This paper analyzes the performance of a dutycycled polling-based access mechanism that exploits the Transmission Opportunity Power Save Mode (TXOP PSM) defined in the IEEE 802.11ac to improve the energy efficiency of Wireless Local Area Networks (WLANs) based on the IEEE 802.11. The basic idea behind the proposed approach, named GreenPoll, is to enable contention free periods, based on polling with beacons, during which wireless stations can save energy by turning off their radio transceivers after exchanging data with the access point. The closed expression of energy efficiency of GreenPoll is formulated in this paper and is used to evaluate the performance of GreenPoll considering important parameters like the traffic load, packet length, data rate, and number of stations in the network. Both analytical and simulation results show the high energy efficiency of GreenPoll with gains of up to 330% and 110% when compared to the legacy Distributed Coordination Function (DCF) and the Point Coordination Function (PCF) defined in the IEEE 802.11, respectively. *