Critical Phenomena provides intriguing and essential insight into many issues in condensed matter physics because of the many length scales involved. As a system approaches its critical point, molecules begin to "stick together" and their finite volume becomes significant, which results in a density fluctuation or "droplet". These droplet sizes vary spatially and temporally; however, an average size, or correlation length, of these droplets diverges close to the critical point as a power of (T - Tc)/Tc, the reduced temperature. The power is called the critical exponent. Very close to the critical point, these droplets become several thousand angstroms across and at the critical point, the droplets become infinite in size and a second phase forms. This phenomenon is easily observed as a milkiness (called critical opalescence) and is readily measured by light scattering in a turbidity experiment.
Remarkably, vastly different system types involving distinctly different materials share a common universal behavior near the critical point, such as the same value of the critical exponent. Since the correlation length is very large near the critical point compared to the molecular size, the behavior of a system is not determined by the type of molecule but by its collective, critical behavior. Physical phenomena describing a system close to its critical point have a universal form independent of the system involved; however, the location of the critical point (critical temperature, density, and pressure) depends on the specific substance. The current consensus is that liquid-gas, binary fluid mixtures, uniaxial ferromagnetism, polymer-solvent, and protein solutions all belong to the same universality class-the three-dimensional Ising model. The diversity of critical systems that can be described by universal relations indicates that experimental measurements on one system should yield the same information as on another.
We are actively pursuing two experiments on branched polymers in a weak solvent. One experiment measures the amount of light that is not scattered by the concentration fluctuations (droplets) and thus determines the turbidity of the sample. Theory allows the correlation length to be determined from the turbidity at various temperatures near the critical point. We can test numerous universal relations that are predicted by theory to hold even in this complex system.
A second experiment would determine how much polymer is in each of the two phases when below the critical temperature. This experiment also determines amplitudes and exponents that can be combined with those from the turbidity experiment to test predictions. This experiment is still being developed and needs someone comfortable with programming (you will learn LabVIEW) and with mechanical systems. These experiments are funded by a Petroleum Research Fund grant.