With improvements in measuring techniques such as atomic force microscopy, confocal microscopy, and scanning electron microscope, researchers were able to produce and image droplets at ever smaller scales. With the reduction in droplet size came new experimental observations of wetting. These observations confirmed that the modified Young’s equation does not hold at the micro-nano scales. Jasper proposed that including a "V" "dP" term in the variation of the free energy may be the key to solving the contact angle problem at such small scales. Given that the variation in free energy is zero at equilibrium: