Synthesis and Self-Assembly of Gradient Copolymers

Master of Chemical Engineering Thesis

Kevin Wylie 260358983

Department of Chemical Engineering McGill University Montréal, Québec, Canada

A Thesis submitted to McGill University in partial fulfillment of the requirements of the degree of Master of Engineering

March 2016

ABSTRACT

Controlled free radical polymerization allows for the fine control of many key properties of polymers such as the molecular weight, dispersity and composition. Consequently, this permits the attainment of interesting microstructures such as block or tapered/gradient copolymers. In particular, nitroxide-mediated polymerization (NMP) was applied and used for the polymerization of methyl methacrylate (MMA) and styrene (St) block and tapered gradient polymers. With the defined composition and molecular weight, such copolymers are able to self-assemble into sub-50 nm domains. In this thesis, gradient copolymers synthesized in semibatch mode were produced with varying composition and gradient profiles by alternating the rate of St addition and the length of the reaction. Their self-assembly performance was assessed relative to block copolymers with identical molecular properties and found to have similar feature sizes. However, with increasing gradient length, the self-assembly is negatively affected, producing films with very little order and much higher defect densities than block copolymers or polymers with short gradient lengths.

RÉSUMÉ

La polymérisation radicale contrôlée permet le contrôle précis de plusieurs propriétés clés des polymères, tels que la masse moléculaire, dispersité et composition. Par conséquent, ce qui permet la réalisation de microstructures intéressants tels que copolymères bloque ou gradient.

En particulier, on a appliqué la polymérisation nitroxide-médié (NMP) pour polymériser le méthacrylate de méthyl (MMA) et le styrène (St) en copolymères bloque et gradient. Avec la composition et masse moléculaire définie, ces polymères peuvent effectuer l’auto-assemblage en domaine moins de 50 nm. Dans cette thèse, des copolymères gradient ont été synthétisé en manière semi-continu avec profils de composition et de gradient variant en alternant le taux d’addition de St et la durée de la réaction. Leur performance d’auto-assemblage a été évaluée par rapport à des copolymères bloque ayant des propriétés moléculaires identiques et ont été trouvés à avoir des tailles de domaines similaire. Cependant, avec l'augmentation de la longueur de gradient, l'auto-assemblage est négativement affecté, la production de films avec très peu d'ordre et beaucoup plus de défauts que des copolymères bloque ou des copolymères avec des longueurs de gradient plus courtes.

ACKNOWLEDGEMENT

I would like to first thank my supervisor Prof. Milan Marić for his support and guidance, without which any of this would be possible.

I also want to thank all of the present and former graduate student group members. Special thanks go to Xeniya Savelyeva and Simon Kwan for teaching me polymer synthesis, characterization and general lab practices.

I would like to thank the Department of Chemical Engineering of McGill University for providing the office space and research facilities to carry out this work. I would also like to thank the

Department of Chemistry, in particular the NMR facility for the use of their analytical equipment.

Thank you as well to the McGill Nanotools Microfab (MNM) for the use of their facilities and equipment. In particular, I would like to thank Dr. Sasa Ristic and Dr. Lino Eugene for their clean room training and guidance.

Finally, I would like to thank the Department of Chemical Engineering for financial support through the Eugene Ulmer Lamothe scholarship as well as the National Sciences and

Engineering Research Council of Canada – Collaborative Research and Development (NSERC-

CRD) grant in partnership with NanoQuébec and PCAS.

iii

CONTRIBUTION OF AUTHORS

This thesis is a manuscript-based thesis, which contains one manuscript where I am the first author and have done the majority of the work. The manuscript is titled “Synthesis of Gradient

Copolymers Synthesized in Semi-Batch Mode” and is Chapter 3 in this thesis. As a contribution to the manuscript, I performed all of the polymer synthesis, characterization and interpretation of the results. All writing, including tables and figures, were produced by me. Prof. Milan Marić performed the editing and aided with some of the writing.

TABLE OF CONTENTS

Abstract ...... i

Résumé...... ii

Acknowledgement ...... iii

Contribution of Authors ...... iv

1. General Introduction...... 3

2. Literature Review ...... 5

2.1 Controlled Radical Polymerization ...... 5

2.2 Copolymer Self-Assembly...... 9

2.3 Electron-Beam Lithography ...... 13

2.4 Gradient Copolymers ...... 14

3. Self-Assembly of Gradient Copolymers Synthesized in Semi-Batch Mode ...... 18

3.1 Abstract ...... 18

3.2 Introduction ...... 18

3.3 Experimental Section ...... 21

3.3.1 Materials ...... 21

3.3.2 Synthesis of Random Terpolymer Brush ...... 22

3.3.3 Block Copolymer Synthesis ...... 23

3.3.4 Synthesis of Blocky Gradient Copolymers ...... 23

3.3.5 Synthesis of Smooth Gradient Copolymers ...... 24

3.3.6 Substrate Preparation ...... 25

3.3.7 Random Copolymer Grafting ...... 25

3.3.8 Copolymer Deposition ...... 25

3.3.9 Rapid Thermal Annealing ...... 25

3.3.10 Analysis ...... 26

3.4 Results & Discussion ...... 26

3.4.1 Polymerization Characteristics ...... 26

3.4.2 Copolymer Self-Assembly ...... 29

3.5 Discussion ...... 32

3.5.1 Effect of Gradients on Self-Assembly ...... 32

3.5.2 Effect of Long Injection Time of Gradient Self-Assembly ...... 35

3.5.3 Effect of Wetting & Film Thickness on Self-Assembly ...... 37

3.6 Conclusion ...... 38

3.7 Acknowledgements ...... 38

4. Conclusion ...... 39

5. Future Work ...... 39

6. References ...... 40

1. GENERAL INTRODUCTION

Due to the ever-growing demand for faster and more efficient electronics, manufacturers must continually reduce the feature size in semiconductor devices. Photolithography, the process whereby light is used to chemically change a photoresist in order to etch it away to produce the desired pattern, is the key step in this feature reduction.1 Manufacturers have traditionally accomplished this reduction in size by using shorter wavelengths of light, from 436 nm light down to 193 nm now commonly used. However, 193 nm is insufficient for the current feature size being manufactured, so novel techniques such as immersion lithography and double exposure have been developed to increase the usefulness of 193 nm light.2 However, these technologies are beginning to reach their limit. Therefore, new alternatives are being sought that can still use the existing 193 nm photolithography equipment. Block copolymers present a unique alternative due to their ability to self-assemble into well-defined structures with nano- scale periodic arrangements.3 This property makes block copolymers candidates for “bottom- up” lithographic processes where the polymer acts as a sacrificial template, eliminating the need for expensive and complicated optics and masks.4 For this to occur, the copolymer must produce almost defect-free patterns with good control over dimensions and shapes at the molecular level.3

This thesis consists of a literature review of the essential topics and one project introducing a novel study of gradient copolymer self-assembly. Chapter 2 consists of a literature review of controlled radical polymerization and copolymer self-assembly. Chapter 3 describes the synthesis of poly(methyl methacrylate-grad-styrene) gradient copolymers by nitroxide-

mediated polymerization and their self-assembly on neutral surfaces to produce vertically orientated nanoscopic domains.

2. LITERATURE REVIEW

In order to synthesize block copolymers for self-assembly, a technique that provides precise control of their molecular weight distribution and composition is necessary. Therefore, controlled radical polymerization (CRP) was applied in this work because it provides several key features useful for such technologies. Thus, I will first review CRP, followed by copolymer self- assembly and lithography.

2.1 Controlled Radical Polymerization

Polymers are macromolecules made up of repeating units called monomers. In order to make a polymer, there are generally three main types of polymerization: step-wise, radical (chain) and ionic polymerization.5 Radical polymerization is typically a very fast process, but is uncontrolled and produces large variations in polymer chain sizes, and the final chain length is sometimes difficult to predict due to varying termination reactions and side reactions.6 Living reactions, such as ionic polymerizations, are defined by IUPAC as “a chain polymerization from which chain transfer and chain termination are absent.”7 It was developed by Szwarc et al. in 1956.8

With the absence of termination reactions in living polymerization, it is possible to achieve a linear number average molecular weight (MN) versus conversion with a very narrow distribution of molecular weights.9 However, ionic polymerization requires very stringent reaction conditions and is therefore not very commonly used outside of lab scale or niche commercial

(REF) applications.10

Controlled radical polymerization (CRP) exhibits some characteristics of a living reaction, namely a linear number average degree of polymerization (MN) versus conversion profile, but

also has the advantages of conventional radical polymerization: extensive purification of monomers/solvents not necessary, can be done in aqueous media and tolerant of impurities.11

CRP can be further divided into three main types: nitroxide mediated polymerization (NMP), atom transfer radical polymerization (ATRP) and reversible addition-fragmentation chain transfer (RAFT). NMP uses nitroxides as reversible chain terminators to control the reaction and minimize chain termination but is limited by the type of monomer, until recently.12 ATRP also uses a reversible termination step but is catalyzed by a transition metal complex that activates and deactivates the polymer. While ATRP has a wider range of monomers it can polymerize, the use of a metal catalyst discolours the polymer, necessitating an extra purification step.13 RAFT differs in that it uses thio-carbonyl compounds in a reversible chain transfer reaction to control the radical concentration during the polymerization. RAFT is compatible with many different solvents and monomers but will also discolour the polymer.14 Historically, NMP has been the most limited in terms of compatible monomers, in that it could only polymerize styrenic monomers. However, recently new nitroxides have allowed other monomers such as acrylates and acrylamides to be polymerized.15 Certain monomers, such as methyl methacrylate (MMA) remain difficult for these newer nitroxides to control, so a small amount of a controlling monomer is added to improve the chain fidelity of the reaction.16 Recently, homopolymerization of MMA has been achieved using specifically designed nitroxide initiators and other novel techniques.17,18 While these methods produce a PMMA polymer free of any styrene (St) or other controlling monomer, they require extra processing steps and in some cases, the synthesis of a novel initiator instead of using a commercially available one. NMP is of

particular interest because the purification step post-polymerization required in ATRP and RAFT is unnecessary, making it more viable in larger scale applications.19

Figure 1. SG1 Nitroxide and BlocBuilder alkoxyamine initiator

Initially, NMP was performed using a bicomponent system consisting of a thermal initiator and a nitroxide.20 Tordo et al. first attempted NMP using SG1 as the nitroxide in 2000 (Figure 1).

Their results indicated it was one of the most potent and versatile nitroxides found at the time due in part to the carbon-phosphorous bond which is inherently thermally stable and allows for increased steric effects.20,21 A unimolecular initiator was first developed by the groups of

Rizzardo and Hawker. This initiator decomposes into both the nitroxide and the initiating radical and provides better control over molecular weight and molecular weight distributions.22,23 The released radical can also be tuned depending on the desired application and has been shown to have a strong effect on the polymerization.24 BlocBuilder (A6a) has drastically increased the controlled character of the bulk polymerization of styrene, as shown below in Figure 2.20 It has also been demonstrated to polymerize n-butyl acrylate (nBA) without any additional nitroxide.25,26

Figure 2. Degree of control of bulk styrene polymerization by different alkoxyamines. Experimental MN (dots), simulated MN

20 (dotted line), theoretical MN (solid line). Reproduced with permission from Elsevier.

Further advances made by Vinas et al. to develop novel initiators led to the production of

BlocBuilder with an N-succinimidyl (NHS) ester (Figure 3). NHS-BlocBuilder was found to have a dissociation rate constant nearly 15 times higher than non-functionalized BlocBuilder.27 Using

NHS-BlocBuilder, Maric et al. demonstrated the polymerization of glycidyl methacrylate (GMA)- rich copolymers without the addition of additional free SG1 typically required for methacrylic copolymerizations using BlocBuilder.28

Figure 3. N-hydroxysuccinimide-BlocBuilder

2.2 Copolymer Self-Assembly

Block copolymers are made of two or more sequences of chemically distinct polymers that are covalently joined. The simplest of these are linear AB copolymers where there are two distinct blocks, A and B.5 The behaviour of block copolymers in bulk is defined by three parameters: the degree of polymerization, the volume fractions of the constituent species and the Flory-Huggins enthalpic interaction parameter between the two species.29 The degree of polymerization and volume fraction are controllable through the stoichiometry of polymerization, however the

Flory-Huggins parameter is temperature-dependant and is primarily determined by the monomers used. Thermodynamic incompatibility between the two blocks drives microphase separation where the blocks will arrange themselves so the contact between dissimilar blocks is minimized, forming domains rich in one species.30 These domains form periodic structures within a lattice with a high degree of regularity.31

Figure 4. a) Phase diagram for a simple A-B diblock copolymer. Reproduced with permission from ACS.32 b) Possible domain morphologies of a block copolymer. Reprinted with permission from Elsevier.33

Block copolymer segregation can be expressed using the parameter χN where χ is the Flory-

Huggins interaction parameter and N is the overall copolymer degree of polymerization. At lower values of χN, the copolymer assumes a disordered, homogeneous state as seen in Figure

4. The transition from a homogeneous phase to an ordered heterogeneous one occurs at the

Order-Disorder Transition (ODT), defined by the spinodal curve. This transition occurs at a critical value of χN, which is determined by the composition of the copolymer. For a symmetrical diblock, this transition occurs at a value of 10.5.34 For values of χN very near to the

ODT, spinodal decomposition dominates self-assembly, resulting in lamellar, hexagonal or body-centered cubic symmetries.35 PS-b-PMMA is very commonly studied for self-assembly for many reasons. The segments are both amorphous blocks, thus making crystallization effects negligible. For lithography, the similarity in PS and PMMA surface tensions, makes vertical

orientation of domains relatively simple.36 However, P(S-b-MMA) is intrinsically limited to feature sizes of about 12 nm because of the small Flory-Huggins parameter of the system.37

The ability of block copolymers to self-assemble into features with a characteristic size of 5-55 nm allows substrates to be patterned with dimensions below those easily achievable by conventional photolithography. However, for advanced lithographic applications, complex geometries are required, necessitating some form of control over the self-assembly of the block copolymer.38 This is typically achieved by chemically38-40 or topographically41,42 patterning of the substrate. Using current lithographic techniques, Nealey et al. demonstrate one approach where a polymer brush was applied to a surface and patterned with an electron beam such that one block would preferentially wet the exposed areas. This approach was used to demonstrate pattern rectification and density multiplication by block copolymers.3

Figure 5. Density multiplication and pattern rectification by a block copolymer. Reprinted with permission from AAAS.3

When using systems with very dissimilar wetting characteristics, additional steps are required to obtain vertical orientation of cylinders or lamellae. Several techniques have been used in the past to orient the block copolymers, including mechanical flow fields,43-45 electric fields,46,47 solvent annealing,48 and chemically neutral surfaces.49-51 In particular, chemically neutral surfaces are a commonly used technique because they require very little extra processing and do not require complicated setups used in solvent annealing. Neutral surfaces can be produced by depositing a brush polymer with a particular composition, rendering it non-preferential for either block. In order to prevent diffusion of the brush polymer into the copolymer film during annealing, it can be covalently grafted to the substrate by dehydration reactions between hydroxyl groups present in the polymer and the native oxide of the substrate. Early attempts at pinning brush copolymers used hydroxyl-functionalized resulting in a single hydroxyl group at the end of each polymer chain. As a result, the grafting process took in excess of 48h.49

However, this time was reduced to only a few hours by introducing a small amount of hydroxyl- functionalized monomer randomly distributed throughout the polymer, providing more binding sites per chain.51

The techniques discussed above all employ some form of confinement to produce the desired morphology. This results in a difference in the behaviour of self-assembly when compared to bulk samples with no confinement effects. In thin films for example, the unit cell becomes stretched, giving smaller lateral spacing than those found in the bulk case.52

2.3 Electron-Beam Lithography

Electron-beam (e-beam) lithography began in the 1960s using modified electron microscopes to write a pattern directly on a substrate without a mask.53 It takes advantage of the very small wavelength of an electron to surpass the maximum resolution of optical lithography by several orders of magnitude.53 E-beam lithography functions by chemically or physically modifying a resist by exposure to high energy electrons. In a positive tone resist, this takes the form of breaking molecule bonds in a polymeric resist while in a negative tone resist, it leads to polymer cross-linking. PMMA is a very commonly used positive resist for e-beam lithography which has been shown to achieve patterns as small as 3-4 nm in size.54 E-beam lithography is much slower than conventional photolithography, since it takes on the order of tens of minutes to expose a pattern on a sample sized wafer in addition to the time it takes to calibrate the microscope prior to exposure. Despite this, it is a very powerful tool for producing complex, well-ordered domains in self-assembled films. Using e-beam lithography, Ruiz et al. produced dense arrays of poly(styrene) (PSt) rectangles with high uniformity. They controlled the orientation of the PMMA-PS block copolymer by using e-beam lithography and oxygen plasma to chemically contrast a neutral brush layer. Following the removal of the PMMA domains, a second e-beam exposure step and subsequent etching left them with the dense array of PS domains seen in Figure 6.55

Figure 6. Dense array of PSt rectangles. Reprinted with permission from ACS.55

2.4 Gradient Copolymers

Gradient copolymers are defined by a continuously varying chemical composition instead of the abrupt change found in block copolymers. In order to synthesize well-defined gradient copolymers with good chain compositional homogeneity, a polymerization technique either lacking termination reactions or with limited termination is required. Thus, conventional radical polymerization is unable to produce gradients due to the short life of the initiating radical.56

Previous work has shown that cationic57 and anionic58 polymerizations can be used as well as

NMP,59 ATRP,60 and RAFT.14 In order to synthesize gradient copolymers, the composition of the medium can be changed throughout the reaction, which can be achieved in batch or semibatch mode.

Figure 7. Depiction of various linear copolymers. a) Block copolymer, b) gradient copolymer, c) random copolymer

In a batch process, the reactivity ratios between the constituent monomers must be sufficiently different so that one monomer is added preferentially until it begins to be depleted, and the reaction must also be allowed to proceed to high conversion.60,61 Reactivity ratios were first studied by Mayo and Lewis to quantify the behaviour of monomers in a copolymerization reaction. They describe the ratio of the rate constants for the reaction of a monomer with another monomer of the same type or the opposite type.62 When the reactivity ratios are similar and close to one, neither reaction is favoured, producing a truly random copolymer.

However, when the reactivity ratios are both high, the homopolymerization reaction is favoured resulting in lengthy sequences of a single type of monomer (i.e. “blocky”). In a semibatch process, the second monomer is added continuously during the reaction to gradually change the composition of the medium.60,61 Table 1 summarizes some different reactivity ratios for the St-MMA copolymerization. Different values arise from the change in temperature and method of curve fitting.

Table 1. Reactivity ratios for St and MMA at different temperatures

Polymerization Temperature rSt rMMA 40°C63 0.523 0.460 60°C64 0.494 0.462 90°C65 0.55 0.58

Previous theoretical work using computational models has predicted that the thermal and bulk properties of gradient copolymers should differ from those of statistical or diblock copolymers.66,67 Like block copolymers, gradient copolymers are predicted to be able to microphase separate, but the minimum order-disorder transition is higher. Additionally, the interface is expected to be more diffuse than that of block copolymers.68 The microphase separation of gradient copolymers also depends on the shape of the gradient in addition to the composition, degree of polymerization, and Flory-Huggins enthalpic interaction parameter. In the case of a fully tapered gradient copolymer, which has a linear transition from pure A to pure

B, the lamellar phase is the only stable phase predicted and occurs at a minimum χN of about

30. 66,69

Figure 8. a) Monomer distribution along polymer chains: —=diblock, =”flat” gradient, - - =”steep” gradient b) “Flat” gradient phase diagram c) “Steep” gradient phase diagram d) Diblock phase diagram. Reprinted with permission from

Springer.56

Thus, gradient or tapered copolymers are obviously of interest to study for their self-assembly behaviour relative to block copolymers. How close can they approach the self-assembly of block copolymers? This is relevant as the possibility of producing tapered block copolymers at an industrial scale is simple to implement and, in the case of controlled radical polymerizations, avoid s intermediate purification steps. Further, using controlled radical polymerizations will permit the development of tapered copolymers that would otherwise not be attainable by truly living polymerizations.

3. SELF-ASSEMBLY OF GRADIENT COPOLYMERS SYNTHESIZED IN SEMI-BATCH

MODE

3.1 Abstract

Gradient copolymers (GCP) of poly(styrene-grad-methyl methacrylate) (PS-grad-PMMA) were synthesized in a semi-batch process using nitroxide-mediated polymerization (NMP) with varied

-1 monomer injection protocols (molecular weights (MN) ranged from 48 000 g mol to 94 000 g mol-1 with dispersities (Đ) between 1.35 and 1.59). The GCPs were spun into thin films on substrates made neutral by poly(S-ran-MMA-ran-hydroxyethyl methacrylate) terpolymers and annealed at elevated temperature to produce vertically orientated microphase-separated domains. The GCPs were found to have similar domain sizing to that estimated for BCPs with identical MN and composition. However, GCPs synthesized with long injection times (i.e. excessive tapering of composition) were found to exhibit very poor self-assembly attributed to their predicted random-copolymer-like middle sequence reducing the effective enthalpic interaction parameter.

3.2 Introduction

Recently, nanolithographic technologies based on self-assembling materials have been receiving significant attention from both industrial3,70 and academic.54,71,72 Block copolymer

(BCP) thin films have been shown to self-assemble into periodic structures with a characteristic size well below 50 nm.73 The emergence of self-assembled BCPs has coincided with the difficulties in traditional photolithographic techniques, which become increasingly complex and costly due to the continued trend of miniaturization.2

Diblock copolymers consist of two chemically distinct polymers, which are covalently joined.

Diblock copolymers can exhibit a wide range of morphologies that occur through microphase separation due to the immiscibility of the two distinct monomeric components and the length of the respective segments. Lamellar, gyroid, hexagonally packed cylinders, and body-centered spheres are all possible equilibrium arrangements.31,74,75 This equilibrium depends primarily on the relative volume fraction of each species (f), the degree of polymerization (N) and the thermodynamic incompatibility of the two species, described by the Flory-Huggins enthalpic interaction parameter (χ).75 The first two factors are controlled during polymerization while the last factor is determined by the choice of the two monomers. Poly(styrene-block-methyl methacrylate) (P(S-b-MMA)) is the most commonly used BCP for self-assembly, partly due to the similarity of their surface tensions, making vertical orientation relatively simple.36 However,

P(S-b-MMA) is intrinsically limited to feature sizes no smaller than 12 nm because of the low χN of the system.37

For BCP self-assembly to be useful for lithographic applications, long-range order is necessary.

This is typically achieved by chemical38-40 or topographic41,42 patterning of the substrate. Using current lithographic techniques, Nealey et al. have demonstrated the ability to direct the self- assembly of BCPs on large scales.3,38 They used extreme ultraviolet interference lithography

(EUV-IL) or electron beam lithography (EBL) to write a pattern on a photoresist, which is then transferred to the substrate using an oxygen plasma. The BCP is then spun onto the chemically patterned substrate and the oxygenated sections will be preferentially wet by one of the blocks.

Additionally, vertical orientation of the BCP domains is generally desired. Several different methods have been developed to address this: Mechanical flow fields,43-45 electric fields,46,47

solvent annealing,48 and chemically neutral surfaces.49-51 In particular, random copolymer brushes are a commonly used technique to achieve vertical orientation. However, vertical orientation also introduces a number of defect structures such as dislocations and disclinations in the plane of the film.76 The random copolymer brushes, which have a finely tuned composition, are covalently bonded to the substrate to prevent them from diffusing into the

BCP film. The grafting is typically achieved through a dehydration reaction between hydroxyl groups on the polymer and the native oxide of the substrate. Pinning using hydroxyl groups positioned at the ends of polymer chains used to take excessively long, in excess of 48 h49, but has been reduced to a few hours at a given temperature.51 More recently, rapid thermal annealing of polymer thin films has been shown to further reduce the annealing time to several minutes.77

In contrast to BCPs, gradient copolymers (GCP) are defined by a continuously varying composition along the polymer chain. They have emerged in the past two decades as an possible alternative to BCPs for many applications.56 In order to synthesize GCPs, a polymerization technique either lacking termination reactions or with limited termination is required, as the chain-to-chain composition can vary widely. Thus, conventional radical polymerization is unable to produce gradients due to the short life of the initiating radical.56

Gradient copolymer synthesis is carried out either as a batch or semi-batch process. In a batch reaction, monomer pairs with sufficiently different reactivity ratios must be chosen and the reaction must be allowed to proceed to very high conversion. In a semibatch or “forced” polymerization, the second monomer is gradually added to the reaction system, changing the composition of the reaction mixture.60,61 GCPs provide an advantage over traditional BCPs for

large scale processing by reducing the amount of reaction steps (i.e. intermediate purification and characterization steps required for BCP synthesis by controlled radical polymerization are avoided). However, the minimum order-disorder transition (ODT) for GCPs changes as a function of the gradient length, becoming higher as the gradient length grows.67

In this study, gradients were synthesized using a semi-batch method where styrene was injected over a certain period of time to a PMMA-rich initiating species. Injecting all of the styrene at once, resulting in “blocky” gradients, produced one class of gradients. The other was produced by injecting styrene over an extended period of time to produce more gradual, smoother gradients (herein classified as smooth gradients). In both cases, the gradients were modeled as hyperbolic composition profiles described below in (1):

Equation 1

where C0 determines the sharpness of the interface and t0 is the position of the interface. The limit C0 → ∞ corresponds to a block copolymer. F0 and A are fitting parameters that take into account the varying initial and final compositions of the real GCPs.66-68

3.3 Experimental Section

3.3.1 Materials

Styrene (St, ≥99%), methyl methacrylate (MMA, 99%), 2-hydroxyethyl methacrylate (HEMA,

≥99%), calcium hydride (CaH2, 95%, reagent grade), and aluminum oxide (Al2O3, Brockmann

Type I, basic) were purchased from Sigma-Aldrich. Methanol (≥99.8%, ACS reagent grade),

tetrahydrofuran (THF, ≥99.9%, HPLC grade), and toluene (≥99.5%, ACS reagent grade) were purchased from Fisher Scientific. Chloroform-d1 (99.8% deuteration) was purchased from

MagniSolv. All above compounds were used as received. St, MMA and HEMA were purified and dehydrated by passing through a column of basic aluminum dioxide mixed with 5 wt% calcium hydride, and stored in a sealed flask under a head of nitrogen. 2- ((tert-butyl[1-

(diethoxyphosphoryl)-2,2-dimethylpropyl]amino)oxy)-2-methylpropionic acid (Blocbuilder,

99%) was obtained from Arkema. N-hydroxysuccinimide (NHS, 98%), and N,N’- dicyclohexylcarbodiimide (DCC, 99.9%) were purchased from Sigma-Aldrich and used in conjuction with BlocBuilder to synthesize the succinimidyl ester terminated alkoxyamine

Blocbuilder (NHS-BlocBuilder) using the same procedure described by Vinas et al.27 Silicon wafers were purchased from University Wafer.

3.3.2 Synthesis of Random Terpolymer Brush

The random copolymer used was synthesized by nitroxide-mediated polymerization following similar procedures adapted from Nealey et al.51 A typical formulation follows. A mixture of NHS-

BlocBuilder initiator (0.0805 g, 0.211 mmol), St (4.6792 g, 44.93 mmol), MMA (8.1498 g, 81.50 mmol), and HEMA (0.2574 g, 1.980 mmol) was purged with nitrogen for 30 minutes at room temperature. The mixture was heated to 100°C for 2 hours while maintaining the nitrogen purge. The contents were then cooled and the resulting copolymer was precipitated in methanol, decanted, and dried under vacuum at 50°C overnight to obtain the final copolymer

-1 (3.16 g, 24% yield), Mn = 39 000 g mol , Ð = 1.25 (by GPC relative to linear PMMA standards in

o 1 THF at 40 C). The mol fraction of St in the terpolymer (FSt) was determined by H NMR spectroscopy to be 0.53, and the mol fraction of HEMA (FHEMA) was 0.01.

3.3.3 Block Copolymer Synthesis

Synthesis of P(MMA-ran-St) Macroinitiator

The macroinitiator (M1) was synthesized by nitroxide-mediated polymerization with a target molecular weight of 42 000 g mol-1. A mixture of initiator (0.0704 g, 0.185 mmol), St (0.6956 g,

66.88 mmol), and MMA (6.9820 g, 69.82 mmol) was purged with nitrogen for 30 minutes at room temperature. The mixture was heated to 90°C for 90 minutes while maintaining the nitrogen purge. The contents were then cooled and the resulting copolymer was precipitated in hexane, decanted, and dried under vacuum at 50°C overnight to obtain the final copolymer

-1 (1.82g, 24% yield), Mn = 28 000 g mol , Ð = 1.27 (by GPC relative to linear PMMA standards in

o 1 THF at 40 C). FSt was determined by H NMR spectroscopy to be 0.15.

Chain Extension of Macroinitiator

The block copolymer (B1) was synthesized by chain extension of macroinitiator M1. A mixture of St (22.72 g, 218.5 mmol), and macroinitiator M1 (1.8784 g, 0.068 mmol) was purged with nitrogen for 30 minutes at room temperature. The mixture was heated to 110°C for 3 hours while maintaining the nitrogen purge. The contents were then cooled and the resulting polymer was precipitated in methanol, decanted, and dried under vacuum at 50°C overnight to

-1 obtain the final copolymer (1.85g, 7.5% yield), Mn = 58 000 g mol , Ð = 1.37 (by GPC relative to

o 1 linear PMMA standards in THF at 40 C). FSt was determined by H NMR spectroscopy to be 0.76.

3.3.4 Synthesis of Blocky Gradient Copolymers

The blocky GCPs used were synthesized by nitroxide-mediated polymerization in semibatch mode following similar procedures, adapted from Gray et al.78 The polymerization procedure

for sample G1 is described below. A mixture of initiator (0.0716 g, 0.188 mmol), St (0.7353 g,

7.07 mmol), and MMA (6.9209 g, 69.21 mmol) was purged with nitrogen for 30 minutes at room temperature. The mixture was heated to 90°C for 1.5 hours while maintaining the nitrogen purge. St (22.399 g, 215.4 mmol) was then added and the temperature was raised to

110°C for 3 hours. The contents were then cooled and the resulting polymer was precipitated in methanol, decanted, and dried under vacuum at 50°C overnight to obtain the final copolymer

-1 (2.32 g, 7.7% yield), Mn = 76 000 g mol , Ð = 1.43 (by GPC relative to linear PMMA standards in

o 1 THF at 40 C). FSt was determined by H NMR spectroscopy to be 0.75.

3.3.5 Synthesis of Smooth Gradient Copolymers

Smooth GCPs used were synthesized by nitroxide-mediated polymerization in semibatch mode.

The polymerization procedure for sample G5 is described below. A mixture of initiator (0.0721 g,

0.189 mmol mmol), St (0.7271 g, 6.99 mmol), and MMA (7.5600 g, 75.60 mmol) was purged with nitrogen for 30 minutes at room temperature. The mixture was heated to 90°C for 30 minutes while maintaining the nitrogen purge. St (21.98 g, 211 mmol) was delivered at a rate of

0.206 ml/min using a syringe pump for 2 hours while the temperature was steadily increased at a rate of 10°C/hour. The pump was then switched off and the reaction proceeded for 1 hour at

110°C. The mixture was then cooled and the resulting polymer was precipitated in methanol, decanted, and dried under vacuum at 50°C overnight to obtain the final copolymer (3.22 g, 39%

-1 o yield), Mn = 64 000 g mol , Ð = 1.44 (by GPC relative to linear PMMA standards in THF at 40 C).

1 FSt was determined by H NMR to be 0.71.

3.3.6 Substrate Preparation

Silicon(100) wafers were cut into approximately 1.5 cm2 pieces and cleaned using successive washing with deionized water, acetone and isopropyl alcohol. The samples were then immersed in Nanostrip 2X solution for 30 minutes at 80°C and then rinsed with deionized water and dried under nitrogen.

3.3.7 Random Copolymer Grafting

Random copolymer brushes were grafted by spin coating films of P(MMA-S-HEMA) solution onto the cleaned wafers. Spin coating from a 1.5 wt% solution in toluene at 4000 rpm gave 40-

45nm thick films. The samples were then annealed in a vacuum oven at 150°C for 18 hours. The samples were sonicated twice in 50°C toluene for 10 minutes to remove any unbound copolymers. The final brush thickness was found to be vary between 10-15 nm.

3.3.8 Copolymer Deposition

The copolymers were deposited on the grafted substrate by spinning at either 3000 or 4000

RPM from a 1 wt% or 1.5 wt% solution. Film thickness varied from 44 to 67 nm.

3.3.9 Rapid Thermal Annealing

Rapid thermal annealing was performed in a Jipelec JetFirst 200 system. The samples were first placed in the chamber, the chamber was then evacuated and finally backfilled with nitrogen.

The heating ramp was set to 19°C/s. The samples were annealed at 220°C for 3 minutes and subsequently cooled to room temperature.

3.3.10 Analysis

1H NMR spectra were recorded on a Varian Mercury 300 MHz spectrometer with tetramethyl silane (TMS) as an internal standard. Molecular weights and dispersity were found using gel permeation chromatography (GPC) (Waters Breeze) equipped with three Waters Styragel HF columns (molecular weight ranges: HR1: 102 – 5×103 g mol-1, HR2: 5×102 – 2×104 g mol-1, HR3:

5×103 – 6×105 g mol-1) and a guard column. The results obtained were from the Waters 2410 refractive index (RI) detector using tetrahydrofuran (THF) as the eluent at 40°C and a flow rate of 0.3 ml/min. Poly(methyl methacrylate) standards were used for calibration.

The thicknesses of the polymer films were measured using a Sopra GES-5E spectroscopic ellipsometer at a 75° incident angle. The characterization of the GCP morphology was done using a Tescan XM scanning electron microscope (SEM) at an accelerating voltage of 3.5 kV. In order to improve image contrast, the PMMA domains were selectively removed by reactive ion etching (RIE). Samples were exposed to a 30 W oxygen plasma at 20 mTorr for 30 seconds. The samples were then coated with a thin layer of chromium to reduce charging effects. Image analysis to determine average feature sizes was performed using ImageJ.

3.4 Results & Discussion

3.4.1 Polymerization Characteristics

-1 The random terpolymer, H1, had a final molecular weight of 39 000 g mol and a FSt of 0.53, sufficient to induce vertical orientation of the copolymer films.51 The BCP, B1, used in this work

-1 had a molecular weight of 58 000 g mol and FSt = 0.76, which should produce cylindrical domains.

P(MMA-grad-St) copolymers were synthesized in one of two ways in order to produce the desired composition and transition length. For the blocky gradients, the polymerization time before and after the addition of St was varied to produce differing final compositions. The results are summarized in Table 2.

Table 2. Properties of Blocky GCPs.

-1 a b Polymer t before injection (min) t after injection (min) Mn (g mol ) Ð FSt C0 G1 90 180 76 000 1.43 0.75 2.69 G2 90 180 94 000 1.59 0.76 2.24 G3 120 150 49 000 1.46 0.62 0.76 G4 120 150 64 000 1.35 0.69 0.90 a. FSt indicates the molar fraction of styrene in the polymer. b. C0 indicates the sharpness of the transition. Higher values indicates more block-like behaviour. In the case of the smooth GCPs, the injection rate was varied to produce a different transition length. Additionally, the temperature was steadily increased from the initial set point of 90°C to the final set point of 110°C over the course of the injection. The results are summarized in Table

Table 3. Properties of Smooth GCPs

a b Polymer Injection time Injection Rate T ramp rate Mn Ð FSt C0 (min) (ml/min) (°C/min) (g mol-1) G5 120 0.206 0.17 64 000 1.44 0.71 0.56 G6 360 0.0688 0.056 62 000 1.43 0.81 3.84

a. FSt indicates the mole fraction of styrene in the polymer. b. C0 indicates the sharpness of the transition. Higher values indicates more block-like behaviour. By plotting the measured cumulative styrene composition against the normalized chain length and fitting the data with Equation 1, we were able to determine the sharpness of each gradient polymer. The plots shown in Figure 9 demonstrate two distinct curve shapes. One is sigmoidal with a relatively sharp transition from the MMA rich segment to the St rich segment. These curves are characterized by C0>2, and 0.5

orientation. The other curve indicates much more gradual transition from the MMA-rich segment to the St-rich segment. These curves are characterized by C0<1 and t0>1 and correspond to lamellar or mixed lamellar orientation.

Figure 9. a) Cumulative St composition as a function of normalized chain length for blocky GCPs. b) Cumulative St composition as a function of normalized chain length for smooth GCP. Lines are a least squares fit of Equation 1.

3.4.2 Copolymer Self-Assembly

To determine whether the copolymers successfully self-assembled, they were spin coated on substrates with a neutral brush to promote vertical orientation of the domains. All samples were annealed using rapid thermal annealing, etched in an oxygen plasma to provide contrast, and sputter coated with chromium to reduce charging effects. Figures Figure 10-Figure 12 below indicate that self-assembly was successful in all cases. The average diameter, standard deviation and eccentricity for all polymers are reported in Table 4.

Table 4. Copolymer self-assembly feature sizes.

a Polymer C0 Film Thickness Feature Size Center-to-Center Spacing Eccentricity (nm) (nm) (nm) b B1 42 ± 0.5 27 ± 8 57 ± 15 0.58 c B1 42 ± 0.5 56 ± 4 - - G1b 2.69 66 ± 0.3 23 ± 7 47 ± 6 0.68 G2b 2.24 61 ± 0.4 25 ±7 57 ± 4 0.63 G3b 0.76 68 ± 1 31 ±12 93 ± 57 0.66 G3c 0.76 68 ± 1 26 ± 2 - - G4c 0.90 67 ± 0.1 42 ± 3 - - G5b 0.56 62 ± 0.2 16 ± 9 39 ± 10 0.77 G6b 3.84 64 ± 0.5 24 ± 9 46 ± 38 0.78 a. Deviation from circularity, where 0 indicates a perfect circle a. Cylindrical domains, feature size indicates the diameter. b. Lamellar domains, feature size indicates the line spacing.

Figure 10. SEM image of B1 on silicon substrate modified with H1. PMMA domains are dark (have been removed), PS domains are lighter.

a) b)

c) d)

Figure 11. SEM images of blocky GCPs (Table 2) on silicon substrates modified with H1. a) G1, b) G2, c) G3, d) G4. PMMA domains are dark (have been removed), PS domains are lighter.

a) b)

Figure 12. SEM images of smooth GCPs (Table 3) on silicon substrates modified with H1. a) G5, b) G6. PMMA domains are dark (have been removed), PS domains are lighter.

3.5 Discussion

In this work, the self-assembly of block and gradient copolymers produced equilibrium microstructures driven by thermodynamics in agreement with previous work, however they lacked any long-range order.29,31 Directed self-assembly and self-assembly under confinement

(graphoepitaxy) are both be used to provide self-assembled morphologies with extended long- range order with near-perfect pattern registration.40,79 Other non-equilibrium techniques, such as controlled solvent evaporation, can also be used to orient self-assembled microstructures in a desirable fashion.48,80

3.5.1 Effect of Gradients on Self-Assembly

Figure 10-Figure 12 clearly demonstrate that GCPs influence self-assembly. Figure 10 shows a block copolymer. The composition of the block copolymer and the nature of the brush suggest

the morphology will be cylinders, however due to thickness effects discussed later, some horizontal cylinder domains were also present. Figure 11 starts showing gradient or tapered block copolymers where the second monomer (St) was added nearly instantaneously after a certain period of time to the MMA-rich chains. Figure 12 indicates the final case studied where the second monomer was added gradually over a period of time (termed smooth gradients hereafter). If we were to compare the results seen in Figures Figure 11 and Figure 12 to block copolymers with compositions and molecular weights identical to each GCP, we would see that cylindrical domains would form in all cases except for G3 and G4 which would self-assemble into lamellar domains.81 In general, we see that the GCP morphologies match those predicted for their equivalent BCPs, however the defect density observed in the gradients G3, G5, and G6 is quite high. Using the domain scaling developed by Semenov,82 and Matsen and Bates81 for

BCPs in the strong-segregation limit, the domain sizes of theoretical BCPs ( ) were estimated in Table 5. With the exception of G3 and G6, we see that the GCPs have average domain sizes close to, but smaller than those predicted for BCPs. This result is in agreement with previous theoretical work, which predicts that GCPs have weaker segregation, and therefore have a lower repeat period than BCPs.66,83 For polymer G3, the larger than predicted values can be attributed to the relatively low molecular weight resulting in more diffuse boundaries which can be confirmed qualitatively by examining the roughness of the interface seen in Figure 11.c. Polymer G6 also had larger than predicted domain sizes, however it has a lower domain spacing, which is unexpected given that its domains are larger. We can see in

Figure 12.b that many of the cylindrical MMA-rich domains are very close together or even end

up blending together giving rise to the high average domain size but low domain spacing. This is also reflected in the high standard deviation for these measurements.

Table 5. Comparison between theoretical BCP domain sizes and actual GCP domain sizes. Polymer BCP Domain Size GCP Domain Size BCP Spacing GCP Domain Spacing (nm) (nm) (nm) (nm) G1a 27 23 ± 7 55 47 ± 6 G2a 31 25 ± 7 62 57 ± 4 G3b 20 28 ± 2 40 56 ± 4 G4b 24 21 ± 1 48 42 ± 2 G5a 25 16 ± 9 51 39 ± 10 G6a 22 24 ± 9 54 46 ± 38 a. Observed morphology corresponds to cylinders, BCP domain size and spacing is estimated for cylinders. b. Observed morphology corresponds to lamellae, BCP domain size and spacing is estimated for lamellae. The cylinders produced by BCP B1 also exhibit a lower eccentricity, 0.58. In contrast, the lowest eccentricity of the cylinder-domain forming GCPs was 0.63. Some of the GCPs had eccentricities as high as 0.78. Figure 11.c demonstrates how the presence of a gradient in composition affects the minimum ODT. With a molecular weight of 49 000 g mol-1 annealed at

220°C, the system has a χN of about 17, which for a BCP would be sufficient to self-assemble into well-defined lamellar domains. Yet in Figure 11.c, we see a weakly separated system exhibiting both lamellar and cylindrical features. In order to more clearly compare the effect of the gradients on self-assembly, Figure 13 presents binary images of Figure 10, Figure 11.a,c and

Figure 12.a.

a) b)

c) d) Figure 13. Binary images of polymers a) B1, b) G1, c) G3 (the darkened regions are due to charging effects) and d) G5.

3.5.2 Effect of Long Injection Time of Gradient Self-Assembly

Despite their similarity to the blocky single injection gradients G1-4, the two smooth gradient copolymers synthesized in this study exhibit poorer self-assembly compared to the blocky gradients. Both smooth gradients were found to have smaller feature sizes but larger variation

in the overall size. They were also the most eccentric of any of the polymers studied. By employing kinetic simulations, Wang and Broadbelt were able to look beyond the composition profiles of GCPs and examine the individual monomer sequence lengths along a GCP. They found that monomer feed composition has a large effect on sequence lengths for polymers with reactivity ratios less than one, as is the case with MMA-St (at 90°C rSt≈0.55,

65,84,85 rMMA≈0.58). Polymers G5 and G6 were synthesized in such a way that they both have an

MMA-rich initial segment. However, due to the slow addition of St and temperature increase

(from 90 to 110 oC to polymerize the styrene more effectively (i.e. increase its polymerization rate), due to its lower propagation rate constant),86,87 a large portion of the middle of the polymer likely resembles a truly random copolymer with monomer sequence lengths close to 1, depicted in Figure 14. For G5, this hypothesis, coupled with the shorter overall polymerization time, meant that a St-rich end segment was never polymerized to the degree expected, giving rise to the small MMA domains and generally poor self-assembly seen in Figure 12.a. The presence of the gradient also increases the compatibility of the blocks, leading to mixing at the domain interface, thereby lowering the effective enthalpic interaction parameter, χ.88,89 In contrast to G5, G6 was polymerized for a much longer time, allowing for more St to be incorporated at the end of the reaction as the St monomer fraction became quite high (final FSt

= 0.81), resulting in better self-assembly than G5. However, like G5, the majority of the middle of the polymer is likely composed of a random copolymer-like structure with short monomer sequence lengths, increasing the compatibility of the blocks and decreasing the effective χ.

Figure 14. Schematic illustration of monomer sequence lengths for different polymer types: a) diblock copolymer, b) gradient copolymer, c) G4, and d) G5.

3.5.3 Effect of Wetting & Film Thickness on Self-Assembly

Previous work has shown that self-assembly behaviour of BCPs has a strong dependence on both the film thickness and the wetting behaviour of the blocks.90,91 In this work, non- preferential wetting at both the substrate and the free interface allowed for vertical orientation of the copolymer domains. However, defects in the films are seen, notably in Figure 10 and

Figure 11.c,d. These defects are the result of a combination of surface energy and film thickness effects. By employing a brush copolymer with a higher St fraction, the surface energy would be better balanced for cylinder-forming copolymers.92 The film thickness for all of the polymers used in this study (t ≈ 42-66 nm) was larger than the average feature size, which also played a role in the mixed orientation of B1 and G3. By controlling the thickness so that it is slightly smaller than the average feature size, more consistent vertical orientation of the domains should be possible.91,93

3.6 Conclusion

In this study, GCPs were synthesized in semi-batch mode by nitroxide polymerization allowing for a single reaction compared to the two steps required for a BCP. The blocky GCPs were able to successfully self-assemble into both vertical cylindrical and lamellar morphologies with feature sizes comparable to BCPs with identical properties. However, the smooth gradients had very poor self-assembly due to their long transition length and random copolymer-like structure in the transition from the MMA-rich to St-rich domains. By further refining the surface wetting and film thickness, it should be possible to produce self-assembled films with very low defect densities.

3.7 Acknowledgements

This work was funded by the Eugene Ulmer Lamothe Scholarship Fund, National Sciences and

Engineering Research Council of Canada – Collaborative Research and Development (NSERC-

CRD) grant in partnership with NanoQuébec and PCAS.

4. CONCLUSION

The copolymerization of MMA with St was successful in producing block and gradient copolymers with well-defined compositions and transitions necessary to study their self- assembly. Gradient copolymers were found to self-assemble into both cylindrical and lamellar morphologies with features similar to values estimated for block copolymers with the same properties. The effect of the gradient was also clearly seen in the poorer performance of the smooth gradient copolymers produced. Compared to the blocky gradient copolymers, their comparatively longer transition zone further reduced the enthalpic interaction parameter of the system resulting in poor self-assembly and diffuse domain boundaries. These results are in accordance with previous theoretical work for gradient copolymer self-assembly.

5. FUTURE WORK

To further extend this work, the directed self-assembly of the gradient copolymers should be investigated. By using a technique like electron-beam lithography, a chemical pattern can be written on the substrate and induce a controlled arrangement of the self-assembled domains.

This type of control would allow for the extension of this technique to more complex processes, such as transferring the pattern into the substrate or producing more complex morphologies.

This investigation would also be worthwhile to determine whether the directed self-assembly improves the performance of the gradients in terms of defect density and pattern roughness.

The synthesis of the gradient copolymer can also be further explored and refined. Currently, yields are relatively low due to the bulk polymerization. By using a solvent or by performing the polymerization in emulsion, yields could be improved.

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