Optimization and Control of Large Block Copolymer Self-Assembly via Precision Solvent Vapor Annealing

The self-assembly of ultra-high molecular weight (UHMW) block copolymers (BCPs) remains a complex and time-consuming endeavor owing to the high kinetic penalties associated with long polymer chain entanglement. In this work, we report a unique strategy of overcoming these kinetic barriers through precision solvent annealing of an UHMW polystyrene-block-poly(2-vinylpyridine) BCP system (Mw: ∼800 kg/mol) by fast swelling to very high levels of solvent concentration (ϕs). Phase separation on timescales of ∼10 min is demonstrated once a thickness-dependent threshold ϕs value of ∼0.80–0.86 is achieved, resulting in lamellar feature spacings of over 190 nm. The threshold ϕs value was found to be greater for films with higher dry thickness (D0) values. Tunability of the domain morphology is achieved through controlled variation of both D0 and ϕs, with the kinetically unstable hexagonal perforated lamellar (HPL) phase observed at ϕs values of ∼0.67 and D0 values of 59–110 nm. This HPL phase can be controllably induced into an order–order transition to a lamellar morphology upon further increase of ϕs to 0.80 or above. As confirmed by grazing-incidence small-angle X-ray scattering, the lateral ordering of the lamellar domains is shown to improve with increasing ϕs up to a maximum value at which the films transition to a disordered state. Thicker films are shown to possess a higher maximum ϕs value before transitioning to a disordered state. The swelling rate is shown to moderately influence the lateral ordering of the phase-separated structures, while the amount of hold time at a particular value of ϕs does not notably enhance the phase separation process. These large period self-assembled lamellar domains are then employed to facilitate pattern transfer using a liquid-phase infiltration method, followed by plasma etching, generating ordered, high aspect ratio Si nanowall structures with spacings of ∼190 nm and heights of up to ∼500 nm. This work underpins the feasibility of a room-temperature, solvent-based annealing approach for the reliable and scalable fabrication of sub-wavelength nanostructures via BCP lithography.


Section S1: Estimation of the partial pressures of THF:chloroform mixtures inside the SVA chamber
In order to fully optimize the SVA process of our UHMW system, it was essential to deduce the optimal choice of solvent to obtain phase separation into lamellar domains. The primary solvents investigated were chloroform and THF, due to their relative neutrality towards both PS and P2VP domains. In an ideal solvent mixture, the vapour pressures of each solvent would exactly match the concentration of the solvent in the liquid mixture as per Raoult's law. Chloroform/THF mixtures are non-ideal, however, and therefore the activity coefficient ( ) of a solvent in a binary mixture must be considered in order to calculate the partial pressure: Where is the molar fraction of solvent in the liquid phase, and , is the saturated vapour pressure of the pure solvent . , can be estimated from the Antoine equation: Where , and are the component-specific constants, and T is the temperature. The values of these constants for chloroform at 21°C are = 6.995, = 1202.29, = 226.25, and for chloroform are = 6.955, = 1170.97, = 226.232 2, 3 . The molar ratio of both solvents in the gas form (y) can be calculated using the following expression: Where is the total pressure of the solvent mixture. The behaviour of chloroform and THF in a binary mixture has been studied in past work. At temperatures of between 20-30 o C it has been found that the mixture displays a negative deviation from ideality, meaning that the total pressure of the mixture passes through a minimum value as the composition of the mixture is changed 4,5 .
To analyse the effect of on the phase separation, the values of for each molar ratio of solvent examined were required. Previous experimental work on chloroform/THF binary mixtures determined that an athermal model based on Flory-Huggins theory can accurately predict the values of obtained from experimental results. 1, 6 The values of from this model for both chloroform and THF were used to determine the partial pressures of both solvents in the vapour phase during annealing (see Figure S1). Various ratios of both solvents were added to the solvent bubbler and used to swell the block copolymer films to a constant ϕ s value of ~0.83. All other parameters, including swelling rate, initial stage temperature, and swelling time, were held constant.

Figure S2
shows AFM images of the BCP films after 200s of swelling to a value of ~0.83, with bubbler temperature of 21C. In the case of pure THF, the film appeared to remain in the original 'as cast' micellar form after SVA. A similar structure is observed when 3 = 0.1, which progresses to a partially phase-separated structure at 3 = 0.54, and eventually to the expected lamellar structure as the chloroform becomes the majority component.
Although the lamellar form was observed using pure chloroform, the solvent mixture that gives 3 = 0.82 was utilised for the kinetic studies outlined in the main text. This is because despite multiple attempts of swelling to high values using pure chloroform, the resulting lamellar structure was observed to contain nano-scale regions of non-uniformity where the ordering was lost, as can be seen in (g). We suggest that this may be the result of increased difficulty in maintaining a constant swelling profile across the film due to the ~20% higher overall equilibrium vapour pressure of pure chloroform vs. the solvent mixture with 3 = 0.82 at 21 o C (calculated from figure 2 values). This is an interesting observation in itself, as it suggests that negative azeotropic solvent mixtures may be better suited for maintaining thickness control at high degrees of swelling where the swollen film thickness becomes increasingly sensitive to temperature changes. A more in-depth examination of the effect of solvent mixtures on film swelling kinetics will be the subject of a future study.

Section S2: Calculation of Refractive Index of Swollen Film
The refractive index values of the solvent mixture, pure BCP film, and swollen BCP film were estimated from their known pure component values (see table 1) using the Lorenz-Lorentz rule of mixing 7 . Where 1 , 2 and 1 , 2 are the volume fractions and refractive indices of pure components 1 and 2, and 12 is the refractive index of the resulting mixture.

Component
Refractive index value: Tetrahydrofuran 8 1.405 ± 0.001 Chloroform 9 1.446 ± 0.001 Polystyrene 10 1.587 ± 0.001 2-vinylpyridine 11 1.550 ± 0.001 For the molecular weight of PS-b-P2VP used in this work, a refractive index value of 1.570 was obtained using the respective volume fractions of each block. For the chloroform/THF mixture, an approximation was made that the ratio of each solvent absorbed into the film during swelling is equal to the solvent ratio in the vapour phase. This yields a value of 1.438 using eq. (4) for 3 = 0.82 . For the swollen film, refractive index values of between 1.503 and 1.453 were obtained for values between 0.5 to 0.88 respectively via incorporating the refractive indices of the both the solvent mixture and block copolymer film.
During a swelling experiment, the refractive index was initially set at a precalculated profile corresponding to the dry film (n=1.438, figure S3a). Once swelling was induced, the precalculated refractive index profile was switched (within the Filmetrics software) to the corresponding index profile of the desired solvent concentration of the swollen film for that experiment (examples in figure S3b, c). Upon initiation of deswelling, the refractive index profile was immediately reverted back to that of the dry film. This ensured that our reflectometer model aligned with the measured BCP film during the experiment. We intend to automate such refractive index changes in our future studies via a feedback loop system in order to further enhance the scalability and precision of the technique