Session T50: Focus Session: Phase Behavior and Structure in Copolymers

Self-assembly of semiflexible-flexible block copolymers

We apply self-consistent Brownian dynamics simulations to study the self-assembly behavior of semiflexible-flexible block copolymers. A Maier-Saupe interaction model was applied for the orientational interactions between the semiflexible polymers, while the enthalpic interactions between semiflexible and flexible polymers were modeled through a standard Flory-Huggins approach. To develop a physical understanding of the phases and their regimes of occurrence as a function of varying persistence length of the semiflexible block, we computed the $2D$ phase diagram for our model. We quantify the progression of the self-assembly morphologies in transitioning from coil-coil block copolymers on the one hand to rod-coil block copolymers on the other hand. The results obtained are in qualitative agreement with the existing experimental and numerical results.   

Effect of chain shape on the self-assembly of bioinspired block copolymers

Polymer chain shape has been shown to affect both polymer properties and block copolymer self-assembly. Polypeptoids, a class of sequence-specific bioinspired polymer, have a chain shape that can be tuned by the introduction of monomers with bulky, chiral side chains, allowing one to change the polymer conformation while preserving the chemical nature of the side chains. Here, it is shown that introducing chiral, aromatic monomers into the polypeptoid chain increases the glass transition by 20 C for a chiral, helical polypeptoid compared to its achiral, non-structured analog. Incorporation of these polypeptoids into block copolymers with poly(methyl acrylate) enables a systematic study of the effect of chain shape while maintaining similar enthalpic interactions. For two otherwise analogous block copolymers, conformational asymmetry is shown to affect both the morphological domain spacing and the order-disorder transition temperature. Future work will focus on interfacial segregation experiments to determine the effect of conformational asymmetry on the Flory-Huggins parameter.   

Processing-Dependent Self-Assembly of Protein-Polymer Diblock Copolymers

Self-assembly of globular protein-polymer diblock copolymers is a novel method for nanopatterning protein-based materials which maintains a high fraction of protein activity as well as the folded protein structure. By subjecting these copolymers to different processing conditions, long range ordering and the fraction of active protein can be controlled. Here, self-assembly of model mCherry-b-poly(N-isopropyl acrylamide) (PNIPAM) block copolymers is induced by water evaporation from dilute aqueous solutions of conjugate material, and followed by solvent annealing of the resulting nanostructures. Different pathways towards self-assembly are accessed by orthogonally manipulating the solvent quality for each block of the copolymer using temperature and pH. Small-angle scattering and transmission electron microscopy show nanostructure depends heavily on PNIPAM coil fraction and solvent annealing condition, with solution self-assembly reflected in the solid state structure under certain conditions. Protein structure is unaffected by the processing pathway, while protein activity levels in the nanodomains depend strongly on processing conditions and can retain up to 80\% of the initial activity.   

Helical Ordering in Chiral Block Copolymers

Introducing molecular chirality into the segments of block copolymers can influence the nature of the resultant morphology. Such an effect was found for poly(styrene-$b$-L-lactide) (PS-$b$-PLLA) diblock copolymers where hexagonally packed PLLA helical microdomains (H* phase) form in a PS matrix. However, molecular ordering of PLLA within the helical microdomains and the transfer of chirality from the segmental level to the mesoscale is still not well understood. We developed a field theoretic model to describe the interactions between segments of chiral blocks, which have the tendency to form a ``cholesteric'' texture. Based on the model, we calculated the bulk morphologies of chiral AB diblock copolymers using self-consistent field theory (SCFT). Experiments show that the H* phase only forms when microphase separation between PS and PLLA block happens first and crystallization of PLLA block is suppressed or happens within confined microdomain. Hence, crystalline ordering is not necessary for H* phase formation. The SCFT offers the chance to explore the range of thermodynamic stability of helical structures in the phase diagram of chiral block copolymer melts, by tuning parameters not only like the block segregation strength and composition, but also new parameters such as the ratio between preferred helical pitch to the radius of gyration and the Frank elastic constant for inter-segment distortions.   

Phase Behavior of Binary Blends of AB+AC Block Copolymers with compatible B and C blocks

Recently the experimental studies of phase behavior of binary blends of PS-b-P2VP and PS-b-PHS demonstrated an interesting effect: blends of symmetric PS-b-P2VP and shorter symmetric (PS-b-PHS) formed cylindrical HEX and spherical BCC phases, while each pure component formed lamellas. The miscibility of P2VP and PHS is caused by the hydrogen bonding between P2VP and PHS,which can be described as a negative Flory ?-parameter between P2VP and PHS. We developed a theory of the microphase segregation of AB+AC blends of diblock copolymers based on strong stretching theory. The main result of our theory is that in the copolymer brush-like layer formed by longer B chain and shorter C chains, the attraction between B and shorter C chains causes relative stretching of short C chains and compression of longer B chains. The latter manifests in an excessive bending force towards the grafting surface (BC$|$AA interface). Such bending force causes a transition from a symmetric lamella phase to a HEX cylinder or BCC spherical phases with the BC phase being a ``matrix'' component. In a blend of asymmetric BCC sphere forming copolymers (where B and C segments are the minor components), such bending force may unfold BCC spherical phase to a HEX cylinder phase, or even highly uneven lamella phases.   

Universality in block copolymers: a corresponding states hypothesis

Phase behavior and fluctuations of very long block copolymers are well described by self-consistent field theory, and by the random-phase (RPA) approximation for concentration fluctuations. The SCF / RPA predicts behavior that depends on only a few dimensionless parameters. More sophisticated coarse-grained theories instead suggest an extended form of this principle of corresponding states, in which the behavior is predicted to depend on one additional parameter, the independent degree of polymerization $\bar{N}$. We are testing this prediction by comparing extensive computer simulations of several different coarse-grained simulation models of AB diblock copolymer melts. We utilize a novel simulation methodology based on graphical processing unit (GPU) accelerated hybrid molecular dynamics / Monte Carlo replica exchange simulations on a cluster of many GPUs. We present data for off-lattice models with soft- and hard-core non-bonded interactions, and a lattice model, comparing simulations of different models that are designed to have matched values of $\bar{N}$. The results provide extremely strong evidence for the corresponding states hypothesis, which is found to remain accurate even for chains that are much too short to be accurately described by SCFT or the RPA   

Manipulating triblock copolymer morphology using tapered block interfaces

Tapered block copolymers offer the opportunity to manipulate copolymer segregation strengths independently of the molecular weight and chemical constituents. This independent control allows the design of materials with designer interactions and improved mechanical properties, while retaining the desired self-assembled nanostructures. The tapered interfaces between blocks have been shown to significantly decrease the effective interaction parameters between blocks, leading to lower order-to-disorder transition temperatures relative to corresponding non-tapered block copolymers. In this work, we synthesized a series of tapered triblock copolymers using a combination of anionic polymerization, atom transfer radical polymerization, and click chemistry. Comparing the morphologies of our tapered and non-tapered triblock copolymers suggests that the phase behavior of the tapered materials can differ from the non-tapered triblock materials due to the manipulated interfacial profile.   

Manipulating the morphological behavior of ABA triblock copolymers with block polydispersity

As an extension of our ongoing efforts to understand the effects of middle B segment polydispersity on the melt-phase behavior of ABA triblock copolymers, we describe the morphological consequences of block polydispersity in the context of poly(lactide-b-1,4-butadiene-b-lactide) (LBL) triblock copolymers. The complete melt-phase behavior of 52 well-defined LBL triblock copolymers was evaluated using a combination of synchrotron small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM). Through careful comparisons with monodisperse copolymer control samples, we show that block polydispersity causes large shifts in the composition-dependent phase windows in a manner consistent with previous reports. However, these polydisperse LBL triblocks do not exhibit the substantial domain dilation observed in more weakly segregated SBS triblock copolymers. Based on these observations, we discuss the possibility of using block polydispersity as a new means of tailoring the morphological behavior of microphase separated ABA triblock copolymers.   

Phase Behavior of Linear ABC Tri Block-Random Copolymers with a Semicrystalline Endblock

The solid-state structure of semicrystalline block copolymers is set either by block incompatibility or by crystallization of one or more blocks. A variety of solid-state morphologies may be observed depending on the block interaction strength, ranging from spherulitic to confined crystallization within preexisting microphase-separated domains. We aim to explore crystallization from both homogeneous and microphase-separated melts and to characterize the resulting solid-state structure of linear ABC ``block-random'' copolymers that incorporate a semicrystalline polyethylene endblock. Linear triblock copolymers, poly[butadiene-$b$-isoprene-$b$-(isoprene-$r$-styrene)], are synthesized via anionic polymerization. Two hydrogenation schemes are then applied, either complete saturation of all double bonds or a selective saturation of only diene units. Both schemes yield semicrystalline polyethylene endblocks but dissimilar interblock segregation strengths. In both derivatives of a 30-14-14 kg/mol triblock-random copolymer, small-angle x-ray scattering reveals the formation of a well-ordered three-domain lamellar melt from which crystallization of the polyethylene endblock proceeds. Crystal orientation within the lamellae has been determined by wide-angle x-ray scattering after lamellar orientation in a channel die. We are currently varying relative block and overall molecular weights, and the block sequence to further explore these materials.   

Discovering Complex Ordered Phases of Block Copolymers

Block copolymers with their rich phase behavior and ordering transitions have become a paradigm for the study of structured soft materials. Understanding the structures and phase transitions in block copolymers has been one of the most active research areas in polymer science in the past two decades. One of the achievements is the self-consistent field theory (SCFT), which provides a powerful framework for the study of ordered phase of block copolymers. I will present a generic strategy to discover complex ordered phases of block copolymers within the SCFT framework. Specifically, a combination of real-space and reciprocal-space techniques is used to explore possible ordered phases in multiblock copolymer melts. These candidate phases can then be used to construct phase diagrams. Application of this strategy to linear and star ABC triblock copolymers has led to the discovery of a rich array of ordered phases.   

Thermodynamic Behavior of Poly(1,4-isoprene-b-DL-lactide) Diblock Copolymers

The phase behavior of a series of poly(1,4-isoprene-$b$-DL-lactide) (IL) diblock copolymers near the order-disorder transition temperature ($T_{ODT}$) was investigated using a combination of dynamic mechanical spectroscopy (DMS), small angle x-ray scattering (SAXS) and differential scanning calorimetry (DSC). IL copolymers of relatively low molecular weight ($\sim$ 2.5 -- 6 kg/mol) formed ordered phases with experimentally accessible $T_{ODT}$s due to the large segment-segment interaction parameter (\textit{$\chi _{IL}$}). The order-disorder transitions were accompanied by distinct signatures in the DSC traces, where the magnitude of the latent heat of the ODT ($\Delta H_{ODT}$) depends strongly on the ordered phase morphology. Symmetric compounds exhibited almost no hysteresis in the onset temperature for ordering and disordering, indicative of an absence of a nucleation barrier, while asymmetric IL diblocks displayed considerable hysteresis. These finding will be discussed in the context of composition fluctuation effects in the disordered melt near $T_{ODT}$.   

Direct Comparisons among Fast Off-Lattice Monte Carlo Simulations, Integral Equation Theories, and Gaussian Fluctuation Theory for Disordered Symmetric Diblock Copolymers

Based on the same model system of symmetric diblock copolymers as discrete Gaussian chains with soft, finite-range repulsions as commonly used in dissipative-particle dynamics simulations, we directly compare, without any parameter-fitting, the thermodynamic and structural properties of the disordered phase obtained from fast off-lattice Monte Carlo (FOMC) simulations$^1$, reference interaction site model (RISM) and polymer reference interaction site model (PRISM) theories, and Gaussian fluctuation theory. The disordered phase ranges from homopolymer melts (i.e., where the Flory-Huggins parameter $\chi=0$) all the way to the order-disorder transition point determined in FOMC simulations, and the compared quantities include the internal energy, entropy, Helmholtz free energy, excess pressure, constant-volume heat capacity, chain/block dimensions, and various structure factors and correlation functions in the system. Our comparisons unambiguously and quantitatively reveal the consequences of various theoretical approximations and the validity of these theories in describing the fluctuations/correlations in disordered diblock copolymers. [1] \textit{Q. Wang and Y. Yin}, \textbf{J. Chem. Phys., 130}, 104903 (2009).   

The power spectrum of thermal composition fluctuations in a lamellar mesophase

We derive an analytic expression for the power spectrum of Gaussian thermal composition fluctuations in an ordered lamellar mesophase. We compare this expression to the power spectrum measured in stochastic simulations of a two-dimensional diblock copolymer melt based on the Leibler-Brazovskii Hamiltonian. The analytic expression fits the simulation data with zero adjustable fitting parameters over a relatively wide range of model parameters. This expression will facilitate line-edge roughness (LER) modeling in block copolymer directed self-assembly applications, and it can serve as a model component in a scattering-based LER metrology framework.