Coexistence of Two Aggregation Modes in Exotic Liquid-Crystalline Superstructure:Systematic Maximum Entropy Analysis for Cubic Mesogen,1,2-Bis(4′-n-alkoxybenzoyl)hydrazine [BABH(n)]

Kazumi Ozawa,† Yasuhisa Yamamura,† Syuma Yasuzuka,† Hiroyuki Mori,‡Shoichi Kutsumizu,‡ and Kazuya Saito*,†

Department of Chemistry, Graduate School of Pure and Applied Sciences, UniVersity of Tsukuba, Tsukuba,Ibaraki 305-8571, Japan, and Department of Chemistry, Faculty of Engineering, Gifu UniVersity,1-1 Yanagido, Gifu 501-1193, Japan

ReceiVed: July 22, 2008; ReVised Manuscript ReceiVed: August 28, 2008

Structure of a complex superstructure self-organized by thermotropic mesogen, 1,2-bis(4′-n-alkoxybenzoyl)-hydrazine [BABH(n), where n is the number of carbon atoms in an alkoxy chain] was studied while payingspecial attention to the structure at the molecular level. Maximum entropy (MEM) analysis revealed that themolecular cores form two kinds of aggregates: Jungle gym with 3-fold junctions roughly on P minimal surfaceand spherical shells.

Self-organization is one of the key concepts in the currentsupramolecular approach in materials chemistry. The simplestorder brought by it is normal crystalline and/or liquid crystallinein the case of anisotropic molecules. The present authors recentlypointed out theoretically the possible formation of highlycomplicated superstructures (space groups Ia3d and Im3m) bysimple, rod-like molecules on cooling from the isotropic liquidstate.1 Experimentally, our previous study has revealed thatcalamitic mesogens, 1,2-bis(4′-n-alkoxybenzoyl)hydrazine[BABH(n), n is the number of carbon atoms in an alkoxy chain]2

and 4′-n-alkoxy-3′-nitrobiphenyl-4-carboxylic acid [ANBC(n)]3

exhibit two peculiar liquid crystalline phases with cubicsymmetry (Ia3d and Im3m) depending on n and temperature.The unit cell of the thermotropic cubic phases contains severalhundred to a few thousand molecules. The space group of theIa3d phase is common to cubic phases with Ia3d symmetry inmicrophase-separated systems such as block copolymers andlyotropic liquid crystals. Nowadays, the basic structure of theseIa3d phases is believed to have a close connection with Gyroid,a triply periodic minimal surface (TPMS) shown in Figure 1.4

On the other hand, the Im3m phase has not been reported inpolymers and lyotropic liquid crystals. In case of BABH(n),the Im3m phase appears for 13 e n e 16 (with the latticeconstant ca. 12-13 nm), outside of which the Ia3d phase does.2

The present letter reports the structure of the Im3m phase ofBABH(n) at the molecular level.

To reveal the aggregation mode of molecules, the identifica-tion of the characteristic surface (such as flat one in lamellarphase or Gyroid in Ia3d phase) is sufficient for the microphase-separated systems because the composition dependence offersthe information on the component forming the surface (inter-face). This is, however, not the case for thermotropic systems.Moreover, there is another issue encountered by the thermotropic

systems. Although X-ray and/or neutron diffraction is widelyused to clarify the structure having periodicity, the diffractionintensities are only related to the contrast of scatterer (electronor nucleus) density. For example, the electron density reflectingthe location of molecules is reconstructed only if the phases ofdiffracted X-ray are known. This is not so severe an issue foran ordered system such as normal crystals consisting of low-molecular-mass molecules but becomes a truly severe one inhighly disordered systems with smeared electron density likeliquid crystals. This issue has recently been considered for theIa3d phase of BABH(n) by the present authors.5 Though ideallythe thickness of the Gyroid surface is zero, it is finite in realsystems. Garstecki and Hołyst6 showed that the relative intensi-ties of diffractions depend on the thickness of the decoratedGyroid. Although the same diffraction pattern is obtainedregardless of the decorating component being chain or core(Babinet’s principle), the examination of the chain lengthdependence enables the identification of the average locationof molecules, because the chain length certainly parallels with

* Corresponding author. E-mail address: kazuya@chem.tsukuba.ac.jp.† University of Tsukuba.‡ Gifu University.

Figure 1. Gyroid (smooth surface) and two interwoven jungle gyms(pink and blue) in a unit cell of the Ia3d phase.

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the volume of the electron deficient part. Indeed, the analysisof the chain length dependence successfully revealed that theterminal methyl groups form Gyroid whereas the molecularcores are located along two interwoven jungle gyms spreadingover the whole system.5

The structure of the Im3m phase was a long-standingproblem.7 In 2002, two of the present authors (KS and SK)independently suggested the same structure on the basis oftotally different reasonings.8 The proposed structure (seen inFigure 2a) is related to, but different from, the familiar periodicstructure with Im3m symmetry, characterized by a TPMS calledSchwarz P surface. The proposed structure, originally proposedfor lyotropic systems,9 involves two P-like surfaces, whichdivide space into three. Because the BABH(n) molecule consistsof two long alkyl chains at both ends and a rather rigid core atthe center, the critical issue on its structure is then translatedinto “core on PP” structure or “chain on PP” structure. In theformer, the cores are on doubled P-like surfaces (Figure 2a)and the chains are on the P surface and on a rectangular junglegym (Figure 2b). The cores and chains exchange their positionsin the “chain on PP” structure.

The attempt to see the structure of the Im3m phase at themolecular level has recently been reported by Zeng et al.10 Theyperformed the small-angle X-ray diffraction (XRD) measure-ments and conventional Fourier synthesis. The phases (sign inreality by virtue of inversion symmetry of the system) of maindiffraction peaks were determined rather arbitrarily by trial anderror. The resultant real space structure is, roughly speaking,compatible with the doubled P structure mentioned above.

In this study, to reveal the aggregation structure at themolecular level while fully taking into account the theoretical

achievement on the stability of the Im3m phases,1 laboratoryX-ray diffraction measurements were performed on BABH(n)(13 e n e 16) around 420 K. We used maximum entropymethod (MEM) to reconstruct the electron density, because theMEM offers the superior spatial resolution compared toconventional Fourier synthesis while not giving unphysical(negative) electron density. Although the MEM can derive themost probable conclusion in terms of information entropy,11 thesituation here is different from the common use of the MEM:Usually it is used for already-solved structures with establishedphases of all diffractions. In this study, therefore, the MEMalgorithm was modified to use the phase information only fortwo prominent reflections [{321} and {400}] while taking onlyintensities into analysis for others [8 diffractions in BABH(15)and less for others].

MEM analyses starting from flat electron density as the initialguess successfully converged in all (four) combinations of signsfor the two diffractions. Consistent and systematic results ofthe analyses imply their reliability. According to our theoreticalanalysis on the formation mechanism of the Im3m phase,1 twomain components of density fluctuations [specified by wavevec-tors {321} and {400}] should have the same sign because onlyin that case does the third-order term in the free-energyexpansion stabilize the structure. This fact allows us to examineonly two combinations of (-, -) and (+, +) as candidates forthe correct combination of the signs of structure factors {321}and {400} in the MEM analysis. The results adopting thosetwo combinations revealed that the volume fraction of the regionwith higher electron density than the average is, for all n, lessthan 0.50 assuming the (-, -) combination whereas it remainsca. 0.52 in the (+, +) combination. Considering the molecular

Figure 2. Unit cell of complementary models of the Im3m phase of BABH(n) and ANBC(n).

Figure 3. (a) Electron density (low to high with transparent f blue f green f orange) and (b) region of high electron density consisting ofmolecular cores in a unit cell of the Im3m phase of BABH(15).

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structure, the higher density region should be less than half, asthe central part has a higher electron density than the alkyl chain.

The electron density reconstructed by adopting the (-, -)combination is shown in Figure 3a for BABH(15). The spatiallocation of the high-density region should reflect the arrange-ment of the central core parts of the molecules. Interestingly,the region (shown in Figure 3b) separates into two: A junglegym having only 3-fold junctions and spherical shells. A junglegym spreads over the whole system. Its location is close to, butslightly deviates from, the P surface (shown in Figure 2b as acontinuous surface). The spherical shells are located on thecorners and the body-center with a low-density inner region inthe unit cell. No connecting rods can be recognized betweenshells in the electron density map. In this respect, the structureis similar to, but different from, the “chain on PP” structure.8

The previous analysis on the Ia3d phases of BABH(n)5

reached the following important conclusions: The cores ag-gregate into two interwoven jungle gyms with 3-fold junctions(Figure 1) for 5 e n e 22 with an intermission by the regionof the Im3m phase. Besides, the region of the Im3m phase seemsto correspond to the quasi-equal volumes of the chain and core,where the lamellar structure with sheet-like aggregates ispredicted by continuum theories.12 The present result has clearlyrevealed that the Im3m phase has similarities with both the Ia3dphase and the lamellar phase: Spreading jungle gym with 3-foldjunctions and sheet-like aggregate (though closed on a sphere).Namely, two aggregation modes coexist in the Im3m phase. Inthis context, the following issues emerge for further study: Domolecules in two regions dynamically exchange their positions?What are the roles of molecular core, alkyl chains and theirbonding? Especially, does the similarity to triblock copolymer(A-B-A) have any effects on the phase behavior and structure?

Finally, a comment should be put on the previous structureanalysis of the Im3m phase.10 The electron density deduced hereresembles that by Zeng et al.10 The reader may be inclined tothink that the conclusion reached in this letter is, at most,equivalent to that. It is, however, not so. They assumed ad hocthat the molecular cores form rods (jungle gyms). On the otherhand, in this letter, the location of the cores is determined fromthe MEM analyses adopting the correct combination of the signsof structure factors by considering the phase stability.1 Thesystematic study on a series of mesogens with different chain

lengths is the key to conclude the location of the molecularcores with sound certainty, as shown in a previous paper.5

Acknowledgment. This work was partly supported by aGrant-in-Aid for Scientific Research on Priority Area “Non-Equilibrium Soft Matter” (No. 463/19031002) from the Ministryof Education, Culture, Sports, Science and Technology, Japan(MEXT) (to K.S.), a Grant-in-Aid for Scientific Research (C)18550121 from Japan Society for the Promotion of Science andby a Grant-in-Aid for Scientific Research on Priority Area“Super-Hierarchical Structures” (No. 446/19022012) from MEXT(both to S.K.).

Supporting Information Available: Experimental details(including input data for MEM analyses), computational detailsfor the MEM analyses, and figures illustrating electron densities.This material is available free of charge via the Internet at http://pubs.acs.org.

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