The potential difference across a battery cannot be greater than its emf. Basically, emf is the maximum potential difference between the terminals of a battery when the terminals are not connected externally to an electric circuit. When the same battery is connected to an electric circuit, current flows in the closed circuit.  When current flows, the potential difference across the terminals of the battery is decreased as some potential drop due to its internal resistance.Due to the internal resistance in the battery, the potential difference across it is less than its emf. However, for an ideal battery, potential difference and emf are equal.