Role of space charges inside a dielectric polymer in the electrohydrodynamic structure formation on a prepatterned polymer (ESF-PP)

Abstract

Electrohydrodynamic structure formation on a prepatterned polymer (ESF-PP) can duplicate structures identical to the initial geometry, but with a higher aspect ratio, under the influence of a spatially modulated electric field. In this process, a voltage is applied between a flat template and a flat substrate, sandwiching a prepatterned polymer and an air gap so as to generate an electrohydrodynamic (EHD) force at the air–polymer interface. Subsequently, the prepatterned polymer can be non-uniformly pulled upwards, causing deformation in its micro/nano-structure. Until now, most of the research into ESF-PP has explored various dielectric polymers, which are all considered to be the perfect dielectrics because of their low electrical conductivity. However, the assumption of a perfect dielectric typically creates discrepancies between theoretical analysis and experimental results in terms of the polymer motion and the final morphology. This phenomenon can be attributed to ignoring the action of the small number of free space charges within dielectric polymer motion (although the electrical conductivity of the dielectric polymer may be even lower than that of deionized water), which emphasizes the importance of the influence of space charges inside the dielectric polymer on deformation. This paper explores the role of free space charges by making a comparison between the perfect dielectric polymer and the leaky dielectric polymer on the progressive development, the surface topography and the aspect ratio from experimental tests and numerical simulations, and a discussion of the effect of the different electrical conductivities. Results show that the free charges inside the dielectric polymer can lead to a larger EHD force because of the additional Coulomb force, even at a low conductivity of 10⁻⁷ S m⁻¹, thus demonstrating the ability to duplicate a mushroom-like structure with a high aspect ratio, which has wide applications in superhydrophobicity, dry adhesion, nanogenerators, etc.

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1. Introduction

Electrohydrodynamic (EHD) behavior is an interesting phenomenon that encourages the conductive or dielectric fluid to move along a prescribed path determined by a spatially modulated electric field,^1–3 which has been explored in many applications, such as micro/nano-fluidics,⁴ optics,⁵ and biomedicine.⁶ Consequently, a functional polymer, as a typical fluid, can be EHD structured into micro/nano-patterns, leading to a novel approach for electrohydrodynamic structure formation on a prepatterned polymer (ESF-PP) to fabricate a structure with a high aspect ratio, as shown in Fig. 1.⁷ In this approach, a prepatterned polymer with a low aspect ratio is fabricated, which is subsequently sandwiched between an electrode pair consisting of a flat template and a flat substrate, with a separating air gap, see Fig. 1A. Activated by a spatially modulated electric field incurred by the initial morphology as well as the temperature exceeding the glass transition temperature simultaneously, the prepatterned polymer will become fluidic to overcome the surface tension and viscous force to move upward to the flat template, see Fig. 1B. This process generates a polymeric structure similar to the initial geometry but with a higher aspect ratio, see Fig. 1C. In the forming process, it is true that it needs an additional step to duplicate prepatterned features on the polymer film, which is usually achieved by imprint or optical lithography. This step is technologically meaningful because only a shallowly prepatterned polymer is needed, alleviating the problems associated with large mechanical pressure and mold removal in creating a high aspect ratio which are typical in a conventional imprinting process,⁸ and the difficulty of controlling scattering in a thick film for a high aspect ratio in conventional optical lithography.⁹

Fig. 1 Sketch of electrohydrodynamic structure formation on prepatterned polymer (ESF-PP).

Attributed to the prominent characteristics of the high aspect ratio, such as large surface area and high linearity in mechanical response to external force,¹⁰ various micro/nano-structures have been fabricated using ESF-PP, with wide applicability in dry adhesive,¹¹ nanogenerator,¹² etc. Because of their low electrical conductivity, the polymers performed thus far are treated as perfect dielectrics, which include polystyrene (PS),¹³ polymethyl methacrylate (PMMA),¹⁴ polyvinylidene fluoride (PVDF),¹² ethyl cellulose (EC),¹⁵ etc. In this case, the driving force is ascribed to the liquid dielectrophoresis, which is deduced from the bound charges or dipoles and is generated on the liquid surface, neglecting the action of small amount of space charges inside on the polymeric motion. In practice, the geometry of the polymeric deformation is different for different dielectric polymers based on the published literature,^7,11,12 consisting of the surface topography and the aspect ratio, which have been analyzed based on the assumption of a perfect dielectric.

The assumption that polymers are perfect dielectrics can be used to describe the EHD behavior of some kinds of polymer motion, such as the deformation of mr-NIL 6000E (a type of acrylate), which can be duplicated as a nearly vertical pillar with an aspect ratio of 3.2.⁷ However, the assumption may also create differences between theoretical analysis and experimental results in terms of the polymer morphology for other dielectric polymers. For instance, mushroom-like structures can be generated on PMMA or PVDF films with aspect ratios of 12 and 9,^11,12 respectively, which contradicts the assumption that these materials are perfect dielectrics. That is, based on the assumption, a high aspect ratio cannot be obtained and the diameter of the pillar tip cannot be very large. Comparing mr-NIL 6000E with PMMA and PVDF, the dielectric permittivity, viscous coefficient, surface tension coefficient, etc. are at the same magnitude, whereas the electrical conductivity does not (the conductivity of mr-NIL 6000E is approximately 10⁻¹⁰ S m⁻¹ and that of PMMA and PVDF is roughly 10⁻⁷ S m⁻¹), which indicates the influence of space charges inside the dielectric polymer on polymer deformation.

It is well-known that the EHD force generated on an isotropic polymer can be determined by the Maxwell stress tensor,¹⁶ which consist of two components: the Coulomb force, originating from the free space charges, and the dielectric force, attributed to an inhomogeneous polarization at the air–polymer interface. This phenomenon raises doubts as to whether the activity of free space charges inside the dielectric polymer should be considered, despite of their small values. That is, the dielectric polymer should be considered as leaky dielectrics or perfect dielectrics. Recently, research on the effect of conductivity on the behavior of dielectric polymers has focused on electrically induced structure formation (EISF), in which a flat polymer film (instead of a prepatterned one) is adopted in the forming process, leading to a cluster of periodic pillars with a low aspect ratio due to the imbalance of EHD force and surface tension.^17–19 For instance, Sharma's group evaluated fluidic behavior under an external electric field and found that the presence of nonzero conductivity in either one or both of the fluids had a significant influence on the length-scale characteristic of the linear instability.^20,21 Pease and Russel theoretically compared the spacing and growth exponent of deformation for perfect and leaky dielectric polymers, concluding that the leaky dielectric polymer can duplicate a dense distribution in a shorter time.^22,23 Koch's group investigated the influence of electrostatic heterogeneity on the electric field induced destabilization of thin ionic liquid films to both control spatial ordering and reduce the lateral dimension of structures forming on the films, demonstrating that the structure size in perfect dielectric films is reduced by a factor of 4 when they are replaced with ionic liquid films.²⁴ Based on the published literature,^25–27 a small amount of space charges can actually affect the periodicity of the deformation in the EISF process via modulation of the EHD behavior. Similar to the EISF process, it is necessary to study the influence of low conductivity inside the dielectric polymer on deformation in ESF-PP. In addition, according to research on the role of free charges inside dielectric polymers, the aspect ratio and the tip diameter of the mushroom-like structures can be modulated by adjusting the process parameters, leading to different deformations and wide applications, such as dry adhesive systems with fast and simple generation of reliable adhesion,²⁸ superomniphobic surfaces with high transmittance and durability,^29,30 and bioinspired structures for wound closure or stabilization implants with high shear resistance against wet tissue.³¹

In this paper, the microstructures are experimentally duplicated on a perfect dielectric polymer with an electrical conductivity of 10⁻¹⁰ S m⁻¹ (which can be safely considered a perfect dielectric), and a leaky dielectric polymer with a small conductivity of 10⁻⁷ S m⁻¹ for ESF-PP. In addition, we perform a theoretical analysis of progressive evolution based on a numerical model that couples electrohydrodynamics and phase field formulation. Furthermore, the unique characteristics of the leaky dielectric polymer on the surface topography and the aspect ratio are demonstrated on the basis of a comparison between the perfect dielectric and the leaky dielectric polymer, as well as the influence of the different electrical conductivities on the process development and the final geometry discussed in depth.

2. Results and discussion

When applying an electric field and maintaining a temperature exceeding the glass transition temperature simultaneously, the prepatterned polymer will move upward to the flat template corresponding to the initial morphology under the driving force, consisting of the dielectric force for both the perfect dielectric and the leaky dielectric and the Coulomb force for only the leaky dielectric polymer (because of its small electrical conductivity).³² This process leads to a structure that is identical to the initial geometry but with a larger aspect ratio, as shown in Fig. 2 which demonstrates polymeric deformation on either a perfect dielectric or a leaky dielectric polymer film for experimental tests and numerical simulations.

Fig. 2 Experimental deformations for ESF-PP process with perfect dielectric polymer (A) and leaky dielectric polymer (B) and the corresponding numerical simulations are shown in (C) and (D), respectively. (E) Polymer height versus progressive time for perfect and leaky dielectric polymers. (F) Initial EHD force at the air–polymer interface for two polymers.

Fig. 2A and B shows the microstructures duplicated on a perfect dielectric polymer (mr-NIL 6000E, a type of acrylate purchased from Micro Resist Technology, Germany, with an electrical conductivity of roughly 10⁻¹⁰ S m⁻¹, which can treated as a perfect dielectric) and a leaky dielectric polymer (PMMA with a conductivity of 10⁻⁷ S m⁻¹) via the ESF-PP process. The height and width of the prepatterned polymers are 24 μm and 30 μm, respectively; the air gap between the flat template and the flat substrate is 45 μm; the externally applied voltage is 500 V. Obviously, a discrepancy exists in the polymeric deformation of the two polymers, i.e., nearly vertical micro-pillars are duplicated on the perfect dielectric polymer whereas mushroom-like structures are duplicated on the leaky dielectric. However, the process parameters are identical or at the same magnitude except for the electrical conductivity, implying that a small amount of space charges in the dielectric polymer may cause the difference in the formed structures for different polymers.

The movement of the perfect and leaky dielectric polymers can be depicted via a generalization of the phase-field modeling of the ESF-PP as originally formulated for a perfect dielectric polymer,³³ with an additional consideration of the influence of free space charges at the air–polymer interface.³⁴

First, the Cahn–Hilliard equation for a dual-phase diffuse is adopted to accurately depict the evolution of the air–polymer interface, which is represented in terms of the phase field function, φ, as the following fashion:³⁵

where u is the fluid velocity, M is the fluid mobility (which determines the diffusivity), and G is the chemical potential. The second term on the left-hand side of the equation represents the convection flux. The right-hand term represents the diffusion flux.

The movement of the polymeric motion can be determined by the Navier–Stokes equations, which consist of momentum conservative and mass conservative equations, as follows:³⁶

where ρ and η are the density and viscosity of the fluid, respectively; p is the hydraulic pressure; ρg and f^st are the gravity and surface tension, respectively; and f^e denotes the electrohydrodynamic force composed of the dielectric force due to bound charges at the air–polymer interface and the Coulomb force due to space charges (only available in a leaky dielectric polymer).

The electric field in the air/polymer domain can be described by Maxwell equation as Gauss's law³⁷

∇·(ε₀ε_rE⃑) = ρ^e (3)

where ρ^e is the spatial density of free charges in a leaky dielectric liquid (which can be set to 0 in the perfect dielectric), ε₀ is the vacuum permittivity, ε_r is the relative permittivity of the problem domain (air and polymer), and E is the electric field. Here, the air and polymer involved in ESF-PP are both dielectrics (perfect or leaky), and the magnetic effect can be assumed to be negligible because the electric field is irrotational.³⁸ In subsequent, the electrohydrodynamic force f^e in eqn (2) can be determined via the following relationship³⁹where the first and second terms on the right-hand side are the contributions from the Coulomb force and the dielectric force, respectively.

Furthermore, the charge conservation law governing spatial charges motion, which is essential to determine the movement of the free space charges, especially at the air–polymer interface, is expressed by⁴⁰

where σ is the electrical conductivity of the leaky dielectric polymer. The second term on the left-hand side represents the transport of free charges by convection. The term on the right-hand side represents the transport by electromigration.

Based on the equations above, the progressive evolution of the perfect and leaky dielectric polymers in ESF-PP can be numerically obtained; here the electrical conductivity σ and the free charge density ρ^e can be set to 0, such that eqn (5) is eliminated for the perfect dielectric. The iteration of this coupled problem is performed using the finite element method in a commercial software, COMSOL Multiphysics v4.2. Once the phase-field function φ is obtained, the moving air–polymer interface can easily be identified by tracing a zero-value contour of the phase-field function or by simply color-mapping the phase-field function, thereby providing a step-by-step visualization of the polymer's deformation.

Fig. 2C and D demonstrate the polymeric evolution of the perfect and leaky dielectric polymers corresponding to the experimental results shown in Fig. 2A and B, respectively. For a perfect dielectric polymer, the prepatterned polymer will move directly upward, driven by the EHD force, until making contact with the template at a single point. Subsequently, the contact area between the template and the polymer increases, which can be attributed to the dielectrowetting phenomenon,^41,42 accompanied with the diameter of the pillar becoming larger and larger, finally leading to a nearly vertical structure, as shown in Fig. 2C. For a leaky dielectric polymer, the prepatterned polymer also moves upward pulled by the EHD force but not coming into direct contact with the template, whereas the polymer expands from the center of the pillar outward as it approaches the template, leading to a bulge at the top of the pillar prior to contact with the template, see Fig. 2D(i)–(iii). Finally, the bulging head of the polymer pillar comes into a surface contact with the flat template, instead of making point contact, resulting in a mushroom-like structure with a bulging head, as shown in Fig. 2D(iv). On the basis of the comparison of the progressive evolution, we conclude that the bulging head for the leaky dielectric polymer prior to making contact with the template determines the discrepancy in the polymer geometry between the perfect dielectric and the leaky dielectric polymer.

Fig. 2E demonstrates the polymer height versus the progressive time for the perfect and leaky dielectric polymers with process parameters identical to those shown in Fig. 2C and D, where the EHD force consists of the Coulomb force and the dielectric force for the leaky dielectric polymer and only the dielectric force for the perfect dielectric. For the same air gap, the perfect dielectric polymer needs a longer time to make contact with the template for the small EHD force. Additionally, there is a dramatic change in the curve of the perfect dielectric polymer height which can be attributed to the relationship between the EHD force and the surface tension. Initially, the EHD force is not sufficient to eliminate the influence of the surface tension due to a large air clearance between the template and the polymer protrusion, leading to a small curvature at the initial stage. As the polymer moves upward, the EHD force increases with decreasing air clearance, resulting in a large curvature as the polymer approaches the template. In contrast, the curvature for the leaky dielectric polymer is always large during the growing process because of the additional Coulomb force.

It is well known that there is a positive feedback effect between the polymer height and the electric intensity during EHD structure formation,⁴³ i.e., a strong electric intensity would be induced at a large polymer height and tend to pull the polymer upward to an even greater height, which would, in turn, induce a stronger electric intensity. It is this mutually positive feedback drives the polymer's upward growth until it reaches the flat template. In consequence, the EHD force for both polymers can be analyzed based on the electric intensity at the air–polymer interface at the initial forming stage, which is shown in Fig. 2F. The EHD force for the leaky dielectric is actually larger than that for the perfect dielectric because of an additional Coulomb force caused by the small amount of space charges inside the dielectric polymer. One interesting phenomenon shown in Fig. 2F is the peak in the electric field, which can be attributed to the corner effect of the electric field due to the initial shape of the polymer structure. However, the corner effect can be neglected because the region corresponding to the peak also has an extremely large surface tension due to the extreme curvature.

The bulging part on the top of the pillar for the leaky dielectric polymer shown in Fig. 2C can be further attributed to the accumulation of free space charges at the air–polymer interface, as shown in Fig. 3A, which shows the distribution of free charges in the polymer domain at different forming stages. Once a voltage is applied between the template and the substrate, the free charges begin to accumulate at the air–polymer interface. Additionally, more charges appear at the region with the larger electric intensity, see Fig. 3A(i). Within polymer movement, the free charges on the interface are not concentrated on one point but have a surface form, which tends to pull the polymer higher and to expand the polymer from the center outward, leading to a top surface that is not as sharp as that of a perfect dielectric, as shown in Fig. 3A(ii). As the polymer approaches the template, a nearly flat top surface of the pillar forms, at which the charges on the edge of the top surface will drive the polymer to move around driven by the Coulomb force, leading to a bulge and subsequently a surface contact between the polymer and the template, as shown in Fig. 3A(iii) and (iv). After the polymer makes contact with the template, the polymer begins to move along the template's surface under the effect of electrowetting,^44,45 in which opposite charges simultaneously appear on the bottom surface of the bulging head that would push the bottom surface downwards, resulting in a mushroom-like structure, see Fig. 3A(v) and (vi). The numerical evolution of the leaky dielectric polymer shows that the surface topography of the deformation is determined by the influence of the free space charges. That is, the actions of the free space charges cause the large head of the deformation, which can be further attributed to electrowetting caused by induced charges and the reverse motion caused by the opposite charges.

Fig. 3 (A) Progressive evolution of free space charges accumulated in the polymer domain corresponding to the case shown in Fig. 2D. (B) Accumulation of space charges at the air–polymer interface versus polymeric height in the case shown in (A).

In the forming process of the leaky dielectric polymer, free charges that are accumulated at the air–polymer interface change with variation of the polymer morphology, as shown in Fig. 3B, from which it can be seen that the free charges at the interface increase as the polymer moves upwards until a contact between the polymer and the template occurs, implying that an enlarged EHD force (due to the additional Coulomb force) could explain the curve of the leaky dielectric polymer shown in Fig. 2E. Once the polymer touches the template, the accumulation of free charges decreases sharply for two reasons. First, the opposite charges that appear on the bottom surface of bulging part could reduce the accumulation of net charge. On the other hand, some charges would be embedded at the polymer–template interface instead of at the air–polymer interface which may also decrease the net charge. Comparing the curve of the polymer height and the accumulation of free charges, the turning point of these two curves seems to be at the identical location, indicating that the free charges play an important role in pulling the dielectric polymer upward to touch the flat template, and thus, determining the final polymer height, i.e., the aspect ratio of the deformation.

The EHD force for the leaky dielectric polymer is known to be larger than that for the perfect dielectric, which provides a possible approach to increasing the aspect ratio by slightly increasing the electrical conductivity, i.e., transforming the perfect dielectric polymer into a leaky dielectric. Fig. 4 theoretically and experimentally demonstrates duplications on the leaky and perfect dielectric polymers with identical process parameters, namely, an initial height of the prepatterned polymer of 24 μm, a diameter of the prepatterned polymer of 15 μm, an air gap between the template and the substrate of 50 μm, and an applied voltage of 700 V. For the leaky dielectric polymer, the prepatterned polymer can be pulled upward to reach the template, driven by the EHD force, see Fig. 4A. This upward force consists of the Coulomb force and the dielectric force, and creates a structure corresponding to the initial geometry shown in Fig. 4B, in which the aspect ratio increases from an initial value of 1.6 to roughly 6. However, for the perfect dielectric polymer, using only the dielectric force generated at the air–polymer interface, the polymer cannot be driven to overcome surface tension and viscous force to move upwards. Therefore, the polymer moves lower and lower, leading to failure to form a conformal structure, as shown in Fig. 4C and D. As a consequence, it is easier to fabricate a structure with a high aspect ratio on the leaky dielectric polymer via ESF-PP, as compared to the perfect dielectric polymer, which can be attributed to the additional Coulomb force.

Fig. 4 Progressive development of leaky dielectric polymer (A) and perfect dielectric polymer (C) for an air gap of 50 μm, and the corresponding experimental results (B) and (D), respectively.

Since free charges in the leaky dielectric polymer play an important role in the progressive development of structures, the surface topography and the aspect ratio, it is necessary to explore the influence of the different electrical conductivities. Fig. 5A shows the polymer height versus the processing time with different electrical conductivities, in which the process parameters are identical to those in Fig. 4A and B, excluding the conductivity. The height of the polymer with a conductivity of 10⁻⁹ S m⁻¹ becomes smaller and smaller, resulting in a nearly flat surface that is similar to the case of a perfect dielectric polymer, indicating that the conductivity of 10⁻⁹ S m⁻¹ is too small to be able to generate sufficient EHD force to promote polymer motion. When the conductivity is increased to 10⁻⁷ S m⁻¹, the EHD force generated at the air–polymer interface is available to move the polymer upwards, leading to a structure with a high aspect ratio. If the conductivity is further increased to 10⁻⁵ S m⁻¹, the polymer can also be pulled to reach the template along with a phenomenon that the curve for conductivity of 10⁻⁵ S m⁻¹ coincides with that for 10⁻⁷ S m⁻¹, revealing that the higher electrical conductivity is not beneficial; instead, there exists a threshold value, which can be understood in terms of accumulation of free charges at the air–polymer interface as follows.

Fig. 5 (A) Polymeric height versus processing time with different conductivities. (B) Influence of polymer conductivity on the accumulation of free space charges at the air–polymer interface. (C) Final geometry of the polymer deformation with different conductivity.

The influence of the polymer conductivity on the accumulation of free space charges is shown in Fig. 5B, where the spatial integral is calculated at 10⁻⁷ s after applying the voltage. The integral of the free charges significantly increases with increasing polymer conductivity, finally approaching a constant. This phenomenon reveals that as the conductivity is increased, it is for charges easier to be pushed to the air–polymer interface to provide an electric field shielding. Once the conductivity exceeds the value at which it achieves electric field shielding, the electric field in the polymer is zero; there is no effect that increases the electrical conductivity, because the extra free charges cannot play a role, which leads to a threshold of electrical conductivity and can be as an explanation for Fig. 5A. Consequently, to obtain a polymer structure with a high aspect ratio, there is no need to continuously increase the electrical conductivity of the dielectric polymer for a larger EHD force. The desired structures can be fabricated at an electrical conductivity that is slightly larger than the threshold of the electric field shielding.

Fig. 5C demonstrates the influence of the electrical conductivity of the dielectric polymer on the polymeric deformation with the parameters of the cases in Fig. 5A and B. For a conductivity of 10⁻⁹ S m⁻¹, the EHD force cannot pull the polymer upward to the template because of the small conductivity value, leading to a nearly flat surface similar to that of the perfect dielectric polymer. With a conductivity greater than 10⁻⁹ S m⁻¹, the EHD force can duplicate a structure with a high aspect ratio; however, the contact area between the template and the polymer is different, as determined by the polymer conductivity. Specially, the diameter of the contact area of the deformation for conductivity of 10⁻⁸ S m⁻¹ is roughly 12.42 μm; diameters of 13.74 μm, 13.94 μm, 13.98 μm are obtained for the conductivities of 10⁻⁷ S m⁻¹, 10⁻⁶ S m⁻¹ and 10⁻⁵ S m⁻¹, respectively. With the increase of the electrical conductivity, the diameter of the contact area increases, and then, remains a roughly constant, which indicates that a threshold on the conductivity, as presented in the aforementioned discussion. When the leaky dielectric polymer makes contact with the template, the polymer will extend along the template's surface, driven by electrowetting, wherein a saturation phenomenon in the contact angle (i.e., the contact angle cannot be decreased further, even with a much larger electric intensity)^46–48 may be caused by electric field shielding. Additionally, electric field shielding is associated with electrical conductivity, leading to a limited maximum affection deduced from the electrowetting, i.e., a threshold of the conductivity on the contacting area. Thus, the diameter of the polymer tips, corresponding to the contact area, can be modulated via the electrical conductivity. Similar to the discussion of the aspect ratio, the threshold of the conductivity on the tips means that a conductivity that is slightly larger than the threshold can lead to the largest tip, removing the need to continuously increase the electrical conductivity.

Based on the discussion above, the polymer deformation can be modulated by adjusting the electrical conductivity. At a very low electrical conductivity, the dielectric polymer may not be pulled into contact with the flat template, resulting in a convex structure, which can be explored for applications in the microlens array.⁴⁹ In contrast, for a large electrical conductivity, a mushroom-shaped structure with a high aspect ratio can be fabricated; the aspect ratio and the tip diameter can be further controlled via the electrical conductivity, which can be widely used for superhydrophobicity,⁵⁰ dry adhesive,⁵¹ etc.

3. Conclusions

ESF-PP has attracted considerable attention for duplicating micro/nano-structures under the influence of a spatially modulated electric field incurred by the initial polymer morphology, leading to a structure that is identical to the initial geometry but with a higher aspect ratio. Thus far, most of the research into the dielectric polymers treated them as perfect dielectrics, neglecting the influence of the small amount of the free space charges inside, i.e., the EHD force generated at the air–polymer interface is the only dielectric force due to an inhomogeneous polarization, excluding the Coulomb force that is attributed to free space charges. In this paper, a comparison between a perfect dielectric polymer and a leaky dielectric polymer from experimental results and numerical simulations is performed to explore the role of free space charges on the progressive development. It can be found that the free charges in the leaky dielectric can generate mushroom-like structures, whereas the deformation of a perfect dielectric is nearly vertical. In addition, the EHD force for the leaky dielectric is larger than that for the perfect dielectric, indicating that the leaky dielectric polymer, which has free charges, is more suitable for the fabricating of a structure with a high aspect ratio. Finally, the influence of electrical conductivity on the behavior of the leaky dielectric polymer is discussed, which exhibits a threshold on the conductivity both in the forming process and in polymeric deformation.

Acknowledgements

This work was supported by the Major Research Plan of NSFC on Nanomanufacturing (Grant No. 91323303), the Funds of NSFC (Grant No. 51505370), the Natural Science Foundation of Shaanxi Province of China (Grant No. 2016JQ5033) and Open Research Fund of State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University (Grant No. sklms2015007).

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