Session B42: Physics of Copolymers I

Block Copolymer Bottlebrushes: New Routes to Ever Smaller Microdomain Sizes

Block copolymer self-assembly presents exciting opportunities for the development of nanotemplates for advanced lithography applications, wherein the microdomain sizes (\textasciitilde 10--100 nm) are governed by the total copolymer degree of polymerization, $N$. However, this methodology is limited in its smallest achievable length scale, since AB diblock copolymers self--assemble only above a critical $N$ that depends on the magnitude of the effective segmental interaction parameter $\chi_{\mathrm{AB}}$. Numerous recent reports have focused on developing ``high $\chi_{\mathrm{AB}}$'' AB diblocks that self--assemble at low values of $N$. In this talk we explore the ability of non-linear polymer architectures to induce block copolymer ordering at reduced length scales. Thus, we describe the melt and thin-film self-assembly behavior of block copolymer bottlebrushes derived from linking the block junctions of low molecular weight AB diblocks. We quantitatively demonstrate that increasing the bottlebrush backbone degree of polymerization ($N_{\mathrm{backbone}})$ results in a larger reduction in the critical copolymer arm degree of polymerization ($N_{\mathrm{arm}})$ required for self-assembly, thus reducing the length scales at which these materials self-assemble.   

Rich Phase Behavior of Sphere-Forming Asymmetric ABA$^{\mathrm{\prime }}$C Block Copolymer Melts

Motivated by self-consistent field theory simulations, the effect of ABA$^{\mathrm{\prime }}$ corona block length asymmetry on the phase behavior of ABA$^{\mathrm{\prime }}$C-type tetrablock terpolymers has been examined. The chosen model system, poly(styrene)-$b$-poly(isoprene)-$b$-poly(styrene)-$b$-poly(ethylene oxide) (SIS$^{\mathrm{\prime }}$O), has been characterized using a combination of small-angle X-ray scattering, transmission electron microscopy, and dynamic mechanical spectroscopy. Asymmetric SIS$^{\mathrm{\prime }}$O tetrablocks reveal a rich variety of sphere-forming phases over compositions and molecular weights where symmetric SISO polymers formed only hexagonally oriented cylinders. These include FCC, HCP, and complex symmetries such as the Frank-Kasper $\sigma $ and A15 phases.   

Formation of Frank-Kasper $\sigma $-phase from polydisperse diblock copolymers

Recent experimental and theoretical studies have revealed a number of complex spherical phases including the complex Frank-Kasper $\sigma $-phase, which consists of 30 spheres in a unit cell. It is desirable to understand the mechanisms for the formation of the complex spherical phases such as the A15-phase and the Frank-Kasper $\sigma $-phase in block copolymers. Based on the observation that the A15-phase and the Frank-Kasper $\sigma $-phase are composed of spherical domains with different sizes, we hypothesize that polydispersity of the block copolymers could be used to obtain these complex phases. We tested this hypothesis by carrying out self-consistent field theory for polydisperse AB diblock copolymers. Specially we studied the relative stability of various spherical phases, including the fcc, bcc, A15 and Frank\textunderscore Kasper $\sigma $-phase, in binary blends composed of AB block copolymers different lengths of the A-blocks. Our results revealed that the Frank-Kasper $\sigma $-phase could be stabilized by tailoring the length ratio as well as the compositions of the two diblock copolymers. The distribution of the diblocks in the system indicates that copolymer segregation is the origin of the formation of spherical domains with different sizes.   

Phase Behavior of SIS$^\prime$O Tetrablock Terpolymers: A Self-consistent Field Theory Study

Block copolymers with three or more blocks show richer phase behavior than diblock copolymers. In this work, we use self-consistent field theory (SCFT) to study the phase behavior of $ABA^\prime C$ type tetrablock terpolymers. In particular, we are motivated by experimental studies on poly(styrene-$b$-isoprene-$b$-styrene-$b$-ethylene oxide) (SIS$^\prime$O) that report interesting phases such as core-shell spheres and cylinders, the Frank-Kasper $\sigma$ phase, and the dodecagonal quasicrystalline morphology. We compare SCFT predictions to experimental results for SIS$^\prime$O copolymers using values of the Flory-Huggins interaction parameters that are estimated from analysis of literature data on related systems.   

Preparation and Morphology of ABn Mictoarm Block Copolymers.

A series of ABn mictoarm block copolymers (bottle brush copolymers) consisting of polystyrene (S) as a backbone and polyisoprenes (I) as grafts were precisely synthesized by an anionic polymerization, and their microphase-separated structures were investigated by transmission electron microscopy (TEM) and small-angle X-ray scattering(SAXS). A copolymer with composition of $\varphi $S$=$0.57 and number of grafts(n) of 10 shows characteristic cylindrical structure, where microdomains of S reveals hexagonal cross section with non-constant mean curvature interface. While a sample with composition of $\varphi $S$=$0.37 and number of grafts(n) of 40 shows spherical structure with rather large S isolated domains and characteristic domain packing manner was found. Furthermore composition dependence of microphase-separated structures for SIn mictoarm block copolymers were investigated and compared to SI diblock copolymer system.   

Frank-Kasper sigma phase stabilized by tailored architectures of block copolymers.

Block copolymer self-assembly forms diverse interesting ordered morphologies, of which the spherical phase is of particular interest because it resembles the similar space symmetry as atomic crystals and has a tunable period on nanoscale. Moreover, the packing lattice of spherical domains dictated by the adjustable competition between the entropic and interfacial energies is programmable. For AB diblock copolymers, it has been known that the stable spherical phase is mainly bcc except for a very narrow region of fcc at the vicinity of the order-disorder transition. When introducing variable number of blocks and architectures to form complex AB-type block copolymers, the A15 phase was predicted as stable. However, a striking experiment observed a new spherical phase, the complex Frank-Kasper sigma phase that consists of 30 spheres in a unit cell, in the PI-b-PLA diblock copolymer as well as a SISO tetrablock terpolymer. Inspired by this experiment, we studied the stability of all known spherical phases of fcc, bcc, A15 and sigma in various block copolymers including conformationally asymmetric AB diblock, ABm miktoarm, and BABC tetrablock copolymers. We have revealed the formation mechanism of the nonclassical A15 and sigma phases due to the tailored architectures.   

From the Disordered State to the Frank-Kasper Sigma Phase: Readily Tuning the Phase Behavior of Block Polymers via Lithium Salt Addition

Sphere-forming block copolymers have long been known to assemble onto a body-centered cubic (BCC) lattice, but recent work has demonstrated that with the correct thermal treatments, more exotic morphologies such as dodecagonal quasicrystals or the Frank-Kasper sigma phase can be observed. In this presentation, we show that a similar variety of morphologies can be obtained by simply adding small amounts of lithium bis(trifluoromethane)sulfonimide (LiTFSI), which preferentially partitions into one of the domains. Using small-angle X-ray scattering, we have found that block copolymers, which are disordered when neat, can form spheres with liquid-like packing, BCC crystals, the Frank-Kasper sigma phase, or hexagonally close packed crystals upon increasing the salt loading. This work demonstrates a unique, alternative route to highly segregated sphere-forming block copolymers and examines the universality of the formation of these complex morphologies.   

Characterization of Lithium Polysulfide Salts in Homopolymers and Block Copolymers

Ion-conducting polymers are important for solid-state batteries due to the promise of better safety and the potential to produce higher energy density batteries. Nanostructured block copolymer electrolytes can provide high ionic conductivity and mechanical strength through microphase separation. One of the potential use of block copolymer electrolytes is in lithium-sulfur batteries, a system that has high theoretical energy density wherein the reduction of sulfur leads to the formation of lithium polysulfide intermediates.~ In this study we investigate the effect of block copolymer morphology on the speciation and transport properties of the polysulfides. The morphology and conductivities of polystyrene-b-poly(ethylene oxide) (SEO) containing lithium polysulfides were studies using small-angle X-ray scattering and ac impedance spectroscopy. UV-vis spectroscopy is being used to determine nature of the polysulfide species in poly(ethylene oxide) and SEO.   

\textbf{Congruent Lamellar-to-Disorder Phase Transitions in Diblock Copolymer-Homopolymer Ternary Blends }

Symmetric ternary blends of AB diblock copolymers and the corresponding A and B homopolymers are predicted to be characterized by a multicritical Lifshitz point within mean-field theory. Previous studies have shown that fluctuations destroy the predicted Lifshitz point and lead to a bicontinuous microemulsion (B$\mu $E) channel, which separates the lamellar and 2-phase regions in the ternary phase prism. Here, we establish the existence of a line of congruent first-order lamellar-to-disorder transitions when appropriate amounts of poly(cyclohexylethylene) (C) and poly(ethylene) (E) homopolymers are mixed with the corresponding symmetric CE diblock copolymer. We present complimentary optical transmission, small-angle X-ray scattering, transmission electron microscopy (TEM), and rheological results obtained using two experimental protocols: (1) fixing the CE volume fraction and varying the C/E ratio, and (2) setting the C/E ratio at the condition of congruency and varying CE volume fraction from 0 to 1. These results establish a quantitative and facile method for identifying the detailed phase behavior in the vicinity of the B$\mu $E, and provide fresh insight into the nature of such mixtures near the nominal Lifshitz conditions. Surprisingly, well-ordered lamellae are revealed by TEM at compositions within 1{\%} of the B$\mu $E channel, suggesting a remarkably close approach to the predicted, mean-field unbinding transition. Moreover, the width of the B$\mu $E narrows to about 1{\%} under congruent conditions.   

Unbinding Transition of the $\alpha$-BN Phase of BABCB Tetrablock Terpolymers

We study the phase behaviour of BABCB/B multiblock terpolymer/homopolymer blends using real-space self-consistent field theory. We focus on the effects of the added homopolymers on the structure of the $\alpha$-BN phase, formed in the pure BABCB system. In the $\alpha$-BN phase, the A and C blocks form spheres sitting on a three dimensional layered structure, resembling that of graphite. Our results demonstrate that the added homopolymers would aggregate in the regions between the layers in the $\alpha$-BN phase. We use this property of the added homopolymers as a mechanism for separating the layers. By examining the effects of homopolymer/multiblock interactions and their relative degree of polymerization on the overall phase behaviour of the system, we identified a critical homopolymer concentration at which the layers composed of A/C spheres unbind to form free standing sheets, resembling the structure of graphene.   

Simulation of free energies of bicontinuous morphologies formed through block copolymer/homopolymer self-assembly

Different types of bicontinuous phases can be formed from A-B diblock copolymers by the addition of A-type homopolymers over a range of compositions and relative chain lengths. Particle-based molecular simulations were used to study three bicontinuous phases -- double gyroid (G), double diamond (D) and plumber's nightmare (P) - near their triple point of coexistence. For 3-D ordered phases, the stability of the morphology formed in simulation is highly sensitive to box size whose exact size is unknown a-priori. Accurate free energy estimates are required to ascertain the stable phase, particularly when multiple competing phases spontaneously form at the conditions of interest. A variant of thermodynamic integration was implemented to obtain free energies and hence identify the stable phases and their optimal box sizes by tracing a reversible path that connects the ordered and disordered phases. Clear evidence was found of D-G and D-P phase coexistence, consistent with previous predictions for the same blend using Self-consistent field theory. Our simulations also allowed us to examine the microscopic details of these coexisting bicontinuous phases and detect key differences between the microstructure of their nodes and struts.   

Sequence-Specific Copolymer Compatibilizers designed via a Genetic Algorithm

For several decades, block copolymers have been employed as surfactants to reduce interfacial energy for applications from emulsification to surface adhesion. While the simplest approach employs symmetric diblocks, studies have examined asymmetric diblocks, multiblock copolymers, gradient copolymers, and copolymer-grafted nanoparticles. However, there exists no established approach to determining the optimal copolymer compatibilizer sequence for a given application. Here we employ molecular dynamics simulations within a genetic algorithm to identify copolymer surfactant sequences yielding maximum reductions the interfacial energy of model immiscible polymers. The optimal copolymer sequence depends significantly on surfactant concentration. Most surprisingly, at high surface concentrations, where the surfactant achieves the greatest interfacial energy reduction, specific non-periodic sequences are found to significantly outperform any regularly blocky sequence. This emergence of polymer sequence-specificity within a non-sequenced environment adds to a recent body of work suggesting that specific sequence may have the potential to play a greater role in polymer properties than previously understood.   

Effect of the Degree of Hydrogen Bonding on Asymmetric Lamellar Phase Transformation in Binary Block Copolymer Blends

A binary mixture of two block copolymers whose blocks are capable of forming the hydrogen bonding allows one to obtain various microdomains that could not be expected for neat block copolymer. For instance, we reported that the binary blend of asymmetric polystyrene-\textit{block}-poly(2-vinylpyridine) copolymer (as-PS-$b$-P2VP) and polystyrene-\textit{block}-polyhydroxystyrene copolymer (as-PS-$b$-PHS) blends where the hydrogen bonding occurred between P2VP and PHS showed asymmetric lamellar microdomains. Since asymmetric lamellar microdomains are formed due to the interface curvature change by favorable hydrogen bonding interaction between the hydroxyl group and nitrogen atom, a large ratio of lamellar width (thus, enhanced asymmetry) could potentially be achieved by increasing the degree of the hydrogen bonding. We employed two kinds of binary blends (polystyrene-\textit{block}-poly(4-vinylpyridine) (as-PS-$b$-P4VP)/as-PS-$b$-PHS and as-PS-$b$-P2VP/as-PS-$b$-PHS). It was observed by SAXS and TEM that as-PS-$b$-P4VP/as-PS-$b$-PHS blend which exhibits much stronger hydrogen bonding formed asymmetric lamellar morphology at more asymmetric volume fraction where as-PS-$b$-P2VP/as-PS-$b$-PHS blend could not form and the experimental results show qualitative agreement with the SST model prediction.   

Microphase-separated structures within randomly end-linked copolymer networks

Self-assembly within randomly cross-linked or end-linked copolymer networks provides a robust method to generate co-continuous nanometer-scale structures. Here, we investigate self-assembly within copolymer networks prepared by end linking of several different pairs of telechelic polymers in a common solvent. For sufficiently high levels of immiscibility between the constituent polymers, removal of solvent leads to microphase separation into disordered nanoscale structures. Using a variety of characterization methods, including transmission electron microscopy, small-angle X-ray scattering, differential scanning calorimetry, and dynamic mechanical analysis, we find that these networks exhibit co-continuous morphologies over a wide range of volume fraction of the two components, with a characteristic length scale that can be tuned by adjusting the molecular weight of the starting polymers.   

Effects of Blockiness on the phase behavior of random copolymers

Theoretical study of random block copolymers remains a challenging topic due in part to the sheer enormity of their phase space. In this study we use the self-consistent field theory to investigate the phase behaviour of linear (AB)n-type and (AB)n-C-type multiblock copolymers with randomly distributed A and B blocks. In particular, we examine the effect of “blockiness” of the random copolymers on the formation of ordered phases. The blockiness can be quantified by the average length of individual A or B blocks, which can be taken as a measure of the heterogeneity of the random copolymers. We observed that the critical value of the $\chi$ parameter, at which the order-disorder transition occurs, decreases with increasing blockiness in the (AB)n copolymers. We also observed that the phase behaviour of the (AB)n-C copolymers depends strongly on the blockiness of the random chain. In particular, the blockiness governs whether or not the A/B blocks can phase separate within the A/B domains, thus dictating whether the (AB)n-C behaves as A/B-C diblock copolymers or as ABC terpolymers. The theoretical phase diagrams will be compared with available experiments.