Growth Rate and Cross-Linking Kinetics of Poly(divinyl benzene) Thin

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Growth rate and cross-linking kinetics of poly(divinyl benzene) thin films formed via initiated chemical vapor deposition Priya Moni, Alan C. Mohr, and Karen K. Gleason Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00624 • Publication Date (Web): 15 May 2018 Downloaded from http://pubs.acs.org on May 16, 2018

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Growth rate and cross-linking kinetics of poly(divinyl benzene) thin films formed via initiated chemical vapor deposition

Priya Moni1, Alan C. Mohr2, and Karen K. Gleason2* 1. Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA, 02139 2. Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA, 02139

ABSTRACT

Initiated chemical vapor deposition (iCVD) allows for the formation of highly cross-linked, polymer thin films on a variety of substrates. Here we study the impact of substrate stage temperature and filament temperature on the deposition and crosslinking characteristics of iCVD from divinyl benzene (DVB). Maintaining a constant monomer surface concentration reveals that deposition rates upwards of 15 nm/min can be achieved at substrate stage temperatures of 50 °C. The degree-of-crosslinking is limited by the rate of initiation of the pendant vinyl bonds. At a filament temperature of 200 °C, the pendant vinyl bond conversion is highly sensitive to the surface concentration of initiator radicals. A significant decrease of the pendant vinyl bond conversion is observed with increasing stage temperatures. At higher filament temperatures, the pendant vinyl bond conversion appears to plateau at approximately 50%.

However, faster

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deposition rates yield lower conversion. This trade-off is mitigated by increasing the filament temperature to increase initiator radical production. A higher flux of initiator radicals toward the surface at a constant deposition rate increases the rate of initiation of pendant vinyl bonds and therefore their overall conversion. At a deposition rate of ~ 7 nm/min, an increase in the filament temperature from 200 °C to 240 °C results in an 18% increase in the pendant vinyl bond conversion. INTRODUCTION Thin films of cross-linked polymer networks fabricated by initiated chemical vapor deposition (iCVD) have utility in a broad variety of applications including 1) integrated circuit fabrication1-2 2) surface energy modification

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3) ablator materials for nuclear fusion5-7 4) electrochemical

power systems8-10. Conventional solution synthesis techniques require multiple steps to form cross-linked polymer films adhered to substrates. Usually a polymer with incorporated crosslinkable moieties is first synthesized and then either spin or dip coated on the substrate of interest. A curing step, such as a thermal anneal, UV exposure, or electron beam exposure, is required to activate the cross-linking reaction to form the final crosslinked thin film11-12. However, iCVD permits the single-step formation of a broad library of cross-linked polymer thin films. During the iCVD process, monomer, crosslinker, and initiator vapors are fed into a lowpressure reactor containing the substrate of interest. A hot filament array thermally cracks the initiator to form radicals. A free-radical polymerization takes place on the substrate surface and results in the formation of the crosslinked polymer thin film in a single step. iCVD cross-linkers have multiple polymerizable moieties (acrylate, methacrylate, or vinyl) on a single monomer unit. Maximizing the reaction of these moieties during film synthesis is key to the functionality of the cross-linked film. For example, Zhao et al. found that unreacted


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vinyl groups in iCVD poly(divinyl benzene) (pDVB) films oxidized over time and reduced the films hydrophobicity 13. The majority of iCVD kinetic studies have focused on mono-functional acrylates and methacrylates, which polymerize swiftly via the free-radical mechanism14-15. By contrast, the majority of cross-linking chemistries used in iCVD are multi-vinyl based. This is significant as the free-radical propagation rate constant for the vinyl groups is typically orders of magnitude lower than for acrylates16. Complete reaction of pendant vinyl groups in multi-vinyl monomers becomes more difficult. Only two studies were found by the authors that specifically studied the degree-of-crosslinking in multivinyl chemistries. Petruczok et al. studied the impact of monomer flow rates on the degree-of-crosslinking in the copolymer poly(4-vinyl pyridine-codivinyl benzene)17. This work used DVB as a cross-linking agent for poly(4-vinyl pyridine) and then examined the subsequent impact of DVB content on the film properties. The conversion of the pendant vinyl bond was used to determine the extent of cross-linking both in pDVB homopolymer films. An elastic modulus of ~5 GPa was obtained through nanoindentation measurements of the pDVB, indicating a cross-linked film.

Coclite et al. examined the cross-

linking of hexavinyldisiloxane (HVDSO), a linear monomer with six vinyl groups, in the iCVD process by determining the percentage of unreacted vinyl bonds within the film as a function of substrate temperature18. They found that higher temperatures reduced the percentage of unreacted vinyl bonds, indicating that cross-linking of HVDSO is a kinetically limited process. Tape tests of a film with 3% conversion of all vinyl bonds showed severe delamination to a film with 95% conversion. The work presented here uses iCVD of DVB with initiator di-tert-butyl peroxide (TBPO, Chart 1a), as a model system to understand both the growth rate and crosslinking kinetics of cyclic multivinyl chemistries. DVB is the simplest of the cyclic multivinyl chemistries used in


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iCVD. Commercially available DVB is a mixture of meta and para isomers, as shown in Chart 1b. The first vinyl bond polymerizes to form a poly(styrene) derivative, with pendant vinyl bonds. Reaction of these pendant vinyl bonds results in a cross-linked structure. Chart 1c presents the structure of iCVD pDVB with both unreacted and reacted pendant vinyl bonds. The effects temperature (filament and substrate stage) are the primary focus of this work. We first study the temperature dependence of the deposition rate and identify regimes were a specific sub-process is rate limiting. Next, we ascertain the pendant vinyl bond conversion using FTIR spectroscopy of the pDVB films. In the previously described iCVD studies, increased vinyl bond conversion resulted in improved mechanical properties associated with higher degrees of cross-linking.6-7, 17-18 Therefore, we focus on the mechanism of pendant vinyl bond conversion and the associated limiting processes as a function of temperature and deposition rate. Finally, the dependence of the film morphology on temperature and deposition rate is investigated. Chart 1. Structures of (a) TBPO Initiator (b) DVB Monomer (combined isomers) (c) pDVB with both reacted and unreacted pendant vinyl bonds. Tert-butoxy moieties from the initiator serve as end groups.


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BACKGROUND Table 1. Summary of gas phase and surface processes and the dependence of rate constants on associated activation energies and temperatures in the iCVD process. Process Group Reaction Rate Behavior Initiator Decomp.

Gas Transport

Monomer Adsorption Polymerization Reactions

∗ () → 2 ()

(,

)

∗ (,

→ (,!")

)

∝ exp −

∗ → (,!")

(,!") → ( )

∗ ∗ (,!") + ( ) → $( ) ∗ ∗ ( ) + ( ) → %$( )

∗ ∗ ( ) + ( ) → %( )

∗ ∗ ( ) + () → ( )

∝ exp −

!

∝ exp −

!

& ∝ exp −

& !

The iCVD process has the same primary reaction steps as conventional solution phase free-radical polymerization: initiator decomposition, primary initiation, propagation, and termination. In addition, two more steps are required for iCVD to successfully proceed: gas transport of reactant molecules to the substrate and the subsequent adsorption of monomer molecules on the substrate surface.14 For a monovinyl species, these processes can be grouped as 1) initiator decomposition 2) gas transport 3) monomer adsorption and 4) polymerization reactions, as presented in Table 1. Each process group has the potential to be deposition rate limiting. Determining the temperature dependence of the deposition rate (Rdep) in these regimes requires relating these processes to the rate of polymerization (Rpoly). Previous studies found that


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Rpoly was proportional to Rdep, which allows us to simultaneously consider the effect on both rates. 15 A general rate of polymerization is given by Equation 1. A combined rate constant (krxn) and stoichiometric coefficient (nrxn) includes the potential effects from the chemical reactions and rate constants (Table 1). These include the rate constants for initiator dissociation (kd), primary initiation (ki), propagation (kp), and termination (kt). The superscripts “a” and “b” are the reaction order with respect to the monomer and initiator concentrations respectively. Equation 1 & =

$

()*

∗ "+ ,- ,-

Initiator decomposition occurs in the gas phase due to the proximity of the hot filament. Therefore, [I]= PI, or the initiator partial pressure in the chamberAs initiator decomposition is a gas phase process, it has an Arrhenius dependence on the filament temperature.19-20 If “b”, the reaction order with respect to initiator concentration, is greater than zero, the dissociation rate constant factors into the combined rate constant. With all other factors held constant, Rp and therefore the deposition rate should increase with filament temperature. However, once the filament temperature is sufficiently high, initiator decomposition is no longer rate limiting. 19 At these high filament temperatures, the initiator is in excess and the film growth rate becomes insensitive to further increases in filament temperature. The chemical reactions involving the monomer occur at the substrate surface. adsorbed monomer.

Therefore, [M]= [M]ads, or the concentration of

Previous iCVD studies have used the Brunauer-Emmett-Teller (BET)

theory for multilayer adsorption to determine [M]ads.14 The BET equation utilizes the monomer saturation pressure (PSat) as a function of temperature, which can be approximated by the Clausius-Claperyon relationship. The adsorbed monomer concentration is proportional to the total adsorbed volume, Vads, as given in Equation 2. The total adsorbed volume is proportional to the volume of a monolayer (Vm), the BET constant (c), the monomer partial pressure during


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deposition (PM), PSat.21-22 The temperature dependencies of c and PSat are given by Equation 3 and Equation 4 respectively, where ∆Hads is the enthalpy of adsorption, ∆Hvap is the enthalpy of vaporization, and Tstage is the stage temperature. Equation 2

,- ! ∝ . ! = lim 23 →7

Equation 3 A ∝ exp
− ()* @ exp > KL U

H65MN

(QF5GH %RQFI5J ) KLH65MN

@


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Equation 8

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V = "+ − WXΔZ ! + 2ΔZ[& \

The enthalpy of adsorption is a negative (exothermic) quantity whereas the enthalpy of vaporization is a positive (endothermic) quantity. When 2a∆Hvap > (Erxn – a∆Hads), a negative apparent activation energy is observed (i.e. deposition rate decreases with increasing stage temperature).

This effect has been observed in previous iCVD studies of acrylates and

methacrylates. This was attributed to the relatively fast propagation rates of these monomers resulting in a low Erxn.14-15, 23 By contrast, styrene and its derivatives can have over a 10-fold reduction in propagation rate.16, 24-26 The impact of stage temperature on the deposition rate for iCVD from styrene derivatives can determine what effect, if any, the reduced propagation rates cause on the deposition rate. EXPERIMENTAL SECTION Synthesis of polymer films Divinyl benzene (DVB, 80%) and di-tert-butyl peroxide (TBPO, 98%) were purchased from Sigma-Aldrich and used without any further purification. Argon gas (100%) was purchased from Airgas and used without any further purification.

All depositions occurred in a custom

built iCVD chamber described elsewhere27. Films were grown on 100 mm Si wafers (WRS Materials). The chamber pressure was controlled using a throttling butterfly valve (MKS Instruments) and substrate temperature controlled using a stage chiller (Thermo-Fisher). Precursor vapors was delivered to the chamber using mass flow controllers (MKS Instruments). A Chromaloy O (Goodfellow) filament array was heated to crack the TBPO peroxide bond. Film growth and thickness were monitored in situ using a 633 nm HeNe Laser (JDS Uniphase). Detailed experimental conditions of the variable PDVB/PSat series are given in Table 2. For these depositions, the filament temperature, chamber pressure, TBPO flow rate, and DVB flow


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rate were held constant. Stage temperature was varied from 15 °C to 30 °C in 5° increments. The change in stage temperature induced a change in in the saturation pressures of both TBPO and DVB. The impact on their respective P/Psat values is also given in Table 2. Films were grown to a thickness of ~150 nm as determined by in-situ laser interferometry. Table 2. Series 1: Deposition constant monomer partial pressure and stage temperature variation. TFilament °C

270

Pchamber mTorr

400

TBPO Flow SCCM

3.2

DVB Flow SCCM

Stage Temperature °C

DVB P/PSat

15

0.55

20

0.38

25

0.27

30

0.19

0.8

Details of the deposition conditions used for the constant PDVB/PSat are given in

Table 3. The chamber pressure (800 mTorr) and TBPO flow rate (2 SCCM) were constant for all depositions. The flow rate of DVB for a given stage temperature was adjusted based on the Clausius-Clapeyron equation to ensure a constant PDVB/PSat of 0.30. An argon patch was introduced to maintain a constant total flow rate of 4.4 standard cubic centimeters per minute (SCCM). The stage temperature was varied from 25 °C to 50 °C in 5° increments. The


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entire series was repeated at three different filament temperatures: 200 °C, 220 °C, and 240 °C. Each deposition lasted for 90 minutes.

Table 3. Series 2: Deposition conditions for constant PDVB/PSat (0.30) and stage temperature variation TFilament °C

200, 220, 240

Pchamber mTorr

800

TBPO Flow SCCM

2

DVB Flow SCCM

Ar Flow SCCM

Stage Temperature °C

0.5

1.9

25

0.7

1.7

30

1.0

1.4

35

1.4

1.0

40

1.9

0.5

45

2.4

0.0

50

DVB P/PSat

0.30

Film Characterization Ex-situ film thicknesses were determined using a J.A. Woollam variable angle spectroscopic ellipsometer at incident angles of 65°, 70°, and 75°. The data were fit to a Cauchy-Urbach isotropic model using WVASE32 modelling software (J.A. Woollam). Fourier transform infrared (FTIR) spectra were obtained using a Thermo-Fisher Nicolet iS50 Spectrometer. The DVB monomer and iCVD pDVB films were measured in transmission mode with a liquid N2 cooled mercury cadmium telluride (MCT-A) detector.

The spectra were

averaged over 256 scans. The DVB monomer was measured in a liquid cell with KBr windows and constant pathlength of 15 µm (Pike technologies). The area of the vinyl bond peak at 903 cm-1 was determined using the software program Omnic (Thermo-Fisher).

The roughness of


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pDVB films on Si wafers was measured using a Veeco Dimension 3100 atomic force microscope (AFM) in tapping mode over a 2µm x 2µm area with 512 points per line and lines per scan.

RESULTS AND DISCUSSION Deposition Rate Characteristics The iCVD pDVB depositions in Series 1 replicates the experimental set-up used in previous iCVD studies of other monomer chemistries.14-15, 20, 28 The total flow rate and chamber pressure are held constant to avoid any convoluting effects of variation in gas residence time in the iCVD chamber. A constant filament temperature ensures the dissociation rate constant of TBPO is constant for all depositions. The initiator and monomer flow rates are held constant, yielding the same partial pressures, PI and PM respectively, for each deposition.

The effect of stage

temperature is presented in Figure 1, which depicts an Arrhenius plot of the deposition rate vs. stage temperature. Usually, activation energies can only be extracted from plots of rate vs. temperature when the relevant monomer and initiator concentrations are held constant. In the case of series 1, the initiator concentration (PI) was held constant, but the variation in Tstage changed the adsorbed monomer concentration. However the monomer partial pressure (PM) was held constant so the only change in [M]ads is due to Tstage.

In this special case, the slope in

Figure 1 can be used to calculate an apparent activation energy of -29 kJ/mol. Based on Equation 8, this indicates that 2a∆Hvap > (Erxn – a∆Hads), where the magnitude of vaporization enthalpy of DVB is sufficiently large to offset the combined activation energy of the chemical reaction and enthalpy of adsorption.


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Figure 1. Series 1: Constant DVB partial pressure and TFilament=270 °C. Deposition rate dependence on stage temperature

To understand the impact of stage temperature alone on the reaction kinetics, the relevant monomer and initiator concentrations must be held constant. In Series 2, we continue to hold the total flow rate and chamber pressure constant for all depositions. The flow rate and therefore partial pressure of TBPO ([I])are held constant for all depositions. Maintaining a constant monomer surface concentration as a function of substrate stage temperature is more difficult to achieve given that [M]ads is a function of Tstage (Equation 2). If we assume the enthalpies of adsorption and vaporization are similar in magnitude (i.e. BET constant is not strongly temperature dependent (Equation 3)), the change in the adsorbed monomer concentration as a function of stage temperature is primarily due to the change in monomer saturation pressure (Equation 4). The quantity PM/PSat, or the ratio of the monomer partial pressure to its saturation pressure, can be used to estimate the change in [M]ads with Tstage . Thus in order to hold the monomer concentration near constant, we operate at the same PM/PSat value for all depositions.. The partial pressure of DVB (PM) is then adjusted for each stage temperature to compensate for


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the changing PSat so that the quantity PM/PSat remains constant for all depositions. The monomer partial pressure is calculated from Equation 9, where Pchamber, UM, and Utot are the total chamber pressure, monomer flow rate, and total flow rate respectively. Equation 9

O] = O;^" ∗

_3

_6`6

Coclite and Ozaydin-Inc et al. adjusted PM to compensate for the change in PSat with Tstage by changing the total chamber pressure for each condition while holding the monomer flow rate and total flow rate constant.

18, 29

In these experiments, the deposition rate was observed to increase

with stage temperature, suggesting that the monomer concentration was not changing significantly as a function of temperature. However, the change in total pressure did cause the initiator partial pressure to change for each stage temperature. If b, the reaction order for the initiator concentration, is greater than zero, then the enhanced deposition rate observed could be due to the larger initiator partial pressures.

Instead, we control PM/PSat via the DVB:Ar flow

ratio as opposed to the total chamber pressure for series 2. This ensures the partial pressure of TBPO is constant for all depositions. The series is repeated at three different filament temperatures to ascertain what effects, if any, the dissociation rate constant has on the deposition rate.


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Figure 2. Series 2: Constant PM/Psat (DVB surface concentration) and PI (TBPO partial pressure). Deposition rate as a function of stage temperature and filament temperature. Filament temperatures are 200 °C(●), 220 °C(■), 240 °C(▲). Grey box highlights slope of regime II used to calculate apparent activation energy (~85 kJ/mol).

Figure 2 depicts the dependence of the natural logarithm of deposition rate on substrate stage temperature when Pm/Psat is held constant (Series 2). The deposition rate is observed to increase with increasing Tstage. This supports our assumption that when Pm/Psat is held constant for all stage temperatures, the monomer surface concentration is nearly constant. Ideally, the rate of polymerization should on depend on the combined rate constant, krxn.

Equation 8 then

simplifies to EA≈Erxn.

The data in Figure 2 can be divided into two regimes based on the change in slope with respect to substrate stage temperature. In regime I, which occurs at deposition rates below 2 nm/min, increases in the deposition rate are seen both with increasing filament temperature and substrate


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stage temperature.

In regime II, which occurs at deposition rates above 2 nm/min, faster

deposition rates are only seen with respect to substrate stage temperature. Additionally, the transition from regime I to regime II occurs at a lower substrate stage temperature at higher filament temperatures. The enhanced deposition rates with respect to filament temperature observed in regime I suggests that the krxn does have some dependence on kd, the dissociation rate constant.16 However, the very slow deposition rates in this regime make it difficult to draw any definitive conclusions from the data. Quantitative analysis of iCVD kinetics is possible at faster deposition rates, such as a range observed in regime II.14, 19, 23 The average calculated apparent activation energy from Figure 2 in regime II is 85 ± 12 kJ/mol.

In this regime, the deposition rate is

essentially independent of kd. This type of behavior is observed when there is a high concentration of primary initiating radicals. The rate of polymerization is independent of the initiator concentration and is given by Equation 10, where ktp is the rate constant for primary termination.16 The combined activation energy for this system is then calculated by Equation 11, where Ei, Ep, and Etp are the activation energies associated with initiation, propagation, and primary termination respectively. ,-R

Equation 10

& =

Equation 11

"+ = + & − &

a J 6J

Ei can be approximated by the activation energy of an alkoxy radical (RO*) reacting with a double bond (CH2=CH-R). This energy is ~ 68 kJ/mol on average.30 Ep can be approximated by the activation energy a propagating styryl radical. This energy is ~30 kJ/mol.16, 25, 31

Finally, Etp is assumed to have a similar value to Et of styrene (8 kJ/mol).16 With these


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values, we estimate Erxn≈ 90 kJ/mol, which falls within the range of experimental apparent activation energies determined from Figure 2. This supports our hypothesis that the rate of polymerization in regime II is given by Equation 10. The second order dependence on monomer concentration is in good agreement with previous iCVD studies.14-15 Additionally, this further supports our hypothesis that the deposition rate is limited by chemical reaction kinetics at constant PM/PSat instead of a combination of reaction kinetics and adsorbed surface monomer concentration as observed at constant PM. Assuming this hypothesis to be true, we can use the results from Series 1 and Series 2 to estimate the value of ∆Hads of DVB using Equation 8. EA and Erxn are given by the apparent activation energies from Series 1 (-29 kJ/mol) and Series 2 (85 kJ/mol) respectively. Second order kinetics indicate a=2 and ∆Hvap of DVB is 48.6 kJ/mol.32 ∆Hads of DVB is then estimated to be approximately -40 kJ/mol, which is in the range of values corresponding to physisorption enthalpies.33

Calculation of Pendant Vinyl Bond Conversion The transmission FTIR spectra the DVB monomer and a representative iCVD pDVB film are presented in Figure 3. The meta and para-substituted benzene vibrations from 700 – 850 cm1

are present in both the monomer and polymer spectra, indicating the ring structure remained

intact after the iCVD process. The reduction in the vinyl peaks from 900 – 1000 cm-1 coupled with the emergence of the methylene peak at 2930 cm-1 in the polymer spectrum confirms polymerization was successful. We note the emergence of methyl peaks at 2870 cm-1 and 2960 cm-1. These can originate from the ethylvinyl benzene (EVB) impurities in technical grade DVB, the t-butyl component of the initiator radical, and backbone methylation during the iCVD process.34 Backbone methylation occurs via reaction with methyl radicals that are produced in


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the beta-scission of TBPO.

34

Gas-phase FTIR studies determined this reaction occurs more

frequently at filament temperatures above 250 °C.19 The same study determined that t-butoxy radicals initiate the vinyl bond whereas methyl radicals do not. The lack of a strong ether peak at ~1100 cm-1 suggests that the number of t-butoxy moieties incorporated in the structure is relatively low. This indicates that the reaction of both the primary and pendant vinyl bonds is in large part due to propagation rather than just primary initiation and termination. In this case, the pendant vinyl bond conversion, or fraction of pendant vinyl bonds that have reacted, can be used to gauge the change in the degree of cross-linking with filament temperature and stage temperature. The aforementioned spectral characteristics were observed in all spectra collected of the iCVD pDVB films. The vinyl bond conversion can be determined using the FTIR spectra of the monomer and polymer. Typical methods compare the areal intensities of the aromatic vibrations to vinyl vibrations.

35-38

When technical grade DVB is used, the effects of impurities in the monomer

must also be accounted for in any analysis. The most significant impurity is EVB, which is made up of meta and para isomers. The certificate of analysis from Sigma-Aldrich informs us of the specific composition of the technical grade DVB used in this work. These values are enumerated in Table 4. Table 4. Composition of technical grade DVB used in this work Constituent

Variable

b,c8d

m-DVB p-DVB m-EVB + p-EVB

b&",c8d

b,U8d + b&",U8d

Fraction 0.56 0.25 0.18


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We follow the same procedure as Petruczok and Yang et al. to calculate the pendant vinyl bond conversion while accounting for the EVB content.17 The meta, para, and vinyl vibrations occurring at 795 cm-1, 837 cm-1, and 903 cm-1 in the FTIR spectra are used to quantify conversion.38-39 These peaks are indicated in Figure 3, which shows the FTIR spectra of DVB and iCVD pDVB. The reduction in the vinyl peak at 903 cm-1 is indicative of polymerization of the primary bond and unreacted pendant vinyl bonds. The Beer-Lambert equation relates the absorbance of a given vibrational peak, A, to the molar absorptivity, ε, path length, l, and mole fraction, x. This is given by Equation 12. T = efb

Equation 12

The molar absorptivity ratio of meta- and para- disubstituted benzenes is then calculated using Equation 13, where the subscript “mon” refers to values measured in the monomer and the mole fractions are from Table 4. g9N65 gJ5(5

Equation 13

+J5(5 V9N65

= >+

9N65

VJ5(5

@

h

+J5(5,ijk %+J5(5,ljk V9N65

= >+

9N65,ijk %+9N65,ljk

VJ5(5

@

h

Exact fractions for m-EVB and p-EVB were not provided. If we assume the mole fraction ratio of m-DVB to p-DVB is approximately equal to the mole fraction ratio of m-EVB to p-EVB, we can estimate xmeta,EVB = 0.12 and xpara,EVB = 0.06. From the monomer FTIR spectrum, we calculate Ameta/Apara= 1.21. Substituting these values and those in Table 4 into Equation 13 results in εmeta/εpara = 0.56. The mole fraction ratio of meta to para disubstituted benzenes in the polymer is then calculated by Equation 14, where the subscript “poly” refers to the polymer.

Equation 14

>

+9 +J

@

&hm

=

gJ5(5

g9N65

∗>

V9N65 VJ5(5

@

&hm

= 7.op > $

V9N65 VJ5(5

@

&hm


18

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The mole fraction of m-DVB in the polymer film, (xmeta,DVB)poly, can be calculated using Equation 15.

Equation 15

Xb,c8d \&hm = q1 −

$

s w9N65 > @ %$ t.uv wJ5(5 J`:x

y Xb,c8d + b&",c8d \h

The final equation they obtained for the fraction of pendant vinyl bonds converted is given by Equation 16. The full derivation of this equation can be found in the 2013 Macromolecules publication by Petruczok and Yang et al.17

Equation 16

z{WA. |}~{ = 1 − q2 ∗

wIa*x:

>

@

w9N65 J`:x wIa*x:

>

@

w9N65 9`*

X+9N65,ijk \J`:x

∗ X+

9N65,ijk \9`*

y

Figure 3. Transmission FTIR spectra of iCVD pDVB (top) and DVB monomer (bottom). Peaks found mainly in the polymer spectra are methyl (filled in circle), and methylene (filled in diamond). Vinyl stretch at 903 cm-1 highlighted in gray, para- vibration at 837 cm-1 highlighted


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Page 20 of 40

in orange, meta- vibration at 795 cm-1 highlighted in blue. The areas under these peaks were used to calculate the pendant vinyl bond conversion. Mechanism of Pendant Vinyl Bond Conversion The crosslinking reaction could occur both at the growing pDVB film surface or within the bulk polymer film already formed.

To fully understand the impact of iCVD process

parameters on the pendant vinyl bond conversion, new reaction processes in addition to those in Table 1 must be considered. The potential iCVD cross-linking reaction routes summarized in

Table 5 were adapted from Tobita and coworkers’ study in solution phase crosslinking4042

.

Table 5. Potential initiation and propagation reactions for the pendant vinyl bond at the film surface and within the bulk film Reaction Equation Pendant Vinyl Initiation (Surface) Pendant Vinyl Propagation (Surface) Pendant Vinyl Initiation (Bulk)

Pendant Vinyl Bond Propagation (Bulk)

∗ ∗ () + ,& (!") → ,& (!")

∗ ∗ ,& (!") + ,& (!") → %(!") ∗ ∗ ( ) → ( ∗ (

)

)

∗ + ,& (!) → ,& (!)

∗ ,& ( ) + ,& (

)

∗ → %,& (

)


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For both the surface and bulk limited reactions, initiation occurs via a radical attacking the pendant vinyl bond of a pre-existing polymer. Propagation occurs when an activated pendant vinyl group reacts with another pendant vinyl group. The first major difference is in initiation. For cross-linking within the bulk, an initiator radical must diffuse from the surface into the bulk to initiate a pendant vinyl bond. The second is the difference in physical constraints. The propagation reaction requires some degree of mobility of the pendant vinyl group such as bond rotation about the C-C single bond or changes in the polymer chain conformation. The bulk film has physical constraints in all directions whereas the film surface imposes fewer physical constraints. At temperatures below the glass transition temperature, polymer chains in the bulk film are effectively frozen in place, making any reaction in the bulk highly unlikely. Sanetra et al. found the glass transition temperature of poly(styrene-co-divinyl benzene) increased from 102 °C at 5 wt% DVB to 133 °C at 20 wt% DVB43. Given the present work uses pure pDVB films and the film temperature during growth does not exceed 50 °C, it is reasonable to assume the growing iCVD pDVB films are well below their glass transition temperature preventing reaction in the bulk. Therefore, it is likely that the cross-linking reaction is limited to the surface. Studying the impact of filament and substrate stage temperatures can elucidate the limiting deposition sub-process for cross-linking during growth. Figure 4 depicts the calculated pendant vinyl bond conversion as a function of inverse stage temperature for deposition series 2. At the lowest filament temperature, 200 °C (Figure 4(left)), the conversion of the pendant vinyl bond decreases rapidly as stage temperature is elevated. This indicates that the reaction of the pendant vinyl bond is strongly dependent on the surface concentration of one of the participating species. It also supports our hypothesis that cross-linking is limited to the film surface. Whereas the surface concentration of DVB was held near constant for all experiments, the surface


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concentration of initiator radicals was not held constant.

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The initiator radical surface

concentration, [R*]ads, is proportional to the ratio of PR and PR,Sat, the respective partial and saturation pressures of the initiating radical. An increase in stage temperature increases the saturation pressure of R*. At constant PR, an increase in PR,Sat would result in a reduced surface concentration of the initiator radicals. Whereas the reaction of the primary vinyl bond for series 2 is relatively insensitive to the gas-phase and surface concentrations of initiating radicals, the conversion of the pendant vinyl bond very much depends on the surface concentration of initiating radicals at the lowest filament temperature. Therefore, there is a non-zero reaction order with respect to t-butoxy radical concentration for the cross-linking reaction.

Figure 4. Pendant vinyl bond conversion as a function of substrate stage temperature and filament temperature for deposition series 2. (left) 200 °C(●) and (right) 220 °C(■), 240 °C(▲). The left (Ln(fraction conversion)and right (fraction conversion) axes apply to both plots.


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At the higher filament temperatures (Figure 4(right)), the pendant vinyl bond conversion is no longer has a strong dependence on stage temperature. Instead, the conversion appears to plateau. A significantly larger number of t-butoxy radicals are produced at high filament temperatures due the enhanced dissociation rate constant. The reaction order appears to be approaching zero with respect to the initiator radical surface concentration. Of note are the slightly higher conversion levels at a filament temperature of 240 °C vs. 220 °C. This behavior can be explained using the kinetic theory of gases. The container wall collision rate, ν, denotes the number of molecules that strike a unit of area per unit of time. From Equation 17, this quantity is related to the number of gas molecules, N, occupying a volume, V, the mass of the molecule, m, and the gas temperature, Tgas. 44

Equation 17

=

8

k LM5H

At higher filament temperatures, a larger number of free-radicals are formed and higher gas temperatures are obtained. Thus, at a fixed stage temperature, increasing the filament temperature increases the container wall collision rate. Since initiation occurs when a gas-phase t-butoxy molecule collides with a surface-bound pendant vinyl bond, the higher collision rate of elevated filament temperatures results in increased pendant vinyl bond conversion.


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Figure 5. Pendant vinyl bond conversion as a function of deposition rate and filament temperature [ 200 °C(●), 220 °C(■), 240 °C(▲)].

The deposition rate is another important factor to consider in the conversion of the pendant vinyl bonds. Figure 5 shows that the pendant vinyl bond conversion decreases as the deposition rate increases. Faster deposition rates cause a given surface layer to become part of the bulk film more quickly as the next layer of DVB monomer adsorbs and reacts to form a polymer film. This trend further supports our assertion that cross-linking is limited to the growing film surface. The reaction of pendant vinyl bonds is effectively quenched once the surface layer is covered with new layers of polymer. These unreacted pendant vinyl bonds are now part of the bulk film and cannot react to cross-link as previously described. This imposes a compromise between deposition rate and pendant vinyl bond conversion. However, Figure 5 also shows that at a given deposition rate, higher conversion levels are possible at higher filament temperatures. This is most clearly illustrated at a deposition rate of ~ 7 nm/min. The


24

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conversion fraction increases from 0.44 at 200 °C to 0.52 at 240 °C.

The deposition rate

describes the time an arbitrary monolayer of pDVB spends at the surface, ts. This quantity can be calculated using Equation 18, where hml is the height of the pDVB monolayer. The total areal dose of radicals, NR/A, impinging on the film surface layer can be calculated as a function of deposition rate as given by Equation 19. Equation 18

Equation 19

! =

V

^9:

KGNJ

= ∗ ! = ∗

^9:

KGNJ

When the collision rate is fixed (i.e. filament temperature), slower deposition rates increase ts thereby increasing the total areal dose of initiating radicals that collide with the surface and initiate pendant vinyl groups. Faster deposition rates result in a lower total areal dose and lower conversion of the pendant vinyl bonds. If the deposition rate is fixed instead, the higher collision rate at elevated filament temperatures increases the total areal dose of initiating radicals and therefore the conversion of the pendant vinyl. Conversion could be due to either true cross-links being formed or increased rates of primary initiation and termination by t-butoxy radicals. The lack of a strong ether peak in all FTIR spectra suggests that true cross-links are being formed at higher filament temperatures. Therefore, operating at higher filament temperatures could reduce the compromise between fast deposition rates and high degrees of cross-linking Film Morphology


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The iCVD pDVB films are relatively smooth, with all the root mean square roughness values falling under 1 nm, as seen in Figure 6. The majority of the roughness values fall in the range of 0.3 nm to 0.7 nm. There appears to be a slight increase in roughness at faster deposition rates and elevated filament temperatures (Figure 6a).

Other iCVD polymer film chemistries and

inorganic hot-wire CVD films demonstrate substantial changes in surface morphology, especially with respect to filament temperature. 23, 45-47 In Figure 6b, we evaluate the spread of roughness values as a function of filament temperature. For each filament temperature, the mean roughness falls in the range of 0.47 nm to 0.56 nm, with an average roughness of 0.51 nm for all filament temperatures. The spread in data for each filament temperature is on the order of 0.2 nm, or ~40% of the mean. The comparatively large spread with respect to the mean indicates the roughness of iCVD pDVB films is not significantly impacted by filament temperature in the range evaluated in this work.


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Figure 6. iCVD pDVB film roughness as a function of (a) deposition rate and filament temperature [200 °C(●), 220 °C(■), 240 °C(▲)]. (b) Box and whisker plots depicting spread in film roughness as a function of filament temperature. Mean roughness (■) and outliers (◊) indicated on plot. Measurements area was 2µm x 2µm.


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CONCLUSION This study investigated the impact of substrate stage temperature and filament temperature on the growth rate, pedant vinyl bond conversion and film morphology of iCVD from divinyl benzene. Maintaining Pm/PSat of DVB as a function of stage temperature yields faster deposition rates at higher stage temperatures. Deposition rates greater than 2 nm/min appear to be insensitive to the filament temperature, suggesting a zero-order dependence on the initiator concentration and second order dependence on the monomer concentration. Whereas the deposition rate depends on the reaction of the primary vinyl bond, cross-linking is determined by the reaction of the pendant vinyl bond. Significantly lower fractions of pendant vinyl bond conversion are observed at increasing stage temperatures at a filament temperature of 200 °C, indicating the t-butoxy surface concentration strongly affects the degree of crosslinking. This effect is reduced at higher filament temperatures. Faster deposition rates also result in lower fractions of pendant vinyl bond conversion, supporting our hypothesis that the cross-linking reactions are limited to the growing film surface. Increased filament temperatures may allow for a greater degree of crosslinking without sacrificing deposition rate. While this study only studied divinyl benzene, the principles of cross-linking gleaned from this study can be extended to the iCVD from other cyclic multivinyl chemistries. AUTHOR INFORMATION Corresponding Author *[email protected] Author Contributions


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The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT The authors acknowledge support from the National Science Foundation (Award # 1344891) and the Kuwait Foundation for the Advancement of Sciences for funding support through the Kuwait-MIT center for Natural Resources and the Environment at MIT. This work made use of the Institute of Soldier Nanotechnologies which is supported by the US Army Research Laboratory and the US Army Research Office under contract no. DAAD-19-02D-0002. REFERENCES

1. Suh, H. S.; Kim, D. H.; Moni, P.; Xiong, S.; Ocola, L. E.; Zaluzec, N. J.; Gleason, K. K.; Nealey, P. F., Sub-10-nm patterning via directed self-assembly of block copolymer films with a vapour-phase deposited topcoat. Nat. Nanotechnol. 2017, 12 (6), 575-581. 2. Seong, H.; Pak, K.; Joo, M.; Choi, J.; Im, S. G., Vapor-Phase Deposited Ultrathin Polymer Gate Dielectrics for High-Performance Organic Thin Film Transistors. Advanced Electronic Materials 2016, 2 (2). 3. Joo, M.; Shin, J.; Kim, J.; You, J. B.; Yoo, Y.; Kwak, M. J.; Oh, M. S.; Im, S. G., OneStep Synthesis of Cross-Linked Ionic Polymer Thin Films in Vapor Phase and Its Application to an Oil/Water Separation Membrane. J Am Chem Soc 2017, 139 (6), 2329-2337. 4. Gao, Y.; Cole, B.; Tenhaeff, W. E., Chemical Vapor Deposition of Polymer Thin Films Using Cationic Initiation. Macromolecular Materials and Engineering 2017. 5. Baxamusa, S. H.; Suresh, A.; Ehrmann, P.; Laurence, T.; Hanania, J.; Hayes, J.; Harley, S.; Burkey, D. D., Photo-oxidation of Polymers Synthesized by Plasma and Initiated CVD Chem. Vapor Depos. 2015, 21 (10-11-12), 267-274. 6. Lepro, X.; Ehrmann, P.; Menapace, J.; Lotscher, J.; Shin, S.; Meissner, R.; Baxamusa, S., Ultralow Stress, Thermally Stable Cross-Linked Polymer Films of Polydivinylbenzene (PDVB). Langmuir 2017, 33 (21), 5204-5212. 7. Baxamusa, S. H.; Lepró, X.; Lee, T.; Worthington, M.; Ehrmann, P.; Laurence, T.; Teslich, N.; Suresh, A.; Burkey, D. D., Initiated chemical vapor deposition polymers for high peak-power laser targets. Thin Solid Films 2017, 635, 37-41. 8. Sassin, M. B.; Long, J. W.; Wallace, J. M.; Rolison, D. R., Routes to 3D conformal solidstate dielectric polymers: electrodeposition versus initiated chemical vapor deposition. Mater. Horiz. 2015, 2 (5), 502-508. 9. Reeja-Jayan, B.; Chen, N.; Lau, J.; Kattirtzi, J. A.; Moni, P.; Liu, A.; Miller, I. G.; Kayser, R.; Willard, A. P.; Dunn, B.; Gleason, K. K., A Group of Cyclic Siloxane and Silazane


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Polymer Films as Nanoscale Electrolytes for Microbattery Architectures. Macromolecules 2015, 48 (15), 5222-5229. 10. Urstöger, G.; Resel, R.; Koller, G.; Coclite, A. M., Deposition kinetics and characterization of stable ionomers from hexamethyldisiloxane and methacrylic acid by plasma enhanced chemical vapor deposition. J. Appl. Phys. 2016, 119 (13), 135307. 11. Ryu, D. Y.; Shin, K.; Drockenmuller, E.; Hawker, C. J.; Russell, T. P., A Generalized Approach to the Modification of Solid Surfaces. Science 2005, 308, 236-239. 12. Knudsen, D.; Harnish, B.; Toth, R.; Yan, M., Creating microstructures on silicon wafers using UV-crosslinked polystyrene thin films. Polym. Eng. Sci. 2009, 49 (5), 945-948. 13. Zhao, J.; Wang, M.; Gleason, K. K., Stabilizing the Wettability of Initiated Chemical Vapor Deposited (iCVD) Polydivinylbenzene Thin Films by Thermal Annealing. Adv. Mater. Interf. 2017, 4 (18), 1700270-9. 14. Lau, K.; Gleason, K. K., Initiated chemical vapor deposition (iCVD) of poly (alkyl acrylates): an experimental study. Macromolecules 2006, 39 (10), 3688-3694. 15. Lau, K. K. S.; Gleason, K. K., Initiated Chemical Vapor Deposition (iCVD) of Poly(alkyl acrylates): A Kinetic Model. Macromolecules 2006, 39 (10), 3695-3703. 16. Odian, G., Principles of Polymerization. John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2004. 17. Petruczok, C. D.; Yang, R.; Gleason, K. K., Controllable Cross-Linking of VaporDeposited Polymer Thin Films and Impact on Material Properties. Macromolecules 2013, 46 (5), 1832-1840. 18. Coclite, A. M.; Ozaydin-Ince, G.; d’Agostino, R.; Gleason, K. K., Flexible Cross-Linked Organosilicon Thin Films by Initiated Chemical Vapor Deposition. Macromolecules 2009, 42 (21), 8138-8145. 19. Ozaydin-Ince, G.; Gleason, K. K., Transition between kinetic and mass transfer regimes in the initiated chemical vapor deposition from ethylene glycol diacrylate. J. Vac. Sci. Technol. A 2009, 27 (5), 1135-1143. 20. O'Shaughnessy, W. S.; Gao, M.; Gleason, K. K., Initiated Chemical Vapor Deposition of Trivinyltrimethylcyclotrisiloxane for Biomaterial Coatings. Langmuir 2006, 22 (16), 7021-7026. 21. Brunauer, S.; Emmett, P. H.; Teller, E., Adsorption of Gases in Multimolecular Layers. J. Am. Chem. Soc. 1938, 60 (2), 309-319. 22. Adamson, A. W.; Gast, A. P., Physical Chemistry of Surfaces. Sixth ed.; John Wiley & Sons, Inc.: New York, 1997. 23. Mao, Y.; Gleason, K. K., Hot Filament Chemical Vapor Deposition of Poly(glycidyl methacrylate) Thin Films Using tert -Butyl Peroxide as an Initiator. Langmuir 2004, 20 (6), 2484-2488. 24. Matheson, M. S.; Auer, E. E.; Bevilacqua, E. B., Rate Constants in Free Radical Polymerizations. IV. Methyl Acrylate. J. Am. Chem. Soc. 1951, 73 (11), 5395-5400. 25. Matheson, M. S.; Auer, E. E.; Bevilacqua, E. B., Rate Constants in Free Radical Polymerization. III. Styrene. J. Am. Chem. Soc. 1951, 73 (4), 1700-1706. 26. Matheson, M. S.; Auer, E. E.; Bevilacqua, E. B.; Hart, E. J., Rate Constants in Free Radical Polymerizations. I. Methyl Methacrylate. J. Am. Chem. Soc. 1949, 71, 497-504. 27. Tenhaeff, W. E.; Gleason, K. K., Initiated Chemical Vapor Deposition of Alternating Copolymers of Styrene and Maleic Anhydride. Langmuir 2007, 23 (12), 6624-6630.


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28. Chen, N.; Reeja-Jayan, B.; Liu, A.; Lau, J.; Dunn, B.; Gleason, K. K., iCVD Cyclic Polysiloxane and Polysilazane as Nanoscale Thin-Film Electrolyte: Synthesis and Properties. Macromol. Rapid. Commun. 2016, 37 (5), 446-452. 29. Ozaydin-Ince, G.; Gleason, K. K., Tunable Conformality of Polymer Coatings on High Aspect Ratio Features. Chem. Vapor Depos. 2010, 16 (1-3), 100-105. 30. Denisov, E. T., Free radical addition: factors determining the activation energy. Russ. Chem. Rev. 2000, 69 (2), 153-164. 31. Kagiya, T.; Sumida, Y., Evaluation of Activation Energy for Addition Reactions of Radicals to Vinyl Compounds. Polymer Journal 1970, 1, 137. 32. Chickos, J. S.; Acree Jr., W. E., Enthalpies of Vaporization of Organic and Organometallic Compounds, 1880–2002. J. Phys. Chem. Ref. Data 2003, 32 (2), 519-876. 33. Hayward, D. O.; Trapnell, B. M. W., Chemisorption. 2nd ed.; Butterworths: Washington DC, 1964. 34. Moni, P.; Suh, H. S.; Dolejsi, M.; Kim, D. H.; Mohr, A. C.; Nealey, P.; Gleason, K. K., Ultrathin and conformal initiated chemical vapor deposited (iCVD) layers of systematically varied surface energy for controlling the directed self-assembly of block co-polymers. Langmuir 2018, 34 (15), 4494-4502. 35. Rackley, F. A.; Turner, H. S.; Wall, W. F., Polymers of Improved Modulus by High Pressure Polymerization. Nature 1973, 241, 524. 36. Rackley, F. A.; Turner, H. S.; Wall, W. F.; Haward, R. N., Preparation of crosslinked polymers with increased modulus by high‐pressure polymerization. Journal of Polymer Science: Polymer Physics Edition 1974, 12 (7), 1355-1370. 37. Hubbard, K. L.; Finch, J. A.; Darling, G. D., Polymers with pendant vinyl groups, including poly(divinylbenzene-co-ethylvinylbenzene). React. Funct. Polym. 1998, 36 (1), 1-16. 38. Hubbard, K. L.; Finch, J. A.; Darling, G. D., The preparation and characteristics of poly(divinylbenzene-co-ethylvinylbenzene), including Ambeflite XAD-4. Styrenic resins with pendant vinylbenzene groups. React. Funct. Polym. 1998, 36 (1), 17-30. 39. Socrates, G., Infrared and Raman characteristic group frequencies: tables and charts. 3rd ed.; John Wiley & Sons, LTD: New York, 2001. 40. Tobita, H.; Hamielec, A. E., Modeling of network formation in free radical polymerization. Macromolecules 1989, 22 (7), 3098-3105. 41. Tobita, H. Crosslinking Kinetics in Free-Radical Copolymerization. McMasteer University, Hamilton, ON, 1990. 42. Tobita, H.; Hamielec, A. E., A kinetic model for network formation in free radical polymerization. Makromolekulare Chemie. Macromolecular Symposia 1988, 20-21 (1), 501-543. 43. Sanetra, R.; Kolarz, B. N.; Wlochowicz, A., Determination of the glass transition temperature of poly(styrene-co-divinylbenzene) by inverse gas chromotography. Polymer 1985, 26 (8), 1181-1186. 44. Mortimer, R. G., Physical Chemistry. 3rd ed.; Elsevier Academic Press: Burlington, 2008. 45. Pryce Lewis, H. G.; Caulfield, J. A.; Gleason, K. K., Perfluorooctane Sulfonyl Fluoride as an Initiator in Hot-Filament Chemical Vapor Deposition of Fluorocarbon Thin Films. Langmuir 2001, 17 (24), 7652-7655. 46. Sperling, B. A.; Abelson, J. R., Kinetic roughening of amorphous silicon during hot-wire chemical vapor deposition at low temperature. J. Appl. Phys. 2007, 101 (2).


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47. Richardson, C. E.; Park, Y.-B.; Atwater, H. A., Surface evolution during crystalline silicon film growth by low-temperature hot-wire chemical vapor deposition on silicon substrates. Physical Review B 2006, 73 (24).

TABLE OF CONTENTS GRAPHIC

TOC Graphic: Initiation and propagation of crosslinking reaction occurs only at growing film surface


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Table of Contents Graphic:Initiation and propagation of crosslinking reaction occurs only at growing film surface 193x99mm (150 x 150 DPI)


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Chart 1:. Structures of A) TBPO Initiator B) DVB Monomer (combined isomers) C) pDVB with both reacted and unreacted pendant vinyl bonds. Tert-butoxy moieties from the initiator serve as end groups. 214x239mm (96 x 96 DPI)


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Figure 1. Series 1: Constant DVB partial pressure and TFilament=270 °C. Deposition rate dependence on stage temperature 272x208mm (300 x 300 DPI)


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Figure 2. Series 2: Constant PM/Psat (DVB surface concentration) and PI (TBPO partial pressure). Deposition rate as a function of stage temperature and filament temperature. Filament temperatures are 200 °C(●), 220 °C(■), 240 °C(▲). Grey box highlights slope of regime II used to calculate apparent activation energy (~85 kJ/mol). 271x207mm (300 x 300 DPI)


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Figure 3. Transmission FTIR spectra of iCVD pDVB (top) and DVB monomer (bottom). Peaks found mainly in the polymer spectra are methyl (filled in circle), and methylene (filled in diamond). Vinyl stretch at 903 cm1 highlighted in gray, para- vibration at 837 cm-1 highlighted in orange, meta- vibration at 795 cm-1 highlighted in blue. The areas under these peaks were used to calculate the pendant vinyl bond conversion. 272x208mm (300 x 300 DPI)


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Figure 4. Pendant vinyl bond conversion as a function of substrate stage temperature and filament temperature for deposition series 2. (left) 200 °C(●) and (right) 220 °C(■), 240 °C(▲). The left (Ln(fraction conversion)and right (fraction conversion) axes apply to both plots. 279x202mm (300 x 300 DPI)


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Figure 5. Pendant vinyl bond conversion as a function of deposition rate and filament temperature [ 200 °C(●), 220 °C(■), 240 °C(▲)]. 272x208mm (300 x 300 DPI)


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Figure 6. iCVD pDVB film roughness as a function of (a) deposition rate and filament temperature [200 °C(●), 220 °C(■), 240 °C(▲)]. (b) Box and whisker plots depicting spread in film roughness as a function of filament temperature. Mean roughness (■) and outliers (◊) indicated on plot. Measurements area was 2µm x 2µm. 289x457mm (300 x 300 DPI)


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Growth Rate and Cross-Linking Kinetics of Poly(divinyl benzene) Thin

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