7158
J. Phys. Chem. B 1997, 101, 7158-7162
Structure Study of Supercritical CO2 near Higher-Order Phase Transition Line by X-ray Diffraction Takeshi Morita and Keiko Nishikawa* Department of DiVersity Science, Graduate School of Science and Technology, Chiba UniVersity, Yayoi, Inage-ku, Chiba 263, Japan
Masakazu Takematsu, Hanae Iida, and Seiya Furutaka Department of Chemistry, Faculty of Education, Yokohama National UniVersity, Tokiwadai, Hodogaya-ku, Yokohama 240, Japan ReceiVed: March 27, 1997; In Final Form: June 18, 1997X
Wide-angle X-ray scattering experiments for supercritical CO2 near the higher-order phase transition line on the isotherm at T ) 308 K were carried out. Radial distribution functions were compared with that of the high-pressure liquid CO2. The results show that the higher-order phase transition line divides supercritical state into two phases, i.e., liquidlike and gaslike regions, from the viewpoint of the structure. Radial distribution functions, however, indicate that this phase transition is remarkably gentle even near the critical point.
Introduction
TABLE 1: Thermodynamic States for the Present X-ray Scattering Measurementsa
Supercritical fluids vary their densities continuously and widely by a slight change of the temperature or pressure and exhibit characteristic activities as solvents. Supercritical fluids, because of their unique properties, have attracted much interest as novel solvents for chemical or biochemical reactions and extractions. In our previous studies by small-angle X-ray scattering (SAXS) experiments for supercritical CO21,2 and CF3H,3 it has been shown that density fluctuations form a ridge along the extension of the coexistence curve of gas and liquid when the contour maps of their values are drawn in the P-T phase diagrams. We have also pointed out that the various physicochemical properties, for example, solubilities, solvent activities, and rate constants in chemical reaction, show anomalies on the ridge.1-3 Similar peculiarities are also observed on other substances in the supercritical state. For instance, the isothermal compressibility obtained by SAXS measurements and sound velocity on supercritical Ar have maxima or minima along the extension line of the vapor pressure curve, respectively.4,5 Thus, it is possible to say that the ridge is a boundary that separates the supercritical region, and we presented the ridge as the locus of the higher-order phase transition.1-3 Much information on behavior near the extension curve is, therefore, interesting from the viewpoints of enrichment of the fundamental understanding of physicochemical properties of supercritical fluids and development of their industrial applications. In recent years, structure investigations for supercritical fluids have been intensively performed by neutron6-14 and X-ray15-17 diffraction experiments. We have reported the structure study on radial distribution functions (RDFs) of supercritical states of CO2 by wide-angle X-ray scattering experiments by use of a two-dimensional detector, usually called an imaging plate.16 However, there has been no report viewed from the higherorder phase transition in the supercritical region mentioned above.2,3,18 In the present study, therefore, the discussion is concentrated on the point of the structure change caused by the * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, August 1, 1997.
S1089-5647(97)01090-0 CCC: $14.00
liquid A B C D E
temp/K
pressure/MPa
density/g cm-3 b
〈(∆N)2〉/N b
277.6 308.2 (1.01) 308.2 (1.01) 308.2 (1.01) 308.3 (1.01) 308.3 (1.01)
6.82 9.34 (1.19) 9.12 (1.16) 8.40 (1.07) 8.12 (1.04) 7.67 (0.98)
0.921 0.6826 (1.46) 0.6692 (1.43) 0.5912 (1.26) 0.4900 (1.05) 0.3121 (0.67)
0.43 3.25 3.87 11.42 31.05 11.91
a The values in parentheses are reduced parameters. b The values of densities and density fluctuations were calculated by use of the equation of state for CO2.22
higher-order phase transition. The simulation study of the liquid structure by the local structure model was also carried out for comparison. Experimental Section X-ray diffraction measurements were performed for five thermodynamic states of supercritical CO2 denoted as A-E, which are at P ) 9.34, 9.12, 8.40, 8.12, and 7.67 MPa on an isotherm at T ) 308 K, and the high-pressure liquid at 6.82 MPa and 277.4 K. The measurement points are listed in Table 1 with the reduced values of T/Tc, P/Pc and F/Fc. The critical constants of CO2 are Tc ) 304.2 K, Pc ) 7.38 MPa, and Fc ) 0.468 g/cm3. A diffractometer with a two-dimensional detector (DIP-100 of MAC Science Co., Ltd., imaging plate) was used.19 The sample holder,20 which is endurable up to 10 MPa, is made of stainless steel, and the windows are made of Be of 2 mm in thickness. It is possible to set the temperature in the range 0-60 °C. Fluid pressure and temperature were monitored with a strain gauge and alumel-chromel thermocouples. During the measurements, temperature and pressure were kept within (0.1 K and (0.01 MPa, respectively. Radiation was Ag KR (wavelength λ ) 0.5608 Å) and camera lengths were set at 90 and 180 mm. The range of the scattering parameter s was 0.3-9.0 Å-1, where s ) 4π sin θ/λ and 2θ is the scattering angle. The accumulation time for intensity measurements of a sample was 2000 s. Measured intensities were corrected for the subtraction of the background intensity, © 1997 American Chemical Society
Supercritical CO2
J. Phys. Chem. B, Vol. 101, No. 36, 1997 7159
Figure 1. Thermodynamic states (A-E) measured in the present study and contour lines of the density fluctuations (dotted curves) on the P-F phase diagram. CP represents the critical point. The critical isochore is shown by the broken line. The higher-order phase transition curve is denoted by the chain line.
Figure 2. Experimental total intensities I(s) for the states A-E and liquid CO2.
the polarization, the uniformity due to the readout system of the recorded X-ray intensities on the imaging plate, averaging from two-dimensional data to one-dimensional ones, the absorption, and the geometrical factor. The absolute scale was obtained by normalizing the asymptotic values of the corrected intensity function at large s to the scattering from independent atoms from a stoichiometric unit. Details have been described previously.19,20 Results and Discussion The measured states A-E are shown in the P-F phase diagram (Figure 1). The dotted curves in the figure are the contour lines of the density fluctuation, 〈(∆N)2〉/N, and the numbers on the curves represent their values. They were obtained by the following relation21
〈(∆N)2〉/N ) Z2(N/V)κTkBT
(1)
where N is the number of molecules in volume V, κT is the isothermal compressibility, kB is the Boltzmann constant, and T is the thermodynamic temperature. The κT values were calculated by using the empirical equation of state for CO2 given by Huang et al.22 The referenced ridge of the density fluctuation is described by the chain line in Figure 1. This line is located near the critical isochore shown by the broken line but does not overlap it.3 States A-C are in the higher-density region and state E is in the lower density region compared to the phase transition line. State D is very near the line. The density fluctuations of the states change from 3.2 (state A) to 31.1 (state D) in the present experiments. Scattering Intensities and Radial Distribution Functions. The experimental total intensities for states A-E are shown in Figure 2 with that of liquid CO2. The extreme increase of intensities in the small s region indicates that the density fluctuations of supercritical fluids are very large, as shown by the following relation between the diffraction intensity and the density fluctuation:
I(0) ) Z2〈(∆N)2〉/N
(2)
where I(0) is the scattering intensity at s ) 0 per molecule and Z is the number of electrons in a molecule.21 The large value of the number-density fluctuation shows that the system is
Figure 3. Weighted structure functions si(s) for the states A-E and liquid CO2.
constructed of mixtures of aggregates that are diverse in size, namely, the molecules are distributed, forming high-density and low-density regions. The aggregates are hereafter called clusters. The peaks centered at about s ) 1.5 Å-1 in Figure 2 contain information on molecular packing and arrangement. They become broader, and the s values of their tops shift to smaller values as the density is decreased. The weighted structure function is defined by
si(s) ) s(I(s) -
∑nifi(s)2)
(3)
where I(s) is the total coherent intensity per molecule, fi is the atomic scattering factor, and ni is the number of the ith atom in the molecule. The weighted structure functions of states A-E are shown in Figure 3. As the densities decrease, their curves are seen to become gentle in shape, especially in the filling-up of the valley near s ) 1.0 Å-1 and the smearing of the peak near s ) 1.5 Å-1. This shows the change of the intermolecular distances or the arrangement of the molecules, which is distinctly
7160 J. Phys. Chem. B, Vol. 101, No. 36, 1997
Morita et al.
Figure 5. Weighted structure function si(s) for liquid CO2. The solid curve is the experimental one, and the broken curve is the calculated one by the local structure model. Figure 4. Radial distribution functions for the states A-E and liquid CO2.
investigated from RDFs obtained by the Fourier transform of the weighted structure functions. The Fourier transform of the weighted structure function si(s) defined by
2r
4πr2(F - F0) ) π
∑
niZi2
∫si(s)sin sr ds
(4)
gives RDFs, including the spread of the electron cloud of each atom. In eq 4, Zi is the number of electrons in the ith atom and ni is the number of the ith atom in a molecule. The notation F(r) is approximately the number density of molecules at r from a molecule, and F0 is the average value of F(r) in the system. The measured range of s values in the present measurements was 0.3-9.0 Å-1. Because the upper limit of 9.0 Å-1 is small in consideration of the Fourier transform analysis, the data of larger s values were supplemented by the calculated structure function for the free molecule of CO2. The intramolecular parameters of gaseous CO223 are used for the calculation. This procedure is justified because of the general agreement between the scattering intensities by the fluid and those by the corresponding free molecule in the s region larger than 5-6 Å-1. The intensity data of the s range smaller than the lower limit of experimental data of s ) 0.3 Å-1 are important for the Fourier transform of the supercritical fluid, because of the large values of their scattering intensities in the region, as shown in Figure 2. Because the X-ray scattering intensity per molecule at s ) 0, I(0), is related to the isothermal compressibility κT as shown by eqs 1 and 2, the intensity data for s ) 0-0.3 Å-1 were also supplemented by extrapolation to calculated I(0) values. The RDFs are shown in Figure 4. The first peak at r ) 1.2 Å and small peak at r ) 2.4 Å are assigned to the C-O and O-O interferences within a molecule, respectively. Other peaks refer to intermolecular interferences. It is well-known that the RDF of a liquid fluctuates around the zero line, which means that the regions of high molecular density and those of low molecular density are alternated around a molecule. This suggests an underlying pseudocrystalline structure for the local region around a molecule. The RDF for the high-pressure liquid CO2 is of the same behavior. On the other hand, all the RDFs for supercritical CO2, A-E, have continuous positive regions up to 20-30 Å. This is general
for the RDFs of supercritical fluids, as also confirmed in other studies by diffraction experiments13,14 and molecular dynamics simulations.14 This directly shows that the supercritical states consist of clusters distributed diversely in the low-density regions. Simulation of Liquid CO2 Structure. To discuss the packing of the molecules in the clusters for the supercritical states, it is necessary to know the structure in the liquid as a standard. As mentioned above, there is a local structure around a molecule for the high-pressure liquid CO2. Generally speaking, in constructing a local lattice structure model, we assume a certain nearest-neighbor configuration around a central molecule and repeat this structural unit by some specific rule. Details of the formula for the scattering intensity of the structure model were presented elsewhere.24,25 In the construction of the structure model of the high-pressure liquid CO2, we started from the crystal structure.26 The rough model of the local structure was searched by a trial and error method, where the arrangement of molecules and the intermolecular distances were gradually changed from the ones for the crystal. It was ascertained that the same arrangement as that of the crystal expanded slightly in the intermolecular dimension is best. Next, a least-squares refinement was carried out with four parameters: the lattice constant of the cell a, the Prins parameter D,24 the radius of the discrete structure region Rc, and its temperature factor lc. The Prins parameter D is related to the mean distance of the ith and jth atoms, rij, and the corresponding root-mean-square deviation, lij, as
lij2 ) 2Drij
(5)
The number of molecules up to the fourth nearest neighbors around the central molecule gave the best fitting with the experimental scattering intensities. Scattering intensities ranging from 1 to 7 Å-1 have been used in the refinement because for the s region smaller than 1 Å-1 spurious peaks inevitably appear, whereas for s region larger than 7 Å-1 the calculated si(s) is approximately equal to that of a free CO2 molecule and is considered hardly affected by the intermolecular interference. The results for the refinements are as follows: a ) 6.20(0.02) Å, D ) 0.18(0.01) Å, Rc ) 9.21(0.02) Å, and lc ) 1.8(0.1) Å, where the numbers in parentheses are the standard deviations. The si(s) curve calculated by use of the refined parameters is compared in Figure 5 with the experimental one. X-ray scattering intensity from the high-pressure liquid could be well
Supercritical CO2 simulated by the local lattice structure model. However, the agreement of the intensities for the s region smaller than 1.5 Å-1, which are omitted in Figure 5, is poor because a spurious peak is inevitable because of the sudden onset of the continuum region to the discrete region. Another reason for the poor agreement in the smaller s region is as follows. As shown in the total scattering intensity (Figure 2), the scattering at the smaller s region is strong even for the liquid because the present state is fairly near the critical point and many voids are considered to be created, judging from the large density fluctuation. The contribution from the density fluctuation was not included in the present formulation by the local lattice structure model. However, the average arrangement of neighboring molecules around a central molecule is thought to be determined by the local structure model. Compared with the crystal structure,26 it is concluded that the main packing in the high-pressure liquid CO2 for the first neighboring molecules is in a twisted X-shape and the one for the second nearest neighbor is in a slipped parallel shape. Structure of Supercritical CO2. One of the important questions regarding the structure of the supercritical fluids is the cluster size and size distribution. From the results of the small-angle X-ray scattering experiments for supercritical CO2,1,2 we reported that the Ornstein-Zernike plots of the scattering intensities form straight lines. This means that the size of clusters in supercritical fluids is varied and that the correlation functions of the distribution of molecules is described by an exponential decay such as exp(-r/ξ)/r, where ξ is the OrnsteinZernike correlation length.27 The values of ξ for various thermodynamic states of supercritical CO2 are figured in the contour map in our previous paper.2 The correlation lengths of the states in the present studies change from about 9 Å (state A) to a value larger than 20 Å (state D). It is certain that the larger value of ξ means the existence of the larger clusters in the system. This value does not mean the dimension of the main species of the clusters first because the correlation function of the molecular distribution is in the exponential decay as mentioned above and second because according to the complementary relation the correlation length obtained from diffraction experiments changes to the correlation of the void in place of the substance. However, the change of the correlation length has a similar tendency as the density fluctuation,2 and it is possible to say that it reflects the inhomogeneity of the sample from the viewpoint of the length. The next problem is the molecular packing in the clusters. Because of nonexistence of the averaged structure, it may be impossible to discuss the packing of the supercritical fluid by a simple model as in the case of the liquid. There are various sizes of clusters, dependent on the molecular packing. However, the pattern of the peaks of the RDFs for the supercritical states resembles very much that for the liquid. The peaks centered at values larger than 4 Å are attributed to molecular interferences. The first, second, and third nearest neighboring peaks of the liquid appear at 4.3, 8.1, and 11.7 Å, respectively, for the liquid. For the supercritical states, they shift to longer distances and the deviation becomes large as the density decreases. The nearest neighbor peaks up to the third are detected clearly for state A. Though the third peak becomes smeared with the decrease of the density, it is observable for states D and E. This is surprising, considering the fact that the variety of the clusters seems to be greatest in state D and that the density of state E is one-third for the liquid. Because RDFs are two-body distribution functions, the molecular arrangements of the high-density region are reflected most. Therefore, the RDFs for the supercritical states show mainly the molecular
J. Phys. Chem. B, Vol. 101, No. 36, 1997 7161 packing in clusters with a large number of molecules. It is possible to say that the molecular packing of the large clusters is fairly similar to that of the liquid up to the second or third nearest neighbors, though the packing becomes loose gradually and the molecular distances expand with a decrease of the density. According to the ab initio MO calculation by Domanski et al. for the CO2 cluster consisting of two molecules, the T-shape and the slipped parallel configuration are the most stable.28 The latter configuration also appears in the crystal26 and in the high-pressure liquid near the critical point. The molecular packing of the nearest neighbors for CO2 does not seem to be different in terms of the dependence of the numbers of molecules of the aggregates. By comparison of the RDFs of states D and E, the peak positions do not change, although the density of the former is 1.6 times larger than that of the latter, while the peak positions gradually shift to larger values for A-D as the density decreases. Roughly speaking, we can say that the higher-density region down to the higher-order phase transition line is liquidlike and that the density region lower than the transition line is gaslike. The point on the line is the state where the density fluctuation becomes maximum as mentioned in the introductory paragraph. As the density fluctuation increases, the structures of the supercritical CO2 in the liquidlike region change in such a way that the voids become large, the variety of the molecular aggregates are created, and the molecular packing in the cluster does not change as much from that of the liquid though the molecular distances expand gradually. On the higher-order phase transition line, the variety in the cluster size becomes extreme. And in the gaslike region the clusters become smaller in size. However, the molecular packing up to the second or third nearest neighbors does not change as much as the one in the state on the phase transition line. The structure change from RDFs is gentle and continuous on the whole. Acknowledgment. This work was partially supported by a Grant-in-Aid for Scientific Research on Priority Area “Supercritical Fluids” and “Chemistry of Small Many-body Systems” from the Ministry of Education, Science and Culture, Japan. References and Notes (1) Nishikawa, K.; Tanaka, I. Chem. Phys. Lett. 1995, 244, 149. (2) Nishikawa, K.; Tanaka, I. J. Phys. Chem. 1996, 100, 418. (3) Nishikawa, K.; Morita, T. J. Phys. Chem. B 1997, 101, 1413. (4) Thomas, J. E.; Schmidt, V. M. J. Chem. Phys. 1963, 39, 2506. (5) Carome, E. F.; Cybowski, C. B.; Havlice, J. F.; Swyk, P. A. Physica 1968, 38, 307. (6) Adya, A. K.; Wormald, C. J. Mol. Phys. 1991, 74, 735. (7) Bausenwein, T.; Bertagnolli, H.; Gutwerk, D.; To¨dheide, K.; Chieux, P. Mol. Phys. 1992, 76, 127. (8) Londono, J. D.; Shah, V. M.; Wignall, G. D.; Cochran, H. D.; Bienkowski, P. R. J. Chem. Phys. 1993, 99, 466. (9) Postorino, P.; Tromp, R. H.; Ricci, M. A.; Soper, A. K.; Neilson, G. W. Nature 1993, 366, 668. (10) Buontempo, U.; Postorino, P.; Ricci, M. A.; Soper, M. K. Mol. Phys. 1994, 81, 217. (11) Strauss, G.; Zweier, H.; Bertagnolli, H.; Bausenwein, T.; To¨dheide, K.; Chieux, P. J. Chem. Phys. 1994, 101, 662. (12) Tromp, R. H.; Postorino, P.; Neilson, G. W.; Ricci, M. A.; Soper, A. K. J. Chem. Phys. 1994, 101, 6210. (13) Ishii, R.; Okazaki, S.; Okada, I.; Furusaka, M.; Watanabe, N.; Misawa, M.; Fukunaga, T. Chem. Phys. Lett. 1995, 240, 84. (14) Ishii, R.; Okazaki, S.; Okada, I.; Furusaka, M.; Watanabe, N.; Misawa, N.; Fukunaga, T. J. Chem. Phys. 1996, 105, 7011. (15) Tamura, K.; Hosokawa, S. J. Non-Cryst. Solids 1992, 150, 29. (16) Nishikawa, K.; Takematu, M. Chem. Phys. Lett. 1994, 226, 359. (17) Yamanaka, K.; Yamaguti, T.; Wakita, H. J. Chem. Phys. 1994, 101, 9830. (18) Douglass, D. H., Jr. Physics 1965, 1, 329. (19) Nishikawa, K.; Sakamoto, Y.; Iijima, T. Jpn. J. Appl. Phys. 1991, 30, 1303.
7162 J. Phys. Chem. B, Vol. 101, No. 36, 1997 (20) Nishikawa, K.; Takematu, M. Jpn. J. Appl. Phys. 1993, 32, 5155. (21) Ziman, J. M. Model of disorder; Cambridge University Press: Cambridge, 1977. (22) Huang, F. H.; Li, M. H.; Lee, L. L.; Starling, K. E.; Chung, F. T. H. J. Chem. Eng. Jpn. 1985, 18, 490. (23) Murata, Y.; Kuchitsu, K.; Kimura, K. Jpn. J. Appl. Phys. 1970, 9, 591.
Morita et al. (24) Prins, J. A.; Peterson, H. Physica 1936, 3, 147. (25) Nishikawa, K.; Iijima, T. Bull. Chem. Soc. Jpn. 1985, 58, 1215. (26) Simon, A.; Peters, K. Acta Crystallogr. 1980, B36, 2750. (27) Stanley, H. E. Introduction to Phase Transition and Critical Phenomena; Oxford University Press: Oxford, 1971. (28) Domanski, K. B.; Kitao, O.; Nakanishi, K. Mol. Simul. 1994, 12, 343.
