Explaining the low-frequency shear elasticity of confined liquids

Experimental observations of unexpected shear rigidity in con-fined liquids, on very low frequency scales on the order of 0.01 to 0.1 Hz, call into question our basic understanding of the elas-ticity of liquids and have posed a challenge to theoretical models of the liquid state ever since. Here we combine the nonaffine theory of lattice dynamics valid for disordered condensed matter systems with the Frenkel theory of the liquid state. The emerg-ing framework shows that applying confinement to a liquid can effectively suppress the low-frequency modes that are responsi-ble for nonaffine soft mechanical response, thus leading to an effective increase of the liquid shear rigidity. The theory suc-cessfully predicts the scaling law G' similar to L & minus;3 for the low-frequency shear modulus of liquids as a function of the confinement length L, in agreement with experimental results, and provides the basis for a more general description of the elasticity of liquids across different time and length scales. field qi (denoted sents in the components shear). a librated (imaginary mass-rescaled