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Controlled Nanoscale Electrohydrodynamic Patterning Using Mesopatterned Template
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Controlled Nanoscale Electrohydrodynamic Patterning Using Mesopatterned Template
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  • Swarit Dwivedi
    Swarit Dwivedi
    Multiscale Computational Fluid Dynamics Laboratory, Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India
  • Raj Narayanan
    Raj Narayanan
    Multiscale Computational Fluid Dynamics Laboratory, Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India
  • Rahul Chaudhary
    Rahul Chaudhary
    Multiscale Computational Fluid Dynamics Laboratory, Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India
  • Rabibrata Mukherjee
    Rabibrata Mukherjee
    Instability and Soft Patterning Laboratory, Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India
  • Arnab Atta*
    Arnab Atta
    Multiscale Computational Fluid Dynamics Laboratory, Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India
    *E-mail: [email protected]. Phone: +91 3222 283910 (A.A.).
    More by Arnab Atta
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ACS Omega

Cite this: ACS Omega 2018, 3, 8, 9781–9789
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https://doi.org/10.1021/acsomega.8b01319
Published August 23, 2018

Copyright © 2018 American Chemical Society. This publication is licensed under these Terms of Use.

Abstract

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We report the path for a possible fabrication of an array of nanogrooves, by electro-hydrodynamic instability-mediated patterning of a thin polymer film using a patterned stamp with much larger features. Using a predictive computational model based on finite element method, we find the route to control the coalescence of initial instabilities that arise with the onset of spatially varying DC electric field generated through topographical patterns in the top electrode. These quasi-steady structures are shown to evolve with the electrostatic and geometric nature of the two-electrode system and are of a stable intermediate during the process of feature replication, under each electrode feature. We identify conditions to obtain nanogrooves for a range of operating conditions. Such simulations are likely to guide experiments, where simultaneous optimization of multiple parameters to fabricate features with lateral dimension smaller than that of the electrode patterns is challenging.

Copyright © 2018 American Chemical Society

1. Introduction

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In a time when miniaturization is the need of hour, rapid and effective techniques of synthesizing nano/mesoscale patterns are in high demand. These structures are used in various fields of nanobiotechnology, (1) lab-on-a-chip devices, (2) microfluidics, (3) hydrophobic and self-cleaning surfaces, (4) bulk heterojunction solar cells, (5,6) organic light-emitting diodes, (7) and so on. Consequently, researchers have turned to various novel patterning techniques to engineer surfaces and structures that are not easily manufactured by conventional top-down lithographic methods. (8) However, lithographic techniques are generically expensive, meticulous, and often has limitations either in terms of throughput or resolution. (9) Recently, spontaneous instability-mediated morphological evolution in ultrathin films, particularly in conjugation with lateral confinement, is being considered as a viable nonlithographic mesofabrication technique for soft materials. (10) Such instabilities result because of applications of thermally excited capillary waves engendered by van der Waals force-mediated disjoining pressure and are thus limited only in ultrathin films (h ≤ 100 nm). On the other hand, much thicker films can be destabilized by the action of an externally applied field, such as an electric field or a thermal gradient. Although the stability and dynamics of fluid–fluid interfaces subject to an externally applied electric field was studied first by Swan (11) in 1897, it was only around the year 2000 when Schäffer et al. (12) pioneered the concept of electric-field-mediated instability for patterning thin polymer films, which has been termed as electro hydrodynamic (EHD) lithography. EHD instability-mediated patterning, which uses a capacitor system with thin/ultrathin films of polymers, provides excellent ability of morphology control, in comparison with direct embossing-based techniques. (8,13−15) Apart from thin films of homopolymers, films of various functional materials such as conductive polymers, block copolymers, inorganic thin films, and so on have been patterned by EHD instability. (16−19) Fabrication of high aspect ratio structures was accomplished by Lv et al. (20,21) in their recent studies.
The destabilizing effect of electric forces on the free surface of a thin film has been well-explored by numerous researchers. (22−30) A significant advantage of using EHD is the accomplishment of control over the length scale of the surface patterns. (31−33) However, required external source of energy, breakdown of dielectric polymer at high voltages, and involvement of several influencing parameters are challenges to this technology. (8,34) Schäffer et al. (12) found that careful control of EHD instabilities can be exploited to generate well-defined pillars because they could replicate a patterned top electrode on a sub-micrometer lateral dimension. Various experimental observations with a flat top and bottom electrode show the evolution of isotropic structures with a dominant wavelength that corresponds to the fastest growing mode of instability, which governs the spatiotemporal evolution and the final morphology of the features. Theoretically, an expression for the fastest growing mode of instability can be obtained from a linear stability analysis, (12,35,36) the expression for which is
(1)
where γ, ψ, ϵ0, ϵp, and Ep are interfacial tension, applied voltage, permittivity of free space, relative permittivity of polymer film to the bounding fluid, and electric field intensity at the polymer–air interface, respectively.
It can be seen that the characteristic wavelength is a function of both the geometry and electrostatic parameters of the system, which is an interplay between the electrostatic and surface tension forces. Additional control and ordering of the instability features including possible miniaturization can be achieved by using a topographically patterned top electrode, where patterns are seen to replicate below each protrusion of the patterned top electrode. Under a patterned top electrode, the gradient in electric field strength because of the presence of heterogeneity strongly influences the evolution process, and consequently the pattern periodicity (Lp) and geometry of the top electrode determine the final morphology, in addition to initial film thickness (h0), gap spacing (d), and field strength. Several theoretical and numerical studies have been carried out to mathematically elucidate the patterning process as well as to identify the conditions for the formation of ordered patterns on single and/or multilayer thin films. (2,34,37−51) With a nonlinear 3D model for polymer/substrate morphology, Verma et al. (52) identified the ideal conditions necessary for pattern replication and indicated that the number density of the replicated patterns can be altered by varying the applied voltage or tuning the mean film thickness, periodicity, and depth of grooves on the top electrode. Moreover, they predicted the possible formation of secondary structures between two parallel ridges, which was also experimentally substantiated by Harkema. (53) The formation of secondary structures has been related to the depletion of liquid during the formation of primary continuous ridges. (54) Atta et al. (55) showed the self-assembly of ordered nanopillars on the introduction of marginal chemical heterogeneity on the surface of electrode assembly. Electrically heterogeneous patterned electrodes have also been used for the fabrication of re-entrant structures which are beyond the fabrication capability of imprint lithography. (56) Recently, researchers have also investigated EHD patterning of prepatterned surfaces in search of novel and miniaturized structures. (57,58)
On the basis of a careful review of published literature, we identify that there is no clear study that elaborates the morphological evolution of stable intermediate structures, particularly capturing the transition of single to multiple pillars under a solitary protrusion of the top electrode. In this study, we report an intermediate structure in case of an insufficient peak splitting during the transitional regime from single to multiple pillars under one protrusion that results in a toothlike cavity, termed as nanogroove. We identify the relation between width of the protrusion (w) and λc, as the effect of Lp on λc is already well-perceived. A numerical model based on finite element method is employed to investigate the influence of filling factor, initial film thickness, applied voltage, protrusion height, and electrode spacing on the obtained quasi-steady-state patterns. These results are of paramount importance in designing, optimization, and fabrication of ordered nanostructures, which particularly will be able to guide toward the desired morphology avoiding undesired coalescence of patterns. Fabrication of such nanoscale structures using a stamp with a much larger lateral dimension is the key novelty of this work, particularly from the standpoint of nanofabrication.

2. Mathematical Formulation

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2.1. System Description

Figure 1 shows the schematic of the EHD assembly, where the bottom electrode is coated with ultrathin polymeric film of initial thickness of h0, and the confined space above the film is occupied by air as the bounding fluid. The electrode assembly with variable d(x) because of protrusion at the top electrode results in heterogeneous electric field, where as the flat plate assembly produces homogeneous electric field in lateral direction. Along with gap spacing (d), other parameters that define a heterogeneous system, such as electrode width (w), pattern height (p), and stamp periodicity (Lp) are depicted in Figure 1b. Figure 1c represents a 3D structure of the physical system with columnlike top-electrode protrusions. The interfacial perturbation with the onset of electric field by applying a DC potential of ψ at the top electrode and keeping the bottom as ground results in film thickness h(x,t) as a function in space and time domain. This thin-film system is considered to be isothermal, incompressible (ρ2 = 1000 kg/m3), Newtonian (μ = 1 Pa·s), and perfect dielectric (ϵ2 = 2.5) with air–polymer interfacial tension (γ) as 0.038 N/m.

Figure 1

Figure 1. Schematic of electrode assembly with polymeric liquid film denoting the geometrical parameters and top electrode as (a) flat plate and (b) patterned stamp with square protrusions, and (c) 3D representation of patterned stamp with column protrusions electrode assembly.

2.2. Governing Equations and Boundary Conditions

2.2.1. Fluid Flow

The governing equation for this incompressible Newtonian fluid is defined by the set of Navier–Stokes (eq 2) and continuity equation (eq 3), coupled with Maxwell equations to account for the presence of external electric field.
(2)
(3)
where fi represents the body forces and the subscript denotes the phases (1 for air and 2 for polymeric film).

2.2.2. Boundary Conditions

At the upper and lower electrodes, no slip boundary conditions are applied.
(4)
At the interface, continuity of velocity is assumed.
(5)
The interfacial velocity (ω) under an infinitesimal perturbation is related to the film thickness by the following kinematic boundary condition. (59)
(6)
To simplify and solve the governing equations for this system, we assume (a) two fluids as immiscible with no interphase mass transfer across the interface, (b) the film is sufficiently thick that continuum assumption is valid but thin enough so that the effect of gravity can be neglected, and (c) inertial effects will be negligible because of ultrathin film condition. These simplifications along with the consideration of long-wave approximation (60) give rise to the temporal evolution of thin-film height that can be described by the following expression (61)
(7)
where
(8)
In eq 8, ψ0, ψel, and ψLW represent atmospheric pressure, electrostatic pressure, and disjoining pressure because of Lifshitz–van der Walls (LW) interactions, respectively. Moreover, ψel and ψLW can be estimated from the following equations (36,55)
(9)
(10)
where AL is the effective Hamaker constant for interactions between the free surface of the film and lower solid surface through the fluid film. In our case, ψLW can be neglected because of the presence of dominant electrostatic force. Detailed derivation of the aforementioned equations can be found elsewhere. (35,38,52,55)

3. Computational Model

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As shown in Figure 2, a 2D model in COMSOL Multiphysics (62) has been developed to realize the evolution of the structure because of the electrostatic force and surface tension at the interface of the liquid polymer. The 2D computational model exemplifies columnlike physical system, as shown in Figure 1c in three dimensions. DC potential is implemented between the bottom (boundary 2) and the top electrode (boundaries 5–21). Other boundary conditions for the solution are (a) no slip at boundaries 2, and 5–21; (b) symmetry on boundaries 1, 3, 22, and 23; (c) initial fluid interface at boundary 4; and (d) pressure point constraint at points a and b, which are the two ends of the air film interface. The polymer–air interface is tracked by using conservative form of the level-set method (eq 11), (62) where a phase is characterized by a level-set function φls, which is 0 in case of air and is 1 for polymer. Consequently, the interface is captured by contour of level function φls = 0.5.
(11)
where γls determines the amount of reinitialization of the level-set function and the parameter ϵls specifies thickness of the interface. A suitable value for γls (0.1) is the maximum magnitude of the velocity field in the model, and ϵls = hc/2, where hc is the maximum element size across the interface.

Figure 2

Figure 2. Schematic of computational domain, boundaries, and points used in this work.

Furthermore, the assumptions of film and air as perfect dielectric media with zero net charge in the bulk results in equations governing the force exerted on the interface. This is resolved using the following Laplace equation.
(12)
where ϵ0 is the dielectric permittivity of the vacuum, ψ is the voltage, and ϵr is the dielectric constant of the air or polymer, defined as ϵr = 1 + 1.5φls. The level-set function smooths the material property such as density, viscosity, and dielectric constant jump across the interface as follows:
(13)
(14)
(15)
The body-force term in eq 2 is implemented as follows
(16)
Two components of the body-force term fi in eq 16 are volumetric forces because of surface tension, Fst = pelδn⃗, and electrostatic force, Fel = pelδ, where the electrostatic pressure pel = γκδn⃗, γ is the surface tension, δ is the numerical interpretation of Dirac delta function that is concentrated at the interface and in level set method, and δ = 6|φls(1 – φls)||∇φls| provides a smooth transition along the interface. n⃗ is the unit outward normal to the interface, and κ is surface curvature estimated as: κ = ∇·n⃗.

4. Results and Discussion

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In case of a homogeneous electric field, EHD-induced patterning is analytically described by characteristic wavelength derived from linear stability analysis of the system. In a system of two flat electrodes (Figure 1a), the gradient of electric pressure at extreme corners is responsible for the initial perturbation of interface, which consequently propagates creating a pressure gradient along the interface. This mechanism is essentially responsible for the formation of nanopatterns in case of a flat electrode assembly. However, in case of a topographically patterned top electrode (Figure 1b), difference in electrical pressure is locally generated over the interface at the level of each feature on the top electrode, and this variation subsequently triggers a flow of polymeric fluid, which manifests in rising morphologies below the protrusions of the top electrode. Fluid drains from the domain between two protrusions toward the region directly under these features. Initially, electric pressure gradient present over the interface and beneath the corner of protrusion is responsible for driving this fluid, which we denote as inflow gradient. An interesting but intuitive morphology is observed when the width of the protrusion is large. Similar to flat plate assembly, a secondary instability is detected, which rises because of the ripple created by the gradient of electrical pressure. For complex systems with patterned top electrode, there is no single characteristic λ owing to varying gap spacing. In such systems, on moving from bottom electrode to the top, we find two gap spacings, d1 and d2, which are minimum and maximum separation distances between top and bottom electrodes. Characteristic wavelength of instability corresponding to d1 and d2 are denoted by λd1 and λd2, respectively. From a number of simulations, it is evident that secondary instability is first observed in between λd1 and λd2, where two separate pillars form under one protrusion, and this leads to a novel and intriguing morphological structure having nanogrooves on the top. In such cases, ripple created by the inflow gradient tries to rip the rising pillar, although it is not strong enough to snap completely. These structures attain quasi-steady state as confirmed by the simulations in our study. In an attempt to estimate this morphological transition and its relation to influencing parameters, we have identified five different electrode widths that are on the basis of characteristic λ (eq 1), as: λd1, λ(d1+davg)/2, λdavg, λ(davg+d2)/2, and λd2 for electrode spacing (d) as d1, (d1 + davg)/2, davg, (davg + d2)/2, and d2, respectively, where davg = (d1 + d2)/2.

4.1. Mechanism of Structural Evolution

Understanding of structural evolution in case of transitional structure not only provides better understanding about the evolution process but also reveal the key parameters that control the transition from single to multiple pillars under one protrusion. Although the flow of polymer is a function of instantaneous electric field distribution, it can be shown that initial electric field distribution can be a fair metric for predicting the final morphology, and the subsequent dynamics. Maximum (Emax) and minimum (Emin) field strengths across the interface are just beneath the center of protrusion and the groove of top electrode, respectively (Figure 3). The inflow gradient drives the fluid from outside toward protrusion and is proportional to (Emax2Emin2) across the interface.

Figure 3

Figure 3. Initial electric field intensity distribution on a 30 nm polymeric film under protruded top electrode having w = λd1 = 214 nm, and p = 20 nm for 70 V, d2 = 100 nm, and Lp = 350 nm.

Figure 4 demonstrates the progressive evolution of a 30 nm liquid film under the applied DC potential of 70 V using a 214 nm (λd1) × 20 nm protruded top electrode and gap spacing (d2) of 100 nm. Instabilities can be seen rising from the edges because of the presence of the inflow gradient, which pulls polymeric fluid from outside of the protrusion inward at the edges, as shown in Figure 4b. Thereafter, these instabilities derive the polymeric fluid toward the center of the protrusion in the horizontal direction and vertically upward because of the electrostatic pressure (Figure 4c). Although inflow gradient drives the flow toward the spatial region beneath the protrusions, incoming fluid does not get equally distributed in the whole region creating two bulges, similar to what is observed under a flat top electrode as is evident from Figure 4c. This growth attains a quasi-steady state, when the rising front of a growing pillar touches the top electrode (Figure 4d) and subsequently remains unaltered (Figure 4e).

Figure 4

Figure 4. Temporal evolution of a 30 nm polymeric film under protruded top electrode having w = λd1 = 214 nm, and p = 20 nm for ψ = 70 V, d2 = 100 nm, and Lp = 350 nm at (a) 0, (b) 2, (c) 6, (d) 15, and (e) 100 μs.

4.2. Influence of Filling Factor

The filling factor, defined as the ratio of w/Lp, is a key parameter in systems with topographically patterned top electrode that limits the patterning range. Its effect on the final morphology can be observed by either changing w or Lp at a time. Figure 5 shows the variation in the final morphology when w is varied from λd1 to λd2 keeping ψ = 70 V, h0 = 30 nm, Lp = 350 nm, d2 = 100 nm, and p = 20 nm. It is evident from Figure 5a that single pillar is observed when the width of top electrode is 210 nm (<λd1). Further increase in the width of protrusion, a pillar with nanogroove is observed at w = λd1 = 214 nm (Figure 5b), and for w = λ(d1+davg)/2, the grooves become deeper that touch the ground electrode (Figure 5c). Two distinct pillars are observed at λdavg (Figure 5d), and further increase in w results in even more distant pillars under one protrusion at w = λd2 (Figure 5f). This development is consistent with our observations of initial electric-field distribution (Figure 6), where it is apparent that the gradient of electric field is maximum at the corners of the protrusion and vanishes on approaching the center. The region of low-electric-field gradient increases with an increase in protrusion width (w). Therefore, the final morphology is seen to shift from a high degree of coalescence (single pillar) to partial coalescence (nanogroove structures) to no coalescence (multiple pillars) (Figure 5). The parameters are selected in such a way that periodicity value is sufficiently larger than the electrode width. For comparable values, one may encounter two major issues. First, fabricating within tens of nanometers with accuracy is a problem, and second, the system will start behaving similar to a flat plate because of very small distance between two protrusions. The gap region with low electric field strength will be negligible compared to area under protrusion, and results similar to a flat plate might be obtained. Figure 7 demonstrates the filling factor variation by changing the pattern periodicity Lp from 250 to 400 nm, keeping voltage at 70 V, film thickness h0 = 30 nm, electrode spacing (d2) = 100 nm, and pattern height (p) at 20 nm. At a fixed electrode width w, the inflow gradient increases with Lp and the system shows higher degree of deviation from a flat electrode system (Figure 8). It can be understood that at higher Lp values, formation of multiple pillar is more favorable as compared to single pillar because of enhanced flow of material resulting from high inflow gradient, which alleviates the nanogroove formation. Therefore, it is worth noting that we show fabrication of structures that are much smaller than features on the stamp, and we circumvent the issue of nanoscale patterning by a mesopatterned stamp, which otherwise involves more complex and costly fabrication procedure.

Figure 5

Figure 5. Quasi-steady-state patterns obtained for ψ = 70 V, h0 = 30 nm, p = 20 nm, d2 = 100 nm, and Lp = 350 nm at (a) w < λd1, (b) w = λd1, (c) w = λ(d1+davg)/2, (d) w = λdavg, (e) w = λ(davg+d2)/2, and (f) w = λd2.

Figure 6

Figure 6. Initial electric-field-intensity distribution on a 30 nm polymeric film under protruded top electrode having w = λc, p = 20 nm for 70 V, d2 = 100 nm, and Lp = 350 nm.

Figure 7

Figure 7. Quasi-steady-state patterns of a 30 nm polymeric film under a protruded top electrode having w = 225 nm, and p = 20 nm at 70 V, and d2 = 100 nm at (a) Lp = 250 nm, (b) Lp = 300 nm, (c) Lp = 350 nm, and (d) Lp = 400 nm.

Figure 8

Figure 8. Initial electric-field-intensity distribution for different Lp on a 30 nm polymer film under protruded top electrode (w = 225 nm, p = 20 nm) at 70 V and d2 = 100 nm.

4.3. Influence of Initial Film Thickness

It can be realized from linear stability analysis (eq 1) that the values of characteristic wavelength decrease with increasing h0. To elucidate the sole effect of film thickness, here, we have shown the sole effect of film thickness by (a) keeping all other parameters fixed including the filling factor (w/Lp = 0.6) and electrode width as w = λ(d1+davg)/2 for all cases (Figure 9) and by (b) maintaining w constant (225 nm) along with all of the other parameters fixed for all h0 (Figure 10). For the first case, Figure 9 illustrates quasi-steady-state structures with electrode width corresponding to λ(d1+davg)/2. Separate pillars are observed in case of thinner film (Figure 9a). With increasing h0, tendency of nanogroove structures and single pillar increases. The nanogroove structure is observed for h0 = 40 nm (Figure 9d). This can be attributed to the fact that on increasing film thickness, interface comes closer to top electrode and enhanced distributed electrical pressure acts on the same. Figure 10 describes the second case, where morphologies are obtained on the variation of film thickness keeping the electrode width constant (w = 225 nm) along with all of the other system parameters. We observed a single pillar under the protrusion in case of h0 = 25 nm (Figure 10a), which is in line with our expectation as w = 225 nm < λd1 = 229 nm (Figure 11). In case of h0 = 30 nm (Figure 10b), the nanogroove structure is observed as λd1 = 213 nm < w = 225 nm < λ(d1+davg)/2 = 240 nm. Similarly, we noticed separated polymeric pillars when h0 = 35 nm (Figure 10c) as λ(d1+davg)/2 = w = 225 nm. Thereafter, pillar separation increases in case of 40 nm thick polymeric film (Figure 10d) as w = 225 nm > λ(d1+davg)/2 = 208 nm. Figure 11 shows the characteristic λ defined for different film thicknesses and summarizes the results obtained through identification of three zones where single, nanogroove, and separate pillars are more likely to be observed.

Figure 9

Figure 9. Quasi-steady-state structure obtained at ψ = 70 V under a protruded top electrode having w = λ(d1+davg)/2 nm, and p = 20 nm with d2 = 100 nm and filling factor = 0.6 for (a) h0 = 25 nm, (b) h0 = 30 nm, (c) h0 = 35 nm, and (d) h0 = 40 nm.

Figure 10

Figure 10. Quasi-steady-state structure obtained at ψ = 70 V under a protruded top electrode having w = 225 nm and p = 20 nm with d2 = 100 nm and Lp = 350 nm for (a) h0 = 25 nm, (b) h0 = 30 nm, (c) h0 = 35 nm, and (d) h0 = 40 nm.

Figure 11

Figure 11. Morphological phase diagram of single, nanogroove, and separate pillars for different electrode widths and initial film thicknesses.

4.4. Influence of Electric Potential

Quasi-steady-state structures of 30 nm polymeric film at varying electric potential for a fixed Lp and h0 is shown in Figure 12. At higher potential, the inflow gradient increases and with increasing voltage, the likelihood of formation of nanoscale groove increases. For example, at 60 V, Lp = 350 and 30 nm initial film thickness, nanogrooved structure is not observed, but it becomes prevalent with increasing the electric potential to 70 V keeping the other parameter fixed. It should be noted that there is an upper limit of applied voltage for a particular system above which the dielectric breakdown point of polymer has to be taken into account.

Figure 12

Figure 12. Quasi-steady-state structure of a 30 nm polymeric film under a protruded top electrode having w = 225 nm and p = 20 nm with d2 = 100 nm and Lp = 350 nm at (a) ψ = 60 V, (b) ψ = 65 V, (c) ψ = 70 V, (d) ψ = 75 V, and (e) ψ = 80 V.

4.5. Influence of Protrusion Height and Electrode Spacing

An increase in protrusion height (p) effectively reduces the gap between the top electrode and the interface, which increases the perturbing force. Accordingly, the characteristic wavelength values decrease while the ease of groove formation is enhanced. In Figure 13a, the formation of a single pillar is observed when the protrusion height (p) is 10 nm with ψ = 70 V, w = 214 nm, d2 = 100 nm, and Lp = 350 nm. By keeping all other operating parameters fixed, we observed the nanogroove structures when p was increased to 20 nm (Figure 13b). Two separate pillars are detected at p = 30 and 40 nm (Figure 13c,d). On the contrary, with increasing electrode spacing (d), exactly opposing behavior is found as the electrode-film interface gap increases with increasing d2 and the formation of nanogrooved structures becomes more difficult (Figure 14).

Figure 13

Figure 13. Quasi-steady-state structure of a 30 nm polymeric film at 70 V for different protrusion heights (p) (a) 10 nm, (b) 20 nm, (c) 30 nm, and (d) 40 nm with w = 214 nm, d2 = 100 nm, and Lp = 350 nm.

Figure 14

Figure 14. Quasi-steady-state structure of a 30 nm polymeric film at 70 V with w = 214 nm, p = 20 nm, and Lp = 350 nm for (a) d2 = 90 nm, (b) d2 = 100 nm, and (c) d2 = 110 nm.

5. Conclusions

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In this article, a 2D computational model based on finite element method has been utilized to study the thin film dynamics under the action of an external electric field in the presence of a topographically patterned top electrode. It is shown that by applying a heterogeneous electric field, nanogrooved structures can be produced through controlled ripple formation at the fluid–air interface. Under topographically patterned top electrode having width corresponding to λc, spatiotemporal variation of the morphological patterns beneath a single protrusion is reported. Effect of filling factor, applied voltage, initial film thickness, protrusion height, and electrode spacing on the formation of structures are systematically characterized. The study is significant in elucidating the sensitivity of several independent parameters such as λc, Lp, h0, and ψ on EHD instability in a thin polymeric film. Systematic investigation indicates λd1 < w < λ(d1+davg)/2 as a first approximation for nanogroove structures, and this study can further be used to optimize the process parameters for desired morphology. It also suggests a recipe for miniaturization with desired nanostructures under appropriate condition in the form of possible fabrication of nanogrooves starting from a patterned stamp with a much wider lateral dimension. Such miniaturization of feature dimension is not possible in any of the direct embossing-based patterning techniques.

Author Information

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  • Corresponding Author
  • Authors
    • Swarit Dwivedi - Multiscale Computational Fluid Dynamics Laboratory, Department of Chemical Engineering, and , Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, IndiaPresent Address: Department of Chemical Engineering, Monash University, Clayton Campus, 3168 Melbourne, AustraliaOrcidhttp://orcid.org/0000-0002-4639-5576
    • Raj Narayanan - Multiscale Computational Fluid Dynamics Laboratory, Department of Chemical Engineering, and , Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India
    • Rahul Chaudhary - Multiscale Computational Fluid Dynamics Laboratory, Department of Chemical Engineering, and , Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India
    • Rabibrata Mukherjee - Instability and Soft Patterning Laboratory, Department of Chemical Engineering, and , Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, IndiaOrcidhttp://orcid.org/0000-0001-7031-9859
  • Notes
    The authors declare no competing financial interest.

References

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This article references 62 other publications.

  1. 1
    Duncan, R. The dawning era of polymer therapeutics. Nat. Rev. Drug Discovery 2003, 2, 347360,  DOI: 10.1038/nrd1088
  2. 2
    Pais, A.; Banerjee, A.; Klotzkin, D.; Papautsky, I. High-sensitivity, disposable lab-on-a-chip with thin-film organic electronics for fluorescence detection. Lab Chip 2008, 8, 794800,  DOI: 10.1039/b715143h
  3. 3
    Stone, H. A.; Kim, S. Microfluidics: Basic issues, applications, and challenges. AIChE J. 2001, 47, 12501254,  DOI: 10.1002/aic.690470602
  4. 4
    Wicks, Z. W., Jr.; Jones, F. N.; Pappas, S. P.; Wicks, D. A. Organic Coatings: Science and Technology; John Wiley & Sons, 2007.
  5. 5
    Hoppe, H.; Niggemann, M.; Winder, C.; Kraut, J.; Hiesgen, R.; Hinsch, A.; Meissner, D.; Sariciftci, N. S. Nanoscale Morphology of Conjugated Polymer/Fullerene-Based Bulk- Heterojunction Solar Cells. Adv. Funct. Mater. 2004, 14, 10051011,  DOI: 10.1002/adfm.200305026
  6. 6
    Liu, M.; Johnston, M. B.; Snaith, H. J. Efficient planar heterojunction perovskite solar cells by vapour deposition. Nature 2013, 501, 395398,  DOI: 10.1038/nature12509
  7. 7
    Sperling, L. H. Introduction to Physical Polymer Science; Wiley-Blackwell, 2005; Chapter 13, pp 687756.
  8. 8
    Wu, N.; Russel, W. B. Micro- and nano-patterns created via electrohydrodynamic instabilities. Nano Today 2009, 4, 180192,  DOI: 10.1016/j.nantod.2009.02.002
  9. 9
    Mukherjee, R.; Sharma, A. Instability, self-organization and pattern formation in thin soft films. Soft Matter 2015, 11, 87178740,  DOI: 10.1039/c5sm01724f
  10. 10
    Bhandaru, N.; Das, A.; Mukherjee, R. Confinement induced ordering in dewetting of ultra-thin polymer bilayers on nanopatterned substrates. Nanoscale 2016, 8, 10731087,  DOI: 10.1039/c5nr06690e
  11. 11
    Swan, J. W. Stress and other effects produced in resin and in a viscid compound of resin and oil by electrification. Proc. R. Soc. London 1897, 62, 3846,  DOI: 10.1098/rspl.1897.0077
  12. 12
    Schäffer, E.; Thurn-Albrecht, T.; Russell, T. P.; Steiner, U. Electrically induced structure formation and pattern transfer. Nature 2000, 403, 874877,  DOI: 10.1038/35002540
  13. 13
    Morariu, M. D.; Voicu, N. E.; Schäffer, E.; Lin, Z.; Russell, T. P.; Steiner, U. Hierarchical structure formation and pattern replication induced by an electric field. Nat. Mater. 2003, 2, 4852,  DOI: 10.1038/nmat789
  14. 14
    Xiang, H.; Lin, Y.; Russell, T. P. Electrically induced patterning in block copolymer films. Macromolecules 2004, 37, 53585363,  DOI: 10.1021/ma049888s
  15. 15
    Lee, S. H.; Kim, P.; Jeong, H. E.; Suh, K. Y. Electrically induced formation of uncapped, hollow polymeric microstructures. J. Micromech. Microeng. 2006, 16, 22922297,  DOI: 10.1088/0960-1317/16/11/007
  16. 16
    Zhou, S.; Zheng, H.; Li, G.; Liu, J.; Liu, S. Formation of controllable polymer micropatterns through liquid film electro-dewetting. Appl. Surf. Sci. 2018, 436, 839845,  DOI: 10.1016/j.apsusc.2017.12.070
  17. 17
    Rickard, J. J. S.; Farrer, I.; Oppenheimer, P. G. Tunable nanopatterning of conductive polymers via electrohydrodynamic lithography. ACS Nano 2016, 10, 38653870,  DOI: 10.1021/acsnano.6b01246
  18. 18
    Goldberg-Oppenheimer, P.; Kabra, D.; Vignolini, S.; Hüttner, S.; Sommer, M.; Neumann, K.; Thelakkat, M.; Steiner, U. Hierarchical orientation of crystallinity by block-copolymer patterning and alignment in an electric field. Chem. Mater. 2013, 25, 10631070,  DOI: 10.1021/cm3038075
  19. 19
    Voicu, N. E.; Saifullah, M. S. M.; Subramanian, K. R. V.; Welland, M. E.; Steiner, U. TiO2 patterning using electro-hydrodynamic lithography. Soft Matter 2007, 3, 554557,  DOI: 10.1039/b616538a
  20. 20
    Lv, G.; Liu, Y.; Shao, J.; Tian, H.; Yu, D. Facile fabrication of electrohydrodynamic micro-/nanostructures with high aspect ratio of a conducting polymer for large-scale superhydrophilic/superhydrophobic surfaces. Macromol. Mater. Eng. 2018, 303, 1700361,  DOI: 10.1002/mame.201700361
  21. 21
    Lv, G.; Zhang, S.; Shao, J.; Wang, G.; Tian, H.; Yu, D. Rapid fabrication of electrohydrodynamic micro-/nanostructures with high aspect ratio using a leaky dielectric photoresist. React. Funct. Polym. 2017, 118, 19,  DOI: 10.1016/j.reactfunctpolym.2017.06.014
  22. 22
    González, A.; Castellanos, A. Nonlinear electrohydrodynamic waves on films falling down an inclined plane. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 1996, 53, 35733578,  DOI: 10.1103/physreve.53.3573
  23. 23
    Wu, N.; Pease, L. F.; Russel, W. B. Electric-field-induced patterns in thin polymer films: weakly nonlinear and fully nonlinear evolution. Langmuir 2005, 21, 1229012302,  DOI: 10.1021/la052099z
  24. 24
    Tseluiko, D.; Blyth, M. G.; Papageorgiou, D. T.; Vanden-Broeck, J.-M. Electrified falling-film flow over topography in the presence of a finite electrode. J. Eng. Math. 2010, 68, 339353,  DOI: 10.1007/s10665-010-9377-9
  25. 25
    Kim, H.; Bankoff, S. G.; Miksis, M. J. The effect of an electrostatic field on film flow down an inclined plane. Phys. Fluids A 1992, 4, 21172130,  DOI: 10.1063/1.858508
  26. 26
    Uma, B.; Usha, R. A thin conducting viscous film on an inclined plane in the presence of a uniform normal electric field: Bifurcation scenarios. Phys. Fluids 2008, 20, 032102,  DOI: 10.1063/1.2896300
  27. 27
    Tseluiko, D.; Blyth, M. G.; Papageorgiou, D. T.; Vanden-Broeck, J.-M. Electrified viscous thin film flow over topography. J. Fluid Mech. 2008, 597, 449475,  DOI: 10.1017/s002211200700986x
  28. 28
    Tseluiko, D.; Blyth, M. G.; Papageorgiou, D. T.; Vanden-Broeck, J.-M. Effect of an electric field on film flow down a corrugated wall at zero Reynolds number. Phys. Fluids 2008, 20, 042103,  DOI: 10.1063/1.2909660
  29. 29
    Lv, G.; Zhang, S.; Shao, J.; Tian, H.; Wang, G.; Yu, D. Preparation, properties, and efficient electrically induced structure formation of a leaky dielectric photoresist. RSC Adv. 2016, 6, 8245082458,  DOI: 10.1039/c6ra17957f
  30. 30
    Wu, D.; Sun, Y.; Teh, K. S.; Zhu, Y.; Luo, Y.; Deng, L.; Zhao, L.; Luo, G.; Zhao, Y.; Wang, L.; Sun, D. Investigation of electrohydrodynamic behaviors from open planar solution under rod-induced electrospinning. J. Phys. D: Appl. Phys. 2017, 50, 455602,  DOI: 10.1088/1361-6463/aa8ddb
  31. 31
    Dickey, M. D.; Gupta, S.; Leach, K. A.; Collister, E.; Willson, C. G.; Russell, T. P. Novel 3-D structures in polymer films by coupling external and internal fields. Langmuir 2006, 22, 43154318,  DOI: 10.1021/la052954e
  32. 32
    Lyutakov, O.; Hüttel, I.; Prajzler, V.; Jeřábek, V.; Jančárek, A.; Hnatowicz, V.; Švorčík, V. Pattern formation in PMMA film induced by electric field. J. Polym. Sci., Part B: Polym. Phys. 2009, 47, 11311135,  DOI: 10.1002/polb.21718
  33. 33
    Wu, N.; Kavousanakis, M. E.; Russel, W. B. Coarsening in the electrohydrodynamic patterning of thin polymer films. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2010, 81, 026306,  DOI: 10.1103/physreve.81.026306
  34. 34
    Lau, C. Y.; Russel, W. B. Fundamental limitations on ordered electrohydrodynamic patterning. Macromolecules 2011, 44, 77467751,  DOI: 10.1021/ma200952u
  35. 35
    Schäffer, E.; Thurn-Albrecht, T.; Russell, T. P.; Steiner, U. Electrohydrodynamic instabilities in polymer films. Europhys. Lett. 2001, 53, 518524,  DOI: 10.1209/epl/i2001-00183-2
  36. 36
    Gambhire, P.; Thaokar, R. Electrokinetic model for electric-field-induced interfacial instabilities. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2014, 89, 032409,  DOI: 10.1103/physreve.89.032409
  37. 37
    Lu, W.; Kim, D. Thin-film structures induced by electrostatic field and substrate kinetic constraint. Appl. Phys. Lett. 2006, 88, 153116,  DOI: 10.1063/1.2195095
  38. 38
    Pease, L. F., III; Russel, W. B. Linear stability analysis of thin leaky dielectric films subjected to electric fields. J. Non-Newtonian Fluid Mech. 2002, 102, 233250,  DOI: 10.1016/s0377-0257(01)00180-x
  39. 39
    Wu, N.; Russel, W. B. Electrohydrodynamic instability of dielectric bilayers: Kinetics and thermodynamics. Ind. Eng. Chem. Res. 2006, 45, 54555465,  DOI: 10.1021/ie0510876
  40. 40
    Yeoh, H. K.; Xu, Q.; Basaran, O. A. Equilibrium shapes and stability of a liquid film subjected to a nonuniform electric field. Phys. Fluids 2007, 19, 114111,  DOI: 10.1063/1.2798806
  41. 41
    Sarkar, J.; Sharma, A.; Shenoy, V. B. Electric-field induced instabilities and morphological phase transitions in soft elastic films. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2008, 77, 031604,  DOI: 10.1103/physreve.77.031604
  42. 42
    Li, B.; Li, Y.; Xu, G.-K.; Feng, X.-Q. Surface patterning of soft polymer film-coated cylinders via an electric field. J. Phys.: Condens. Matter 2009, 21, 445006,  DOI: 10.1088/0953-8984/21/44/445006
  43. 43
    Roberts, S. A.; Kumar, S. Electrohydrodynamic instabilities in thin liquid trilayer films. Phys. Fluids 2010, 22, 122102,  DOI: 10.1063/1.3520134
  44. 44
    Bandyopadhyay, D.; Sharma, A.; Thiele, U.; Reddy, P. D. S. Electric-field-induced interfacial instabilities and morphologies of thin viscous and elastic bilayers. Langmuir 2009, 25, 91089118,  DOI: 10.1021/la900635f
  45. 45
    Gambhire, P.; Thaokar, R. M. Electrohydrodynamic instabilities at interfaces subjected to alternating electric field. Phys. Fluids 2010, 22, 064103,  DOI: 10.1063/1.3431043
  46. 46
    Reddy, P. D. S.; Bandyopadhyay, D.; Sharma, A. Self-Organized Ordered Arrays of Core–Shell Columns in Viscous Bilayers Formed by Spatially Varying Electric Fields. J. Phys. Chem. C 2010, 114, 2102021028,  DOI: 10.1021/jp106253k
  47. 47
    Srivastava, S.; Reddy, P. D. S.; Wang, C.; Bandyopadhyay, D.; Sharma, A. Electric field induced microstructures in thin films on physicochemically heterogeneous and patterned substrates. J. Chem. Phys. 2010, 132, 174703,  DOI: 10.1063/1.3400653
  48. 48
    Ghosh, A.; Bandyopadhyay, D.; Sharma, A. Electric field mediated elastic contact lithography of thin viscoelastic films for miniaturized and multiscale patterns. Soft Matter 2018, 14, 39633977,  DOI: 10.1039/c8sm00428e
  49. 49
    Tian, H.; Shao, J.; Hu, H.; Wang, L.; Ding, Y. Role of space charges inside a dielectric polymer in the electrohydrodynamic structure formation on a prepatterned polymer (ESF-PP). RSC Adv. 2016, 6, 7727577283,  DOI: 10.1039/c6ra14479a
  50. 50
    Tian, H.; Shao, J.; Ding, Y.; Li, X.; Hu, H. Electrohydrodynamic micro-/nanostructuring processes based on prepatterned polymer and prepatterned template. Macromolecules 2014, 47, 14331438,  DOI: 10.1021/ma402456u
  51. 51
    Tian, H.; Shao, J.; Ding, Y.; Li, X.; Liu, H. Simulation of polymer rheology in an electrically induced micro- or nano-structuring process based on electrohydrodynamics and conservative level set method. RSC Adv. 2014, 4, 2167221680,  DOI: 10.1039/c4ra00553h
  52. 52
    Verma, R.; Sharma, A.; Kargupta, K.; Bhaumik, J. Electric field induced instability and pattern formation in thin liquid films. Langmuir 2005, 21, 37103721,  DOI: 10.1021/la0472100
  53. 53
    Harkema, S. Capillary Instabilities in Thin Polymer Films. Ph.D. Thesis, University of Groningen, The Netherlands, 2006.
  54. 54
    Dwivedi, S.; Vivek; Mukherjee, R.; Atta, A. Formation and control of secondary nanostructures in electro-hydrodynamic patterning of ultra-thin films. Thin Solid Films 2017, 642, 241251,  DOI: 10.1016/j.tsf.2017.09.029
  55. 55
    Atta, A.; Crawford, D. G.; Koch, C. R.; Bhattacharjee, S. Influence of electrostatic and chemical heterogeneity on the electric-field-induced destabilization of thin liquid films. Langmuir 2011, 27, 1247212485,  DOI: 10.1021/la202759j
  56. 56
    Dwivedi, S.; Mukherjee, R.; Atta, A. Re-entrant structural evolution using electrically heterogeneous patterned electrode. Comput.-Aided Chem. Eng. 2017, 40, 12131218,  DOI: 10.1016/b978-0-444-63965-3.50204-x
  57. 57
    Nazaripoor, H.; Koch, C. R.; Sadrzadeh, M. Ordered high aspect ratio nanopillar formation based on electrical and thermal reflowing of prepatterned thin films. J. Colloid Interface Sci. 2018, 530, 312,  DOI: 10.1016/j.jcis.2018.06.080
  58. 58
    Hu, H.; Tian, H.; Shao, J.; Ding, Y.; Jiang, C.; Liu, H. Fabrication of bifocal microlens arrays based on controlled electrohydrodynamic reflowing of pre-patterned polymer. J. Micromech. Microeng. 2014, 24, 095027,  DOI: 10.1088/0960-1317/24/9/095027
  59. 59
    Williams, M. B.; Davis, S. H. Nonlinear theory of film rupture. J. Colloid Interface Sci. 1982, 90, 220228,  DOI: 10.1016/0021-9797(82)90415-5
  60. 60
    Oron, A.; Davis, S. H.; Bankoff, S. G. Long-scale evolution of thin liquid films. Rev. Mod. Phys. 1997, 69, 931980,  DOI: 10.1103/revmodphys.69.931
  61. 61
    Li, H.; Yu, W.; Zhang, L.; Liu, Z.; Brown, K. E.; Abraham, E.; Cargill, S.; Tonry, C.; Patel, M. K.; Bailey, C.; Desmulliez, M. P. Y. Simulation and modelling of sub-30 nm polymeric channels fabricated by electrostatic induced lithography. RSC Adv. 2013, 3, 1183911845,  DOI: 10.1039/c3ra40188j
  62. 62
    COMSOL, COMSOL Multiphysics User’s Guide , 2015.

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  1. Guowei Lv, Hongmiao Tian, Jinyou Shao, Demei Yu. Pattern formation in thin polymeric films via electrohydrodynamic patterning. RSC Advances 2022, 12 (16) , 9681-9697. https://doi.org/10.1039/D2RA01109C
  2. Jaeseok Hwang, Hyunje Park, Jaejong Lee, Dae Joon Kang. Parametric scheme for rapid nanopattern replication via electrohydrodynamic instability. RSC Advances 2021, 11 (30) , 18152-18161. https://doi.org/10.1039/D1RA01728D
  3. Sumita Sahoo, Nandini Bhandaru, Rabibrata Mukherjee. Reversible morphological switching and deformation hysteresis in electric field mediated instability of thin elastic films. Soft Matter 2019, 15 (18) , 3828-3834. https://doi.org/10.1039/C8SM02622J

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  • Abstract

    Figure 1

    Figure 1. Schematic of electrode assembly with polymeric liquid film denoting the geometrical parameters and top electrode as (a) flat plate and (b) patterned stamp with square protrusions, and (c) 3D representation of patterned stamp with column protrusions electrode assembly.

    Figure 2

    Figure 2. Schematic of computational domain, boundaries, and points used in this work.

    Figure 3

    Figure 3. Initial electric field intensity distribution on a 30 nm polymeric film under protruded top electrode having w = λd1 = 214 nm, and p = 20 nm for 70 V, d2 = 100 nm, and Lp = 350 nm.

    Figure 4

    Figure 4. Temporal evolution of a 30 nm polymeric film under protruded top electrode having w = λd1 = 214 nm, and p = 20 nm for ψ = 70 V, d2 = 100 nm, and Lp = 350 nm at (a) 0, (b) 2, (c) 6, (d) 15, and (e) 100 μs.

    Figure 5

    Figure 5. Quasi-steady-state patterns obtained for ψ = 70 V, h0 = 30 nm, p = 20 nm, d2 = 100 nm, and Lp = 350 nm at (a) w < λd1, (b) w = λd1, (c) w = λ(d1+davg)/2, (d) w = λdavg, (e) w = λ(davg+d2)/2, and (f) w = λd2.

    Figure 6

    Figure 6. Initial electric-field-intensity distribution on a 30 nm polymeric film under protruded top electrode having w = λc, p = 20 nm for 70 V, d2 = 100 nm, and Lp = 350 nm.

    Figure 7

    Figure 7. Quasi-steady-state patterns of a 30 nm polymeric film under a protruded top electrode having w = 225 nm, and p = 20 nm at 70 V, and d2 = 100 nm at (a) Lp = 250 nm, (b) Lp = 300 nm, (c) Lp = 350 nm, and (d) Lp = 400 nm.

    Figure 8

    Figure 8. Initial electric-field-intensity distribution for different Lp on a 30 nm polymer film under protruded top electrode (w = 225 nm, p = 20 nm) at 70 V and d2 = 100 nm.

    Figure 9

    Figure 9. Quasi-steady-state structure obtained at ψ = 70 V under a protruded top electrode having w = λ(d1+davg)/2 nm, and p = 20 nm with d2 = 100 nm and filling factor = 0.6 for (a) h0 = 25 nm, (b) h0 = 30 nm, (c) h0 = 35 nm, and (d) h0 = 40 nm.

    Figure 10

    Figure 10. Quasi-steady-state structure obtained at ψ = 70 V under a protruded top electrode having w = 225 nm and p = 20 nm with d2 = 100 nm and Lp = 350 nm for (a) h0 = 25 nm, (b) h0 = 30 nm, (c) h0 = 35 nm, and (d) h0 = 40 nm.

    Figure 11

    Figure 11. Morphological phase diagram of single, nanogroove, and separate pillars for different electrode widths and initial film thicknesses.

    Figure 12

    Figure 12. Quasi-steady-state structure of a 30 nm polymeric film under a protruded top electrode having w = 225 nm and p = 20 nm with d2 = 100 nm and Lp = 350 nm at (a) ψ = 60 V, (b) ψ = 65 V, (c) ψ = 70 V, (d) ψ = 75 V, and (e) ψ = 80 V.

    Figure 13

    Figure 13. Quasi-steady-state structure of a 30 nm polymeric film at 70 V for different protrusion heights (p) (a) 10 nm, (b) 20 nm, (c) 30 nm, and (d) 40 nm with w = 214 nm, d2 = 100 nm, and Lp = 350 nm.

    Figure 14

    Figure 14. Quasi-steady-state structure of a 30 nm polymeric film at 70 V with w = 214 nm, p = 20 nm, and Lp = 350 nm for (a) d2 = 90 nm, (b) d2 = 100 nm, and (c) d2 = 110 nm.

  • References


    This article references 62 other publications.

    1. 1
      Duncan, R. The dawning era of polymer therapeutics. Nat. Rev. Drug Discovery 2003, 2, 347360,  DOI: 10.1038/nrd1088
    2. 2
      Pais, A.; Banerjee, A.; Klotzkin, D.; Papautsky, I. High-sensitivity, disposable lab-on-a-chip with thin-film organic electronics for fluorescence detection. Lab Chip 2008, 8, 794800,  DOI: 10.1039/b715143h
    3. 3
      Stone, H. A.; Kim, S. Microfluidics: Basic issues, applications, and challenges. AIChE J. 2001, 47, 12501254,  DOI: 10.1002/aic.690470602
    4. 4
      Wicks, Z. W., Jr.; Jones, F. N.; Pappas, S. P.; Wicks, D. A. Organic Coatings: Science and Technology; John Wiley & Sons, 2007.
    5. 5
      Hoppe, H.; Niggemann, M.; Winder, C.; Kraut, J.; Hiesgen, R.; Hinsch, A.; Meissner, D.; Sariciftci, N. S. Nanoscale Morphology of Conjugated Polymer/Fullerene-Based Bulk- Heterojunction Solar Cells. Adv. Funct. Mater. 2004, 14, 10051011,  DOI: 10.1002/adfm.200305026
    6. 6
      Liu, M.; Johnston, M. B.; Snaith, H. J. Efficient planar heterojunction perovskite solar cells by vapour deposition. Nature 2013, 501, 395398,  DOI: 10.1038/nature12509
    7. 7
      Sperling, L. H. Introduction to Physical Polymer Science; Wiley-Blackwell, 2005; Chapter 13, pp 687756.
    8. 8
      Wu, N.; Russel, W. B. Micro- and nano-patterns created via electrohydrodynamic instabilities. Nano Today 2009, 4, 180192,  DOI: 10.1016/j.nantod.2009.02.002
    9. 9
      Mukherjee, R.; Sharma, A. Instability, self-organization and pattern formation in thin soft films. Soft Matter 2015, 11, 87178740,  DOI: 10.1039/c5sm01724f
    10. 10
      Bhandaru, N.; Das, A.; Mukherjee, R. Confinement induced ordering in dewetting of ultra-thin polymer bilayers on nanopatterned substrates. Nanoscale 2016, 8, 10731087,  DOI: 10.1039/c5nr06690e
    11. 11
      Swan, J. W. Stress and other effects produced in resin and in a viscid compound of resin and oil by electrification. Proc. R. Soc. London 1897, 62, 3846,  DOI: 10.1098/rspl.1897.0077
    12. 12
      Schäffer, E.; Thurn-Albrecht, T.; Russell, T. P.; Steiner, U. Electrically induced structure formation and pattern transfer. Nature 2000, 403, 874877,  DOI: 10.1038/35002540
    13. 13
      Morariu, M. D.; Voicu, N. E.; Schäffer, E.; Lin, Z.; Russell, T. P.; Steiner, U. Hierarchical structure formation and pattern replication induced by an electric field. Nat. Mater. 2003, 2, 4852,  DOI: 10.1038/nmat789
    14. 14
      Xiang, H.; Lin, Y.; Russell, T. P. Electrically induced patterning in block copolymer films. Macromolecules 2004, 37, 53585363,  DOI: 10.1021/ma049888s
    15. 15
      Lee, S. H.; Kim, P.; Jeong, H. E.; Suh, K. Y. Electrically induced formation of uncapped, hollow polymeric microstructures. J. Micromech. Microeng. 2006, 16, 22922297,  DOI: 10.1088/0960-1317/16/11/007
    16. 16
      Zhou, S.; Zheng, H.; Li, G.; Liu, J.; Liu, S. Formation of controllable polymer micropatterns through liquid film electro-dewetting. Appl. Surf. Sci. 2018, 436, 839845,  DOI: 10.1016/j.apsusc.2017.12.070
    17. 17
      Rickard, J. J. S.; Farrer, I.; Oppenheimer, P. G. Tunable nanopatterning of conductive polymers via electrohydrodynamic lithography. ACS Nano 2016, 10, 38653870,  DOI: 10.1021/acsnano.6b01246
    18. 18
      Goldberg-Oppenheimer, P.; Kabra, D.; Vignolini, S.; Hüttner, S.; Sommer, M.; Neumann, K.; Thelakkat, M.; Steiner, U. Hierarchical orientation of crystallinity by block-copolymer patterning and alignment in an electric field. Chem. Mater. 2013, 25, 10631070,  DOI: 10.1021/cm3038075
    19. 19
      Voicu, N. E.; Saifullah, M. S. M.; Subramanian, K. R. V.; Welland, M. E.; Steiner, U. TiO2 patterning using electro-hydrodynamic lithography. Soft Matter 2007, 3, 554557,  DOI: 10.1039/b616538a
    20. 20
      Lv, G.; Liu, Y.; Shao, J.; Tian, H.; Yu, D. Facile fabrication of electrohydrodynamic micro-/nanostructures with high aspect ratio of a conducting polymer for large-scale superhydrophilic/superhydrophobic surfaces. Macromol. Mater. Eng. 2018, 303, 1700361,  DOI: 10.1002/mame.201700361
    21. 21
      Lv, G.; Zhang, S.; Shao, J.; Wang, G.; Tian, H.; Yu, D. Rapid fabrication of electrohydrodynamic micro-/nanostructures with high aspect ratio using a leaky dielectric photoresist. React. Funct. Polym. 2017, 118, 19,  DOI: 10.1016/j.reactfunctpolym.2017.06.014
    22. 22
      González, A.; Castellanos, A. Nonlinear electrohydrodynamic waves on films falling down an inclined plane. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 1996, 53, 35733578,  DOI: 10.1103/physreve.53.3573
    23. 23
      Wu, N.; Pease, L. F.; Russel, W. B. Electric-field-induced patterns in thin polymer films: weakly nonlinear and fully nonlinear evolution. Langmuir 2005, 21, 1229012302,  DOI: 10.1021/la052099z
    24. 24
      Tseluiko, D.; Blyth, M. G.; Papageorgiou, D. T.; Vanden-Broeck, J.-M. Electrified falling-film flow over topography in the presence of a finite electrode. J. Eng. Math. 2010, 68, 339353,  DOI: 10.1007/s10665-010-9377-9
    25. 25
      Kim, H.; Bankoff, S. G.; Miksis, M. J. The effect of an electrostatic field on film flow down an inclined plane. Phys. Fluids A 1992, 4, 21172130,  DOI: 10.1063/1.858508
    26. 26
      Uma, B.; Usha, R. A thin conducting viscous film on an inclined plane in the presence of a uniform normal electric field: Bifurcation scenarios. Phys. Fluids 2008, 20, 032102,  DOI: 10.1063/1.2896300
    27. 27
      Tseluiko, D.; Blyth, M. G.; Papageorgiou, D. T.; Vanden-Broeck, J.-M. Electrified viscous thin film flow over topography. J. Fluid Mech. 2008, 597, 449475,  DOI: 10.1017/s002211200700986x
    28. 28
      Tseluiko, D.; Blyth, M. G.; Papageorgiou, D. T.; Vanden-Broeck, J.-M. Effect of an electric field on film flow down a corrugated wall at zero Reynolds number. Phys. Fluids 2008, 20, 042103,  DOI: 10.1063/1.2909660
    29. 29
      Lv, G.; Zhang, S.; Shao, J.; Tian, H.; Wang, G.; Yu, D. Preparation, properties, and efficient electrically induced structure formation of a leaky dielectric photoresist. RSC Adv. 2016, 6, 8245082458,  DOI: 10.1039/c6ra17957f
    30. 30
      Wu, D.; Sun, Y.; Teh, K. S.; Zhu, Y.; Luo, Y.; Deng, L.; Zhao, L.; Luo, G.; Zhao, Y.; Wang, L.; Sun, D. Investigation of electrohydrodynamic behaviors from open planar solution under rod-induced electrospinning. J. Phys. D: Appl. Phys. 2017, 50, 455602,  DOI: 10.1088/1361-6463/aa8ddb
    31. 31
      Dickey, M. D.; Gupta, S.; Leach, K. A.; Collister, E.; Willson, C. G.; Russell, T. P. Novel 3-D structures in polymer films by coupling external and internal fields. Langmuir 2006, 22, 43154318,  DOI: 10.1021/la052954e
    32. 32
      Lyutakov, O.; Hüttel, I.; Prajzler, V.; Jeřábek, V.; Jančárek, A.; Hnatowicz, V.; Švorčík, V. Pattern formation in PMMA film induced by electric field. J. Polym. Sci., Part B: Polym. Phys. 2009, 47, 11311135,  DOI: 10.1002/polb.21718
    33. 33
      Wu, N.; Kavousanakis, M. E.; Russel, W. B. Coarsening in the electrohydrodynamic patterning of thin polymer films. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2010, 81, 026306,  DOI: 10.1103/physreve.81.026306
    34. 34
      Lau, C. Y.; Russel, W. B. Fundamental limitations on ordered electrohydrodynamic patterning. Macromolecules 2011, 44, 77467751,  DOI: 10.1021/ma200952u
    35. 35
      Schäffer, E.; Thurn-Albrecht, T.; Russell, T. P.; Steiner, U. Electrohydrodynamic instabilities in polymer films. Europhys. Lett. 2001, 53, 518524,  DOI: 10.1209/epl/i2001-00183-2
    36. 36
      Gambhire, P.; Thaokar, R. Electrokinetic model for electric-field-induced interfacial instabilities. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2014, 89, 032409,  DOI: 10.1103/physreve.89.032409
    37. 37
      Lu, W.; Kim, D. Thin-film structures induced by electrostatic field and substrate kinetic constraint. Appl. Phys. Lett. 2006, 88, 153116,  DOI: 10.1063/1.2195095
    38. 38
      Pease, L. F., III; Russel, W. B. Linear stability analysis of thin leaky dielectric films subjected to electric fields. J. Non-Newtonian Fluid Mech. 2002, 102, 233250,  DOI: 10.1016/s0377-0257(01)00180-x
    39. 39
      Wu, N.; Russel, W. B. Electrohydrodynamic instability of dielectric bilayers: Kinetics and thermodynamics. Ind. Eng. Chem. Res. 2006, 45, 54555465,  DOI: 10.1021/ie0510876
    40. 40
      Yeoh, H. K.; Xu, Q.; Basaran, O. A. Equilibrium shapes and stability of a liquid film subjected to a nonuniform electric field. Phys. Fluids 2007, 19, 114111,  DOI: 10.1063/1.2798806
    41. 41
      Sarkar, J.; Sharma, A.; Shenoy, V. B. Electric-field induced instabilities and morphological phase transitions in soft elastic films. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2008, 77, 031604,  DOI: 10.1103/physreve.77.031604
    42. 42
      Li, B.; Li, Y.; Xu, G.-K.; Feng, X.-Q. Surface patterning of soft polymer film-coated cylinders via an electric field. J. Phys.: Condens. Matter 2009, 21, 445006,  DOI: 10.1088/0953-8984/21/44/445006
    43. 43
      Roberts, S. A.; Kumar, S. Electrohydrodynamic instabilities in thin liquid trilayer films. Phys. Fluids 2010, 22, 122102,  DOI: 10.1063/1.3520134
    44. 44
      Bandyopadhyay, D.; Sharma, A.; Thiele, U.; Reddy, P. D. S. Electric-field-induced interfacial instabilities and morphologies of thin viscous and elastic bilayers. Langmuir 2009, 25, 91089118,  DOI: 10.1021/la900635f
    45. 45
      Gambhire, P.; Thaokar, R. M. Electrohydrodynamic instabilities at interfaces subjected to alternating electric field. Phys. Fluids 2010, 22, 064103,  DOI: 10.1063/1.3431043
    46. 46
      Reddy, P. D. S.; Bandyopadhyay, D.; Sharma, A. Self-Organized Ordered Arrays of Core–Shell Columns in Viscous Bilayers Formed by Spatially Varying Electric Fields. J. Phys. Chem. C 2010, 114, 2102021028,  DOI: 10.1021/jp106253k
    47. 47
      Srivastava, S.; Reddy, P. D. S.; Wang, C.; Bandyopadhyay, D.; Sharma, A. Electric field induced microstructures in thin films on physicochemically heterogeneous and patterned substrates. J. Chem. Phys. 2010, 132, 174703,  DOI: 10.1063/1.3400653
    48. 48
      Ghosh, A.; Bandyopadhyay, D.; Sharma, A. Electric field mediated elastic contact lithography of thin viscoelastic films for miniaturized and multiscale patterns. Soft Matter 2018, 14, 39633977,  DOI: 10.1039/c8sm00428e
    49. 49
      Tian, H.; Shao, J.; Hu, H.; Wang, L.; Ding, Y. Role of space charges inside a dielectric polymer in the electrohydrodynamic structure formation on a prepatterned polymer (ESF-PP). RSC Adv. 2016, 6, 7727577283,  DOI: 10.1039/c6ra14479a
    50. 50
      Tian, H.; Shao, J.; Ding, Y.; Li, X.; Hu, H. Electrohydrodynamic micro-/nanostructuring processes based on prepatterned polymer and prepatterned template. Macromolecules 2014, 47, 14331438,  DOI: 10.1021/ma402456u
    51. 51
      Tian, H.; Shao, J.; Ding, Y.; Li, X.; Liu, H. Simulation of polymer rheology in an electrically induced micro- or nano-structuring process based on electrohydrodynamics and conservative level set method. RSC Adv. 2014, 4, 2167221680,  DOI: 10.1039/c4ra00553h
    52. 52
      Verma, R.; Sharma, A.; Kargupta, K.; Bhaumik, J. Electric field induced instability and pattern formation in thin liquid films. Langmuir 2005, 21, 37103721,  DOI: 10.1021/la0472100
    53. 53
      Harkema, S. Capillary Instabilities in Thin Polymer Films. Ph.D. Thesis, University of Groningen, The Netherlands, 2006.
    54. 54
      Dwivedi, S.; Vivek; Mukherjee, R.; Atta, A. Formation and control of secondary nanostructures in electro-hydrodynamic patterning of ultra-thin films. Thin Solid Films 2017, 642, 241251,  DOI: 10.1016/j.tsf.2017.09.029
    55. 55
      Atta, A.; Crawford, D. G.; Koch, C. R.; Bhattacharjee, S. Influence of electrostatic and chemical heterogeneity on the electric-field-induced destabilization of thin liquid films. Langmuir 2011, 27, 1247212485,  DOI: 10.1021/la202759j
    56. 56
      Dwivedi, S.; Mukherjee, R.; Atta, A. Re-entrant structural evolution using electrically heterogeneous patterned electrode. Comput.-Aided Chem. Eng. 2017, 40, 12131218,  DOI: 10.1016/b978-0-444-63965-3.50204-x
    57. 57
      Nazaripoor, H.; Koch, C. R.; Sadrzadeh, M. Ordered high aspect ratio nanopillar formation based on electrical and thermal reflowing of prepatterned thin films. J. Colloid Interface Sci. 2018, 530, 312,  DOI: 10.1016/j.jcis.2018.06.080
    58. 58
      Hu, H.; Tian, H.; Shao, J.; Ding, Y.; Jiang, C.; Liu, H. Fabrication of bifocal microlens arrays based on controlled electrohydrodynamic reflowing of pre-patterned polymer. J. Micromech. Microeng. 2014, 24, 095027,  DOI: 10.1088/0960-1317/24/9/095027
    59. 59
      Williams, M. B.; Davis, S. H. Nonlinear theory of film rupture. J. Colloid Interface Sci. 1982, 90, 220228,  DOI: 10.1016/0021-9797(82)90415-5
    60. 60
      Oron, A.; Davis, S. H.; Bankoff, S. G. Long-scale evolution of thin liquid films. Rev. Mod. Phys. 1997, 69, 931980,  DOI: 10.1103/revmodphys.69.931
    61. 61
      Li, H.; Yu, W.; Zhang, L.; Liu, Z.; Brown, K. E.; Abraham, E.; Cargill, S.; Tonry, C.; Patel, M. K.; Bailey, C.; Desmulliez, M. P. Y. Simulation and modelling of sub-30 nm polymeric channels fabricated by electrostatic induced lithography. RSC Adv. 2013, 3, 1183911845,  DOI: 10.1039/c3ra40188j
    62. 62
      COMSOL, COMSOL Multiphysics User’s Guide , 2015.