When water-coated hydrophobic surfaces meet, direct contacts form between the surfaces, driving water out. However, long-range attractive forces first bring those surfaces close. This analysis reveals the source and strength of the long-range attraction between water-coated hydrophobic surfaces. The origin is in the polarization field produced by the strong correlation and coupling of the dipoles of the water molecules at the surfaces. We show that this polarization field gives rise to dipoles on the surface of the hydrophobic solutes that generate long-range hydrophobic attractions. Thus, hydrophobic aggregation begins with a step in which water-coated nonpolar solutes approach one another due to long-range electrostatic forces. This precursor regime occurs before the entropy increase of releasing the water layers and the short-range van der Waals attraction provide the driving force to "dry out" the contact surface. The effective force of attraction is derived from basic molecular principles, without assumptions of the structure of the hydrophobe-water interaction. The strength of this force can be measured directly from atomic force microscopy images of a hydrophobic molecule tethered to a surface but extending into water, and another hydrophobe attached to an atomic force probe. The phenomenon can be observed in the transverse relaxation rates in water proton magnetic resonance as well. The results shed light on the way water mediates chemical and biological self-assembly, a long outstanding problem.
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