Portable mobile devices like smartphones and tablets are the enablers for communications in mobile ad hoc networks. In order to optimise their energy usage, one of the most popular techniques is to implement a duty cycling policy, which periodically puts the user device in a energy saving mode (e.g., Bluetooth inquiry scan phase or turning off the WiFi interface) for a certain amount of time. Clearly, this strategy increases the battery lifetime, but it also has the net effect of reducing the number of usable contacts for delivering messages, increasing intercontact times and delays. In order to understand the effect of duty cycling in opportunistic networks, in this paper we propose a general model for deriving the pairwise intercontact times modified by a duty cycling policy. Then, we specialise this model when the original intercontact times are exponential (an assumption popular in the literature), and we show that, in this case, the intercontact times measured after duty cycling are, approximately, again exponential, but with a rate proportional to the inverse of the duty cycle. Once we have the distribution of the intercontact times after duty cycling, we use it for analysing how duty cycling affects the delay of message forwarding and the network lifetime.