Two-dimensional (2D) polyacrylic acid (PAA) nano-nets that comprise interlinked ultrathin nanowires with diameters of 10-30 nm are successfully prepared by a facile electro-netting process. Nano-nets feature a clear geometric characteristic with ideal and weighted Steiner networks due to the rapid phase separation process and its obeyed minimal energy principle. The versatile nano-nets create enhanced interconnectivity and additional surface area and facilitate the diffusion of analytes into the membranes, which significantly boost the gas diffusion coefficient and sensing properties. As one example, PAA membranes containing fibers and nano-nets used as sensing materials are deposited by electrospinning/electro-netting on an electrode of a quartz crystal microbalance (QCM) for trimethylamine (TMA) detection, which exhibits a quick response (∼180 s), low detection limit (1 ppm) and ideal selectivity at room temperature.