Continuous self-avoiding walk with application to the description of polymer chains.

We develop the continuous self-avoiding walk (CSAW) methodology for investigating temperature dependent thermodynamic properties of finite polymer chains without imposing a lattice. This leads to a new concept: the free energy theta temperature, T(theta)(F), at which the free energy is proportional to chain length. Above T(theta)(F), the polymer chain-solvent mixture leads to a single phase, whereas below T(theta)(F) the polymer solvent system has a positive surface tension with a tendency to phase separation to form a globular phase. For finite chains this coil-globule transition lies above the geometric theta temperature at which the distribution describes a Gaussian coil. CSAW provides the basis for a new approach to predict globular properties of real polymers.