Hierarchical micro- and nanofabrication by pattern-directed contact instabilities of thin viscoelastic films

A surface of a thin viscoelastic film forms spinodal patterns when brought in contact proximity of another surface due to the dominance of destabilizing intermolecular interaction over the stabilizing elastic and surface tension forces. In this study, we theoretically explore such contact instabilities of a thin viscoelastic film, wherein the patterns generated on the surface of the film is developed with the help of a contactor decorated with periodic physical, chemical, and physicochemical features on the surface. The nonlinear analysis shown here considers the movement of the patterned contactor during the adhesion and debonding processes, which is unlike most of the previous works where the contactor is considered to be stationary. The simulations reveal that the amplitude and periodicity of the patterns decorated on the contactor together with the contactor speed can be the key parameters to stimulate pattern formation on the film surface alongside causing changeover of the various modes of debonding of the surfaces. In particular, the ratio of the elastic to viscous compliances of the film is found to play a critical role to stimulate the changeover of the modes from catastrophic to peeling or coalescence. The study uncovers that a higher wettability contrast across the patterned contactor leads to the catastrophic collapse of the patterns decorated on the film surface when the contactor debonds at a moderate speed. In comparison, a moderately high wettability contrast alongside a faster withdrawal speed of the contactor results in the gradual peeling of columns during the debonding cycle. Remarkably, a higher withdrawal speed of the contactor from the film-proximity can increase the aspect ratio of the patterns fabricated on the film surface to about fourfold during the peeling mode of debonding. The results show the importance of the usage of patterned contactors, their controlled movement, and extent of elastic to viscous compliance ratio of the film for the improvement of the aspect ratio of the patterns developed using the elastic contact lithography of the thin viscoelastic films. The simulations also reveal the possibilities of the fabrication of biomimetic micro- or nanostructures such as columns, holes, cavities, or a combination of these patterns with large-area ordering employing the patterned contactors. A few example cases are shown to highlight the capacity of the proposed methodology for the fabrication of higher aspect ratio hierarchical micro- or nanostructures.

Figure 1

Schematic representation of a thin viscoelastic film resting on a flat surface and confined by a contactor with topographic or chemical heterogeneities. The approach and the withdrawal of the contactor through the adhesion–debonding cycle are depicted in the images (a) and (b), respectively. During the adhesion cycle, the free film surface initiates deforming when the contactor attains a critical separation distance of $s_c$, with a finite velocity of $v_c$. Subsequently, surface patterns develop due to the contact instability and the contactor is pulled away from the contact vicinity during the debonding cycle. The notations, $d,h_0$, and $s_0\left(=d-h_0\right)$ denote the distance between the contactor and substrate, the base-state thickness of the film, and air gap, respectively. The variable local thickness of the film and the air gap is denoted by $h(x,y,t)$ and $s(x,y,t)\left(=d-h(x,y,t)\right)$. The height and the width of the topographic (chemical) patterns of the contactor are denoted by $h_p$ and $l_p\left(l_c\right)$. The patterned contactor is represented as $z=d-h_p\psi (x,y)$, where $\psi (x,y)$ is the shape function for physical heterogeneity.

Figure 2

The nonlinear space-time evolutions of the viscoelastic film undergoing peeling, catastrophic, and coalescence modes of debonding in the presence of a periodically striped pattern contactor $\left(L_p=\mathrm{\Lambda }/2\right)$ in a $3\mathrm{\Lambda }\times 3\mathrm{\Lambda }$ domain when the compliance ratio $\left(C_R\right)$ of the film is varied. Column (a) depicts the contactor geometries while columns (b)–(e) show the morphological evolution of the free film-air interface at time $T=0.2$, 1.4, 2.5, and 3.6 for rows (I) and (II), $T=0.002$, 0.012, 0.2, and 0.3 for rows (III) and (IV), and $T=0.4$, 4.4, 22.7, and 40.7 for rows (V) and (VI). Rows (I), (III), and (V) [(II), (IV), and (VI)] show the isometric [top] views of the images. Plots (f)–(h) show the variations in the fractional contact area (α) and average pull-off force $\left(F\right)$ with the separation distance $\left(S\right)$ of the systems shown in the same row. The compliance ratio, for peeling mode, $C_R=2.7\times {10}^4(\mu ={10}^3\mathrm{Pa},s_e=45\mathrm{nm}$, and $v_c=250\mu \mathrm{m}/\mathrm{s})$; for catastrophic mode, $C_R=1.1\times {10}^3(\mu ={10}^2\mathrm{Pa},s_e=40\mathrm{nm}$, and $v_c=1\mu \mathrm{m}/\mathrm{s})$; for coalescence mode, $C_R=1.0\times {10}^{-4}(\mu ={10}^6\mathrm{Pa},s_e=20\mathrm{nm}$, and $v_c=1\mathrm{nm}/\mathrm{s})$. The amplitudes of the physical heterogeneities $\left(H_p\right)$ employed for the simulations are $\sim 0.03H$ [rows (I) and (II)], $\sim 0.025H$ [rows (III) and (IV)], and $\sim 0.01H$ [rows (V) and (VI)], where $H$ is the dimensionless film thickness. Other typical parameters used for the simulations are enlisted in Table 1.

Figure 3

The nonlinear space-time evolutions of the viscoelastic film showing the transition from coalescence to peeling mode with the use of striped pattern contactor $\left(L_p=\mathrm{\Lambda }/2,H_p=0.01H\right)$ instead of a homogeneous contactor in a $3\mathrm{\Lambda }\times 3\mathrm{\Lambda }$ domain. Column (a) depicts the contactor geometries while columns (b)–(e) show the morphological evolution of the thin film free surface at time $T=0.002$, 0.014, 0.04, and 0.09 for rows (I) and (II) and $T=0.003$, 0.04, 0.08, and 0.09 for rows (III) and (IV). Rows (I) and (III) [(II) and (IV), respectively] show the isometric [top] views of the images. Plots (f) and (g) show the variations in α and $F$ with $S$ of the systems shown in the same row. Compliance ratio for both the modes mode is $C_R=1.1\times {10}^5\left(s_e=20\mathrm{nm}\right)$. Other dimensional parameters are listed in Table 1.

Figure 4

The nonlinear space-time evolutions of the viscoelastic film showing the transition from the catastrophic to peeling mode with the reduction in height $\left(H_p\right)$ of the stripe patterns on the contactor $\left(L_p=\mathrm{\Lambda }/2\right)$ from 0.$01H$ to 0.$005H$, respectively, in a $3\mathrm{\Lambda }\times 3\mathrm{\Lambda }$ domain. Column (a) depicts the contactor geometries while columns (b)–(e) show the morphological evolution of the thin film-air interface at time $T=0.0002$, 0.002, 0.003, and 0.004 for rows (I) and (II) and $T=0.0002$, 0.006, 0.008, and 0.01 for rows (III) and (IV). Rows (I) and (III) [(II) and (IV)] show the isometric [top] views of the images. Plots (f) and (g) show the variations in α and $F$ with $S$ of the systems shown in the same rows. Compliance ratio for both the modes mode is $C_R=1.1\times {10}^6\left(s_e=20\mathrm{nm},\mu ={10}^2\mathrm{Pa}\right)$. Typical dimensional parameters are listed in Table 1.

Figure 5

Spatiotemporal evolutions of viscoelastic films with the variations in the elastic and viscous compliances $(E_c$ and $V_c)$ in a $3\mathrm{\Lambda }\times 3\mathrm{\Lambda }$ domain. Column (a) depicts the contactor geometries and columns (b)–(e) show the morphological evolution of the free surface of the thin film at time $T=0.2$, 0.6, 0.8, and 1.1 for rows (I) and (II) and $T=0.004$, 0.03, 0.04, and 0.08 for rows (III) and (IV). Rows (I) and (III) show the isometric profiles and rows (II) and (IV) show the top views. Plots (f) and (g) show the variations in α and $F$ with $S$ of the systems shown in the same row. The width of the stripe patterns on the patterned contactor for rows (I)–(IV) are $L_p=\mathrm{\Lambda }/2$ and the height of the patterns for rows (I)–(IV) are $H_p=0.03H$. The elasticity of the film used for rows (III) and (IV) is $\mu ={10}^2\mathrm{Pa}$. The other parameters used are listed in Table 1.

Figure 6

Spatiotemporal evolutions of viscoelastic films with the variations in the width $\left(L_p\right)$ and the amplitude $\left(H_p\right)$ of the stripe patterns on the contactor in a $3\mathrm{\Lambda }\times 3\mathrm{\Lambda }$ domain. Column (a) depicts the contactor geometries and columns (b)–(e) show the morphological evolution of the free surface of the thin film at time $T=0.07$, 0.3, 0.5, and 0.7 for rows (I) and (II) and $T=0.3$, 0.6, 0.7, and 0.8 for rows (III) and (IV). Rows (I) and (III) show the isometric profiles and rows (II) and (IV) show the top views. Plots (f) and (g) show the variations in α and $F$ with $S$ of the systems shown in the same row. The width of the stripe patterns on the patterned contactor for rows (I)–(IV) are $L_p=\mathrm{\Lambda }/4$ and the height of the patterns for rows (I) and (II) [(III) and (IV)] are $H_p=0.03H\left[H_p=0.01H\right]$. The other parameters used are listed in Table 1.

Figure 7

The nonlinear space-time evolutions of the viscoelastic thin film throughout the changeover of three distinct debonding modes—coalescence, peeling, and catastrophic, in presence of a chemically patterned contactor, in a $3\mathrm{\Lambda }\times 3\mathrm{\Lambda }$ domain. In the column (a) of rows (I) and (II) the contactor has homogeneous adhesive energy of $\mathrm{\Delta }{G}_0$ while in the rows (III)–(VI) the contactor has dark (light) checkerboard patches with higher (lower) adhesive energy $\mathrm{\Delta }{G}_0^h\left(\mathrm{\Delta }{G}_0^l\right)$. Columns (b)–(e) show the morphological evolution of the free surface at time $T=0.002$, 0.012, 0.05, and 0.08 for rows (I) and (II), $T=0.002$, 0.02, 0.04, and 0.05 for rows (III) and (IV), $T=0.0006$, 0.008, 0.01, and 0.3 for rows (V) and (VI). Rows (I), (III), and (V) [(II), (IV), and (VI)] show the isometric [top] views of the images. Plots (f)–(h) show the variation in α and $F$ with $S$ of the systems shown in the respective rows. Compliance ratio is kept constant at, $C_R=1.1\times {10}^5\left(s_e=15\mathrm{nm}\right)$.

Figure 8

Example cases of spatiotemporal evolutions of viscoelastic thin film to achieve higher aspect ratio microstructures by altering contactor property, geometry, and $C_R$, in a $3\mathrm{\Lambda }\times 3\mathrm{\Lambda }$ domain. Contactor geometries are shown in the images at (a), (c), (e), and (g) while images at (b), (d), (f), and (h) show the dimensions of final microstructures obtained after debonding cycle at time $T=0.2$ for case (I); $T=0.7$ for case (II); $T=0.007$ for case (III); and $T=0.01$ for case (IV). The parameter, $\mu =10\mathrm{Pa}$, is used for cases (III) and (IV). Other necessary dimensional parameters for the simulations are listed in Table 1. The parameter $\mathrm{\Lambda }$ is kept constant for all the cases. The plot (i) shows the procedure to calculate the aspect ratio $\left(A_r\right)$ and the taper ratio $\left(T_r\right)$ of the thin film microstructures and introduces some of the relevant dimensional variables like height $\left(h_c\right)$, base $\left(c_b\right)$, and top $\left(c_t\right)$ dimensions of the structures. The plots (j)–(l) show the variation of $A_r,T_r$, and $S_p$, respectively, for all the four cases.

Figure 9

Fabrication of nano- and multiscale composite structures using spatiotemporal evolutions (3D) of the viscoelastic thin film in the presence of patterned contactors of different geometries and chemical patches in a $\mathrm{\Lambda }\times \mathrm{\Lambda }$ domain for cases (I)–(III). Column (a) depicts the contactor geometries while columns (b) and (c), respectively, show the final structures of the thin film after the adhesion and debonding cycle at time $T=0.0002$ and 0.004 for case (I); $T=0.004$ and 0.23 for case (II); and $T=0.006$ and 0.12 for case (III). The parameters, for case (I), $\mu =10\mathrm{Pa}$ and $s_e=60\mathrm{nm}$; for case (II), $s_e=40\mathrm{nm}$; for case (III), $\mu ={10}^2\mathrm{Pa}$ and $s_e=60\mathrm{nm}$. $\mathrm{\Lambda }$ is kept constant for all the cases. Other necessary dimensional parameters are shown in Table 1.