Fabrication and characterization of non-linear parabolicmicroporous membranes

Pradeep Ramiah Rajasekaran a,1, Payam Sharifi b, Justin Wolff a, Punit Kohli a,n

a Department of Chemistry and Biochemistry, Southern Illinois University, Carbondale, IL 62901, USAb Department of Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, IL 62901, USA

a r t i c l e i n f o

Article history:Received 14 July 2014Received in revised form22 August 2014Accepted 24 August 2014Available online 16 September 2014

Keywords:Micro-opticsMicro-mirrorsNon-linear parabolic poresParabolic membranesPolydimethylsiloxane membranes

a b s t r a c t

Large scale fabrication of non-linear microporous membranes is of technological importance in manyapplications ranging from separation to microfluidics. However, their fabrication using traditionaltechniques is limited in scope. We report on fabrication and characterization of non-linear parabolicmicropores (PMS) in polymer by utilizing flow properties of fluids. The shape of the fabricated PMScorroborated well with simplified Navier–Stokes equation describing parabolic relationship of the formL–t1/2. Here, L is a measure of the diameter of the fabricated micropores during flow time (t). The surfaceof PMS is smooth due to fluid surface tension at fluid–air interface. We demonstrate fabrication of PMSusing curable polydimethylsiloxane (PDMS). The parabolic shape of micropores was a result of interplaybetween horizontal and vertical fluid movements due to capillary, viscoelastic, and gravitational forces.We also demonstrate fabrication of asymmetric “off-centered PMS” and an array of PMS membranesusing this simple fabrication technique. PMS containing membranes with nanoscale dimensions are alsopossible by controlling the experimental conditions. The present method provides a simple, easy toadopt, and energy efficient way for fabricating non-linear parabolic shape pores at microscale. Theprepared parabolic membranes may find applications in many areas including separation, parabolicoptics, micro-nozzles/-valves/-pumps, and microfluidic and microelectronic delivery systems.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

The fabrication of non-linear microporous membranes inex-pensively in large quantity using traditional fabrication techniquesis scarce in a literature [1,2]. There are a number of non-conventional polymer flow based fabrication techniques thatexploit intrinsic properties of materials [3]. These fabricationtechniques include capillary force based clustering [4], capillaryforce lithography [5], capillary nanomolding [6], microtransfermolding [7] and multiphase laminar flow patterning [8]. Capillaryforce has also been utilized for fabricating simple energy efficientfunctional devices [9,10]. The simplicity for these methods stemsfrom the fact that the driving force behind the fabrication andfunctionality is intrinsic in nature and little or no external energyis required for the fabrication of the micropores.

In this manuscript, we report design, fabrication, and charac-terization of high aspect ratio non-linear parabolic micropores

(PMS) with diameter in 150 mm–5 mm range. The fabrication forPMS utilizes polymer flow properties including capillary andviscoelastic under gravitational forces. We demonstrate that ourexperimental results corroborated well with a simple mathe-matical model derived from Navier–Stokes equation of a non-compressible fluid and finite element analysis. This fabricationtechnique is energy efficient, and the fabrication protocol does notrequire any special equipment. This method was extended tofabricate an array of PMS that were used as templates for thefabrication of replicated PDMS microporous membrane. The finalPMS membranes were independent of the roughness present inthe starting substrate used in the fabrication procedure. This is anadvantage for this fabrication method compared to many existingfabrication techniques where roughness in the mask or masterstructures can propagate to the fabricated daughter devices. Thesemembranes may find potential applications in separation, biology,material sciences, electronics and medicine. For example, thepolymeric microstructures can be used for the fabrication ofparabolic micro-optics including mirrors and lenses, nozzles forthe printing of biomolecules [11], fabrication of microfluidic andmicroelectronic delivery systems [12], polymeric mechanicalvalves and pumps [13], and micro-bioreactors to study cellcultures and cell behavior in microfluidic channels [14–16].

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/memsci

Journal of Membrane Science

http://dx.doi.org/10.1016/j.memsci.2014.08.0420376-7388/& 2014 Elsevier B.V. All rights reserved.

n Corresponding author. Tel.: 618 453 2895; fax: 618 453 6408.E-mail address: pkohli@chem.siu.edu (P. Kohli).1 Present address: Department of Chemistry, University of Florida, Gainesville,

FL 62901, USA.

Journal of Membrane Science 473 (2015) 28–35

2. Experimental section

2.1. Microfabrication procedure

Glass and aluminum substrates were used for the fabrication ofPMS. A Hitachi B13F 10 in. bench top drill press was used to drillpores (diameter �5 mm) in glass or aluminum substrate. Thediameter of the hole in the substrate dictated the base diameter ofPMS. Sylgard 184 (Dow Corning) composed of 10:1 ratio of Part A(prepolymer) to Part B (curing agent) was degassed for 15 min priorto its use in the fabrication process [17]. Fig. 1 schematically showsthe steps involved in the fabrication of PDMS PMS. The polymermixture (0.1–0.5 g) was then drop cast onto the glass/aluminumsubstrate (�25�25 mm2) with a hole in the center. The thickness ofthe drop cast PDMS film was in 200–1300 μm range. Whennecessary, the substrate was placed on a vortex instrument toproduce a uniform PDMS coating. The polymer was then placed ona hot plate at 70–120 1C for 1–3 min to enhance degree of polymer-ization. Next, a thin microscope cover glass (MCG) with an areadensity �0.33 g/cm2 was placed over the polymer film covering thehole in the substrate. The placement of MCG initiated polymer flowin two directions: a horizontal flow along MCG and a vertical flowalong the wall of hole. The solidification of polymer was accom-plished through application of heat resulting in the formation of PMS.Further, an array of parabolic PDMS micropores was fabricated byusing an array of holes drilled in the substrate. Finally, a PMS arraywas subsequently used as a master template to fabricate an array ofreplicated PDMS micropores.

2.2. Surface modification of PDMS for template synthesis

In order to facilitate the peeling of mold from the template,PDMS surface was modified with a fluorosilane. The original

protocol [18] was modified by replacing the silane with fluorosi-lane to fit our needs. A fluorosilane solution composed of 95% (v/v)ethanol/water, 4% (v/v) tridecafluoro-1,1,1,2-tetrahydrooctyl)triethoxysilane and 1% (v/v) acetic acid was used as a releasingagent in our experiments. The polymer–substrate assembly wasfluorinated by immersing it in this mixture for approximately onehour. The assembly was dried under argon, and then baked for10 h at 110 1C that facilitated peeling of the parabolic PDMSmembranes from PDMS master.

3. Theoretical consideration

Understanding physics involved in the fabrication processdemands utilization of powerful tools for solving multiple equa-tions in three dimensions at continuum scale. For present pro-blem, theory requires multiple parameters describing fluid flow,heat transfer, fluid–solid phase change, as well as free interfaceboundary conditions. The polymer in our system solidified whileflowing along surfaces of the substrates. We have modeled thepolymer flow using a simplified quasi-steady Navier–Stokes equa-tion of a non-compressible fluid moving between two parallelplates with “d” spacing [19–21]. Previous studies with a modifiedNavier–Stokes equation showed excellent agreement betweentheory and experiments for such systems [22–25]. This encour-aged us to utilize a similar theoretical approach for estimating thefluid flow behavior in our experiments.

The Navier–Stokes equation is of the following form [26]:

0¼ �δPδr

þμ∂2U∂z2

ð1Þ

where P, r, μ and U are PDMS fluid pressure, radius of the drilledhole in the glass substrate, viscosity of PDMS, and z-directionalvelocity of the PDMS fluid front respectively. Here, we assume thatinertial effects were negligible and that both the fluid properties(viscosity and density) and film thickness remained constantduring experiments. Although, the viscosity, density, and surfacetension changes in our experimental conditions, a simplifiedequation provides us useful information on the shape of the fluidfront. Fig. 2a provides a cross-section view of PDMS fluid, where δ,z and r(t) represent initial thickness of the film, gravitational forcedirection, and time-dependent radius of the top face of PMSrespectively. The top and side views of fluid flow are depicted inFigs. 2b and c respectively.

Balance of forces at the PDMS front required:

ΔPð2πrÞδ¼ γ cos θð2πrÞ ð2ÞTherefore, the pressure difference at the PDMS front yielded:

ΔP ¼ γ cos θδ

ð3Þ

where θ denotes the contact angle of PDMS on the glass. FromEq. (2), we obtained:

�∂P∂r

¼ �ΔPrðtÞ ¼ �γ cos θ

δrðtÞ ð4Þ

The velocity of the PDMS front u is obtained by substituting Eq. (3)in Eq. (4)

uðzÞ ¼Z 0

z ¼ δ

dudz

dz¼ γ cos θδμrðtÞ

zδ

� ��12

zδ

� �2� �

ð5Þ

We solved for the spatially averaged velocity (U) over the wholearea which is given by:

U ¼R 0A uðzÞdA

Að6Þ

Fig. 1. A two dimensional schematic of the structure evolution-time of thefabrication process. (a) PDMS (green) was drop cast around a pore drilled on glassor aluminum substrate (gray) and was kept on a heating block for partial curing/solidification. (b) and (c) show initial PDMS flow after placement of an MCG on thepolymer film. The blue and orange arrows show horizontal and vertical polymerflow respectively. The interplay of polymer flow along these two directions yieldedparabolic micropores in the polymer matrix. The base diameter (2R), tip diameter(2r), and height (H) of PMS are shown in (d). After complete solidification of thepolymer, MCG and substrate were removed to yield the desired PMS. A schematiccross section and SEM of these PMS are shown in (e) and (f) respectively. The shapeof PMS cross-section matches well with a parabolic curve (blue dashed line in f).An SEM micrograph of a free standing PMS without MCG and aluminum block isshown in (g). This structure was used as a template for the fabrication of daughterPDMS PMS replica (h). Scale bar is 1 mm. (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of this article.)

P.R. Rajasekaran et al. / Journal of Membrane Science 473 (2015) 28–35 29

where A¼2πr(t)δ. Solving Eq. (6) gave us the spatially averagedvelocity in terms of r(t) as follows:

U ¼ δγ cos θ6μrðtÞ ð7Þ

This velocity is defined as follows:

U ¼ �drdt

ð8Þ

Combining Eqs. (7) and (8) yielded the following equation for theinstantaneous radius of PDMS:Z r

RrðtÞdr ¼ �

Z t

0

δγ cos θ6μ

dt ð9Þ

Solving Eq. (9) for r(t) provided the position of the PDMS front at agiven time:

rðtÞ ¼ R2−δγ cos θ

3μt

� �1=2ð10Þ

Eq. (10) predicts a power relation between the distance movedby the PDMS front with time (t). r(t)–t1/2 relationship is parabolicin nature confirming that the polymer fluid movement followsparabolic form. Our experimental data corroborates well with Eq.(10) (Fig. 3).

4. Results and discussion

4.1. Mechanism of parabolic membrane fabrication

The underlying principle involved in the fabrication of PMSmembrane was discovered serendipitously when we observed acharacteristic polymer flow in our earlier experiments wherePDMS was used as an adhesive to sandwich two sheets of glasssubstrates [27]. This phenomenon was analyzed and exploredfurther to develop it into a simple microfabrication technique.

Fig. 1(a–e) shows a schematic of two-dimensional structureevolution-time for the PMS fabrication process. PDMS (green) wasdrop cast around a pore in a substrate (gray). The substrate waskept on a heating block for partial curing/solidification (Fig. 1a).Fig. 1b shows an initial PDMS flow pattern after placement of an

MCG on the polymer film. The placement of MCG initiated apolymer flow along two directions: horizontally towards thecenter of MCG (blue line, Fig. 1b) and vertically down along thepore wall (orange line, Fig. 1c). Thermally curing of the polymerprovided parabolic micropores whose shape is an interplay ofhorizontal and vertical polymer displacements at the time ofsolidification. The cured PMS implies that the polymer movementis negligible as compared to whole experimental time scale (manytens of seconds in duration). Thus, by controlling the polymer flowcharacteristics (capillary and gravitational forces) and curingkinetics (heating rate), the parabolic shaped micropores werecontrolled in size and shape (please see below). Cured PMS wereremoved to yield desired free standing membranes. The shapeof PMS matches well with a parabolic curve (blue, Fig. 1f).A schematic of cross-section and an SEM of the microstructuresdepicting parabolic pores are shown in Figs. 1e and f respectively.An SEM micrograph of a free standing fabricated PMS withoutMCG and substrate is shown in Fig. 1g. This PMS was used as atemplate for the fabrication of replicated PDMS membrane(Fig. 1h).

4.2. Flow characteristics of fluids

Prior to the placement of MCG, the polymer did not flow overthe edge of the macro-hole in the glass substrate. The polymerhowever formed a curved polymer–air interface at the edge of thehole due to surface tension of the polymer. The polymer move-ment along horizontal and vertical directions immediatelyoccurred after an MCG was placed on the polymer film. Theplacement of MCG provided at least two crucial forces for thepolymer flow. First, it provided a capillary force along the surfaceof MCG that induced polymer flow in the horizontal directiontoward the center of MCG. Second, a gravitational force wasinduced following MCG placement on the polymer film whichfacilitated a vertical polymer movement along the wall of the hole.The interplay between horizontal and vertical polymer flowsyielded PMS after polymer curing. The radius of smaller pore (r)of PMS depends on the polymer curing rate and horizontalpolymer flow rate. Whereas smaller r was formed with largehorizontal polymer flow rate and slower curing rate, the larger r isa consequence of increased curing rate and slower horizontalpolymer flow rate. The base radius (R) of PMS is relatively largeand is close in dimension of the hole diameter in the glass oraluminum substrate. Interestingly, Eq. (10) provides a convenientway of controlling r by controlling tpoly. r can be made in nano-meter scale (o100 nm) by appropriately controlling the experi-mental conditions (including polymer curing kinetics and MCGplacement timing on the polymer film). For example, a slowpolymerization kinetics can in principle provide non-linear para-bolic pores where complete solidification occurs when r is innanoscale dimension.

Two extreme cases for Eq. (10) exist that will result in eithercylindrical microstructures (r-R) or completely closed parabolicstructures (r-0). When t-0, r -R; i.e., the polymer flow in thehorizontal direction along MCG surface is insignificant relative todimension of R at the time of complete polymer curing. Thiscondition will provide cylindrical microstructures. In physicalsense, r-R can happen if the polymer curing rate is extremelyfast such that polymer front movement is extremely small ascompared to R. A similar situation that would result in r-R whenpolymer flow is dominant by gravity and that horizontal flow isnegligible. A second extreme case is noted when t-1, i.e.; in thiscase, the curing rate is extremely slow such that r becomesinfinitesimally small or r-0. These conditions will result incoalesce of the polymer front. This can happen for uncuredpolymer or for fluids that are not reactive and takes a long time

Fig. 2. Theoretical analysis of parabolic microstructure. (a) Schematically shows thecross-section of the parabolic microstructure formation. r(t) is the instantaneousradius of the pore. (b) Top view of figure in (a). (c) represents the movement of thepolymer front with film thickness (δ) and polymer front velocity (u(z)) parallelto MCG.

P.R. Rajasekaran et al. / Journal of Membrane Science 473 (2015) 28–3530

to cure (please see, for example, Videos 1 and 2 for uncured PDMS,glycerol, and water flow under similar experimental conditions).

Supplementary material related to this article can be foundonline at http://dx.doi.org/10.1016/j.memsci.2014.08.042.

Fig. 3a shows a relationship between flow distance (L) and time(tpoly) for three polymer films with different area densities (in mg/cm2)at 72 1C after MCG was placed on the film. L represents the fluid flowdistance after anMCGwas kept on the polymer film. The placement ofMCG on polymer film provided activation energy for the polymer toflow both horizontally and vertically directions. L was measured usingan optical microscope with a white light illumination by observing thepolymer front. The error in our measurements was optical diffractionlimit (ds¼2λ/NA�750 nm; where λ�600 nm is wavelength of thelight, and NA�0.4 is numerical aperture of the microscope) of themicroscope. The value of L ranges between 0 (no fluid movement) andR (fluid covered the hole). PMS consistently yielded curved innerconfiguration for which the experimental data points fit well with L–

t1/2 parabolic equation (Fig. 3a and Eq. (10)). The parabolic shape ofPMS was a result of polymer flow which can be represented usinga simplified Navier–Stokes equation. Fig. 3b shows an SEM of thecross-section of a PMS fabricated with smaller and larger diameters of2r and 2R respectively. The experimental cross-section profile of PMSmatches well with a theoretical parabolic curve shown by the bluedashed curve in Fig. 3b. Video V1 shows flow characteristics ofuncured PDMS under similar experimental conditions for the forma-tion of cured PMS. In this video, at �1 s after placement of MCG,PDMS is seen flowing towards the center of MCG. At �22 s in thevideo, the center of the hole is zoomed in to show the convergence ofthe uncured PDMS. In the fabrication protocol, heating of PDMSresulted in the solidification of PDMS in the center yielding parabolicmicropores. A careful observation of PMS cross-section in Fig. 3brevealed a slight deviation in shape from ideal parabolic equation nearthe bottom of the larger pore diameter (indicated by green arrows inFig. 3b). The deviation of experimental data from ideal parabolic curve

Fig. 3. PDMS flow and microstructure parameters. (a) A relationship between L and tpoly. L represents distance traveled by the PDMS in time (tpoly). (b) An SEM of the cross-section of a typical parabolic microstructure fabricated with smaller diameter, larger diameter, and apex angle of 2r, 2R and ϕ respectively. Scale bar is 1 mm. The blue dottedline in the figure represents a curve fit to a parabolic equation. The fit between the curve and micrograph of cross-section of the PMS clearly confirm its parabolic shape. (c) Atop SEM view of a typical PMS. (For interpretation of the references to false colors in this figure legend, the reader is referred to the web version of this article.)

P.R. Rajasekaran et al. / Journal of Membrane Science 473 (2015) 28–35 31

is not entirely clear at this point. It is attributed to surface-assistedcapillary action enhancing the fluid flow rate when fluid thickness issmall at the bottom of PMS. Due to surface tension of the polymer atpolymer–air interface, the fabricated PMS were shown to possesssmooth surfaces (see below). In the absence of air bubbles in pre-polymer and other defects due to curing and post-curing, the surfaceof PMS appeared smooth without defects. These smooth structures areuseful for the fabrication of high-quality optical components whereextremely smooth parabolic surfaces are sought.

Interestingly, the thickness of PDMS membrane was found toinfluence the polymer flow characteristics after an MCG wasplaced on it. For example, for a PDMS film with an area densityof 0.32 mg/mm2 deposited on a substrate took �650 s to flow ahorizontal distance of 3 mm along MCG after placement of an MCGon polymer membrane (red data points Fig. 3a). However, it onlyrequired �150 s to cover the same distance of 3 mm for a polymermembrane with an area density of 0.48 mg/mm2 (blue data points,Fig. 3a). The distance-time measurements were recorded by takingdigital micrographs of the polymer at different times. Apparently,under the same experimental conditions, a thicker prepolymerfilm on a glass or an aluminum substrate showed enhancedhorizontal flow rate after placement of an MCG on the membrane(Fig. 3a). A possible explanation for enhanced flow rate for thickerPDMS films on MCG is that increased prepolymer weight filmpossibly required a smaller activation energy to cross the poly-mer–air surface tension barrier resulting in increasedfluid flow rate after an MCG placement on the film. Thiswas confirmed experimentally in our experiments when thickmembranes (42 mm) over flowed glass edges without placementof MCG on it.

Fig. 4 shows the relationship between tMCG and r, where tMCG

represents time for which PDMS coated on a substrate wasallowed to polymerize before MCG was placed on PDMS film.In other words, tMCG is a measure of polymer viscosity. WithtMCG�30 s, the smaller diameter (r) and apex angle (φ) of PMSwere �300 μm and �301 respectively. However, tMCG �130 syielded PMS with r and φ of 2500 μm and close to 1301 (i.e. acylinder-like structure is resulted) respectively. φ is a measure ofapproximate apex angle because it does not take into account thecurvature of PMS due to parabolic flow (Figs. 3b and 1S). The apexangle ϕ is defined in Fig. 1S. ϕ ranges from 01 to 1801. Interestingly,ϕ�0 gives when r¼R�0; whereas ϕ¼180 when r44R andr�0. The former case (ϕ�0) will occur for an uncured fluid whichwill fill up the whole available space in the drilled hole (cylindricalstructure). With the horizontal fluid movement dominates thevertical fluid movement provided ϕ¼1801 (a thin polymer film-like structure). These results imply that a larger polymer viscositydue to increased polymerization resulted in smaller polymer flowrate before it was solidified. Thus, the polymer front underwent alarger displacement for smaller tMCG providing smaller ‘r’ andlarger ‘φ’ (Figs. 4 and 1S respectively). These results suggest thatwith a careful control over polymer viscosity through tuning oftMCG, the dimension of PMS can be controlled. Photopolymeriza-tion provides an interesting opportunity for creating interestingPMS by controlling local prepolymer viscosity in space and timeusing photo-excitation of pre-polymer and monomers. Thus, thismay allow the researchers to modulate spatial and temporalviscosity of the flowing polymer providing tuning of dimensionand shape of PMS.

4.3. Effect of fluid properties

We studied the effects of viscosity and surface tension of fluidsin an attempt to better understand how these properties of fluidsmay affect the formation of membranes. Both the fluid viscosityand surface tension also come in equation describing the fluid flow

for our experiments (Eq. (10)). We studied three additional fluidsfor their flow behaviors: water, dichloromethane (DCM) andglycerol. All the experimental conditions for these fluids werethe same except that these fluids do not solidify upon heating. Thesurface tension and viscosity values of these liquids were takenfrom standard reference sources [28]. Table 1 provides viscosity,surface tension, density, and fluid flow characteristics of uncuredfluids used in our studies. We observed that three fluids (PDMS,water, and glycerol) showed parabolic-like flow in our experi-ments whereas a gravity-induced vertical downward flow wasdominant for DCM (Video V2). DCM is a hydrophobic fluid with adipole moment of 1.6D. DCM possesses a high density of 1.326g/mL and an extremely low viscosity of �0.45 cP (Table 1). In ourexperiments, both uncured PDMS and DCM are relatively non-polar and possess low surface tension; however, the flow char-acteristics of DCM differ considerably that from uncured PDMS(Table 1 and Fig. 3S). These differences in the flow characteristicsare likely due to large differences in the viscosity and densityvalues of the two liquids. The viscosity of uncured PDMS 47000times larger than that of DCM. PDMS prepolymer possesses longmolecular chains providing viscoelastic properties which contri-butes to horizontal flow along MCG for PDMS. The viscoelasticproperty in DCM is absent. Further, a larger density for DCMcontributed to increased vertically dominant flow for DCM. Thus,the placement of MCG provided an activation energy that led to avertical dominant flow for DCM. However, although PDMS is anon-polar in nature, the viscoelastic and capillary force influencedits flow characteristics such that non-linear parabolic microstruc-tures were obtained under similar experiment conditions.

Interestingly, both water and glycerol showed both horizontaland vertical flow characteristics in our experiments (Video V2).This flow is likely due to high polarity and surface tension forthese fluids (Table 1 and Fig. 3S) providing strong capillary forceswhen MCG was placed on fluid surface. Clearly, MCG surfaceprovided fluids a means of overcoming surface tension-associatedactivation energy to move both along horizontal and verticaldirections. Overall, the formation of parabolic polymer porecontaining membranes appeared to require a balanced interplaybetween surface tension, capillary, viscous and gravitationalforces. Curing of PDMS provided parabolic micropores wheremanipulation of these forces yielded controllable micropores.Although we have not fabricated parabolic micropores composedof different polymers, the above discussion suggests that non-linear micropores with many other curable fluids are possible withsome changes in the experimental conditions and physical para-meters used in our experiments.

0 30 60 90 120 1500

1000

2000

3000

r ( µ

m)

tMCG (s)

Fig. 4. Relationships between r and tMCG. tMCG represents time for which PDMS washeated before MCG was placed on the substrate. Heating of PDMS for longer time(larger tMCG values) resulted in higher polymer viscosity and larger r value.

P.R. Rajasekaran et al. / Journal of Membrane Science 473 (2015) 28–3532

4.4. Influence of placement of MCG

The placement of MCG was observed to have a significantimpact on the shape of the PMS fabricated with this technique. It iscritical that the entire surface area of MCG comes in contact withthe PDMS simultaneously to avoid uneven contact points on thepolymer film. Any factors that may interfere with the isotropicflow of the polymer front may result in irregular or asymmetricalPMS or other structural defect in them. MCG placed parallel toPDMS film surface produced symmetrical parabolic micropores.We performed experiments by placing MCG on polymer film thatwas not parallel to the polymer membrane. This asymmetric MCGplacement on polymer resulted in the formation of asymmetricPMS (Fig. 5). The asymmetrical PMS formation is due to asym-metric PDMS flow because the gravitation force of MCG was notuniformly distributed over PDMS film. That is, the flow initiatedfirst towards the center of the hole from those areas where MCGcame in contact with the PDMS surface first. The movement ofpolymer front where MCG came in contact at a later stage wasdelayed, thus, this polymer front traveled a shorter distance priorto polymer curing compared to a polymer front that made contactwith MCG at an earlier time. Consequently, the effect of non-parallel polymer–MCG contact resulted in asymmetric PMS withoff-centered smaller pores (Fig. 5).

The cleanness of MCG, that is, the presence of dust or surfaceparticles can also influenced the shape of PMS. For example, thepresence of dust particles on the substrate and MCG may result ina non-uniform isotropic PDMS flow because the flow may gethindered or flow pattern may change due to the presence ofparticles on MCG surface. The result of this hindered flow will benon-symmetrical PMS. Interestingly, this provides opportunitiesfor creating a wide range of asymmetric pores through carefulcontrol over MCG placement on polymer films, and by tuning MCGsurface properties.

4.5. Influence of hole shape in the glass or aluminum substrateon PMS characteristics

Another interesting observation regarding PMS fabrication wemade was the fabrication of smooth and circular polymer mem-branes when drilled holes in the substrates were rough at micro-scopic scale. We have found that the top polymeric surface of thefabricated PMS was always extremely smooth even the substratehole had visual surface roughness at microscale (Fig. 2S).To demonstrate this, we used a hexagonal shaped hole in thesubstrate instead of a circular hole previously used in our experi-ments and repeated the polymeric fabrication process as describedabove. Fig. 2S shows that even though the fluid front started out asa hexagonal polymer front, it transformed into a circular cross-sectional pore (top view) after polymerization. The hexagonal tocircular fluid flow transformation is a consequence of loweredsurface energy of fluid front with less number of edges in it. The

circular fluid front has a lower surface energy than for a flowingfluid front that contained edges in them. This also provides aflowing polymer front independent of surface roughness in thehole. Thus, the flowing polymer forms a smooth circular cross-section even if the holes were rough and non-circular in shape.These experiments demonstrated that the shape and roughness ofthe drilled holes had a little impact surface roughness of thefabricated PMS and that the smaller openings possesses a circulargeometry (Fig. 2S). Unlike flow based fabrication technique suchas demonstrated in this manuscript, other etching-based orphotolithography-based fabrication processes may leave behindrough edges after fabrication process and may also need additionalpolishing and other related post-fabrication steps for its rectifi-cation. The self-rectification of rough edges is unique to the fluidflowing nature involved in this fabrication process. The parabolicshape and smooth surfaces of these structures are especially usefulfor micro-optical applications. For example, PMS and arraysfabricated using this technique may find potential applications inseparation and parabolic micro-optical lenses and mirrors [29].Other applications of PMS are in nozzles for printing, deliverysystem, polymeric valves and pumps and template synthesis ofdifferent materials [11–16].

4.6. Fabrication of arrays and template synthesis

The technique described in this manuscript was further utilizedfor the fabrication of an array of PMS. An array of holes measuring5 mm in diameter was drilled into an aluminum substrate (Fig. 6a).Following the same protocol as described above, MCG measuring22 mm�40 mm and weighing 0.4 g was placed on a spin-coated(o 500 rpm) PDMS film. After fabrication of the membranes,

Table 1Various fluid, their properties, and their fluid flow characteristics in our experiments.

Fluid Viscosity (cP) Surface tension (dyne/cm) Fluid flow characteristics

Uncured PDMS 3500a 20b Parabolic flow was observedWater 1.002c1 72.75c2 Both vertical and horizontal flows were observedGlycerol 1412d1 63.4d2 Both vertical and horizontal flows were observedDicholoromethane 0.449e1 26.52e2 Flow was vertically gravity dominated leading a small movement in horizontal direction

a: Sylgard 184 technical sheet from Dow Corning. http://www.dowcorning.com/applications/search/products/details.aspx?prod=01064291&type=PROD Retrieved on May 72014 [30].b: Langmuir 2000, 16, 1256–1260 [31].c: CRC Handbook of Chemistry and Physics, Student Ist Edition, Page F-19 (for c1); page F-14 (for c2); page F-16 (for d1 and e2); and page F-22 (for e1) [32].d1: Segur, J. B.; Oberstar, H. E. Industrial and Engineering Chemistry, 1951, 2117–2020 [33].

Fig. 5. An optical micrograph of an asymmetric PMS. The formation of a pore withits small opening offset from the center due to unparallel placement of MCG withrespect to polymer film. The sides of MCG that contacted PDMS first and last arelabeled in the micrograph.

P.R. Rajasekaran et al. / Journal of Membrane Science 473 (2015) 28–35 33

PDMS containing the micropores were peeled off providing afreestanding polymer film with an array of PMS in it. Fig. 6b andc shows optical and SEM images respectively of a typical PMS array

fabricated using this technique. These parabolic micropores weresubsequently used as templates for the fabrication of replicatedPDMS PMS containing membranes (Fig. 7). Fig. 7a shows two

Fig. 6. Fabrication of an array of PMS. (a) A typical substrate with drilled holes used for the fabrication of PMS. Scale bar is 6 mm. (b) An optical micrograph of an array of PMSformed. Scale bar is 6 mm. (c) An SEM of PMS array. Scale bar is 500 μm.

Fig. 7. SEM micrographs of replicated PDMS PMS fabricated using template-assisted synthesis. (a) SEM image of two separate PMS. (b) An array of two replicated PMSformed using a master containing two PMS. Scale bar is 50 μm for all the images.

P.R. Rajasekaran et al. / Journal of Membrane Science 473 (2015) 28–3534

individual replicated PMS formed utilizing two different masters,whereas Fig. 7b shows two replicated PMS formed from a singlemaster. In principle, it is possible to fabricate many thousands ofPMS of desired shapes and dimensions using this simple fabrica-tion technique.

4.7. Porosity and ionic transport through PMS

Considering the diameter of larger pore of our PMS, theporosity of our membranes is considerably lower than commer-cially available polymer membranes. Thus, we expect that thetransport flux of the PMS membranes is much lower than those forcommercially available membranes. However, our membranes canbe potentially useful for applications where individual poresneed to be addressed under an external stimulus (or stimuli). Forexample, our PMS may provide exciting opportunities for ions/molecular/particles transport under an electric field becauseindividual pores are separated enough to allow for electric con-nections to them. Further, it will be interesting to investigate ionicflow behavior under electric field in nanoscale PMS where PMSmay show a different electric potential-driven response as com-pared to those for cylindrical and conical pores [34].

5. Conclusions

We described a simple fabrication technique that employscontrolled fluid flow and curing dynamics for the synthesis ofnon-linear parabolic micropores containing membranes. Ourexperimental results corroborate well with theoretical analysesbased on simplified Navier–Stokes equation. The presented tech-nique utilizes capillary, gravitational forces and viscoelastic forcesfor the fabrication of PMS. PMS membranes possess a smoothsurface due to surface tension of pre-polymer. We discussedvarious ways to tune the microfabrication protocol for fabricatingdesired parabolic microstructures. The shape and size of PMS canbe readily manipulated by controlling the fluid and substrateproperties. The fabricated PMS membranes were also employedfor template synthesis of replicated microporous membranes. Thistechnique can also be used to fabricate PMS composed of metallic,semiconducting or dielectric materials embedded in a polymermatrix that can provide parabolic microporous membranes withversatile properties without use of microscale masters or masks.

Acknowledgment

We would like to thank National Science Foundation andNational Institutes of Health (to PK) for partial financial support.Scanning electron micrographs were acquired using an SEMpurchased through an NSF grant (CHE 0959568). Financial supportfrom Office of Vice-Chancellor of Research (OVCR) at SIUC was alsoacknowledged.

Appendix A. Supplementary material

Supplementary data associated with this article can be found inthe online version at http://dx.doi.org/10.1016/j.memsci.2014.08.042.

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