Stability of parallel/perpendicular domain boundaries in lamellar block copolymers under oscillatory shear

Huang, Zhi Feng; Viñals, Jorge

doi:10.1122/1.2399088

Cited by 6 publications

(8 citation statements)

References 49 publications

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“…Steady and oscillatory shear flows have been applied with some success, [14][15][16][17][18] although the mechanisms leading to the selection of a particular orientation of the copolymer relative to the imposed shear are not yet well understood. 19) Graphoepitaxy is another of the strategies being used to control long range order of block copolymer microphases. 20,21) Topographic relief on a substrate orients the subsequent epitaxial growth of a deposited copolymer film.…”

Section: Introductionmentioning

confidence: 99%

Defect Dynamics in Mesophases

Viñals

2009

J. Phys. Soc. Jpn.

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Block copolymer phases are a fertile ground in which to investigate both equilibrium and nonequilibrium properties of mesophases (phases that exhibit partial broken symmetries, intermediate between a completely disordered fluid and a perfectly order crystal). We focus here on two particular phases: a lamellar phase (of smectic symmetry, solid like in one direction and fluid in the two other directions), and a columnar phase (a hexagonal solid in two dimensions, and fluid in the third dimension). Starting from a mesoscopic model of the copolymer, we present the amplitude equations of motion for tilt and twist grain boundaries, and the resulting equations of motion for slightly distorted boundaries. We also examine the assumptions underlying the separation of scales in the derivation of the amplitude equations, and analyze corrections to the equations due to the coupling to the Oð1Þ variation of the order parameter in the vicinity of the boundaries. These corrections can lead to defect pinning. The effect of pinning on defect motion depends on whether the bifurcation originating the mesophase is super or sub critical.

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Section: Introductionmentioning

confidence: 99%

Defect Dynamics in Mesophases

Viñals

2009

J. Phys. Soc. Jpn.

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“…The limit of small Reynolds number implies that both Re (1) and Re (2) H 2 /h 2 are small. Now we solve the equations of motion (27) for the stream function order by order in q x by taking the expansion in Re and g (α) as…”

Section: Linear Stability Analysismentioning

confidence: 99%

“…For an incompressible system, such a symmetry requires three viscosity coefficients and three elastic moduli 26 . We extend here the earlier analysis of a purely viscous uniaxial fluid 27 , to incorporate viscoelasticity. As shown below, a uniaxial viscoelastic medium readily allows for differential rheology in, say, parallel and perpendicular orientations, including the observed terminal behavior of the perpendicular orientation versus viscoelastic response of other orientations.…”

Section: Introductionmentioning

confidence: 95%

The role of viscoelastic contrast in orientation selection of block copolymer lamellar phases under oscillatory shear

Yoo

Viñals

2013

Soft Matter

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The mesoscale rheology of a lamellar phase of a block copolymer is modeled as a structured fluid of uniaxial symmetry. The model predicts a viscoelastic response that depends on the angle between the the local lamellar planes and velocity gradients. We focus on the stability under oscillatory shear of a two layer configuration comprising a parallel and a perpendicularly oriented domain, so that the two layers have a different viscoelastic modulus G * (ω). A long wave, low Reynolds number expansion is introduced to analytically obtain the region of stability. When the response of the two layers is purely viscous, we recover earlier results according to which the interface is unstable for non zero Reynolds number flows when the thinner layer is more viscous. On the other hand, when viscoelasticity is included, we find that the interface can become unstable even for zero Reynolds number. The interfacial instability is argued to dynamically favor perpendicular relative to parallel orientation, and hence we suggest that the perpendicular orientation would be selected in a multi domain configuration in the range of frequency ω in which viscoelastic contrast among orientations is appreciable. I. INTRODUCTIONA stability analysis of two superposed fluid layers to oscillatory shear is given when the frequency dependent viscoelastic modulus of each layer is different. At vanishing Reynolds number, we find that an initially planar interface can be rendered linearly unstable to long wavelength perturbations by viscoelastic contrast. Our analysis is motivated by rheology and alignment studies of structured phases, mostly in soft and biological matter, in which local viscoelastic response couples to a broken symmetry variable of the phase (e.g., orientation).

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“…B(x, y, z, t) = B (0) (z) + qx,qy B(q x , q y , z, t)e i(qxx+qyy) , (10) substitute these expansions into Eqs. ( 3) and ( 4), and linearize the resulting equations with respect to the perturbations Â and B.…”

Section: Stability Analysismentioning

confidence: 99%

“…A common practical limitation to widespread use, however, is the considerable difficulty encountered in producing well ordered microstructures [3,5,6,7]. Given that the longest relaxation times of partially ordered microstructures are often controlled by existing topological defects, much attention has been paid to the motion of disclinations [5,8] and grain boundaries in lamellar [9,10] and cylindrical phases [11].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of twist grain boundaries in lamellar phases of block copolymers

Zhang,

Huang,

Viñals

2008

Preprint

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Twist grain boundaries are widely observed in lamellar phases of block copolymers. A mesoscopic model of the copolymer is used to obtain stationary configurations that include a twist grain boundary, and to analyze their stability against long wavelength perturbations. The analysis presented is valid in the weak segregation regime, and includes direct numerical solution of the governing equations as well as a multiple scale analysis. We find that a twist boundary configuration with arbitrary misorientation angle can be well described by two modes, and obtain the equations for their slowly varying amplitudes. The width of the boundary region is seen to scale as ǫ −1/4 , with ǫ being the dimensionless distance to the order-disorder transition. We finally present the results of the linear stability analysis of the planar boundary.

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Stability of parallel/perpendicular domain boundaries in lamellar block copolymers under oscillatory shear

Cited by 6 publications

References 49 publications

Defect Dynamics in Mesophases

Defect Dynamics in Mesophases

The role of viscoelastic contrast in orientation selection of block copolymer lamellar phases under oscillatory shear

Stability analysis of twist grain boundaries in lamellar phases of block copolymers

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