Growth of Polystyrene Pillars in Electric Field - Langmuir (ACS

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Growth of polystyrene pillars in electric field Pai-Ting Cheng, Wenxiao Zhou, Fuqian Yang, and Sanboh Lee Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b00207 • Publication Date (Web): 15 Mar 2019 Downloaded from http://pubs.acs.org on March 26, 2019

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Growth of polystyrene pillars in electric field Pai-Ting Cheng 1), Wenxiao Zhou 2), Fuqian Yang 3), and Sanboh Lee 1)*

1) Department of Materials Science and Engineering, National Tsing Hua University, 101, Kuang Fu Rd., 2nd Sec., Hsinchu 300, Taiwan 2) Department of Mechanical Engineering, University of Rochester, 235 Hopeman Building, Rochester, NY 14604 3) Materials Program, Department of Chemical and Materials Engineering, University of Kentucky, 177 FPAT, Lexington, KY 40506

Surface patterning on polymer films, which is a self-assembly process under the action of external and/or internal impetus, has a variety of applications, including drug delivery and flexible electronics. In this work, we study the growth of polystyrene pillars in electric field for different combinations of annealing temperature, film thickness, and electrode separation (electric field intensity). There are five stages for the growth of the polystyrene pillars for all the configurations used in this work, including a nucleation stage, a linear growth stage, an acceleration stage in the pillar length prior to the contact between the top surface of a pillar and the upper electrode, a radial growth stage after the contact, and a stationary stage without further growth of the pillar. In the linear growth stage, there exist linear relationships between the pillar length and the annealing time and between the square of the pillar diameter and the annealing time. The activation energies for the rate processes controlling the radial growth and the length growth in the linear growth stage are 30.2 kJ/mol and 25.3 kJ/mol, respectively. There are two rate processes controlling the radial growth of the pillars; one is the field-induced flow of polymer through the polymer film to the roots of pillars, and the other is the coalescence of pillars. The activation energy for the coalescence is 16.5 kJ/mol. The results obtained in this work offer a practical route to control the geometrical dimensions of polymer pillars through the processing parameters.

Keywords: field-induced patterning; polystyrene pillar; electric field; temperature.

*

Corresponding author. Email address: [email protected]; Tel/Fax: 886-3-5719677.

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Introduction Surface patterns on solid substrate have a variety of potential applications, including microelectronics 1, biofluidics 2, optical lenses 3, and control/measurement of cell behavior 4. There are different techniques available to form surface patterns on the surface of polymers, including solvent evaporation 5-7, surface buckling 8-9, laser lithography 10, nanoimprint 11, and field-induced surface patterning

12-13.

Among these techniques, field-induced surface patterning provides a

unique way to construct patterns on the surface of polymer from liquid-like state. The discovery of field-induced textures on the surface of polymer films can be attributed to the study of the surface instability of materials under the action of electric field 14-18. In the heart of the field-induced textures on the surface of polymer films is the field-induced surface instability of polymer films of “liquid” state on “rigid” substrates and the growth of the surface instability in the form of self-organization. The driving force for the field-induced textures on the surface of polymer films is the electric stresses acting onto the surface of polymer films. Using the concept of field-induced instability, various surface textures have been formed on the surface of polymers, including micropillars surface patterns

22

18-20,

closed-cell structures

21,

and “irregular”

via the geometrical configuration of parallel-plate capacitor. Using a wedge-

like structure geometrical configuration 23-24, the surface textures with spatial-gradient distribution have been constructed. There are two controlling factors determining the sizes of the field-induced surface textures; one is the growth behavior of the surface textures along the field direction, and the other is the growth behavior of the surface textures along the direction perpendicular to the field direction. Wu et al. 25 observed two distinctive regimes for the radial growth (coarsening) of PDMS (Polydimethylsiloxane) pillars; one follows linear growth, and the other follows logarithmic growth. Peng et al. 26 derived a quadratic relationship between the coarsening time and the pillar diameter for the pillars with the pillar length the same as the electrode separation under the action of electric field, which was validated by the experimental results of the field-induced coarsening of BPAPC (bisphenol-A-polycarbonate) pillars

26

and PMMA (Poly(methyl

methacrylate)) pillars 27. They did not analyze the growth behavior of the surface textures along the field direction. As discussed above, the surface textures formed under the action of electric field are also dependent on the growth behavior of the textures along the direction of electric field. Leach et al. 28

characterized the evolution of the surface instability on PDMS at the early and intermediate 2 ACS Paragon Plus Environment

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stages prior to the formation of pillars. They found that the peak height increases approximately linearly with the increase of the growth time and there exists an acceleration in the growth rate at the later stage of the growth. However, their study was not focused on the growth behavior of the pillars. Tian et al. 29 performed numerical simulation of surface pattering in the pattern-modulated electric field from the framework of liquid dielectrophoresis. Their simulation results show that the pillar height is proportional to the growth time for the relative time less than one under the sole action of electrostatic attraction. They did not provide any analytical relationship between the pillar height and the growth time. Currently, there are few reports focusing on the field-induced growth of pillars along the field direction. In general, it is the electromechanical interaction between electric field and the flow of polymer in polymer film that determines the formation and growth of surface textures in an electric field 26. Considering the potential applications of field-induced surface textures on soft matter in nanoelectronics 30 and nanophotonics 31, we study the field-induced growth of polymer pillars from polystyrene (PS) films in the configuration of a parallel capacitor without surface modulation on both electrodes. In contrast to the work by Peng et al.

26,

this work is focused on the growth

behavior of the pillars before the pillars touch the upper electrode. The dependence of the pillar growth on annealing temperature, film thickness and electrode separation (electric field intensity) are investigated experimentally. We establish a simple analytical relation between the growth rate of a pillar and electric stress from the framework of laminar flow of Newtonian fluid under the condition that the pillar diameter remains unchanged (see Appendix). Experimental details PS (polystyrene) pellets of 250,000 g/mol in average molecular weight (Mw) was obtained from Acros Organics (Acros Organics, Geel, Belgium). Ultraclean silicon (100) wafers of p-type were obtained from Summit-tech Co. (Hsinchu, Taiwan); the thickness of the silicon wafers is 525 H*4 Polymer solutions made from PS pellets in toluene (JT Baker Chemical Co, Phillipsburg, New Jersey, USA) were prepared. Si wafers with SiO2 spacers of 670 nm in thickness and a layer of SiO2 of ~15 nm in thickness were prepared via the microelectronic fabrication process. The distance between spacers was 0.8 cm. Plasma sputtering was used to deposit a layer of TiN of ~600 nm in thickness on the rear side of Si wafers on a Pelco SC-6 sputter coater (Ted Pella Inc., Redding, CA, USA) to increase electric conduction. The Si wafers with TiN film were sliced to Si plates of 3 ACS Paragon Plus Environment

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1.2 1.2 cm2. The Si plates were sonicated in acetone for 30 minutes and dried with the flow of nitrogen gas prior to the coating of a polymer film. Following the method given by Peng et al. 26, a monolayer of n-octadecyltrichlorosilane (OTS) (90%+, Aldrich Chemical Company, Inc., Milwaukee, WI, USA) was formed on the surface of the SiO2 film on Si plates to limit the effect of adhesive contact between the surface of the SiO2 film and the polystyrene. Using the prepared polymer solutions, polymer films of thicknesses in a range of 30 nm to 90 nm were spin-coated on the Si plates without SiO2 spacers at room temperature on a spin coater (SWIENCO PM-490). Note that the measured thicknesses of the polymer films excluded the edge effect. Parallel capacitors consisting of the Si plate with the polymer film as the bottom-electrode and the Si plate with SiO2 spacers as the upper-electrode were constructed. A DC power supply (PPS-2018A, Motech, New Taipei, Taiwan) was used to apply an electric voltage/field to the PS film in the configuration of a parallel capacitor. The field-induced surface patterning was accomplished in an oven (DV-303, Channel Co., New Taipei, Taiwan) in air at different temperatures, as measured by a thermocouple. After reaching the pre-determined “growth” (annealing) time during the surface patterning, the parallel capacitors were removed from the oven, and a freeze spray (Max Pro FR-777-777 Freeze Spray) was used to solidify the formed surface patterns. Finally, electric power was switched off after solidification. Topological imaging of the field-induced surface patterns was performed on an optical microscope (Olympus Optical Co., Tokyo, Japan) and an atomic force microscope (AFM) (Dimension 3100, Bruker, Billerica, MA, USA), respectively. The surface patterns were analyzed by Image J (National Institute of Health, Bethesda, MD, USA) 32. Results The surface roughness of the freshly prepared polymer films on Si wafers was measured by AFM. Table 1 lists the surface roughnesses over an area of 20 20 H*2 for the polymer films of different thicknesses without the action of an electric field. All the root-mean square roughnesses are less than 2 nm. The spin-coating did not introduce any surface features (patterns) on the polymer films, and did produce polymer films with surfaces of high quality. There were no surface features, which could likely lead to local instability in electric field for the formation of surface patterns. (Figure 1)


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Table 1. Root-mean square roughness of PS films on Si wafers Film thickness (nm)

30

50

70

90

Rq (nm)

1.14±0.04

1.02±0.11

1.32±0.13

1.55±0.20

Figure 1 depicts the optical micrographs of the surface patterns on the surfaces of PS films of 70 nm in thickness, which formed at different temperatures and different annealing times, using spacers of 700 nm in height and an electric field of 42.8 MV/m. Due to fast growth of the surface patterns at temperature of 190 °C, optical micrograph of the surface patterns was taken at the annealing time of 45 min instead of 50 min. It is evident that electric field induces the change of surface topology of the PS films, which evolves to pillars on the PS films without the use of patterned electrode 22. (Figure 2) Figure 2 shows the AFM images of the PS pillars on the surfaces of PS films of 70 nm in thickness, corresponding to the optical micrographs shown in Fig. 1. From Figs. 1 and 2, we conclude that both the density and average size of the PS pillars vary with the annealing time. More optical micrographs and AFM images of the PS pillars are given in the Supporting Information. (Figure 3) Using the AFM images, we measured the height and diameter of the PS pillars formed on PS films of different thicknesses at various instants under the action of different electric field intensities. Note that line scanning of the pillars, as shown in Fig. S1 in the Supporting Information, was performed to obtain the pillar heights. Standard deviations, which were calculated from the measured pillar heights and diameters over different domains, are included in Figs. 3 and 4. The maximum height of pillars cannot exceed the electrode gap in height. Therefore, the error bars of data points at long time are asymmetric as shown in Figure 3. Figure 3 shows temporal evolution of the average height of the PS pillars formed under different conditions. It is evident that the growth rate of the pillar height increases with the increase of electric field and the annealing temperature and decrease with the decrease of the film thickness before the pillars touch the upper electrode. There is a linear correlation between the pillar height and the annealing time for a range of the growth period for all the configurations used in this work. Also, there exists an acceleration period when the pillar is nearly in touch with the upper electrode. 5 ACS Paragon Plus Environment

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Such behavior is consistent with the observation by Leach et al. 28, and is due to the increase of the electric field between the top surface of the pillar and the upper electrode. From Fig. 3, we note that the linear relationship between the pillar height and the annealing time cannot extend to the onset of the annealing process, i.e. annealing time = 0 min, for most configurations. There likely exists an incubation period for the formation of the PS pillars. The incubation time increases with the decreases of the annealing temperature and the film thickness and with the increase of the electrode separation. All of these can be attributed to the counter balance between viscous resistance to the flow of polymer and the driving force for the growth of the PS pillars. The higher the annealing temperature, the lower is the viscous resistance; the thinner/smaller the film thickness/electrode field, the smaller is the driving force for the growth of the pillars. It needs to be pointed out that the extrapolation of the linear relationship between the pillar height and the annealing time for the results corresponding to the configurations of the thickest film, smallest separation (largest electric field intensity) and highest annealing temperature in Fig. 3 leads to “negative” incubation time. Such a result is likely due to that the resistances to the nucleation of pillars and viscous flow of polymer are much smaller than the driving force (electric stress) for these configurations. Nucleation likely occurs almost immediately upon the action of electric field, i.e. there is almost no incubation period. Fast growth of the pillars then takes place. (Figure 4) Figure 4 shows temporal evolution of the average diameter of the PS pillars formed under different conditions. The pillar diameter increases with the increase of the annealing time and the film thickness and with the decrease of the electrode separation, i.e. the increase of electric field, for the same annealing time. There are five stages for the temporal evolution of the PS pillars for all the configurations used in this work. The first stage is the nucleation stage, at which small dots (pillars) are formed; the second stage is the growth stage with a linear relationship between the square of the pillar diameter and the annealing time prior to the contact between the top surfaces of the pillars and the upper electrode; the third stage is the stage prior to the contact between the top surfaces of the pillars and the upper electrode, in which there are fast growth in the pillar length along the field direction and slow growth in the radial direction; the fourth stage is the radial growth after the contact between the top surfaces of the pillars and the upper electrode; and finally, the pillars stop to grow. Similar to the temporal evolution of the pillar height, the linear relationship between the square of the pillar diameter and the annealing time cannot extend to the onset of the 6 ACS Paragon Plus Environment

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annealing process, i.e. annealing time = 0 min, for some configurations. This trend again suggests that there exists an incubation period for the formation of the PS pillars, which is dependent on the annealing temperature, film thickness and electric field intensity. Note that the extrapolation of the linear relationship between the square of the pillar diameter and the annealing time for some of the results in Fig. 4 leads to “negative” incubation time. Such a result supports that there is almost no incubation period if the resistances to the nucleation of pillars and viscous flow are much smaller than the driving force (electric stress). (Figure 5) Using the AFM images, we calculated the density of pillars. Figure 5 shows temporal evolution of the density of the PS pillars under different conditions. It is evident that the density of the PS pillars at the initial stage for all the configurations used in this work is relatively low. There is a sudden increase in the density of the PS pillars after the initial stage, which likely is associated with the critical size of nucleus needed for the formation of the PS pillars. The time for the sudden increase in the density of the PS pillars decreases generally with the increase of the annealing temperature. After the initial stage, the density of the PS pillars reaches maximum, starts to decrease with the increase of the annealing time, and reaches plateau. Such behavior suggests the vanishing of the PS pillars through mass transport between the pillars and the polymer film and/or the coalescence of pillars during the annealing, which is qualitatively in accord with the increase of the average pillar diameter. For the same annealing time after the initial stage, the density of the PS pillars decreases with the increase of the annealing temperature and the film thickness due to the less resistance to the mass transport. Discussion Currently, most modeling analyses have been focused on the field-induced surface instability of thin films for the field-induced surface patterning 33-37. Assuming that a polymer pillar can be approximated as a cylindrical rod, Peng et al. 26 derived a linear relationship between the square of the pillar diameter and the annealing time with the coefficient of proportionality being inversely proportional to the viscosity of polymer under the condition that the pillar length remains unchanged during the radial growth. For the cross-section profile of a pillar shown in Fig. S1 in the Supporting Information, it is reasonable to assume that the geometry of the pillars can be approximated as cylinder. Following the approach given by Peng et al.

26,

we derived a linear

relationship between the pillar length and the annealing time with the coefficient of proportionality 7 ACS Paragon Plus Environment

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being also inversely proportional to the viscosity of polymer under the condition that the pillar diameter remains unchanged during the length growth (see Appendix). According to the results shown in Figs. 2 and 3, we can conclude that both the length and diameter of pillars vary with the annealing time during the growth stage. Using the principle of mass conservation, the amount of the polymer flowing to the root of a pillar through the polymer film is equal to the summation of the amount of the polymer for the radial growth and the amount of the polymer for the length growth. Thus, the resistances to the growth of the pillars in both the radial direction and the length direction are inversely proportional to the viscosity of the polymer even though the pillars grow in both directions. According to the results shown in Figs. 3 and 4, there is a linear growth period, which gives D2

D02

t and L L0

t

(2)

where D and L are the pillar diameter and the pillar length at time t, respectively, D0 and L0 are the pillar diameter and the pillar length at time t=0, and P and Q are two constants depending on the geometry of the PS pillar and the rheological property of PS. The first equation in Eq. (2) is similar to Eq. (21) in Peng et al.’s work 26, and the second equation in Eq. (2) is similar to Eq. (A19). According to the above discussion, there are 1

and

1

(3)

with S being the PS viscosity. It is known that the temperature dependence of the viscosity of a polymer can be expressed as 0

eQ / RT

(4)

where S0 is a pre-exponential factor, Q is activation energy, R is the gas constant, and T is absolute temperature. Substituting Eq. (4) in Eq. (3) yields e

Q1 / RT

and

e

Q2 / RT

(5)

with Q1 and Q2 being the activation energies for the rate processes controlling the growth of the PS pillars in the radial and length directions, respectively. For the same rate process, there is Q1 = Q2. (Figure 6) Using Eq. (2) to curve-fit the results shown in Figs. 3 and 4 for the linear growth period, we obtain the parameters of P and Q4 Figure 6 shows the temperature dependence of the parameters of P and Q for the PS thin film with the film thickness of 70 nm, electrode separation of 700 nm, and 8 ACS Paragon Plus Environment

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electric field of 42.8 MV/m. It is evident that both the parameters of P and Q follow the relationships of Eq. (5). Using Eq. (5) to curve-fit the results, we obtain the activation energies of Q1 and Q2 as 30.2 kJ/mol and 25.3 kJ/mol, respectively. The Chi values, , for the curve-fitting are 0.08 and 0.10 for the activation energies of 25.3 kJ/mol and 30.2 kJ/mol, respectively, as shown in Fig. 6. The small Chi values suggest the statistically distinct difference in the activation energys for these two processes. There likely exists the other process controlling the radial growth of the pillars in addition to the PS flow through the PS film into the pillars. For the range of the annealing temperature used in this work, the pillars grow at a relatively larger rate along the radial direction than that along the length direction. (Figure 7) Figure 7 depicts the variation of the parameters of

and with the film thickness for electrode

separation of 700 nm and electric field of 42.8 MV/m at an annealing temperature of 180 °C. It is evident that the thickness dependence of the parameter of

is different from that of the parameter

of . For thicker films, the PS pillars grow at a relatively larger rate along the radial direction than that along the length direction. Such a trend suggests again that there likely exists the other process controlling the radial growth of the PS pillars in addition to the PS flow through the PS film into the pillars. (Figure 8) To investigate the effect of electric field on the parameters of

and , we varied the electrode

separation (electric field) and maintained a constant voltage of 30 V between the two parallel electrodes at the annealing temperature of 180 °C. Figure 8 shows the variations of the parameters of

and with the electrode separation and electric field. Both the parameters of

and decrease

with the increase of the electrode separation, suggesting that decreasing electric field intensity decreases the growth rates of the PS pillars, as expected. According to the results given by Peng et al. 26 and in Appendix, it is believed that the growth rates, i.e.

and , in the linear growth period can be expressed semi-analytically as m 0

V h

n

e

Q1 / RT

m

and

0

V h

n

e

Q2 / RT

where P0 and Q0 are two constants for the corresponding parameters,

(6) is the film thickness, V is

electric voltage applied to the electrodes, h is the electrode separation, and m and n are two power


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indexes. The subscripts of P and Q represent the corresponding parameters. Note that we use the results in Eq. (5) to propose Eq. (6). Using Eq. (6) to curve-fit the results shown in Figs. 7 and 8, we obtain (mP, nP) = (3/4, 1) and (mQ, nQ) = (1/4, 0.5), which are different from the power indexes given by Peng et al.

26

and in Appendix. Such differences reveal that there exists the interaction

between the radial growth and the length growth. It is known that the volume of a cylindrical pillar,

LdD 2 dt

d dt

, can be calculated as

= D2L. There is

D 2 dL dt

(7)

Substituting Eqs. (2) and (6) in Eq. (7), we obtain

where

0

D02 )t

( L0

0

t2

(8)

is the pillar volume at t=0. In the linear growth period of the square of the pillar diameter

and the pillar length, the pillar volume is a quadratic function of the annealing time. (Figure 9) The difference between the activation energies of Q1 and Q2 reveals that the radial growth of the PS pillars likely involves multiple rate processes. Figure 9 shows an AFM image of PS pillars taken at an annealing time of 30 min for the configurations of the film thickness of 70 nm, the electrode separation of 700 nm, electric field of 42.8 MV/m, and the annealing temperature of 180 °C. From Fig. 9, we note that there exists the coalescence of two PS pillars, suggesting that the radial growth of the PS pillars involves the coalescence during the annealing. There are two parallel processes controlling the radial growth of the dense PS pillars; one is the electric stress on the side surface of the PS pillars, which leads to the radial growth of the PS pillars, and the other is the coalescence of the PS pillars, which is driven by the reduction of surface energy. (Figure 10) Assume that the coalescence of two PS pillars can be described as a first-order reaction. The decrease rate of the number density of the PS pillars can be expressed as d dt

with

(

(9)

)

being the number density of the PS pillars at time t,

pillars as t

being the number density of the PS

, and being the rate constant. The solution of Eq. (9) is e

( t t0 )

(10)


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where

is a constant, and t0 is the time at which the number density of the PS pillars starts to

decrease. Eq. (10) is used to curve-fit the results shown in Fig. 5 for the growth period, in which the number density of the PS pillars decreases, and the fitting curves are also included in Fig. 5. From the curve fitting, we obtain the rate constant. Figure 10 depicts the variations of the rate constant with the annealing temperature, the film thickness and the electrode separation (electric field). It is evident that the rate constant increases with the increase in the annealing temperature and the film thickness and with the decrease (increase) in the electrode separation (electric field). The higher the temperature, the less is the resistance to the PS flow. Similarly, increasing the film thickness and the electric field allows PS to flow at a large velocity. According to Fig. 10b and c, the rate constant linearly increases with the increase of the film thickness and with the decrease of the electrode separation. In general, the temperature dependence of the rate constant for the first-order reaction follows the Arrhenius relation, i.e. 0

with

0

e

Qc / RT

(11)

being a pre-exponential constant and Qc being the activation energy for the first-order

reaction. Using Eq. (11) to curve-fit the results in Fig. 10, we obtain the activation energy of 16.5 kJ/mol, which is less than 30.2 kJ/mol calculated from Fig. 6 for the growth of the PS pillars along the radial direction. Such a difference suggests that the coalescence of the pillars exhibits different temperature dependence, since the coalescence of the PS pillars is dependent on the PS flow and the surface tension of PS. Both the viscosity and surface tension of PS are temperature-dependent. Note that the other force associated with the coalescence of the pillars is electric stress, which is independent of temperature. In addition to the coalescence of two PS pillars, the disappearance of non-coalesced pillars can also be applied to the first order kinetics for the analysis of the number density of PS pillars. The pillar size is expected to decrease with increasing the annealing time for the first order kinetics of mono-pillars. According to Fig. 5, the pillar size increases with the increase of the annealing time. Thus, the annihilation mechanism of non-coalesced pillars is excluded. Summary In summary, we have systemically investigated the field-induced growth of PS pillars under different combinations of the processing parameters. The experimental results reveal that the growth of the pillars are dependent on the annealing temperature, annealing time, film thickness 11 ACS Paragon Plus Environment

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and electric field intensity. Increasing the annealing temperature, film thickness and electric field intensity can increase the growth rate of the PS pillars. There exists an incubation period, after which the PS pillars grow in both the radial and length directions. There exists a linear growth period, in which the growth rates of the pillar length and the square of the pillar diameter are linear functions of the annealing time. The temporal evolutions of the pillar length and diameter in the linear growth period have similar relationships to those derived for the geometrical configuration of either the pillar length or the pillar diameter remaining unchanged during the annealing, even though both the pillar diameter and length vary during the growth. The activation energies for the growth of the PS pillars along the radial direction and the length direction in the linear growth period are 30.2 kJ/mol and 25.3 kJ/mol, respectively. There are two rate processes controlling the radial growth of the pillars; one is the field-induced flow of PS through the PS film to the roots of PS pillars, and the other is the coalescence of PS pillars. The driving force for the coalescence is the surface tension of PS. The coalescence of the PS pillars leads to the decrease of the number density of the PS pillars, which can be described by the first-order reaction. The activation energy for the first-order reaction is found to be 16.5 kJ/mol, which is smaller than 30.2 kJ/mol and 25.3 kJ/mol for the growth of the PS pillars along the radial direction and the length direction in the linear growth period, respectively.

Supporting Information Optical micrographs and AFM images of surface patterns on surface of PS films: different film thicknesses; different annealing temperatures; different annealing times; different electric fields and electrode separations.

Acknowledgment This work was financially supported by the Ministry of Science and Technology, Taiwan.


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Appendix

h

V

2r0

Figure A1. Schematic of the growth of a polymer pillar between two parallel electrodes in an electric field Consider the temporal evolution of a single pillar between two parallel electrodes as schematically shown in Fig. A1. A pillar of r0 in radius grows from a polymer film of T in thickness, whose flow behavior is Newtonian and incompressible; the flow takes place in the polymer film of an average radius R (R>> T 4 Under the condition that the contribution of the surface tension of the polymer pillar is negligible and |R- r0| >> T for the geometric configuration of Fig. 1, Peng et al. 26 obtained the rate of the polymer flowing through the root of the polymer pillar, m& , as m&

where

3 ( V 0) 3 ln( R / r0 ) h

2

(A13)

is the viscosity of the polymer,

0

is the dielectric constant of vacuum,

(> 0 ) is the

dielectric constant of the polymer, V is the voltage applied between the electrodes, and h is the gap between the electrodes. Note that Eq. (A13) was derived under the condition that electric stress acting on the pillar remains constant 26. Replacing V/h with electric field intensity, E, in Eq. (A13), we obtain & m

3 ( 0) E2 3 ln( R / r0 )

(A14)

Here, E represents the electric field intensity between the upper electrode and the top surface of the polymer pillar. Approximating the structure of electrode/pillar/air/electrode as a parallel bilayer capacitor, the electric field, E, can be calculated as E

V h L(1

0

(A15)

/ )

Substituting Eq. (A15) in Eq. (A14) yields


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3 ( 0) & m 3 ln( R / r0 ) h

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2

V L(1

0

(A16)

/ )

According to Eq. (A16), the mass rate increases with the increase of the pillar length due to the increase of the electric field intensity between the upper electrode and the top surface of the polymer pillar. Using Eq. (A16) and the mass balance, we obtain L&

3 1 ( 0) 3 r02 ln( R / r0 ) h

V L(1

2

0

(A17)

/ )

which gives the temporal evolution of the pillar length as L

L2 (1

0

/ )

L3 (1

h

3h

0 2

/ )2

3 V 1 ( 0) 2 3 r0 ln( R / r0 ) h

2

t

(A18)

under the condition of L=0 at t=0 (t is the growth time). For L= W0;W XXh, Eq. (A18) gives L

3 1 ( V 0) 3 r02 ln( R / r0 ) h

2

(A19)

t

The pillar length is proportional to the growth time, which is in accord with the observation by Leach et al. 28.


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References: 1. Bucknall, D., Nanolithography and Patterning Techniques in Microelectronics. Elsevier: 2005, ISBN-13: 978-1-85573-931-4 2. Kho, K.-W.; Qing, Z. M.; Shen, Z.-X.; Ahmad, I. B.; Lim, S.; Mhaisalkar, S.; White, T. J.; Watt, F.; Soo, K. C.; Olivo, M., Polymer-based microfluidics with surface-enhanced Ramanspectroscopy-active periodic metal nanostructures for biofluid analysis. Journal of Biomedical Optics 2008, 13, 054026, DOI: 10.1117/1.297614 3. Toshiyoshi, H.; Su, G.-D. J.; LaCosse, J.; Wu, M. C., A surface micromachined optical scanner array using photoresist lenses fabricated by athermal reflow process. Journal of Lightwave Technology 2003, 21, 1700-1708, DOI: 10.1109/JLT.2003.814399 4. Ito, Y., Surface micropatterning to regulate cell functions. Biomaterials 1999, 20, 2333-2342, DOI: 10.1016/S0142-9612(99)00162-3 5. Sun, W.; Yang, F. Q., vaporation-induced formation of self-organized gradient concentric rings on sub-micron pre-cast PMMA films. Soft matter 2014, 10, 4451-4457, DOI: 10.1039/c4sm00245h 6. Park, W. K.; Kim, T.; Kim, H.; Kim, Y.; Tung, T. T.; Lin, Z.; Jang, A.-R.; Shin, H. S.; Han, J. H.; Yoon, D. H., Large-scale patterning by the roll-based evaporation-induced self-assembly. Journal of Materials Chemistry 2012, 22, 22844-22847, DOI:10.1039/c2jm34212j 7. Mampallil, D.; Eral, H. B., A review on suppression and utilization of the coffee-ring effect. Advances in Colloid and Interface Science 2018, 252, 38-54, DOI: 10.1016/j.cis.2017.12.008 8. Ouchi, T.; Yang, J.; Suo, Z.; Hayward, R. C., Effects of stiff film pattern geometry on surface buckling instabilities of elastic bilayers. ACS Applied Materials & Interfaces 2018, 10 (27), 23406-23413, DOI: 10.1021/acsami.8b04916 9. González-Henríquez, C.; Vallejos, M. S.; Rodríguez-Hernández, J., Strategies for the fabrication of wrinkled polymer surfaces. In Wrinkled Polymer Surfaces, Springer: 2019; pp 19-59, DOI: 10.1007/978-3-030-05123-5 10. Reif, J., Surface functionalization by laser-induced structuring. In Advances in the Application of Lasers in Materials Science, Springer: 2018; pp 63-88, DOI: 10.1007/978-3-319-96845-2 11. Chen, Y.; Wang, Z.; Kulkarni, M. M.; Wang, X.; Al-Enizi, A. M.; Elzatahry, A. A.; Douglas, J. F.; Dobrynin, A. V.; Karim, A., Hierarchically patterned elastomeric and thermoplastic polymer films through nanoimprinting and ultraviolet light exposure. ACS Omega 2018, 3, 15 ACS Paragon Plus Environment

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15426-15434, DOI: 10.1021/acsomega.7b01116 12. Pease, L. F.; Russel, W. B., Limitations on length scales for electrostatically induced submicrometer pillars and holes. Langmuir 2004, 20, 795-804, DOI: 10.1021/la035022o 13. Copenhaver, K.; Luna, M.; Nadler, J., Polymer Patterning via Electrohydrodynamic Instabilities. MRS Advances, 2019, 1-8, DOI: 10.1557/adv.2019.63 14. Tonks, L., A theory of liquid surface rupture by a uniform electric field. Physical Review 1935, 48 (6), 562-568, DOI 10.1103/PhysRev.48.562 15. Melcher, J. R., Field-Coupled Surface Waves. MIT: 1963, ISBN: 9780262130158 16. Yang, F. Q.; Song, W., Influence of electromechanical interaction on the morphological instability of an elastic conducting halfspace. Physical review B 2005, 72, 165417, DOI: 10.1103/PhysRevB.72.165417 17. Yang, F. Q.; Song, W., Morphological instability of elastic thin films-effect of electromechanical interaction. Applied Physics Letters 2005, 87, 111912, DOI: 10.1063/1.2045544 18. Trease, C. H.; Foot, P. J.; Augousti, A. T., Electrohydrodynamic patterning in a curable resin over a wide range of fabrication parameters. European Polymer Journal 2017, 91, 315-325, DOI: 10.1016/j.eurpolymj.2017.04.011 19. Chou, S. Y.; Zhuang, L.; Guo, L. J., Lithographically induced self-construction of polymer microstructures for resistless patterning. Applied Physics Letters 1999, 75 (7), 1004-1006, DOI: 10.1063/1.124579 20. Itoh, K.; Ishida, M.; Kakinuma, Y.; Anzai, H.; Sakurai, K., Development of an electro-adhesive micro pillar array via EHD patterning. Smart Materials and Structures 2019, 28, 034003, DOI: 10.1088/1361-665X/aafeb8 21. Leach, K. A.; Gupta, S.; Dickey, M. D.; Willson, C. G.; Russell, T. P., Electric field and dewetting induced hierarchical structure formation in polymer/polymer/air trilayers. Chaos 2005, 15, 047506 DOI: 10.1063/1.2132248 22. Tian, H. M.; Ding, Y. C.; Shao, J. Y.; Li, X. M.; Liu, H. Z., Formation of irregular micro- or nano-structure with features of varying size by spatial fine-modulation of electric field. Soft Matter 2013, 9, 8033-8040, DOI: 10.1039/c3sm51050f 23. Schaffer, E.; Thurn-Albrecht, T.; Russell, T. P.; Steiner, U., Electrohydrodynamic instabilities in polymer films. Europhysics Letters 2001, 53, 518-524, DOI 10.1209/epl/i2001-00183-2 16 ACS Paragon Plus Environment

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24. Salac, D.; Lu, W.; Wang, C.-W.; Sastry, A. M., Pattern formation in a polymer thin film induced by an in-plane electric field. Applied Physics Letters 2004, 85, 1161-1163, DOI: 10.1063/1.1781751 25. Wu, N.; Kavousanakis, M. E.; Russel, W. B., Coarsening in the electrohydrodynamic patterning of thin polymer films. Physical Review E 2010, 81, 026306, DOI: 10.1103/PhysRevE.81.026306 26. Peng, J.-S.; Yang, F.; Chiang, D.; Lee, S., Kinetics of field-induced surface patterns on PMMA. Langmuir 2016, 32 (18), 4602-4609, DOI: 10.1021/acs.langmuir.6b01304 27. Chuang, Y.-F.; Peng, J.-S.; Yang, F.; Chiang, D.; Lee, S., Field-induced formation and growth of pillars on films of bisphenol-A-polycarbonate. RSC Advances 2017, 7, 9015-9023, DOI: 10.1039/C6RA27783G 28. Leach, K. A.; Lin, Z.; Russell, T. P., Early stages in the growth of electric field-induced surface fluctuations. Macromolecules 2005, 38, 4868-4873, DOI: 10.1021/ma048157p 29. Tian, H.; Shao, J.; Ding, Y.; Li, X.; Liu, H., Numerical characterization of electrohydrodynamic micro-or nanopatterning processes based on a phase-field formulation of liquid dielectrophoresis. Langmuir 2013, 29, 4703-4714, DOI: 10.1021/la400535p 30. Galatsis, K.; Wang, K. L.; Ozkan, M.; Ozkan, C. S.; Huang, Y.; Chang, J. P.; Monbouquette, H. G.; Chen, Y.; Nealey, P.; Botros, Y., Patterning and templating for nanoelectronics. Advanced Materials 2010, 22, 769-778, DOI: 10.1002/adma.200901689 31. Zhao, Q.; Yetisen, A. K.; Sabouri, A.; Yun, S. H.; Butt, H., Printable nanophotonic devices via holographic laser ablation. ACS Nano 2015, 9, 9062-9069, DOI: 10.1021/acsnano.5b03165 32. Schneider, C. A.; Rasband, W. S.; Eliceiri, K. W., NIH Image to ImageJ: 25 years of image analysis. Nature methods 2012, 9, 671-675, DOI: 10.1038/nmeth.2089 33. Schäffer, E.; Thurn-Albrecht, T.; Russell, T. P.; Steiner, U., Electrohydrodynamic instabilities in polymer films. EPL (Europhysics Letters) 2001, 53, 518-524, DOI: 10.1209/epl/i200100183-2 34. Morariu, M. D.; Voicu, N. E.; Schäffer, E.; Lin, Z.; Russell, T. P.; Steiner, U., Hierarchical structure formation and pattern replication induced by an electric field. Nature Materials 2003, 2, 48-52, DOI: 10.1038/nmat789 35. Verma, R.; Sharma, A.; Kargupta, K.; Bhaumik, J., Electric field induced instability and pattern formation in thin liquid films. Langmuir 2005, 21, 3710-3721, DOI: 17 ACS Paragon Plus Environment

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10.1021/la0472100 36. Pease III, L. F.; Russel, W. B., Linear stability analysis of thin leaky dielectric films subjected to electric fields. Journal of Non-Newtonian Fluid Mechanics 2002, 102, 233-250, DOI: 10.1016/S0377-0257(01)00180-X 37. Arun, N.; Sharma, A.; Shenoy, V. B.; Narayan, K., Electric field controlled surface instabilities in soft elastic films. Advanced Materials 2006, 18, 660-663, DOI: 10.1002/adma.200502199


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List of Table: Table 1. Root-mean square roughness of PS films on Si wafers Figure captions: 1. Optical micrographs of surface patterns on surface of PS films formed at different temperatures and different annealing times (film thickness: 70 nm, electrode separation: 700 nm, and electric field: 42.8 MV/m) 2. AFM images of surface patterns on surface of PS films formed at different temperatures and different annealing times (film thickness: 70 nm, electrode separation: 700 nm, and electric field: 42.8 MV/m) 3. Temporal evolution of average pillar height for different conditions at an electric voltage of 30 V: (a) different temperatures (film thickness: 70 nm, and electric field: 42.8 MV/m), (b) different, initial film thicknesses (temperature: 180 C, and electric field: 42.8 MV/m), and (c) different electric field intensities (film thickness: 70 nm, and temperature: 180 C) 4. Temporal evolution of average pillar diameter for different conditions at an electric voltage of 30 V: (a) different temperatures (film thickness: 70 nm, and electric field: 42.8 MV/m), (b) different, initial film thicknesses (temperature: 180 C, and electric field: 42.8 MV/m), and (c) different electric field intensities (film thickness: 70 nm, and temperature: 180 C) 5. Temporal evolution of the density of pillars for different conditions at an electric voltage of 30 V: (a) different temperatures (film thickness: 70 nm, and electric field: 42.8 MV/m), (b) different, initial film thicknesses (temperature: 180 C, and electric field: 42.8 MV/m), and (c) different electric field intensities (film thickness: 70 nm, temperature: 180 C) 6. Temperature dependence of the parameters of

(solid symbol) and

(open symbol) (film

thickness: 70 nm, electrode separation: 700 nm, and electric field: 42.8 MV/m) 7. Thickness dependence of the parameters of

(solid symbol) and

(open symbol) (electrode

separation: 700 nm, electric field: 42.8 MV/m, and annealing temperature: 180 °C) 8. Effect of electrode separation (electric field) on the parameters of

(solid symbol) and (open

symbol) (film thickness: 70 nm, electric voltage: 30 V, and annealing temperature: 180 °C) 9. AFM image of the coalescence of two pillars during the pillar growth (film thickness: 70 nm, electrode separation: 700 nm, electric field: 42.8 MV/m, annealing temperature: 180 °C, and annealing time: 30 min)


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10. Variations of the rate constant with the variables of (a) temperature (film thickness: 70 nm, and electrode separation: 700 nm), (b) film thickness (temperature: 180 C, and electrode separation: 700 nm), and (c) electrode separation (electric field) (film thickness: 70 nm, temperature: 180 C)


Page 20 of 29

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Figure 1. Optical micrographs of surface patterns on surface of PS films formed at different temperatures and different annealing times (film thickness: 70 nm, electrode separation: 700 nm, and electric field: 42.8 MV/m)


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Figure 2. AFM images of surface patterns on surface of PS films formed at different temperatures and different annealing times (film thickness: 70 nm, electrode separation: 700 nm, and electric field: 42.8 MV/m)


Page 22 of 29

Page 23 of 29

(a)

800

600

600 400

o

200 0

(b)

800

Height (nm)

Height (nm)

0

10

20

Temperature ( C): 190 180 170 160 30 40 50 60 70 80 Time (min)

400 200 0

0

10

20

Film thickness (nm): 90 70 50 30 30 40 50 60 70 Time (min)

1400 1200

(c)

1000 Height (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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800 600

Electric field (MV/m):

400 200 0

20

40

60

80

27.3 33.3 42.8 60 100 120

Time (min)

Figure 3. Temporal evolution of average pillar height for different conditions at an electric voltage of 30 V: (a) different temperatures (film thickness: 70 nm, and electric field: 42.8 MV/m), (b) different, initial film thicknesses (temperature: 180 C, and electric field: 42.8 MV/m), and (c) different electric field intensities (film thickness: 70 nm, and temperature: 180 C)


Langmuir

3.5

(a)

(b)

3

3.0 2

Diameter ( m )

2.5

2

Diameter ( m )

2

2.0

2

1.5

Temperature (oC) 190 180 170 160

1.0 0.5 0.0 0

20

40 60 Time (min)

80

0

100

Film thickness (nm): 90 70 50 30

1

0

10

20

30

40 50 Time (min)

60

70

80

3

2

2

2

(c)

4 Diameter ( m )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 29

2

Electric field (MV/m): 27.3 33.3 42.8 60

1 0

0

20

40

60

80

100

120

140

Time (min)

Figure 4. Temporal evolution of average pillar diameter for different conditions at an electric voltage of 30 V: (a) different temperatures (film thickness: 70 nm, and electric field: 42.8 MV/m), (b) different, initial film thicknesses (temperature: 180 C, and electric field: 42.8 MV/m), and (c) different electric field intensities (film thickness: 70 nm, and temperature: 180 C)


Page 25 of 29

0.8

0.8

(a) 2

Density of pillars (#/ m )

(a)

2


o

0.6

Temperature ( C):

0.4

190 180 170 160

0.2

0.0

0

20

40

60

80

0.4

0.2

0.0

100

Film thickness (nm): 90 70 50 30

0.6

0

20

Time (min)

40

60

80

100

Time (min)

(a)

0.6

2


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Electric field (MV/m): 27.3 33.3 42.8 60

0.4

0.2

0.0

0

20

40

60

80

100

120

140

Time (min)

Figure 5. Temporal evolution of the density of pillars for different conditions at an electric voltage of 30 V: (a) different temperatures (film thickness: 70 nm, and electric field: 42.8 MV/m), (b) different, initial film thicknesses (temperature: 180 C, and electric field: 42.8 MV/m), and (c) different electric field intensities (film thickness: 70 nm, temperature: 180 C)


Langmuir

0.09

20

0.08 Q=25.3 kJ/mol, =0.08

0.06

2

( /min)

0.07

(nm/min)

0.05 0.04

Q=30.2 kJ/mol, =0.10 10 9

0.03 0.255

8

0.26

0.265 0.27 0.275 1000/RT (mol/kJ)

Figure 6. Temperature dependence of the parameters of

0.28

(solid symbol) and

(open symbol)

(film thickness: 70 nm, electrode separation: 700 nm, and electric field: 42.8 MV/m)

0.08 0.07

20 Power index: 3/4

2

( m /min)

0.06

16

0.05 1/4

0.04 0.03

0.02 30

18

14

(nm/min)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 29

12

40

50 60 70 Film thickness (nm)

Figure 7. Thickness dependence of the parameters of

10 80 90 100

(solid symbol) and

(open symbol)

(electrode separation: 700 nm, electric field: 42.8 MV/m, and annealing temperature: 180 °C)


0.1 0.09 0.08 0.07 0.06

60

Electric field (MV/m) 42.86 33.33 27.27

30

Power index: -1 20 (nm/min)

0.05

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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( m /min)

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-0.5

0.04 0.03

0.02 400

500

600 700 800 900 1000 Electrode separation (nm)

10 9 8 1200

Figure 8. Effect of electrode separation (electric field) on the parameters of

(solid symbol) and

(open symbol) (film thickness: 70 nm, electric voltage: 30 V, and annealing temperature: 180 °C)

Figure 9. AFM image of the coalescence of two pillars during the pillar growth (film thickness: 70 nm, electrode separation: 700 nm, electric field: 42.8 MV/m, annealing temperature: 180 °C, and annealing time: 30 min)


Langmuir

0.1

0.1 0.09

0.09

0.08

(1/min)

(1/min)

0.07

0.08 0.07

0.06

0.06 0.05 0.255

0.26

0.265 0.27 1000/RT (mol/kJ)

0.275

0.12

60

0.28

0.05 20

30

40

Electric field (MV/m): 42.86 33.3

50 60 70 80 Film thickness (nm)

90

100

27.3

0.1 0.08

(1/min)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.06 0.04 0.02 0 400

500

600 700 800 900 1000 1100 1200 Electrode separation (nm)

Figure 10. Variations of the rate constant with the variables of (a) temperature (film thickness: 70 nm, and electrode separation: 700 nm), (b) film thickness (temperature: 180 C, and electrode separation: 700 nm), and (c) electrode separation (electric field) (film thickness: 70 nm, temperature: 180 C)


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TABLE OF CONTENTS GRAPHIC

Coalescence of pillars and temporal evolution of the density of pillars at different temperatures (film thickness: 70 nm, and electric field: 42.8 MV/m). 0.8

(a) 2


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

o

0.6

Temperature ( C):

0.4

190 180 170 160

0.2

0.0

0

20

40

60

80

100

Time (min)


Growth of Polystyrene Pillars in Electric Field - Langmuir (ACS

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