In a pioneering work published more than 50 years ago, Benjamin Widom proposed a scaling form for the equation of state of near-critical fluids.  The scaling approach has become the foundation of the modern views on critical phenomena in condensed matter. Later, in another remarkable paper, Widom has elegantly shown that a Flory-like mean-field theory of polymer solutions can also be formulated in a universal scaling way if the thermodynamic properties are represented as homogeneous functions of the distance to the critical temperature and the degree of polymerization. <br/><br/>In this presentation I will show how a mean-field scaling, proposed by Benjamin Widom for the description of phase separation in polymer solutions, can be generalized to account for critical fluctuations and for crossover between a regime with “Ising” (fluctuation-induced) critical behavior, where the correlation length of the critical fluctuations prevails, and a mean-field tricritical regime with theta-point behavior controlled by the mesoscopic polymer chain. This theoretical description is compared with experimental data on liquid–liquid phase-equilibria and light-scattering measurements of the osmotic susceptibilities and correlation lengths. I will also demonstrate how a coupling between the relaxation of critical fluctuations and the relaxation of polymer chains generates a classical analog of the quantum Landau-Zener effect, a so-called “avoided crossing” of two effective relaxation modes observed in polymer solutions by dynamic light scattering.<br/>

Finding simplicity in complexity: Lessons I have learned from Ben Widom

254th National Meeting (2017)

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