Self-assembled filament layers in drying sessile droplets: from morphology to electrical conductivity

TL;DR

The paper tackles how evaporation kinetics shape filament self-assembly and electrical connectivity in drying droplets. By coupling a color-gradient lattice Boltzmann fluid solver with a bead-spring filament model, it isolates the effects of diffusion- versus reaction-limited evaporation on deposition patterns, percolation, and conductivity. Key findings show that reaction-limited drying suppresses edge coffee-ring effects and promotes centralized, more conductive networks, while diffusion-limited evaporation yields pronounced ring-like deposits with lower connectivity; filament length and stiffness further tune percolation thresholds and conductivity exponents. The results provide actionable guidelines for designing robust, high-conductivity filament networks in printed electronics and flexible sensors, with implications for mult droplet configurations and experimental validation.

Abstract

Controlling the deposition of filaments, such as nanowires and nanotubes, from evaporating droplets is critical for the performance of emerging technologies like flexible sensors and printed electronics. The final deposit morphology strongly governs functional properties, such as electrical conductivity, yet remains challenging to control. In this work, we numerically investigate how filament length, stiffness, and concentration affect deposition patterns during the drying process. We compare reaction-limited and diffusion-limited evaporation regimes, demonstrating that their distinct velocity fields and flow magnitudes fundamentally alter filament arrangement. While diffusion-limited evaporation drives the ``coffee-ring effect", compromising network uniformity, reaction-limited evaporation suppresses edge accumulation, promoting centered conductive deposits. We map out the spatial variation of filament alignment - tangential at the contact line, radial in the intermediate region, and random near the center. Longer filaments tend to favour more tangential alignment overall and suppress edge accumulation. We find that by tuning the evaporation regime, filament deposition can lead to significantly lower percolation thresholds and significantly higher conductivity exponents. These results quantify the link between evaporation kinetics and microstructure, providing guidelines for optimizing conductive network formation in printed electronics.

Figures (8)

• Figure 1: Geometry of a spherical cap droplet with radius of curvature $R$, base radius $a$, height $h_0$, and local height $h$ at radial position $r$. The droplet rests on a patterned substrate with variable wettability: a circular hydrophilic area (red, $\theta\approx 40^\circ$) is located at the center, surrounded by a neutral wetting area (green, $\theta=90^\circ$).
• Figure 2: Time evolution $\tilde{t} =\frac{t}{N_t}$ of the relative droplet height $\tilde{h}=h/h_0$ at the droplet center ($r=0$) during stick-slide evaporation. For $K=10$, simulation (blue circles) follows Eq. \ref{['Prediciton_height']} (blue line) during the pinned (CCR) stage; for $K \approx 0$, simulation (green squares) agrees with the theoretical prediction (green line), obtained by numerically solving Eq. \ref{['Volume_SC']} and Eq. \ref{['change_vol']}. At late stages ($\tilde{t} \gtrsim 0.6$), when the droplet height falls below roughly 10 lattice units, deviations appear due to the CGLB discretization limits.
• Figure 3: Time evolution $\tilde{t} =\frac{t}{N_t}$ of the relative radial velocity $\tilde{v}(r,t)=v(r,t)/v_c$ at $r/a=0.79$ for an evaporating droplet in stick–slide mode. Simulation results (dots) are compared to theory (Eq. \ref{['eq:vel_r']}) with correction (solid lines) and without correction (dashed lines), with the time evolution of the base radius $a$ and the local height $h$ described by polynomial fits.
• Figure 4: Snapshots of the drying process at different time $\tilde{t}$, where $\tilde{t} =\frac{t}{N_t}$ is non-dimensionalized. Top: diffusion-limited regime ($K\approx 0$). Bottom: reaction-limited regime ($K=10$). Filaments shown are 31 units long and have an area fraction of $c\approx31\%$. The color bar denotes the $z$-coordinate, with light red indicating regions nearest to the substrate and purple the most distant.
• Figure 5: Nematic order $S_t(\tilde{r})$ and radial distribution $g(\tilde{r})$ versus normalized radial distance $\tilde{r}$ for fully flexible filaments in the reation-limited evaporation $K=10$ (left) and the diffusion-limited regime $K\approx0$ (right).