Using an accurate method, we prove that no matter what the initial superposition may be, neither a superposition of desired states nor a unique desired state can be found with certainty in a possible three-dimensional complex subspace, provided that the deflection angle Φ is not exactly equal to zero. By this method, we derive such a result that, if N is sufficiently large (where N denotes the total number of the desired and undesired states in an unsorted database), then corresponding to the case of identical rotation angles, the maximum success probability of finding a unique desired state is approximately equal to cos 2 Φ for any given Φ ∈ [0, π/2).

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The adsorption of five polycarboxylate ethers (PCEs) oligomers with different side-chain number and side-chain length on the ettringite (100) surface in explicit solution is studied by all-atom molecular dynamics (MD) simulations. The adsorption conformations, adsorption energies, the radial distribution functions (RDF) between PCEs and ettringite surface and density distribution profile of water perpendicular to the substrate are analyzed. After dynamic equilibrium, negatively charged carboxylate groups are absorbed on the surface of the disordered ettringite crystal and the side-chains are extended to solution. The influence of the number of side-chain on the adsorption strength of PCEs on the ettringite (100) surface is more significant than that of the length of side-chain. The less number of grafted side-chains, the weaker electrostatic shielding, the electrostatic interaction between PCEs and ettringite (100) surface is stronger, which is favorable for the adsorption. The conformation of adsorbed PCEs is closely related to the length of side chain. The greater the length of side-chains is, the larger will be the coverage area of PCE on surface and the degree of water reduction. The mechanism of adsorption of PCEs on ettringite surface is concluded and the major contribution to the adsorption includes ion pairs, hydrogen bonds and an entropic compensation.

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