Macroscopic behavior of polar nematic gels and elastomers

Brand, Helmut R.; Pleiner, Harald; Svenšek, Daniel

doi:10.1140/epje/i2016-16105-7

Cited by 3 publications

(3 citation statements)

References 71 publications

(90 reference statements)

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“…The static behavior of the macroscopic system studied here is conveniently described by the energy functional in harmonic approximation Refs. [ 29 , 31 ] including the kinetic energy densities where denotes deviations from the equilibrium value, in particular , , . We only consider a spatially homogeneous ground state, meaning , and are constant and the direction of is arbitrary.…”

Section: Two-fluid Model For Polar Nematics With a Nonchiral Solventmentioning

confidence: 99%

“…In this first subsection, we discuss how the two-fluid macroscopic dynamics is modified when a strain field and relative rotations are incorporated for polar nematics to make the equations applicable to gels and elastomers. We will make extensive use of the macroscopic dynamics for 1-fluid polar nematic gels and elastomers [ 31 ].…”

Section: Incorporation Of a Strain Field For Polar Nematic Gels And E...mentioning

confidence: 99%

“…Thus, we refer again to the 1-fluid expression (Eq. (46) of [ 31 ]), which we will not duplicate here.…”

Section: Incorporation Of a Strain Field For Polar Nematic Gels And E...mentioning

confidence: 99%

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A two-fluid model for the macroscopic behavior of polar nematic fluids and gels in a nonchiral or a chiral solvent

Brand

Pleiner

2022

Eur. Phys. J. E

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We present the macroscopic dynamics of polar nematic liquid crystals in a two-fluid context. We investigate the case of a nonchiral as well as of a chiral solvent. In addition, we analyze how the incorporation of a strain field for polar nematic gels and elastomers in a solvent modifies the macroscopic dynamics. It turns out that the relative velocity between the polar subsystem and the solvent gives rise to a number of cross-coupling terms, reversible as well as irreversible, unknown from the other two-fluid systems considered so far. Possible experiments to study those novel dynamic cross-coupling terms are suggested. As examples we just mention that gradients of the relative velocity lead, in polar nematics to heat currents and in polar cholesterics to temporal changes of the polarization. In polar cholesterics, shear flows give rise to a temporal variation in the velocity difference perpendicular to the shear plane, and in polar nematic gels uniaxial stresses or strains generate temporal variations of the velocity difference. Graphical abstract

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Section: Two-fluid Model For Polar Nematics With a Nonchiral Solventmentioning

confidence: 99%

Section: Incorporation Of a Strain Field For Polar Nematic Gels And E...mentioning

confidence: 99%

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A two-fluid model for the macroscopic behavior of polar nematic fluids and gels in a nonchiral or a chiral solvent

Brand

Pleiner

2022

Eur. Phys. J. E

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Macroscopic dynamics of the ferroelectric smectic $$A_F$$ phase with $$C_{\infty v} $$ symmetry

Brand,

Pleiner

2024

Eur. Phys. J. E

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We present the macroscopic dynamics of ferroelectric smectic A, smectic $$A_F$$ A F , liquid crystals reported recently experimentally by three groups. In this fluid and orthogonal smectic phase, the macroscopic polarization, $${\textbf{P}}$$ P , is parallel to the layer normal thus giving rise to $$C_{\infty v}$$ C ∞ v overall symmetry for this phase in the spatially homogeneous limit. A combination of linear irreversible thermodynamics and symmetry arguments is used to derive the resulting dynamic equations applicable at sufficiently low frequencies and sufficiently long wavelengths. Compared to non-polar smectic A phases, we find a static cross-coupling between compression of the layering and bending of the layers, which does not lead to elastic forces, but to elastic stresses. In addition, it turns out that a reversible cross-coupling between flow and the magnitude of the polarization modifies the velocities of both, first and second sound. At the same time, the relaxation of the polarization gives rise to dissipative effects for second sound at the same order of the wavevector as for the sound velocity. We also analyze reversible cross-coupling terms between elongational flow and electric fields as well as temperature and concentration gradients, which lend themselves to experimental detection. Apparently this type of terms has never been considered before for smectic phases. The question how the linear $${{\textbf{P}} \cdot \textbf{E}}$$ P · E coupling in the energy alters the macroscopic response behavior when compared to usual non-polar smectic A phases is also addressed. Graphical abstract

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Symmetry aspects in the macroscopic dynamics of magnetorheological gels and general liquid crystalline magnetic elastomers

Pleiner

Brand

2020

Physical Sciences Reviews

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We investigate theoretically the macroscopic dynamics of various types of ordered magnetic fluid, gel, and elastomeric phases. We take a symmetry point of view and emphasize its importance for a macroscopic description. The interactions and couplings among the relevant variables are based on their individual symmetry behavior, irrespective of the detailed nature of the microscopic interactions involved. Concerning the variables we discriminate between conserved variables related to a local conservation law, symmetry variables describing a (spontaneously) broken continuous symmetry (e.g., due to a preferred direction) and slowly relaxing ones that arise from special conditions of the system are considered. Among the relevant symmetries, we consider the behavior under spatial rotations (e.g., discriminating scalars, vectors or tensors), under spatial inversion (discriminating e.g., polar and axial vectors), and under time reversal symmetry (discriminating e.g., velocities from polarizations, or electric fields from magnetic ones). Those symmetries are crucial not only to find the possible cross-couplings correctly but also to get a description of the macroscopic dynamics that is compatible with thermodynamics. In particular, time reversal symmetry is decisive to get the second law of thermodynamics right. We discuss (conventional quadrupolar) nematic order, polar order, active polar order, as well as ferromagnetic order and tetrahedral (octupolar) order. In a second step, we show some of the consequences of the symmetry properties for the various systems that we have worked on within the SPP1681, including magnetic nematic (and cholesteric) elastomers, ferromagnetic nematics (also with tetrahedral order), ferromagnetic elastomers with tetrahedral order, gels and elastomers with polar or active polar order, and finally magnetorheological fluids and gels in a one- and two-fluid description.

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Macroscopic behavior of polar nematic gels and elastomers

Cited by 3 publications

References 71 publications

A two-fluid model for the macroscopic behavior of polar nematic fluids and gels in a nonchiral or a chiral solvent

A two-fluid model for the macroscopic behavior of polar nematic fluids and gels in a nonchiral or a chiral solvent

Macroscopic dynamics of the ferroelectric smectic $$A_F$$ phase with $$C_{\infty v} $$ symmetry

Symmetry aspects in the macroscopic dynamics of magnetorheological gels and general liquid crystalline magnetic elastomers

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