ELECTROHYDRODYNAMIC PATTERNING OF

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ELECTROHYDRODYNAMIC PATTERNING OF POLYETHERSULFONE MEMBRANES Ali Malekpour Koupaei, Hadi Nazaripoor, and Mohtada Sadrzadeh Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b01948 • Publication Date (Web): 16 Aug 2019 Downloaded from pubs.acs.org on August 19, 2019

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Langmuir

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ELECTROHYDRODYNAMIC PATTERNING OF POLYETHERSULFONE

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MEMBRANES

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Ali Malekpour Koupaei†, Hadi Nazaripoor†, Mohtada Sadrzadeh*

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Department of Mechanical Engineering, 10-367 Donadeo Innovation Center for Engineering,

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Advanced Water Research Lab (AWRL), University of Alberta, Edmonton, AB, Canada T6G 1H9

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†Authors

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* Corresponding author: E-mail address: [email protected]

with equal contribution

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ABSTRACT

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Microstructuring the surface of membranes is recognized as one of the effective strategies to

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mitigate fouling phenomenon. Over the years, significant efforts have been undertaken to develop

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new techniques for altering the membrane surface topography at the micro and nanoscale.

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However, all the previously suggested approaches suffer from some serious drawbacks that impede

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their widespread implementations including, cost, time, and cumbersomeness. In this study, we

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show that the electrohydrodynamic (EHD) patterning process can be successfully adopted to form

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surface patterns on polyethersulfone (PES) microfiltration membranes. The linear stability

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analysis and non-linear numerical simulation is performed to theoretically predict the size of the

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created raised columnar structure (often called pillar). Contrary to the conventional EHD

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patterning process, the developed method works at room temperature and non-solvent induced

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phase separation is used to solidify the formed structures. The arrays of pillars formed on the

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membrane surface where their height and width tuned to be as low as 31 ± 5 μm and 98 ± 12 μm,

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respectively. It is demonstrated that fabricating surface-patterned PES membranes does not require

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sophisticated facilities and precise control of process condition using this simple mold-less

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method.

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Keywords:

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Membrane, electrohydrodynamic, micro-patterning, polyethersulfone, phase separation

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INTRODUCTION

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Micro and nanofabrication are best known as the driving force behind significant advancements in

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microelectronics, optoelectronics, novel sensors, and micro-/nanofluidic systems in the late 90’s

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1–4.

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tailor the surface topography of the polymer leading to membrane’s performance enhancement and

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lowering the operating cost in separation processes such as liquid-based separation, gas permeation

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separation

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properties of the membrane active surface, which is the main parameter dictating the interaction

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between the contacting phase and the membrane

More recently, the lithographic techniques have received attention in membrane technology to

5–9

and polymer electrolyte membrane fuel cells 12,13,

10,11.

In addition to physicochemical

the surface topography also affects 14,15.

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membrane wettability and the attachment of particles to its surface

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membranes not only benefits from an increased the interfacial/active surface area (an area that is

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in contact with the contaminated water) but also affected the hydrodynamic by forming secondary

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flow in the feed stream and creating more pathways for feed to a path through the membrane.

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Despite recent advancements in membrane material development, the fouling phenomenon is still

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recognized as a bottleneck for efficient water and wastewater treatment operations. As dissolved

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or suspended solids deposit on the membrane, another resistance to water transport is generated,

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and thus, a higher transmembrane pressure (TMP) will be required to recover the designed water

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flux. The increase in TMP ultimately leads to a substantial increase in the operating cost of

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filtration

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several studies have demonstrated that surface patterning could effectively improve the antifouling

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characteristics of membranes

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resistance of membranes depends on the type and application of the membrane whether it is used in liquid

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or gas filtration processes. For instance, in liquid filtration, the higher the surface area the higher is the flux

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but increasing the aspect ratio may lead to a very low pressure area in between pillars and thus poses a

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potential risk for the accumulation of foulants 8,30–33.

16–20.

Properly patterned

Targeting the interactions between the feed solution and the membrane surface, 21–29.

Effect of geometry of created patterns on the flux and fouling

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Phase separation micro-molding (PSµM) 9,34–39 and thermal-embossing 8,9,40 are two conventional

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approaches used to fabricate surface patterned membrane. Peters et al.

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patterns using a silicon wafer mold, manufactured by standard photolithography in a clean room.

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They cast the polymer solution on the mold and produced the final product after solvent

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evaporation and post overnight drying at 303 K in a vacuum chamber. Yong et al. 41 introduced a 2 of 25 ACS Paragon Plus Environment

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fabricated micro ridge

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soft-lithographic technique to make patterned photoresist master mold for the fabrication of PDMS

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replica molds. In their approach, the polymer solution was cast on the PDMS replica, and the stack

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was dipped into a non-solvent coagulation bath for several hours before the ultimate membrane is

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made through a non-solvent induced phase separation (NIPS). A novel soft-molding lithography

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approach was presented by Vogelaar et al. 35,36 where a thin membrane polymer solution was cast

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on the surface of a mold with microstructures made by micromachining. NIPS and thermally

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induced phase separation (TIPS) methods were employed to disturb the thermodynamic

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equilibrium of the solution and, hence, generate solidified membrane phase adopting the shape of

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the features on the mold. Culfaz et al.

34,39

produced patterned hollow fiber membranes with

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periodic round features using microstructured spinneret, fabricated by laser ablation. They applied

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the NIPS method at the coagulation bath temperature of 57 oC to generate the ultimate product.

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Ding et al. 42produced surface patterns using thermal-embossing nanoimprint lithography (NIL)

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process under high temperatures and pressures. In the NIL process, a viscous polymer film is

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squeezed into a rigid silicon mold while controlling its temperature above the glass transition. The

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ultimate membrane product then forms as the temperature declines to below the glass transition

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temperature.

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The need for clean room and the sophisticated micromachining facilities in addition to the

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requirement of precise control of fabricating conditions, such as temperature and pressure, renders

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the abovementioned novel techniques cumbersome, expensive and time-consuming. Furthermore,

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the number of materials that can successfully be used in each method is limited. Electrically

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induced patterning (EIP), or electrohydrodynamic (EHD) patterning technique, however, offers a

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cheaper, easier and faster soft-lithographic approach that can be implemented at room temperature

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and pressure without the need for any sophisticated facility. Over the past few decades, there has

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been the extensive dedication of studies proving the merit of the EHD method 43–48. In this method,

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a molten polymer film, at a temperature above the glass transition temperature of the polymer, is

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sandwiched between two electrodes while leaving a gap for air, as bounding layer. The electrodes

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are separated by an electrically insulating material (see the schematic shown in Figure 1(a)).

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Application of a direct current (DC) voltage to the electrodes imposes an electric field normal to

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the polymer film. The difference between the electrical properties of the liquid film and the

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bounding air layer gives rise to a net electrostatic force at the air/film interface due to the Maxwell

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stress 49. This force triggers the instabilities in the film leading to the interface deformation and 3 of 25 ACS Paragon Plus Environment

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pattern evolution. On the other hand, capillary and viscous forces perform against these

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instabilities and tend to flatten the surface. When the net electrostatic force outweighs these

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damping effects, growing features will commence emerging at the interface. Pillar formation using

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EHD is considered as a multi-stage process which starts with a nucleation stage followed by

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growth stage. The growth stage includes first an increase in the pillar length until it touches the

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top surface, second electrowetting with a radial growth of pillars after the contact, and finally a

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stationary stage without further growth in size47,48,50,51.

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Eventually, the created features will be solidified by cooling down the system to room temperature.

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Here we present a modified approach, based on the conventional EHD method, to produce porous

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polyethersulfone (PES) membranes, with surface patterns ranging from 90 to 130 microns, while

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the whole patterning process is conducted at room temperature and pressure. Our approach is fast,

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reproducible, and practical at room temperature without a need for any temperature and pressure

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control. To the best of our knowledge, there is no such technique employed for membrane surface

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patterning in the literature. First, a theoretical analysis of the phenomena is provided where the

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physics of the EHD pattern evolution is explained in detail. Subsequently, the fabrication process

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of the emerging microstructures is illustrated, which includes temporal pattern formation, as well

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as the phase separation stage and the final solidification and conversion of the liquid film into a

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porous membrane.

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THEORETICAL SECTION

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In the EHD patterning process, like other self-organizing pattern formation methods, an external

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force only initiates the instabilities within the polymer film, and the resulting features are formed

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based on the competition between dominant wavelength for growing instabilities. The electrostatic

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force triggers the instabilities leading to interface deformation, whereas interfacial tension and

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viscous forces dampen the growth of instabilities to flatten the interface. The electrically induced

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instability generated in thin viscous film, when flat electrodes are used (having a homogenous electric filed),

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is indeed a long-wave mode of instability. The resulting low aspect ratio pillars (In both simulation and the

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experimental observations) also confirms the validity of long-wave approximation assumption. It should be

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noted that the final formed pillars are the combination of EHD instabilities where the initially flat film

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deforms until it reaches top electrode followed by the electro-wetting of top electrodes until it balances

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capillary force, which opposes the wetting 47,52,53.

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The spatiotemporal evolution of the interface, h(x,y,t), in the long-wave limit is governed by the

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thin film equation, which is a 4th order nonlinear partial differential equation. 3μ(∂h ∂t) + ∇.(h3∇P) = 0

(1)

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In the derivation of eq. (1), it is assumed that polymer film is Newtonian and incompressible and

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boundary conditions are a no-slip condition on the walls, and no penetration on the interface as

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two media (polymer-air) are immiscible. In thin film equation, the first term 3μ(∂h ∂t) represents

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the viscous effect in the film dynamics. The normal component of the stress balance at the

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interface relates the total pressure, P, to the Maxwell stress (disjoining pressure) due to transverse

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electrostatic field, the Laplace pressure (conjoining pressure) due to curvature, and the

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intermolecular pressure (conjoining pressure) as follows, (2)

P = γ∇2h ― ϕ 10

The Laplace pressure (the first term in P) is a result of an interfacial tension, γ , and local

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curvature of the interface which tends to minimize the interface area and the free energy of the

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system. The conjoining/disjoining pressure, ϕ, is defined as the summation of intermolecular

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interaction pressure, ϕin, Born repulsion pressure, ϕBr, and electrostatic pressure, ϕel. The van

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der Waals interaction are included for the apolar interactions between the electrodes and the

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polymer film 54,55 via ϕin. The van der Waals interaction pressure is defined as ϕvdW = Al 6πh3

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+ Au 6π(d ― h)3 , Al and Au are the effective Hamaker constants for the lower and upper

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electrode, respectively. The Hamaker constant depends on the type of materials used for

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electrodes and polymer. The Born repulsive force with a cut-off distance of l0 = 5 nm is defined,

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ϕBr = ―8Bl h9 + 8Bu (d ― h)9, to avoid singularity in van der Waals force as interface height

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approaches to zero, h→0, under the dewetting condition or to d, h→d, in case of film touching

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the top electrode. Details about the derivation steps are available elsewhere 51.

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The electrostatic pressure is the most dominant component in conjoining/disjoining pressure and

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is found from Maxwell stress, 𝐌𝐢 = εiε0[𝐄i𝐄i ―0.5𝐈𝐄i𝟐] acting on the interface

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denotes each layer (polymer film and air). Term 𝐄 is the electric field vector and defined as the

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gradient of electric potential (𝐄 = ― ∇V),ε is the relative dielectric constant of film and ε0 is the

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vacuum dielectric constant. Under the long-wave limit approximation and for the perfect


49.

Subscript i

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dielectric liquids, the net electrostatic pressure acting on the interface (at each local height of h)

2

is obtained as follows, (3)

ϕel = ―0.5 εpε0(εp ― 1)Ep2 3

where, Ep is the electric field (normal component) applied to the polymer film. For the air-polymer

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bilayer system, it is given byEp = {V [(1 ― εp)h + εpd]}. The EHD patterning process is modified

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in the current study by adding an extera lower electrically conductive layer to lower electro-

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chemical reactiong between the electrode and polymer film. In the modified system, glass-air-

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polymer (trilayer) system, the applied electric field to the polymer film is found as Ep =

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{V [(1 ― εp) h + εp d ― εp εg ―1 l]}. εp is the polymer dielectric constant, εg is the glass dielectric

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constant, V is the applied voltage, d is the electrode separation distance, and l is the glass layer

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thickness. In the experimental section, further explanation will be provided regarding this

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modification in the EHD process. In the theoritical and numerical section, we present the results

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for the equivalent bilayer system (V = Veq) with similar initial electric field applied to the polymer

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film (Ep at h(x,y,t = 0) = h0). Veq =

[

(1 ― εp)h0 + εpd (1 ― εp) h0 + εp d ― εp εg ―1 l

]

(4) V

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The linear stability analysis (LSA) is performed to find the characteristic wavelength, λc, for the

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growth of instabilities based on the initial linear stage of interface deformation. It has been shown

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that LSA predicted wavelength is a good estimate for the size of the pillars forming on the film 56

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. In LSA, the local interface height of h in eq. (1) is replaced with a small sinusoidal perturbation

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around the initial base state as h = h0 + ξeiκ(x + y) + St. In this relation, h0 is the mean initial film

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thickness, ξ is the small amplitude, κ is the wave number, and S is the growth coefficient. The

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growth coefficient S shows how fast the instabilities grow or damp over time. The induced

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instabilities on the interface, have a range of wavenumbers (corresponding to a wavelength) that

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grow with different rate. The fastest growing wave, which governs the interface deformation and

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eventually pattern formation, is found by the dominant wavenumber. In the electrically induced

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instabilities of thin films, the electrostatic force has the most contribution to the growth of

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instabilities compared to other intermolecular interaction forces acting on the film such as polar

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and non-polar interactions. Therefore, the term conjoining/disjoining pressure, ϕ is set to ϕel in 6 of 25 ACS Paragon Plus Environment

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the LSA calculations. By neglecting the resulting nonlinear terms a dispersion, relation is found

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as, S(κ) +

3

[

h03κ2 3μ

2

γκ ―

εpε0(εp ― 1)2Veq2

]

(εpd ― (εp ― 1)h0)3

(5) =0

and the dominant wavenumber which corresponds to the fastest growing wave is found by setting dS

0.5εpε0(εp ― 1)2Veq2

2π

4

as κmax = dκ = 0

. Accordingly, the characteristic wavelength is given by λc = κmax

5

. Based on the LSA, increasing applied voltage, increasing the film thickness at a constant

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separation distance, and utilizing more conductive polymers results in a smaller λc. Recent studies

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on the EHD pattern formation process have shown that the annealing temperature where the pillars

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form also affects the size and distribution of pillars

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information about the growth rate of instabilities in the EHD patterning process, the pattern

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deformation undergoes nonlinear stages that could only be found by direct solving of eq. (1). The

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final shape and size of features forming in EHD process is found to be sensitive to initial filling

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ratio parameter (ratio of initial film thickness to the separation distance), conductivity of polymer

13

film, interfacial tension, and the applied voltage. In short, numerical simulation is required to find

14

the dynamics and spatiotemporal behavior of the polymer film under an applied electrostatic force.

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Following assumptions are made for the numerical simulations: (i) the edge effects are negligible

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in the pattern formation and their size, (ii) the final formed patterns have low aspect ratio (low

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height to width ratio) following the lubrication approximation used in deriving the thin film

18

equation, (iii) the pattern formation process is short enough to have isothermal condition in thin

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film with negligible evaporation effects.

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The thin film equation is expanded and normalized using scaling factors found through the LSA

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as follows,

γ(εpd ― (εp ― 1)h0)3

47.

Although the LSA provides valuable

∂ 3∂Ψ ∂2H ∂2H ∂H ∂ 3∂Ψ H H + + =0 ; Ψ=( 2+ )―Φ ∂X ∂Y ∂Y ∂τ ∂X ∂X ∂Y2

[ ] [ ]

(6)

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where nondimensional height is H = h(x,y,t) h0, nondimentional time is τ = t ts, nondimentional

23

length is (X, Y) = (x, y) ls, and nondimentional conjoining/disjoining pressure is Φ = ϕ ϕs. The

24

normalizing factors are given by,


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γh03

ts =

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(7)

0.5εpε0(εp ― 1)Veq2

ls =

ϕs =

3μγh03

(8)

0.5εpε0(εp ― 1)Veq2 0.5εpε0(εp ― 1)Veq2

(9)

h02

1

EXPERIMENTAL SECTION

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Materials and Methods. Indium tin oxide (ITO) coated microscope glass slides (50 × 75 × 1.07

3

mm) where purchased from Delta Technologies (Loveland, CO, USA). Polyethersulfone (PES)

4

(Mw: 58,000), was purchased from BASF (Wyandotte, MI, USA). Polyvinylpyrrolidone (PVP)

5

(Mw: 360,000), and N-methyl-2-pyrrolidone (NMP) were procured from Sigma-Aldrich.

6

The solution of PES (13 wt%) was prepared by dissolving PES powder in NMP and mixing

7

overnight at room temperature. To facilitate wettability of the polymer solution, 2 wt% PVP was

8

later added to the solution. The density of the polymer solution was calculated as 1.2 gr/cm3 by

9

measuring the weight of a known volume of the solution. The air-polymer solution interfacial

10

tension was measured, using a Krüss drop shape analyzer, as 32.92 ± 0.29 mN/m. The experimental

11

cell (the schematic is shown in Figure 1(a)) was fabricated by using two pre-cleaned ITO coated

12

glass slides as electrodes. The electrodes were washed with Acetone (Sigma-Aldrich) and DI-

13

Water multiple times and dried by Air prior to use. A thin liquid film of PES solution was coated

14

on the ITO-coated side of the slide at 4000 rpm for A) 40 s and B) 50 s using a spin coater

15

(Specialty Coating Systems, Spincoat G3P-15), forming the bottom (anode) electrode. Given the

16

density of the solution, the surface area of the film (3.5 × 3.5 cm2), and the mass difference before

17

and after the film coating stage, the thickness of the film was determined to be ~9.5 µm and ~7.5

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µm for A and B spin coating processes, respectively. The other ITO-coated slide was used as the

19

upper (cathode) electrode on top of the thin film. The electrodes were separated by a 25 µm-thick

20

plastic separators. In this study, we minimized the difference between electrode separation

21

distances over the domain to avoid the wedge-shaped electrode effects on the resulting patterns.

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The wedge-shaped electrode provides laterally varying electric field over the domain, which

23

causes the instability to sweep across the sample. This phenomenon results in different instability 8 of 25 ACS Paragon Plus Environment

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stages and thus creates larger pillars (both height and size increases) at edges with higher electrodes

2

distance57.To prevent optical and electrical degradation

3

coating at the cathode side, in contact with the PES/PVP/NMP solution, the upper electrode was

4

inverted to have the ITO-coated side facing away from the film. A video capturing chemical

5

reaction between the polymer solution and the ITO-coated electrode and its optical degradation

6

upon application of voltage is provided in the supplementary material. The electrodes were

7

connected via Copper tapes to the DC power supply (Stanford Research Systems, Inc.). Features

8

were visualized by Axio CSM 700 optical confocal scanning microscopy (Carl Zeiss) equipped

9

with 5X and 10X lenses as objective and eyepiece, respectively, and color detector with digital

10

confocal diaphragms (Figure 1(b)). The dynamics of the patterning process was recorded by the

11

freely distributed screen capture software, oCam (http://ohsoft.net).

58–60


of the chemically sensitive ITO

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Figure 1. Schematic of (a) experimental cell and (b) the confocal microscopy setup used in this study (Note:

2

components are not scaled).

3

RESULTS AND DISCUSSION

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Surface Pattern Formation. Application of DC power to the upper and lower electrodes

5

generates a net electrostatic force at the polymer solution-air interface as a result of a mismatch in

6

the electrical conductivity of the sandwiched layers. The net electrical force unbalances the

7

interface while the surface tension polymer viscosity tends to flatten the interface. When the

8

electrical force exceeds, electrohydrodynamic (EHD) instabilities grow at the surface of the thin

9

film leading to a pattern formation. Figure 2A-E show two-dimensional (2D) real-time evolution

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progress of the polymer film (case A: film with ~9.5 µm thickness), visualized by optical confocal

11

microscopy, after a 2100 DC voltage was applied to the cell. The air gap and the thick glass slide 10 of 25 ACS Paragon Plus Environment

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shield between the upper electrode and the polymer solution film (thickness: 1070 µm) lead to a

2

large decline of electric field strength; and hence, the associated Maxwell stress 49,55 applied to the

3

interface. Therefore, applying lower voltages, surface tension at the air-polymer solution interface

4

would flatten out any protruding feature. To compensate for this, a large voltage is needed to

5

induce features and produce surface patterns. In the theoretical section, further details will be

6

provided to find the net electric field applied to the polymer film in the EHD patterning process.

7

The initial electrical field strength at the polymer solution-air interface in case A was calculated

8

as 0.41 V/µm. According to our observations and analysis, application of such a high voltage did

9

not trigger electrical break-down of either air or the polymer in our experiments. In Figure 2A,

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three randomly distributed EHD-induced pillars can be seen which start to form only after 1.56 s.

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At the same time, bicontinuous diagonally-oriented parallel patterns were also observed at other

12

locations (Figure 2B). The continuous supply of mass from regions in the proximity of the formed

13

protrusions gives rise to the further growth of pillars, hence a more discernible field of view of the

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patterns19 ms later, captured in Figure 2B. As the regions with higher heights experience larger

15

upward pull, they grow faster than nearby regions leading to their shrinkage at the expense of the

16

raising ones. This ultimately results in a discrete periodic distribution of individualized pillar-shape

17

microstructures. Black arrows in Figure 2C and Figure 2D demonstrate the disappearance of the

18

initially grown pillars compensated for the growing ones indicated by red arrows. In Figure 2B,

19

we can see seven of these pillars that have made it move further towards the upper bounding

20

electrode until contacting the electrode. There are two main stages in the pattern formation; first

21

is when the interface deforms and moves further towards the upper bounding electrode until

22

contacting the electrode. Second is from this stage onward as the polymer solution creeps along

23

the wettable surface of the electrode. The second stage has a slower rate compared to the initial

24

growth of pillars as demonstrated by the rate of the liquid surface area spreading with time in the

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top left inset in Figure 2G. The initial abrupt surface area growth in the first half second after the

26

touch is due to the surface tension in effect between the glass and polymer solution attempting to

27

reach the corresponding surface contact angle. We measured the contact angle as 31.7° using a

28

Krüss drop shape analyzer. After this stage, the growth will be slower that corresponds to the

29

upward flow of mass supported by the electrohydrodynamic force in action. In Figure 2F, a single

30

raising conic pillar can be seen moments before touching the upper electrode. Reflected light

31

intensity versus horizontal length is plotted in the bottom middle inset in this figure. As the light 11 of 25 ACS Paragon Plus Environment

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1

reflected from the in-focus peak of the pillar passes through the detector pinhole, it appears brighter

2

than the surrounding raised regions, within 50 µm radius, where the detected light intensity is

3

lower due to being out of focus 61.

4

5 6

Figure 2. Optical images of EHD surface-patterned membrane produced after voltage application. Initial liquid film

7

composition: PES 13%, PVP 2% in NMP solvent. Electrode distance: 10 µm, Applied voltage: 2100 DC. A-E) in-situ

8

visualization of the growing features with time - scale bar: 200 µm. F) demonstration of a growing pillar before

9

touching the surface of the upper electrode - scale bar: 50 µm. G) surface area spreading rate with time H) top view

10

showing the collection of grown pillars - scale bar: 100 µm.

11 12

Continuously applying the voltage to the cell results in the expansion of pillars by the material

13

supply from either the residual layer at their base or from a nearby pillar. This will cause their

14

boundaries to overlap, and subsequently, two side-by-side pillars will merge into one bigger pillar

15

which is referred to as Ostwald ripening

16

demonstrate five instances of these coarsening events. Circular black regions in Figure 2H

17

illustrate the optical image of polymer solution pillars in contact with the upper electrode 260 s

18

after voltage application. There were five instances of coarsening after 47 s in case A) compared

19

to only two after 260 s in case B. Evidently coarsening mechanism is slower for case B) with a

20

lower filling ratio of 0.3 versus 0.38 in case A. The filling ratio is defined as the ratio of initial film

21

thickness to upper-lower electrode separation. This pattern is in agreement with Wu et al. study of

62.

Black arrows in the field of view, in Figure 2E,


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1

coarsening in the electrohydrodynamic patterning of thin polymer films62. Brighter regions in

2

Figure 2H are the residual layers at the base of the pillars. Some of these regions demonstrate

3

fringe patterns that are characteristics of thin-film interference phenomena in effect, proving

4

nanometer to micrometer length scale of the thickness of these layers after losing mass at the

5

expense of the grown pillars.

6 7

Mathematical Simulation

8

Here, the spatiotemporal evolution of interface (transient behavior in both linear and nonlinear

9

stages of deformation) is investigated using a numerical solution of the normalized thin film eq.

10

(6). The second order central finite difference scheme is used to discretize the spatial derivatives

11

leading to sets of coupled differential algebraic equation (DAE) in time. The DAEs are solved

12

using an adaptive time step solver of DASSL available in the library of SLATEC63. In all the

13

numerical simulation results, a square domain (with a size of 64Λ2) with periodic boundary

14

condition on the edges are used. The domain length is also defined based on the LSA analysis

15

where Λ = ls is the normalized characteristic wavelength. To initialize the interface deformation,

16

a small random perturbation is used while the volume of fluid is conserved. Details about the

17

numerical scheme are available elsewhere51.

18

Based on the electrostatic component of conjoining/disjoining pressure (eq. (3)), thicker regions

19

are exposed to higher electrostatic force compared to the thinner areas of the film. Therefore, the

20

interface is pulled toward the top electrode at the ridges while the valleys are forced downward to

21

conserve the mass continuity. This results in fluid flow from the thinner region to the thicker

22

regions and often called negative diffusion. In the present work, we examined the pattern formation

23

process for two sets of the geometrical condition, (1) h0 = 7.5 μm, d = 25 μm (shown in Figure

24

3(a)-(c)), (2) h0 = 15 μm, d = 25 μm (shown in Figure 3(d)) while keeping other properties the

25

same. List of all constants and parameters used in the simulation are presented in Table 1.

λc

26

Table 1: Constants and parameters Parameter

Value

dielectric constant of polymer solution, εp

30 [-]

dielectric constant of glass, εg

7 [-]


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Page 14 of 37

8.854 × 10 ―12 F m-1

dielectric constant of vacuum, ε0 Born Repulsion cut off distance, l0

0.4 ― 1 μm

electrodes separation distance, d

20 ― 150 μm

Initial thickness of polymer film, h0

5 ― 100 μm

glass layer thickness, l

1070 μm

Hamaker constant, A

―1.5 × 10 ―19 J

applied voltage, V

2100 V 365 × 10 ―3 Pa s

dynamic viscosity, μ Initial film thickness, h0

7.5 ― 36 μm

separation distance, d

20 ― 150 μm

number of grid points in NS, nx = ny

121 ― 171

1 2

Time evolution of electrically induced instabilities and the pattern formation are presented using

3

3D and 2D snapshots of the interface height profile in Figure 3. Thes results show all the

4

subsequent steps in pattern formation and possible pattern features in the EHD technique. The

5

initial rearrangement of instabilities leads to low amplitude ridges and valleys (image a(i) and τ1

6

in image (b)). Next, fragmentation occurs in ridges and isolated cone shape pillars form (image

7

a(ii), τ2 and τ3 in image (b)). Height of pillars then increases due to negative diffusion of fluid

8

from lower thickness to the thicker region until they bridge the two electrodes (image b(iii) and τ4

9

in image (b)). After reaching the top electrode the contact area increases and columnar shape pillars

10

form (τ5 in image (b)). The pillar formation is finally continued in other areas as time passes (image

11

a(iv)). To elucidate the progress and amplification in electrically induced instabilities in both linear

12

and nonlinear stages of interface deformation, the maximum and minimum interface height is

13

tracked over time and shown in the image (c). Despite the slow initial deformation of the interface,

14

the nonlinear stages of pillar formation (from isolation to reaching the top electrode) is shown to

15

be a relatively fast process.

16


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Figure 3. a(i-iv) and d(i-iv) the 3D snapshots of the interface height profile, (b) 2D height profile showing the single

3

pillar growth, (c) maximum and minimum interface height profile versus time

4 5

The LSA analysis predicted that using thicker films, and higher filling ratio results in smaller size

6

pillars. Hence, we increased the film thickness from h0 = 7.5 μm to 15 μm while keeping the

7

electrode distance constant. Based on the LSA, λc decreases from 192.08 μm to 141.45 μm by

8

increasing the film thickness from 7.5 μm to 15 μm Although the nonlinear simulation results show

9

similar stages of pillar formation for the thicker film, the created pillars have a strong tendency to

10

merge, resulting in larger pillars over time. This merging phenomenon, so called coarsening, are


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1

marked using dashed squares and circles in images d(i-iii). At early stages of coarsening, pillars

2

with the same size are merged (d(i) to d(ii)) due to the mechanism of the collision of pillars. At

3

later stages, smaller sized pillars are merged to the larger ones through the Ostwald ripening

4

mechanism62. This merging of pillars, lowers the surface area of the features and leads to the lower

5

energy of the system, which is more stable from a thermodynamic standpoint64. The coarsening

6

mechanism is found to be more dominant for higher filling ratios. This mechanism leads to the

7

formation of larger sized pillars despite the LSA predictions. Meanwhile, it lowers the

8

predictability of the size and shape of the created features during the EHD process.

9

As shown in Figure 3, increasing the filling ratio has led to the formation of coarse and poly-

10

dispersed pillars or bicontinuous features (a combination of ridge and valleys). In the EHD-

11

induced pattern studies, h0/d = 0.5 is found to be a critical filling ratio with the systems having h0/d

12

>0.5 merely create pillars53. In our earlier study, we showed that this threshold also depends on

13

the relative dielectric constant of polymer film and the bounding layer65. Our numerical simulation

14

results show that (see Figure 4), based on the current experimental condition εp = 30, the optimum

15

range of filling ratio, that leads to stable pillar formation without a sacrifice in their size, lies within

16

the range of 0.3 < h0/d < 0.4.

17

The size of pillars formed in experiments (EXP) is compared with the numerical simulation (NS)

18

and the LSA predictions for λc and two sets of d =25 μm and d =114 μm in Figure 4. The effects

19

of electrodes separation distance and the filling ratio on the initial electric field applied to the film

20

and consequently, the feature size are also investigated. Lowering the size of the system (smaller

21

d), results in a higher initial electric field and the net electrostatic force (based on eq. (3)) applied

22

to the polymer film. As a result, the LSA predicts smaller characteristic wavelength for the growth

23

of instabilities as the size of system decreases which is shown for two cases of d =25 μm (solid

24

line) and d =114 μm (dash-dot line).


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1 2

Figure 4. Variation of characteristic wavelength, λc, (left axis) and the electric field applied to the polymer film at the

3

initial stage (right axis) for different filling ratios, h0/d. Linear stability analysis (LSA), numerical simulation (NS)

4

predictions and experiment (EXP) results (before solidification stage) comparison for two separation distances of

5

d=114 µm and d = 25 µm

6 7

Keeping the separation distance unchanged and increasing the initial film thickness (increasing the

8

filling ratio) also leads to an increase in the applied electric field (an electrostatic force) and a

9

decrease in λc predicted by LSA. However, both NS and EXP results concretely confirmed that

10

having a thicker film leads to the formation of larger pillars in the EHD patterning process as the

11

formed pillars strongly tend to merge at the early stages of the formation. We also found that the

12

LSA and NS predicted values for the size of pillars are in closer agreement with EXP data when

13

the film thickness and electrodes separation distance are smaller as shown for the case d =25 μm.

14

Membrane Formation. To produce the ultimate membrane product, we employed NIPS

15

technique

16

surface patterned polymer solution film. Due to the small length scale of the air gap in this cell and

17

the high surface tension of water (72 dynes/cm at 25°C), according to the Laplace–Young equation

18

(∆P ∝ σ/h), capillary pressure will be the main driving force to flood the cell. Furthermore, since

66

by injecting deionized water into case B) cell compartment that now contains the


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1

the cell is maintained horizontally, gravity will not influence the flooding event. Using a micro-

2

pipette, about 5 L of deionized water was put in contact with an open edge of the cell to trigger

3

the spontaneous surface-driven injection. Figure 5 shows bright field view of the cell seen from

4

the top, before (top left) and moments after (top right) water gets pulled into the cell. The water

5

interface can be distinguished as there is a difference in contrast between the two flooded and yet

6

to be flooded regions. To prevent electrical short-circuit due to the conductivity of deionized water

7

(5.5 μS/m at 25 °C) and the applied high voltage, the power source was turned off before the

8

flooding event. According to our observations no evidence of pillar deformation could be seen, as

9

a result of electrical power source disconnection, which is due to the wettable surface of the upper

10

electrode in contact with the polymer solution.

11

The ternary-system of polymer (PES and PVP), solvent (NMP), and non-solvent (water) undergoes

12

NIPS process 66 where the diffusional mass transfer of water into the polymer film and the miscible

13

NMP into water changes local PES composition and ultimately leads to the formation of a

14

solidified rigidly interconnected network of porous polymer precipitate. The polymer precipitation

15

was accompanied by a strong decline in the reflected light intensity. Figure 5 (top middle and right)

16

demonstrates the solidified pillars in the flooded regions. Once the region of interest was completely

17

flooded with water, its bright field view was further processed by an image processing software,

18

ImageJ (https://imagej.nih.gov), to calculate size distribution of the pillars before flooding. As is

19

evident in the histogram in Figure 2H, the majority of pillar sizes are seen to be distributed between

20

160 and 170 µm, whereas after the phase separation stage their sizes shrink to between 100 and

21

110 µm range in Figure 5 (top right) histogram. This size shrinkage might be caused by the flow

22

of non-solvent around the pillars during the capillary induced flood, as is evident by the dark

23

stream traces downstream of pillars in Figure 5 top middle. The polymer-rich phase is probably

24

washed away by the bulk of capillary flow as the NIPS process progresses. Analyzes of the

25

waterfront line between Figure 2H top left and right reveals that the non-solvent flows at

26

approximately 3830 µm/s velocity imposing strong hydraulic drag on the pillars perimeter.

27

However, the overall arrangement and configuration of pillars stayed, qualitatively, the same

28

before and after the phase separation.

29 30


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1 2

Figure 5. Top: phase separation of the polymer solution film by using water flooding - scale bar: 200 µm. Bottom

3

left: single pillar representation: scale bar: 50 µm. Bottom right: a diagram showing phase separation advancement

4

with time.

5

Figure 5 bottom left captures the dynamic transition of light intensity as NIPS progresses in a pillar

6

once flooded with water. Evidently, the onset of NIPS is at the perimeter where the nanoporous

7

solidified membrane starts to emerge inwardly towards the center of the pillar. The growth appears

8

to be symmetric and unbiased concerning the direction of the non-solvent flow, which is due to

9

the diffusion-controlled nature of NIPS process. The initial skin layer around the pillar is

10

mechanically robust enough to hold the internal polymer solution for the yet to be completed NIPS

11

in progress. The rate of the solidification of the pillar, as is captured by the diagram in Figure 5

12

bottom right, features a logarithmic shape since the skin layer acts as a nanoporous mass transfer

13

barrier to the exchange of solvent and non-solvent with the surrounding replenishing bulk. This

14

sluggishness in mass exchange will cause the local concentration of the solvent remains high,

15

delaying the demixing of solvent and polymer, and consequently leads to the formation of

16

symmetric nanostructure in the absence of macrovoids 67. Since the produced membrane was very

17

thin and structurally flexible, analysis of the cross-sectional regions of the polymer film was not

18

possible. Hence only the top surface of the membrane was analyzed, by SEM, in this study.


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Page 20 of 37

1

The developed membrane in the flooded cell was left in a water bath overnight to ensure a complete

2

phase separation before SEM analysis. The upper electrode was then carefully removed from the

3

cell, and the membrane was allowed to dry in ambient temperature. Figure 6 shows SEM images

4

of the formed membrane from different perspectives. Figure 6A is the top view of the membrane

5

showing the emerged pillar patterns (darker regions) that are formed on the base of the membrane

6

(brighter regions). Image analysis indicated that the majority of the pillar diameter sizes are

7

distributed between 100 and 110 µm as is plotted in the histogram. This is in agreement with the

8

dominant size distribution calculated after the completion of NIPS shown in Figure 5 (top right

9

image). The drying stage has not recognizably influenced the shape and size of the pillars. Figure

10

6B shows a close-up of a single pillar and the membrane base around it. The regions near edges

11

are seen brighter than the central regions due to charging phenomena in the microscopy. These

12

thin lateral edges are extended as a result of electrowetting of top electrode during EHD patterning.

13

Figure 6C demonstrates nanoporous structure as seen from above of the pillar depicted in Figure

14

6B. Accordingly, the interconnected pores are between 50 to about 400 nm in diameter which is

15

in the range of microfiltration membranes. It is worth mentioning that the pore size of the

16

membrane is affected by the influential parameters on the NIPS process. These parameters include

17

concentration of main polymer (PES here), molecular weight and concentration of additives, type

18

of solvent, and the temperature of non-solvent

19

the EHD process parameters, including applied voltage and electrode separation distance, to

20

initiate pillars. Due to the high sensitivity of the hybrid EHD/NIPS process, a systematic study

21

must be conducted to adjust both EHD and NIPS parameters in order to fabricate membranes with

22

different pore sizes. Figure 6D and 6E show oblique views of the surface patterns and a single

23

pillar. From these figures, it can be seen that the column of the pillar has a concave shape. During

24

the flood phase, the fluid velocity near the central region of the microchannel is higher compared

25

to the regions near the lower and upper walls due to no-slip condition at the surface which results

26

in the concave shape profile for the pillars. In fact, the higher velocity at the center could possibly

27

wash away more material by the non-solvent flow. Based on Figure 6E the height of the pillar is

28

calculated as ~31 µm that is about 6 µm larger than the 25 µm electrode spacer that would have

29

determined the ultimate height of pillars in this study. Because of the nano-meniscus formed at the

30

thin liquid film, removal of the upper electrode during SEM sample preparation imposes axial

68-70.

Changing these parameters requires altering


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Langmuir

1

stress to the pillars, and thus are stretched upward due to the plastic deformation of the

2

thermoplastic PES polymer.

3 4 5

The lateral surface of the pillar, however, manifests a different morphology, in Figure 6F,

6

compared to the top (Figure 6C ) and the base of the membrane in Figure 7. We can see a more

7

rather chaotic and stretched porous architecture that is due to the tangential drag imposed by the

8

ambient non-solvent flow during flood stage. For both the top and base of the pillar, the velocity

9

is nearly zero due to the no-slip condition and subsequently, the porosities are similar in shape and

10

order. Since Figure 7 was taken days after the other images, the analyzed membrane had become

11

drier, and as a result, more nano-cracks were emerged compared to the top of the pillar in Figure

12

6C.

13 14

Figure 6. SEM images of EHD surface-patterned membrane produced after phase inversion. Initial liquid film

15

composition: PES 13%, PVP 2% in NMP solvent. Electrode distance: 25 µm, Applied voltage: 2100 DC. A) top view

16

showing a collection of pillars - scale bar: 200 µm. B) top view showing a single pillar – scale bar: 20 µm. C) top view

17

showing the porous structure of the surface of a single pillar – scale bar: 400 nm. D) side view featuring a cylindrical

18

concave shape of pillars – scale bar: 20 µm. E) side view of a single pillar – scale bar: 20 µm. F) side view featuring

19

the porous structure of a single pillar – scale bar: 1 µm.

20


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1 2

Figure 7. SEM image of the EHD surface-patterned membrane produced after phase separation by water. Top view

3

showing the base of the membrane being porous – scale bar: 400 nm.

4 5

CONCLUSION

6

Herein we demonstrated, for the first time, that micron-sized surface patterns can be reliably

7

produced by an EHD process on nanoporous polyethersulfone membranes. We showed that

8

periodic circular columns of features could be produced within a few seconds without using a mold

9

at room condition, which makes it cheap and easy to implement. The real-time process of EHD

10

patterning, leading to the growth of pillars, and the membrane formation, through phase-separation

11

reactions, were also visualized using confocal microscopy. The size of these pillars ranged between

12

98 µm and 150 µm and their structures determined to be porous at the base, top, and perimeter.

13

The average pore size for this membrane was 155 ± 45 µm based on SEM results. Also, to capture

14

the dynamic evolution of the interface instabilities, a normalized thin film model is developed and

15

solved numerically. Qualitative agreement between the experimental and numerical was observed.

16

The filtration performance and fouling characteristics of such membranes will be described in the

17

following research.

18 19

Acknowledgment

20

Financial support for this work through Canada's Oil Sands Innovation Alliance (COSIA), Natural

21

Sciences and Engineering Research Council of Canada and Natural Resources Canada is gratefully

22

acknowledged.

23 22 of 25 ACS Paragon Plus Environment

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Figure 1. Schematic of (a) experimental cell and (b) the confocal microscopy setup used in this study (Note: components are not scaled). 280x343mm (96 x 96 DPI)


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Figure 2. Optical images of EHD surface-patterned membrane produced after voltage application. Initial liquid film composition: PES 13%, PVP 2% in NMP solvent. Electrode distance: 10 µm, Applied voltage: 2100 DC. A-E) in-situ visualization of the growing features with time - scale bar: 200 µm. F) demonstration of a growing pillar before touching the surface of the upper electrode - scale bar: 50 µm. G) surface area spreading rate with time H) top view showing the collection of grown pillars - scale bar: 100 µm. 424x203mm (96 x 96 DPI)


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Figure 3. a(i-iv) and d(i-iv) the 3D snapshots of the interface height profile, (b) 2D height profile showing the single pillar growth, (c) maximum and minimum interface height profile versus time 322x304mm (96 x 96 DPI)


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Figure 4. Variation of characteristic wavelength, λ_c, (left axis) and the electric field applied to the polymer film at the initial stage (right axis) for different filling ratios, h0/d. Linear stability analysis (LSA), numerical simulation (NS) predictions and experiment (EXP) results (before solidification stage) comparison for two separation distances of d=114 µm and d = 25 µm 238x165mm (96 x 96 DPI)


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Figure 5. Top: phase separation of the polymer solution film by using water flooding - scale bar: 200 µm. Bottom left: single pillar representation: scale bar: 50 µm. Bottom right: a diagram showing phase separation advancement with time. 405x238mm (96 x 96 DPI)


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Figure 6. SEM images of EHD surface-patterned membrane produced after phase inversion. Initial liquid film composition: PES 13%, PVP 2% in NMP solvent. Electrode distance: 25 µm, Applied voltage: 2100 DC. A) top view showing a collection of pillars - scale bar: 200 µm. B) top view showing a single pillar – scale bar: 20 µm. C) top view showing the porous structure of the surface of a single pillar – scale bar: 400 nm. D) side view featuring a cylindrical concave shape of pillars – scale bar: 20 µm. E) side view of a single pillar – scale bar: 20 µm. F) side view featuring the porous structure of a single pillar – scale bar: 1 µm. 265x133mm (144 x 144 DPI)


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Figure 7. SEM image of the EHD surface-patterned membrane produced after phase separation by water. Top view showing the base of the membrane being porous – scale bar: 400 nm. 242x166mm (144 x 144 DPI)


ELECTROHYDRODYNAMIC PATTERNING OF

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