Effect of surface interactions on the settlement of particles on a sinusoidally corrugated substrate

Abstract

Naturally-occurring surface topographies abound in nature and endow diverse properties, i.e., superhydrophobicity, adhesion, anti-fouling, self-cleaning, anti-glare, anti-bacterial, and many others. Researchers have attempted to replicate such topographies to create human-made surfaces with desired functionalities. For example, combining the surface topography with judicial chemical composition could provide an effective, non-toxic solution to combat non-specific biofouling. A systematic look at the effect of geometry, modulus, and chemistry on adhesion is warranted. In this work, we use a model system that comprises silica (SiO _x ) beads interacting with a substrate made of a commercial polydimethylsiloxane kit (PDMS, Sylgard 184) featuring a sinusoidal topography. To examine the impact of interactions on particle settlement, we functionalize the surfaces of both the PDMS substrate and the SiO _x beads with polyacrylic acid (PAA) and polyethyleneimine (PEI), respectively. We also use the PDMS commercial kit coated with liquid glass (LG) to study the effect of the substrate modulus on particle settlement. Substrates with a higher aspect ratio (i.e., amplitude/periodicity) encourage adsorption of particles along the sides of the channel compared with substrates with lower aspect ratio. We employ colloidal probe microscopy to demonstrate the effect of interaction between the substrate and the particle. The interplay among the surface modulus, geometry, and interactions between the surface and the particle governs particle settlement on sinusoidally-corrugated substrates.

Fig. 1. The position of a settling spherical particle depends on interactions with the surface. Cartoons in (a) and (b) show the effect of substrate geometry and interactions between the surface and the particle on the location of the particle. (c) Optical microscopy image of spherical SiO_x particle settling upon sinusoidal PDMS channels. Scale bar: 200 μm. (d) Laser scanning microscopy image of a particle settling in between sinusoidal features. The colors represent different depths inside the specimen. Scale bar: 500 μm.

Fig. 2. Dimensions of the substrate–particle system. Parameters to consider are amplitude (A), wavelength (λ), particle radius (R). The coordinate system used in the analysis is also depicted.

Fig. 3. Settlement of silica particles mapped on the PDMS substrate as a function of increasing aspect ratio, AR, (A/λ), where A and λ represent the feature amplitude and wavelength, respectively: (a) AR = 0.69, (b) AR = 1, (c) AR = 1.13. x′ and z′ describe particle center. The shaded area represents the substrate. Particle is mapped on axes normalized to λ and A. When (x′, z′) is (0, 0), the particle is at the top of the sinusoid and when it is (0.5, −1) the particle is at the bottom of the sinusoidal channel. Symbols represent different surface and particle interactions where squares indicate unmodified PDMS surface and particle surface. Circles indicate the surface of PDMS has been modified with PEI. Stars indicate that the PDMS surface has been modified with PEI, and particle surface has been modified with PAA. Refer to Table 1 for mapping symbol type to system surface chemistries. The black and blue symbols and lines correspond to the settlement of particles with nominal diameters of ∼100 μm and ∼200 μm, respectively.

Fig. 4. The deformation of PDMS features by silica (SiO_x) particles is shown on corrugated surfaces with a square profile using optical microscopy in reflectance mode. (a) Surface before silica particle deposition shows parallel features. Scale bar: 200 μm. (b) Silica particles once deposited cause the features to deform around the particle. Scale bar: 50 μm. (c) A cross-sectional view of the substrate with particle shows perpendicular features deforming due to the particle. Scale bar: 50 μm.

Fig. 5. The settlement of silica particles mapped on the PDMS:UVO substrate coated with LG as a function of increasing aspect ratio, AR, where A and λ represent the feature amplitude and wavelength, respectively: (a) AR = 0.69, (b) AR = 1, (c) AR = 1.13. x′ and z′ describe particle center. The shaded area represents the substrate. Particles are mapped on axes normalized to λ and A. When (x′, z′) is (0, 0), the particle is at the top of the sinusoid and when it is (0.5, −1) the particle is at the bottom of the sinusoidal channel. Symbols represent different surface and particle interactions where squares indicate unmodified PDMS/LG surface and particle surface. Circles indicate the surface of PDMS:UVO/LG has been modified with PEI. Stars indicate that PDMS:UVO/LG surface has been modified with PEI, and the particle surface has been modified with PAA. Refer to Table 1 for mapping symbol type to system surface chemistries. The black and blue symbols and lines correspond to the settlement of particles with nominal diameters of ∼100 μm and ∼200 μm, respectively.

Fig. 6. Force resulting from interactions between unfunctionalized substrates and particles measured using AFM. (a) Approach (black data) and retrace (red data) when a spherical SiO_x particle is used to probe a PDMS surface. (b) Approach and retrace data for PDMS:UVO surface coated with LG and probed with a spherical SiO_x particle.

Fig. 7. Force resulting from interactions between PAA-functionalized substrates and unfunctionalized particles. (a) Approach (black data) and retrace (red data) when a spherical SiO_x particle is used to probe a PDMS surface modified with the PAA surface. (b) Approach and retrace data for PDMS surface coated with LG, functionalized with PAA probed with a spherical SiO_x particle.

Fig. 8. AFM traces of interactions between PAA-functionalized substrates and PEI–SiO_x particles. (a) Approach (black data) and retrace (red data) when a particle probes a PDMS surface modified with PAA. (b) Approach and retrace data for PDMS coated with LG and functionalized with PAA. (c) The effect of functionalization on the interactions between the surfaces. Red represents PEI, and green represents PAA. Red and green clouds depict the interactions between the PAA and PEI layers.

Fig. 9. Calculated work done to separate the substrates and particle as a function of chemical modification and surface modification. (a) PDMS substrate probed by SiO_x particle; (b) PDMS substrate coated with LG probed by SiO_x particle. Experimental conditions represented by the symbols are as follows: PDMS–SiO_x (□), PDMS:UVO/PAA–SiO_x (○), PDMS:UVO/PAA–SiO_x/PEI (●), PDMS:UVO/PEI/LG-SiO_x (△), PDMS:UVO/PEI/LG/PAA–SiO_x (▽), PDMS:UVO/PEI/LG/PAA–SiO_x/PEI (▼). Error bars represent the standard deviations.