The force between silica surfaces in NaCl, KCl and CsCl aqueous solutions is studied at pH 5.5 using an atomic force microscope (AFM). As ion concentration is increased, more cations adsorb to the negatively charged silica, gradually neutralizing the surface charge, hence, suppressing the electrostatic double layer repulsion and revealing van der Waals attraction. At even higher salt concentrations, repulsion reemerges due to surface charge reversal by excess adsorbed cations. Adsorption grows monotonically with cation radius. At pH 5.5 the smallest ion, Na+, neutralizes the surface at 0.5-1 M, K+ at 0.2-0.5 M, and Cs+ at approximately 0.1 M. Titration with HCl to pH 4.0 shifts surface neutralization and charge reversal to lower salt concentrations compared with pH 5.5. When attraction dominates, the force curves are practically identical for the three salts, independent of their concentration.

Overall, existing models do not account for the force curves presented below. Yet, the data provide indispensable information about a truly generic phenomenon, correlation induced attraction between identically charged bodies.Attraction between macroscopically similar surfaces has been reported in the literature. For instance, the long range attraction between hydrophobic surfactantcoated surfaces 7 has recently been attributed to charge inhomogeneity 8 . Charge inversion due to over-screening by high valence ions may also lead to attraction between dissimilar surfaces. As the large Z-ion concentration is increased, one of the surfaces reverses its polarity before the other surface does, leading to "conventional" attraction between two oppositely charged objects. An AFM study of the force in the latter case has been published recently 9 . We emphasize that the attraction reported here is different than either phenomena. Unlike the first one, it takes place between two bare surfaces and unlike the latter it occurs also between identical surfaces. The resulting force is of a fundamentally shorter range compared with either phenomenon.The force between a m µ 5 silica bead 10 glued to an AFM tip and an oxidized silicon wafer or the tip-mounted silica bead and an identical bead glued to a silicon wafer was measured using a commercial AFM 11 . The microscope was placed in an acoustic hood and the AFM's piezoelectric crystal was driven by a low noise synthesizer

Application of two complementary AFM measurements, force vs separation and adhesion force, reveals the combined effects of cation size and charge (valency) on the interaction between silica surfaces in three 1:1, three 2:1, and three 3:1 metal chloride aqueous solutions of different concentrations. The interaction between the silica surfaces in 1:1 and 2:1 salt solutions is fully accounted for by ion-independent van der Waals (vdW) attraction and electric double-layer repulsion modified by cation specific adsorption to the silica surfaces. The deduced ranking of mono- and divalent cation adsorption capacity (adsorbability) to silica, Mg(2+) < Ca(2+) < Na(+) < Sr(2+) < K(+) < Cs(+), follows cation bare size as well as cation solvation energy but does not correlate with hydrated ionic radius or with volume or surface ionic charge density. In the presence of 3:1 salts, the coarse phenomenology of the force between the silica surfaces as a function of salt concentration resembles that in 1:1 and 2:1 electrolytes. Nevertheless, two fundamental differences should be noticed. First, the attraction between the silica surfaces is too large to be attributed solely to vdW force, hence implying an additional attraction mechanism or gross modification of the conventional vdW attraction. Second, neutralization of the silica surfaces occurs at trivalent cation concentrations that are 3 orders of magnitude smaller than those characterizing surface neutralization by mono- and divalent cations. Consequently, when trivalent cations are added to our cation adsorbability series the correlation with bare ion size breaks down abruptly. The strong adsorbability of trivalent cations to silica contrasts straightforward expectations based on ranking of the cationic solvation energies, thus suggesting a different adsorption mechanism which is inoperative or weak for mono- and divalent cations.

In this paper we prove the Random Van der Waerden Theorem:q 1 (q 2 −1) , extending the results of Rödl and Ruciński for the symmetric case qi = q. The proof for the 1-statement is based on the Hypergraph Container Method by Balogh, Morris and Samotij and Saxton and Thomason. The proof for the 0-statement is an extension of Rödl and Ruciński's argument for the symmetric case.