CRITICAL POINT

A. Z. Golik, Dnepropetrovsk

The present review is devoted to phenomena observed in the region of the critical state. These phenomena are now acquiring special interest in connection with new views on the nature of liquids and, as will be seen below, show that modern ideas about the structure of liquids may be useful in constructing a theory of real gases and vapors.

1. SCATTERING OF X-RAYS NEAR THE CRITICAL POINT

Before considering the scattering of X-rays in the critical region, let us briefly examine the features of X-ray scattering in gases and liquids. A detailed description of these phenomena may be found in the monographs of V. I. Danilov[^1] and Randall[^2].

The most characteristic feature of the scattering of X-rays in rarefied gases is their high intensity at small scattering angles (the angle between the scattered and the primary beam).

For monatomic gases the dependence of the intensity of the scattered rays on the angle has the form of a monotonically decreasing curve. In this case the character of the scattering is determined only by the structure of the atom, i.e., by the distribution of electrons in it.

In polyatomic gases the dependence of the intensity of the scattered rays on the angle is of a more complicated character (the curve has several maxima) and is determined, in addition, by the relative arrangement of the atoms in the molecules.

The presence of several maxima on the curve is a consequence of the molecular structure of the gas.

In liquids, the scattering of X-rays has more similarity to scattering in solids than in gases. The intensity curve for a liquid is completely similar to the intensity curve for a crystalline powder of the same substance, except that in the former case the maxima on the curve are somewhat broadened. This similarity of the scattering curves also gave rise to the idea of the structure of a liquid.

In connection with the explanation of the pattern of X-ray scattering, there are at present two points of view on the structure of liquids.

According to the first, developed by Zernike and Prins and somewhat later by Debye, a liquid is a homogeneous medium, the distribution of molecules in which, just as in crystals, is characterized by a suitably chosen distribution function giving the probability of finding atoms at a given distance. This theory was subsequently developed in detail by a number of authors1, 2 (the literature on this question is given there).

The second point of view on the structure of liquids was developed by Stewart and Morrow. In this case the liquid is regarded as an inhomogeneous medium consisting of regions within which the molecules are in an ordered state (cybotactic groups), and regions within which the molecules are in a disordered state. Between these regions there are no sharply expressed boundaries; with time, the boundaries between regions of ordered and disordered states may shift, regions of ordered state may pass into a disordered state and conversely. Consequently, a peculiar dynamic equilibrium exists between regions of ordered and disordered states. The number of molecules included in a region of ordered state is, generally speaking, different—from several tens to several thousands. At ordinary temperatures that part of the molecules which is in the disordered state constitutes a small part of their total number. Stewart’s theory is qualitative in character; nevertheless, as we shall see below, it proves very useful for understanding a number of phenomena observed both in liquids and in gases.

The number of works devoted to the study of X-ray scattering near the critical point is very small.

In Stewart’s laboratory, Spengler3 studied the scattering of X-rays in ethyl ether, and Benoit and Stewart4 in isopentane. The results of these works are presented in Figs. 1–6. In Fig. 1 are shown intensity curves obtained in isopentane at \(p = \mathrm{const}\) and variable \(v\) and \(T\). As \(T\) and \(v\) increase, the intensity curve gradually changes its shape from that characteristic of a liquid (the first) to that characteristic of a gas (the ninth). However, the critical point is not distinguished in any essential way in the family of these curves.

The maximum on the intensity curve, so characteristic of the liquid state, is retained at \(T > T_c\). An analogous picture is also observed in the case of ether (Fig. 2).

At constant temperature (above the critical temperature) the maximum on the intensity curve gradually decreases as \(v\) increases and \(p\) decreases and, finally, disappears (Figs. 3, 4). In this case the critical point is not distinguished in any essential way,

At constant specific volume above or below \(v_c\) (Figs. 5, 6), no substantial changes in the intensity curve occur when \(p\) and \(T\) are varied.

Thus, both in ether and in isopentane, indications of a “liquid structure” are found in the region above the critical one. In different substances the indications of a “liquid structure” disappear earlier or later, but this is not the essential point; what is important is that, from the point of view of structure, the critical point differs in no essential way from the nearest neighboring points.

It is interesting to note that, in the case of isopentane, the maximum on the intensity curve

Fig. 1. Scattering of X-rays in isopentane at different volumes and temperatures
\(1\)—\(T=20^\circ,\ v=1.6\); \(2\)—\(T=120^\circ,\ v=1.9\); \(3\)—\(T=170^\circ,\ v=2.4\); \(4\)—\(T=183^\circ,\ v=2.7\); \(5\)—\(T=190^\circ,\ v=3.0\); \(6\)—\(T=195^\circ,\ v=5.0\); \(7\)—\(T=200^\circ,\ v=6.7\); \(8\)—\(T=205^\circ,\ v=7.8\); \(9\)—\(T=210^\circ,\ v=8.8\)

Fig. 2. Scattering of X-rays in ether at different temperatures and volumes
\(1\)—\(T=25^\circ,\ v=1.4\); \(2\)—\(T=184^\circ,\ v=2.2\); \(3\)—\(T=196^\circ,\ v=25\); \(4\)—\(T=200^\circ,\ v=27.2\); \(5\)—\(T=205^\circ,\ v=32.5\); \(6\)—\(T=207^\circ,\ v=38\); \(7\)—\(T=210^\circ,\ v=45.3\)

Fig. 3. Scattering of X-rays in isopentane at different pressures and volumes
\(1\)—\(v=3.0,\ p=45.9\); \(2\)—\(v=3.7,\ p=41.4\); \(3\)—\(v=4.0,\ p=40.6\); \(4\)—\(v=5.0,\ p=39.2\); \(5\)—\(v=6.7,\ p=37.2\)

persists longer than in the case of ether, in which it disappears near \(v_c\), despite the fact that the dipole moment of the ether molecule is considerably greater than that of isopentane.

2. COMBINATION SCATTERING OF LIGHT NEAR THE CRITICAL TEMPERATURE

The study of the spectrum of scattered light near the critical point was carried out by G. S. Landsberg and Ukholin\(^{5,6,7}\). They studied the spectrum of water and methyl alcohol. In both

... cases, similar results were obtained, in complete agreement with the investigations described in the preceding paragraph.

Tables 1 and 2 present the results of these works; briefly, they amount to the following. For water, as the temperature increases,

Fig. 4. X-ray scattering in ether at different pressures and volumes

1—\(p=53.5,\ v=2.4\); 2—\(p=44.1,\ v=2.72\); 3—\(p=39.2,\ v=4.54\); 4—\(p=37.43,\ v=6.12\)

Fig. 5. X-ray scattering in ether at constant volume

1—\(T=184.5^\circ,\ p=34.8\); 2—\(T=190^\circ,\ p=39.7\); 3—\(T=200^\circ,\ p=53.5\); 4—\(T=205^\circ,\ p=57.8\)

Fig. 6. X-ray scattering in isopentane at constant volume

1—\(p=37.2,\ T=195^\circ\); 2—\(p=32.2,\ T=205^\circ\); 3—\(p=41.4,\ T=205^\circ\); 4—\(p=43.4,\ T=210^\circ\)

the band characteristic of a liquid in the spectrum of scattered light gradually narrows and shifts into the region of higher frequencies. On passing through the critical region the band continues to narrow, but does not disappear.

At density \(\delta=0.096\) (pressure about \(135\ \mathrm{atm}\)), alongside the band there appears a sharp line \(\Delta \nu = 3\,646\ \mathrm{cm}^{-1}\), characteristic of vapor at low pressures (of isolated molecules).

At density \(\delta=0.055\) (pressure about \(100\ \mathrm{atm}\)) the band practically disappears, and only a slightly broadened line \(\Delta \nu = 3\,646\ \mathrm{cm}^{-1}\) remains. With further change in density the spectrum changes almost not at all.

Analogous results were also obtained for methyl alcohol. The only difference is that, in the case of methyl alcohol, the line appears already in the liquid phase at \(T=190^\circ\) and \(\delta=0.577\), occurring alongside the band. “Isolated molecules” in methyl alcohol appear considerably earlier than in water.

Thus, in the spectrum of scattered light as well, the critical point is not distinguished by anything essential.

Table 1

Combination spectrum of water and steam as a function of temperature and density. Exciting lines \(\nu_1 = 27\,388\ \mathrm{cm}^{-1}\), \(\nu_2 = 27\,353\ \mathrm{cm}^{-1}\), \(\nu_3 = 27\,293\ \mathrm{cm}^{-1}\)

Table 2

Combination spectrum of methyl alcohol as a function of temperature and density. Exciting lines \(\nu_1 = 27\,388\ \mathrm{cm}^{-1}\), \(\nu_2 = 27\,353\ \mathrm{cm}^{-1}\), \(\nu_3 = 27\,293\ \mathrm{cm}^{-1}\)

3. CHANGE IN THE DENSITY OF A SUBSTANCE NEAR THE CRITICAL TEMPERATURE

New investigations of the change in the density of a substance near the critical temperature were undertaken by Canadian physical chemists about 10 years ago. As early as 1904 Teichner\(^8\), and then in 1912 Traube\(^9\), found that at the critical point, with the disappearance of the meniscus, the difference in density between those phases of the substance which occupy the regions formerly occupied by liquid and vapor does not disappear. At that time these phenomena did not attract attention.

Subsequently these investigations were repeated\(^ {10,11}\) and expanded by Maass and his coworkers. They showed that the difference in the density of the substance in that region of the vessel where the liquid had previously been located and in the region where, before the disappearance of the meniscus, the vapor had been located, does not disappear at temperatures above the critical temperature. Mechanical stirring did not lead to the disappearance of this difference in densities. A series of substances was studied: ethylene, dimethyl ether, propylene, and the effect proved to be general, although for different substances it had different magnitudes.

As the temperature increased (above the critical temperature), the difference in densities decreased and reached zero at a certain quite definite temperature. On reverse tracking, upon cooling, the change in density followed a different path: the curve

density–temperature curve upon cooling did not coincide with that which had been obtained upon heating.

Figure 7, which is typical, shows the results obtained for ethylene. Curve \(A\) represents the change in the density of the substance upon heating. At the temperature \(T_c\) the meniscus disappears. Upon cooling, the change in density follows curve \(B\). The restoration of the meniscus now occurs already at point \(e\), after which the density of the liquid increases rapidly as cooling proceeds (curve \(C\)).

Fig. 7. Change in the density of ethylene as a function of temperature near the critical point.

Upon repeated heating and cooling, all points of the cycle are reproduced completely.

The process can be stopped at any point, and the existing phases of the substance are preserved for as long as desired, if \(T=C\).

If heating is stopped before \(T_d\) and the substance is then cooled, a curve is obtained all of whose points lie inside the region bounded by curves \(A, B, C\).

Mechanical stirring, if it is not accompanied by expansion or compression of the substance, does not eliminate the density difference.

If an arbitrary point on curve \(A\) is chosen and the substance is subjected to small alternating heatings and coolings, following one after another, then the density of the substance tends toward a lower value lying either on curve \(B\) or on curve \(C\). A similar effect is produced by alternating expansion and compression. If the manipulations are stopped, the density remains unchanged for as long as desired. The dielectric constant and heat capacity of the states of the substance represented by different points of curves \(A, B, C\) were also measured. They likewise proved to be different.

Thus, all the phenomena described here, in full agreement with one another, attest not only to the presence in a liquid of a structure different from that which characterizes a gas, but also to the fact that this structure, characterizing the liquid, does not disappear, generally speaking, at the critical point.

Regions of an ordered state continue to exist in gases at sufficiently high densities. Near the critical point, very complex processes of destruction (or restoration) of elements of the “liquid structure” take place; these elements exist over a certain interval alongside isolated molecules.

The forces responsible for the appearance of ordered regions depend very strongly on the mean distance between molecules and are not directly connected with the dipole moments of the latter.

References

1. V. I. Danilov, Scattering of X-rays in Liquids (monograph). Series “Problems of the Newest Physics,” issue 32, ONTI, 1935.
2. Randall, The diffraction of X-rays and electrons by amorphous solids, liquids and gases, London, 1934.
3. Spengler, Phys. Rev., 46, 698, 1934.
4. Benz and Stewart, Phys. Rev., 46, 703, 1934.
5. Landsberg, Izvestiya Akademii nauk SSSR, physical series, no. 3, 373, 1938.
6. Ukholin, DAN, 16, 403, 1937.
7. Landsberg and Ukholin, DAN, 16, 399, 1937.
8. Teichner, Ann. d. Phys., 13, 595, 1904.
9. Traube, Ann. d. Phys., 8, 267, 1904.
10. Maas, Chem. Rev., 23, 17, 1938 (with literature cited there).
11. Maas and Geddes, Phyl. Trans., A, 236, 303, 1937.