Tunneling and activation in reactions at interfaces may be facilitated or hampered depending on the degree of structural ordering. "Scalar" coupling of the reaction with the system structure, independent of the sign of the order parameter, is considered. It is shown that near the temperature of a second-order phase transition such coupling can lead to a singularity of the reaction current as a function of temperature, which appears as a spike or dip in real systems. Experimental data that may be indicative of this effect are discussed.