Heliconical smectic phases formed by achiral molecules

Chiral symmetry breaking in soft matter is a hot topic of current research. Recently, such a phenomenon was found in a fluidic phase showing orientational order of molecules—the nematic phase; although built of achiral molecules, the phase can exhibit structural chirality—average molecular direction follows a short-pitch helix. Here, we report a series of achiral asymmetric dimers with an odd number of atoms in the spacer, which form twisted structures in nematic as well as in lamellar phases. The tight pitch heliconical nematic (NTB) phase and heliconical tilted smectic C (SmCTB) phase are formed. The formation of a variety of helical structures is accompanied by a gradual freezing of molecular rotation. In the lowest temperature smectic phase, HexI, the twist is expressed through the formation of hierarchical structure: nanoscale helices and mesoscopic helical filaments. The short-pitch helical structure in the smectic phases is confirmed by resonant X-ray measurements.

nematic and smectic phases, including several phases with heliconical arrangement of the achiral mesogenic molecules. These brocken-chiral-symmetry phases include the twist-bend nematic (NTB), which has been recently discovered and is actively investigated in the last few years. Two smectic phases with the same spontaneous short-pitch heliconical structure has been reported for a first time. Moreover, the appearance of the NTB and the heliconical smectic phases in the phase diagrams of the same homologous series is discussed and the Authors suggest that the symmetry breaking in all the three phases may arise from the same mechanism which has been proposed for the NTB phase. A rich variety of experimental techniques is applied for characterizing the different liquid crystal phases, their phase transitions, the positional and orientational order of the phases and their optical and electro-optical properties.
In my opinion, the paper matches well the main criteria for publication in NCOMMS; - The manuscript is very important to scientists in the field of liquid crystals (and in many other fields) - The results are surely novel, with two new phases and original phase diagrams claimed and supported by strong evidence - The results are technically sound and well discussed I think that the paper represents a significant advance in the understanding of the symmetrybreaking phenomena and will stimulate new theoretical and experimental investigations in the already very active field of bent-shaped mesogenic molecules and their phases.
Therefore, I strongly recommend the publication of this work in Nature Communications after the Authors have considered the minor remarks listed below.
Minor remarks and suggestions: 1) The chiral symmetry breaking in liquid crystal phases was first reported in two seminal papers of H. Takezoe group concerning the smectic phases of bent-core molecules (Niori et al., J. Mater. Chem., 6 (1996) 1231Sekine et al., Jpn. J. Appl. Phys., 36 (1997) 6455). I think that these papers should be cited and more detailed arguments should be given to prove that the SmCTB phase is different from the already reported phases.
By the way, I speculated in Ref.
[4] that the elastic instability proposed for the NTB phase may also be involved in the chiral symmetry breaking in smectic phases of bent-shaped molecules, as an alternative to the polar in-layer interactions ("the nematic elasticity can give rise to a similar symmetry breaking, even in apolar banana smectics"). Also, I suggested that the NTB may be preempted by a smectic phase due to the similar scale of the NTB and smectic pitches ("It is also possible that a nematic-to-smectic transition precedes the sign change of K3, induced by the coupling of the director spatial modulation with the smectic mass density wave."). In my knowledge, the present work gives the first experimental evidence supporting these speculations.

2)
The discussion of the optical properties may be improved, by giving more details about the observation geometry and by more precise analysis of the observations. For example, the fact that no rotatory power (or optical activity in other terms) has been detected in the NTB and SmCTB phases does not imply that "the size of the chiral domains in these phases is smaller than the optical wavelength.". Indeed, the optical activity here is not of molecular origin, it is structural (also called "extrinsic"). As in a cholesteric with small pitch, P << λ, the rotatory power decreases as P<sup>3</sup>: therefore, for so small pitch it will be undetectable. The real question is: why it is observed in the even shorter-pitch HexI phase? The answer is simple: as in this phase the pitch is about 2.2 layers, the optical axis rotates azimuthally at about 160° from layer to layer; optically, this is equivalent to rotation of the optical axis at -20° ; then, the optical period of the structure is 18 layers, and the rotatory power is about 100 times larger than in the NTB or SmCTB.
For the CD the situation is exactly the same -it is extrinsic, not due to the molecular chirality (for the N* phase see, e.g., F.D. Saeva, J.J. Wysocki, JACS, 93 (1971) 5928). In fact, the CD is an exact analog of the rotatory power, with the imaginary part of the dielectric tensor replacing the real one.
In several places in the optical discussions there are some conclusions, not fully supported by the observations. For example, the statement "This optical uniaxiality (of the SmCTB phase) is inconsistent with a simple synclinic or anticlinic SmC phase structure, and indicates that averaging of molecular orientation must take place through the formation of a helioconical structure" disregards the possibility of a synclinic or anticlinic <i>chiral</i> SmC phases, as those observed in banana-like smectics. 3) The absence of a flexoelectric response is surprising, as in the right geometry it is a symmetry-defined property (see C. Meyer et al., PRL 111, 067801 (2013)) and should exist in any twisted structure (NTB, SmCTB, HexI), even if the molecules are achiral. It will be useful to give , e.g. in SI, the exact experimental conditions of the flexoelectric experiment, as a guideline for further studies.

Ivan Dozov
Reviewer #3 (Remarks to the Author): The manuscript "Heliconical smectic phases formed by achiral molecules " by Abberley et al., reports the observation of a heliconical smectic phase with an extraordinary small pitch. The paper is well written and provides an essential contribution to the understanding of novel materials exhibiting self-assembled helical structures on a nano-scale. Some minor points about the text: -The introduction could be a bit enhanced by discussing of spontaneously assembled helical structures in the broader perspective of the soft matter.
-Considering the variety of phase behaviour of the liquid crystals with N-Ntb-Smectic transition, the authors could also mention the formation of undulated smectic phases as described in Sebastian et al., PCCP, DOI: 10.1039/c6cp03899a and a similar discussion of a possible smectic-twist-bend structure by Tamba et al. in RSC Adv., DOI: 10.1039/c4ra14669g.
-Why do the authors claim that the smectic-C phase is the twist-bend type? Why isn't different from a helical SmC*? Is there particular experimental evidence?
-Are the Smectic-A phases of de-Vriese type?
Apart from that, I find the paper very interesting, accurately written. I suggest publication it in Nature Communications.
We thank the referees for their very favourable comments. Our responses to their specific comments are:

Reviewer #1 (Remarks to the Author):
1) Minor comment: the domains in fig S6 are very hard to see. Could the grey scale be adjusted?
The contrast and brightness of Fig. S6 have been adjusted as suggested, and now the chiral domains are more visible

Reviewer #2 (Remarks to the Author):
Minor remarks and suggestions: 1) The chiral symmetry breaking in liquid crystal phases was first reported in two seminal papers of H. Takezoe group concerning the smectic phases of bent-core molecules (Niori et al., J. Mater. Chem., 6 (1996) 1231Sekine et al., Jpn. J. Appl. Phys., 36 (1997) 6455). I think that these papers should be cited and more detailed arguments should be given to prove that the SmCTB phase is different from the already reported phases.
In the Niori et al paper cited by referee, the ferroelectric properties of bent core mesogens were described for the first time but chiral symmetry breaking is not specifically mentioned in this article. The chiral properties (helical structure) of achiral bent core mesogens (B4 phase) were described by the same Tokyo group a year later, and therefore we have decided to cite the Sekine et al paper in the introduction (new reference 1) as suggested by the referee.
2) By the way, I speculated in Ref.
[4] that the elastic instability proposed for the NTB phase may also be involved in the chiral symmetry breaking in smectic phases of bent-shaped molecules, as an alternative to the polar in-layer interactions ("the nematic elasticity can give rise to a similar symmetry breaking, even in apolar banana smectics"). Also, I suggested that the NTB may be preempted by a smectic phase due to the similar scale of the NTB and smectic pitches ("It is also possible that a nematic-to-smectic transition precedes the sign change of K3, induced by the coupling of the director spatial modulation with the smectic mass density wave."). In my knowledge, the present work gives the first experimental evidence supporting these speculations.
We have added a statement that Dozov raised the possibility of the formation of helical smectic phases by achiral bent-core molecules ( reference 5).
3) The discussion of the optical properties may be improved, by giving more details about the observation geometry and by more precise analysis of the observations. For example, the fact that no rotatory power (or optical activity in other terms) has been detected in the NTB and SmCTB phases does not imply that "the size of the chiral domains in these phases is smaller than the optical wavelength.". Indeed, the optical activity here is not of molecular origin, it is structural (also called "extrinsic"). As in a cholesteric with small pitch, P << λ, the rotatory power decreases as P3: therefore, for so small pitch it will be undetectable. The real question is: why it is observed in the even shorter-pitch HexI phase? The answer is simple: as in this phase the pitch is about 2.2 layers, the optical axis rotates azimuthally at about 160° from layer to layer; optically, this is equivalent to rotation of the optical axis at -20° ; then, the optical period of the structure is 18 layers, and the rotatory power is about 100 times larger than in the NTB or SmCTB. For the CD the situation is exactly the same -it is extrinsic, not due to the molecular chirality (for the N* phase see, e.g., F.D. Saeva, J.J. Wysocki, JACS, 93 (1971) 5928). In fact, the CD is an exact analog of the rotatory power, with the imaginary part of the dielectric tensor replacing the real one.
In our opinion the chiral optical effects are not related to the helical structure. Even if the helical pitch length is 18 smectic layers in the HexI phase, the ORP should be negligible because the pitch (~90 nm) is much shorter than the wavelength of the visible light. Therefore we believe the mechanism of OA could be similar to that in the B4 phase, i.e. the 'layer chirality'. This effect is related to the strongly hindered rotation of non-rod-like molecules. However, we would rather avoid further speculation as this hypothesis still requires additional verification.

4)
In several places in the optical discussions there are some conclusions, not fully supported by the observations. For example, the statement "This optical uniaxiality (of the SmCTB phase) is inconsistent with a simple synclinic or anticlinic SmC phase structure, and indicates that averaging of molecular orientation must take place through the formation of a helioconical structure" disregards the possibility of a synclinic or anticlinic chiral SmC phases, as those observed in banana-like smectics.
On this matter we disagree with the referee. Synclinic or anticlinic SmC phases consisting of not only rod-like molecules but also banana-like molecules are in general biaxial. Only for a very special tilt angle and/or molecular bend, might the phase become uniaxial (for example, the orthoconic SmCA phase).
5) The absence of a flexoelectric response is surprising, as in the right geometry it is a symmetry-defined property (see C. Meyer et al., PRL 111, 067801 (2013)) and should exist in any twisted structure (NTB, SmCTB, HexI), even if the molecules are achiral. It will be useful to give , e.g. in SI, the exact experimental conditions of the flexoelectric experiment, as a guideline for further studies.
The set-up for the flexoelectric measurements was a conventional one, and the experimental conditions have been added to the SI as requested by the referee.