Crystallography and molecular arrangement of polymorphic

Article Cite This: Langmuir XXXX, XXX, XXX−XXX

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Crystallography and Molecular Arrangement of Polymorphic Monolayer J‑Aggregates of a Cyanine Dye: Multiangle Polarized Light Fluorescence Optical Microscopy Study Valery V. Prokhorov,* Sergey I. Pozin, Olga M. Perelygina, and Eugene I. Mal’tsev A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, RAS, Leninsky Prospect 31, Moscow 199071, Russia ABSTRACT: The molecular orientation in monolayer J-aggregates of 3,3-di(γ-sulfopropyl)5,5-dichlorotiamonomethinecyanine dye has been precisely estimated using improved linear polarization measurements in the fluorescence microscope in which a multiangle set of polarization data is obtained using sample rotation. The estimated molecular orientation supplemented with the previously established crystallographic constraints based on the analysis of the well-developed two-dimensional J-aggregate shapes unambiguously indicate the staircase type of molecular arrangement for striplike J-aggregates with the staircases oriented along strips. The molecular transition dipoles are inclined at an angle of ∼25° to the strip direction, whereas the characteristic strip vertex angle ∼45° is formed by the [100] and [1− 10] directions of the monoclinic unit cell. Measurements of the geometry of partially unwound tubes and their polarization properties support the model of tube formation by close-packed helical winding of flexible monolayer strips. In the tubes, the long molecular axes are oriented at a small angle in the range of 5−15° to the normal to the tube axis providing low bending energy. At a nanoscale, high-resolution atomic force microscopy imaging of J-aggregate monolayers reveals a complex quasi-one-dimensional organization.

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INTRODUCTION

The noncovalent molecular π-stacking interaction of a large conjugated π-electron system in cyanine dyes promotes selfassembly in water solutions into supramolecular structures, the so-called J-aggregates, which exhibits unusual optical properties, that is, the nearly resonant fluorescence (very small Stokes shift) and characteristic narrow and intense visible absorption band shifted toward longer wavelengths compared with that of the monomers.1−4 Remarkable optical and transport properties of molecular aggregates have led to a variety of optoelectronic applications.5 J-aggregates were used as light-emitting and charge-transport dopants to electron−hole conducting polymer layers,6−8 in biosensing,9 as materials for nonlinear optical applications, 10 efficient reversible light-driven optical switches,11 single-mode optical waveguides,12 and as components of hybrid nanostructures consisting of dye molecules and semiconducting nanocrystals.13,14 Excited states in a single conjugated polymer chain with stacked coupled chromophores are also commonly considered in terms of excitons, and strong photophysical similarities are noted between emissive conjugated polymers and linear J-aggregates.15−19 The bathochromic (red) shift of the absorption band and charge transport properties in J-aggregates are excitonic in nature and are strongly determined by the molecular arrangement at the nanoscale, particularly by the (large) lateral translation (slippage) of the transition dipoles of the adjacently stacked dye. For planar chromophore conformations of dye molecules achieved in monolayers, the large lateral slippage is realized in the one-dimensional (staircase and ladder), two-dimensional (brickwork), and two-strap herringbone20,21 models (Figure 1), © XXXX American Chemical Society

Figure 1. Staircase (a), ladder (b), brickwork (c), and herringbone (d) molecular arrangements of dye molecules in J-aggregates: sslippage distance, αslip angle. Molecular planes are normal to the figure plain and heterocycles are denoted by green.

which are regarded as basic models for possible molecular packing arrangements in J-aggregates.1 At the mesoscale, depending on dye concentrations and solution conditions, Jaggregates of cyanine dyes manifest a complex morphological and structural variability observed by various microscopic techniques such as fluorescence optical microscopy (FOM),22,23 cryogenic transmission electron microscopy,24−27 and atomic force microscopy (AFM).22,23,26,28−31 The Jaggregate polymorphous structures can be roughly subdivided into two large classes of two-dimensional monolayer-based polygonal sheets or giant tubes22,23,25,28,29,31 and quasi-onedimensional fibrils or tubules with a small diameter in the nanometer range.24−27,30 Molecular models of J-aggregates Received: March 27, 2018 Published: March 30, 2018 A

DOI: 10.1021/acs.langmuir.8b01008 Langmuir XXXX, XXX, XXX−XXX

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Langmuir typically imply the planar conformation of dye molecules promoting the slipped face-to-face columnar stacking arrangement in monolayers (both flat and wrapped in nanotubes).27,31 The nonplanar molecular conformation with twisted πconjugated core naturally explaining the axial periodicity observed in twisted J-aggregate fibrils has also been considered.32 It is noteworthy that despite decades of study, choosing between different models of the molecular arrangement is difficult even in the structurally simpler monolayer case. Direct crystallographic information on the parameters and the symmetry of the elementary cell is derived from X-ray diffraction analysis of three-dimensional dye monocrystals or powder samples and not for J-aggregates floating in a solution with the crystal structure depending on solvents and counterions.33 With a deficit of crystallographic data at the nanoscale, the standard crystallographic approach based on the analysis of crystal habits, that is, the geometry of external shapes of individual crystals can be informative and useful. Being in the routine for three-dimensional minerals, it has not been used up to now for the study of two-dimensional J-aggregate crystals. It was first demonstrated for the monolayer J-aggregates of the cyanine dye that the fixed angle in the vertices of the welldeveloped two-dimensional polygons is the angle between low Miller-index crystallographic planes.31 However, crystallographic analysis is generally ambiguous.31 To resolve the ambiguity, supplementary information is necessary, which could be obtained from polarized light microscopy sensitive to the orientation of the molecular transition dipole. However, standard microscopic linear polarization measurements with a light polarized in two crossed directions are intrinsically inaccurate (and also ambiguous) and allow drawing only qualitative conclusions about the molecular dipole orientation.23 Much better accuracy can be obtained using a more elaborate experimental approach in which the set of polarization data is obtained under continuous rotation of the polarizer and/or analyzer.34−37 However, such measurements using a standard fluorescence microscope are accompanied by a large distortion of the polarization state of the incident light in the microscope optics, which must be taken into account.35,36 In the present study, we used an experimentally simpler realization of the multiangle polarization measurements, which is free from the polarization distortion artifacts. For the microscopic images of two J-aggregate polymorphs of a cyanine dye (i.e., monolayer strips and tubes with a monolayer wall), we analyzed the fluorescence intensity excited by the (undistorted) linear polarized light depending on the rotation angle of the Jaggregate sample mounted under the fluorescence microscope objective. Combined with the crystallographic consideration, the polarization data allowed specifying the staircase structural model in the J-aggregate monolayer and also established the orientation of the transition dipoles of dye molecules and the elementary cell in the two J-aggregate polymorphs.

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Figure 2. (a) Schematic drawing of a single TC molecule with the heterocycles denoted by light green. (b) Absorption spectra (optical path 1 mm) of the TC solution (c = 140 μM in 5 mM ammonium acetate) at 70 °C (red) and 20 °C (blue) and the fluorescence spectrum at 20 °C (green). (c) Comparison of the TC absorption (10 mm optical path) and fluorescence in the monomer form in methanol (light blue and green curves) and in the J-aggregate form in 200 mM ammonium acetate aqueous solution (intense blue and green curves). The TC concentration in both solutions is 5 μM. Excitation was at the absorption maxima (425 and 465 nm). ammonium acetate) was then added to stimulate J-aggregation. The early aggregation stages with a dimension of J-aggregates below the optical resolution limit were followed spectroscopically by monitoring the rapidly growing narrow J-band (Figure 2b) and by AFM observations.31 The J-aggregate growth conditions (the dye and salt concentration and the growth time) are given in captions to figures. The geometric shapes of giant J-aggregates formed in the late evolution stages can be well-characterized by FOM observations both in a solution drop and on dry samples. To prepare the dry samples for FOM and AFM measurements (Figures 4 and 7), the TC J-aggregate solution was applied on a freshly cleaved mica surface for a time within several minutes in dependence on the TC concentration, and the excess solution was then removed by blotting and subsequent drying in a nitrogen gas flow. In the alternative experimental protocol, giant monolayer J-aggregates morphologically identical to those formed in the solution bulk were rapidly grown directly on the mica surface (Figure 5a). The advantage of the surface-induced growth is that it can proceed at dye concentrations below the threshold of J-aggregation in a solution (∼50 μM in water), and the dye threshold concentration can be additionally highly reduced by the addition of multivalent cations.31 FOM Measurements. The FOM measurements were performed on a Meiji MT6000 epifluorescence laboratory microscope (Japan) with the blue excitation filter at 470 nm (40 nm spectral width) and an emission filter at 515 nm. Dry samples were observed with

EXPERIMENTAL SECTION

Chemicals and Samples Preparation. Figure 2 shows the chemical structure of the 3,3-di(γ-sulfopropyl)-5,5-dichlorotiamonomethinecyanine (TC) molecule (Figure 2a) and the absorption and fluorescence spectra of nonaggregated and aggregated TC solutions (Figure 2b,c). Samples were prepared similar to the protocol described in ref 31. For the J-aggregate growth, the aqueous TC stock solution was heated to ∼80 °C to reach monomeric and dimeric states (no molecular aggregates) and cooled to the room temperature. An appropriate amount of a salt solution (sodium bicarbonate or B


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the image in Figure 3b) which was sine-fitted (red curve in the Fl(φn) plot in Figure 3c). The transition dipole direction (yellow line in Figure 3b) corresponds to the sine maximum φ*, and the transition dipole tilt (θ) with respect to the J-aggregate long axis was then calculated.

magnifications of 20×, 40×, and 60×. For in situ optical observations, a 1 μL drop of TC J-aggregates was placed directly under the microscope objective at magnifications of 20×, and single images or videos were captured. Multiangle Polarized Light Fluorescence Optical Microscopy Measurements. The experimental setup for multiangle polarized light FOM (MPLFOM) based on the Meiji MT6000 epifluorescence microscope is shown in Figure 3a. The linear polarizer (LP) was fixed

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RESULTS AND DISCUSSION General Characterization of TC J-Aggregate Polymorphism. For the TC dye, flexible monolayer strings and rigid rods (suggested to be tubules) have been previously observed as two polymorphic J-aggregate states by in situ FOM.22,23 Moreover, a slow morphological transformation (taking days) of string to rods has been reported.22,23 The string-to-rod transformation was speculated to be a dissolutiongrowth process in which metastable strings dissolve prior to forming tubes, which were supposed to have a different molecular arrangement. We showed the tubular structure of rods by direct in situ observations of their reorientation in a solution drop.31 In addition, several morphological arguments have been found in the FOM and AFM imaging that unambiguously indicate that the tubes were formed by the mechanism of a close-packed helical winding of flexible monolayer strips (“strings” in the terminology used in refs 22 and 23). This structural finding implies that the underlying monolayer structure and its nanoscale organization is the same for both TC J-aggregate polymorphs, in contrast to the consideration in ref 23. The characteristic time scale of strip-totube transformation is highly dependent on the salt conditions and strip width and varies in a wide range from minutes to days. Figure 4 shows an FOM image in unpolarized light of a dried sample of both TC J-aggregate polymorphs, that is, strips (S)

Figure 3. (a) Experimental setup for the fluorescence polarized light multiangle measurements with the fluorescence optical microscope and the rotated sample. The polarization plane of the linear polarized excitation light (blue double-headed arrow) is set either vertical or horizontal. (b,c) Scheme of determining the transition dipole orientation θ in a J-aggregate from the sine fluorescence angular dependence Fl(φ) on the sample rotation angle φ. in one of the two possible positions which preserve the polarization state of the linear polarized excitation light on the pathway to the sample (i.e., with the polarization plane set either vertical or horizontal), whereas the sample with J-aggregates was rotated under the microscope objective. For this, we constructed a rotation stage that allowed manual rotation of the sample through an arbitrary angle with an accuracy of ∼1°. The lateral position of the rotation stage was adjusted so that its optical axis was in the center of the image. We note that the alternative configuration with a rotated LP and a fixed sample, which is experimentally more convenient, fails because of the large distortion of the polarization state of the incident linear polarized light. The main source of these distortions and concomitant large artifacts is the reflection of the linear polarized light from the 45° dichroic mirror plane (Figure 3a), inducing both the (angle-dependent) rotation of the polarization plane and a notable ellipticity. As a result, the angular dependence of the fluorescence intensity deviates significantly from the simple Malus’s law periodic sine dependence, leading to large systematic angular errors in the calculated transition dipole directions which can be taken into account only by complex recalculations (see the Supporting Information in ref 35). The scheme of measurements of transition dipole orientation in J-aggregates is shown in Figure 3b. During the polarization measurements, the sample stage was rotated with a discrete step of 30°, 45°, or 60°, and the set of J-aggregate images in the range of 0−360° was captured. We then determined the angular dependence of the fluorescence intensity Fl(φn) for the selected area of any chosen J-aggregate (shown by the white circle in

Figure 4. Unpolarized FOM image of polymorphous TC J-aggregates adsorbed from a solution on a mica surface: Sflexible monolayer oblique strips with the angle in the vertices close to 45° and T flattened tubes transformed to bilayer rectangles. The image size is 160 μm. J-aggregate growth conditions: c = 0.2 mM in 9 mM NaHCO3, t = 1 h.

and tubes (T), which were formed in a solution and deposited on mica and dried. Some flexible strips are self-folded at the adsorption on the surface (the axes of self-folding are shown by dashed white lines). Rigid tubes of various diameters in the range of ∼1−10 μm are flattened to almost rectangular bilayer rods. The bilayer structure of the rods results in their brightness being about twice as large as the brightness of the monolayer strips, as can be seen in Figure 4. Generally, under the action of strong adhesive forces induced by the interaction with a surface, the tubes can undergo much more complex structural rearrangements (than simple flattening to rectangular rods) with unwinding and peeling of monolayer walls and formation C


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Figure 5. Determination of the orientation of transition dipoles in TC strips from MPLFOM measurements of the rotated sample. (a) FLPOM (back-rotated) images of surface-grown TC strips obtained with the unpolarized fluorescence excitation light (a0) and the linear polarized light along the directions 0°, 120°, and 240° shown by blue double-headed arrows (a1−a3). (b) Angular dependences of the fluorescence intensity for Jaggregates 1 to 4 in (a): the yellow lines in (a) show the calculated orientation of transition dipoles. (c) Histogram of the distribution of transition dipoles tilt angle θ for n = 52 strips. J-aggregate growth conditions on a mica surface: c = 0.02 mM in 0.03 mM EuCl3 and t = 5 min.

of characteristic zigzags.31 Precise AFM height measurements reveal the bilayer thickness for flattened tubes (see the profile in Figure 9a1 below) and monolayer thickness for the strips with the particular value for the monolayer thickness of ∼1.30−1.40 nm corresponding to the symmetric monolayer, that is, sulfopropyl chains of dye monomers in an all-trans conformation occupy both its sides.28,31 The crystallographically important feature of TC strips formed in a solution (Figure 4) and grown directly on a mica surface (Figure 5) is their asymmetric shape with the oblique ends fixed at the vertices with a single skew angle close to 45°. This intrinsic crystal habit has been consistently explained by two models of the molecular arrangement with the same staircase stacking of dye molecules and different staircase orientations with respect to the strip sides, that is, along the long or short sides of the strips.31 The correct structural model can be selected by a precise estimation of the molecular dipole direction (different for these two models) from PLFOM measurements, which we present below. MPLFOM of Monolayer TC Strips. Figure 5a shows the fluorescence microscopic image of the monolayer skew TC Jaggregate strips captured with the unpolarized (a0) and the linear polarized excitation light at three orientation of the polarization plane (a1−a3). The plots in Figure 5b show the particular angular F(φ) dependences of the fluorescence intensity for J-aggregates 1 to 4 in Figure 5a, which were used at the calculation of the orientation of transition dipoles in strips (shown by yellow lines in Figure 5a). Figure 5c shows a histogram of the distribution of the transition dipole tilt angles obtained by analyzing the PLFOM images in 52 strips captured with angular gaps of 30° (a total of 624 images). Two peaks with opposite signs in Figure 5c correspond to mirrorsymmetric skewed strips, as shown schematically by green insets in Figure 5c. We calculated the transition dipole tilt θ = 24.9 ± 1.2° as half of the distance between peaks in Figure 5c. The advantage of such an estimate is that it is insensitive to the possible error of the polarizer mechanical setup (which can result in a horizontal shift in Figure 5c of both peaks in the same direction while the separation between peaks remains unchanged).

Using samples of surface-grown strips for the PLFOM measurements is advantageous because they have a larger S/N ratio and smaller angular error as a result of less background noise. The same transition dipole tilt with a larger error was obtained for TC strips formed in a solution and then deposited on mica and dried (see Figure 4). We note that the qualitative conclusion on the inclined configuration of transition dipoles in strips can be easily drawn from the comparison of the PLFOM images of mirror-symmetric strips with the same orientation. This particular case is exemplified by two adjacent closely oriented J-aggregates enclosed by the dotted circle in Figure 5a. Staircase Model of the Molecular Arrangement in TC J-Aggregate Monolayer. The obtained transition dipole tilt θ = 24.9 ± 1.2° within the error is equal to the expected acute angle α of the TC monoclinic unit cell estimated from the stacking geometry with the overlapped heterocycles (Figure 6a,b). The estimated value is 26.2° for completely overlapped heterocycles, and the typical stacking distance D = 0.35 nm. A large degree of heterocycles’ overlapping is observed at the computer modeling of the aggregation of theamonomethinecyanine dye in water (predicting the ladderlike structures).38 The elementary unit cell is shown by the parallelogram marked by light yellow in Figure 6b,c; the long [100] side is chosen along the molecular long axis (which is also the transition dipole direction) and the short [010] side is directed along the translation vector connecting the adjacent stacked molecules (which is the slippage vector for the staircase molecular arrangement). The transition dipole inclination of ∼25° in TC strips thus selects the staircase molecular model with the staircases directed along the strips, as shown in Figure 6c. The consensus model of the molecular arrangement in the TC strips that explains both the particular tilt of transition dipoles and their oblique shapes is shown in Figure 6c. In this model, the characteristic angle of ∼45° at the strip vertices is formed by the [010] and the diagonal [1−10] directions of the unit cell (shown by the red line in Figure 6b,c), as it was previously noted from the crystallographic analysis, which adopts two configurations.31 The model in Figure 6c corresponds to the model in Figure 4c in ref 31. The alternative model (Figure 4d in ref 31) with the staircases directed along the short strip side D


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MPLFOM of Flattened Tubular J-Aggregates. The multiangle PLFOM measurements considered above for the oblique monolayer strips were also conducted for the bilayer rods formed by tubes flattened during surface adsorption (Figure 7). The transition dipoles in the upper and lower monolayers correspond to the opposite tube sides and are therefore inclined, forming the angle (β) of the opposite sign with respect to the normal to the tube axis, as shown in Figure 7f, which represents the model of the flattened tube proposed in ref 31. The net transition dipole (θT in Figure 7a) is expected to be directed either along the rod axis (if β > 45°) or normal to it (if β < 45°). The transition dipole inclination β in the tube wall can be found by measuring the variable (Iv) and constant (Ic) components in the sine-interpolated angular dependence of the rod fluorescence intensity I, as shown in Figure 7b I(φ) = I0(cos2(φ + β) + cos2(φ − β))

Figure 6. Staircase organization of TC strips. (a) Staircase arrangement of TC molecules with completely overlapped heterocycles (denoted by light green), (b) unit cell and designations of crystallographic axes. (c) Staircase model of the molecular arrangement in TC strips explaining both the transition dipoles tilt and the characteristic angle of ∼45° in strip vertices.

= I0(1 + cos 2φ cos 2β) r = I v /Ic = |cos(2β)|

where I0 is the maximum monolayer fluorescence intensity and φ is the angle between the tube axis and the polarization plane. The PLFOM measurements demonstrate a strong blackout of the rods for the polarization plane of the excitation light oriented along the rod axis (as observed for the J-aggregate indicated by the dashed circle in Figure 7a1) indicating that the transition dipoles in the tube walls are oriented closer to the tube normal. The experimentally obtained r values were distributed in the range of 0.7−1.0 with a maximum at ∼0.85 (see the histogram in Figure 7c), which corresponds to the variation of the inclination angle β in the range 0−22° with the most probable value of ∼15°. This result can be selfconsistently tested by independently measuring the entrance angle (γ in Figure 7d) formed with respect to the tube normal by oblique strips exiting from the end of some tubes, as shown in Figure 7d (see also the AFM images in Figures 6 and 8 in ref 31). The strip ends have the characteristic oblique angle of ∼45°, implying a molecular arrangement as in Figure 6c and a

is rejected by the MPLFOM data. For the model of TC strips shown in Figure 6c, the π−π electron stacking is achieved only along the one-dimensional molecular rows (staircases), as shown for the bottom molecular row (marked by dark green). We note that arguments from analyzing the symmetry of TC J-aggregates exclude the one-dimensional ladder and twodimensional brickwork alternatives for the molecular arrangement. The low symmetry of the staircase molecular arrangement (Figure 1a) manifests itself in the oblique shapes of monolayer strips, whereas shapes with a higher symmetry (e.g., rectangles or rhombs) are expected for J-aggregates with the more symmetric ladder and brickwork arrangements (Figure 1b,c). We would like to stress that these general important crystallographic arguments have not been taken into consideration up to now on the J-aggregates study.

Figure 7. Determination of the orientation of transition dipoles in TC-squashed tubes from MPLFOM measurements of the rotated sample. Jaggregate growth conditions: c = 0.15 mM in 5 mM NaHCO3, t = 3 days. (a) PLFOM (back-rotated) images of TC-squashed tubes obtained with the unpolarized fluorescence excitation light (a0) and linear polarized along the directions shown by blue lines (a1−a3). (b) Typical angular I(φ) dependence, where I is the fluorescence intensity of the tube and φ is the sample rotation angle. (c) Histogram of the distribution of the ratio of the variable (Iv) and constant (Ic) components [designations are in (b)]. (d) Designation of the strip entrance angle γ in tubes and (e) histogram of the γ distribution. (f) Schematic of the transition dipoles orientation in the squashed tube bilayer with the partially unwounded strip. E


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are observed, but the transition dipoles remain oriented sufficiently close to the tube normal, that is, β = 10−20°. Noteworthy, the monolayer curvature generally induces the curvature-dependent shift in the position of J-bands.39 In our case, this effect is not expected because of the very large radius of curvature of the tube as the tube wall is well-approximated at a molecular scale as a plane. No difference in the position and shape of optical spectra has been observed for strips and tubes. Quasi-One-Dimensional Organization of Monolayer TC Strips at the Nanoscale. Finally, we make important comments on the structure of the J-aggregate monolayer at the nanoscale. The self-consistent complementary results of the strict crystallographic analysis and precise MPLFOM measurements imply the staircase organization of the J-aggregate monolayer at the molecular scale (of adjacent neighbors) which is directly reproduced in the simple oblique geometry of Jaggregate strips at the micron and submicron (meso) scale. Surprisingly, this simplicity vanishes at the intermediate scale of ∼10 nm. High-resolution AFM imaging of TC strips reveals an unexpected inclined fine linear substructure formed by closepacked parallel nanostrips separated by a characteristic large molecular scale distance in the range of 6−10 nm (Figure 9, see

transition dipole orientation as in Figure 7f. In accordance with the geometry in Figure 7f, the tilt of the transition dipoles with respect to the normal to the tube axis is β = α − γ, where α = 25° is the determined above-transition dipole tilt with respect to the long axis of the exiting strip. Measurements of the entrance angle γ yield a distribution in the range of ∼7−30° (Figure 7e), with the most probable value in the relatively narrow range of ∼10−20°. This estimate gives a β distribution in the range of 5−15° in satisfactory quantitative correspondence with the estimates of β from measuring the ratio r. We can finally resume that the transition dipoles in tubes are oriented close to the normal to the tube. Interestingly, a similar J-aggregate wrapping geometry has been reported for 1,1′,3,3′tetraethyl-5,5′,6,6′-tetrachlorobenzimidazolocarbocyanine (TTBC) nanotubes with diameters of only 3.5 nm; in this case, the TTBC molecules were directed strictly normal to the nanotube axis.27 We suggest that this similarity in the structural organization of cylindrical J-aggregates whose diameters differ by orders of magnitude (i.e., the giant tubes for TC and the nanotubes for TTBC) has the following physical justification. In wrapping a highly anisotropic stacked monolayer onto a cylindrical surface, the bending energy depends strongly on the wrapping direction (wrapping vector W in Figure 8). The

Figure 8. Lowest bending energy model of the TC tube with the staircase molecular arrangement. The tube curvature is highly exaggerated.

lowest bending energy is expected if the molecular long axes (and the wrapping vector W) are directed normal to the tube axis (i.e., β = 0), as shown for the model in Figure 8. In this case, no molecular torsion is observed, and the wrapping is reduced to molecular rotations in the plane normal to the tube axis, which is the molecular plane. As a result, the heterocycles of adjacent stacked molecules remain parallel to each other, and the intermolecular (stacking) distance is unchanged (as evident from Figure 8) providing the lowest bending energy in comparison with the β ≠ 0 monolayer deformations. The requirement of the lowest bending energy is especially important for the nanotubes because they have an extremely small radius of curvature and a correspondingly large bending energy (the bending energy surface density ≈ R−2). In this case, the single configuration with a molecular orientation normal to the nanotube axis is expected, as reported in ref 27. For the weakly bent TC giant tubes formed by helical winding of strips,24 the absolute minimum in the bending energy is not achieved for kinetic reasons and the strict requirement β= 0 is not valid. At the close-packed helical winding of the strip over the cylinder, the strip entrance angle γ (distributed as shown in Figure 7e) is determined by the ratio of the strip width S and the tube diameter D: γ = arctan(S/πD),31 where β = α − γ (see Figure 7f). Because of this mechanism, nonzero β inclinations

Figure 9. (a,b) High-resolution AFM imaging of a fine linear substructure of a TC strip self-folded along the axis shown by the white dashed and dotted line. The substructure is inclined with respect to the strip by the angle of ∼27°. Panels (a1,b1) show the height profiles along the green lines a1 and b1, respectively. Sample preparation conditions: c = 0.1 mM in 1.33 mM ammonium acetate solution, adsorption time on mica t = 1 min.

also Figures 5b−d and 6b1 in ref 31). Moreover, a very similar substructure has been observed by AFM for J-aggregates of another cyanine dye29 and by electron microscopy for Haggregates of a carbocyanine dye.40 Figure 9 highlights one more unexpected feature, that is, the nonzero inclination of nanostrips with respect to the long axis of the strip (particular values were in the range of 25−30°). The inclined nanostrips’ orientation seemingly contradicts the expectations of the staircase structural model of strips in Figure 6c; the nanostrips’ F


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direction is expected to be strictly along the strip if one assumes that the nanostrips inherit the staircases’ directions. The origin of such a complex quasi-one-dimensional organization which seem to be intrinsic for two-dimensional stacked monolayers of various dyes is currently unclear and needs a relevant interpretation in future studies. We suggest that it is closely connected with the very first stages of self-assemblage of the large monolayer from small “elementary” building units, which are supposedly the staircases with the length in the range of several nanometers. Noteworthy, the determined linear substructure characteristic spatial inhomogeneity imposes an upper limit on the exciton coherence length and can strongly influence the exciton transport in J-aggregates.

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CONCLUSIONS In summary, the obtained results demonstrate the informativeness of the developed structural approach combining the crystallographic analysis of crystal habits with supplementary precise multiangle fluorescence polarized light microscopy measurements of the transition dipole orientation in twodimensional J-aggregate crystals. Several strict structural conclusions for the strips and tubular J-aggregate polymorphs of the studied cyanine dye have been drawn. The staircase molecular arrangement is consistently implied as a single structural alternative for oblique monolayer strips. The staircases are aligned along strips, and the transition dipoles are inclined by ∼25° to the long strip side, whereas the angle of ∼45° in strip vertices is formed by the [100] and [1−10] directions of the monoclinic unit cell. In addition, the geometry of tubes formed by the mechanism of close-packed helical winding of strips is studied. The orientation of transition dipoles in the tube walls close to the normal to the tube axis is determined by the anisotropy of the monolayer bending energy and the kinetics of tube formation by the cylindrical wrapping of the strips. As a whole, the obtained dye structural results are selfconsistent and reveal the simplicity of J-aggregates’ structure at the basic molecular arrangement level (exclusively staircase arrangement can be accepted) and at the mesoscale (the oblique strip is a single observed polymorph which can be transformed to the tubular shape by a simple helical winding). However, there is an unexpected structural complexity at a scale of ∼10 nm revealed by high-resolution AFM which needs a relevant interpretation in future studies.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Valery V. Prokhorov: 0000-0002-2523-0828 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the grant from the Russian Foundation for Basic Research (project 17-03-01179 A). REFERENCES

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Crystallography and molecular arrangement of polymorphic

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