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Crossover behavior in the distance dependence of hydrophobic force law

Understanding about both the range and the strength of the effective force between two hydrophobic surfaces suspended in water is important in many areas of natural science but unfortunately has remained imperfect. Even the experimental observations have not been explained quantitatively. Here we find by varying distance (d) between two hydrophobic walls in computer simulations of water that the force exhibits a bi-exponential distance dependence. The long range part of the force can be fitted to an exponential force law with correlation length of 2 nm while the short range part displays a correlation length of only 0.5 nm. The crossover from shorter range to longer range force law is rather sharp. We show that the distance dependence of the tetrahedrality order parameter provides a reliable marker of the force law, and exhibits similar distance dependence.