Pis’ma v ZhETF, vol. 116, iss. 4, pp. 251 - 252
© 2022 August 25
Non-Newtonian rheology in twist-bend nematic liquid crystals
E. I. Kats1)
Landau Institute for Theoretical Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russia
Submitted 5 July 2022
Resubmitted
5 July 2022
Accepted 7
July 2022
DOI: 10.31857/S1234567822160108, EDN: jhxqbt
A number of exciting and relatively recent publi-
The main feature which distinguishes the standard
cations (about ten years ago, compared to more than
nematic N and the twist-bend nematic NTB liquid crys-
100 years of the discovery of the classical liquid crys-
tals is a short wavelength modulation of the orientation
tals) report on a discovery of a new type of equilib-
order φ presented in the NTB phase. This two com-
rium liquid crystals, termed twist-bend nematics, NTB
ponent vector φ, orthogonal to the nematic director n
(see the papers [1-6]). The discovery of NTB nematics
(φ · n = 0) can be chosen as the order parameter de-
opened “Pandora box” with new kinds of modulated liq-
scribing N - NTB phase transition. With this vector
uid crystals (see very influential pioneering works and
order parameter in hands one can write the Landau free
a few review papers [17-19]). Naturally (as it was the
energy functional.
case in great geographical discoveries of 15-th - 17-th
Recent progress in rheology of the NTB liquid crys-
centuries) after the first step devoted mainly to obser-
tals has led to a number of new and exciting experi-
vations and structural identifications of new liquid crys-
mental results [20, 21]. In the paper we propose a simple
tals, the interest moves to investigations and explor-
heuristic approach to rationalize these new experimental
ing of physical properties of these new phases. Since
data. The key starting point of our approach is based on
then the NTB, and other modulated nematics is becom-
a simple observation that the anisotropic viscous prop-
ing one of the hottest topics in physics of liquid crys-
erties of the liquid crystals introduce a host of novel phe-
tals.
nomena in rheology. We find that at relatively low shear
Our paper is motivated by two very recent works
rate (γ ≤ γc1) the stress tensor σ created by this shear
[20, 21] on rheological studies of the NTB liquid crys-
strain, scales as σ ∝ γ1/2. Thus the effective viscosity
tals. The authors of these papers found nontrivial non-
decreases with the shear rate (η ∝ γ-1/2) manifesting
Newtonian behavior of sheared NTB nematics. At rel-
so-called shear-thinning phenomenon. At intermediate
atively low shear rate ( γ ≤ γc1) the stress tensor σ
shear rate γc1 ≤ γ ≤ γc2, σ is almost independent of γ
created by this shear strain, scales as σ ∝ γ1/2. Thus
(a sort of plateau), and at large shear rate ( γ ≥ γc2),
the effective viscosity decreases with the shear rate
σ ∝ γ, and it looks like Newtonian rheology. Within
(η ∝ γ-1/2) manifesting so-called shear-thinning phe-
our theory the critical values of the shear rate scales as
nomenon. At intermediate shear rate γc1 ≤ γ ≤ γc2, σ
γc1 ∝ (η02/η03)2, and γc2 ∝ (η02/η03)4 respectively. Here
is almost independent of γ (a sort of plateau), and at
η02 and η03 are bare coarse grained shear viscosity coeffi-
large shear rate ( γ ≥ γc2, σ ∝ γ), and it looks like
cients of the effective smectics equivalent to the NTB
Newtonian rheology. The critical values of the shear
phase at large scales. Our mainly qualitative theory
rate (γc1 , γc2) indicating transitions between dynami-
may not have the right numbers for the dynamic shear
cal regimes depend on temperature. Above certain tem-
rate thresholds. However theory predicts the right scal-
perature T∗ (below N - NTB phase transition point
ing laws observed in the experiments. Our consideration
Tc, where N stands for conventional nematic state) the
suggests that the described phenomena and mechanisms
behavior becomes pure Newtonian. The aim of this pa-
can bring about different rheological scenarios worthy of
per is to present theoretical rationalization for the ob-
further studies. In this work we have only scratched the
served in these works [20, 21] results. In what follows we
surface of this reach subject, focusing only on the most
integrate the input from recent works and discussions,
simple questions, which can be answered by calculations
however my own contribution to this field will be also
“on a back of the envelope”.
presented.
All obtained results of this work and short discus-
sions of the cited articles (see [1-44]) can be found in
1)e-mail: efim.i.kats@gmail.com
the full version of this paper.
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251
252
E. I. Kats
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