  We present results from extensive molecular dynamics simulations of collapse
transitions of hydrophobic polymers in explicit water focused on understanding
effects of lengthscale of the hydrophobic surface and of attractive
interactions on folding. Hydrophobic polymers display parabolic, protein-like,
temperature-dependent free energy of unfolding. Folded states of small
attractive polymers are marginally stable at 300 K, and can be unfolded by
heating or cooling. Increasing the lengthscale or decreasing the polymer-water
attractions stabilizes folded states significantly, the former dominated by the
hydration contribution. That hydration contribution can be described by the
surface tension model, $\Delta G=\gamma (T)\Delta A$, where the surface
tension, $\gamma$, is lengthscale dependent and decreases monotonically with
temperature. The resulting variation of the hydration entropy with polymer
lengthscale is consistent with theoretical predictions of Huang and Chandler
(Proc. Natl. Acad. Sci.,97, 8324-8327, 2000) that explain the blurring of
entropy convergence observed in protein folding thermodynamics. Analysis of
water structure shows that the polymer-water hydrophobic interface is soft and
weakly dewetted, and is characterized by enhanced interfacial density
fluctuations. Formation of this interface, which induces polymer folding, is
strongly opposed by enthalpy and favored by entropy, similar to the
vapor-liquid interface.
