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Keywords:

  •  block copolymers;
  • directed self-assembly;
  • lithography;
  • self-consistent field theory;
  • solvent annealing;
  • thin films

ABSTRACT

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. EXPERIMENTAL RESULTS AND DISCUSSION
  6. SELF-CONSISTENT FIELD THEORY RESULTS AND DISCUSSION
  7. CONCLUSIONS
  8. Acknowledgments
  9. REFERENCES AND NOTES
  10. Supporting Information

Controlling the morphology, domain orientation, and domain size of block copolymer (BCP) thin films is desirable for many applications in nanotechnology. These properties can be tuned during solvent annealing by varying the solvent choice and degree of swelling which affect the effective miscibility and volume fraction of the BCP domains. In this work, we demonstrate with a bulk lamellae-forming BCP, poly(4-trimethylsilylstyrene-block-D,L-lactide) (PTMSS-b-PLA), that varying the composition of a mixture of solvent vapors containing cyclohexane (PTMSS-selective) and acetone (PLA-selective), enables formation of perpendicularly oriented lamellae with sub-20-nm pitch lines. The BCP domain periodicity was also observed to increase by 30%, compared to bulk, following solvent annealing. Furthermore, solvent annealing alone is shown to induce a transition from a disordered to an ordered BCP. We rationalize our observations by hypothesizing that the use of a combination of domain selective solvent mixtures serves to increase the effective repulsion between the blocks of the copolymer. We furnish results from self-consistent field theory calculations to support the proposed mechanism. © 2013 Wiley Periodicals, Inc. J. Polym. Sci. Part B: Polym. Phys. 2014, 52, 36–45


INTRODUCTION

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. EXPERIMENTAL RESULTS AND DISCUSSION
  6. SELF-CONSISTENT FIELD THEORY RESULTS AND DISCUSSION
  7. CONCLUSIONS
  8. Acknowledgments
  9. REFERENCES AND NOTES
  10. Supporting Information

Self-assembly of block copolymers (BCPs) in thin films have been used in a variety of applications such as nanoporous membranes[1] and lithography.[2] Generally, such applications require a perpendicular orientation of BCP domains relative to a substrate. For lithography applications, materials with an etch-resistant block and a high degree of incompatibility (quantified by a high χ-parameter) that enable self-assembly at low molecular weights into small domains are highly desirable.[3-7] We have previously introduced poly(4-trimethylsilylstyrene-block-D,L-lactide) (PTMSS-b-PLA) as a high-χ material with large etch contrast.[4] However, favoring a perpendicular orientation of domains with these types of materials presents a formidable challenge because the component blocks often have very different surface energies. The difference in interfacial energies between the two domains of a BCP typically causes preferential wetting by one of the blocks at the air and substrate interfaces, resulting in a domain orientation parallel to the plane of the substrate.[8] While the substrate surface can be modified to create a neutral surface (i.e., the interfacial energy between the substrate and one block is similar to the interfacial energy between the substrate and the other block), BCPs with such large differences in surface energies still prove impossible to orient without altering the interfacial energy of the top surface.[9] Some of the most common strategies used to promote perpendicular domain orientation include solvent annealing,[10] substrate roughening,[11] thermally annealing a BCP on neutral substrate surface treatments whose blocks have a small difference in surface energy at the free surface,[12-14] and thermal annealing with a neutral substrate surface treatment and neutral top coat.[9]

Among the different strategies, solvent annealing in a solvent vapor environment has proven to be a versatile process to promote reorganization of a polymer film. The solvent vapor swells the film giving the polymer chains mobility to reassemble and, under certain conditions where the sorbed solvent neutralizes interactions between the blocks and film surfaces, equilibrium perpendicular domain orientations can form. Subsequent rapid solvent removal has been shown to quench the structure present in the swollen state, resulting in deswelling only in the out of plane direction of the film.[15] Many variables such as solvent selectivity,[16] composition of the solvent/polymer system,[17, 18] and annealing time,[19] among others, have been investigated to reveal their important role in achieving the desired BCP domain orientation.

In previous work, it has been shown that domain periodicity of a BCP decreases in the presence of a nonselective solvent, which increases the miscibility of the solvent-modified domains, thus decreasing the effective χ parameter, χeff, between the block domains.[20] χ is related to domain periodicity (d) in the strongly segregated regime by the relationship dN2/3χ1/6, where N is the degree of polymerization.[21] In the case of constant N, a decrease in χeff will result in a decrease in domain periodicity. It has also been observed that the domain size of a BCP can increase when annealed with a single domain-selective solvent.[20] A solvent selective for one domain will partition primarily into that domain, decreasing the miscibility of the two block domains and increasing χeff. Morphological transformations due to changes in the effective relative volume fractions can also occur, provided that all BCP domains are in their liquid state.[18, 22]

Herein, we utilize a mixture of two domain-selective solvents to promote self-assembly and perpendicular orientation of a lamellae-forming silicon-containing PTMSS-b-PLA BCP. This solvent mixture imparts significant mobility into both blocks, which are glassy in the absence of solvent, enabling reorganization. We observe that, similarly to a single selective solvent annealing condition, an increase in χeff increases the domain periodicity by 30%. However, swelling both blocks with selective solvent mixtures avoids volume fraction and morphology changes that can occur with a single selective solvent. Increasing χeff with solvent vapor treatment introduces opportunities to induce phase segregation in disordered BCPs (i.e., χN of neat BCP is not high enough to produce self-assembled domains) that is not possible with conventional thermal annealing. We exploited this concept to induce order in a PTMSS-b-PLA sample that is ordinarily disordered in thin films and bulk. Some of our key observations are explained on a qualitative basis by using the results of self-consistent field theory.

EXPERIMENTAL

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. EXPERIMENTAL RESULTS AND DISCUSSION
  6. SELF-CONSISTENT FIELD THEORY RESULTS AND DISCUSSION
  7. CONCLUSIONS
  8. Acknowledgments
  9. REFERENCES AND NOTES
  10. Supporting Information

PTMSS-b-PLA BCPs and corresponding homopolymers were synthesized as described elsewhere[4] using a combination of anionic and ring-opening polymerization techniques. Detailed characterization data for the polymers used in this study are reported elsewhere[4] and summarized in Table 1. Gel permeation chromatography (GPC) measurements were performed using a Viscotek VE 2001 triple-detector gel permeation chromatograph. Tetrahydrofuran (THF) was used as the eluent, with a flow rate of 1.0 mL min−1. Samples were dissolved in THF (5 mg mL−1) before analysis. All 1H NMR spectra were recorded on a Varian Unity Plus 400 MHz instrument using CDCl3 as the solvent. Chemical shifts are reported in ppm downfield from TMS using the residual protonated solvent as an internal standard (CDCl3, 1H 7.24 ppm).

Table 1. Characterization Data for the Polymers Used in This Study
SampleMn PTMSSOHaPDI PTMSSOHaMn PLAbPDI PTMSS-b-PLAaVol. % PLAc
  1. a

    The Mn of the PTMSSOH block and the PDIs of PTMSSOH and PTMSS-b-PLA were determined by GPC using the dn/dc of PTMSS, 0.138.23

  2. b

    Mn of PLA determined by 1H NMR.

  3. c

    Volume percentages of each block were calculated using a density of 0.963 g cm−3 for PTMSS[24] and 1.15 g cm3 for PLA.[25]

PTMSS5.5-b-PLA6.65,5001.156,6001.0650.0
PTMSS2.3-b-PLA1.72,3001.111,7001.1038.7
PTMSSOH5.55,5001.15
PLA3.03,000

Small angle X-ray scattering (SAXS) measurements were collected using Cu Kα radiation (λ = 1.5418 Å) from a molecular metrology instrument using a high brilliance rotating copper anode source and a two-dimensional (2D) 120-mm gas filled multiwire detector. Vertical focus was achieved with a single crystal Ge mirror, and horizontal focus and wavelength selection were achieved with an asymmetric cut Si(111) monochromator. The beam center was calibrated using silver behenate with the primary reflection peak at 1.076 nm−1. Grazing incidence SAXS (GISAXS) measurements were performed using a RIGAKU-GISAXS S-MAX3000 with X-ray energy irradiated from a Cu target with an energy of 8.04 keV (λ = 0.154 nm). The incident angle was adjusted to be above the critical angle of the polymer film and the diffracted intensity was recorded using a 2D single photon counting detector. The exposure times ranged from 10 to 15 min. The dataset is a map of intensity, I(2Θ, αf) where 2Θ is the in-plane diffraction angle and αf is the out of plane diffraction angle. The sample to detector distance was calibrated using a silver behenate standard.

Surface treatments were prepared as follows. An 8 kg mol−1 63% PS hydroxyl-terminated PS-r-PMMA brush[26] was prepared by spin-coating on a silicon wafer with a native oxide layer and heating to 200 °C for 30 min under vacuum to graft the hydroxyl end moieties to the substrate. Nongrafted brush polymer was removed by rinsing with toluene three times. A crosslinked polystyrene mat surface treatment[27] was prepared by spin coating the solution to produce an 8.8-nm film. This polymer contains mostly styrene repeat units with a small fraction of repeat units that can undergo crosslinking during thermal annealing. The surface treatment was heated to 300 °C for 5 min in air to crosslink the film. Thin films of the BCP were prepared by spin-coating polymer solutions from toluene for 60 s onto a silicon wafer with a surface treatment on top of a native oxide layer. Film thicknesses were determined by scratching the film and measuring the scratch depth by AFM. AFM images were collected on a Veeco Dimension 3100 AFM. SEM images were collected on a Zeiss Ultra 55 SEM.

Solvent annealing was performed on a custom system described in Figure 1. In each experiment, the thickness of a 55-nm sample of the same material being annealed was monitored by a Filmetrics F20 reflectometer in the chamber with the sample of interest. The film thickness of this thicker film was monitored instead of the actual sample to reduce noise in the thickness measurements of the thinner films. The periodicities of the domains in the SEM images were determined by performing a standard fast Fourier transform on the image as detailed elsewhere.[28]

image

Figure 1. Custom solvent annealing system used in this study. Nitrogen was bubbled through two room temperature solvent reservoirs and also through a diluting line, which was always kept constant at 5 sccm. Solvent-containing nitrogen was delivered to the chamber for annealing samples. Film thickness was monitored in situ by a reflectometer and solvent vapor exited the chamber through an outlet in the chamber.

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With the exception of the homopolymer film swelling experiments in single solvent conditions, the same annealing conditions were used for all experiments. Sixty standard cubic centimeters per minute (sccm) nitrogen gas was passed through the cyclohexane solvent reservoir, 40 sccm nitrogen gas was passed through the acetone reservoir, and 5 sccm nitrogen gas was passed through the bypass stream at room temperature. All samples were exposed to the annealing conditions for 15 min. Based on gravimetric analysis of condensed solvents from the outlet stream, samples in the solvent annealing chamber were exposed to vapor with a composition of xCyclohexane = 0.049, xAcetone = 0.084, and xN2 = 0.867, where x is the mole fraction of the component. Assuming the molar ratio of cyclohexane to acetone in the vapor is identical to the ratio of the mass flow rates of nitrogen through the respective solvent reservoirs, this composition is approximately consistent with an assumption of saturated vapor based on the vapor pressures of the solvents (pcyclohexane* = 77 mmHg and pacetone* = 184 mmHg, data from Sigma Aldrich) at 20 °C.

EXPERIMENTAL RESULTS AND DISCUSSION

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. EXPERIMENTAL RESULTS AND DISCUSSION
  6. SELF-CONSISTENT FIELD THEORY RESULTS AND DISCUSSION
  7. CONCLUSIONS
  8. Acknowledgments
  9. REFERENCES AND NOTES
  10. Supporting Information

In previous work, PTMSS-b-PLA films were placed inside a sealed jar and annealed with a cyclohexane solvent vapor atmosphere that was created from an open vial of cyclohexane inside. A bulk lamellae sample of this material assembled into fingerprint patterns in thin films, which by top-down imaging alone could be evidence of either lamellae oriented perpendicular to the plane of the substrate or cylinders oriented parallel to the substrate.[4] In the work reported here, the self-assembly of PTMSS-b-PLA during solvent annealing was investigated more thoroughly. A custom solvent annealing system capable of controlling and monitoring the degree of swelling was used. Solvent vapor was introduced to thin polymer films by bubbling a constant flow rate of nitrogen through solvent reservoirs and into a chamber containing the thin film samples. The degree of swelling was adjusted by changing the flow rate of nitrogen through the bubblers, adjusting the mole fraction (or partial pressure) of the solvent within the chamber.

Based on polymer–solvent interaction parameter (χP-S) values and homopolymer constituent swelling data for PTMSS-b-PLA, cyclohexane is preferential for the PTMSS block. χP-S is a value calculated based on the solubility parameters of a polymer–solvent pair and used to determine the miscibility of a polymer and a solvent. Typically, χP-S values smaller than 0.5 represent a miscible polymer–solvent pair while values greater than 0.5 indicate polymer/solvent immiscibility. The χP-S values calculated in this study are 0.347 for PTMSS-cyclohexane and 0.937 for PLA-cyclohexane, indicating that cyclohexane is preferential for the PTMSS domain. Detailed calculations for χP-S values are reported in the Supporting Information. Homopolymer film-swelling data also support this conclusion. As shown in Figure 2(a), a homopolymer film of PTMSS swells significantly more than a PLA film when 60 sccm of nitrogen is bubbled through cyclohexane into the chamber.

image

Figure 2. Swelling of polymer films under different annealing conditions. The * represents the time at which the N2 flow rate through the solvent reservoirs was stopped and the N2 flow rate through the diluting line was set to 500 sccm, enabling rapid removal of solvent from the film and return to the initial film thickness. (a) Swelling of PTMSS and PLA homopolymer films with a flow rate of 60 sccm N2 through only the cyclohexane reservoir; (b) swelling of PTMSS and PLA homopolymer films with a flow rate of 40 sccm N2 through only the acetone reservoir; (c) swelling of PTMSS and PLA homopolymer films with a flow rate of 60 sccm N2 through the cyclohexane reservoir and 40 sccm through the acetone reservoir; and (d) swelling of lamellae-forming PTMSS5.5-b-PLA6.6 film with a flow rate of 60 sccm N2 through the cyclohexane reservoir and 40 sccm through the acetone reservoir.

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A second solvent that is predicted to preferentially swell the PLA domain was introduced to prevent a significant change in relative block volume fraction, thus avoiding a morphological transition from occurring. Acetone is a selective solvent for the PLA block as evidenced by χP-S values of 0.625 for PTMSS-acetone and 0.341 for PLA-acetone. Homopolymer film swelling data collected when 40 sccm of nitrogen was bubbled through acetone also supports this conclusion as shown in Figure 2(b). Unfortunately, the degree of PLA homopolymer swelling cannot be identified because the film dewets quickly, but dewetting indicates that PLA is likely highly swollen by the acetone. The PTMSS film swells significantly less in acetone than in cyclohexane. When swollen with a mixture of the solvents, both homopolymer films swelled to similar thicknesses as shown in Figure 2(c). This suggests that when solvent annealing under these conditions, a BCP of these two components would likely not change significantly in volume fraction from the bulk material. When a PTMSS5.5-b-PLA6.6 film was annealed under these conditions, the film thickness swelled approximately 20% as shown in Figure 2(d).

A 10-nm film of PTMSS5.5-b-PLA6.6 on a PS-r-PMMA brush was solvent annealed using the annealing conditions described in the Experimental section. The PS-r-PMMA brush was identified as a neutral substrate surface treatment by screening with island/hole experiments;[29] BCPs and neutral substrates composed of dissimilar chemical moieties is an established design technique.[9] These experiments, as well as those used to identify optimal solvent annealing and thickness conditions are summarized in the Supporting Information. The fingerprint pattern observed in Figure 3(a) suggests this solvent annealing condition oriented lamellar domains perpendicular to the plane of the substrate. Based on water contact angle measurements and the fact that we are able to image these domains by SEM, we believe that there may be a very thin (i.e., less than a few nanometers in thickness) wetting layer of PTMSS. By GISAXS [Fig. 3(b) and integrated I(q) in Fig. 3(c,d)], the in-plane structure in this film has peaks in a ratio of 1:2, which could be interpreted as perpendicular lamellae or parallel cylinders, and the out-of-plane structure has fringes that indicate a feature height 8–10 nm tall. This is most consistent with a perpendicular orientation of lamellae since it is unlikely that parallel cylinders with a domain periodicity of 17.7 nm identified in the GISAXS pattern would propagate nearly the entire thickness of a 10-nm thick film. Additionally, parallel cylinders with this domain periodicity would be expected to terrace at this film thickness but this film was completely smooth after solvent annealing. When the thickness was increased by a few nanometers, regions of parallel orientation were observed in patches on the film as shown in the Supporting Information. Since a perpendicular orientation on the entire film is attainable only within a small thickness range, the solvent annealing condition is likely slightly preferential for one block at the free surface.[9]

image

Figure 3. (a) SEM image of PTMSS5.5-b-PLA6.6 on a PS-r-PMMA brush after solvent annealing. The inset shows the power spectral density (PSD) and corresponding Lo value of 18.7 nm. (b) GISAXS pattern of the film in (a). (c) In-plane I(q) from (b) shows a domain periodicity of 17.7 nm, with peak ratios 1:2. (d) Out-of-plane I(q) from (b) is consistent with a domain height of 8–10 nm.

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The domain spacing of the solvent annealed thin film was identified by image analysis of Figure 3(a) to be 18.7 nm and the GISAXS pattern in Figure 3(b) to be 17.7 nm, which are consistent within 1 nm. In contrast, thermally annealed PTMSS5.5-b-PLA6.6 self-assembles into lamellae domains with a domain spacing of 14.6 nm (bulk) and about 14–15 nm as measured in thin films by AFM (see Supporting Information). Solvent annealing with two domain-selective solvents produces a nearly 30% greater domain spacing than thermally annealed samples. As domain spacing is proportional to χeff, the interaction parameter between the domains modified to include the energetic contributions of the solvent, the domain size of a BCP is expected to increase by the relationship dN2/3χ1/6 when χeff increases. Domain size swelling thus implies that the two domain-selective solvents increase χeff.[30]

To fully explore the implications of increased χeff during solvent annealing, a polymer disordered in the bulk (χN < 10.5) was solvent annealed using the same conditions described previously. Disordered PTMSS2.3-b-PLA1.7 was solvent annealed in a thin film on an 8.8-nm thick crosslinked polystyrene substrate surface treatment. Crosslinked PS was used as a surface treatment to prevent the hydroxyl end group on the BCP from grafting to hydroxyls on the substrate surface during subsequent thermal annealing experiments. We found that some BCP can be grafted to the substrate when a brush substrate surface treatment is used due to the hydroxyl functionalization on the BCP. After thin film solvent annealing, a fingerprint pattern with a pitch of 13.5 nm was calculated by the image analysis shown in Figure 4(a). The Bragg peaks in the corresponding GISAXS pattern [Fig. 4(b) and integrated I(q) in Fig. 4(c)] and an AFM height trace [Fig. 4(d)] of the terracing of the film indicate a parallel cylindrical morphology in agreement with the Lo value of the pattern in Figure 4(a).

image

Figure 4. (a) Top-down SEM image of PTMSS2.3-b-PLA1.7 after solvent annealing. The inset shows the PSD and corresponding Lo value of 13.5 nm. (b) GISAXS pattern of the film in (a). (c) In-plane I(q) from (b) with a Lo value of 12.6 nm and (d) AFM trace of (a) showing terracing of the cylinder domains. Inset shows the height profile across two terraces. A dry terrace height of 10 nm corresponds to a swollen terrace height (Lo) of approximately 12 nm with 20% film thickness swelling during solvent annealing.

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The sample disorders after a subsequent thermal anneal at 160 °C for 15 min as observed in the top-down SEM image in Figure 5(a). The corresponding GISAXS pattern also indicates disorder [Fig. 5(b) and integrated I(q) in Fig. 5(c)] evidenced by a broad, low-intensity halo scattering pattern. The sample orders into a cylindrical morphology again after a second solvent annealing step as indicated by top-down SEM imaging and GISAXS (not shown). Bulk PTMSS2.3-b-PLA1.7 exposed to identical solvent annealing conditions orders into a cylindrical morphology, disorders after a subsequent thermal anneal, and orders again after a second solvent anneal as evidenced by SAXS [Fig. 5(d)]. The measured pitch of the bulk and thin-film solvent annealed samples is nearly identical at 13.4 and 13.5 nm, respectively.

image

Figure 5. (a) SEM image after thermally annealing the film in (a) for 15 min at 160 °C, (b) GISAXS pattern of the film in (a), and (c) integrated GISAXS pattern in (b). (d) SAXS patterns of a bulk sample of PTMSS2.3-b-PLA1.7 after (i) a first solvent anneal (ii) solvent anneal followed by a subsequent thermal anneal at 160 °C for 15 min, and (iii) a second solvent anneal after the thermal anneal.

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Lithographic applications often require orientational and/or translational order. This is commonly achieved using directed self-assembly (DSA), typically utilizing either chemical[31, 32] or topographic guiding patterns.[33] For PTMSS2.3-b-PLA1.7, a topographic pattern was created by patterning sparse lines of crosslinked polystyrene using electron beam lithography (Fig. 6). The pitch of the DSA pattern was designed to be three times that of the solvent annealed polymer to multiply the density of the underlying pattern by a factor of three. The width of the prepatterned line was designed to be commensurate with the half-pitch of the solvent annealed cylinder-forming BCP. The bare silicon substrate between the crosslinked polystyrene was filled with a 1.2-kDa polystyrene brush [Fig. 6(b)]. The BCP was assembled on the prepattern after solvent annealing with the same conditions as the unaligned sample (Fig. 4), so the line pattern observed in the SEM image in Figure 6(a) is also likely parallel cylinders. As there is little chemical contrast between the crosslinked polystyrene and the polystyrene brush, a small difference in height between the crosslinked polystyrene (6 nm) and the PS brush (1.5 nm) contributes most significantly to the alignment of the domains.

image

Figure 6. (a) SEM micrograph of directed self-assembly of PTMSS2.3-b-PLA1.7 after solvent annealing on a topographical pattern and (b) the dimensions of the underlying pattern and assembled block copolymer.

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Several high χ materials such as poly(styrene-block-dimethylsiloxane), PS-b-PDMS,[34] and a polyhedral oligomeric silesquioxane-containing polymer, poly(methyl methacrylate-block-PMAPOSS), PMMA-b-PMAPOSS[35] have been similarly aligned by DSA techniques and solvent annealing. However, the alignment of PTMSS-b-PLA described here enables the formation of a line pattern with a domain periodicity similar to 12 nm PMMA-b-PMAPOSS hexagonally packed dot patterns formed from a spherical morphology and is smaller than the 17.5-nm pitch line pattern formed from PS-b-PDMS cylinders.

SELF-CONSISTENT FIELD THEORY RESULTS AND DISCUSSION

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. EXPERIMENTAL RESULTS AND DISCUSSION
  6. SELF-CONSISTENT FIELD THEORY RESULTS AND DISCUSSION
  7. CONCLUSIONS
  8. Acknowledgments
  9. REFERENCES AND NOTES
  10. Supporting Information

The results presented in the prior sections demonstrate an interesting strategy whereby a mixture of solvents can be used to (a) orient the BCP domains perpendicular to the substrate; (b) promote ordering even when the pure BCP exhibits disordered morphologies; and (c) increase the domain spacing of the resulting morphologies. Feature (a) can be understood to be a direct result of the approximately “neutral” top environment presented by the solvent mixture. We hypothesized that (b) and (c) were driven by the opposite preferences of the blocks of the copolymer to the two solvents. To confirm if indeed our hypothesis regarding the role of solvents is valid, and also to explore the parametric limits of this strategy, we undertook theoretical calculations of a simple model, which mimics the qualitative features of the system considered in this study.

Toward the above objective, we used self-consistent field theory (SCFT) methodology to study the bulk phase behavior of an AB diblock copolymer (PTMSS-b-PLA) with two selective solvents, S1 (cyclohexane) and S2 (acetone). SCFT has been used as a successful tool for predicting, with quantitative accuracy, phase behavior of BCP systems in both the presence and absence of solvents.[30, 36-46] In this work, we considered the variation in the equilibrium domain spacing and the shift in order–disorder temperature (ODT, as quantified by the critical χAB required for ordering) with solvent selectivity. Specifically, we probe whether a combination of selective solvents (similar in spirit to the configuration considered in the experimental portion of our study) can serve to: (i) Lower the bare segregation strength χAB required for achieving ordering—an effect which is equivalent to our proposed hypothesis of solvent-induced enhanced χeff between the solvent containing A and B domains; (ii) Increase the domain spacing of lamellar domains as seen in the experiments.

Since a number of earlier studies have described the SCFT methodology in detail, we present the most pertinent details in the Supporting Information. Our model system is described by a “symmetric” diblock copolymer (volume fraction, f = 0.5) and degree of polymerization, N = 100. To model the main features of our study, we adopted a parameterization wherein the selectivity of solvent S1 to the A block and selectivity of solvent S2 to the B block was chosen such that −χAS1 = χBS1 = χAS2 =χBS2 = χ, where χij is the Flory–Huggins interaction parameter between the components i and j, and χ>0 (χ ≠ χAB). The above parameterization accounts for the selectivity of A (B) blocks to the solvent S1 (S2) and the (relative) incompatibility between A (B) blocks and the solvent S2 (S1) (in our model, a negative χ parameter models favorable interactions between the components). Moreover, to limit the number of parameters to as few as possible, we assume that the solvents do not interact with each other (χS1–S2 = 0). To ensure that such simplifications do not influence the trends seen in our results, we compared the domain spacing results for the case of χS1–S2 = 0 with those obtained for a finite value of χS1–S2 (results not displayed). Such comparisons confirmed that the qualitative features of the results discussed below were not impacted by our parametric assumptions. We vary the selectivity of solvents for the diblock copolymer in the range χ = 0.2 − 1.0 (corresponding to an increasing affinity of the solvents to the preferential block) and study the effect on domain spacing and ODTs. We note that these χ values differ from the experimentally deduced χs between the segments and the solvents, and hence we only offer qualitative comparisons between our model results and experiments.

In Figure 7, we display the ODT χs, denoted as (χABN)s, for the diblock copolymer system. For small χ, corresponding to a pair of almost neutral solvents, we observe that the ODT (χABN)s increases with increasing solvent fraction. Such a trend is consistent with earlier studies in the context of neutral solvents.[45, 46] However, we observe that beyond a critical χ (for our parameters, the critical χ = 0.3) the χABN corresponding to the ODT decreases with increasing solvent fraction. Moreover, we observe that in such cases the system can form ordered phases at χABN even lower than the critical value for a pure melt which corresponds to χABN = 10.495. Such results indicate that a pair of highly preferential solvents can serve to promote the ordering of BCPs even at χABN well below that required for the pure BCP system and is consistent with the experimentally observed formation of the ordered phase by solvent annealing of the disordered sample (cf. Fig. 5). An interesting outcome of our theoretical model is the prediction that only solvents with sufficiently strong preferential interactions can facilitate such a behavior.

image

Figure 7. ODT (χABN)s predicted by SCFT as a function of copolymer volume fraction for varying monomer–solvent interaction parameters (χ). The black circle indicates the ODT for pure diblock system (copolymer volume fraction = 1). The lines are a guide to the eye.

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In Figure 8, we display the variation in domain spacing (normalized by radius of gyration, Rg of the copolymer) with copolymer volume fraction, for varying monomer–solvent interaction parameters (χ) at fixed χABN = 30 (the lines are guide to the eye). For low to moderate values of solvent selectivity (χ), we observe that the domain spacing decreases with increasing solvent volume fraction. Such a trend is consistent with the increase in ODT observed for such parameters in Figure 7, and mirrors the behavior expected for neutral solvents. In contrast, for moderate–high solvent selectivity, we observe that the domain spacing can increase with increasing solvent fractions. In order to understand this result further, in Figure 9, we display the density profiles for copolymer and solvent at a fixed copolymer volume fraction, φ = 0.8 for two values of χ. At low χ, we observe that the solvents are almost equally distributed among the copolymer domains. Upon increasing χ, the solvents preferentially segregate in the respective domains causing both domains to swell. In order to minimize unfavorable contacts (B-S1 and A-S2), the copolymer chains stretch which leads to an increase in the domain spacing. Such observations are consistent with the experimentally noted increase in the domain spacing (cf. Fig. 3) in the solvent annealed sample as compared to the thermally annealed sample. Moreover, for appropriate parameters, we observe that domain spacing enhancements of the order noted in the experimental (∼30%) can indeed be achieved.

image

Figure 8. Variation in domain spacing (normalized by Rg) with copolymer volume fraction for varying monomer–solvent interaction parameters (χ) at fixed χABN = 30. The black circle indicates the domain spacing for pure diblock system (copolymer volume fraction = 1). The lines are a guide to the eye.

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image

Figure 9. Solvent and polymer segment profiles for χ = 0.3 and χ = 1.0 at fixed copolymer volume fraction, φ = 0.8 and χABN = 30.

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An interesting prediction of our theoretical model is the observation that even for strongly selective systems, an increase in domain spacing manifests only over a small range of solvent volume fractions. Indeed, there are solvent selectivity parameters (such as χ = 0.5) for which the ODT is observed to decrease for all solvent volume fractions, but the domain spacing is also predicted to decrease with increasing solvent volume fraction. Such trends indicate that while concepts like a “solvent-induced effective χAB” may prove useful to rationalize observations, extrapolation of such ideas to derive quantitative conclusions may not always be warranted.[44]

In summary, the above theoretical results lend support to our hypothesis that the solvent selectivity and differing preferences for the segments of the BCP leads to the formation of ordered phases and the increase in the domain spacing observed in the experiments.

CONCLUSIONS

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. EXPERIMENTAL RESULTS AND DISCUSSION
  6. SELF-CONSISTENT FIELD THEORY RESULTS AND DISCUSSION
  7. CONCLUSIONS
  8. Acknowledgments
  9. REFERENCES AND NOTES
  10. Supporting Information

Solvent annealing in a mixture of domain selective solvents can be used to avoid asymmetric swelling, therefore maintaining the effective volume fraction and morphology of the BCP. It can also be used to tune the domain spacing of a BCP by changing the effective interaction parameter between the blocks. This work reports evidence of a ∼30% increase in the pitch of a lamellae-forming BCP sample by annealing with a mixture of domain-selective solvents. This phenomenon of an increase in the domain spacing with solvent selectivity was captured by SCFT results. The lamellar domains are oriented perpendicular to the plane of the substrate under these conditions, increasing the potential of this polymer for substrate patterning applications. Using these same solvent annealing conditions, order was induced in a disordered BCP sample due to an increased effective χN that pushes the BCP above the order–disorder transition on the phase diagram, and this was also predicted by SCFT. The 13.5-nm pitch cylinders were then directed by a topographical pattern and the density of the features was multiplied by a factor of three.

Acknowledgments

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. EXPERIMENTAL RESULTS AND DISCUSSION
  6. SELF-CONSISTENT FIELD THEORY RESULTS AND DISCUSSION
  7. CONCLUSIONS
  8. Acknowledgments
  9. REFERENCES AND NOTES
  10. Supporting Information

The authors thank Nissan Chemical Company for financial support. C. J. Ellison thanks the Robert A. Welch Foundation (grant #F-1709) for partial financial support. This work was also supported by the National Science Foundation through a Graduate Research Fellowship to J. Cushen. Bulk SAXS experiments were performed using facilities at the Texas Materials Institute. VG acknowledges support from Robert A. Welch Foundation (Grant F1599), National Science Foundation (DMR 1005739), and the US Army Research Office under grant W911NF-10-10346. The Rigaku SAXS/GISAXS line was funded by the Nation Science Foundation under award No. 1040446.

REFERENCES AND NOTES

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. EXPERIMENTAL RESULTS AND DISCUSSION
  6. SELF-CONSISTENT FIELD THEORY RESULTS AND DISCUSSION
  7. CONCLUSIONS
  8. Acknowledgments
  9. REFERENCES AND NOTES
  10. Supporting Information

Supporting Information

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. EXPERIMENTAL
  5. EXPERIMENTAL RESULTS AND DISCUSSION
  6. SELF-CONSISTENT FIELD THEORY RESULTS AND DISCUSSION
  7. CONCLUSIONS
  8. Acknowledgments
  9. REFERENCES AND NOTES
  10. Supporting Information

Additional Supporting Information may be found in the online version of this article.

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