The truncation of a pair potential at a distance $r_{\mathrm{c}}$ is well known to imply, in general, an impulsive correction to the pressure and other moments of the first derivatives of the potential. That, depending on $r_{\mathrm{c}}$, the truncation may also be of relevance to higher derivatives is shown theoretically for the Born contributions to the elastic moduli obtained using the stress-fluctuation formalism in $d$ dimensions. Focusing on isotropic liquids for which the shear modulus $G$ must vanish by construction, the predicted corrections are tested numerically for binary mixtures and polydisperse Lennard-Jones beads in, respectively, $d=3$ and 2 dimensions. Both models being glass formers, we comment briefly on the temperature ($T$) dependence of the (corrected) shear modulus $G\left(T\right)$ around the glass transition temperature $T_{\mathrm{g}}$.

• Received 1 August 2012

DOI:https://doi.org/10.1103/PhysRevE.86.046705