  Using extensive molecular dynamics simulation of a coarse-grained model, we
demonstrate the possibility of sustained unidirectional motion (durotaxis) of
droplets without external energy supply when placed on a polymer brush
substrate with stiffness gradient in a certain direction. The governing key
parameters for the specific substrate design studied, which determine the
durotaxis efficiency, are found to be the grafting density of the brush and the
droplet adhesion to the brush surface, whereas the strength of the stiffness
gradient, the viscosity of the droplet, or the length of the polymer chains of
the brush have only a minor effect on the process. It is shown that this
durotaxial motion is driven by the steady increase of the interfacial energy
between droplet and brush as the droplet moves from softer to stiffer parts of
the substrate whereby the mean driving force gradually declines with decreasing
roughness of the brush surface. We anticipate that our findings indicate
further possibilities in the area of nanoscale motion without external energy
supply.
