2.12.3 Critical Opalescence

The lab can support the observation and measurement of critical opalescence in a binary fluid mixture, methanal-cyclohexane. The equipment includes a moderately well controlled optical bath (a fish tank containing paraffin oil), laser source and photodiod es. Precision thermometry is done with a GPIB interfaced DMM (e. g., a Keithley 193) as a 6-1/2 digit resistance reading of a stable thermistor in the bath. A similar thermistor provides the temperature sensing for the control circuit.

A careful measurement of the optical transmission of the sample as it clouds up near the critical point provides the opportunity to follow the divergence of the critical fluctuations in concentration in this system. The cross over from diverging with the exponent  to a weak logarithmic divergence can be seen.

Extensions and improvements of the experiment would be to use a photomultiplier to measure the scattered light intensity itself at some angle like 90. One could see it diverging far from Tc and cross-over into a saturation when the correlation range becomes longer than the scattering Fou rier component wavelength as Tc is approached. The experiment is a quantitative test of the understanding of fundamental scaling relations for binary mixtures and the Ornstein-Zernike theory, which connects them to critical opalescence. The lab at present has a stable 10 ml sample sealed in an all glass cell.

References

  1. A. C. Mowery and D. T. Jacobs, "Undergraduate experiment in critical phenomena: Light scattering in a binary fluid mixture," Am. J. Phys. 51, 542 (1983). Good description of the basic experiment. 
  2. D.T. Jacobs, "Turbidity in the binary fluid mixture methanol-cyclohexane," Phys. Rev. A 33, 2605 (1986).
  3. V. G. Puglielli, and N. C. Ford, Jr., "Turbidity measurements in SF6 near its critical point," Phys. Rev. Lett. 25, 143 (1970). Useful information on Ornstein Zernike Theory; and measurement of .
  4. R.B. Kopelman, R.W. Gammon, and M.R. Moldover, " Turbidity very near the critical point of mehthanol-cyclohexane mixtures," Phys. Rev. A 29, 2048 (1984).
  5. K.C. Zhang, M.E. Briggs, R.W. Gammon, "The susceptibility critical exponent for a nonaqueous ionic binary mixture near a consolute point," J. Chem. Phys. 97, 8692 (1992).
  6. K. Hamano, N. Kuwahara, and M. Kaneko, "Scatterng light intensity in the strongly opalescent region of the system polystyrene-diethyl malonate," Phys. Rev. A 21, 1312 (1980). Independent measurement of .
  7. A. L. Sengers, R. Hocken, J. V. Sengers, "Critical Point Universality and Fluids," Physics Today No. 12, 42 (1977). 
  8. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (New York: Oxford University Press, 1971). QD501.S78. 
  9. M. E. Fisher, "Correlation Functions and the Critical Region of Simple Fluids," Jour. Math. Phys. 5 944 (1964).
  10. Moore, J. H., Davis, C. C., Coplan, M. A., Building Scientific Apparatus, 2nd Edition, London: Addison Wesley & Co., 1989. Has a good discussion of temperature control. Q185.M66.
  11. YSI Super-Stable Thermistor descriptions of bridge resistance measurement, temperature probe details, spec sheets for 5K thermistor, least square fitting results for 45 to 55 C for T(R).
  12. YSI Thermistor Info and Hg thermometer emergent stem corrections.
  13. United Detector Planar-Diffused Silicon Photodiodes spec sheets including the photodiode used for detection in this experiment.
  14. P. G. Witherell and M. E. Faulhaber, "The Silicon Solar Cell as a Photometric Detector," Appl. Optics 9, 73 (1969)
  15. Properties of Common Liquids.  Useful for calculating heat capacity and time constant of bath.
  16. M. E. Fisher, "Renormalization group theory: Its basis and formulation in statistical physics," Reviews of Modern Physics, 70, 653 April (1998)

 

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