Integrability in statistical physics and quantum spin chains

This chapter illustrates basic concepts of quantum integrable systems on two important models of statistical physics: the Q-state Potts model and the O(n) model. Both models are transformed into loop and vertex models that provide representations of the dense and dilute Temperley–Lieb algebras. The identification of the corresponding integrable R-matrices leads to the solution of both models by the algebraic Bethe Ansatz technique. Elementary excitations are discussed in the critical case and the link to conformal field theory in the thermodynamic limit is established. The concluding sections outline the solution of a specific model of the theta point of collapsing polymers, leading to a continuum limit with a non-compact target space.

Effect of Solvent Quality on the Friction Forces Between Polymer Brushes

ABSTRACTWe have used the surface forces apparatus to measure the structural and frictional force profiles between opposing, solvated brush layers as a function of temperature. Two different polyvinylpyridine-polystyrene [PVP-PS] diblock copolymers were used to make PS brushes. The molecular weights (in thousands) of these PVP-PS materials were [114/103]k, [30/70]k, respectively. Structural and frictional force profiles in toluene and cyclohexane were measured, and the cyclohexane experiments were conducted at temperatures ranging from the theta-point to 50 C. In toluene the PS brushes needed to be compressed to ∼1/5th of their equilibrium height before frictional forces were measured, but this onset of frictional forces was detected at a much lower level of compression in near-theta cyclohexane. In cyclohexane the structural force profiles were basically insensitive to the temperature change, but the frictional forces depended strongly on the solvent temperature. When the cyclohexane temperature was raised, the onset of frictional forces decreased toward the good-solvent onset. We also discuss the dependence of frictional force on shearing parameters.

Effect of Solvent Quality on the Friction Forces Between Polymer Brushes

ABSTRACTWe have used the surface forces apparatus to measure the structural and frictional force profiles between opposing, solvated brush layers as a function of temperature. Two different polyvinylpyridine-polystyrene [PVP-PS] diblock copolymers were used to make PS brushes. The molecular weights (in thousands) of these PVP-PS materials were [114/103]k, [30/70]k, respectively. Structural and frictional force profiles in toluene and cyclohexane were measured, and the cyclohexane experiments were conducted at temperatures ranging from the theta-point to 50°C. In toluene the PS brushes needed to be compressed to ∼1/5th of their equilibrium height before frictional forces were measured, but this onset of frictional forces was detected at a much lower level of compression in near-theta cyclohexane. In cyclohexane the structural force profiles were basically insensitive to the temperature change, but the frictional forces depended strongly on the solvent temperature. When the cyclohexane temperature was raised, the onset of frictional forces decreased toward the good-solvent onset. We also discuss the dependence of frictional force on shearing parameters.