From the outset, batteries have been the main power source for the Internet of Things (IoT). However, replacing and disposing of billions of dead batteries per year is costly in terms of maintenance and ecologically irresponsible. Since batteries are one of the greatest threats to a sustainable IoT, battery-less devices are the solution to this problem. These devices run on long-lived capacitors charged using various forms of energy harvesting, which results in intermittent on-off device behaviour. In this work, we model this intermittent battery-less behaviour for LoRaWAN devices. This model allows us to characterize the performance with the aim to determine under which conditions a LoRaWAN device can work without batteries, and how its parameters should be configured. Results show that the reliability directly depends on device configurations (i.e., capacitor size, turn-on voltage threshold), application behaviour (i.e., transmission interval, packet size) and environmental conditions (i.e., energy harvesting rate).