Flow-induced alignment of lamellar block copolymer melts

Beyond the Rosenfeld Equation: Computation of Vibrational Circular Dichroism Spectra for Anisotropic Solutions

The difference in absorption of left and right circularly polarized light by chiral molecules can be described by the Rosenfeld equation for isotropic samples. It allows the assignment of the absolute stereochemistry by comparing experimental and computationally derived spectra. Despite the simple form of the Rosenfeld equation, its evaluation in the infrared regime remained challenging, as the contribution from the magnetic dipole operator is zero within the Born-Oppenheimer (BO) approximation. In order to resolve this issue, "beyond BO" theories had to be developed, among which Stephen's magnetic field perturbation (MFP) approach offers a computationally easily accessible form. In this work, optical activity is discussed for cylindrically symmetric solutions, which cannot be described anymore by Rosenfeld's equation due to broken spherical symmetry. Mathematical properties of natural and electric-field induced anisotropies are discussed on the basis of the gauge-independent theoretical framework of Buckingham and Dunn. The issue of achiral noise arising from external field perturbations is considered, and potential remedies are introduced. Natural anisotropic vibrational circular dichroism (VCD) equations are solved numerically by applying the MFP approach within the Hartree-Fock (HF) formalism. Properties of anisotropic VCD spectra are discussed for R-(+)-methyloxirane and (1 S,2 S)-cyclopropane-1,2-dicarbonitrile. In particular, by using a group theoretical argument, a gauge-independent lower bound for the quadrupole contribution of C₂-symmetric molecules can be identified, which allows the importance of additional quadrupole terms in anisotropic VCD spectra calculation to be assessed.

Reorientation mechanisms of block copolymer/CdSe quantum dot composites under application of an electric field

Time- and temperature-resolved in situ birefringence measurements were applied to analyze the effect of nanoparticles on the electric field-induced alignment of a microphase separated solution of poly(styrene)-block-poly(isoprene) in toluene. Through the incorporation of isoprene-confined CdSe quantum dots the reorientation behavior is altered. Particle loading lowers the order-disorder transition temperature, and increases the defect density, favoring nucleation and growth as an alignment mechanism over rotation of grains. The temperature dependent alteration in the reorientation mechanism is analyzed via a combination of birefringence and synchrotron SAXS. The detailed understanding of the effect of nanoparticles on the reorientation mechanism is an important prerequisite for optimization of electric-field-induced alignment of block copolymer/nanoparticle composites where the block copolymer guides the nanoparticle self-assembly into anisotropic structures.

Dynamic orientation transition of the lyotropic lamellar phase at high shear rates

The dynamic orientation behavior of the lamellar phase of a triblock copolymer is studied in a wide range of shear rates as a function of solvent composition. We find that various phases can be induced by increasing the shear rate. At low shear rates, the onion phase forms from planar lamellae with many defects. A further increase of the shear rate caused the onion structure to break down, and the lamellar phase recovers with fewer defects. Finally, the transition of the orientation from parallel to perpendicular is observed at high shear rates. In the orientation transition at high shear rates, a stable intermediate structure, to our knowledge, is found for the first time. We also find that the critical shear stress of the rupture of the onion phase coincides with the orientation transition. The consistency of the critical shear stress suggests that all orientation transitions at a high shear rate are dominated by a mechanical balance between the applied viscous stress and the internal relaxation mode of the lamellae.

Influence of Composition Fluctuations on the Linear Viscoelastic Properties of Symmetric Diblock Copolymers near the Order-Disorder Transition

Rheological evidence of composition fluctuations in disordered diblock copolymers near the order-disorder transition (ODT) has been documented in the literature over the past three decades, characterized by a failure of time-temperature superposition (tTS) to reduce linear dynamic mechanical spectroscopy (DMS) data in the terminal viscoelastic regime to a temperature-independent form. However, for some materials, most notably poly(styrene-b-isoprene) (PS-PI), no signature of these rheological features has been found. We present small-angle X-ray scattering (SAXS) results on symmetric poly(cyclohexylethylene-b-ethylene) (PCHE-PE) diblock copolymers that confirm the presence of fluctuations in the disordered state and DMS measurements that also show no sign of the features ascribed to composition fluctuations. Assessment of DMS results published on five different diblock copolymer systems leads us to conclude that the effects of composition fluctuations can be masked by highly asymmetric block dynamics, thereby resolving a long-standing disagreement in the literature and reinforcing the importance of mechanical contrast in understanding the dynamics of ordered and disordered block polymers.

Facile control of long range orientation in mesoporous carbon films with thermal zone annealing velocity

Ordered mesoporous carbons exhibit appealing properties for many applications, but their function and performance can depend critically on their structure. The in-plane orientation of 2D cylinders from the cooperative assembly of Pluronic P123 and resol has been controlled by application of cold zone annealing (CZA). By varying the moving rate, the preferential in-plane orientation of the self-assembled cylinders can be tuned through the entire 180° range possible from ϕ = 50° to ϕ = -130° (relative to the moving direction). At a moving rate of 2 μm s(-1), this simple and easy CZA process leads to cylinders that are well aligned parallel to the moving direction with a high orientational factor of S = 0.98. Moreover, the in-plane oriented cylinders can be nearly perfectly aligned transverse to the moving direction (S = 0.95) by simply decreasing the moving velocity to 0.5 μm s(-1). We attribute the parallel alignment to the flow that develops from the motion of the thermal gradients, while the transverse alignment is related to flow cessation (inertial effect). The preferential orientation is retained through the carbonization process, but there is some degradation in orientation due to insufficient crosslinking of the resol during CZA; this effect is most prominent for the higher moving rates (less time for crosslinking), but can be overcome by post-CZA annealing at uniform elevated temperatures to further crosslink the resol. CZA is a simple and powerful method for fabricating well-aligned and self-assembled mesoporous carbon films over large areas.

Direct nanorod assembly using block copolymer-based supramolecules

Developing routes to control the organization of one-dimensional nanomaterials, such as nanorods, with high precision is critical to generate functional materials since the collective properties depend on their spatial arrangements, interparticle ordering, and macroscopic alignment. We have systematically investigated the coassemblies of nanorods and block copolymer (BCP)-based supramolecules and showed that the energetic contributions from nanorod ligand-polymer interactions, polymer chain deformation, and rod-rod interactions are comparable and can be tailored to disperse nanorods with control over inter-rod ordering and the alignment of nanorods within BCP microdomains. By varying the supramolecular morphology and chemical nature of the nanorods, two highly sought-after morphologies, that is, nanoscopic networks of nanorods and nanorod arrays parallel to cylindrical BCP microdomains can be obtained. The supramolecular approach can be applied to achieve morphological control in nanorod-containing nanocomposites toward fabrication of optical and electronic nanodevices.

Shear alignment and realignment of sphere-forming and cylinder-forming block-copolymer thin films

In common with many other structured fluids, block copolymers can be effectively oriented by shear. This susceptibility to shear alignment has previously been shown to hold even in thin films, containing as few as two layers of spherical microdomains, or even a single layer of cylindrical microdomains. A phenomenological model has been proposed [M. W. Wu, R. A. Register, and P. M. Chaikin, Phys. Rev. E 74, 040801(R) (2006)] to describe the alignment of such block-copolymer films, yielding the microdomain lattice order parameter as a function of shearing temperature, stress, and time. Here we directly test the central idea of that model, that the grains which are most misaligned with the shear direction are selectively destroyed, to reform in a direction more closely aligned with the shear. Films are first shear aligned from a polygrain state into a monodomain orientation and are then subjected to a second shear, at a variable stress (sigma) and misorientation angle (deltatheta) relative to the monodomain director, allowing the effects of sigma and deltatheta to be independently and systematically probed. For both cylinder-forming and sphere-forming block copolymers, these experiments confirm the basic premise of the model, as the stress required for realignment increases monotonically as deltatheta becomes smaller. For a cylinder-forming block copolymer, we find that the characteristic stress sigma(c) required to realign cylinders from one monodomain orientation to another is indistinguishable from that required to generate a monodomain orientation from the polygrain state. By contrast, the hexagonal lattice of spheres requires a value of sigma(c) more than 3 times as high for reorientation than for generation of the initial monodomain orientation.

Electric field alignment of a block copolymer nanopattern: direct observation of the microscopic mechanism

Using quasi-in-situ scanning force microscopy we study the details of nanopattern alignment in ABC terblock copolymer thin films in the presence of an in-plane electric field. Because of the surface interactions and electric field the lamellae are oriented both perpendicular to the plane of the film and parallel to the electric field. We identified two distinct defect types which govern the orientation mechanism. Ring-like (tori) and open-end defects dominate at the early stage of the orientation process, while mainly classic topological defects (disclinations and dislocations) are involved in long-range ordering at the late stages. Comparison of the time evolution of the defect density with the evolution of the orientational order parameter suggests that tori-defects are essential for the effective reorientation. Further, the quasi-in-situ SFM imaging allowed us to elucidate the influence of the electric field strength on the propagation velocity of the topological defects.

Phase-field modeling of the formation of lamellar nanostructures in diblock copolymer thin films under inplanar electric fields

Recent experiments show that external inplanar electric field can be employed to guide the molecular self-assembly in diblock copolymer (BCP) thin films to form lamellar nanostructures with potential applications in nanotechnology. We study this self-assembly process through a detailed coarse-grained phase-separation modeling. During the process, the free energy of the BCP films is modeled as the Ginzburg-Landau free energy with nonlocal interaction and electrostatic coupling. The resulting Cahn-Hilliard (CH) equation is solved using an efficient semi-implicit Fourier-spectral algorithm. Numerical results show that the morphology of order parameter formed in either symmetric or asymmetric BCP thin films is strongly influenced by the electric field. For symmetrical BCPs, highly ordered lamellar nanostructures evolved along the direction of the electric field. Phase nucleation and dislocation climbing in the BCP films predicted by the numerical simulation are in a good agreement with those observed in recent BCP electronanolithography. For asymmetrical BCPs, numerical simulation shows that nanodots are guided to align to the electric field. Furthermore, in the case of high electric field, nanodots formed in asymmetrical BCPs may further convert into highly ordered lamellar nanostructures (sphere-to-cylinder transition) parallel to the electric field. Effects of the magnitude of electric field, BCP asymmetry, and molecular interaction of BCPs on the self-assembly process are examined in detail using the numerical scheme developed in this study. The present study can be used for the prediction of the formation of nanostructures in BCP thin films and the quality control of BCP-based nanomanufacturing through optimizing the external electric fields.

A rheo-optical apparatus for real time kinetic studies on shear-induced alignment of self-assembled soft matter with small sample volumes

In soft materials, self-assembled nanoscale structures can allow new functionalities but a general problem is to align such local structures aiming at monodomain overall order. In order to achieve shear alignment in a controlled manner, a novel type of rheo-optical apparatus has here been developed that allows small sample volumes and in situ monitoring of the alignment process during the shear. Both the amplitude and orientation angles of low level linear birefringence and dichroism are measured while the sample is subjected to large amplitude oscillatory shear flow. The apparatus is based on a commercial rheometer where we have constructed a flow cell that consists of two quartz teeth. The lower tooth can be set in oscillatory motion whereas the upper one is connected to the force transducers of the rheometer. A custom made cylindrical oven allows the operation of the flow cell at elevated temperatures up to 200 degrees C. Only a small sample volume is needed (from 9 to 25 mm(3)), which makes the apparatus suitable especially for studying new materials which are usually obtainable only in small quantities. Using this apparatus the flow alignment kinetics of a lamellar polystyrene-b-polyisoprene diblock copolymer is studied during shear under two different conditions which lead to parallel and perpendicular alignment of the lamellae. The open device geometry allows even combined optical/x-ray in situ characterization of the alignment process by combining small-angle x-ray scattering using concepts shown by Polushkin et al. [Macromolecules 36, 1421 (2003)].

Large scale alignment of a lamellar block copolymer thin film via electric fields: a time-resolved SFM study

We have devised a novel route towards a nanoscopically striped surface pattern with long range order the self-assembly of an ABC triblock terpolymer thin film exposed to an in-plane electric field. the interplay between surface interactions and the effect of the electric field the lamellae were oriented both perpendicular to the plane of the film and parallel to the electric field. Moreover, quasi scanning force microscopy measurements were used to follow the reorientation process as a function of time and to yield insight into the microscopic steps eventually leading to the ordered microdomain structure.

Electric field versus surface alignment in confined films of a diblock copolymer melt

The dynamics of alignment of microstructure in confined films of diblock copolymer melts in the presence of an external electric field was studied numerically. We consider in detail a symmetric diblock copolymer melt, exhibiting a lamellar morphology. The method used is a dynamic mean-field density functional method, derived from the generalized time-dependent Ginzburg-Landau theory. The time evolution of concentration variables and therefore the alignment kinetics of the morphologies are described by a set of stochastic equations of a diffusion form with Gaussian noise. We investigated the effect of an electric field on block copolymers under the assumption that the long-range dipolar interaction induced by the fluctuations of composition pattern is a dominant mechanism of electric-field-induced domain alignment. The interactions with bounding electrode surfaces were taken into account as short-range interactions resulting in an additional term in the free energy of the sample. This term contributes only in the vicinity of the surfaces. The surfaces and the electric field compete with each other and align the microstructure in perpendicular directions. Depending on the ratio between electric field and interfacial interactions, parallel or perpendicular lamellar orientations were observed. The time scale of the electric-field-induced alignment is much larger than the time scale of the surface-induced alignment and microphase separation.

Orientation selection in lamellar phases by oscillatory shears

In order to address the selection mechanism that is responsible for the unique lamellar orientation observed in block copolymers under oscillatory shears, we use a constitutive law for the dissipative part of the stress tensor that respects the uniaxial symmetry of a lamellar phase. An interface separating two domains oriented parallel and perpendicular to the shear is shown to be hydrodynamically unstable, a situation analogous to the thin layer instability of stratified fluids under shears. The resulting secondary flows break the degeneracy between the parallel and perpendicular lamellar orientation, leading to a preferred perpendicular orientation in certain ranges of parameters of the polymer and of the shear.