Binary-Solution Critical Opalescence Mole Fraction versus Temperature Phase Diagram
J. Chem. Educ. 1995.72:560. Downloaded from pubs.acs.org by UNIV DE BARCELONA on 01/02/19. For personal use only.
Chris Stenland and B. Montgomery Pettitt1 University of Houston, Houston, TX 77204-5641
Phase-transition phenomena often give dramatic observable effects by the sudden alteration in the properties of a substance. Although the most widely known phase transitions are melting/freezing and vaporization/condensation, there exist many other kinds (1, 2). Phase transitions and critical phenomena are active areas of research because phase transitions and critical phenomena are vitally important in both techand basic science. The number of nology common “critical parameters” in the condensed-phase literature, such as superconductivity’s Tc, the critical micelle concentration, and the Curie temperature indicate the importance of this phenomena. The phase separation of a binary liquid mixture as a function of both mole fraction and temperature makes an excellent exercise in physical chemistry. This paper will give the procedure and apparatus used to investigate the spinodal decomposition of binary fluid mixtures.
Figure 1. Experimental setup for the methanol-cyclohexane mixture. The water-triethylamine mixture does not need the water bath (C) nor 1he hot plate (D) and uses air as the thermostatting bath. Legend: (A) laser; (B) beam path; (C) 3-L water bath; (D) hot plate; (E) test tube; (F) ring stand and clamp; (G) thermocouple probe: (H) screen; (I) digital thermometer.
The physical chemistry laboratory experi-
ment described here investigates the ther-
mally controlled critical demixing of water-triethylamine or methanol-cyclohexane binary fluid mixtures. The transition from the one-phase solution to the two-phase solution passes through an intermediate stage called the spi-
nodal decomposition, which is characterized by a solution that strongly scatters light. The temperature, corresponding to the state of maximum scattering, is plotted as a function of mole fraction, yielding a phase diagram. The point at which the curve has zero slope is the critical point. In this vicinity the solution becomes opalescent. An example of both an upper consolute point (methanol-cyclohexane) and a lower consolute point (triethylamine and water) are chosen. The experimental equipment can be quite modest. The chemicals and procedures used are reasonably safe for either undergraduate experimentation or as a lecture demonstration. Although simple in material and technique, the theory behind the experiment covers a number of topics in order to explain the scattering at the critical state. The thermodynamic, statistical mechanical, and the electrodynamic aspects of this system will be discussed at a level that can be appreciated by most senior chemistry students. In this paper we focus on the results of the classical model of critical phenomena. It is beyond the scope of this paper to outline recent progress in the theory of critical phenomena.
tal setup is a modified procedure of Green (3). It uses a small (few milliwatt) light beam from a He-Ne or an argon ion laser, which is passed through a large test tube or large rectangular cuvette held by a ring stand (Fig. 1). To monitor the light scattering, a beam stop using white paper or poster board is mounted behind the test tube. The sample may be open to the atmosphere or may be attached to a molecular sieve filter to trap vapors for rooms without good ventilation. The temperature in the solution at the laser beam height is measured using a digital thermometer with a thermocouple probe. The active part of the thermocouple probe, which is at the tip of the thin stainless steel housing, is placed adjacent to the laser beam to prevent scattering the laser light beam and to reduce the error in measuring the phase-transition temperature due to temperature gradients in the sample. It is important that the tip not be in contact with the vessel walls. The solvents were of reagent quality and used as received. The water was house-deionized, with a resistivity greater than 2 Mil cm at 25 °C. Methanol (MeOH) was obtained from Mallinckrodt. Triethylamine (TEA) and cyclohexane were obtained from Fisher and Baker. If the liquids are not clear to the eye, the experiment will not work. Samples
Experimental Equipment and Reagents The equipment and reagents for this experiment can be simple and still yield satisfactory results. The experimen1
Author 1o whom correspondence should be addressed
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Next, 25-mL samples with various mole fractions for
each solvent were made for HaO-TEA and MeOH-cyclohexane volumetrically. The mole fraction for each solvent set included 0.5, 5, 10, 20, 30, 50, 70, 80, 90, and 95 mol% as the initial investigation range. Once the phase-transition temperatures for this initial range is determined, the
tions, whereas MeOH-cyclohexane needs gentle warming to form a single-phase solution for most mole fractions of the respective solutions. ( Notice the boiling points of these liquids are well above the demixing temperatures.) Temperature Control
10 20 30 40 50 60
0
Mole % Triethylamine Figure 2. Temperature vs. mole percent triethylamine (T~x) phase diagram for water-triethylamine. Solid circles are from Hales et al. J. Phys. Chem. 1966 70, 3970. Open squares are data taken by authors with no purification nor degassing (especially CO2) of the mixture, sample cuvette open to the atmosphere. Data is fit with a fourth-order polynomial. ,
To control the temperature, simple apparatus was used. The H20-TEA samples are chilled using an ice-water bath to about 10 °C, which is well below the critical temperature for this mixture. The samples then slowly warm up to room temperature, which is above the phase-transition temperature for most of the samples. The rest of the samples may be warmed gently with a heat gun. The rate of heating should be no more than 2 or 3 °C/min. For MeOH-cyclohexane solutions, the samples were heated in a water bath above the critical temperature and then allowed to slowly cool. The bath may be filled with hot tap water (60 °C) and need not be heated. If the bath is used only to heat the sample, then when removed the rate of cooling of a small cuvette near the transition temperature is quite fast, and accurate determination of the Tc is not easy. We have found using thick-walled, large (1-in. diameter) test tubes with a total solution volume of about 25 mL slows the rate of cooling down sufficiently to allow accurate determination of Tj> A larger test tube also allows for the insertion of a mercury thermometer and, if desired, stir bars. Even larger volumes of 100 to 500 mL are desirable for lecture demonstrations.
Determination of the Demixing Point
The judgment of Tc is quite important. Here we recommend the procedure of Green (3). The Tc is determined when the beam displayed on the screen begins to disappear. Other criteria to judge the demixing point are possible, but careful consideration should be made to correlate the temperature as measured by the thermocouple and the phase behavior of the solution. At the critical point, opalescent scattering is quite striking. The macroscopic composition waves are easily visible on the white paper screen by the collimated light of a small wattage laser. Predicting the Critical Point
Mole % Cyclohexane Figure 3. Temperature mole percent cyclohexane (T-%) phase diagram for methanol-cyclohexane. Solid circles are from Jones et al. J. Chem. Soc. 1930,1316. Open squares are data taken by the authors with no solvent purification or degassing of the mixture, with sample cuvette open to atmosphere. Data is fit with a quadratic function.
experiment can focus on easily accessible phase-transition temperatures near the critical point (see Figs. 2 and 3). The phase-transition temperature depends on the quality of solvents and preparation of samples (see below). The solutions must be taken to the one-phase region by either heating or cooling the sample until the meniscus disappears. This in itself is an interesting part of the experiment because for the same chemical systems some compositions may need to be warmed, whereas others need cooling with respect to room temperature. The sample is then mixed by swirling, and the one-phase solution is poured into the cuvette. The large sample size has two benefits: the ease of measuring the materials, and a rate of temperature change in the sample near the spinodal decomposition slow enough to make a good temperature determination. Generally, H20-TEA mixtures must be chilled for most mole frac-
The students may be encouraged to fit their data in x T near the maximum or minimum to a simple quadratic form. From this they can “predict” the critical point more precisely and after more solution preparation measure the predicted critical-point solution temperature. In our experience some students get spectacular results with this method, whereas others learn the problems in interpolation and extrapolation with noisy data. versus
Results The Opalescence
Consider a water-triethylamine mixture of 55% water and 45% TEA. A two-phase mixture is formed with a welldefined meniscus at room temperature. If the sample is cooled to about 10 °C and stirred, a single-phase solution is formed. Slow heating to room temperature eventually causes the sample to become opalescent, spreading waves throughout the entire volume. The once well-defined laser beam spot becomes diffuse and begins to spread out, eventually becoming obscured as the transition temperature is reached. At that point, the entire volume of the solvent glows white due to strong light scattering of the laser light. Soon a meniscus reappears, but the two layers are still cloudy. Later, the turbidity clears, and the original twophase solution is present. Volume 72
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Transition from
a
Single Phase
One phase region
For MeOH-cyclohexane mixtures, an initial two-phase system is formed at room temperature. Heating the sample causes convection currents to form with brief moments of turbidity, and eventually the sys-
a single phase. On slow cooling, the solution scatters light throughout the mixture as with the previous example. Next, a meniscus forms with turbid layers: Droplets of one liquid form in the other and move according to their density. These observations tell us that the transition from a single phase to a two-phase system is spontaneous (in gravity) in the absence of mixing. The other possible experiment that takes the two-phase system into the one-phase regime offers a bit of a challenge with the equipment at hand. Careful thermostating of the solution and other considerations (see below) are needed the Tc when going to accurately measure from two to one phase. Figure 4. Temperature vs. mole percentage (T-%) diagram for an idealized upper-consoFigures 2 and 3 show typical phase dia- lute-point system. The upper line is the coexistence curve above the spinodal decomposition which is terminated by the spinodal curve. The region enclosed by the spinodal grams obtained by the authors and by stu- curve region, is the region in which a two-phase system is unstable. Above the coexistence curve dents in the physical chemistry lab at the is the one-phase system. At the critical point the derivative of the coexistence curve with University of Houston along with phase respect to % occurs. (Note: there is another set of definitions reversing the roles of the diagrams published in the literature. The spinodal and coexistance curves.) uncertainty in the temperature is about 1 °C and in solution concentration about 2% mol fraction. Two distinct trends are measured with the two-solvent systems. For The phase diagram for an idealized upper-eonsolutewater-triethylamine mixtures, the curve has a minimum, whereas the methanol-cyclohexane mixture has a maxipoint binary fluid is shown in Figure 4. The plot of x versus T shows the coexistence curve above a metastable region mum. The critical points are named the lower consolute bounded by the spinodal curve. The area enclosed by the temperature (LCT) and the upper consolute temperature (UCT). These trends were observed long ago (4, 5) and inspinodal curve is the thermodynamically unstable region {i.e., unstable for a single phase). From this diagram, we vestigated extensively (6-19). see that Tc is defined where the derivative, with respect to Discussion X of the coexistence curve, goes to zero. The spinodal region is reasonably well-predicted by analogy with the Van der Correspondence with Theory Waals equation of state for the condensation of a gas to a liquid. The derivative of the isotherms (3p/3V)r=0 for Several question arise from this experiment. Why does T < Tc yields the spinodal curve shown in Figure 4. the mixture become opalescent? How is the opalescence Earlier we suggested that students fit their data in'/ vercreated? Why does one solution have an UCT, whereas the sus T to a simple quadratic form to refine the data. The other has a LCT? Why is there a discrepancy between the shape of the coexistence curve from the classical theory is phase diagram in the literature and our results for the predicted to be a quadratic form, but the student may wish water-triethylamine mixtures and not the methanol-cyto investigate other curves as models to fit the data. Modclohexane mixture? ern theories (1, 12-19) indicate that the coexistence curve is in principle not a quadratic form. Intermolecular Interactions
tem forms
When we mix water and triethylamine or methanol and cyclohexane at room temperature, they are found to be immisible. We will call the binary solvent components A and B. In a very simple interaction model, molecules Aand B in the two-phase system predominately form A-A and B-B interactions, whereas A-B interactions are not free-energetically favored. When the temperature changed appropriately, the separate solutions mixed to form one phase, indicating the presence of favored A-B interactions or correlations. As the system returns to room temperature, the nature of the predominant interactions must change going from A-B to A-A and B-B. At the phase-transition temperature the two liquid structures implied are both probable. The implication of the three possible interactions at the phase-transition temperature means that domains of varying composition can coexist. At the critical point, the distinction between phases ceases to exist, and intermoleeular correlations extend over macroscopic dimensions. 562
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Type of Phase Diagram
An increase in entropy, the entropy of mixing, is obtained when a multiphase system merges into a single phase. Here the two phases mutually transfer material from the more concentrated to the less concentrated solution. This is what we would intuitively expect, and such systems lead to an upper critical point (20). It is possible for a decrease in entropy to occur when strong, directional intermolecular interactions (e.g., hydrogen bonding) are present. Introduction of a molecule as a solute into another liquid can cause a considerable degree of orientational correlations of the solvent molecules. This can lower the entropy of the solution so that transfer of a solute molecule from a concentrated to a dilute one will actually result in a net decrease in entropy (20). A molecular interaction picture has been proposed (21) for hydrogen-bonding systems. Hydrogen bonding is only
---O’
the solvents (8, 10) and the ability of the strongly basic triethylamine to attack glass (8). If the water-triethylamine mixture is degassed by the freeze-pump-thaw technique (8) and protected from the atmosphere, then the results agree better with the literature results. Although our methanol-cyclohexane results agree well with the literature result, recent work (12) has shown that this older reference and our work have a small impurity artifact.
O-H
0
“-Q>0-H—(3>o —H---
0
0
Figure 5. A caricatured representation of a water-triethylamine hydrogen-bonding network. At temperatures below the phase transition these hydrogen bonds are present as evidenced by the mixing of the two solvents.
effective at short range and is highly dependent on orientation compared to Van der Waals forces that are relatively isotropic and more long ranged than the repulsive forces responsible for molecular shapes. On cooling, these systems mix because they are lower in enthalpy despite the negative change in entropy (3,20). At the lower critical solution temperature at least one of the components of the solution begins to rotate (21). Although the pure phases may retain the hydrogen-bonding structures, they interact less strongly with their own kind. In water-triethylamine systems, we imagine that at the temperatures below the phase transition, the system is enthalpically mixed, forming a network of water and triethylamine, as caricatured in Figure 5. As the temperature increases, these weak H20-triethylamine hydrogen bonds are broken, and the only hydrogen bonds that survive are the H30-H20. Thus, a phase separation results because orientational entropy is gained by separation. From Two Phases to One
natural that we could do the experiment in the direction, taking the two-phase system into the single phase. This has been reported by Green (3). However, this is a more challenging experiment. Suppose you were to cool a water-triethylamine mixture down without stirring in hopes of watching the meniscus vanish. A laser beam could be reflected off the liquid-liquid interface to monitor the state of the meniscus. We might naively assume that as we approached Tc, symmetry-breaking perturbations in the lab would drive the amplitude of oscillations of the meniscus until we entered the opalescent regime. This of course does not readily happen. As we cool the mixture of triethylamine and water, the system is gravity-stabilized with the dense phase at the bottom. In addition, but of less importance, the sample becomes more viscous. In fact, the mixture can easily be supercooled, forming a two-layer system that is metasIt
seems
reverse
table. The methanol-cyclohexane system might be a better candidate for a meniscus oscillation experiment. Thermally induced convection overcomes the density distribution barrier to mixing as the mixture is warmed in order to effect a phase transition. However, a quick attempt at this experiment will show that exceedingly careful thermostatting (apparatus more sophisticated than described above) must be used to get the desired result. Because the cyclohexane-methanol system near Tc is very fluid, the creation of thermal gradients will cause convective rolling in the sample cell, effectively mixing the sample, eliminating the static room-temperature meniscus. The discrepancies in our water-triethylamine mixture phase diagram may be due to impurities (e.g., H20, C02) in
Light Scattering
Light can be scattered by several processes. One mechanism of light scattering is the refraction of light at material interfaces with different indices of refraction. The difference in the index of refraction of two materials, for example, allows us to see the meniscus. If two solvents had equal indices of refraction, then no meniscus would be visible. The index of refraction can be related to the density of transparent matter by the Lorenz-Lorentz law (22). Consequently, variations in density of transparent material can lead to light scattering. Scattering Power
For single molecules in uncorrelated motion, the total scattering cross section, crs, for light can be written (23)
8jtr| —
If
to0 > co
5 6
co4
(co
2
T2
-to^r
then 1
where co is the frequency of incident light; is the harmonic frequency of the valence electrons in a molecule; and r0 is the radius of the scattering object. (This is related to an effective cross section and not a real area because a target would diffract light.) For co0 > to, which is realistic for electrons bound to molecules for visible light, the scattering power is seen to increase as the fourth power of the frequency. We can express this equation in terms of wavelength to yield an equivalent statement but one that now relates to the size of the scattering centers. The effect of correlated motion of the scattering centers gives rise to more efficient light scattering than for uncorrelated scatterers. Because visible light has wavelengths in the range of 400 to 800 nm and molecules are fractions of nanometers in length, aggregates of molecules that are correlated in space have the light’s electric field influencing all the molecules in phase. Thus, more energy is scattered than from individual molecules (23). The total scattering amplitude is proportional to N, the number of molecules that have coalesced (e.g., into a droplet), but the intensity of scattered light is proportional to N2. There is, however, a limit to the scattering power: Once the size of the scattering domain becomes comparable to the wavelength of light, the scattering does not increase as rapidly. The alert reader will see that we have just explained why the sky is blue, why sunsets are red, and why clouds are white. What does this have to do with the scattering at demixing and critical opalescence? Basically the same underlying electrodynamics take place in binary solutions. In the one-phase system we only have Rayleigh scattering or the Tyndal effect (24 if particulate matter is floating in the solution. The wavelength dependence in the spinodal region is, in some ways, analogous to light scattering by clouds. )
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Shifted Temperature Parameter The scattering cross section of light for a critical point, as the temperature approaches the critical temperature, expressed in terms of a shifted temperature parameter 0, where 0= \T -Tc\ -» 0, has been shown to have the mathematical form (24) do
1 +
A
dQ
0
where A is a correlation function parameter (24)\ dQ is the differential solid angle; and X is the wavelength of the incident light. In the limit as 0 -h> 0, which is the same as T —> 7c, we find dc dQ
For 0
>
0,
we
get the Rayleigh scattering result. do dQ
Fluctuations The implication of the shift from X-4 to X-2 is quite important. The color of the scattered light goes from bluish to whitish. It can be shown that at Tc, the range of correlation, the size of the solvent domains can extend to macroscopic lengths. In a more practical sense, the correlation lengths fill the entire solution volume. At Tc, a molecular picture of dynamic interconnecting domains of solvent A, solvent B, and the solvent mixture AB emerges.
The domains of varying composition are continuously dissolving and reforming all length scales from small molecular clusters to structures that fill the container’s volume. These fluctuations give rise to the opalescent phase. The larger the fluctuations in refractive index, the more intense the scattering becomes. This picture of composition fluctuations is identical to that of a two-phase system in the absence of a gravitational field (25). The two liquids that differ in density are free to within surface tension effects to wander through each other in microgravity (16, 25). Thermal motions give rise to density fluctuations in the region of observation. If a symmetry-breaking field is applied, in our case gravity, these fluctuations are quenched. But at the critical point a different situation occurs. Due to the indistinguishability of the phases, the density differences between the phases tends to zero, and the application of a gravitational field is not sufficient to break the symmetry and quench the macroscopic fluctuations. The critical point is a manifestation of highly correlated molecular fluctuations manifested over large (macroscopic) distances.
Scattered light goes from blue to white, so an argon ion line at 488 nm will give the same Tq as measured by a He-Ne laser operating at 633 nm. The growth of the scattering domains is very rapid and tightly centered about Tq-
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Journal of Chemical Education
Significant density fluctuations based
on the Van der Waals equation of state occur very close to Tc, with variation no more than 0.1% away from this value (25, p 83). Although far from Tc, it can be shown that the probability of observing significant density fluctuations is proportional to (pVT1/2, where p is the density, and V is the volume. Clearly for macroscopic samples (seen with the unaided eye) with normal densities, the relative density fluctuations away from the critical point become negligible.
Conclusion This paper has outlined an experiment devised for the physical chemistry curriculum. The exercise as given takes 3 to 4 h if both solutions are used. The experimental side of the project requires standard solution preparation, temperature measurements, and the use of collimated (low wattage laser) light to detect the scattering. In terms of the theory, a combination of molecular interactions, thermodynamics of mixing, and some electrodynamics of light scattering is used. The value of this laboratory exercise is its ability to connect the fluctuations at the molecular scale with the thermodynamics and gross appearance at the
macroscopic scale. We chose two systems with very different thermodynamic behaviors to illustrate the range of phenomena. The idea of a substance becoming more soluble as the temperature is decreased (LCT behavior) is often foreign to students even though common examples, such as the salvation of corn starch, are often all around us (26). The observation of an opalescent critical point is quite striking and memorable the first time a student encounters it.
Acknowledgment The authors thank Larry Sims and Randy Wilkin for technical help. C. Stenland thanks L. Kevan for partial support. B. M. Petttitt acknowledges support from the Alfred P. Sloan foundation. Literature Cited 1.
Stanley, H. E. Introduction to Phase Transitions and Critical Phenomena-, Clarendon: Oxford, 1971. Wiley: New York, 1980; Chapters 24 and 25. Green, W, J. J. Chem. Eng. Data 1979,24, 92. Laftey, R. T. Phil. Mag. 1905, 10, 397. Jones, D. C.; Amstell, S. J. Chem. Soc. 1930. 1316. Eckfeldt, E. L.; Lucasse, W. W. J. Chem. Phys. 1943, 47, 169. Zimm, B. J. Phys. and Coll. Chem. 1950, 54, 1306. Kohler, F.; Rice, O. K. J. Chem. Phys. 1957,26, 1614. Chu, B.; Kao, W. P. Can. J. Chem. 1965,43, 1803. Hales, B. J.; Bertrand, G. L.; Hepler, L. G. J. Phys. Chem. 1966. 70, 3970. Kartzmark, E. M. Can. J. Chem, 1967. 45, 1089. Tveekrem, J. L.; Jacobs, D. T. Phys. Rev. A. 1983,27, 2773. Beysens, D.; Zaiczer, G. Europhys. Lett. 1989, 8, 111. Bloemen, E.; Thoen, J.; Van Dael, W. J. Chem. Phys. 1980, 73, 4628. Chaar, H.; Moldover, M. R.; Schmidt, J. W. J. Chem. Phys. 1986, 85, 418. Guenoun, P.; Gastaud, R.; Perrot, F.; Beysens, D. Phys. Rev. A. 1987, 36, 4876. Beysens, D.; Guenoun, P.; Perrot, F. Phys. Rev. A. 1988. 37, 4173. Chan, C. K.; Goldberg, W. I.; Maher, J. V. Phys. Rev. A. 1987.35 1756. Shanks, J. G.; Sengers, J. V. Phys. Rev. A. 1988.38. 885. Rice, O. K. Chem. Revs. 1949. 44, 69. Hirschfelder, J.; Stevenson, D.; Eyring, H. J. Phvs. Chem, 1937, 5, 896. Wangsness, R. Electromagnetic Fields-, Wiley: New York, 1979; p 612. Feynman, R. P.: Leighton, R. B.; Sands, M. Lectures on Physics-, Addison Wesley: New York, 1977; Vol. 1, Chapter 32; pp 6-9. Kocinski, J.; Wojtczak. L. Critical Scattering Theory: An Introduction-, Elsevier: New York, 1978. Chandler, D. Introduction to Modem Statistical Mechanics-, Oxford: New York, 1987. Anderson, G. R.: Wheeler, J. C. J. Chem, Phys. 1978,69. 3403.
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