Light Scattering for the Masses™ by Light Scattering

e know from our daily lives that matter can of- -γ ° γ ten exist in several different phases as the tem- A (1-T/Tc) , A = 26.0,Tc = 315.507 K, = 1.270 5 -ν ° ν perature or changes. Common 10 A (1-T/Tc) , A = 0.497, Tc = 315.507 K, = 0.635 examples include a liquid which changes to a gas as one increases the temperature, or a permanent magnet which loses its magnetism as it is heated. 101 A less commonly known system is a binary fluid mix- 104 ture which can be miscible below a certain temperature and immiscible above it. The group theory by Kenneth Wilson in the 1970’s—a crowning accomplish- ment in condensed matter —shows that the criti- 103 0 10 Correlation Length (arb) cal behavior of many disparate systems have certain Osmotic Susceptibility (arb) properties in common which are independent of the de- tails of their specific interactions. Wilson was awarded the Nobel Prize in physics in 1982 for the development of this theory. 295 300 305 310 315 Temperature (°K) Wilson’s remarkable discovery is that the critical ex- ponents are the same for many different systems. For fer- romagnets, liquid-gas phase transitions, and binary fluid Figure 1. The osmotic susceptibility and correlation length diverge as the temperature approaches Tc at 315.507K. This phenomena is mixtures, the 3D predicts the critical expo- called critical opalescence or the cloud point transition. g u nents and to be 1.24 and 0.63, respectively. 102 ν We have reproduced an experiment by Dietler and A ε- , A=0.497, ν = 0.635 γ Cannell1 furthering the work of Corti, Minero, and A ε- , A=26.0, γ = 1.27 Degiorgio,2 to demonstrate that the critical phenomena of 105 binary mixtures of water and nonionic surfactants indeed show the predicted Ising exponents. 101 For the binary fluid system, the osmotic susceptibil- ity is proportional to what Wyatt Technology’s ASTRA software reports as molar mass, and the correlation length 104 is proportional to what ASTRA reports as the rms radius. 100 The osmotic susceptibility and correlation length are Correlation Length (arb)

plotted as a function of temperature, as depicted in Fig. 1. Osmotic Susceptibility (arb) They were then fit to a to obtain the critical 103 temperature, Tc, and the critical exponents. When the data are plotted against reduced temperature, e, 1-T/T, on log- 10-1 c -3 -2 -1 log scales, the curves are linear, as shown in Fig. 2. We 10 10 10 g u ε found Tc = 315.51K, = 1.27, and = 0.635, which compare favorably to the theoretical values. In conclusion, we have demonstrated the ease with Figure 2. The osmotic susceptibility and correlation length are plotted vs reduced temperature. This shows that they diverge as which the new temperature control features of the DAWN power laws. The slope of each curve is its . EOS and ASTRA can help to reproduce a classic result from a critical phenomenon experiment. Without an EOS, this experiment can take months, whereas with it, it can be performed in a matter of days or even hours.

Samples provided courtesy of Professor Michael Wiener, University of Virginia, Health Sciences Center, Charlottesville, VA 6300 Hollister Avenue ● Santa Barbara, CA 93117 1 G. Dietler and D. S. Cannell, Phys. Rev. Lett., 60, 1852 (1988). TEL (805) 681-9009 ● FAX (805) 681-0123 E-mail: [email protected] ● URL http://www.wyatt.com 2 M. Corti, C. Minero, and V. Degiogio, J Phys. Chem., 88, 309 (1984). DAWN®, ASTRA®, AURORA®, and the Wyatt Technology logo are registered trademarks of Wyatt Technology Corporation. ©2000 Wyatt Technology Corporation 4/11/00