Unidirectional Droplet Propulsion onto Gradient Brushes without External Energy Supply

Abstract

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.

Antidurotaxis Droplet Motion onto Gradient Brush Substrates

“…16,17,23 Also, durotaxis motion is usually observed in experiments in the lab and biological systems, 11−15 while antidurotaxis motion has only been observed for a particular experimental setup. 24 As in the case of durotaxis onto brush substrates, 23 our analysis here confirms that the minimization of the interfacial energy constitutes the driving force that underpins the antidurotaxis phenomenon. However, in the case of antidurotaxis, this minimization is caused by the gradual penetration of the droplet into the brush as the droplet moves to the softer parts of the substrate with lower grafting density.…”

“…Hence, we anticipate that our study will have a broader impact beyond engineering applications. Moreover, the fact that the design of the brush substrate only depends on the variation (gradient) of the grafting density, compared to a previous design that the chain stiffness and possibly the chemistry of the chains had to be varied to tune the substrate properties, might suggest that the brush system investigated here might hold greater hope for experiments, thus offering further possibilities for relevant applications. In the following, we provide details of the system, simulation model, and methodology.…”

“…38 Other options requiring external sources may include the use of electrical current, 39−42 charge, 43−45 or even simple stretching, 46 as well as chemically driven droplets, 47,48 droplets on vibrated substrates 49−52 or wettability ratchets. 53−56 In our previous studies, we have investigated various substrate designs that can cause and sustain the motion of liquid droplets, 16,23,25 which were mainly motivated by relevant experiments. 24,26 In particular, in the context of durotaxis droplet motion, a new design based on brush polymer substrates was proposed, where the stiffness gradient was imposed by varying the chain stiffness of the grafted polymers along the gradient for a given grafting density.…”

“…In our previous studies, we have investigated various substrate designs that can cause and sustain the motion of liquid droplets, ,, which were mainly motivated by relevant experiments. , In particular, in the context of durotaxis droplet motion, a new design based on brush polymer substrates was proposed, where the stiffness gradient was imposed by varying the chain stiffness of the grafted polymers along the gradient for a given grafting density . In this case, it has been found that the grafting density of polymer chains and the droplet adhesion to the brush are the key parameters determining whether the motion will be realized, as well as its efficiency.…”

Charge-Powered Electrotaxis for Versatile Droplet Manipulation

“…In particular, the taxis of living organisms endows them to survive and evolve in resource-limited settings. Less apparent is that taxis can also be manifested in artificial systems. − A typical application scenario of artificial taxis is droplet manipulation; for example, a recently reported durotaxis, referred to as the taxis motion directed by the stiffness gradients of the underlying substrate, can effectively drive the directional motion of droplets. − However, such durotaxis-enabled droplet manipulation is limited by the poor controllability for droplet motion because durotaxis is passively triggered by the predetermined substrate properties. Accordingly, introducing the external force source, such as electricity, to actively evoke the taxis property of droplets might be a more promising means for droplet manipulation.…”