Small-angle neutron scattering and Kirkwood–Buff integral study of aqueous solutions of pyridine

Journal of Molecular Liquids 113 (2004) 61–66

Small-angle neutron scattering and Kirkwood–Buff integral study of aqueous solutions of pyridine ´ ´ Almasy ´ a,b,*, Gabor ´ Laszlo Jancso´ c a

KFKI Research Institute for Solid State Physics and Optics, POB 49, 1525 Budapest, Hungary b ´ Brillouin, CEA–Saclay, 91191 Gif-sur-Yvette, France Laboratoire Leon c KFKI Atomic Energy Research Institute, POB 49, 1525 Budapest, Hungary

Abstract Solutions of pyridine in heavy water were studied by small-angle neutron scattering at 25 8C in the pyridine mole fraction range of 0.02–0.25. From the experimental data Kirkwood–Buff integrals and the closeness to phase separation parameters were calculated and compared with those obtained for pyridine – light water solutions from thermodynamic data available in the literature. The detailed analysis shows that a significant clustering of similar species occurs in the solution. In spite of the strongly non-ideal behavior these solutions are still far away from macroscopic phase separation. 䊚 2004 Elsevier B.V. All rights reserved. Keywords: Pyridine; Phase separation; Non-ideal mixture; Concentration fluctuation; isotope effects

1. Introduction Aqueous solutions of pyridine and methyl-substituted pyridines exhibit pronounced deviations from the ideal mixing, which are reflected, for example, in the miscibility behavior of pyridine homologues with water and heavy water. The deviation from the ideal mixing in these systems becomes more pronounced when more methyl groups are attached to the pyridine ring: pyridine and various methyl-pyridines are completely, whereas dimethyl-pyridines are only partially miscible with water w1x. However, 2-methyl-pyridine, 3-methyl-pyridine and dimethyl-pyridine – heavy water mixtures display closed-loop miscibility curves in the temperature-concentration phase diagram w2x. A systematic study of the mixing behavior in the series of methyl-substituted pyridines can provide some insight into the relation of the mixing behavior of these small organic molecules to their structure, in particular to the role of the position of the methyl group on the ring or the strength of the hydrogen bond between the N atom of the ring and a water molecule w3x. Pyridine–water mixtures have been recently studied by wide-angle neutron diffraction w4x and Monte Carlo simulations w5x. The results of the simulation studies *Corresponding author. Fax: q36-1-392-2501. ´ E-mail address: [email protected] (L. Almasy).

indicate the enhancement of the water–water interaction in the mixture, which leads to the clustering of water molecules and the formation of water-rich regions in the bulk of the pyridine–water mixture. The thermodynamic state of a mixture is closely related to its structure, which is commonly described in terms of the time-averaged and angle-averaged pair correlation functions (pcfs) of the different types of molecules. X-ray and neutron scattering techniques provide, in principle, a direct way to determine the atomic pcfs, however, in most cases the experimental difficulties do not make it possible to obtain the complete set of the atomic pcfs. According to Bhatia and Thornton w6x, the intensity scattered at zero angle is proportional to the magnitude of the average fluctuations in the molecular density and the concentration of the different species. The magnitude of the fluctuations can be determined from the measured forward scattering (zeroangle) intensity, the partial molar volumes of the components and the compressibility of the mixture, as it was shown by Nishikawa w7x. These fluctuations are related through the Kirkwood–Buff integrals to the interactions between the components in the mixture. In the Kirkwood–Buff theory the deviations from the ideal mixing behavior are related to the non-homogeneous distribution of the two species, which can be quantified by the excess number of molecules around a central one

0167-7322/04/$ - see front matter 䊚 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2004.02.037

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´ L. Almasy, G. Jancso´ / Journal of Molecular Liquids 113 (2004) 61–66

Fig. 1. Small-angle neutron scattering curves of some of the pyridine – heavy water solutions measured at 25 8C. I(q) and q are the scattering intensity and the scattering vector, respectively. The compositions are given in solute mole fractions. The solid lines represent fits to Eq. (1).

as defined in terms of the integrals of the molecular pair correlation functions w8x. This allows one to obtain some information about the structural arrangement of the molecules in the solution without the explicit knowledge of the pcfs. The present work is the continuation of our investigation aimed at understanding the origin of the nonideal behavior and the demixing phenomena in aqueous solutions of small organic molecules w3,9–11x. In this article, we present the results of small-angle neutron scattering (SANS) measurements on pyridine–heavy mixtures and analyze the obtained data in the framework of the Kirkwood–Buff approach. The results are compared with those obtained in previous studies. 2. Experimental Small-angle neutron scattering on heavy water solutions of pyridine was measured on the PACE instrument at the LLB, Saclay. Heavy water was used in order to enhance the contrast between the two species, thus increasing the coherently scattered intensity and making the measurement more precise. The measurements were performed at 25 8C in the pyridine mole fraction range of 0.02–0.25. The solutions were prepared by weighing from pyridine (Aldrich) and heavy water (99.83 at.% deuterium content). The samples were filled in 2-mm thick quartz cuvettes, which were thermostated at 25 8C within 0.1 8C. The sample-detector distance and the

˚ respectively, incoming wavelength were 1.36 m and 5 A, and a typical counting time was 20 min for each sample. The measured scattering was corrected for transmission, room background, detector efficiency, scattering from the cuvette and normalized to absolute scale using the scattering of a light water sample w12x. The scattering curves are shown in Fig. 1. The increased scattering at small angles evidences the non-homogeneous distribution of the two components in the mixtures. The strongest scattering is observed at approximately 0.1 mole fraction of pyridine. The dependence of the scattering intensity I(q) on the scattering vector q could be well described by the Ornstein– Zernike model of concentration fluctuations w13x: I(q)s

A qBg 1qq2j2

(1)

where A is the magnitude of the q-dependent coherent forward scattering intensity, j is the correlation length of the fluctuations in the scattering length density, and Bg is a q-independent background, arising mainly from the in-coherent scattering of the protons of the pyridine. The results of the fits are given in Table 1. 3. Analysis Enhanced small-angle neutron scattering in aqueous solutions of pyridine has been first briefly reported by

´ L. Almasy, G. Jancso´ / Journal of Molecular Liquids 113 (2004) 61–66

Bako´ et al. w14x, and interpreted tentatively as arising from solute aggregates in an isotropic matrix (water). This type of analysis of SANS experimental data was used before in studies of aqueous solutions of alcohols w15x and tetramethylurea w16x. In the present work, we followed a different approach, in which the measured zero-angle scattering intensity is related to the molecule number and concentration fluctuations in accordance with statistical thermodynamics w6x. The experimental data have been used to calculate the ‘closeness to phase separation parameter’ (vide infra), the fluctuations and Kirkwood–Buff integrals (KBIs) in pyridine–D2O mixtures. The method of calculation of the fluctuations and KBIs using SANS data has been described in detail in Ref. w11x and the relevant expressions are given in Appendix A. The coherent forward scattering intensity was obtained from fitting Eq. (1) to the experimental scattering curves. The closeness to phase separation and Kirkwood–Buff integrals were calculated also for pyridine – H2O mixtures using thermodynamic data available in the literature. (See Appendix A for the expressions used to calculate the KBIs in terms of macroscopic thermodynamic quantities.) 3.1. Closeness to phase separation For characterizing the closeness of the system to phase separation a useful quantity was suggested by Andon et al. w17x. The closeness to phase separation parameter (closeness parameter) can be expressed in terms of the concentration fluctuations (SCC(0)) w11x or of the excess Gibbs free energy (G e) w17x: x1x2 y1 SCC(0)

(2)

B ≠2Ge yRT E

x1x2C D

≠x21

F

(3)

G

where x1 and x2 are the mole fractions of species 1 and

63

Fig. 2. Closeness to phase separation in aqueous solutions of pyridine at 25 8C. Points for pyridine – D2O are calculated from SANS data wfilled squaresx; the solid line for pyridine – H2 O is calculated using thermodynamic data w24x only.

2, respectively. The closeness parameter is equal to y1 at the critical solution points and within the miscibility gap. In Fig. 2 the values of the closeness parameter at 25 8C are plotted for light and heavy water solutions of pyridine. It can be seen that for both solutions the closeness parameter reaches its minimum value of approximately y0.9 around the pyridine mole fraction of 0.1, so the isotope substitution on water does not drive the mixture closer to phase separation, as it occurs for example in the case of 3-methyl-pyridine solutions. Chan and van Hook w18x calculated the closeness parameters at 70 8C from their vapor pressure data for the pyridine – H2O and deuterated pyridine – H2O mixtures and from Rabinovich’s data w19x for the pyridine – D2O mixture. In each system the closeness parameter curve shows a minimum of y0.9 at pyridine mole fraction of 0.105, which is very similar to our results obtained for 25 8C (y0.85"0.02 at xpyridines0.1). Such value of the closeness parameter reflects strong deviations from the

Table 1 Results of the SANS measurements and calculations for the pyridine (1) – heavy water (2) solutions xpyridine

Aycmy1

Bgycmy1

˚ jyA

SCC(0)

G11

G22

G12

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.20 0.25

0.025"0.005 0.115"0.005 0.207"0.003 0.265"0.002 0.302"0.003 0.293"0.004 0.275"0.007 0.237"0.006 0.134"0.008 0.061"0.008

0.086"0.005 0.098"0.005 0.120"0.003 0.149"0.005 0.176"0.004 0.201"0.005 0.210"0.007 0.241"0.007 0.304"0.008 0.353"0.009

3.6"0.8 3.73"0.18 4.61"0.11 5.07"0.08 5.03"0.09 4.84"0.11 4.22"0.14 4.22"0.16 4.08"0.29 3.59"0.58

0.027 0.146 0.311 0.467 0.619 0.693 0.746 0.732 0.529 0.320

160 943 840 755 597 410 279 163 y8.1 y82

y10 27 77 123 168 189 203 198 132 62

y98 y260 y357 y390 y401 y365 y329 y276 y153 y71

The errors of the parameters A and Bg do not include the possible errors in the absolute calibration. The typical uncertainity of the Kirkwood– Buff integrals (Gij) is approximately 10–15%. The Gij-s are given in (cm3 ymol).

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Fig. 3. Kirkwood–Buff integrals (Gij ) in aqueous solutions of pyridine at 25 8C. The KBIs were calculated for pyridine – heavy water solutions (large symbols) using SANS data and for pyridine – water solutions (lines with small symbols) from thermodynamic data only.

ideal mixing. However, both the pyridine – light water and the pyridine – heavy water solutions are far from being macroscopically phase separated over a large temperature range; apparently there is no sign of approach to an immiscibility region with increasing temperature. The minimum value of the closeness parameter in 3-methyl-pyridine – D2O mixtures at 25 8C is y0.992 w11x. 3.2. Kirkwood–Buff integrals The Kirkwood–Buff integrals (Gij) are defined (see e.g. w7x) in terms of the molecular pair correlation functions (gij(r)) between the species i and j:

|

`

ŽgijŽr.y1.4pr2dr

Gijs

(4)

0

They are related to the total number of molecules type i around a central molecule j, thus characterizing the clustering of the species. Another quantity, the excess number of molecules around a central one gives a more clear picture about the character of the clustering: Dnijs

xi ŽGijyGREF ij . Vmol

(5)

where Dnij is the excess (or deficit) number of molecules type i around a central molecule j and GREF are the ij KBIs for a reference system corresponding to a symmetrical ideal system w20,21x. The values of GREF are ij

usually small enough to be neglected for mixtures in which strong clustering occurs, as it is the case, for example, in aqueous solutions of methyl-pyridines w11x. We used the reference system proposed in w21x and in the present case the GREF values correspond to correcij tions of less than 10%. Kirkwood–Buff integrals for pyridine – light water solutions at 25 8C were first calculated by Matteoli and Lepori w22x, and recently by Marcus w23x using various sets of thermodynamic data. We calculated the KBIs for pyridine – heavy water solutions using the forward scattering intensities measured in the present work; for the molar volumes and the isothermal compressibilities the experimental data of the corresponding pyridine – H2O mixtures were taken from w24,25x, respectively. The same molar volume and compressibility data along with the excess Gibbs free energy of mixing data of Abe et al. w24x were used to calculate the KBI values for the pyridine – water solutions. The KB integrals calculated for pyridine – heavy water solutions are given in Table 1 and shown together with those calculated for pyridine – water solutions in Fig. 3. The KB integrals for the pyridine – water solutions agree within the limits of precision of the experimental data with the curves reported by Matteoli and Lepori (Fig. 1 in w22x) and the KBI curves of Marcus (Fig. 6 in w23x) that were calculated using the G e values of Abe et al. w24x. The KBIs calculated by Marcus (see Fig. 6 in w23x) using the activity coefficients of Chan and Van Hook w18x differ from ours by a factor of two for pyridine mole fractions less than 0.4.

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Fig. 4. Excess numbers of molecules i around a central molecule j (Dnij) in the pyridine – heavy water solutions at 25 8C. Subscript 1 refers to pyridine, 2 refers to D2O.

Our SANS measurements covered the dilute region (xpyridines0.02–0.25) while out of the twelve experimental vapor pressure data points w24x, from which the G e values and their second derivatives were derived by fitting, only three (at xpyridines0.05, 0.1, 0.2) fall in this concentration range. By taking this into consideration it seems reasonable to conclude that the KB integrals for the pyridine – water and pyridine – heavy water solutions are the same within the combined uncertainties in the SANS measurements and the thermodynamic data. The similarity between the KBIs obtained by the two methods (though for different isotopic mixtures) indicates the superiority of the thermodynamic data of w24x over those of w18x at room temperature. 3.3. Excess numbers The excess numbers calculated from the SANS experimental data in the pyridine – heavy water solutions are shown in Fig. 4. The positive Dn22 and Dn11 values indicate the enhancement of water – water and pyridine – pyridine interactions, although to a lesser extent than those observed in the 3-methyl-pyridine – heavy water solutions w11x. The large negative values of Dn21 suggest that the direct solute–solute pair interaction is favored over ‘solvent–separated’ interactions, however, the positive values of Dn22 and negative values of Dn12 can be considered as an indication of the formation of water clusters in the mixture in accordance with the results of Monte Carlo simulations w5x.

urements demonstrated the presence of solute-rich and solvent-rich regions, or in other words the solute pyridine was seen to aggregate in the mixture. The most pronounced clustering was observed at 0.1 mole fraction of pyridine. The thermodynamic analysis of the mixing behavior indicated the closeness of both pyridine – water and pyridine – heavy water solutions to phase separation. By comparing the so-called closeness parameter for aqueous solutions of pyridine and 3-methyl-pyridine it was found that the 3-methyl-pyridine solution is much closer to the phase separation than the pyridine solution. This result is in accord with the presence of a liquid– liquid immiscibility region in heavy water solutions of 3-methyl-pyridine. The low spatial resolution of the SANS technique does not allow us to identify the possible configurations which may form in the liquid, only a characteristic length of the inhomogeneities can be obtained. At room temperature the characteristic size of regions with dif˚ for pyridine ferent compositions was found to reach 5 A ˚ for 3-methyl-pyridine solutions w11x, solutions and 20 A thus the clusters in the latter solutions contain a fairly large number of molecules. Besides the large positive values of the solute–solute and solvent–solvent KBIs, this is another, perhaps more direct evidence of the inhomo-geneous distribution of solute and solvent molecules (clustering of similar species). Analysis of the mixing behavior of binary systems using the Kirkwood–Buff approach gives a new possibility to check the results of computer simulations: the KBIs calculated from the molecular pair correlation functions can be compared with the experimentally determined KBI values. Our SANS study points to the importance of selecting a sufficiently large box size while performing molecular dynamics or Monte Carlo simulations in liquid mixtures with large microscopic inhomogeneities. Acknowledgments We thank M. Avdeev and I. Brovchenko for useful discussions. Hungarian Research Fund under grant OTKA T 031829, and the research grant of the MTA – JINR Hungarian – Russian cooperation program are gratefully acknowledged. Appendix A: The main formulas for the calculation of the KBIs from SANS measurements w10,11x:

4. Conclusions The mixing behavior in aqueous solutions of pyridine was studied by small-angle neutron scattering, and by the use of the Kirkwood–Buff theory. The SANS meas-

65

SCC(0)s

Aqrx1x2(b1yb2)2 w z2 ¯ rybdy(b 1yb2)~ x

(6)

|

where SCC(0) is the concentration fluctuation of the

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66

species 1, A is the q-dependent coherent forward scattering intensity (see Eq. (1)), r is the number density of the molecules, b1 and b2 are the sums of the coherent scattering lengths of the nuclei forming the molecules ¯ 1b1qx2b2, of the two components of the mixture, bsx ds(V1yV2)yVmol is the dilatation factor, V1 and V2 are the partial molar volumes of the components, Vmol is the molar volume of the mixture and x1 is the mole fraction of the solute. The Kirkwood–Buff integrals are given by w11x: B

G11sNACy D B

G22sNACy D

E 1 1B 1 E2 qkBTkTq Cdy F SCC(0)F G x1r rD x1 G

(7)

E 1 1B 1 E2 qkBTkTq Cdq F SCC(0)F G x2r rD x2 G

(8)

B E 1B 1 EB 1E G12sNACkBTkTq Cdy FCdq FSCC(0)F D G rD x1 GD x2 G

V1V2 VmolD

E 1 B Vj GiisG12q C yVmolF, i/j G xi D D

Ds1qx1x2

≠2ŽGeyRT. ≠x21

where G e is the excess Gibbs free energy.

w1 x w2 x w3 x w4 x w5 x w6 x w7 x w8 x w9 x w10x

(9)

where NA is the Avogadro number and kT is the isothermal compressibility. The expressions for the calculation of the KBIs from thermodynamic data w22x: G12sG21sRTkTy

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w15x w16x w17x w18x

(10)

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(12)

w19x

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