Modeling of Poly(Methylmethacrylate) Viscous Thin Films by Spin-Coating

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Article Modeling of Poly(methylmethacrylate) Viscous Thin Films by Spin-Coating

Navid Chapman, Mingyu Chapman and William B. Euler *

Department of Chemistry, University of Rhode Island, Kingston, RI 02881, USA; [email protected] (N.C.); [email protected] (M.C.) * Correspondence: [email protected]

Abstract: A predictive film thickness model based on an accepted equation of state is applied to the spin-coating of sub-micron poly(methylmethacrylate) viscous thin films from toluene. Concentration effects on density and dynamic viscosity of the spin-coating solution are closely examined. The film thickness model is calibrated with a system-specific film drying rate and was observed to scale with the square root of spin speed. Process mapping is used to generate a three-dimensional design space for the control of film thickness.

Keywords: spin-coating; PMMA; film thickness model

1. Introduction In this work, we report methods for the controlled deposition of poly(methylmethacrylate) (PMMA) coatings on glass slides. Owing to its high transparency, PMMA is often chosen



 as an optical substrate, so control of polymer film thickness is critical to determining the optical thickness, which, for example, can influence sensor efficiency and performance [1]. Citation: Chapman, N.; Chapman, When used as a substrate for fluorophores, PMMA has been demonstrated to increase M.; Euler, W.B. Modeling of the stability of the fluorophore against both thermal and photo degradation [2]. Coatings Poly(methylmethacrylate) Viscous are applied by spin-coating, a common process for the repeatable deposition of films of Thin Films by Spin-Coating. Coatings uniform thickness and surface roughness. Toluene is frequently used as solvent to dissolve 2021, 11, 198. https://doi.org/ PMMA in fundamental spin-coating studies [3–5]. The PMMA–toluene solution is miscible 10.3390/coatings11020198 at all concentrations and has relatively weak solvent–solute interactions [6–8]. Newtonian fluid behavior has been demonstrated with linear shear stress and shear rates over a large Academic Editor: Bartosz Handke concentration range [9]. Received: 18 January 2021 In our previous studies of sensors composed of a fluorophore deposited on a polymer Accepted: 3 February 2021 Published: 9 February 2021 substrate [10], the thickness of the polymer layer was an important parameter in the sensor performance. In that study, the polymer thicknesses were thinner than typical, a few hundred nanometers, on the order of the wavelength of the light used. The previous Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in studies examined polymer solutions of dilute to medium concentrations and thin films published maps and institutional affil- up to a few microns in thickness. The focus of this study is to analyze materials and iations. fluid properties for process mapping of a predictive spin-coating model for depositing sub-micron polymer layers.

2. Materials and Methods Glass microscope slides (~1 mm thick) were cut into 37.5 mm × 25 mm sections. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. Slides were cleaned and treated by submersion in ethanol (EtOH, 95%, Pharmco-Aaper, This article is an open access article Brookfield, CT, USA), followed by 15 min of sonication, then rinsed with purified water, distributed under the terms and submerged in purified water, sonicated for an additional 15 min, and dried under N2. conditions of the Creative Commons Atactic PMMA (Mw~120,000, Polydispersity index 2.0–2.4) was obtained from Sigma- Attribution (CC BY) license (https:// Aldrich and used without further purification. A 20 g/dL stock solution was prepared in creativecommons.org/licenses/by/ toluene (Honeywell, HPLC grade, Smithfield, RI, USA). The polymer stock solution was 4.0/). sonicated for 8 h with intermittent shaking to ensure full solvation. The resulting solution

Coatings 2021, 11, 198. https://doi.org/10.3390/coatings11020198 https://www.mdpi.com/journal/coatings Coatings 2021, 11, 198 2 of 12

was optically clear. Dilutions ranging from 0.75 to 10.00 g/dL were prepared directly from the stock. The dynamic viscosity of the polymer solutions was measured with cylindrical spin- dles and a Brookfield DV2T spring-torque rotational viscometer (Middleboro, MA, USA) at a shear rate of 200 s−1. Sample temperature was measured by a thermocouple attached to the sample chamber and maintained at 20.0 ◦C. A Laurell Technologies spin-coater was used for spin-coating films. An ultra-thin PMMA film was applied to the glass slides in dry conditions (<20% relative humidity) by depositing a 250 µL aliquot of polymer solution in the center of a slide and then spin- coating for 45 s, accelerating at 1080 s−2, and with a maximum rotation speed in the range of 400 to 8000 RPM. Spin-coating was carried out under a constant flow of dry N2 and films were air dried for 15 min and then transferred to an oven set at 60 ◦C for 2 min to facilitate residual solvent removal. Fourier transform infrared (FTIR) spectra were obtained with a Perkin Elmer Spectrum 100 (Waltham, MA, USA) fitted with a diamond ATR crystal. Background and sample spectra were collected with 128 scans and a resolution of 4 cm−1. Thermal mass loss experiments were performed with a TA Instruments (New Castle, DE, USA) thermogravimetric analyzer (TGA). Static evaporation rate (ω = 0) investiga- tions were conducted in open cylindrical aluminum pans (20 µL capacity, 5 mm diameter). Samples were held isothermally at an ambient temperature. Dry compressed air was used to purge the balance and sample at a flow rate of 25 mL/min. A second investi- gation for polymer characterization was conducted with open aluminum sample pans (80 µL). Samples were first equilibrated at 30 ◦C and then heated to 500 ◦C at a rate of 10 ◦C/min. Dry nitrogen was used to purge the balance and sample at flow rates of 40 and 30 mL/min, respectively. Reflection spectra of polymer films in the range of 400–900 nm were acquired with a Filmetrics F40 microscope thin film analyzer (Fairport, NY, USA) using a tungsten–halogen light source. PMMA thin film optical constants for the refractive index, n, and absorption coefficient, k, were obtained from the literature [11]. Spectral fitting and film thickness calculations were performed with Filmeasure software (version 7.18.6). Examples of spectra and fits are given in Figure S1. Transmittance spectra of polymer films were collected with a Perkin Elmer Lambda 1050 UV/Vis spectrometer (Waltham, MA, USA). The slit width and integration time were set at 2 nm and 0.20 s, respectively. Wavelengths generated from tungsten–halogen and deuterium lamps were collected in the 1100 to 300 nm range.

3. Results 3.1. Spin-Coating Theory Foundations for the spin-coating model were laid by Emslie, Bonner, and Peck in their study of hydrodynamic flow of a non-volatile Newtonian fluid [12]. They proposed that influence from gravitational and Coriolis acceleration could be neglected when the thinning fluid possesses a disproportionate viscosity to thickness ratio and is rotated at speeds of 100 RPM or more. With these conditions met, fluid thinning could be described as a force balance between viscous drag and rotational acceleration dependent upon radial and hydrodynamic forces, as described by the parameter:

K = ω2/3ν (1)

where K is the force parameter, ω is rotational velocity and ν is kinematic viscosity. Mey- erhofer adapted this approach to incorporate a volatile solvent [13]. Considerations were provided for evaporation and fluid dynamics while assuming a lubrication approximation (no slip due to sufficient substrate wetting) and negligible impacts from surface tension or substrate acceleration. Viscous film thinning is described as a two-stage sequential domination of hydrodynamic and evaporative forces. Initial fluid thinning is directed by radial outflow and continues until solute enrichment reaches a critical point where fluid viscosity retards flow and solvent evaporation becomes the dominant force. The Coatings 2021, 11, 198 3 of 12

final stages of film formation continue at a constant evaporation rate until a solid film has formed. From the transition point onward, the contributions to thinning due to radial outflow are negligible in comparison to evaporation. The rate of film thinning per unit area was described by

dh/dt = −2Kh3 − E (2)

where h is the vertical thickness of the fluid. The parameter E was proposed for evaporation and captures an observed scaling of the static evaporation rate, e, by rotation speed:

1 E = eω− ⁄2 (3)

Haas reported that the rate of solvent evaporation is reliant on solvent partial pressure. Solvent mass transfer to the vapor phase is inhibited by diffusion within the film at low partial pressure and resisted by the saturated environment above the film at high partial pressure. The evaporation rate is a static system-specific parameter that encompasses solvent vapor pressure effects and diffusivity into the overlying gas [14]. Using high speed imaging techniques, Danglad-Flores refined Meyerhofer’s models and proposed a first-order approach to quantitative predictions of final film thickness [3]. This simple method requires only a few initial fluid properties, spin speed, and a calibration experiment to determine the system-specific evaporation rate.

1 1/3 1/3 − ⁄2 hf = (3e/2) χo(ηo/ρo) × ω (4)

where hf is the final dry film thickness, χo is the polymer mass fraction, ηo is the dynamic viscosity, and ρo is the density, all at pre-spinning conditions. Solution density and viscosity properties are closely related to polymer concentration. The viscous behavior of the polymer solutions can be described with the reduced specific viscosity, ηred: ηred = (ηo/ηs − 1)/c (5)

where ηo is the initial viscosity of the polymer solution, ηs is the viscosity of the pure solvent, and c is the concentration of the polymer in the spin-coating solution. Dynamic viscosity relates to the solution concentration per the Martin equation [15]:

cKH × [η] ηred = [η] × e (6)

where [η] is intrinsic viscosity and KH is Huggin’s viscosity constant. The value of KH is expected to be near 0.4, which is the reciprocal of the Einstein–Stokes constant in an ideal dilute solution where the probability of interactions between polymer chains is negligible. Matsuoka and Cowman have reported a systematic overestimation of KH during analysis of high molecular weight compounds at low concentrations [16]. This error has been attributed to straight line approximations, which can be accommodated for by restricting KH to 0.4 ± 0.1. The application of Equation (6) is limited to dilute through to medium concentrated solutions. The deviation at higher concentrations is associated with interactions from overlapping polymer coils. Matsuoka and Cowman [16] propose that the viscous behavior arising from polar, ionic, and hydrogen bonding interactions can be better approximated by expanding Equation (6) into a Taylor series:

η ≈ [η] × ∞ ( × [η])i red ∑i = 0 cKH /i!. (7) A conservative approximation of entanglement effects is made by truncating expan- sion after the third term [15]. Coatings 2021, 11, 198 4 of 12

3.2. PMMA Solution Characterization Polymer solutions were prepared at concentrations ranging from 0.125 to 20.0 g/dL and were observed to be clear and free flowing. Optical transparency for all solutions was identical to the pure solvent. Polymer mass fraction and solution density determinations were conducted at an ambient temperature of 20 ◦C. Both mass fraction and density increased linearly with polymer concentration. The relationship between polymer mass fraction and concentration is described by:

χ = 1.12 × 10−2c (8)

The relationship between solution density and concentration is described by:

ρs = 2.94c + ρsol (9)

where ρsol is the density of the pure solvent. For both regressions, the coefficient of determination R2 was greater than 0.999. The dynamic viscosity of fluids was observed between 1.13 and 8.31 mPa·s. Viscosity measurements were taken at constant shear rates of 200 s−1 for semi-dilute polymer to moderately concentrated solutions (2.5 to 10.0 g/dL). Solution viscosity was observed to increase exponentially with polymer concentration. Figure1 shows a Huggin’s plot of reduced specific viscosity versus concentration. Non- linear regression by Equation (7) was found to converge by the sixth term ([η] = 0.292 ± 0.031, KH = 0.500 ± 0.101,). Potentially due to differences in fractional polydispersity [17] or systematic fitting errors [16], a wide range of literature values have been reported for [η] and KH combinations [18]. For this reason, experimental intrinsic viscosity determinations were compared to estimations made with the Mark–Houwink equation:

α [η] = KMHMw (10)

where Mw is PMMA molecular weight and KMH and α are the Mark–Houwink coefficients. Calculations were made with reported Mark–Houwink coefficients [19–21] and the results are listed in Table1. Experimentally determined intrinsic viscosity for PMMA is also shown in Table1 and is in good agreement with estimates calculated from literature values. Limitations of the fitting regression are observed by the assignment of KH at the upper limit which was implemented to avoid erroneous straight line approximations [16]. When the fitting was performed without variable constraints, KH and [η] converged near ~0.7 and ~0.18 dL/g, respectively. The higher than expected KH suggests that the solution rheology may be impacted by undetermined polymer–solvent dynamics or synergistic effects.

Table 1. Poly(methylmethacrylate) (PMMA) intrinsic viscosity estimated from Mark–Houwink parameters. Intrinsic viscosity estimates determined from Equation (10). Coefficients, KMH and a, were obtained from studies that utilized different analytical techniques. Presented results and referenced studies were performed at comparable temperatures.

−3 ◦ [η] (dL/g) MMH (10 mL/g) α T ( C) Measurement Reference 0.292 ± 0.031 – – 20 Viscosity this work 0.28 7.0 0.71 30 Viscosity [20] 0.33 8.12 0.71 25 Osmometry [21] 0.27 7.79 0.697 25 light scattering [19]

Figure2 shows a plot between dynamic viscosity and concentration. This relationship is fit reasonably well by Equation (7) truncated at the third term (R2 = 0.97, error: ±0.34) with the largest deviations occurring at the highest concentrations. Coatings 2021, 11, x FOR PEER REVIEW 4 of 12

3.2. PMMA Solution Characterization Polymer solutions were prepared at concentrations ranging from 0.125 to 20.0 g/dL and were observed to be clear and free flowing. Optical transparency for all solutions was identical to the pure solvent. Polymer mass fraction and solution density determinations were conducted at an ambient temperature of 20 °C. Both mass fraction and density in- creased linearly with polymer concentration. The relationship between polymer mass fraction and concentration is described by:

χ =1.12×10 (8) The relationship between solution density and concentration is described by:

ρs = 2.94c + ρsol (9)

where ρsol is the density of the pure solvent. For both regressions, the coefficient of deter- mination R2 was greater than 0.999. The dynamic viscosity of fluids was observed between 1.13 and 8.31 mPa·s. Viscosity measurements were taken at constant shear rates of 200 s−1 for semi-dilute polymer to moderately concentrated solutions (2.5 to 10.0 g/dL). Solution viscosity was observed to increase exponentially with polymer concentration. Figure 1 shows a Huggin’s plot of reduced specific viscosity versus concentration. Nonlinear regression by Equation (7) was found to converge by the sixth term ([η] = 0.292 ± 0.031, = 0.500 ± 0.101,). Potentially due to differences in fractional polydispersity [17] or systematic fitting errors [16], a wide range of literature values have been reported for [η] and combinations [18]. For this reason, experimental intrinsic viscosity determi- nations were compared to estimations made with the Mark–Houwink equation:

α [η] = KMHMw (10)

where Mw is PMMA molecular weight and KMH and α are the Mark–Houwink coefficients. Calculations were made with reported Mark–Houwink coefficients [19–21] and the results are listed in Table 1. Experimentally determined intrinsic viscosity for PMMA is also shown in Table 1 and is in good agreement with estimates calculated from literature val- ues. Limitations of the fitting regression are observed by the assignment of at the up- per limit which was implemented to avoid erroneous straight line approximations [16]. When the fitting was performed without variable constraints, and [η] converged near ~0.7 and ~0.18 dL/g, respectively. The higher than expected suggests that the so- Coatings 2021, 11, 198 lution rheology may be impacted by undetermined polymer–solvent5 of 12 dynamics or syner- gistic effects.

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Table 1. Poly(methylmethacrylate) (PMMA) intrinsic viscosity estimated from Mark–Houwink parameters. Intrinsic viscosity estimates determined from Equation (10). Coefficients, KMH and a, were obtained from studies that utilized different analytical techniques. Presented results and referenced studies were performed at comparable temperatures.

[η] (dL/g) MMH (10−3 mL/g) α T (°C) Measurement Reference 0.292 ± 0.031 – – 20 Viscosity this work 0.28 7.0 0.71 30 Viscosity [20] 0.33 8.12 0.71 25 Osmometry [21] 0.27 7.79 0.697 25 light scattering [19] FigureFigure 1. Huggin’s 1. Huggin’s plot of reduced plot specificof reduced viscosity versusspecific polymer viscos concentration.ity versus Nonlinear polymer concentration. Non- regressionFigure by 2 shows series expansion a plot between of Equation dynamic (7) and visc parametersosity and convergedconcentration. by the This sixth relation- term for η ± ± 2 ship[ linear] = is 0.292 fit reasonablyregression0.031 and wellKH = by 0.500 Equati series0.101on (7)expansion (R truncated= 0.96). Lines at ofthe for Eqthird theuation first term six (R term 2(7) = 0.97, expansionsand error: parameters of± converged by the Equation (7) have been plotted. Vertical error bars are presented for all points. 2 0.34)sixth with term the largest for deviations[η] = 0.292 occurring ± 0.031 at the andhighest concentrations. = 0.500 ± 0.101 (R = 0.96). Lines for the first six term expansions of Equation (7) have been plotted. Vertical error bars are presented for all points.

Figure 2. Dynamic viscosity as a function of spin-coating solution concentration. The fit line was Figure 2. Dynamic viscosity as a function of spin-coating solution concentration. The fit line was determineddetermined by by combining combining Equation Equation (5) (5) with with Equati Equationon (7) (7) (truncated (truncated at at the the third third term) term) and and solving solving 2 η 2 ± forfor η0,, with with RR == 0.973 0.973 and and standard standard error error ± 0.34.0.34.

AA theoretical theoretical examination examination of of solvent–polymer solvent–polymer interactions interactions can can be be approached approached by by Hansen’s three-component solubility parameter, Ra: Hansen’s three-component solubility parameter, Ra:

h i1/2 = [4(δ −δ )2 + (δ −δ )2 + (δ −δ )2] (11) Ra = 4(δD2 − δD1) + (δP2 − δP1) + (δH2 − δH1) (11)

where the three solubility parameters are: δ, dispersion; δ, polar; and δ, hydrogen bonding.where the Table three 2 displays solubility the parameters parameters are: for δPMMAD, dispersion; and tolueneδP, polar; [22,23]. and HansenδH, hydrogen solubil- itybonding. parameter Table (HSP)2 displays theory the describes parameters relative for PMMA energy and difference toluene (RED) [ 22,23 as]. Hansenthe ratio solubility of HSP distance,parameter Ra,(HSP) to the theoryinteraction describes radius, relative Ro. Solubility energy is difference expected (RED)when RED as the < 1 ratio and ofpartial HSP distance, R , to the interaction radius, R . Solubility is expected when RED < 1 and partial solubility whena RED is at unity. For PMMAo in toluene, Ra = 10.7 (from Equation (11)) and solubility when RED is at unity. For PMMA in toluene, R = 10.7 (from Equation (11)) and Ro = 11.1 [24]. While the calculated RED value of 0.96 correctlya predicts full solubility, it suggests relatively weak solute–solvent interactions. The degree of variance between in- dividual solubility parameters describes interactions as mainly dispersion–van der Waals forces, with some polar interactions, and relatively little hydrogen bonding.

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Ro = 11.1 [24]. While the calculated RED value of 0.96 correctly predicts full solubility, it suggests relatively weak solute–solvent interactions. The degree of variance between Coatings 2021, 11, x FOR PEER REVIEW individual solubility parameters describes interactions as mainly dispersion–van6 of 12 der Waals forces, with some polar interactions, and relatively little hydrogen bonding.

Table 2. Hansen solubility parameters for PMMA and toluene. Data from Refs. [22,23]. Table 2. Hansen solubility parameters for PMMA and toluene. Data from Refs. 22 and 23. 1/2 1/2 1/2 Material δD (MPa) δP (MPa) δH (MPa) Material δD (MPa)½ δP (MPa)½ δH (MPa)½ PMMA 19.74PMMA 4.92 19.74 4.92 11.5 11.5 Toluene 18.0 1.4 2.0 Toluene 18.0 1.4 2.0

ThermogravimetryThermogravimetry was used to screen was usedfor a solute to screen effect for on a solute the evaporation effect on the rate. evaporation A rate. A slow flow of purgedslow flowN2 was of purgedused to Nfacilitate2 was used solvent to facilitate vapor removal solvent vaporwithout removal encouraging without encouraging convection. Figureconvection. 3 shows Figure the mass3 shows loss thecurves mass and loss the curves static and evaporation the static evaporationrates (ω = 0) rates ( ω = 0) of of toluene and tolueneof a 10.0 andg/dL of polymer a 10.0 g/dL solution polymer. The two solution. mass Theloss twocurves mass are loss very curves similar are very similar for the first twentyfor theminutes first of twenty drying. minutes Beginni ofng drying. at around Beginning 20 min of drying, at around when 20 PMMA min of drying, when is approximatelyPMMA χ ≈ 0.2, is the approximately polymer solutionχ ≈ 0.2, begins the to polymer dry slower solution than the begins pure to solvent. dry slower than the The initial verticalpure thinning solvent. rate The is initial 590 nm/s. vertical As thinningtime goes rate on, isthe 590 polymer nm/s. Assolution time goesevap- on, the polymer χ ≈ oration rate decreasessolution to evaporation 195 nm/s at ratearound decreases 85 min to (χ 195 ≈ 0.8) nm/s when ataround the rate 85 of minevaporation ( 0.8) when the rate in the polymer ofsolution evaporation is strongly in the suppressed. polymer solution In contrast, is strongly pure toluene suppressed. evaporates In contrast, stead- pure toluene ily through depletion.evaporates steadily through depletion.

(a) (b)

Figure 3. (aFigure): TGA 3. thermogram (a): TGA thermogram showing isothermal showing isothermal evaporation ev ofaporation pure toluene of pure and toluene a 10 g/dL and PMMA–toluenea 10 g/dL solution PMMA–toluene solution under N2 purge. Both solutions were monitored until dry. The residue under N2 purge. Both solutions were monitored until dry. The residue mass in the 10 g/dL PMMA curve represents the mass in the 10 g/dL PMMA curve represents the dried polymer. (b): Derivative TGA thermogram dried polymer. (b): Derivative TGA thermogram of solvent and polymer solution at ambient temperature with respect to of solvent and polymer solution at ambient temperature with respect to polymer mass fraction. polymer mass fraction.

Solvent evaporationSolvent is evaporationcontrolled by is diffus controlledivity within by diffusivity the film within and solvent the film partial and solvent partial pressure abovepressure the film. above The observed the film. decrease The observed in evaporation decrease inrate evaporation over time ratecontrasts over time contrasts with the expectedwith constant the expected evaporation constant rates evaporation that have ratesbeen thatreported have for been the reported spin-coating for the spin-coating process [4,25]. processIt is likely [4, 25that]. Itsurface is likely tension that surface effects tensionhelp shape effects evaporation help shape rates. evaporation The rates. The slow removal ofslow toluene removal in the of final toluene stages in theof film final formation stages of filmmay formationbe indicative may of be a solvent indicative of a solvent mass transfer beingmass diffusion transfer being rate limited diffusion in the rate enriched limited in polymer the enriched environment. polymer environment. The derivative TheTGA derivative plots give TGAthe evaporatio plots given therates evaporation directly. The rates evaporation directly. Therate evaporationof rate the polymer solutionof the polymerat concentrations solution less at concentrations than 0.2χ are nearly less than identical 0.2χ are to nearlythe pure identical sol- to the pure vent. Evaporationsolvent. rates Evaporationare slightly reduced rates are at slightly polymer reduced concentrations at polymer less concentrationsthan 0.8χ. Sig- less than 0.8χ. nificantly slowerSignificantly evaporation slower rates are evaporation observed ratesat the arefinal observed stages of at polymer the final enrichment stages of polymer enrich- and may be correlatedment and with may a glass be correlated transition. with The a observed glass transition. constant The decrease observed in evapo- constant decrease in ration rates is possiblyevaporation a solvent rates retention is possibly effect a solvent caused retention by interactions effect caused with the by sample interactions with the container walls.sample container walls.

3.3. PMMA Thin Film Characterization TGA and FTIR were measured on both the PMMA starting material and final dried film to verify that no chemical changes occurred. Figure 4 shows mass loss associated with thermal decomposition occurring between an ambient temperature and 500 °C. An initial mass loss is observed near 153 °C and followed by a larger mass loss near 260 °C, in agree- ment with previous reports [26–28]. These two mass loss stages are generally associated with depolymerization, starting from head-to-head linkages and unsaturated vinyl ends.

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3.3. PMMA Thin Film Characterization TGA and FTIR were measured on both the PMMA starting material and final dried film to verify that no chemical changes occurred. Figure4 shows mass loss associated with thermal decomposition occurring between an ambient temperature and 500 ◦C. An Coatings 2021, 11, x FOR PEER REVIEW ◦ 7 of◦ 12 initial mass loss is observed near 153 C and followed by a larger mass loss near 260 C, in agreement with previous reports [26–28]. These two mass loss stages are generally associated with depolymerization, starting from head-to-head linkages and unsaturated vinylThe third ends. and The largest third mass and largestloss shown mass near loss 370 shown °C is near often 370 associated◦C is often with associated a methoxycar- with abonyl methoxycarbonyl side group scission side group and random scission scissions and random of the scissions main chain. of the Highly main similar chain. thermal Highly similarbehavior thermal is observed behavior for both is observed samples, forwhic bothh suggests samples, that which the bulk suggests chemical that properties the bulk chemicalof the polymer properties were of not the affected polymer by were the notspin affected-coating by process. the spin-coating The small process. differences The smallasso- differencesciated with associatedthe spin-cast with film the can spin-cast be attributed film can to beloss attributed of residual to losssolvent. of residual solvent.

◦ Figure 4. TGATGA thermogram thermogram of of bulk bulk PM PMMAMA and and spin-cast spin-cast film film at at10 10 °C/min;C/min; 10.95 10.95 mg mgof PMMA of PMMA powder and 0.28 mg of spin-cast filmfilm werewere usedused inin thethe measurements.measurements.

Additional chemical characterization of bulk and spin-cast polymer was carried out by FTIR analysis. Figure 55 overlaysoverlays thethe infraredinfrared absorbanceabsorbance spectraspectra ofof thethe twotwo samples samples −1 from 4000 to 1200 cm . The observed absorbance bands for methyl, carbonyl, and ester from 4000 to 1200 cm−1. The observed absorbance bands for methyl, carbonyl, and ester stretching modes at ~2900, ~1700, and ~1450 cm−1 have also been reported in the literature stretching modes at ~2900, ~1700, and ~1450 cm−1 have also been reported in the literature for PMMA as a bulk substance and thin film [7,17,29]. The FTIR spectra of the bulk material for PMMA as a bulk substance and thin film [7,17,29]. The FTIR spectra of the bulk mate- and the 720 nm spin-cast film are similar, consistent with the TGA results. rial and the 720 nm spin-cast film are similar, consistent with the TGA results. The conclusion is that the thin films cast from a toluene solution at room temperature The conclusion is that the thin films cast from a toluene solution at room temperature have the same chemical and molecular weight properties as the pre-processing powder. have the same chemical and molecular weight properties as the pre-processing powder. This conclusion is also supported by the weak solvent–solute interactions predicted by the This conclusion is also supported by the weak solvent–solute interactions predicted by Hansen solubility parameters. the Hansen solubility parameters. Polymer film thickness was measured using the thin film interference fringing patterns from both transmission (UV–Vis) and reflectance (Vis) spectra. Film thicknesses ranged from 65 nm to 1 µm and the transmission and reflectance determinations were in agreement to within 5%. A minimum of three locations on each film were measured and the variation across the film was less than 5%. The polymer layer thickness was varied using both the rotation rate and the solution concentration and the measured thicknesses agreed with a previous report [10].

Figure 5. FTIR spectra of bulk PMMA and spin-cast film collected in ATR mode with a diamond crystal. The thin film was not removed from the glass substrate prior to measuring spectra, which limited the spectral range to 1200 cm−1 due to the strong silicate absorbance from the glass sub- strate.

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The third and largest mass loss shown near 370 °C is often associated with a methoxycar- bonyl side group scission and random scissions of the main chain. Highly similar thermal behavior is observed for both samples, which suggests that the bulk chemical properties of the polymer were not affected by the spin-coating process. The small differences asso- ciated with the spin-cast film can be attributed to loss of residual solvent.

Figure 4. TGA thermogram of bulk PMMA and spin-cast film at 10 °C/min; 10.95 mg of PMMA powder and 0.28 mg of spin-cast film were used in the measurements.

Additional chemical characterization of bulk and spin-cast polymer was carried out by FTIR analysis. Figure 5 overlays the infrared absorbance spectra of the two samples from 4000 to 1200 cm−1. The observed absorbance bands for methyl, carbonyl, and ester stretching modes at ~2900, ~1700, and ~1450 cm−1 have also been reported in the literature for PMMA as a bulk substance and thin film [7,17,29]. The FTIR spectra of the bulk mate- rial and the 720 nm spin-cast film are similar, consistent with the TGA results. The conclusion is that the thin films cast from a toluene solution at room temperature have the same chemical and molecular weight properties as the pre-processing powder. Coatings 2021, 11, 198 This conclusion is also supported by the weak solvent–solute interactions predicted8 of 12by the Hansen solubility parameters.

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Polymer film thickness was measured using the thin film interference fringing pat- terns from both transmission (UV–Vis) and reflectance (Vis) spectra. Film thicknesses ranged from 65 nm to 1 μm and the transmission and reflectance determinations were in FigureFigureagreement 5.5. FTIR to spectrawithin of5%. bulk bulk A PMMAminimum PMMA and and ofspin-cast spin-cast three locationsfilm film collected collected on eachin in ATR ATR film mode mode were with with measured a adiamond diamond and crystal.crystal.the variation TheThe thinthin across filmfilm waswas the not film removed was less from than the glass5%. Thesubstrate polymer prior layer to measuring thickness spectra, spectra, was whichvaried which −1 limitedlimitedusing both the the spectral spectral the rotation range range to torate 1200 1200 and cm cm −the1 duedue solution toto thethe strong strongconcentration silicate silicate absorbance absorbance and the frommeasured from the the glass glass thicknesses substrate. sub- strate.agreed with a previous report [10]. OwingOwing toto thethe highhigh molecularmolecular weightweight ofof thethe polymer,polymer, filmfilm thicknessthickness isis largelylargely dictateddictated byby spin-coating parameters parameters related related to to the the tran transportsport of ofthe the solution solution over over the thesubstrate. substrate. The Thereported reported thicknesses thicknesses are averages are averages since sincethe films the filmshave measurable have measurable roughness roughness that will that be willaddressed be addressed in detail in in detaila forthcoming in a forthcoming manuscript. manuscript. The primary The and primary secondary and factors secondary with factorsthe largest with impact the largest on film impact thickness on film are thickness initial solution are initial concentration solution concentration and spin speed and spin[12,13,30]. speed Figure [12,13 ,306 shows]. Figure the6 finalshows film the heig finalht as film a function height as of a combined function ofconcentration combined concentrationand viscosity variables and viscosity from variables Equation from (4). At Equation a given (4). spin At speed, a given the spin final speed, film thickness the final ⁄ 1/3 filmincreases thickness linearly increases as a function linearly of as the a function fluid properties of the fluid given properties by χ(η given⁄)ρ by. χFigure0(η0/ρ 70 plots) . Figurefinal film7 plots height final against film height spin speed, against as spingiven speed, in Equation as given (4). in At Equation a given initial (4). At concentra- a given initialtion, the concentration, final film thickness the final filmalso thicknessincreases alsolinearly increases with linearlythe inverse with square the inverse root squareof spin rootspeed. of spinComparisons speed. Comparisons of slopes in of Figures slopes in6 Figuresand 7 imply6 and 7that imply changes that changes in solution in solution concen- concentrationtration have a havegreater a greater impact impact on film on thickness film thickness than changes than changes in angular in angular velocity. velocity.

Figure 6. Film thickness as a function of the casting solution properties, per Equation (4). χo is the Figure 6. Film thickness as a function of the casting solution properties, per Equation (4). χo is the polymer concentration (mass fraction) and ν0 is the kinematic viscosity. Error bars are the standard polymer concentration (mass fraction) and ν0 is the kinematic viscosity. Error bars are the stand- deviation of at least 3 measurements per point. ard deviation of at least 3 measurements per point.

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FigureFigure 7. 7. ScatterScatter plot plot of of spin spin speed speed contribution to film film thickness. Scatter plot of finalfinal filmfilm heightheight by byFigure spin 7.speed Scatter scaled plot by of Equationsspin speed (1)–(4). contribution Error ba tors film are thickness. the standard Scatter deviation plot of of final at least film 3height meas- spin speed scaled by Equations (1)–(4). Error bars are the standard deviation of at least 3 measure- urementsby spin speed per point. scaled by Equations (1)–(4). Error bars are the standard deviation of at least 3 meas- mentsurements per per point. point. FigureFigure 88 combinescombines thethe twotwo previousprevious plots,plots, asas givengiven inin EquationEquation (4),(4), toto determinedetermine thethe staticstatic Figureevaporation 8 combines rate,rate, e ethe.. TheThe two slopeslope previous of of the the plots, fit fit line line as is given (3is e(3/2)e /2)in1/3 1/3Equation,, giving givinge (4),e= = 140 to140 determine nm/s nm/s1/½2 .. The The the 1/3 √ ½ evaporationevaporationstatic evaporation rate underunder rate, spinning spinninge. The slope conditions conditions of the is fitis then thenline found isfound (3e to/2) to be be, giving ω√ω× ×140 e 140= nm/s140 nm/s nm/s1/½2,, which which. The √ ½ isisevaporation somewhat somewhat less rate thanunder √ ωspinning× 180 nm/s nm/s conditions1½/2 reportedreported is then in in similar similarfound studies studiesto be √ [3,25]. [ω3, 25×]. 140 Possible Possible nm/s reasons reasons, which ½ forforis somewhat this this difference difference less than may may √be be related related× 180 nm/sto the tereported temperaturemperature in similar or the studies vapor phase [3,25]. composition. Possible reasons As wouldwouldfor this be be difference expected, expected, may the the spinning spinningbe related significantly significantly to the temperature increases or the the evaporation vapor phase rate composition. compared Asto thethewould static static be evaporation evaporationexpected, the found found spinning from from significantly the open pan increases (195 to 570 the nm/s). evaporation rate compared to the static evaporation found from the open pan (195 to 570 nm/s).

FigureFigure 8. 8. FilmFilm thickness thickness as a function of deposition parameters,parameters, EquationEquation (4).(4). TheThe slopeslope ofof thethe linearlin- earfitFigure (redfit (red 8. line) Film line) gives thickness gives the the static asstatic a evaporationfunction evaporation of deposition rate, rate,e. e. Error Error parameters, bars bars areare Equation thethe standardstandard (4). The deviation slope ofof of theat at least leastlin- 33ear measurements measurements fit (red line) givesper per point. point. the static evaporation rate, e. Error bars are the standard deviation of at least 3 measurements per point. FigureFigure 99 showsshows a a contour contour plot plot of of film film thicknesses thicknesses as as a function a function of solutionof solution concentration concentra- tionand and spinFigure spin speed 9 speedshows experimental experimental a contour variables. plot variables. of film The thickn The predictive predictiveesses as model a functionmodel is reasonable is of reasonable solution for concentra- thicknessfor thick- nessestimations.tion estimations.and spin This speed This plot experimental isplot a design is a design space variables. space for the for The selection the predictive selection of polymer modelof polymer solution is reasonable solution and spin andfor speedthick- spin combinationsness estimations. that This are likelyplot is to a design generate space films for of the a specified selection thickness, of polymer while solution each and contour spin represents films of similar mean thickness.

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Coatings 2021, 11, 198 10 of 12 speed combinations that are likely to generate films of a specified thickness, while each contour represents films of similar mean thickness.

FigureFigure 9. 9.Contour Contour plot plot of of thickness thickness as as a a function function spin spin speed speed and and solution solution concentration. concentration. 4. Conclusions 4. Conclusions A predictive model for the thickness of sub-micron PMMA thin films by spin-coating from tolueneA predictive has beenmodel generated. for the thickness The bulk of sub-micron chemical propertiesPMMA thin of films the polymerby spin-coating were demonstratedfrom toluene tohas be been unaffected generated. by theThe solvation bulk chemical and coating properties processes. of the Staticpolymer solvent were evaporation,demonstrated at zeroto be shearunaffected film thinning, by the solvation was demonstrated and coating to processes. deviate from Static evaporation solvent evap- of pureoration, solvent, at zero beginning shear atfilm ~0.2 thinning,χ. Solvent was evaporation demonstrated in the polymerto deviate solution from evaporation was observed of topure be strongly solvent, suppressedbeginning fromat ~0.2 ~0.8. Solventχ onward. evaporation Surface tension in the effects polymer may solution help shape wasthe ob- evaporationserved to be rate. strongly Coating suppressed solution fluid from properties ~0.8 onward. were modeled Surface to tens polymerion effects concentration. may help Becauseshape the solution evaporation properties rate. significantly Coating solution impact fluid film thicknessproperties only were during modeled hydrodynamic to polymer thinning,concentration. relationships Because between solution solutionproperties properties significantly were impact limited film to concentrationsthickness only during up to 10hydrodynamic g/dL. Process thinning, mapping relationships was used to between generate solution a three-dimensional properties were design limited space to con- for controlcentrations of film up thickness. to 10 g/dL. Process mapping was used to generate a three-dimensional de- sign space for control of film thickness. Supplementary Materials: The following are available online at https://www.mdpi.com/2079-641 2/11/2/198/s1Supplementary, Figure Materials: S1: Reflection The following spectra are of available PMMA films online with at fits.www.mdpi.com/xxx/s1, (A): 168 nm thick PMMA Figure film S1: withReflection fit (red spectra line). The of nonuniformityPMMA films with of the fits. fit is(A±):19 168 nm nm and thick the goodness PMMA film of fit with is 0.9444. fit (red (B ):line). 292 nmThe thicknonuniformity PMMA film of with the fitfit (redis ±19 line). nm Theand nonuniformitythe goodness of fit the is fit 0.9444. is ±23 ( nmB): 292 and nm the thick goodness PMMA of fit film is 0.9666.with fit (C (red): 302 line). nm thickThe nonuniformity PMMA film with of the fit (red fit is line). ±23 nm The and nonuniformity the goodness of theof fit fit is is 0.9666.±114 nm (C): and 302 thenm goodness thick PMMA of fit film is 0.9700. with (fitD ):(red 443 line). nm thick The nonu PMMAniformity film with of fitthe (red fit is line). ±114 The nm nonuniformityand the goodness of theof fit fit is ±0.9700.69 nm (D and): 443 the nm goodness thick PMMA of fit is film 0.9538. with ( Efit): 581(red nm line). thick The PMMA nonuniformity film with of fit the (red fit line).is ±69 Thenm nonuniformityand the goodness of theof fit fit is 0.9538.±56 nm (E and): 581 the nm goodness thick PMMA of fit isfilm 0.9304. with (fitF): (red 686 nmline). thick The PMMAnonuni- filmformity with of fit the (red fit line). is ±56 The nm nonuniformity and the goodness of the of fit fit is is± 0.9304.14 nm and(F): 686 the goodnessnm thick PMMA of fit is 0.9258.film with (G ):fit (red line). The nonuniformity of the fit is ±14 nm and the goodness of fit is 0.9258. (G): 722 nm thick 722 nm thick PMMA film with fit (red line). The nonuniformity of the fit is ±29 nm and the goodness PMMA film with fit (red line). The nonuniformity of the fit is ±29 nm and the goodness of fit is of fit is 0.8792. 0.8792. Author Contributions: Conceptualization, N.C. and M.C.; methodology, N.C. and M.C.; software, Author Contributions: Conceptualization, N.C. and M.C.; methodology, N.C. and M.C.; software, N.C. and M.C.; validation, N.C. and M.C.; formal analysis, N.C. and M.C.; investigation, N.C. and N.C. and M.C.; validation, N.C. and M.C.; formal analysis, N.C. and M.C.; investigation, N.C. and M.C.; resources, W.B.E.; data curation, N.C. and M.C.; writing—original draft preparation, N.C.; M.C.; resources, W.B.E.; data curation, N.C. and M.C.; writing—original draft preparation, N.C.; writing—review and editing, M.C. and W.B.E.; visualization, N.C. and M.C.; supervision, W.B.E.; writing—review and editing, M.C. and W.B.E.; visualization, N.C. and M.C.; supervision, W.B.E.; project administration, W.B.E.; funding acquisition, N.C. and W.B.E. All authors have read and agreed project administration, W.B.E.; funding acquisition, N.C. and W.B.E. All authors have read and to the published version of the manuscript. agreed to the published version of the manuscript. Funding: This research was funded by Rhodes Pharmaceuticals L.P. and by the U.S. Department of Homeland Security’s Science and Technology Directorate. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the

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official views and policies, either expressed or implied, of Rhodes Pharmaceuticals L.P. or any of its affiliates, or the U.S. Department of Homeland Security. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available in article. Conflicts of Interest: The authors declare no conflict of interest.

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