Preferential solvation of N-methylformamide, N,N ...

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Preferential solvation of N-methylformamide, N,N-dimethylformamide and N-methylacetamide by water and alcohols in the binary and ternary mixtures Jan Zielkiewicz

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Department of Chemistry, T echnical University of Gdan sk, Narutowicza 11/12, 80-952 Gdan sk, Poland. E-mail : jaz=altis.chem.pg.gda.pl Received 22nd February 2000, Accepted 2nd May 2000 Published on the Web 30th May 2000

Using the KirkwoodÈBu† theory of solutions, the preferential solvation of the N-methylacetamide molecule has been investigated in the binary and ternary mixtures containing N-methylacetamide (NMA), aliphatic alcohol and water. The results are compared with those obtained previously for N-methylformamide (NMF) and N,N-dimethylformamide (DMF). The thermodynamic investigations, based on the KirkwoodÈBu† theory of solutions, lead to the unexpected conclusion that both NMA and DMF are solvated in the investigated binary and ternary mixtures in a very similar manner, but solvation of NMF di†ers from other amides. For all the investigated amides, the local mole fractions di†er only slightly from the bulk onesÈthe deviations are only a few per cent or less. Moreover, for the Mamide ] methanolN binary mixtures, where amide \ NMF, DMF and NMA, molecular dynamics calculations at x \ 0.518 were performed. From the obtained amide moleculeÈmolecule radial distribution functions (rdf ) and atomÈatom rdf, it was possible to estimate the local mole fractions around the amide molecule, the orientation e†ects of molecules within the solvation shell, and a possibility of the formation of complexes. The general picture obtained from analysis of the molecular dynamics results is consistent with the deductions derived from thermodynamic data.

Introduction This work is the third of a series of papers describing the solvation of amides in binary and ternary mixtures containing amide, water and/or aliphatic alcohol. In the previous papers, the solvation of N,N-dimethylformamide1 (DMF) and Nmethylformamide2 (NMF) was investigated at temperature 313.15 K. In this work, the solvation of N-methylacetamide (NMA) is investigated, and a comparison with previous results obtained for DMF and NMF is given. The amide group can serve as a model of the peptide bond, and interactions between hydroxy and amide groups play an important role in the solvation of peptides in aqueous solutions. As a result of the intermolecular interactions, a preferential solvation of molecules is observed. We understood that preferential solvation arises if the local mole fractions of solvent components in a solvation microsphere surrounding the solute di†er from the bulk ones. Preferential solvation is always present and, although in some cases it is relatively weak, it a†ects the thermodynamic properties of solution. It is well known that amides interact with water or alcohol as solutions by dipoleÈdipole interactions, and form some hydrogenbonded complexes or hetero-associates.3h6 The amideÈwater and amideÈalcohol hetero-associations should be di†erent, however, on the molecular level. The water molecule creates four hydrogen bonds, while alcohol molecules may create only two hydrogen bonds, forming linear polymeric structures.7 Thus, we can expect that the mentioned di†erences will cause di†erences in the structure of the solvation shell. The previously obtained results2 do not, however, conÐrm this expectation. We want to compare the thermodynamic results obtained for various amides in their mixtures with water and/or alcohol to obtain some information on the process of solvation of amides. DOI : 10.1039/b001443p

A valuable tool for investigation of the changes in the solvation microsphere is the KirkwoodÈBu† theory of solutions.8 It describes thermodynamic properties of solutions in an exact manner over the whole concentration range using quantities :

P

= [g (r) [ 1]4nr2 dr (1) ij 0 where g (r) is the radial distribution function. G is called the ij ij KirkwoodÈBu† integral or Ñuctuation integral. In other words, if radial distribution functions, g , are known (and ij then the G quantities are known too), we can determine the ij thermodynamic properties of solution using the equations of the KirkwoodÈBu† theory.8 On the other hand, as was pointed out Ðrst by Ben Naim,9 inversion of the original KirkwoodÈBu† theory allows the G parameters to be deterij mined from experimental values of thermodynamic quantities such as chemical potential, partial molar volumes, and isothermal compressibility factor.9 Next, the c G product (where i ij c \ N /V is the concentration of species i in the mixture) i i describes the total average excess (or deÐciency) of i molecules in the entire neighbourhood of a j molecule.9,10 Then, exploiting the idea presented previously in the literature,1,2,10 it is possible to estimate the local mole fractions of the components of the solution. The possibility of evaluating these quantities was pointed out by many authors.10h12 This seems a valuable and convenient tool for the description of the solvation process. It should be stressed that the KirkwoodÈBu† theory is an exact one, and the determination of the G values ij from thermodynamic data does not involve any assumptions. That is why the description of the solvation phenomena obtained using this approach is fully reliable, and the KirkwoodÈBu† integral formalism is a frequently applied method in investigations of solutions.13 G \ ij

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The above considerations represent the ““ pure thermodynamic ÏÏ point of view. It is quite obvious, however, that the thermodynamic data cannot give a detailed insight into the structure of the solvation shell. More information on the structure of the solvation microsphere around the given j molecule is contained in the radial distribution functions, g , ij but these details are lost in the integration process [eqn. (1)]. The complete information on the solution structure (the radial distribution functions, formation of complexes, or orientational e†ects), can be obtained from molecular dynamics (MD) calculations. We can say that the results of MD calculations may complement and conÐrm the conclusions obtained from the thermodynamic measurements. This is why these calculations were initiated. In this work, calculations are performed for the binary mixtures Mamide ] methanolN, where amide \ NMF, DMF and NMA at the composition x \ amide 0.518, and the results of these calculations are compared with the ““ thermodynamic ÏÏ conclusions.

Data sources The excess Gibbs energies, GE, excess volumes of mixing, V E, all at temperature 313.15 K, and isothermal compressibilities, i, required for calculations were selected from the literature, mainly from previous work from this laboratory. The references for Mamide ] alcohol ] waterN systems are given in Table 1. The isothermal compressibility factors for pure amides were taken from ref. 28 for NMF and from ref. 29 for DMF. Unfortunately, there are no compressibility data for NMA ; this value was assumed to be the same as for NMF ; the Monte Carlo simulations of neat liquid amides indicate30 that the compressibilities of NMA and NMF should be almost the same. The isothermal compressibility factors for alcohols were taken from ref. 31, and from ref. 32 for water. Compressibilities of binary and ternary mixtures were calculated assuming the ideal behaviour, according to the equation : i\; i / (2) i i i where i is the isothermal compressibility factor of the ith i compound, and / is its volume fraction in the mixture. i

Data treatment and sources of error The G values and linear coefficients of preferential solvation, ij d0 , for binary and ternary mixtures were calculated as ij described previously.1,2 The general equation for d0 was ij obtained in the form : d0 \ x G [ x ; x G (3) ij i ij i k kj k For binary mixtures and for the ternary mixture in a very diluted region, these equations reduce to the expressions given by Ben Naim.10 Using the d0 values, the local mole fraction, ij x , may be determined as : ij x B x ] d0/V (4) ij i ij c where V (\4 nR3) is the volume of the solvation shell of c 3 c radius R . The volume V may be roughly estimated2 as c c (1000È2000) cm3 mol~1.

The inÑuence of experimental errors in the measured thermodynamic quantities on the calculated G and d0 values is ij ij not easy to evaluate. Discussion of this problem for the G ij values in the case of binary mixtures was given in detail by Matteoli and Lepori33 and by Zaitsev et al.34 The main sources of error are the di†erentiation procedures and, especially, the double di†erentiation used in calculations of the G ij values from experimental data. The error in the isothermal compressibility factor is negligible.33 The original experimental works14h27 contain detailed information about the error in the measured thermodynamic quantities. The estimation of the uncertainties in the calculated values of the KirkwoodÈBu† integrals, G , was made by ij using the well-known propagation of error formula.35 In the case of the binary mixtures these errors were calculated analytically. For the ternary mixtures the problem was solved by multiple calculations with subsequent determination of error limits for the Ðnal G values. The uncertainties in the d0 ij ij depend on those in G according to eqn. (3). ij

Molecular dynamics calculations The molecular dynamics calculations were carried out by using the GROMOS 87 package.36 Each model system consisted of 729 molecules in a cubic box with periodic boundary conditions. The calculations were conducted for an NTP ensemble, assuming a temperature of T \ 313 K and a pressure p \ 1 atm. The molecules were represented as a collection of interacting sites : three sites for methanol and six sites for amides. The methyl group, CH , was taken as a single site 3 centered on the carbon atom (the united atom approximation). There are static, nonpolarizable models whose siteÈsite interactions are sums of a Coulombic potential and the short range LennardÈJones (LJ) term. The energy of intermolecular interactions between the A and B molecules is given in the form :

G CA B A B D

H

p 12 p 6 qq ij [ ij ] i j (5) E \ ; ; 4e ij r AB r r2 ij ij ij i j where i represents the ith site of molecule A, and j represents the jth site of molecule B. The following combining rules, included in the GROMOS package, were used : p \ Jp p and e \ Je e (6) ij i j ij i j The LJ potential well depth, e , and diameter, p , for the ij ij ith site were taken from the GROMOS data base. The partial charges, q , were taken from ref. 37 for methanol and from ref. i 38 for amides. The geometry parameters for amides and alcohol molecules are presented in Table 2. Table 3 contains the values of the partial charges q at the ith site of a molecule. i The initial conÐgurations of the investigated mixtures were created by arranging the 378 NMF molecules and 351 methanol molecules in a cubic box. The system was equilibrated for 150 ps. To reduce the calculation time, the SHAKE procedure was switched on, and the time step of a single iteration was equal to 2 fs. Next, the SHAKE was switched o†, and the system was equilibrated by the following 40 ps with the time step of a single iteration equal to 0.5 fs. Next, in place of the NMF molecules in the conÐguration obtained by this means,

Table 1 References for Mamide ] alcohol ] waterN systems Thermodynamic quantity

Amide

Methanol

Ethanol

Propan-1-ol

GE

NMA NMF DMF

14 16 18

15 17 19

20

VE

NMA NMF DMF

21 23 25

22 24 26

27

2926

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Table 2 Geometrical parameters of amide and methanol moleculesa Bond lengths/nm Methanol OÈH OÈC

0.1037 0.1483

Amides CÈO CÈR1

0.1272 0.1520 0.1035 0.1520 0.1034 0.1520 0.1375

CH ÈN 3 R2ÈN NÈC

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Bond angles/deg

(NMA) (NMF, DMF) (NMA, NMF) (DMF)

CÈOÈH

120

R1ÈCÈO R1ÈCÈN

120 120

CÈNÈCH 3 CÈNÈR2

117 120

a R1 and R2 symbolise the hydrogen atom or CH group, linked with 3 the C and N atoms of amide molecule, respectively.

the appropriate amide molecules were introduced. The system was equilibrated by the following 40 ps or more, and Ðnally the 20 ps run was performed for data collection.

Results and discussion (a) Binary {amide (1) + cosolvent (2)} mixturesÈthermodynamic results For a description of the solvation of amides the linear coefficients of preferential solvation, d0 , deÐned by eqn. (3) are ij used. These are adequate quantities for this description : they reÑect changes in the local mole fractions of all species around the selected central molecule. Fig. 1 shows the KirkwoodÈBu† integrals, G , calculated ij from the experimental data for the binary mixtures MNMA ] AN, where A \ water, methanol and ethanol. Values of the KirkwoodÈBu† integrals at the equimolar composition are given in Table 4 for all of the amides. Fig. 2 shows the d0 21 values (describing solvation of an amide molecule by water or alcohol) determined from the experimental data for NMA, and compares with previous results2 for NMF and DMF. As stated previously,2,9,10 the small absolute values of the G ij parameters (about 100 cm3 mol~1) and the d0 values (less 21 than 10 cm3 mol~1) allow us to conclude that the radius of the solvation shell is small, and probably does not exceed the radius of the Ðrst coordination sphere around the amide molecule. We deÐne the solvation shell as a sphere of radius R , c centered on the amide molecule, and within this sphere the mole fractions of components di†er from the bulk ones.10h12 The above conclusion can be supported by two results : (1) MarcusÏ investigations of binary mixtures of water and organic solvents39 indicate that, for amides (formamide, NMF, DMF, NMA) as organic solvents, the correlation in the second solvation (coordination) shell is very weak and disappears altogether from the third shell onwards. (2) In Table 3 Partial charges q at the ith site of the methanol and amide i moleculesa Atom

q

Atom

q

Methanol C O

0.265 [0.700

H

0.435

Amides C N O

i

0.500 [0.570 [0.500

CH R1 R2

3

i

0.285 0.200 0.000 0.285 0.370

(DMF) (NMA, NMF) (DMF) (NMA, NMF)

a R1 and R2 symbolise the hydrogen atom or CH group, linked with the C and N atoms of amide molecule, respectively.3

Fig. 1 The KirkwoodÈBu† integrals for the binary mixture MNmethylacetamide (1) ] A (2)N at temperature 313.15 K. (a) A \ water, (b) A \ methanol, (c) A \ ethanol. The vertical bars show the estimated error ; at the equimolar composition this error is invisible (about 1 cm3 mol~1 or less).

the case of strongly associated solutions (for example for Malcohol ] hydrocarbonN or Mwater ] hydrocarbonN mixtures) this radius is expected to be large, and absolute values of the G parameters are also large,40 exceeding 1000 ij cm3 mol~1, and the d0 are large as well, exceeding40a 200 cm3 ij mol~1. It can be estimated from Fig. 2 and eqn. (4) that, for all the investigated amides, the local mole fractions di†er only Table 4 Values of the KirkwoodÈBu† integrals at equimolar composition, calculated from thermodynamic data for the Mamide ] AN binary mixtures at T \ 313.15 Ka G 11

G 22

G

N-methylacetamide Water Methanol Ethanol

[86.7 [92.2 [86.6

16.4 [31.5 [53.2

[21.5 [42.1 [59.7

N-methylformamide Water Methanol Ethanol

[68.1 [63.3 [44.6

9.13 [24.6 [44.2

[22.8 [48.0 [69.7

[20.8 [35.8 [55.4 [80.0

[22.6 [41.1 [58.1 [67.9

A

N,N-dimethylformamide Water [87.7 Methanol [92.8 Ethanol [86.3 Propan-1-ol [84.2

12

a A symbolises water, methanol, ethanol or propan-1-ol. All the values are given in cm3 mol~1 units.

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between experimental and ““ reference ÏÏ values can be interpreted as a reÑection of intermolecular interactions between the amide and cosolvent molecules. For more clarity, in place of the di†erences (d0 ) [ (d0 ) , we take into account the 21 exper 21 size quantity d deÐned as :

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(d0 ) [ (d0 ) 21 size d \ 21 exper x2

(7)

where x is the mole fraction of water or alcohol in the 2 mixture. This quotient divided by V [eqn. (4)] shows the relac tive deviation of the local mole fraction of water or alcohol from the bulk one. Fig. 3 shows the d values for all the investigated mixtures. From this Ðgure we can draw the same conclusion as previously : the local mole fractions di†er only slightly from the bulk ones, and they are nearly the same for DMF and NMA in their mixtures with methanol and ethanol ; but NMF di†ers from other amides. For the Mamide ] waterN mixtures, the di†erences between amides are not clearly visible. Recently, Matteoli42 has proposed to use the ideal solution as a ““ reference level ÏÏ for interpretation of the d0 values. The ij ideal system was obtained assuming the activity coefficients c \ 0 over the whole concentration range, and partial molar i volumes of the ith component are equal to the molar volumes of the pure component (ideal behaviour : no deviations from RaoultÏs law and no volume change in the mixing process). In our opinion, MatteoliÏs42 concept is controversial. Our argument can be summarised as follows : (a) The ideal system is deÐned43 as the heat of mixing HE \ 0, and the molar entropy of mixing is given by S/R \ [; x ln x over the whole concentration range ; the equation i i V E \ 0 (no volume change) results from these assumptions.41 Fig. 2 Concentration dependence of d0 values calculated from 21 mixtures. From top to experimental data for Mamide ] AN binary bottom : (a) A \ water, (b) A \ methanol, (c) A \ ethanol. The vertical bars show the estimated error.

slightly (\1%) from the bulk ones. In other words, they are nearly the same as for an ideal solution. Thus, we can conclude that, in spite of the possible interactions between amide and water or alcohol molecules, the distribution of molecules in the solution structure is practically random. The only arrangement in the solution is the one resulting from orientational e†ects. We can say that amide molecules ““ build in ÏÏ to the existing polymeric structure of water or alcohol. This indicates that some complexes between amide and water or alcohol molecules are formed. Formation of such complexes was reported previously3h6 in the literature. It should be stated, however, that the solvation of amides (measured using d0 quantities) di†ers : DMF and NMA are solvated in nearly ij the same manner, but for NMF the di†erences are visible, especially for alcohols (Fig. 2). A similar behaviour is observed if we compare values of the KirkwoodÈBu† integrals, G , ij given in Table 4. It is interesting to note that volumetric data show a similar arrangement of these amides : the V E values for MNMA ] (water or alcohol)N binary mixtures are close to the ones for MDMF ] (water or alcohol)N, but the values for MNMF ] (water or alcohol)N mixtures are clearly di†erent.22 The local mole fractions, and consequently the d0 values, ij depend on the energy of intermolecular interactions and the di†erences in molecular size. As shown previously,1,2 it is possible to separate both of these e†ects as follows. We take into account the Ðctitious ““ reference ÏÏ mixture : (1) we assume the athermal mixing of components (and therefore V E \ 0 in the whole concentration range too41), and (2) we estimate the entropy of mixing for this mixture from the FloryÈHuggins theory. Calculated in this way, the (d0) values depend on ij size di†erences in molecular size only, and they can serve as a ““ reference level ÏÏ. Then, the di†erence (d0 ) [ (d0 ) 21 exper 21 size 2928

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Fig. 3 Concentration dependence of the d values calculated from eqn. (7) for Mamide ] AN binary mixtures. From top to bottom : (a) A \ water, (b) A \ methanol, (c) A \ ethanol. The vertical bars show the estimated error.

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(b) If molar volumes of components di†er, V D V , the 1 2 entropy of mixing will be di†erent from the above ideal form.44 Then, such a mixture cannot be regarded as ideal : for athermal mixing we cannot assume c \ 0. i As a consequence of his assumption, Matteoli found42 that for an ““ ideal ÏÏ (according to his assumption) solution, the d0 ij values are not all equal to zero. This result conÐrms the fact that the starting assumption is not correct. Estimation of the size e†ect by using the FloryÈHuggins theory should be treated as a Ðrst-order approximation only. Hildebrand45 concluded that this theory gives an upper limit for the size e†ect. Various more complicated models for calculations of entropy of mixing were proposed46,47 in the literature. Recently, Kumar et al.48 show, however, that the FloryÈHuggins theory overestimates the molecular size e†ects by 10È25% only. We can also expect that the application of the FloryÈHuggins theory produces approximately the same systematic error for all the investigated amides. It should be noted here that the mentioned di†erences between the investigated amides are beyond estimated experimental error ; moreover, we are discussing not a single system but a series of mixtures, and regularities are observed. This indicates, therefore, that both NMA and DMF interact with water or alcohol in a very similar manner, but interactions between NMF and alcohol molecules are slightly di†erent. This is an unexpected result. Di†erences between these amides in the local mole fractions increase in the order : water \ methanol \ ethanol. (b)

Molecular dynamics calculations

Among the investigated amides two, NMA and NMF, can exist in two forms : the cis and trans conformers (see Fig. 4). The trans-to-cis and cis-to-trans energy barrier heights for these amides are49 22.6 and 19.8 kcal mol~1, respectively, determined from NMR measurements, and using 1,2-dichloroethane and water as solvents. Easy to calculate, the trans conformer is 2.8 kcal mol~1 more stable. The error of these measurements is estimated49 to be 1.8 kcal mol~1, and, therefore, it is not possible to evaluate the solvent e†ect on the relative stability of both conformers. On the other hand, we can expect that these conformers may be di†erent in their ability for hydrogen bond formation. Dixon et al.50 have found that, for NMA, the cis isomer is predicted to be 2.3 kcal mol~1 less stable than the trans isomer for the uncomplexed NMA. In water solution, the cis-NMA Æ H O complex is only 2 0.5 kcal mol~1 less stable than the trans-NMA Æ H O complex. 2 Taking into account the dimeric molecule, (NMA) , formed 2 by two amide molecules, they found that the cis isomer forms a dimer that is 6.7 kcal mol~1 more stable than the dimer formed by the trans isomer. This indicates that both isomers interact with water or other amide molecules in a di†erent manner. We can expect that, in the alcohol solution, a similar behaviour should be observed. Then, for the MNMF ] MeOHN and MNMA ] MeOHN mixtures, the calculations for both the cis and trans isomers were performed separately. The moleculeÈmolecule radial distribution functions, rdf, g (r) and g (r), are shown in Fig. 5, for all the investigated 11 12 amides. As can be seen from this Ðgure, a well-deÐned Ðrst peak on the rdf is observed ; this peak corresponds to the Ðrst

Fig. 4 The cis and trans conformers of NMA and NMF molecules.

Fig. 5 MoleculeÈmolecule radial distribution functions g (r) and g (r) calculated for Mamide (1) ] methanol (2)N binary 11 mixtures. 12 top to bottom : (a) amide \ N-methylacetamide, (b) amide \ NFrom methylformamide, (c) amide \ N,N-dimethylformamide.

coordination sphere around the amide molecule. The radius of this sphere can be estimated from the position of the Ðrst minimum of the rdf. This radius is equal to approximately 0.65 nm, and is roughly independent of the amide kind. Moreover, the second peak of the rdf is clearly visible too, and it corresponds to the second coordination sphere. Additionally, it can be concluded that the moleculeÈmolecule rdfs for both the cis and trans conformers di†er only slightly. As was deduced from thermodynamic results above, the local mole fractions are nearly the same as for the bulk ones, and the radius of the solvation shell does not exceed the radius of the Ðrst coordination sphere. This deduction can be examined by using the MD results as follows. According to the deÐnition of the molecular radial distribution function, g (r), ij r g (x) Æ 4nx2 dx (8) n (r) \ o ij ij i 0 where n (r) symbolises the number of i molecules within the ij sphere of radius r around the central j molecule ; and o is the i number density of i molecules. The local mole fractions within this sphere can be calculated as follows :

P

n (r) xloc(r) \ ij (9) ij ; n (r) k kj All the xloc(r) functions, calculated from this equation, are disij played in Fig. 6. As can be seen, the local mole fractions at r \ 0.65 nm (at the limit of the Ðrst coordination sphere) di†er only slightly from the bulk ones. This means that the radius of the solvation shell does not exceed the value R \ 0.65 nm, c which conÐrms the previous ““ thermodynamic ÏÏ deductions. It is interesting to try to estimate the KirkwoodÈBu† integrals from the molecular rdf, and further to compare these with the experimental data. The calculated G (r) functions, ij deÐned as : G (r) \ ij

P

r

0

[g (x) [ 1]4nx2 dx ij

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Fig. 6 Values of the local mole fractions, xloc(r), as a function of ij radius r, calculated from eqn. (9). (a) NMA, (b) NMF and (c) DMF.

should converge asymptotically to a Ðnite value if r increases inÐnitely. In this limit, the G (O) value should be equal to the ij experimental one. Such asymptotic behaviour was observed for the calculated G (r), obtained by solving the PercusÈ ij Yevick equation (see Fig. 1 in ref. 51). For our systems, however, the G (r) functions diverge (Fig. 7). This result can be ij explained as follows : Since the [g (x) [ 1] function [eqn. ij (10)] is multiplied by the factor x2 prior to the integration, even small deviations (Ñuctuations) of the g (x) value from ij unity give, at large x, large contributions to the G value. ij These Ñuctuations of the g (x) around unity arise as a conseij quence of the Ðnite number of molecules used in the calculations. Then, the divergence of G (r) is observed. In our ij calculations, we used a relatively large number of molecules (N \ 729) because we expected that convergence should increase with the increasing number of molecules. The results obtained indicate, however, that even 729 molecules are insufÐcient to calculate the KirkwoodÈBu† integrals by integration of the molecular rdf. A similar observation was made by Adams52 for the simple binary Mbenzene ] argonN mixture : he found that even 864 argon molecules are insufficient for determination of the KirkwoodÈBu† integrals by the integration procedure. We propose here, however, a simple procedure for avoiding this difficulty. Our argumentation is as follows : If the radius of the solvation shell is approximately equal to the radius of the Ðrst coordination sphere, the following approximation should be fulÐlled : 10 G \ ij B

P P

Rc

0 Rc

[g (r) [ 1]4nr2 dr ] ij

P

= [g (r) [ 1]4nr2 dr ij Rc

[g (r) [ 1]4nr2 dr ij

(11)

0 where R symbolises the radius of the solvation shell. The c above estimated radius is equal to 0.65 nm approximatelyÈ then we can estimate the G values. Estimated by this means, ij the G values are collected in the Table 5. ij The observed di†erences between calculated (Table 5) and experimental (Table 4) results can be explained as follows. 2930

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Fig. 7 Plots of G (r) as a function of radius r, calculated from eqn. ij (10).

First, it is quite obvious that this procedure cannot produce the exact values of the KirkwoodÈBu† integrals. Second, the model used in calculations is approximate only. For example, a simplifying feature built into this model is the ““ united atom ÏÏ approximation. Another approximation is to use a set of Ðctitious partial charges distribution. These values were Ðtted to the best reproduction of the thermodynamic properties of pure components,37,38 not the mixture. Calculated moleculeÈmolecule rdfs depend, of course, on the form of the potential energy of interactions, especially within the Ðrst coordination sphere. This is why the di†erences between calculations and experiment are observed. We can say that conclusions derived from molecular rdf agree, in general, with the thermodynamic conclusions. It is visible, moreover, both that cis and trans conformers di†er, and that this di†erence reÑects a di†erence in solvation of the two conformers by methanol. In previous work2,17 the orientational entropy was calculatedÈthe entropy change originating from orientational e†ects within the solvation shell. These e†ects result from dipoleÈdipole interactions and the possibility of hydrogen bond formation between molecules. The T *S quantities orient for Mamide ] methanolN binary mixtures at equimolar composition and at 313.15 K are : 17 93 J mol~1 for DMF and 116 J mol~1 for NMF. Unfortunately, there are no experimental data available for the heat of mixing of MNMA ] waterN and MNMA ] alcoholN binary mixtures at T \ 313.15 K, and Table 5 Calculated, for Mamide ] methanolN binary mixtures, values of the KirkwoodÈBu† integrals [from the molecular radial distribution functions obtained in MD simulations, and using eqn. (11)]a Amide

Conformer

N-methylacetamide

cis trans

N-methylformamide

cis trans

N,N-dimethylformamide

G 11

G 22

G

[16 6.5

0 [17

[35 [18

[14 22

[35 [48

12

34

[7

1 [0.5

12

a Composition of binary mixture x \ 0.518, radius R \ 0.65 nm. amideunits. c All the values are given in cm3 mol~1

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therefore it is impossible to calculate T *S for these orient systems, especially for the MNMA ] methanolN systems. The HE results for MNMA ] waterN mixtures at T \ 308.15 K53,54 and at T \ 323.15 K55 are the only ones in the literature, allowing estimation of the orientational e†ects for this system ; the estimated values of T *S are strongly negative, as well orient as for MDMF ] waterN binary mixture.2,17 The orientational e†ects should be, nevertheless, visible in the atomÈatom radial distribution functions calculated from MD simulations. We take into account the following methanolÈamide atomÈatom rdfs : g , g , g , g and HO OO HN ON g , and display these functions in Fig. 8. As can be seen, OH strong orientational e†ects around the oxygen atom of the amide are observed for all the investigated amides ; as we can expect, the orientation of methanol molecules around the nitrogen atom is less visible. These e†ects are clearly visible within the solvation shell ; within the second coordination sphere they are nearly invisible (Fig. 8). A similar behaviour was observed for the Mformamide ] waterN binary mixture. Recently Puhovski and Rode56 have carried out simulations of this system, using the polarisable test particle model (T-model) for both formamide and water molecules. They found that the local mole fractions of components around the formamide molecule are nearly equal to the bulk ones, and this result agrees with the experiment.

Moreover, orientational e†ects of water molecules around the formamide molecule were observed : there are signiÐcant orientational e†ects for both waterÈwater and waterÈ formamide interactions, observed at short ranges corresponding to the Ðrst solvent shell. The clearly visible Ðrst peak on the methanolÈamide g rdf HO indicates the existence of a hydrogen bond between amide and methanol molecules. This hydrogen bond is responsible for the formation of the complexes between these molecules. Thus, we may consider the stable complexes, ““ living ÏÏ at least 20 ps (a time of a single simulation run) in the resulting Ðles obtained from MD simulations. We have considered the complex as stable, if the H ÈO distance never methanol amide exceeds (in the 20 ps interval) the limiting value, assumed to be equal to 0.23 nm (the position of the Ðrst minimum on the methanolÈamide g rdf ) ; a similar procedure can be applied HO to the H ÈO hydrogen bond. The results of the amide methanol research are collected in Table 6. We can say, therefore, that MD simulations conÐrm the existence of stable complexes in the Mamide ] methanolN binary mixtures. Finally, we can say that the picture obtained from the analysis of the molecular dynamics results is consistent with the thermodynamic data and with all deductions derived from these measurements. (c)

Ternary {amide (1) + alcohol (2) + water (3)} mixtures

Just as for binary mixtures, the solvation of amides in ternary mixtures can be described by using the d0 quantities. The i1 concentration dependence of these quantities was calculated at the constant value of ratio r, x 3 (12) x ]x 2 3 where x and x symbolise the mole fractions of alcohol and 2 3 water, respectively. As for binary mixtures, we take into account the di†erences r\

Fig. 8 AtomÈatom radial distribution functions, calculated for Mamide (1) ] methanol (2)N binary mixtures.

dter \ (d0 ) [ (d0 ) (13) i1 i1 exper i1 size between (d0 ) values, determined from thermodynamic i1 exper results, and (d0 ) values, determined for the reference i1 size mixture containing the size e†ect only. The reference mixture was deÐned assuming HE \ 0 and V E \ 0 (athermal mixing and no volume change) and the entropy of mixing was calculated according to the FloryÈHuggins model. Fig. 9 presents the concentration dependence of the dter quantity, calculated i1 at various values of the r ratio. Just as for binary mixtures, the local mole fractions di†er from the bulk ones slightly, exceeding the bulk values by only a few per cent ; moreover, their absolute values are larger in the alcohol-rich region. This means that, in this region, the amide molecule is preferentially hydrated and that this hydration is larger than the one resulting from the size e†ect only. While comparing the results obtained for NMA with the previous one obtained for NMF and DMF (see Fig. 5 and 6 in

Table 6 Number of amide molecules forming stable complexes in the investigated Mamide ] methanolN binary mixtures H

methanol

ÈO

amide

bond

H

Nvamide

N-methylacetamide

cis trans

51 53

13 37

N-methylformamide

cis trans

61 22

18 13

28

È

N,N-dimethylformamide

ÈO

methanol

bond

The limiting value for H ÈO and H ÈO distance is equal to 0.23 nm ; total numbers of amide and methanol molecules are Nvamide methanol 378 and 351, respectively.methanol amide

Phys. Chem. Chem. Phys., 2000, 2, 2925È2932

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Fig. 9 The dter \ (d0 ) [ (d0 ) values for MNMA ] i1 i1 exper i1 size alcohol ] waterN ternary mixtures, calculated from eqn. (13). The individual curves are calculated at various values of r [eqn. (12)] : (1) r \ 1.00, (2) r \ 0.75, (3) r \ 0.50, (4) r \ 0.25, (5) r \ 0.00. Error in dter is estimated equal to 4 cm3 mol~1. i1

ref. 2) we can state, similarly as in the case of binary mixtures, that NMA and DMF are solvated in the ternary mixtures in nearly the same manner, but the solvation of NMF di†ers from the other amides. The results obtained from thermodynamic data are unexpected ; we remember that both NMA and NMF are able to form a hydrogen bond created by the ““ amide ÏÏ hydrogen, in contrast to the DMF molecule. It is not easy to explain this behaviour. The simple observation that NMA and DMF have nearly the same size (the molar volumes are : 77.66 cm3 mol~1 and 78.46 cm3 mol~1, respectively, and 59.89 cm3 mol~1 for NMF22) is not sufficient because the entropy contributions originating from di†erences in molecular size were taken into consideration in the FloryÈHuggins theory. It is possible that the additional entropy term, originating from di†erences in the molecular shape between amide and cosolvent molecules, is responsible for these e†ects. It is difficult, however, to estimate this quantitively. Another question is : Why do all the investigated amides form solutions with small deviations from ideality (the excess Gibbs energy of mixing is small, and the local mole fractions di†er only slightly from the bulk ones), but with nonzero heat of mixing values. The most probable explanation for this behaviour is that the interactions between amide and cosolvent molecules do not lead to the formation of chains or clusters but rather to orientational e†ects within the solvation shell, as is clearly visible in the case of binary mixtures. For ternary mixtures, the evaluation of these e†ects is, however, difficult.

Acknowledgements This work was Ðnanced by KBN (Polish Committee for ScientiÐc Research) within the grant no. 3 T09A 071 15.

References 1 J. Zielkiewicz, J. Phys. Chem., 1995, 99, 4787. 2 J. Zielkiewicz, J. Chem. Soc., Faraday T rans., 1998, 94, 1713. 3 E. D. Schmid and E. Brodbek, Can. J. Chem., 1985, 63, 1365. 4 G. Eaton, M. C. R. Symons and P. P. Rastogi, J. Chem. Soc., Faraday T rans., 1989, 85, 3257. 5 E. S. Eberhardt and R. T. Raines, J. Am. Chem. Soc., 1994, 116, 2149. 6 L. Pikkarainen, T hermochim. Acta, 1991, 178, 311. 7 W. Acree, T hermodynamic Properties of Nonelectrolyte Solutions, Academic Press, New York, 1984, ch. 8.

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Phys. Chem. Chem. Phys., 2000, 2, 2925È2932

8 J. G. Kirkwood and F. P. Bu†, J. Chem. Phys., 1951, 19, 774. 9 A. Ben Naim, J. Chem. Phys., 1977, 67, 4884. 10 (a) A. Ben Naim, J. Chem. Phys., 1989, 93, 3809 ; (b) A. Ben Naim, Pure Appl. Chem., 1990, 62, 25. 11 A. G. Mansoori and J. F. Ely, Fluid Phase Equilib., 1985, 22, 253. 12 (a) R. G. Rubio, U. Prolongo, M. Cabrerizo, M. Diaz Pena and J. A. R. Renuncio, Fluid Phase Equilib., 1986, 26, 1 ; (b) R. G. Rubio, U. Prolongo, M. Diaz Pena and J. A. R. Renuncio, J. Phys. Chem., 1987, 91, 1177. 13 (a) Fluctuation T heory of Mixtures, ed. E. Matteoli and G. A. Mansoori, Taylor and Francis, New York, 1990 ; (b) K. E. Newman, Chem. Soc. Rev., 1994, 23, 31. 14 J. Zielkiewicz, J. Chem. T hermodyn., 1999, 31, 819. 15 J. Zielkiewicz, J. Chem. T hermodyn., 2000, 32, 55. 16 J. Zielkiewicz, J. Chem. T hermodyn., 1996, 28, 887. 17 J. Zielkiewicz, J. Chem. T hermodyn., 1997, 29, 229. 18 J. Zielkiewicz and P. Oracz, Fluid Phase Equilib., 1990, 59, 279. 19 J. Zielkiewicz and A. Konitz, Fluid Phase Equilib., 1991, 63, 129. 20 J. Zielkiewicz and A. Konitz, J. Chem. T hermodyn., 1991, 23, 59. 21 J. Zielkiewicz, J. Chem. T hermodyn., 1999, 31, 1597. 22 J. Zielkiewicz, J. Chem. T hermodyn., 2000, in press. 23 J. Zielkiewicz, J. Chem. T hermodyn., 1995, 27, 1275. 24 J. Zielkiewicz, J. Chem. T hermodyn., 1996, 28, 313. 25 J. Zielkiewicz, J. Chem. T hermodyn., 1995, 27, 415. 26 J. Zielkiewicz, J. Chem. T hermodyn., 1994, 26, 1317. 27 J. Zielkiewicz, J. Chem. T hermodyn., 1995, 27, 225. 28 Y. Uosaki, S. Kitaura, F. Iwama and T. Moriyoshi, J. Chem. T hermodyn., 1991, 23, 1125. 29 S. B. Brummer, J. Chem. Phys., 1965, 42, 1636. 30 J. Gao, J. J. Pavelites and D. Habibollazadeh, J. Phys. Chem., 1996, 100, 2689. 31 M. Diaz Pena and G. Tardajos, J. Chem. T hermodyn., 1979, 11, 441. 32 Handbook of Chemistry, 10th edn., ed. N. A. Lange, McGrawHill, New York, 1961, p. 1670. 33 E. Matteoli and L. Lepori, J. Chem. Phys., 1984, 80, 2856. 34 A. L. Zaitsev, V. E. Petrenko and Yu. M. Kessler, J. Solution Chem., 1989, 18, 115. 35 Report of the IUPAC Commision 1.2 on Thermodynamics, J. Chem. T hermodyn., 1981, 13, 603. 36 W. F. van Gunsteren and H. J. C. Berendsen, Groningen Molecular Simulation (GROMOS), library manual, Biomos, Groningen, 1987. 37 W. L. Jorgensen, J. Phys. Chem., 1986, 90, 1276. 38 W. L. Jorgensen and C. J. Swenson, J. Am. Chem. Soc., 1985, 107, 569. 39 Y. Marcus, J. Chem. Soc., Faraday. T rans., 1990, 86, 2215. 40 (a) J. Zielkiewicz, J. Phys. Chem., 1995, 99, 3357 ; (b) H. Liu and E. Ruckenstein, J. Phys. Chem. B, 1998, 102, 1005. 41 J. H. Hildebrand and R. L. Scott, T he Solubility of Nonelectrolytes, Dover, New York, 3rd edn., 1964, ch. VIII. 42 E. Matteoli, J. Phys. Chem. B, 1997, 101, 9800. 43 J. H. Hildebrand and R. L. Scott, T he Solubility of Nonelectrolytes, Dover, New York, 3rd edn., 1964, p. 47. 44 (a) J. H. Hildebrand and R. L. Scott, T he Solubility of Nonelectrolytes, Dover, New York, 3rd edn., ch. VI ; (b) I. Prigogine, T he Molecular T heory of Solutions, North Holland, Amsterdam, 1957, ch. IV. 45 (a) J. H. Hildebrand, J. Chem. Phys., 1947, 15, 225 ; (b) J. H. Hildebrand and R. L. Scott, T he Solubility of Nonelectrolytes, Dover, New York, 3rd edn., ch. VI. 46 R. N. Lichtenthaler, D. S. Abrams and J. M. Prausnitz, Can. J. Chem., 1973, 51, 3071. 47 M. D. Donohue and J. M. Prausnitz, Can. J. Chem., 1975, 53, 1586. 48 S. K. Kumar, I. Szleifer, K. Sharp, P. J. Rossky, R. Friedman and B. Honig, J. Phys. Chem., 1995, 99, 8382. 49 T. Drakenberg and S. Frosen, J. Chem. Soc., Chem. Commun., 1971, 1404. 50 D. A. Dixon, K. D. Dobbs and J. J. Valentini, J. Phys. Chem., 1994, 98, 13435. 51 K. Kojima, T. Kato and H. Nomura, J. Solution Chem., 1984, 13, 151. 52 J. E. Adams, J. Phys. Chem., 1998, 102, 7455. 53 J. Manczinger and G. KortuŽm, Z. Phys. Chem. NF, 1975, 95, 177. 54 A. M. Zaichikov and O. E. Golubinski, Zh. Fiz. Khim., 1996, 70, 1175. 55 A. B. de Haan and J. Gmehling, J. Chem. Eng. Data, 1996, 41, 474. 56 Y. P. Puhovski and B. M. Rode, J. Phys. Chem., 1995, 99, 1566.