA V. VOLKOVA,2 OLEG V. SUROV,2 KLAUS-JU 1 Department of Computer-Aided Molecular Design, Institute of Physiologically Active Compounds, Russian Academy of Sciences, 142432 Chernogolovka, Russia 2

Institute of Solution Chemistry, Russian Academy of Sciences, 153045 Ivanovo, Russia

3

Laboratory of Structural Chemistry, Institute of Problems of Chemical Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russia 4

Research Center Borstel, Leibniz Center for Medicine and Biosciences, D-23845 Borstel, Germany

Received 22 December 2008; accepted 12 March 2009 Published online 30 April 2009 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jps.21784

ABSTRACT: The crystal structures of three sulfonamides with the general structure 4-NH2-C6H4-SO2NH-C6H4/3-R (R ¼ 4-Et; 4-OMe; 5-Cl-2-Me) have been determined by X-ray diffraction. On the basis of our previous data and the results obtained a comparative analysis of crystal properties was performed: molecular conformational states, packing architecture, and hydrogen bond networks using graph set notations. The thermodynamic aspects of the sulfonamide sublimation process have been studied by investigating the temperature dependence of vapor pressure using the transpiration method. A regression equation was derived describing the correlation between sublimation entropy terms and crystal density data calculated from X-ray diffraction results. Also correlations between sublimation Gibbs energies and melting points, on the one hand, and between sublimation enthalpies and fusion enthalpies at 298 K, on the other hand, were found. These dependencies give the opportunity to predict sublimation thermodynamic parameters by simple thermo-physical experiments (fusion characteristics). Solubility processes of the compounds in water, n-hexane, and n-octanol (as phases modeling various drug delivery pathways and different types of membranes) were investigated and corresponding thermodynamic functions were calculated as well. Thermodynamic characteristics of sulfonamide solvation were evaluated. For compounds with similar structures processes of transfer from one solvent to another one were studied by a diagram method combined with analysis of enthalpic and entropic terms. Distinguishing between enthalpy and entropy, as is possible through the present approach, leads to the insight that the contribution of these terms is different for different molecules (entropy- or enthalpy-determined). Thus, in contrast to interpretation of only the Gibbs energy of transfer, being extensively used for pharmaceuticals in the form of the partition coefficient (log P), the analysis of thermodynamic functions of the transfer process provides additional mechanistic information. This may be important for further evaluation of the physiological distribution of drug molecules and may provide a better understanding of biopharmaceutical properties of drugs. ß 2009 WileyLiss, Inc. and the American Pharmacists Association J Pharm Sci 98:4738–4755, 2009

Correspondence to: German L. Perlovich (Telephone: þ7-4932-533784; Fax: þ7-4932-336237; E-mail: [email protected])

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Keywords: 4-amino-N-(4-ethylphenyl)-benzene-sulfonamide; 4-amino-N-(4-methoxyphenyl)-benzene-sulfonamide; 4-amino-N-(5-chloro-2-methylphenyl)-benzene-sulfonamide; sublimation thermodynamics; solubility; solvation; crystal structure; transfer process

INTRODUCTION Sulfonamides (SAs) 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 extensive use of antibiotics has diminished the usefulness of SAs, they still occupy a relatively small but important place in the therapeutic resources of physicians. It should be mentioned, that there have been some successful attempts to correlate different physicochemical characteristics of these compounds with chemotherapeutic activity: pKa, NMR shifts, protein binding, and electronic charge distribution.1–5 Unfortunately, the in vivo action of SAs is complicated and cannot be described in a simple way. There is not enough detailed information available to propose suitable mechanisms for the process of transfer of SAs between immiscible liquid phases or between aqueous media and biological membrane models. Probably this information is needed in order to explain the differences in the pharmacological power as a function of the molecular structure.6 A careful analysis of published SA crystal lattice structures has been carried out by Adsmond and Grant.7 In this work special attention has been paid to the characterization and systematization of hydrogen bond networks by using graph set notations. Moreover, the authors tried to describe donor and acceptor affinities of atoms in the molecules studied on the basis of a statistical analysis of hydrogen bonds of solvated and nonsolvated crystals. In our previous work8,9 we tried to study the packing architecture and topology of hydrogen bond networks in the non-solvated phase of some SAs. The hydrogen bond networks are very sensitive to molecular topology. It has been shown that there is a maximal critical free volume per molecule in the crystals when the packing architecture is changed. The sublimation, solubility, and solvation characteristics of some SAs such as N-(2-chlorophenyl)benzenesulfonamide (I), N-(2,3-dichlorophenyl)benzenesulfonamide (II), N-(4-chlorophenyl)-benzenesulfonamide (III), 4-amino-N-(4-chlorophenyl)-benzenesulfonamide (IV), 4-amino-N-(2,3dichlorophenyl)-benzenesulfonamide (V), 4-aminoDOI 10.1002/jps

N-(3,4-dichlorophenyl)-benzenesulfonamide (VI), and 4-amino-N-(2,5-dichlorophenyl)-benzenesulfonamide (VII) (Scheme 1) have been described by us before.8,9 As a continuation of this study, the solvation and structural aspects of 4-amino-N-(4ethylphenyl)-benzenesulfonamide (VIII), 4-aminoN-(4-methoxyphenyl)-benzenesulfonamide (IX), 4amino-N-(5-chloro-2-methylphenyl)-benzenesulfonamide (X) (Scheme 1) are presented in this work. The choice of the compounds has been dictated by the following aims. Firstly, to analyze the impact of various substituents on the interaction of molecules in the crystal lattice: (a) packing architecture of the crystal lattices; (b) geometry and topology of hydrogen bond networks; (c) thermodynamic aspects (enthalpic and entropic terms) of the crystals; (d) thermophysical characteristics of the crystals. Secondly, to characterize the properties of the molecules in pharmaceutically important solvents in order to find out correlations between the structure or topology of the molecules with their solubility, solvation, and partitioning properties. The presented approach could help to design drug molecules with defined characteristics and to predict their drug transport properties.

Scheme 1.

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EXPERIMENTAL Compounds and Solvents The chemical synthesis of SAs (VIII–X) has been performed according to procedures described earlier10–12 by reaction of a substituted aromatic amine (here 4-ethyl-, 4-methoxy- or 5-chloro-2methyl-aniline) with 4-acetylaminobenzenesulfonyl chloride in dry pyridine, followed by hydrolytic deacetylation in alkaline aqueous medium (1 M NaOH) and precipitation of the end product by acidification (1 M HCl) to pH 5. The compounds have been carefully purified by re-crystallization from water–ethanol solution. The precipitate has been filtered and dried at room temperature under vacuum until the mass of compounds remained constant. The outlined procedure has been repeated several times and the product checked by NMR after each re-crystallization step until the proton NMR signals corresponded to purity of the compound better than 99%. Single crystals of the title compounds were grown from a water–ethanol solution (initial composition 20:1, v/v) by vapor diffusion of ethanol vapor into pure water.13 1-Octanol (lot 11K3688) as obtained from Sigma-Aldrich Inc. (St. Louis, MO), and n-hexane (lot 07059903C) was obtained from SDS (Peypin, France). Methods X-Ray Diffraction Experiments Single-crystal X-ray measurements were carried out using a Nonius CAD-4 diffractometer with graphite-monochromated Mo Ka radiation ˚ ). Intensity data were collected at (l ¼ 0.71069 A 258C by means of a v  2u scanning procedure. The crystal structures were solved using direct methods and refined by means of a full-matrix leastsquares procedure. CAD-414 was applied for data collection, data reduction, and cell refinement. Programs SHELXS-97 and SHELXL-9715 were used to solve and to refine structures, respectively. Solubility Determination All the experiments were carried out by the isothermal saturation method at several temperature points: 20, 22, 25, 30, 37, and 42  0.18C. The solid phase was removed by isothermal filtration (Acrodisc CR syringe filter, PTFE, 0.2 mm pore

size) or centrifugation (Germany Thermo Electron Corporation, Langenselbold, Germany). The experimental results are stated as the average of at least three replicated experiments. The molar solubilities of the drugs were measured spectrophotometrically with an accuracy of 2–2.5% using a protocol described previously.16 Standard Gibbs energies of the dissolution processes DG0sol were calculated using the following equation: DG0sol ¼ RT ln X2

(1)

where X2 is the drug molar fraction in the saturated solution. The standard solution enthal0 pies DHsol were calculated using the van’t Hoff equation: 0 dðln X2 Þ DHsol ¼ dT RT2

(2)

assuming that the activity coefficients of the considered drugs in the solvents are equal to 1 and solution enthalpies are independent of concentration. The temperature dependence of the solubility of drugs within the chosen temperature interval can be described by a linear function: ln X2 ¼ A 

B T

(3)

This indicates that the change in heat capacity of the solutions with the temperature is negligibly small. The standard solution entropies DS0sol were obtained from the well-known equation: 0  TDS0sol DG0sol ¼ DHsol

(4)

Sublimation Experiments Sublimation experiments were carried out by the transpiration method as was described elsewhere.17 In brief: a stream of an inert gas passes above the sample at a constant temperature and at a known slow constant flow rate in order to achieve saturation of the carrier gas with the vapor of the substance under investigation. The vapor is condensed at some point downstream, and the mass of sublimate and its purity determined. The vapor pressure over the sample at this temperature can be calculated from the amount of sublimated sample and the volume of the inert gas used. The equipment was calibrated using benzoic acid. The standard value of sublimation enthalpy 0 obtained here was DHsub ¼ 90:5  0:3 J mol1 .

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This is in good agreement with the value 0 recommended by IUPAC of DHsub ¼ 89:7 1 18 0:5 J mol . The saturated vapor pressures were measured five times at each temperature with the standard deviation being within 3–5%. Because the saturated vapor pressure of the investigated compounds is low, it may be assumed that the heat capacity change of the vapor with temperature is so small that it can be neglected. The experimentally determined vapor pressure data may be described in (ln P; 1/T) co-ordinates in the following way: lnðPÞ ¼ A þ

B T

(5)

The value of the enthalpy of sublimation is calculated by the Clausius–Clapeyron equation: T DHsub ¼ RT2

@ðln PÞ @ðTÞ

(6)

whereas the entropy of sublimation at a given temperature T was calculated from the following relation: DSTsub ¼

T DHsub

 T

DGTsub

298 T DHsub ¼ DHsub þ DHcor T ¼ DHsub þ ð0:75 þ 0:15C298 p;cr Þ

(8)

Differential Scanning Calorimetry Differential scanning calorimetry (DSC) was carried out using a Perkin–Elmer Pyris 1 DSC differential scanning calorimeter (Perkin–Elmer Analytical Instruments, Norwalk, CT) with Pyris software for Windows NT. DSC runs were DOI 10.1002/jps

performed in an atmosphere of flowing (20 mL min1) dry helium gas of high purity 99.996% using standard aluminum sample pans and a heating rate of 10 K min1. The accuracy of weight measurements was 0.005 mg. The DSC was calibrated with an indium sample from Perkin–Elmer (P/N 0319-0033). The value determined for the enthalpy of fusion corresponded to 28.48 J g1 (reference value 28.45 J g1). The melting point was 156.5  0.18C (n ¼ 10). The enthalpy of fusion at 298 K was calculated by the following equation: 298 DHfus ¼ DHfus  DSfus ðTm  298:15Þ

(9)

where the difference between heat capacities of the melt and solid states has been approximated by entropy of fusion (as an upper estimate). This approach has been used by Dannenfelser and Yalkowsky20 and Verevkin and Schick.21 The enthalpy of vaporization has been calculated as: 298 298 298 ¼ DHsub  DHfus DHvap

(10)

(7)

with DGTsub ¼ RT lnðP=P0 Þ, where P0 is the standard pressure of 1.013  105 Pa. For experimental reasons sublimation data are obtained at elevated temperatures. However, in comparison to effusion methods, the temperatures are much lower, which makes extrapolation to room conditions easier. In order to further improve the extrapolation to room conditions, heat capacities ðC298 p;cr valueÞ of the crystals were estimated using the additive scheme proposed by Chickos et al.19 Heat capacity was introduced as a correction for the recalculation of the sublimation T 298 enthalpy DHsub  value at 298 K ðDHsub  valueÞ, 19 according to Eq. (8) (the procedure of C298 p;cr  value calculation is presented in Tab. 5):

 ðT  298:15Þ

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Calculation Procedure The free molecular volume in the crystal lattice has been estimated on basis of the X-ray diffraction data and van der Waals molecular volume (Vvdw), calculated by GEPOL:22 V free ¼

Vcell  ZV vdw Z

(11)

where Vcell is the volume of the unit cell and Z is the number of molecules in the unit cell.

RESULTS AND DISCUSSION Crystal Structure Analysis The results of the X-ray diffraction experiments are presented in Table 1. In order to characterize the conformational states of the molecules a view of representative molecule VIII is shown with atomic numbering on Figure 1. This numbering was used for all compounds under investigation. The compounds IV–VI have two molecules (A and B) in the asymmetric unit of the crystal lattices. Based on the presented numbering a comparative analysis of conformational states of molecules I–X may be carried out. The results are summarized in Table 2.

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Table 1. Crystal Lattice Parameters of the Substances Under Investigation

Deposition number Crystal system Space group Crystal size (mm) ˚) a (A ˚ b (A) ˚) c (A a (8) b (8) g (8) ˚ 3) Volume (A Z Dcalc (g cm3) Radiation T (K) m (mm1) Data collection Measured reflections Independent reflections Independent reflections with >2s(I) Rint umax (8) Refinement Refinement on R[F2 > 2s( F2)] vR( F2) S Reflections Parameters (D/s)max ˚ 3) Drmax (e A ˚ Drmin (e A3)

VIII

IX

X

CCDC 719464 Monoclinic P21/c 0.11  0.2  0.12 16.613(1) 5.453(1) 16.753(2) 90.00 117.19(1) 90.00 1349.6(3) 4 1.360 Mo Ka 293(2) 0.239

CCDC 719465 Monoclinic P21/c 0.2  0.15  0.2 14.786(2) 5.354(1) 16.603(2) 90.00 90.54(2) 90.00 1314.3(3) 4 1.407 Mo Ka 293(2) 0.252

CCDC 719466 Monoclinic P21/c 0.48  0.33  0.30 12.664(4) 7.352(2) 14.882(3) 90.00 104.50(2) 90.00 1341.2(6) 4 1.470 Mo Ka 293(2) 0.439

2951 2146 1913 0.0409 24.99

2873 2075 1887 0.0353 25.0

2599 2485 1880 0.0630 25.58

F2 0.036 0.0967 1.041 2146 181 0.000 0.209 0.294

F2 0.0323 0.0938 1.045 2075 182 0.001 0.187 0.251

F2 0.0366 0.1010 1.025 2485 172 0.000 0.411 0.395

Standard deviations are presented in brackets.

Figure 1. A view of molecule VIII with atomic numbering. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 12, DECEMBER 2009

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Table 2. Some Parameters (8) Describing Molecular Conformational States in the Crystal Lattices

Ia IIb IIIc IV(A)d IV(B)d V(A)e V(B)e VI(A)d VI(B)d VIIf VIII IX X

nO1–S1–C1–C2

nN1–S1–C1–C2

nS1–N1–C7–C12

nPh1–Ph2

5.8(2) 7.4(4) 30.7(4) 41.2(4) 39.2(4) 47.3(2) 37.4(2) 45.2(9) 41.6(9) 40.6(3) 38.39(17) 35.77(16) 39.57(19)

108.5(2) 106.8(3) 83.5(3) 71.3(4) 74.4(3) 64.8(2) 75.6(2) 66.7(9) 71.2(8) 72.4(3) 74.99(16) 78.02(15) 73.39(18)

68.3(2) 63.8(4) 71.1(4) 36.4(5) 79.1(4) 28.1(2) 43.0(2) 33(1) 80(1) 65.9(3) 72.70(22) 76.95(19) 62.07(24)

49.14(9) 54.8(2) 54.4(2) 80.7(1) 60.5(2) 81.56(6) 79.11(7) 84.7(3) 60.7(4) 64.9(1) 64.37(6) 60.73(7) 67.61(8)

a

Ref. 27 Ref. 28 c Ref. 29 d Ref. 8 e Ref. 30 f Ref. 31 b

The packing of molecules in the crystal lattices of the three new substances under investigation is presented in Figure 2. To describe the conformational state of the molecules the following four parameters have been chosen: the angle between the SO2-group and the phenyl motif Ph1 (C1–C2–C3–C4–C5–C6) nO1–S1–C1–C2; the angle nN1–S1–C1–C2, describing the orientation of the NH-group in relation to Ph1; the torsion angle nS1–N1–C7– C12, which characterizes the location of the second phenyl ring Ph2 (C7–C8–C9–C10–C11– C12) with respect to the NH-group and, finally, the angle between the two phenyl rings nPh1– Ph2 (the acute angle between the least-squares planes through the two phenyl rings). It is interesting to analyze the influence of the molecular packing in the crystal lattices (here the parameter Vfree/Vvdw has been introduced) on the angle between the two phenyl rings (nPh1–Ph2). The result of the analysis is presented in Figure 3. It is not difficult to see that the spectrum of angles is composed of two branches: the first one (corresponding to molecules A of compounds IV–VI) with angle values lying within 80–858; the second branch includes the smaller angle values (within 50–658). For both branches the same trend is observed: the discussed angle decreases with decreasing molecular packing density in the crystal lattices (i.e., with increasing V free/Vvdw value). The observed pattern can be DOI 10.1002/jps

explained by superposition of at least three factors: the topological structure of the molecule, the topological structure of the hydrogen bond network and p–p phenyl ring interactions. The outlying values of compound I may be connected with both the compactness of the molecule and absence of the close p–p phenyl ring contacts. The investigated class of compounds forms various hydrogen bond networks in the crystals. Special topological peculiarities of the hydrogen bond networks in crystals and crystallosolvates of sulfonamides have been described in the article of Adsmond and Grant.7 In contrast to the substances considered by those authors, our group of compounds presents non-solvated phases with only systematic variation of different substituents in one of the phenyl rings. This collection of substances gives the opportunity to analyze the impact of topology of molecules and the nature of substituents on the topological structure of the hydrogen bond networks. Moreover, we may take into account that the molecular packing architecture of the discussed crystals stays approximately the same (Fig. 2). Evidence for this observation can be the fact that the molecular free volume in the outlined crystal lattices has ˚ 3) and approximately the same value (within 3 A does not depend on the molecular van der Waals volume (Fig. 4). The crystal lattices of IV and VI are isomorphic:9 the same space groups— orthorhombic Pna21; Vcell(IV) ¼ 2560.0(9) and

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Figure 3. Plot of the angle between phenyl rings (nPh1–Ph2) of the sulfonamides versus Vfree/Vvdw values in the crystal lattices.

If the molecular packing of the projections presented in Figure 2 (along [0 1 0] direction) is compared, the following regularities can be revealed. The molecules are packed in layers in xz-plane. Each layer can be presented as a set of molecular chains. The molecules within the chains interact with each other by van der Waals forces and hydrogen bonding energy: c, d, e—for VIII and IX, and a, b, c—for X. The adjacent chains have two types of contacts: on the one hand by van der Waals forces between the first phenyl fragments (amino-phenyl); on the other hand by van der Waals forces between the second phenyl

Figure 2. Molecular packing architectures (VIII)—a, (IX)—b, and (X)—c crystal lattices.

of

˚ 3; Vvdw(IV) ¼ 216.1 and Vcell(VI) ¼ 2632.1(9) A vdw 3 ˚ V (VI) ¼ 231.8 A ; Vfree(IV) ¼ 103.9 and ˚ 3. Therefore, the accommodation Vfree(VI) ¼ 97.2 A of the additional Cl-atom of compound VI (in comparison with IV) occurs in the free volume of the unit cell of substance IV. In the next step we analyzed the hydrogen bond network topology using the graph set notation terminology introduced by Etter23 and revised by Bernstein.24 Comparative characteristics of the hydrogen bond geometric parameters, graph set assignments for the two levels are summarized in Table 3. The graph set notations mentioned in Table 3 are illustrated in Table 4.

Figure 4. Relationship between the free molecular volumes (Vfree) in the crystal lattices and the van der Waals volumes (Vvdw) of the compounds.

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a b c

X

a b c d e

0.80(2) 0.85(3) 0.85(3) 0.78(3) 0.78(3)

N1–H1...N2 N2–H22...O1ii N2–H21...O2iii

i

D—H. . .Ac

N1–H1. . .O2 N2–H2a. . .O1ii N2–H2a. . .O1iii N2–H2b. . .O1iv N2–H2b. . .O2iv

D—H

0.84(3) 0.86(3) 0.86(3) 0.86(3) 0.86(3)

0.94 0.84 0.88

D. . .A

159(2) 149(3) 130(3) 158(3) 145(3)

2.404 2.401 2.377

H. . .A

163(2) 152(3) 125(3) 150(3) 153(3)

D—H. . .A

3.217(3) 3.290(3) 3.308(3) 3.405(3) 3.325(3)

3.149(2) 3.261(3) 3.220(3) 3.368(3) 3.260(3)

D—H

2.375(22) 2.481(28) 2.653(29) 2.545(30) 2.667(30)

H. . .A

2.412(26) 2.523(33) 2.691(33) 2.591(35) 2.583(32)

a b c d e a

3.113(3) 3.080(3) 3.129(3)

D. . .A

b

c

d

e

b

c

d

e

C(8) C(8) þ C(8) ¼ R24 (8) C(8) C(8) þ C(8) ¼ R24 (8) C(8) þ C(8) ¼ C22 (4) C(8) C(8) þ C(8) ¼ R44 (8) C(8) þ C(8) ¼ C22 (4) C(8) þ C(8) ¼ R21 (8) C(8)

b

132 135 148

D—H. . .A a b c

C(8) R22 (6) C22 (6)

a

C22 (4)

C(8)

b

C(8)

c

C(8) C(8) þ C(8) ¼ R24 (8) C(8) C(8) þ C(8) ¼ R24 (8) C(8) þ C(8) ¼ C22 (4) C(8) C(8) þ C(8) ¼ R44 (8) C(8) þ C(8) ¼ C22 (4) C(8) þ C(8) ¼ R21 (8) C(8)

C(4) R33 (20) C(4) þ C(8) ¼ R44 (24)d C(4) þ C(8) ¼ R44 (24) C(4) þ C(8) ¼ R34 (22)

a

a C(4) b R33 (20) c C(4) þ C(8) ¼ R44 (24) d C(4) þ C(8) ¼ R44 (24) e C(4) þ C(8) ¼ R34 (22)

˚ ] H. . .A [A ˚ ] D. . .A [A ˚ ] D—H. . .A [8] D—H [A

Symmetry code::(i) x, y  1, z; (ii) 1  x, 1/2 þ y, z þ 1/2; (iii) x, 1/2  y, z  1/2; (iv) x, 3/2  y, z  1/2. Symmetry code: (i) x, y  1, z; (ii) x, 1/2 þ y, z þ 1/2; (iii) x, 1/2  y, z  1/2; (iv) x, 1/2  y, z  1/2. c Symmetry code:(i) x, y  1/2, z  1/2; (ii) x, y  1/2, z þ 1/2; (iii) x, 1/2  y, z þ 1/2. a C(4) þ C(8) ¼ R44 (24): Combination of C(8) þ C(8) is equivalent of R44 (24) pattern.

a

D—H. . .Ab

IX

i

N1–H1. . .O2 N2–H2a. . .O1ii N2–H2a. . .O1iii N2–H2b. . .O1iv N2–H2b. . .O2iv

i

D—H. . .Aa

a b c d e

VIII

Table 3. Hydrogen Bond Geometry and Graph Set Notations of the Molecules VIII–X

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Table 4. Graph Set Notations of the Hydrogen Bond Networks of the Crystal Structures Studied

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Table 4. (Continued)

motifs (substituted phenyl). In contrast to compound X the molecular chains of drugs VIII (and IX) interact with each other by hydrogen bond (b), in addition to the noted van der Waals forces. For VIII and IX the molecules in the adjacent layers (parallel to xz-plane) create hydrogen bonds (mentioned as (a)) and these hydrogen bonds form a three-dimensional network. For compound X this hydrogen bond is not observed.

Sublimation Characteristics The temperature dependencies of saturated vapor pressure of VIII–X are shown in Table 5. The thermodynamic functions of the drugs sublimation, fusion and vaporization processes are presented in Table 6. If we select structurally similar molecules IV,9 VIII, IX, and compare the influence of the para-substituent on the thermodynamic characteristics of the sublimation process, then the following conclusion is obtained. A proportional increase of the sublimation enthalpy with increasing van der Waals volume of the sub298 stituent is not observed: DHsub ðIV: 4  ClÞ ¼ DOI 10.1002/jps

298 ðVIII: 4  C2 H5 Þ ¼ 143:6 134:1  1:2; DHsub 298 0:9; DHsub ðIX: 4  OCH3 Þ ¼ 124  1 kJ mol1 This fact is not surprising because the compounds are conformationally flexible with complicated topology of the hydrogen bond networks. Moreover, the volume of the substituent is much smaller than the total van der Waals volume of the molecule. Replacement of the Cl-substituent at orthoposition of the phenyl fragment by a methyl group (VII: 2,5-Cl2 ! X: 2-CH3-5-Cl) leads to a decrease of the crystal lattice energy by 25.4 kJ 298 298 mol1: DHsub ðVIIÞ ¼ 155:4  1:66 and DHsub ðXÞ ¼ 1 130  1 kJ mol . As the van der Waals volumes of these o-substituents are approximately equal, this difference may be due to the close contacts between Cl- and Ph-group associated with some charge transfer. In our previous work9 correlations have been 298 revealed for compounds I–VIII between DHsub and the crystal density (Dcal) calculated from Xray diffraction experiments. For the total number of the drugs I–X two branches are observed for this relationship. As the Dcal parameter is an entropic characteristic of a crystal, we tried to compare these values with entropic terms of the sublimation process ðTDS298 sub Þ of the compounds.

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Table 5. Temperature Dependencies of Saturation Vapor Pressure of Compounds VIII–X VIIIa T (8C) 121.0 123.0 124.0 125.0 127.0 128.5 131.0 132.0 134.0 135.5 137.0 139.0 141.5 142.5 143.0 146.5 148.0

IXb P (Pa)

T (8C) 3

7.08  10 8.83  103 9.85  103 1.06  102 1.32  102 1.58  102 2.04  102 2.28  102 2.65  102 3.05  102 3.51  102 4.29  102 5.67  102 6.27  102 6.72  102 9.26  102 1.02  101

Xc P (Pa) 3

5.25  10 6.35  103 7.75  103 1.22  102 1.44  102 1.61  102 1.62  102 1.94  102 2.76  102 3.65  102 4.16  102 5.5  102 5.73  102 9.16  102 1.03  101 1.92  101

131.0 133.0 135.0 141.0 143.0 144.0 145.0 147.5 152.0 155.0 157.0 160.5 161.0 167.0 168.5 177.0

T (8C)

P (Pa)

111.0 112.0 114.0 115.0 117.0 118.5 120.5 122.0 123.0 124.0 125.0 127.0 128.0 129.0 130.0 131.0 132.0

7.99  103 8.74  103 1.01  102 1.11  102 1.44  102 1.66  102 2.02  102 2.31  102 2.45  102 2.71  102 3.02  102 3.54  102 4.12  102 4.33  102 4.93  102 5.50  102 5.96  102

ln( P[Pa]) ¼ (37.0  0.3)  (16522  1115)/T; s ¼ 2.29  102; r ¼ 0.9999; F ¼ 21,958; n ¼ 17. ln( P[Pa]) ¼ (29.5  0.3)  (14063  119)/T; s ¼ 3.44  102; r ¼ 0.9997; F ¼ 13,905; n ¼ 16. c ln( P[Pa]) ¼ (34.2  0.4)  (14993  155)/T; s ¼ 2.71  102; r ¼ 0.9992; F ¼ 9352; n ¼ 17. a b

Table 6. Thermodynamic Characteristics of Processes of Sublimation, Fusion, and Vaporization of the Compounds VIII–X

1 DG298 sub (kJ mol ) T DHsub (kJ mol1) 298 (kJ mol1) DHsub 298 Cp;cr (J mol1 K1)a 1 TDS298 sub (kJ mol ) 1 1 298 DSsub (J mol K ) b H (%) b TS (%)

Tm (K) T DHfus (kJ mol1) 298 DHfus (kJ mol1) DSTfus (J mol1 K1)c 298 (kJ mol1) DHvap

VIII

IX

X

74.2 137.4  0.9 143.6  0.9 341.4 69.4 233  2 67.4 32.6 436.2  0.2 36.3  0.5 24.8 83.2 118.8

72.4 117  1 124  1 364.3 51.6 173  2 66.6 33.4 467.4  0.2 38.6  0.5 24.6 82.6 99.4

68.5 125  1 130  1 351.7 61.5 206  3 67.9 32.1 422.7  0.2 36.8  0.5 26.0 87.1 104.0

a 298 Cp;cr has been calculated by additive scheme with the following group values (in J K1 mol1): Cp (–SO2–) ¼ 88.7; Cp (internal quaternary aromatic ¼ C–) ¼ 9.1; Cp (tertiary aromatic C sp3 ¼ CaH–) ¼ 17.5; Cp (–NH–) ¼ 0.3; Cp (–Cl) ¼ 28.7; Cp (–C2H5) ¼ 63.5; Cp (–OCH3) ¼ 86.4; Cp (–CH3) ¼ 36.6 the error of the calculation procedure corresponds to significant digit. b 298 298 298 298 298 & H ¼ ðDHsub =ðDHsub þ DS298 sub ÞÞ100%; & TS ¼ ðTDSsub =ðDHsub þ TDSsub ÞÞ100%. c DSfus ¼ DHfus/Tm.

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The result of the correlation analysis is presented in Figure 5 and (after exclusion of the outlier VIII) can be described by the equation: TDS298 sub ¼ ð206  18Þ þ ð181  12ÞDcal ;

(12)

r ¼ 0:9846; s ¼ 2:29; n ¼ 9 The experimentally obtained crystal density values can be expected to be correlated with the calculated ones. Therefore, the entropic sublimation term can be directly estimated by the experimental density values, without any knowledge of the crystal structure. In our earlier article9 correlations have been found (for the drugs I– VIII) between thermodynamic sublimation characteristics and thermophysical parameters of fusion processes. Including the substances studied here the correlations can be described by the following equations: DG298 sub ¼ ð61:2  24:6Þ þ ð0:29  0:06ÞTm ;

(13)

r ¼ 0:8792; s ¼ 6:13; n ¼ 10 where Tm is melting point, and 298 298 DHsub ¼ ð1  30Þ þ ð5:3  1:1ÞDHfus ;

(14)

r ¼ 0:8521; s ¼ 11:1; n ¼ 10 In comparison with Eq. (12) these equations have lower correlation coefficients. However, it should be noted that the thermophysical characteristics of the fusion process are easily accessible by standard DSC experiments. This fact makes application of Eqs. (13) and (14) more convenient

Figure 5. Correlation between the sublimation entropic term ðTDS298 sub Þ and calculated molecular densities (Dcal) in the crystal lattices (see text for numbering of the compounds). DOI 10.1002/jps

4749

(though less precise) for the estimation of sublimation thermodynamic parameters.

Solubility and Solvation Thermodynamics The temperature dependencies of solubility of sulfonamides VIII–X in water, n-hexane, and noctanol are summarized in Table 7. The thermodynamic functions of the drugs solubility process in the solutions at 298 K are presented in Table 8. The choice of these solvents was determined by the following reasons. The immiscible solvent pair water–octanol can be regarded as a model for intestinal tract membranes, whereas the pair water–hexane may imitate the blood brain barrier (where non-specific/van der Waals interactions predominate to specific/hydrogen bonding forces).25,26 It should be noted, that we had some difficulties in the solubility experiments of drug X in n-hexane, due to poor reproducibility of results in comparison with the other drugs (therefore, the solubility experiments have been repeated at least 10 times at the each temperature). Table 8 shows 0 that the solubility enthalpy ðDHsol Þ of X in hexane is two times higher than the values for the other two drugs. Moreover, its solvation enthalpy 0 ðDHsolv Þ is approximately two times lower than that of the other substances. Therefore, it may be assumed that molecules of X form dimers in nhexane solution. The investigated compounds can be arranged by increasing solubility in the solvents in the sequence water < n-hexane < n-octanol. The solution enthalpies of VIII–X in all three solvents have positive values, and this means that the crystal lattice energy outweighs the energy required for solvation. It is interesting to note, that the entropies of the solubility process ðDS0sol Þ in these solvents have a positive sign (exception: IX in n-hexane). The positive value of the solution entropy can be explained by the higher degree of order of the molecules in the crystal than in solution. In order to estimate the interaction of the drugs with the solvents on the absolute energetic scale, solvation thermodynamic functions have been calculated for the compounds on the base of results of sublimation and solubility experiments: 0 0 298 DYsolv ¼ DYsol  DYsub

(15)

where Y is one of the thermodynamic functions G, H, or S.

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4.27 — 5.09 7.74 11.6 14.5 5.4  0.5 5934  160 0.9989 3.08  102

20 22 25 30 37 42 Aa Ba Rb sc

2.15 — 2.77 3.84 5.05 6.59 2.8  0.6 4654  181 0.9977 3.48  102

8.68 — 10.4 12.4 17.2 22.2 6.5  0.4 3975  134 0.9983 2.58  102

1.74 — 2.24 2.81 3.35 4.25 1.0  0.8 3575  234 0.9936 4.49  102

1.92 — 2.33 3.05 4.18 5.21 6.0  0.3 4259  93 0.9993 1.79  102

n-Octanol (X2  104) — 6.16 7.72 10.3 15.1 21.2 4.8  0.6 5645  176 0.9985 3.12  102

Water (X2  107) 1.82 — 2.94 5.18 8.56 14.0 15.8  1.0 8504  310 0.9980 5.94  102

n-Hexane (X2  106)

X

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13.4 9.1 12.0 7.0 2.5 35.1 16.0 14.7 10.1

49.3  1.3 42.6  1.2 46.9  1.5 38.7  1.5 29.7  1.9 70.7  2.6 33.0  1.1 35.4  0.8 25.7  0.6

35.9 33.5 34.9

31.7 32.2 35.6

17.0 20.7 15.6

b

0 0 &Hsol ¼ ðDHsol =ðjDHsol j þ jTDS0sol jÞÞ100%. 0 & TSsol ¼ ðTDS0sol =ðjDHsol j þ jTDS0sol jÞÞ100%. c 0 0 &Hsolv ¼ ðjDHsolv j=ðjDHsolv j þ jTDS0solv jÞÞ100%. d 0 0 &TSsolv ¼ ðjTDS0solv j=ðjDHsolv j þ jTDHsolv jÞÞ100%.

a

Water VIII 5.09  107 IX 1.32  106 X 7.72  107 n-hexane VIII 2.77  106 IX 2.24  106 X 2.94  106 n-octanol VIII 1.04  103 IX 2.33  104 X 1.88  103 54  2 49  2 34  1

23  2 8  2 118  2

45  2 31  2 40  1

67.3 70.7 71.8

84.7 92.2 66.8

78.6 82.4 79.6

32.7 29.3 28.2

15.3 7.8 33.2

21.4 17.6 20.4

0 X2298 DG0sol DHsol TDS0sol DS0sol & Hsol a & TSsol b 1 1 1 1 1 (mol. frac.) (kJ mol ) (kJ mol ) (kJ mol ) (J K mol ) (%) (%)

57.2 51.7 52.9

42.5 40.2 32.9

38.3 38.9 33.6

110.6 88.6 104.3

104.9 94.3 59.3

94.3 81.4 83.1

53.4 36.9 51.4

62.4 54.1 26.4

56.0 42.5 49.5

179 124 172

209 181 89

188 143 166

67.4 70.6 67.0

62.7 63.5 69.2

62.7 65.7 62.7

32.6 29.4 33.0

37.3 36.5 30.8

37.3 34.3 37.3

& TSsolv d (%)

1.53 — 1.88 2.21 2.73 3.23 4.1  0.2 3097  69 0.9993 1.32  102

n-Octanol (X2  103)

0 DG0solv DHsolv TDS0solv DS0solv & Hsolv c 1 1 1 1 1 (kJ mol ) (kJ mol ) (kJ mol ) (J K mol ) (%)

Table 8. Thermodynamic Solubility and Solvation Functions of the Compounds Studied in Water, n-Hexane, and n-Octanol at 298 K

b

1.02 — 1.32 1.94 2.68 3.33 3.7  0.5 5120  142 0.9988 2.73  102

Water (X2  106)

n-Hexane (X2  106)

n-Octanol (X2  104)

n-Hexane (X2  106)

Parameters of the correlation equation: ln X2 ¼ A  B/T. R, pair correlation coefficient. c s, standard deviation.

a

Water (X2  107)

T (8C)

IX

VIII

Table 7. The Temperature Dependencies of Solubility, X2 [mol. frac.], of Compounds VIII–X in Water, n-Hexane, and n-Octanol

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The thermodynamic functions of solvation processes for the studied compounds in water, n-hexane, and n-octanol at 298 K are presented in Table 8. It is interesting to compare the solvation characteristics of the compounds differing by substituents in one position. For example, the compounds IV (4-Cl), VIII (4-Et), and IX (4-OMe) are different only in their substituent at para-position (Scheme 1). The hydration enthalpies can be arranged in the w w following way: DHsolv ðIVÞ ¼  96:19 < DHsolv 1 w ðVIIIÞ ¼  94:3 < DHsolv ðIXÞ ¼ 81:4 kJ mol . This trend is also observed for n-octanol: oct oct DHsolv ðIVÞ ¼ 123:49 < DHsolv ðVIIIÞ ¼ 110:6 < 1 oct DHsolv ðIXÞ ¼ 88:6 kJ mol . Thus these drugs interact more strongly with n-octanol than with water. In an analogous manner the substances VII (2,5-Cl2) and X (2-Me-5-Cl) can be compared, which are different in their orthoposition. In comparison with X the drug VII interacts more strongly with both water and w w n-octanol: DHsolv ðVIIÞ ¼ 131:29 < DHsolv ðXÞ ¼ 1 9 oct oct 83:1 kJ mol and DHsolv ðVIIÞ  120:3 < DHsolv 1 ðXÞ ¼ 104:3 kJ mol . Partitioning Process The thermodynamic functions of transfer of the studied compounds from water to n-octanol, being

4751

widely discussed as reflecting some biopharmaceutical properties of drugs, were also calculated by the equations: 298 298 ðnoctanolÞ  DYsol ðwaterÞ (16) DYtrw!o ¼ DYsol

where Y is one of the thermodynamic functions G, H, or S. The experimental data of the thermodynamic functions of the compounds under investigation are collected in Figure 6 and Table 9. The 0 regions where ðTDS0tr > DHtr Þ triangular 0 0 sectors A , and ðDHtr < 0; TDStr > 0; jTDS0tr j > 0 jDHtr jÞ triangular sectors B correspond to entropy-determined processes. The regions of 0 0 the diagram where ðDHtr < 0; TDS0tr > 0; jDHtr j 0 0 > jTDStr jÞ triangular sectors C , and ðDHtr < 0 0; TDS0tr < 0; jDHtr j > j TDS0tr jÞ triangular sectors D correspond to enthalpy-determined processes. A schematic depiction of these relationships is given in Scheme 2. Isoenergetic curves of the DG0tr function are marked as dotted lines in Figure 6. Analysis of the chemical potential differences observed for the process of transfer from water to n-octanol phases, combined with a comparison of enthalpic and entropic terms is a useful approach to understand: (a) the size of the supra-structural unit which takes part in a partitioning process; (b) driving forces of the outlined processes. For

Figure 6. Relationship between the enthalpic and entropic terms of the water to noctanol transfer functions (see text for numbering of the compounds). The isoenergetic curves of the DG0tr function are marked by dotted lines. DOI 10.1002/jps

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Table 9. Thermodynamic Functions of Transfer from Water to n-Octanol of Compounds Studied at 298 K Compound VIII IX X

(kJ mol1) DGw!o tr

w!o DHtr (kJ mol1)

TDSw!o (kJ mol1) tr

DSw!o (J mol1 K) tr

& Htr a (%)

& TStr b (%)

18.9 12.8 19.3

16.3 6.7 21.2

2.6 6.1 1.9

8.7 20.5 6.4

86.2 52.3 91.8

13.8 47.7 8.2

a

0 0 &Htr ¼ ðDHtr =ðjDHtr j þ jTDS0tr jÞÞ100%. 0 & TStr ¼ ðTDS0tr =ðjDHtr j þ jTDS0tr jÞÞ100%.

b

example, if the water ! octanol transfer enthalpy is positive then it may be assumed that the drug molecule interacts stronger with the solvate shell in the water phase than in the octanol phase. Therefore, there is a high probability of the drug molecule being transferred with the partial or complete solvation shell (i.e., water molecules). Furthermore, it has to be considered that the equilibrium solubility of water in n-octanol is 0 2.5 mol L1. Therefore, in the case ðDHtr > 0Þ the transferred unit is the drug molecule þ solvation 0 shell. For DHtr < 0 the opposite is observed: practically total resolvation of drug molecule occurs at the process of transfer from water to octanol. Thus the transferred unit is just a drug molecule. The entropic term shows system order changes when transferring the supra-structural unit from one phase to the other. Thus, the sector A in Figure 6 corresponds to transfer of (drug þ solvation shell) from water phase to octanol phase with essential disordering of the latter one. The sector B corresponds to transfer of an individual drug molecule with also essential octanol phase disordering. The sector C corresponds to transfer of an individual drug molecule with no essential octanol phase disordering. Finally, the sector D corresponds to transfer of an individual drug molecule with increasing octanol phase order. This type of information can be useful to analyze the process of diffusion of drug molecules through biological barriers (pas-

sive transport), because the size of the suprastructural unit plays a key role and determines the diffusion coefficient values as well as the mechanism of diffusion. It is not difficult to recognize that the transfer processes are very sensitive to structural changes of the compounds. The transfer process of compounds I, II, and V–VII is entropy-determined. Moreover, the enthalpic term of drugs I, V, and VII has a positive sign, whereas that one of II and VI is negative. Obviously the entropydetermined process corresponds to an essential change of the entropy term occurring at the transfer of drug molecules from water to n-octanol (in comparison to the enthalpy term). The explanation of the observed fact can be connected with strong hydrophobic effects of the compounds, which cannot be compensated by introducing into the molecule a hydrogen bonding substituent (amino-group). For the compounds III, IV, VIII, and X the transfer process is enthalpy-determined. However, like in the previous case,8,9 for drugs III and VIII the entropic term is positive, whereas for IV and X it is negative. It should be noted, that for drug IX a special situation is observed where the absolute values of the enthalpic and entropic terms are practically equal. The maximal driving force of the transfer process ðDGw>o Þ is shown by the sulfonamides tr without amino-group (I, II, and III). Moreover, the outlined substances are located in different

Scheme 2. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 98, NO. 12, DECEMBER 2009

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triangular sectors of the diagram (Fig. 6) and this situation corresponds to various contributions of the thermodynamic terms to the discussed processes. An analogous situation is observed for the amino derivatives of the sulfonamides. For these compounds the values characterizing the driving force of the transfer process ðDGw>o Þ are in a tr range within 6 kJ mol1, but the ratios and signs of the enthalpic and entropic terms are essentially different. Introduction of an amino group into the molecule III (to give compound IV) keeps the transfer process as enthalpy-determined, however, the entropic term changes the sign from positive to negative. Introduction of an amino group into the molecule II (to give drug V) keeps the transfer process entropy-determined, however, the enthalpic term changes the sign from negative to positive. Introduction of an additional Cl atom into compounds without amino-group (I ! II) changes the transfer process from enthalpy- to entropy-determined. The compounds with different substituents in para-position (Cl (IV), C2H5 (VIII), and OCH3 (IX)) are located within the enthalpy-determined area. Moreover, the substances have absolutely different proportions and signs with respect to enthalpic and entropic terms. Drug IV is located in sector D (see Fig. 6), drug VIII—in sector C, and drug IX—on the boundary of sectors B and C. Thus modification of substituent nature in para-position of the sulfonamides gives the opportunity to alter the ratio between enthalpic and entropic terms at approximately the same Gibbs energy values. According to our opinion this conclusion may be important for the screening and design of drugs with the same delivery pathway (with approximately the same Gibbs energy values) but with different permeability. We assume that future studies in this direction may result in valuable knowledge. Replacement of the Cl substituent in VII by the methyl group (to give X) leads to considerable change of the ratio between enthalpic and entropic terms (sector A for drug VII, and sector D for drug X). It should be noted, that in this case the driving force of the partitioning process ðDGw>o Þ is altered as well (within 5 tr kJ mol1) and this effect could be used for development of drug molecules (at least for the discussed class) with desired properties. It is interesting to note, that the maximal dispersion (vector between the points discussed in TDStr vs. DHtr space) of TDStr and DHtr values corresponds to drugs I and III for the group of substances without amino substituent and for DOI 10.1002/jps

4753

drugs IV and V for the group of substances with amino substituent. If comparable variants of the molecules (I and II) and (IV and V) (i.e., pairs with and without amino-group) are considered then it may be assumed that in particular the aminogroup promotes the essential dispersion of TDStr and DHtr values. Thus, the presented approach gives the opportunity to analyze contributions of various substituents and of their position to mechanism and driving forces of the transfer processes.

CONCLUSION The crystal structures of three sulfonamides (VIII–X) have been solved by X-ray diffraction experiments. Comparative analyses of molecular conformational states, of packing architecture and hydrogen bond networks (by graph set notations) in the crystal lattices have been carried out. The thermodynamic aspects of the sulfonamide sublimation processes have been studied by investigating the temperature dependence of vapor pressure by means of transpiration method. A regression equation has been derived connecting the crystal density (obtained from X-ray data) with sublimation entropy terms. Correlations between the sublimation Gibbs energies and the melting points, as well as between sublimation and fusion enthalpies at 298 K have been found. These dependencies give the opportunity to predict sublimation thermodynamic parameters on the basis of fusion experiments only. The thermodynamic functions of solubility and solvation processes have been analyzed using temperature dependencies of solubility in water, nhexane, and n-octanol and sublimation characteristics of the compounds. The enthalpic term contributes dominantly to the solvation Gibbs energy. A study of the water ! octanol transfer process has been carried out using a diagram method combined with analysis of enthalpic and entropic terms. Distinguishing between the influence of enthalpy and entropy, as is possible through the present approach, leads to the insight that the contribution of these terms is different for different molecules (entropy- or enthalpy-determined). Thus, in contrast to interpretation of only the Gibbs energy of transfer, being extensively used for pharmaceuticals in the form of the partition coefficient (log P), the analysis of thermodynamic functions of the transfer process, as outlined in the present work, provides additional

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mechanistic information. This may be important for further evaluation of the physiological distribution of drug molecules and may provide a better understanding of biopharmaceutical properties of drugs.

ACKNOWLEDGMENTS This work was supported by ISTC (project No. 0888).

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