Navailles, Barois, and Nguyen reply

Abstract

Navallles, Barols, and Nguyen Reply: Our Letter [1] was devoted to an x-ray diffraction study of a well aligned sample of the newly discovered twist grain boundary smectic-C (TGBC) phase. We reported the observation of a q-fold modulated ring of scattering in the plane q»q, perpendicular to the helical axis with q =16, 18, or 20. %e interpreted this observation as the discovery of the commensurate TGB structure predicted by Renn and Lubensky [2]. Similar experiments on TGB~samples by Srajer et al. [3] and ourselves on other homologs of the same series (10and ] ]F2BTFOIM7) always showed uniform rings of scattering which we interpreted as incommensurate states.Two origins can be invoked to explain the observed commensurability.1. The finite thickness of the cell (-25 pm) contains a limited number n of helical pitches (from 12 to 25 on increasing temperature) and a limited number ns of smectic slabs (of order 16 to 20 times n). The structure is thus commensurate by construction with a rational commensurability ratio nb/n of order qo, the natural irrational value. This is well described by Galerne and we agree totally on this point.2. The possible existence of long range interaction of the smectic slabs favoring a commensurate lock-in of the structure. Unlike the previous one, this commensurability is intrinsic and would survive infinite sample thickness.The origin of such an interaction is indeed unclear to us: We pointed out in our Letter that the ferroelectric polarization of the smectic slabs of the TGBC material might play a role. But this possibility has not been demonstrated yet. Let us emphasize in this case that the finite thickness effect is always present and may compete with intrinsic commensurability.Galerne's Comment [4] suggests that the first effect alone can explain our observations. The best reply would obviously be a new experiment with free boundaries which would keep showing the commensurability. This is unfortunately not possible since rigid boundary conditions are required to align the sample. Increasing the thickness also destroys the quality of the alignment.Let us see, however, if the data of our Letter can be consistent with the interpretation of the Comment.We recall first that scattering patterns exhibiting well defined rings of spots were recorded at all temperatures within the TGBC domain: The 32 data points of Fig. 3 of Ref.[1] come from scattering patterns very similar to Fig. 1(b) [1]. Basically the contrast did not change very much with temperature and uniform rings (i.e. , incommensuratelike) were never observed. Galerne's interpretation produces successions of commensurate and incommensurate patterns unless several values of n and nb coexist in the sample at a given temperature. In this latter case, commensurate zones are always present and the contrast does not deviate very much from an average value calculated over all possible values of n and nb. Such a distribution of values is actually quite acceptable and consistent with experimental observations under a polarizing micros...

The commensurate and incommensurate TGBC^* liquid crystal phases

“…In this case of the normal TGBC phase, however, such a result is very surprising, and to-date, only extrinsic arguments, implying external interactions from the sample plates, have been proposed to explain it [5]. Considering that the two phases, the TGBC and TGBC * phases, could rather be resembling to each other from the X-ray point of view, one may therefore wonder if some confusion could arise between them, and if the commensurability reported in reference [10] really concerned the TGBC phase instead of the TGBC * one. At least, it seems that such a possibility should not be discarded too fast, all the more as the domain of existence of the TGBC phase could appear to be limited in terms of the chirality parameter −A /B (the chirality has to be strong enough to produce the TGB structure on the one hand, but not too much, on the other hand, to avoid the TGBC* phases, which are stabler at the large −A /B values, see Fig.…”

“…The commensurability, equivalent to π/χ 0 being an integer number, should then be marked by the observation of 2χ 0 Bragg spots in the X-ray scattering ω-scans performed on uniformly oriented TGBC * samples. The experiment could be similar as already performed in the normal TGBC phase [10], where π/χ 0 has precisely been found to be an integer number. In this case of the normal TGBC phase, however, such a result is very surprising, and to-date, only extrinsic arguments, implying external interactions from the sample plates, have been proposed to explain it [5].…”

“…that 2l H /Λ = χ 1 /π is an irrational number, the associated δϕ distortions have different Z-orientations, and do not interfere. They just add up their energies which on the average, keep the same expression as (10).…”

“…In this manner, the molecules keep parallel to the twist grain boundaries [9]. Meanwhile, the TGBC phase is reported to be a commensurate phase, with the ratio of the TGB helical pitch over the smectic block thickness, Λ/l b , being an integer [10]. However, the intrinsic nature of the TGBC commensurability is still an open question, since to-date no physical mechanism has been proposed to explain the observations, except the trivial anchoring effect of the smectic layers onto the glass plates of the sample [5].…”

X-ray studies of the phases and phase transitions of liquid crystals

“…Historically, X-ray measurements on oriented samples were made on the TGBC phase before the TGBA phase. On cooling the sample from the N Ã phase into the TGBC phase, the continuous ring of scattering from shortrange smectic correlations is seen to become strongly modulated in intensity (Navailles et al, 1993). The period of the modulation varies discontinuously on cooling.…”