Twist, splay, and uniform domains in ferroelectric nematic liquid crystals

Maxim O. Lavrentovich; Oleg D. Lavrentovich; Priyanka Kumari

REVIEW 4 major objections 4 minor 44 references

Twist, splay, and uniform domains in ferroelectric nematic liquid crystals

T0 review · 4 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper establishes that stripe and pie-slice polarization domains in a ferroelectric nematic liquid crystal are selected by a balance between screened Coulomb electrostatics and domain-wall elasticity, with the measured domain sizes…

desk verdict Useful combined experimental-theory study of NF domain patterns, but the h-scaling of domain-wall energy is fit-supported rather than pinned down. read the letter →

arxiv 2502.03747 v2 pith:GSINMAZ7 submitted 2025-02-06 cond-mat.soft cond-mat.mtrl-sci

Maxim O. Lavrentovich , Priyanka Kumari , Oleg D. Lavrentovich This is my paper · ORCID

classification cond-mat.softcond-mat.mtrl-sci PACS 61.30.-v77.80.-e

keywords ferroelectricnematicliquidcrystalpolarizationdomainsstripepie-slicedepolarizationfieldDebyescreeningdomainwallenergycell-thicknessscaling

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

A ferroelectric nematic liquid crystal is a fluid whose molecules carry a spontaneous electric polarization. Confining such a material between plates that impose an in-plane apolar alignment should in principle yield a uniform polarization, but this paper shows that instead the material splits into stripe-like domains in planar cells and pie-slice domains around a seeded +1 radial defect. The central claim is that the observed domain size is set by a competition: reducing the depolarization field favors finer domains, while the elastic cost of domain walls favors coarser ones. The paper's calculations, using screened Coulomb electrostatics plus one of three wall-energy models, match its measurements of stripe width and slice count over a range of cell thicknesses. The data favor a domain-wall energy proportional to cell thickness, meaning a wall whose elastic distortion spans the cell, rather than thickness-independent disclination walls or walls scaling as the square root of thickness.

What carries the argument

The central machinery is the free-energy functional $F=F_\rho+F_{\mathrm{dw}}$, where $F_\rho$ is the screened Coulomb self-energy of the bound-charge distribution and $F_{\mathrm{dw}}$ is an elastic domain-wall cost. The argument works by minimizing this total energy to obtain a preferred stripe wavelength $\lambda_x$ from Eq. (19) and an optimal number of pie slices $2n_\theta^*$ from Eq. (26). The balance is carried by a characteristic wall length $\lambda_{\mathrm{dw}}=\sqrt{2f_\pi\epsilon\epsilon_0}/P_0$, whose scaling with $h$ encodes the three candidate wall structures: thickness-independent disclination pairs, $\sqrt{h}$ solitons, and $h$-proportional fixed-width walls.

What would settle it

Measure the internal structure and width of a domain wall in cells of several thicknesses using high-resolution polarizing microscopy, and repeat the stripe and pie-slice measurements with independently controlled ion concentrations. If the wall's elastic distortion is localized near the surfaces rather than spanning the cell, or if relaxing the $h\kappa\gg 1$ approximation moves the free-energy minimum, the inferred $f_\pi\propto h$ scaling would not follow.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the size of polarization domains in a ferroelectric nematic is quantitatively predictable from a free-energy balance, and that comparing theory with experiment identifies how the domain-wall cost depends on cell thickness. Minimizing the total free energy—screened Coulomb energy of the bound charge density $\rho=-\nabla\cdot\mathbf{P}$ plus a domain-wall term—reproduces both the measured stripe wavelength in planar cells and the measured number of pie slices around a +1 defect. The authors find that domain walls with energy density $f_\pi$ proportional to $h$, corresponding to a fixed-width wall whose elastic distortion spans the cell, match the data across thicknesses from about 1 to 16 micrometers; the inferred characteristic wall lengths are $\lambda_{\mathrm{dw}}=(0.0437~\mu\mathrm{m}^{1/2})\,h^{1/2}$ for stripes and $(1.3~\mu\mathrm{m}^{1/2})\,h^{1/2}$ for pie slices. They also predict and observe that added ionic screening suppresses domain formation.

Load-bearing premise

The load-bearing premise is that a mathematical shortcut used to derive the stripe formula, treating the cell as thick compared with the electric screening length, does not shift the predicted stripe width even in cells where that shortcut is not valid.

Editorial extensions

If this is right

In thin planar cells the ground state is a lattice of uniform domains with antiparallel polarization, while in thicker cells it is $\pi$-twisted stripes, with the crossover set by the same electrostatic-elastic balance.
Adding ionic dopants suppresses both stripe and pie-slice domains, consistent with the predicted critical ion concentration for the twisted state.
If the wall energy is proportional to $h$, the stripe wavelength should be nearly independent of cell thickness, which the measurements confirm, while the pie-slice count should grow with $h$.
The same free-energy formalism can be applied to other patterned anchoring geometries, predicting where uniform, twisted, and splayed domains will appear based on the local bound-charge density.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial extension: the paper fixes one screening length, $\kappa^{-1}=10~\mu\mathrm{m}$, for both geometries; independently measuring the ion concentration and dielectric constant in each cell would test whether the ten-to-thirty-fold difference in inferred $\lambda_{\mathrm{dw}}$ between stripes and pie slices is physical or an artifact of that single-$\kappa$ assumption.
Editorial extension: the derivation of the stripe wavelength assumes $h\kappa\gg 1$, a condition violated in the thinnest cells measured; relaxing that approximation could shift the predicted minimum and change the inferred wall-energy scaling.
Editorial extension: a direct prediction of the paper's picture is that varying ionic strength at fixed cell thickness should shift stripe width and pie-slice count in a coordinated way, since both are governed by the same domain-wall parameter if the walls are of the same type.
Editorial extension: the same electrostatics-versus-wall-energy balance likely governs stripe domains in thin ferroelectric solid films, so the ferroelectric nematic provides a tunable fluid analog for testing thickness-dependent wall-energy models.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Bottom line: this is a solid, readable paper with real new data and a useful theoretical framework. The new pieces are the stripe and pie-slice free-energy models for apolar anchoring and the systematic thickness dependence of stripe width and sector count. The twist pitch result (Eq. 12) is not new—it reproduces Khachaturyan and Paik/Selinger, and the authors say so. What they add is the three-way comparison of domain-wall cost scalings against their own measurements.

The experiments look careful: photoaligned cells, thickness series, controls with added ionic liquid that suppress domains, and optical measurements of the π twist. The pie-slice counting in the +1 defect geometry is a nice structural test. The fact that both stripe widths and pie-slice counts prefer the fixed-width-wall model (λdw ∝ h^1/2, so fπ ∝ h) is genuinely suggestive.

Now the soft spots, in order of importance.

The main conclusion—fπ ∝ h—rests on holding κ fixed at 0.1 µm^-1. The authors acknowledge κ may depend on h. That matters: with κ free to vary with h, the fitted λdw(h) can absorb the κ(h) dependence, and the data cannot uniquely separate constant fπ with κ ∝ h^-1/2 from fπ ∝ h with constant κ. The stress-test note gets this right. It's not fatal, because the authors are explicit about the assumption, but the Discussion would be stronger if it framed fπ ∝ h as 'consistent with, given constant κ' rather than 'likely.'

Second, the hκ >> 1 assumption used to get Eq. (19) is violated for the thinner cells (hκ between 0.07 and 1.6 over the fit range). The term it affects appears independent of λx, so it probably acts as a constant offset and does not move the minimum. But 'probably' isn't proof, and a one-line numerical check would settle it.

Third, the three theoretical curves in Fig. 8 are not parameter-free: each has λdw tuned to match. This makes the comparison a consistency test of scaling exponents rather than a prediction. That's legitimate, but it would be better labeled as such.

Who is this for? Anyone working on ferroelectric nematics, especially on domain patterning and electro-optics. It deserves a serious referee. My recommendation: send it out, ask for a short revision that (a) states the κ-dependence limitation in the conclusions, (b) numerically verifies the hκ >> 1 step, and (c) tones down the 'likely' to 'consistent with.'

Referee Report

4 major / 4 minor

Summary. The paper reports experimental and theoretical work on domain formation in ferroelectric nematic liquid crystals (DIO) confined in thin cells with apolar photoalignment. In planar cells, thin samples form uniform polarization domains and thick samples form pi-twisted stripe domains; in cells patterned with a +1 radial defect, the system forms pie-slice splay domains. The authors develop a screened-Coulomb electrostatic model combined with a phenomenological domain-wall energy cost parameterized by a length lambda_dw. They compare the predicted stripe wavelength and number of pie-slice sectors with measurements as a function of cell thickness h, testing three forms for the domain-wall energy (disclination pairs, solitons, and fixed-width walls). The paper concludes that the domain-wall energy density f_pi scales approximately linearly with h. The central comparison is not fully circular, because the three wall models predict different h-dependences of the stripe wavelength and sector number, but the quantitative support is weakened by parameter fitting and the unconstrained screening length.

Significance. The experimental observations are valuable: the paper documents a clean thickness-dependent crossover between uniform domains, pi-twisted stripes, and radial pie-slice domains, and it demonstrates that ionic doping suppresses the twisted states. The theoretical framework combining screened electrostatics and domain-wall elasticity is a useful starting point for quantitative modeling of ferroelectric-nematic textures. The strongest parts are the optical characterization of the pi-twist (Figs. 1j, 3c) and the systematic thickness dependence of the domain sizes. However, the paper's headline quantitative claim, that the domain-wall energy density scales as f_pi proportional to h, is not established with the same rigor: the comparison in Fig. 8 relies on fitting the prefactor in lambda_dw for each assumed exponent, and the inverse Debye length kappa is fixed by hand without an independent measurement. If the claim survives a more careful treatment of these free parameters, it would be a useful constraint on microscopic theories of domain walls in ferroelectric nematics; at present, the conclusion is plausible but conditional.

major comments (4)

[Quantitative comparisons between models and experiments (Fig. 8), Eqs. (19) and (26)] The central conclusion f_pi proportional to h is inferred by tuning lambda_dw(h) to the same experimental data against which the theory is compared. In Eq. (19), the wall term is proportional to (kappa*lambda_dw)^2 L/(kappa*lambda_x h), and in Fig. 8 the three model curves are generated by choosing, for each assumed exponent alpha, a prefactor so that lambda_dw = C h^alpha gives a 'favorable match' (Methods: 'expressions for lambda_dw are varied ... to get a reasonable match'). The data can therefore discriminate among the three assumed exponents only if the model family is accepted and the screening length is known. Because lambda_dw is defined directly from f_pi, comparing fitted lambda_dw(h) curves is partly circular. I recommend either fixing the prefactors from independent estimates of K, W, and epsilon, or reporting a genuine fit with parameter uncertainties and a defined goodness-of-fit criterion that shows the data reject alpha = 0 and alpha = 1/4 in favor of alpha = 1/2. Until then, the phrase 'predictions' in the Abstract and Results overstates the status of the curves in Fig. 8.
[Discussion and Fig. 8] The paper fixes kappa = 0.1 inverse micrometers and states that 'kappa may well be h-dependent.' This is load-bearing because Eq. (19) depends on kappa through kappa*lambda_x in the electrostatic sum and through the combination kappa*lambda_dw in the wall term. With no independent measurement of kappa(h) in the NF cells, a model with constant f_pi and a suitably chosen kappa(h) (for example kappa proportional to h^{-1/2}) could reproduce the same lambda_x(h) data. The low-screening approximation in Eq. (20) hides this degeneracy because lambda_x* becomes independent of kappa, but the actual minima in Fig. 8 are obtained from the full Eq. (19), where kappa enters. I request a sensitivity analysis over plausible kappa(h) forms, or an experimental determination of kappa as a function of h, before the f_pi proportional to h conclusion can be accepted.
[Fig. 8, models of stripe and pie-slice domains] The best-fit fixed-width-wall curves use lambda_dw = 0.0437 h^{1/2} micrometers for stripes and lambda_dw = 1.3 h^{1/2} micrometers for pie slices. These differ by a factor of about 30, which translates through lambda_dw = (2 f_pi epsilon*epsilon_0)^{1/2}/P_0 into a difference of roughly three orders of magnitude in the inferred domain-wall energy density f_pi for the same material. The paper attributes this to different epsilon or kappa in the two geometries, but epsilon enters lambda_dw only as sqrt(epsilon), so an order-of-magnitude change in lambda_dw would require epsilon to differ by about three orders of magnitude, which is not plausible. If the difference is instead due to kappa, then the fitted lambda_dw is not a direct measure of the physical wall energy, and the claim that both geometries support the same f_pi proportional to h scaling is not justified. The authors should either develop a unified model with a single f_pi and geometry-dependent screening or explicitly restrict the conclusion to the particular wall type in each geometry.
[Fig. 2c-f and Fig. 8b] The number of pie-slice domains depends strongly on the cooling rate (Fig. 2c,d), yet the theory in Eq. (26) is an equilibrium free-energy minimization. The caption of Fig. 8b does not state which cooling rate was used for the data points. If the counts are taken from slow-cooled samples, the equilibrium assumption should be stated and, ideally, the sensitivity of the count to cooling rate should be discussed in the context of the model. If the counts are kinetically controlled, the apparent agreement with an equilibrium calculation is not decisive evidence for the model.

minor comments (4)

[Eqs. (18)-(19)] The assumption h*kappa >> 1 used in passing from Eq. (18) to Eq. (19) is violated for the thin cells considered (h*kappa ranges from about 0.07 to 1.6 with kappa = 0.1 inverse micrometers). The authors state without proof that the approximation does not change the location of the minimum. From the structure of Eq. (18), the affected 'left-over' term is independent of lambda_x, so the minimum location is likely indeed unaffected; however, the statement should be demonstrated explicitly, for example by a numerical comparison of the exact and approximated free-energy curves for a few values of h*kappa.
[Abstract and Fig. 8 caption] The word 'prediction' is used for curves whose prefactors have been tuned to the data. I suggest using 'fit' or 'model comparison' in the Abstract, Results, and Fig. 8 caption, and reserving 'prediction' for parameter-free comparisons.
[Eq. (19)] The summation in Eq. (19) contains the factor [1-(-1)^n], which selects odd n. This can be simplified to 2 times the sum over odd n, which would make the numerical evaluation and the low-screening limit more transparent.
[Figs. 2 and 8] The experimental error bars in Fig. 8 are estimates of counting uncertainty only. The theory curves have no uncertainty bands reflecting the unknown kappa and the fitted prefactors. A plot showing the sensitivity of the curves to reasonable variations in kappa would help the reader judge the significance of the agreement.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fπ∝h conclusion is a model-comparison fit, not a definitional reduction.

full rationale

The theoretical derivation is self-contained: Eqs. (19) and (26) follow from screened Coulomb electrostatics (Eq. 2), Frank elasticity, and a phenomenological domain-wall energy, with the target scaling not inserted among the input assumptions. The domain-wall energy scale λdw is indeed adjusted to match the stripe and pie-slice data, so the absolute curves in Fig. 8 are fits, not parameter-free predictions; however, the paper's central claim concerns the h-scaling of fπ, and the three wall models (constant, √h, h) produce different predicted h-dependences of λ*x and n*θ. Only the fπ∝h (fixed-width-wall) model reproduces the observed near-constant stripe width and the sector-count trend, so the agreement is not forced by construction. The acknowledged possibility that κ depends on h ('κ may well be h-dependent') could allow an unknown κ(h) to be absorbed into the fitted λdw(h), making the inference underdetermined; that is an identifiability/correctness limitation, not circularity. Self-citations to the authors' prior work supply experimental context (e.g., ref. [10]) and one alternative wall-energy estimate (ref. [7]); they are not used to veto alternative models or to import the central result.

Assumptions & free parameters 8 free parameters · 8 assumptions · 0 invented entities

The paper's quantitative claims rest on several fitted parameters, chiefly the characteristic domain wall length λdw (fitted separately for three wall models and two geometries) and the inverse Debye length κ = 0.1 µm^-1. These are matched to the experimental data rather than derived from first principles. The structural conclusion that wall energy scales linearly with h survives because the three wall models give different h-scalings, but the absolute domain sizes are not independent predictions. No new physical entities are introduced.

free parameters (8)

λdw (stripe, disclination model) = 0.12 µm
Fitted to match the stripe width data in Fig. 8a; this is the characteristic domain wall length for the disclination wall model.
λdw (stripe, soliton model) = (0.0608 µm^3/4) h^1/4
Fitted to match the stripe data; corresponds to fπ ∝ sqrt(h).
λdw (stripe, fixed-width wall model) = (0.0437 µm^1/2) h^1/2
Fitted to match the stripe data; central to the conclusion that fπ ∝ h.
λdw (pie-slice, disclination model) = 1.5 µm
Fitted to match the pie-slice count data in Fig. 8b.
λdw (pie-slice, soliton model) = (1.4 µm^3/4) h^1/4
Fitted to match the pie-slice data.
λdw (pie-slice, fixed-width wall model) = (1.3 µm^1/2) h^1/2
Fitted to match the pie-slice data; supports the fπ ∝ h conclusion.
κ (inverse Debye length) = 0.1 µm^-1
Chosen by hand: 'We will fix κ = 0.1 µm^-1 in our analysis, which seems to work well for the samples considered here.' This is a fit, not a measured quantity.
L (sample lateral size) = 1 cm
Used in the model minimization for stripes; presumably the sample size, but treated as an input without independent verification.

assumptions (8)

standard math Frank elastic free energy Eq. (3) with splay, twist, and bend constants K1, K2, K3 describes the nematic elastic cost.
Standard nematic elasticity, cited to de Gennes and Prost [21].
domain assumption Screened Coulomb energy Eq. (2), based on Debye-Hückel screening, captures the electrostatic cost of bound charge.
Used throughout; assumes a homogeneous screening length and that the screened interaction acts everywhere, including outside the polarized domain.
domain assumption The polarization magnitude is fixed, |P| = P0, and the nematic director n always aligns with P.
Invoked in the theory section; the authors state that any other effects will be incorporated in renormalized constants.
ad hoc to paper The stripe ansatz Eq. (17), which includes a π twist along z with cos(πz/h) and sin(πz/h), describes the striped domains compared to experiment.
This ansatz is imposed for the stripe model; it is applied in Fig. 8a even though thin-cell UDs are experimentally uniform along z.
ad hoc to paper The condition hκ >> 1 can be imposed in the leftover integration of Eq. (18) without changing the location of the minimum.
Stated without proof; violated for κ = 0.1 µm^-1 and h < 10 µm, the range compared to data.
ad hoc to paper A single-mode approximation cos[φ(θ)] ≈ cos(nθ θ) describes the pie-slice polarization orientation.
Used in the pie-slice model, Eq. (25); the authors note it breaks down near the +1 defect core.
domain assumption Domain wall energy densities take one of three forms: disclination pairs (fπ ≈ 2K), solitons (fπ ≈ 2 sqrt(2KhW)), or fixed-width walls (fπ ≈ Kh/λwall).
Borrowed from prior literature on disclinations and solitons; the paper tests all three against data.
domain assumption Flexoelectric contributions to splay are negligible in the NF phase.
The authors cite Refs. [14,15] for suppression of flexoelectric splay by space charge in the NF phase.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Twist, splay, and uniform domains in ferroelectric nematic liquid crystals." pith.science (2026). https://pith.science/paper/GSINMAZ7

@misc{pith2026250203747,
  author       = {Pith},
  title        = {Pith review of: Twist, splay, and uniform domains in ferroelectric nematic liquid crystals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GSINMAZ7}},
  note         = {Machine review of arXiv:2502.03747}
}

read the original abstract

The newly-discovered ferroelectric nematic liquid crystal exhibits a variety of unique defect phenomena. The depolarization field in the material favors spontaneous spatial variations in polarization, manifesting in diverse forms such as bulk twists and arrangements of alternating polarization domains. The configuration of these domains is governed by a balance between depolarization field reduction and molecular alignment at interfaces. We investigate a ferroelectric nematic confined in a thin cell with apolar surface anchoring, patterned using photoalignment. Under uniform planar alignment, the system forms stripes, while a radial +1 defect pattern results in pie-slice domains. Neighboring domains show either opposite directions of uniform polarization (thin cells) or opposite handedness of the spontaneous twist (thick cells). Our calculations and experiments demonstrate that electrostatic interactions tend to shrink domain size, whereas elastic and surface anchoring effects promote larger domains. In this work, we make predictions and measurements of the domain size as a function of cell thickness, and show that ionic screening suppresses domain formation.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

44 extracted references · 43 canonical work pages

[1]

Mandle, R.J., Cowling, S.J., Goodby, J.W.: A nematic to nematic transformation exhibited by a rod-like liquid crystal. Phys. Chem. Chem. Phys. 19(18), 11429–11435 (2017)

work page 2017
[2]

Nishikawa, H., Shiroshita, K., Higuchi, H., Okumura, Y., Haseba, Y., Yamamoto, S.-i., Sago, K., Kikuchi, H.: A fluid liquid-crystal material with highly polar order. Adv. Mater. 29(43), 1702354 (2017)

work page 2017
[3]

Sebasti´ an, N., Cmok, L., Mandle, R.J., Fuente, M.R., Drevenˇ sek-Olenik, I.,ˇCopiˇ c, M., Mertelj, A.: Ferroelectric-ferroelastic phase transition in a nematic liquid crystal. Phys. Rev. Lett.124(3), 037801 (2020)

work page 2020
[4]

Chen, X., Korblova, E., Dong, D., Wei, X., Shao, R., Radzihovsky, L., Glaser, M.A., Maclennan, J.E., Bedrov, D., Walba, D.M., et al.: First-principles experimental demonstration of ferroelectricity in a thermotropic nematic liquid crystal: Polar domains and striking electro-optics. Proc. Natl. Acad. Sci. U.S.A. 117(25), 14021–14031 (2020)

work page 2020
[5]

Adaka, A., Rajabi, M., Haputhantrige, N., Sprunt, S., Lavrentovich, O.D., J´ akli, A.: Dielectric prop- erties of a ferroelectric nematic material: quantitative test of the polarization-capacitance Goldstone mode. Phys. Rev. Lett. 133(3), 038101 (2024)

work page 2024
[6]

Erkoreka, A., Martinez-Perdiguero, J.: Constraining the value of the dielectric constant of the ferroelectric nematic phase. Phys. Rev. E 110, 022701 (2024) 18

work page 2024
[7]

Basnet, B., Rajabi, M., Wang, H., Kumari, P., Thapa, K., Paul, S., Lavrentovich, M.O., Lavrentovich, O.D.: Soliton walls paired by polar surface interactions in a ferroelectric nematic liquid crystal. Nat. Commun. 13, 3932 (2022)

work page 2022
[8]

Kumari, P., Basnet, B., Wang, H., Lavrentovich, O.D.: Ferroelectric nematic liquids with conics. Nat. Commun. 14, 748 (2023)

work page 2023

Show all 44 references

[9]

Hedlund, K.G., Martinez, V., Chen, X., Park, C.S., Maclennan, J.E., Glaser, M.A., Clark, N.A.: Freely suspended nematic and smectic films and free-standing smectic filaments in the ferroelectric nematic realm. Phys. Chem. Chem. Phys. 27, 119–128 (2025)

2025
[10]

Science 383, 1364–1368 (2024)

Kumari, P., Basnet, B., Lavrentovich, M.O., Lavrentovich, O.D.: Chiral ground states of ferroelectric liquid crystals. Science 383, 1364–1368 (2024)

2024
[11]

Guo, Y., Jiang, M., Peng, C., Sun, K., Yaroshchuk, O., Lavrentovich, O., Wei, Q.-H.: High-resolution and high-throughput plasmonic photopatterning of complex molecular orientations in liquid crystals. Adv. Mater. 28(12), 2353–2358 (2016)

2016
[12]

Crystals 7(1), 8 (2016)

Guo, Y., Jiang, M., Peng, C., Sun, K., Yaroshchuk, O., Lavrentovich, O.D., Wei, Q.-H.: Designs of plasmonic metamasks for photopatterning molecular orientations in liquid crystals. Crystals 7(1), 8 (2016)

2016
[13]

Soft Matter 21, 1122–1133 (2025)

Zhong, B., Shuai, M., Chen, X., Martinez, V., Korblova, E., Glaser, M.A., Maclennan, J.E., Walba, D.M., Clark, N.A.: Thermotropic reentrant isotropy and induced smectic antiferroelectricity in the ferroelectric nematic realm: comparing RM734 and DIO. Soft Matter 21, 1122–1133 (2025)

2025
[14]

Rupnik, P.M., Hanˇ zel, E., Lovˇ sin, M., Osterman, N., Gibb, C.J., Mandle, R.J., Sebasti´ an, N., Mertelj, A.: Antiferroelectric order in nematic liquids: Flexoelectricity versus electrostatics. Sci. Adv. 2025, 2414818 (2025)

2025
[15]

Ma, Z., Jiang, M., Sun, A., Yi, S., Yang, J., Huang, M., Aya, S., Wei, Q.-H.: Double splay nematic order in confined polar fluids. Phys. Rev. Lett. 134, 238101 (2025)

2025
[16]

Soft Matter 16, 4814–4822 (2020)

Susser, A.L., Harkai, S., Kralj, S., Rosenblatt, C.: Transition from escaped to decomposed nematic defects, and vice versa. Soft Matter 16, 4814–4822 (2020)

2020
[17]

Chiccoli, C., Feruli, I., Lavrentovich, O.D., Pasini, P., Shiyanovskii, S.V., Zannoni, C.: Topological defects in schlieren textures of biaxial and uniaxial nematics. Phys. Rev. E 66, 030701 (2002)

2002
[18]

Crystals 14, 1058 (2024)

Haputhanthrige, N.P., Rajabi, M., Lavrentovich, O.D.: Effects of photopatterning conditions on azimuthal surface anchoring strength. Crystals 14, 1058 (2024)

2024
[19]

Clark, N.A., Chen, X., MacLennan, J.E., Glaser, M.A.: Dielectric spectroscopy of ferroelectric nematic liquid crystals: Measuring the capacitance of insulating interfacial layers. Phys. Rev. Res. 6(1), 013195 (2024)

2024
[20]

Khachaturyan, A.G.: Development of helical cholesteric structure in a nematic liquid crystal due to the dipole-dipole interaction. J. Phys. Chem. Solids 36, 1055–1061 (1975)

1975
[21]

Oxford Univ

de Gennes, P.G., Prost, J.: The Physics of Liquid Crystals, 2nd edn. Oxford Univ. Press, New York (1995)

1995
[22]

Sebasti´ an, N.,˘Copi˘ c, M., Mertelj, A.: Ferroelectric nematic liquid-crystalline phases. Phys. Rev. E 106, 021001 (2022) 19

2022
[23]

Crawford, G.P., ˇZumer, S.: Saddle-splay elasticity in nematic liquid crystals. Int. J. Mod. Phys. B 9, 2469–2514 (1995)

1995
[24]

Paik, L., Selinger, J.V.: Flexoelectricity versus electrostatics in polar nematic liquid crystals. Phys. Rev. E 111, 053402 (2025)

2025
[25]

arXiv preprint arXiv:2406.19728 (2024)

Lukyanchuk, I.A., Razumnaya, A.G., Kondovych, S., Tikhonov, Y.A., Vinokur, V.M.: Topological ferroelectric chirality. arXiv preprint arXiv:2406.19728 (2024)

2024 arXiv
[26]

Lukyanchuk, I.A., Razumnaya, A.G., Kondovych, S., Tikhonov, Y.A., Khesin, B., Vinokur, V.M.: Topological foundations of ferroelectricity. Phys. Rep. 1110, 1–56 (2025)

2025
[27]

Fernandez, A., Acharya, M., Lee, H.-G., Schimpf, J., Jiang, Y., Lou, D., Tian, Z., Martin, L.W.: Thin-film ferroelectrics. Adv. Mater. 34, 2108841 (2022)

2022
[28]

Streiffer, S.K., Eastman, J.A., Fong, D.D., Thompson, C., Munkholm, A., Murty, M.V.R., Auciello, O., Bai, G.R., Stephenson, G.B.: Observation of nanoscale 180 ◦ stripe domains in ferroelectric PbTiO3 thin films. Phys. Rev. Lett. 89(6), 067601 (2002)

2002
[29]

Feigl, L., Yudin, P., Stolichnov, I., Sluka, T., Shapovalov, K., Mtebwa, M., Sandu, C.S., Wei, X.-K., Tagantsev, A.K., Setter, N.: Controlled stripes of ultrafine ferroelectric domains. Nat. Commun. 5, 4677 (2014)

2014
[30]

Kittel, C.: Theory of the structure of ferromagnetic domains in films and small particles. Phys. Rev. 70, 965 (1946)

1946
[31]

Stephenson, G.B., Elder, K.R.: Theory for equilibrium 180 ◦ stripe domains in PbTiO 3. J. Appl. Phys. 100, 051601 (2006)

2006
[32]

Landau, L., Lifshits, E.: On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Phys. Zeitsch. der Sow. 8, 153–169 (1935)

1935
[33]

Kittel, C.: Physical theory of ferromagnetic domains. Phys. Mod. Phys. 21(4), 541–583 (1949)

1949
[34]

Li, J., Nishikawa, H., Kougo, J., Zhou, J., Dai, S., Tang, W., Zhao, X., Hisai, Y., Huang, M., Aya, S.: Development of ferroelectric nematic fluids with giant-ϵ dielectricity and nonlinear optical properties. Sci. Adv. 7, 5047 (2021)

2021
[35]

Yi, S., Hong, Z., Ma, Z., Zhou, C., Jiang, M., Huang, X., Huang, M., Aya, S., Zhang, R., Wei, Q.-H.: Chiral π domain walls composed of twin half-integer surface disclinations in ferroelectric nematic liquid crystals. Proc. Natl. Acad. Sci. U.S.A. 121(52), 2413879121 (2024)

2024
[36]

Kumari, P., Kurochkin, O., Nazarenko, V.G., Lavrentovich, O.D., Golovaty, D., Sternberg, P.: Conic sections in ferroelectric nematics: Experiments and mathematical modeling. Phys. Rev. Res. 6, 043207 (2024)

2024
[37]

Zhuang, Z., Maclennan, J.E., Clark, N.A.: Device applications of ferroelectric liquid crystals: Impor- tance of polarization charge interactions. Proc. Soc. Photo Opt. Instrum. Eng. 1080, 110–114 (1989)

1989
[38]

Academic Press, Cambridge (2007)

Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products, 7th edn. Academic Press, Cambridge (2007)

2007
[39]

Sidi, A., Hoggan, P.E.: Asymptotics of modified Bessel functions of high order. Int. J. Pure Appl. 20 Math. 71(3), 481–498 (2011)

2011
[40]

Mandle, R.J., Cowling, S.J., Goodby, J.W.: Rational design of rod-like liquid crystals exhibiting two nematic phases. Chem. Eur. J. 23(58), 14554–14562 (2017)

2017
[41]

Chen, X., Martinez, V., Korblova, E., Freychet, G., Zhernenkov, M., Glaser, M.A., Wang, C., Zhu, C., Radzihovsky, L., Maclennan, J.E., et al.: The smectic Z A phase: Antiferroelectric smectic order as a prelude to the ferroelectric nematic. Proc. Natl. Acad. Sci. U.S.A. 120(8)...

2023
[42]

Champaign, IL, 2024

Wolfram Research, Inc.: Mathematica, Version 14.2. Champaign, IL, 2024. https://www.wolfram. com/mathematica

2024
[43]

Gao, F., Han, L.: Implementing the Nelder-Mead simplex algorithm with adaptive parameters. Comput. Optim. Appl. 51, 259–277 (2012)

2012
[44]

arXiv preprint arXiv:2507.03235 (2025) 21

Paik, L., Selinger, J.V.: Spontaneous cholesteric phase in ferroelectric nematic liquid crystals: Preference for integer number of pitches. arXiv preprint arXiv:2507.03235 (2025) 21

2025

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

[1] [1]

Mandle, R.J., Cowling, S.J., Goodby, J.W.: A nematic to nematic transformation exhibited by a rod-like liquid crystal. Phys. Chem. Chem. Phys. 19(18), 11429–11435 (2017)

work page 2017

[2] [2]

Nishikawa, H., Shiroshita, K., Higuchi, H., Okumura, Y., Haseba, Y., Yamamoto, S.-i., Sago, K., Kikuchi, H.: A fluid liquid-crystal material with highly polar order. Adv. Mater. 29(43), 1702354 (2017)

work page 2017

[3] [3]

Sebasti´ an, N., Cmok, L., Mandle, R.J., Fuente, M.R., Drevenˇ sek-Olenik, I.,ˇCopiˇ c, M., Mertelj, A.: Ferroelectric-ferroelastic phase transition in a nematic liquid crystal. Phys. Rev. Lett.124(3), 037801 (2020)

work page 2020

[4] [4]

Chen, X., Korblova, E., Dong, D., Wei, X., Shao, R., Radzihovsky, L., Glaser, M.A., Maclennan, J.E., Bedrov, D., Walba, D.M., et al.: First-principles experimental demonstration of ferroelectricity in a thermotropic nematic liquid crystal: Polar domains and striking electro-optics. Proc. Natl. Acad. Sci. U.S.A. 117(25), 14021–14031 (2020)

work page 2020

[5] [5]

Adaka, A., Rajabi, M., Haputhantrige, N., Sprunt, S., Lavrentovich, O.D., J´ akli, A.: Dielectric prop- erties of a ferroelectric nematic material: quantitative test of the polarization-capacitance Goldstone mode. Phys. Rev. Lett. 133(3), 038101 (2024)

work page 2024

[6] [6]

Erkoreka, A., Martinez-Perdiguero, J.: Constraining the value of the dielectric constant of the ferroelectric nematic phase. Phys. Rev. E 110, 022701 (2024) 18

work page 2024

[7] [7]

Basnet, B., Rajabi, M., Wang, H., Kumari, P., Thapa, K., Paul, S., Lavrentovich, M.O., Lavrentovich, O.D.: Soliton walls paired by polar surface interactions in a ferroelectric nematic liquid crystal. Nat. Commun. 13, 3932 (2022)

work page 2022

[8] [8]

Kumari, P., Basnet, B., Wang, H., Lavrentovich, O.D.: Ferroelectric nematic liquids with conics. Nat. Commun. 14, 748 (2023)

work page 2023