Coarse-grained molecular dynamics simulation of wettability and bleed out of capillary underfill

Abstract

Coarse-grained molecular dynamics simulations were performed to elucidate the capillary flow process of liquid state capillary underfill (CUF), a sealing resin material. First, we ran a wettability simulation with the CUF consisting of a monomer with small and large fillers. We observed that a certain amount of the monomer spreads ahead on the substrate, while many fillers are left inside the droplet. This was confirmed by subsequent mean square deviation (MSD), which showed that the monomer had a higher MSD, 25–45 σ2, than the small and large fillers, which were 0.4–1.4 σ2 and 0.02–0.2 σ2, respectively. When one part of large fillers was replaced with small fillers, small fillers helped accelerate the wetting dynamics because they could move fast. However, when the small filler ratio was high (20%), the MSD of small fillers decreased. Next, we performed a capillary flow simulation in which the CUF flowed between parallel walls and observed that it formed a ridgeline at the upper wall edge. Small fillers contributed to a decreased flow time. However, when the small filler ratio was even higher, the flow time increased. Then, the small fillers slowed themselves down, as shown in the MSD. This is due to an increase in monomer interactions and less space to move. We also found that the bleed length decreased with an increase in the small filler ratio. This study clarified the effects of filler usage on the flow time and bleed length and contributed to new insight into the capillary actions and material design relevant to CUF.

Improved Coarse-Grained Model for Nanoparticles Based on the Martini Force Field and Its Application in Molecular Dynamics Simulation on Gel Ink

“…The magnification rate of 8 times for K bond is determined based on the result of trial and error by which the bond can have enough stiffness. 34,40,41,59 The values of r bond are exactly the center distances between beads to limit their movement. With the above-mentioned settings for bonds, the deformation problem of the core−shell model can be figured out well (see the simulation results) even for NPs of large size.…”

“…All bonds are described by a harmonic potential U bond ( r ij ) U bond ( r ij ) = 1 2 K bond false( r italicij − r bond false) 2 where the equilibrium distance r bond is set to σ R + σ min for bonds between surface beads and ( d – σ R )/2 for bonds between surface and core beads and the force constant K bond is magnified to 8 times the default value set for C1 beads in the Martini 2.2 FF, i.e., 10 4 kJ·mol –1 ·nm –2 . The magnification rate of 8 times for K bond is determined based on the result of trial and error by which the bond can have enough stiffness. ,,, The values of r bond are exactly the center distances between beads to limit their movement. With the above-mentioned settings for bonds, the deformation problem of the core–shell model can be figured out well (see the simulation results) even for NPs of large size.…”

“…Another hollow sphere NP model of Figure d is completely hollow and formed by a shell of evenly distributed CG beads. − Compared with the three other models mentioned above, this one is the most simple in construction but the easiest to deform and consequently the most appropriate for small NPs (diameter of ∼5 nm in general). Specifically, Starr et al built an icosahedral-shaped and completely hollow NP model (with an equivalent diameter of about 10 nm) for MD simulation.…”