Double flip of orientation for a lamellar diblock copolymer under shear

Leist, Heike; Maring, Daniel; Thurn‐Albrecht, Thomas; Wiesner, Ulrich

doi:10.1063/1.478734

Cited by 61 publications

(65 citation statements)

References 32 publications

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“…Depending on the system either multi-lamellar vesicles [10,12,13] ("onions", typically in lyotropic systems) or layers perpendicular to the vor- * Electronic address: guenter.auernhammer@uni-bayreuth.de ticity direction [1,2,3,4,5,8,9,14] ("perpendicular" orientation, typically in solvent free systems) form. In some of the systems a third regime is observed at even higher shear rates with a parallel orientation [5,10]. If the starting point is rather a randomly distributed lamellar phase, the first regime is not observed [1,4,12,16].…”

Section: Introductionmentioning

confidence: 99%

“…Experiments on a variety of systems which differ significantly in their microscopic details show nevertheless striking similarities in their macroscopic behavior under shear. The systems under investigation include block copolymers [1,2,3,4,5,6], low molecular weight (LMW) liquid crystals [7,8,9], lyotropic lamellar phases (both LMW [10,11,12] and polymeric [13]), and liquid crystalline side-chain polymers [14,15]. These experiments use either a steady shear (typically for the low viscosity systems e.g.…”

Section: Introductionmentioning

confidence: 99%

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Shear-induced instabilities in layered liquids

2002

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Motivated by the experimentally observed shear-induced destabilization and reorientation of smectic A like systems, we consider an extended formulation of smectic A hydrodynamics. We include both, the smectic layering (via the layer displacement u and the layer normalp) and the director n of the underlying nematic order in our macroscopic hydrodynamic description and allow both directions to differ in non equilibrium situations. In an homeotropically aligned sample the nematic director does couple to an applied simple shear, whereas the smectic layering stays unchanged. This difference leads to a finite (but usually small) angle betweenn andp, which we find to be equivalent to an effective dilatation of the layers. This effective dilatation leads, above a certain threshold, to an undulation instability of the layers. We generalize our earlier approach [Rheol. Acta 39 (3), 15] and include the cross couplings with the velocity field and the order parameters for orientational and positional order and show how the order parameters interact with the undulation instability. We explore the influence of various material parameters on the instability. Comparing our results to recent experiments and molecular dynamic simulations, we find a good qualitative agreement.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shear-induced instabilities in layered liquids

2002

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“…1 Orientation of the microstructure both in the melt [13][14][15] and in solution, 16 either parallel or perpendicular to the direction of flow, can be achieved by carefully manipulating the flow fields and conditions. However, coassembly in polymer-sol nanoparticle hybrids is accompanied by inorganic nanoparticle gelation, preventing straightforward extension of these approaches to obtain macroscopically aligned nanostructured bulk hybrids.…”

Section: Introductionmentioning

confidence: 99%

Flow-Induced Alignment of Block Copolymer−Sol Nanoparticle Coassemblies toward Oriented Bulk Polymer−Silica Hybrids

et al. 2005

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Macroscopically oriented bulk organic-inorganic hybrid materials were cast from solutions subjected to hydrodynamic flow by utilizing a simple flow device. The hybrids were prepared from an amphiphilic diblock copolymer, poly(isoprene-block-ethylene oxide) (PI-b-PEO), used as a structure directing agent for organically modified ceramic precursors, (3-glycidyloxypropyl)trimethoxysilane (GLYMO) and aluminum sec-butoxide (Al(O s Bu)3), prehydrolyzed into sol nanoparticles. Varying amounts of these ceramic precursors (sol) were used to obtain different mesoscale structures, i.e., lamellae, and the regular and inverse hexagonal mesophases. To align the microstructure, flow fields were applied during microstructure setting. To this end, a custom-built device operated in a Bü chi evaporator subjected solutions of the polymer and ceramic precursors to a steady flow while the solvent evaporated. The flow induced a shearing force causing macroscopic alignment of the mesoscale structures. Small-angle X-ray scattering (SAXS) was used to characterize the oriented hybrids. From these data order parameters were calculated to quantify the degree of alignment in the hybrids in different directions. Order parameters as high as 0.77 were obtained for hybrids with lamellae lying parallel to the substrate. Alignment could also be evidenced in the hexagonal and inverse hexagonal samples with cylinder orientations along the flow direction. The results suggest the efficacy of this relatively simple flow technique in providing bulk polymer-inorganic hybrids with macroscopic alignment needed for realization of their true application potential.

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“…Thus, in the vicinity of ODT at low frequencies the lamellae orient with their normal parallel to the shear gradient (the parallel orientation), while at higher frequencies their normal is perpendicular to the velocity and the gradient directions (the perpendicular orientation). Further increase of frequency results in reappearance of the parallel orientation 5 . In this Letter we propose an explanation of this orientation behaviour which is usually referred to as a double-flip phenomena.…”

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confidence: 99%

“…The behaviour of the lamellar phase (a stripped pattern) of block copolymer melts under oscillatory shear flow have attracted attention of numerous experimental studies [1][2][3][4][5][6] . Shear flow is known to influence the orderdisorder transition (ODT) temperature and the orientation of the lamellae with respect to the shear geometry.…”

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Orientations of the lamellar phase of block copolymer melts under oscillatory shear flow

Morozov

Fraaije

2002

Phys. Rev. E

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We develop a theory to describe the reorientation phenomena in the lamellar phase of block copolymer melt under reciprocating shear flow. We show that similar to the steady-shear, the oscillating flow anisotropically suppresses fluctuations and gives rise to the →⊥ transition. The experimentally observed high-frequency reverse transition is explained in terms of interaction between the melt and the shear-cell walls.The behaviour of the lamellar phase (a stripped pattern) of block copolymer melts under oscillatory shear flow have attracted attention of numerous experimental studies 1-6 . Shear flow is known to influence the orderdisorder transition (ODT) temperature and the orientation of the lamellae with respect to the shear geometry. Thus, in the vicinity of ODT at low frequencies the lamellae orient with their normal parallel to the shear gradient (the parallel orientation), while at higher frequencies their normal is perpendicular to the velocity and the gradient directions (the perpendicular orientation). Further increase of frequency results in reappearance of the parallel orientation 5 . In this Letter we propose an explanation of this orientation behaviour which is usually referred to as a double-flip phenomena.Earlier theories, which deal with steady shear, emphasize the role of compositional fluctuations 7-9 . The stable orientation is seen as a result of interaction between the shear flow and the fluctuation spectra. In equilibrium fluctuations destroy the long-range correlations and therefore lower the ODT temperature with respect to its mean-field value. Imposition of shear breaks the rotational symmetry and anisotropically suppresses fluctuations. The direction of the strongest suppression will have the highest ODT temperature and the corresponding orientation of lamellae will be selected. We will show that the selected orientation depends on the amplitude and frequency of the flow. We base our analysis on the Fokker-Planck equation for the probability densityHere φ k is a fluctuating scalar field described by the Brazovskii Hamiltonian 10τ is a temperature-controlling parameter, k −1 0 is an intrinsic length-scale of the block-copolymer melt arising from the interplay of interactions and the chain connectivity, µ is an Onsager coefficient which is approximated by µ = µ(k 0 ) and assumed to be frequency independent 11-13 . The last term in Eq.(1) describes a coupling between the shear flow v = A ω cos ωt y e x and the gradient of the order parameter. Here we assume that this form of flow is valid for all ω and A. The Fokker-Planck equation (1) generates the equations for the amplitude of the average order-parameter profile φ k = a(δ k,k0n + δ k,−k0n ) oriented along the unit vector nand for the structure factorwhereThe interaction 14 between fluctuations λ(k, −k, q, −q) = λ 1 − β(k ·q) 2 , withk = k/k, renormalizes the temperature r(k) and makes it anisotropic in the presence of shear.The stability criterion for an orientation is derived from Eq.(3).It has a potential form ∂a/∂t = −(µ/2)∂Φ(a)/∂a, w...

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Double flip of orientation for a lamellar diblock copolymer under shear

Cited by 61 publications

References 32 publications

Shear-induced instabilities in layered liquids

Shear-induced instabilities in layered liquids

Flow-Induced Alignment of Block Copolymer−Sol Nanoparticle Coassemblies toward Oriented Bulk Polymer−Silica Hybrids

Orientations of the lamellar phase of block copolymer melts under oscillatory shear flow

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