Session C42: Physics of Copolymers II: Bulk and Thin Films

Fluids Density Functional Theory of Diblock Copolymers for Electrolyte Applications

We use classical, fluids density functional theory (fDFT) to study microphase separation in block copolymer systems. We are motivated by systems used as battery electrolytes or in other transport applications, in which the two blocks of the system have different mechanical, dielectric, and transport properties that allow one phase to act as a charge/penetrant carrier and the other to make the film mechanically strong. We find density profiles of penetrants, showing to what degree they segregate into the A phase and their concentration near the interface, depending on the penetrant-A and penetrant-B interaction strengths as well as the A-B segregation strength. We also study the effect of tapering, or adding a gradient region (taper) between the pure A and B blocks of an AB diblock copolymer; the taper changes in composition along its length from pure A to pure B (or from B to A for an inverse taper). The effect of both penetrants and tapering on microphase domain spacing as a function of segregation strength will be discussed. Adjusting taper length allows one to tune the phase behavior of the system for easier processing or access to specific desired microphase structures.   

Unguided discovery of BCP self-assembly: challenges and outlook

The unguided search for the stable phases of a block copolymer of a given composition and architecture is a problem of global optimization. The appeal of this pursuit arises from both a materials design perspective and also from the perspective of solving global optimization problems via heuristic algorithms. A diverse collection of such algorithms is available to employ, including evolutionary and swarm strategies. In this talk we discuss the development, successes, and challenges of a real-space genetic algorithm (GA)-SCFT method as applied to a diblock copolymer. We then consider alternative representations and algorithms for solving the forward problem in bulk block copolymer systems.   

Orientational control of block copolymer microdomains by sub-tesla magnetic fields

Magnetic fields offer a versatile approach to controlling the orientation of block copolymer (BCP) microdomains during self-assembly. To date however, such control has required the imposition of large magnetic fields (\textgreater 3T), necessitating the use of complex magnet systems -- either superconducting or very large conventional resistive magnets. Here we demonstrate the ability to direct BCP self-assembly using considerably smaller fields (\textless 1T) which are accessible using simple rare-earth permanent magnets. The low field alignment is enabled by the presence of small quantities of mesogenic species that are blended into, and co-assemble with the liquid crystalline (LC) mesophase of the side-chain LC BCP under study. In situ SAXS experiments reveal a pronounced dependence of the critical alignment field strength on the stoichiometry of the blend, and the ability to generate aligned microdomains with orientational distribution coefficients exceeding 0.95 at sub-1 T fields for appropriate stoichiometries. The alignment response overall can be rationalized in terms of increased mobility and grain size due to the presence of the mesogenic additive. We use a permanent magnet to fabricate films with aligned nanopores, and the utility of this approach to generate complex BCP microdomain patterns in thin films by local field screening are highlighted.   

Morphology of diblock copolymers under confinement

The structure adopted by polymer chains is of particular intrest for materials design. In particular, a great deal of effort has been made to study diblock polymers due to the importance they have in industrial applications. The bulk structure of most systems has been the most widely studied. However, when under the effect of confinement, the polymer chains are forced to adopt structures differing from the familiar bulk phases. As many applications utilize polymers in sizes and shapes that lead to these non bulk structures, the confinement effects are important. A commonly used tool for computationally determining structures is the continuum self consistant field theory (SCFT). We discuss our highly scalable parallel framework for SCFT using real space methods (finite element) that is especially well suited to modelling complex geometries. This framework is capable of modeling both Gaussian and worm like chains. We illustate the use of the software framework in determining structures under varying degrees of confinement. We detail the method used and present selected results from a systematic study of confinement using arbitrary structures.   

Selective Stabilization of the Fddd Diblock Copolymer Microphase in an Applied Electric Field

Using self-consistent field theory, we explore the phase behavior of AB diblock copolymer melts in a uniform applied electric field. We assign an isotropic polarizability to each monomer type, such that the electric field selectively destabilizes AB interfaces that are perpendicular to the applied field. Under the mean-field approximation of the present model, lamellar and cylindrical structures align such that their AB interfaces are parallel to the electric field, and their relative stability with respect to the disordered phase is unchanged. Sphere and network phases do not have an axis of uniformity, so the preferred orientation for each of these phases must be identified by simulation. Small distortions in morphology are induced by the electric field for these phases, such that the free energy response includes non-harmonic terms. We compute the phase diagram for a melt in an applied electric field by comparing free energies of each morphology at its preferred orientation. We find that the stability regions for the sphere and network phases shrink with increasing electric field strength. Moreover, the double gyroid phase is relatively destabilized against the Fddd phase, extending the stability region for the Fddd phase to larger segregation strengths.   

Process-directed self-assembly of copolymers

Using computer simulation and numerical self-consistent field theory of an unentangled diblock copolymer melt, we study the interplay between relaxation of molecular conformations from a highly stretched, non-equilibrium state and structure formation of the local, conserved density during self-assembly from a disordered state. In agreement with experiments, we observe that the planar elongation of molecular conformations in the initial, disordered state results in an alignment of lamella normals perpendicular to the stretch direction during the subsequent self-assembly. Although thermodynamically the parallel orientation is favored by the non-Gaussian conformations, the alignment of the lamella normal perpendicular to the stretch direction is characterized by the larger growth rate of composition fluctuations during the spinodal ordering process. Theoretical approachs to account for the transient, non-Gaussian conformations are discussed.   

Morphology Control of Multicomponent Polymeric Surfactants Using Pressure

The development of nanoscale morphologies for a molten polymeric surfactant under pressure is investigated by using a recently formulated self-consistent field theory. A linear ABC block copolymer is taken as our model system that allows a disparity in the propensities for curved interfaces and pressure responses of ij-pairs. The interplay of those features lead the copolymer to new morphologies at a moderate segregation level and at ambient condition such as networks and pillars of 2-dimensional array. It is shown that pressure is an effective means of morphology control and identification for those new structures. The role of volume fluctuations in the development of those structures is discussed.   

Analysis of Relaxation Spectra and Influence of Molecular Weight on the Dynamics of Block Copolymers

We use molecular dynamics simulations to study both the normal mode dynamics of block copolymers and the influence of MW on the dynamics of the block copolymer. We considered two models to isolate the specific effects arising from the morphological ordering and mobility disparities between the blocks. We effected an explicit normal mode analysis of the chain dynamics in the ordered phases in the directions parallel and perpendicular to the plane of the lamella. For systems with no mobility disparity between the blocks, our analysis demonstrates that the normal modes and their relaxations in the planes parallel and perpendicular to the lamella exhibit significant deviations from the Rouse modes. For systems in which the mobility of one of the blocks was frozen in the lamellar phase, the normal modes closely resembled the Rouse modes for tethered polymers. To understand the spatial inhomogeneities in segmental dynamics of lamellar diblock copolymer systems we probed the local average relaxation times and the dynamical heterogeneities as a function of distance from the interface. Scaling of our results indicate that the interfacial width of the ordered phases serves as the length scale underlying the spatial inhomogeneities in segmental dynamics of the fast monomers.   

Acoustic and ultrasonic characterization constraints of self-healing (ethylene-co-methacrylic acid) copolymers

Recent experiments indicate that small sample poly (ethylene-co-methacrylic acid) copolymers (EMAA copolymers) exhibit time dependent variation in their acoustic and ultrasonic resonant spectra after exposure to a damage event. However, due to the relatively soft nature of these thermoplastic materials, several experimental constraints affect efficacy of resonant spectral analysis. In this work we will the address the effect of several characterization constraints on a self-healing EMAA ionomer (commercially known as Dupont Surlyn 8920) including the effects of transducer loading, continuous rapid resonant excitation and temporally separated long-term resonant excitation. In some circumstances, these experimental constraints can influence the time dependence of sample resonant frequency evolution, quality factor, and variation in spectral waveform. By quantifying these effects, robust characterization of post-damage self-healing EMAA samples is possible and will be presented.   

\textbf{The role of symmetry of chain extender in controlling the morphology of thermoplastic polyurethanes}

Although polyurethane is a well-studied subject, the specific role of chain extender in the alteration of segmental dynamics and morphology formation has yet to be elucidated. Relatively low molecular weight thermoplastic polyurethanes synthesized from a two-step polymerization method were utilized in this study. The effect of the symmetry of chain extenders used in the polymerization on the morphological behavior has been studied. Comparison has been made for a number of chain extenders, including a symmetric 1,4 butanediol or 1,6 hexanediol and an asymmetric 1,2 propanediol or 1,3 butanediol. Using a combination of thermal analysis, spectroscopy and mechanical properties measurements, the development of morphological features were determined as a function of time and temperature. The symmetric chain-extended polyurethanes promotes the formation of hydrogen bonding, shows two glass transition temperatures consistent with a phase separation behavior and furthermore gives a more rigid, less extensible mechanical property when compared with the asymmetric chain-extended polyurethanes. In the latter case, the reacted polymer exhibits poor chain packing thus limiting the formation of robust hydrogen bonding behavior. It showed a singular glass transition representative of a more phase mixed system and shows more extensibility in terms of its mechanical behavior.   

Phase diagram of rod-coil diblock copolymer melts by self-consistent field theory

A unified phase diagram is presented for rod-coil diblock copolymer melts in the isotropic phase regime as a function of the asymmetric parameter. The study is based on free-energy calculation, which incorporates three-dimensional spatial variations of the volume fraction with angular dependence. The wormlike-chain model is used in a self-consistent field treatment. Body-centered cubic, A15, hexagonal, gyroid, and lamellar structures where the rod segments are packed inside the convex rod-coil interface are found stable. As the conformational asymmetric parameter increases, the A15 phase region expands and the gyroid phase region reduces. The stability of the structures is analyzed by concepts such as packing frustration, spinodal limit, and interfacial curvature.   

Temperature effects on the interfacial properties of semifluorinated diblock copolymer thin films.

The interfacial composition and structure of polymer films influence their response to external stimuli and their wetting behavior. Here we probe temperature effects on the interfacial morphology and surface energies of polytrifluoro propyl methyl siloxane-$b$-polystyrene (SiF-b-PS) films with SiF volume fraction of $\varphi \quad =$ 0.03 to 0.46 using atomic force microscopy and surface tension measurement. Films were cast from toluene, selective for PS, and annealed at temperatures ranging from 75 to 210\textdegree C, below and above T$_{\mathrm{g}}$ of the PS block (\textasciitilde 98\textdegree C). For $\varphi \quad =$ 0. 03 a network of small aggregates is formed and hardly changed over the temperature range studied. For $\varphi \quad =$ 0.16 an asymmetric diblock, spherical aggregates at room temperature transformed to elongated ones at elevated temperatures whereas in the symmetric case, spherical assemblies at room temperature merged into larger structures. Independent of SiF fraction the contact angle increased with temperature which is indicative of migration of fluorine to the interface. Surprisingly, dewetting was not observed even annealing the film at much higher temperature than T$_{\mathrm{g}}$ of PS.   

Evaluation of the end-to-end distance of chains solubilized in a polymer Langmuir monolayer by atomic force microscopy

Polymer chain packing in two-dimensional (2D) condense state is still not well understood. Direct observation of the chain packing in a monolayer should be the best way to understand this, however, it is still difficult even using atomic force microscopy (AFM) except for extraordinarily thick polymers. In this study, we successfully evaluate the end-to-end distance of the chains in a Langmuir-Blodgett monolayer composed of a conventional polymer by AFM. We successfully solubilized a small amount of a polystyrene-b-poly(methyl methacrylate)-b-polystyrene (PS-b-PMMA-b-PS) triblock copolymer in a PMMA Langmuir monolayer with the PS blocks being condensed as single-PS-block particles which could be used as a probe of the position of the chain ends. The evaluated end-to-end distance was 2.5 times longer than that of the 2D ideal chain, indicating the chains in the 2D monolayer are not strongly segregated but interpenetrates into other chains.   

Block copolymer adsorbed layers on solids.

Block copolymer thin films offer a simple and effective route to fabricate highly ordered periodic microdomain structures. The fundamental, yet unsolved question is whether these highly oriented microdomain structures persist even near an impenetrable solid wall. We here report the adsorbed structures of polystyrene-block-poly (4-vinylpyridine) (PS-\textit{block}-P4VP, M$_{\mathrm{w}}=$41,000, PS (weight fraction$=$0.81) formed on planar silicon substrates. Perpendicularly aligned cylindrical microdomains were created by solvent vapor annealing (Gowd et al., Soft Matter, 2014\textbf{,} 10, 7753), and the adsorbed layer was derived by solvent leaching with chloroform, a good solvent for the polymers and thereafter characterized by using atomic force microscopy, scanning electron microscopy, grazing incidence small angle x-ray scattering, and x-ray reflectivity. The results showed that both PS and P4VP chains lie flat on the substrate, forming a microphase-separated structure (MSS) without long-range order. Moreover, a spin-coated PS-\textit{block}-P4VP thin film annealed under vacuum at 190 \textdegree C showed similar MSS on the substrate, indicating the generality of the interfacial polymer structure. Details will be discussed in the presentation.