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The scattering of fast radio bursts (FRBs) by the intergalactic medium (IGM)is explored using cosmological hydrodynamical simulations. We confirm that thescattering by the clumpy IGM has significant line-of-sight variations. Wedemonstrate that the scattering by the IGM in the voids and walls of the cosmicweb is weak, but it can be significantly enhanced by the gas in clusters andfilaments. The observed non-monotonic dependence of the FRB widths on thedispersion measures (DM) cannot determine whether the IGM is an importantscattering matter or not. The IGM may dominate the scattering of some FRBs, andthe host galaxy dominates others. For the former case, the scattering should beprimarily caused by the medium in clusters. A mock sample of 500 sources showsthat $\tau_{\rm{IGM}} \propto \rm{DM_{IGM}}^{1.6-2.1}$ at $z<1.5$. Assumingthat the turbulence follows Kolmogorov scaling, we find that an outer scale of$L_0\sim 5\,$pc is required to make $\tau_{\rm{IGM}} \sim 1-10\,$ms at $\nu=1\,$ GHz. The required $L_0\sim 5\, $pc can alleviate the tension in thetimescales of turbulent heating and cooling but is still $\sim 4$ orders ofmagnitude lower than the presumed injection scale of turbulence in the IGM. Thegap is expected to be effectively shortened if the simulation resolution isfurther increased. The mechanisms that may further reduce the gap are shortlydiscussed. If future observations can justify the role of the IGM in thebroadening of FRBs, it can help to probe the gas in clusters and filaments.

The scattering of FRBs by the intergalactic medium: variations, strength and dependence on dispersion measures