A systematic study on the influences of linkage length on phase behaviours and charge carrier mobilities of discotic dimers

ABSTRACT Two series of discotic dimers T3Dn and T5Dn based on hexapropoxytriphenylene (HAT3) and hexapentyloxytriphenylene(HAT5), respectively, with polymethylene linkage O(CH2)nO (n = 3–12) have been synthesised. Their mesomorphism was investigated by differential scanning calorimetry, polarising optical microscopy and X-ray diffraction. The results showed that side chains induced a phase transition from colhp phase to colh phase, namely dimers T3Dn (n = 6–12) based on HAT3 exhibiting a single colhp phase, dimers T4Dn (n = 6, 7, 11, 12) based on HAT4 showing a highly ordered colhp phase in low-temperature region and a colh phase in high-temperature region, dimers T4Dn (n = 8–10) based on HAT4 displaying a single colhp phase and dimers T5Dn (n = 6–11) based on HAT5 indicating a single colh phase. Dimers T4Dn showed a phase competition between colh phase and colhp phase induced by linkages. Surprisingly, a unique phenomenon was found by us, that is, those compounds in which linkage lengths were twice those of side chains showed the largest enthalpies, the smallest intracolumnar spacings and the highest charge-carrier mobilities among their homologues, respectively, which implied that they formed the most highly ordered phase among their homologues. Graphical Abstract


Introduction
In the family of organic semiconductors, discotic liquid crystals (LCs) with polycyclic aromatic mesogens attract grown attention for their excellent processability and unique advantages, such as self-healing structural defects and self-assembly nanostructure with remarkable one-dimensional charge-carrier transport properties. Only a minor change in molecular structure can lead to unpredictable influences on phase behaviour and charge-carrier mobility, since the self-assemblies of discotic LCs are closely related to chemical structures, therefore, it is crucial to elucidate the structureproperty relationship in discotic LCs. [1][2][3][4][5][6][7] Discotic LC dimers as an ideal model compound [8,9] for discotic polymers have been extensively studied in terms of benzene, [10] triphenylene, [11,12] anthraquinone [13] and hexabenzocoronene. [14] Derivatives of triphenylene are undeniable work horses of discotic LCs for their easy synthesis and purification, several substitutions on triphenylene rings and rich mesophases. [15,16] The mesophase properties of discotic LC dimers are mainly influenced by chemical structures, such as substituents, substitutional positions and linkages. Herein, let us take triphenylene as an example, the earliest systematic study on HAT6 dimers via changing the length of linkage shows that they as well as their monomer HAT6 exhibit just a col h phase. [17] According to our previous work of dimers based on HAT4, the introduction of flexible linkage leads to dimers exhibiting not just a single col hp phase as their monomer HAT4, some of them showing a transition from col h phase to col hp phase and even forming a new rectangular columnar plastic phase. [18,19] It is very exciting to find that dimer T4D8 with five butyloxy groups on a triphenylene core and linked by O(CH 2 ) 8 O forms the most ordered phase and is of the highest charge-carrier mobility among its homologues in the previous work performed by us. [20] Dating back to the former works, the dimer T5D10 with five pentyloxy groups on a triphenylene core and linked by O(CH 2 ) 10 O [11,21] forms a hexagonal columnar phase with a charge-carrier mobility, which is comparable to its monomer. According to the phenomenon, Zamir et al. [11] suggested a term for this kind of dimer 'perfect twin', in which both the side chains and the linkages are connected to the core by ether bonds and the linkage lengths are exactly twice those of the side chains. We have strong curiosity about the phase behaviours and charge-carrier mobilities of other two series of discotic dimers based on HAT3 and HAT5. If they indicate the perfect twin dimers form the most ordered phase and are of the highest charge-carrier mobility among their corresponding homologues, it would provide a good strategy for discotic LC polymers' synthesis and the functional film forming via in suit polymerisation for electronics devices maintaining high orientation order of the columns as well as the high charge-carrier mobility, which is at least comparable to their corresponding monomers. Thus, it is worthy for us to do an exhaustive study on dimers of HAT3 and HAT5.

Experimental
The synthesis of chemical characterisation of T3Dn and T5Dn including differential scanning calorimetry (DSC) scan and polarising optical microscopy (POM) can be found in the supplementary material.
All solvents employed were purchased from Aldrich used without further purification unless stated otherwise. Column and thin layer chromatography were performed on silica gel 60 (200-300 mesh ASTM) and Silica Gel 60 glass backed sheets, respectively. 1 H NMR spectra were recorded in CDCl 3 on Bruker NMR spectrometers (DMX 300 MHz), chemical shifts are given in parts per million (δ) and are referenced from tetramethylsilane (TMS). Multiplicities of the peaks given as s = singlet, d = doublet, t = triplet and m = multiplet. Fourier transform infrared spectroscopy (FT-IR) was carried out on a shimadzu FTIR-8400 spectrometer using KBr pellets. The high-resolution mass spectrum was recorded on a Bruker Apex IV FTMS mass spectrometer. Elemental analysis (C, H) was performed on Elementar Vario EL CUBE elements analyser.
Polarising optical microscopy was carried out on a lecia DM4500P microscope equipped with a linkam TMS94 hot stage. DSC was carried out on a Netzsch DSC 200. X-ray diffraction (XRD) studies were conducted on a Bruker D8 advance diffractometer equipped with a variable temperature controller. All of the measurements were carried out at heating and cooling rates of 10°C min −1 .
Compounds 1-3 were prepared according to literature procedures and characterised by 1 H NMR and FT-IR; compounds T3D3-T3D12 and T5D3-T5D12 were synthesised from 3 and appropriate α,ω-dibromoalkane according to our previous work on dimers of HAT4.
Charge mobility was measured using a time-of-flight devices. The LC cells with a thickness of 15 μm were purchased from E.H.C. company with semi-transparent indium tin oxide (ITO) electrodes. The purified compounds were capillary-filled into the cell at the temperature 10°C higher than their clear point, and then slowly cooled to their mesophases at a rate of 0.1°C min −1 in order to obtain a well defined homeotropic alignment. The cell was placed on the hot stage and illuminated by light pulses from an N 2 laser (USHO KEC 160, wavelength 337 nm, and the pulse width is 600 ps). The transient photocurrent across the cell was amplified by using a NF low-noise current preamplifier (model 5307) and monitored using a digital phosphor oscilloscope (Tektronix TDS 3032c). The bias voltage was applied to the sample with a power supply unit (Kikusui PAN110-3A). Measurements were carried out under atmospheric conditions. The products were purified by flash chromatography and recrystallised from ethanol and dichloromethane.

Mesomorphism
The phase behaviour of dimers T3D3-T3D12 and T5D3-T5D12 was investigated by DSC, POM and variable temperature XRD. All of the measurements were carried out at cooling and heating rates of 10°C min −1 . The results of these investigations are summarised in Table 1.
Compounds T3D3 and T3D4 did not show LC behaviour. Each of their DSC curves showed just one endothermic peak upon heating and one exothermic upon cooling, corresponding to crystalline phase-isotropic phase transition and isotropic phase-crystalline phase transition, respectively. Both of them were spherulites for typical spherulitic textures (Figs. 47S and 48S in the supplementary material) observed by POM.
The DSC curve of compound T3D5 exhibited one exothermic peak at 99.9°C (−12.3 kJ/mol) and a glass transition at 80°C upon cooling ( Fig. 49S in the supplementary material). A typical focal conic texture of columnar phase with many defects among the texture was observed at 90°C [ Figure 1(a)], which is the defined signature of a rectangular lattice. [20,24] The texture did not disappear with decreasing temperature and even at room temperature, which indicated the LC  phase can be preserved in glass state. Upon heating, a glass transition and one endothermic peak at 148°C (23.8 kJ/mol) corresponding to mesophase-isotropic phase transition were also detected ( Fig. 49S in the supplementary material). To confirm the rectangular columnar structure, X-ray diffraction measurements have been performed for compound T3D5. In the small angle region of XRD pattern at 147°C [ Figure 1 (c)], two splitted peaks were at 2θ = 5.90°and 6.15°c orresponding to d = 14.96 and 14.35 Å, respectively. The two peaks were indexed as reflections (200) and (110) of a two-dimensional rectangular lattice. [25,26] The rectangular lattice constants a = 30.0 and b = 16.6 Å were calculated by the Equation (1) [26] and listed in Table 2.
In the wide angle region, a sharp peak at 2θ = 20°( 4.5 Å) came from the peripheral alkyl chains and a pair of peaks at 2θ = 24.8°and 25.5°corresponding to d = 3.59 and 3.49 Å were indexed as (002) and (102) reflections, which is the signature of columnar plastic phase. [26,27] It can be concluded that compound T3D5 formed a rectangular columnar plastic phase which has ever been first reported by our group. [20] The DSC curve of compound T3D6 (Fig. 50S in the supplementary material) displayed one exothermic peak at 158.0°C (−22.2 kJ/mol) during cooling. When the sample of T3D6 was cooled from the isotropic phase, a dendritic texture of hexagonal columnar phase [28] was observed by POM [ Figure 1(b)]. Although no glass transition was observed in DSC curve, the texture did not show any change with decreasing temperature which indicated the hexagonal lattice can be preserved in glass state. Upon heating, two endothermic peaks at 158.6°C (10 kJ/mol) and 170.0°C (28 kJ/mol) were detected (Fig. 50S in the supplementary material). In the small angle region of XRD pattern [ Figure 1(d)] at 156°C, one intensity peak at 2θ = 6.0°(d = 14.7 Å), two weak peaks 2θ = 10.35°a nd 2θ = 15.9°corresponding to d = 8.5 Å and d = 5.6 Å with the reciprocal d-spacing ratio 1:√3:√7, were observed. [26] These peaks were indexed as (100), (110), (210) reflections of a two-dimensional hexagonal lattice. The hexagonal lattice constants a = 17.0 Å was calculated by the Equation (2) [26] and listed in Table 2.
In the wide angle region [ Figure 1  chains and a pair of peaks at 2θ = 24.7°and 25.4°c orresponding to d = 3.6 and 3.5 Å were indexed as (002) and (102) reflections, which is the signature of columnar plastic phase. [27,29] It can be concluded that compound T3D6 formed a hexagonal columnar plastic phase. Although two endothermic peaks were detected at 158.6°C and 170.0°C, there were no changes observed in XRD pattern when heating powder sample to 166°C.
The DSC curves of T3D7-T3D12 showed just one phase transition upon cooling (Table 1). When the samples of T3D7-T3D11 were cooled from their isotropic phase, a dendritic texture (Fig. 51S-55S in the supplementary material) of hexagonal columnar phase was observed by POM except for the mosaic texture (Fig. 56S in the supplementary material) of compound T3D12. Upon heating, compounds T3D7-T3D10 gave analogous X-ray diffraction (Table 2), such as T3D6, two diffractions in the wide angle region which is the signature of columnar plastic phase and reflections of a two-dimensional hexagonal phase were observed, which indicated a col hp phase was formed. For T3D11 and T3D12, no reflection peaks in the small angle region and only a pair of sharp peaks indexed as (002) and (102) reflections which is the signature of columnar plastic phase, were observed for their edgeon alignment with discotic columnar axes oriented parallel to substrate. [20] In combination with the dendritic and mosaic texture, compounds T3D11 and T3D12 formed a hexagonal columnar plastic phase. The XRD pattern of T3D7-T3D12 all showed no changes upon heating and cooling, which was consistent with their results of DSC and POM. It can be concluded that their mesophase can be preserved at room temperature. [20] Compounds T5D3, T5D4 and T5D5 showed no LC behaviour. The DSC curve of T5D3 showed a single crystalline-isotropic phase transition upon both heating and cooling, while the DSC curve of T5D4 and T5D5 displayed a crystalline 1 -crystalline 2 and crystalline 2 -isotropic phase transitions upon heating and one exothermic peak upon cooling with a typical spherulitic texture of crystalline observed by POM. A typical spherulitic texture (Figs. 57S and 58S in the supplementary material) was observed for the three compounds, when cooled from isotropic phase.
The DSC curves of T5D6-T5D12 (Table 1) displayed one exothermic peak upon cooling. Their phases were identified as columnar phase on the basis of their typical fan-shaped textures (Figs. 59S-66S in the supplementary material). [20,24,26] In combination with the only one endothermic peak upon heating which was corresponding to mesophase-isotropic transition, all of the compounds T5D6-T5D12 can form a glass state. For compounds T5D6-T5D11, one intensity peak at about 2θ～5°was observed in the small angle region (Table 2), which was indexed as (100) reflection of a two-dimensional hexagonal lattice. [30] In the wide angle region, a broad peak at around 2θ～19°came from the peripheral alkyl chains and a narrow peak at 2θ～25°was indexed as (001) reflection, which is the signature of columnar phase. Thus, these compounds formed a hexagonal columnar phase. But a unique XRD pattern was observed for T5D12. In the wide angle region, a broad peak at around 2θ～19°come from the peripheral alkyl chains and a narrow at 2θ = 24.24°(d = 3.67 Å) indexed as (001) reflection, which is the signature of columnar phase, was observed, similarly to T5D6-T5D11, while two intensity peaks at 2θ = 5.

Discussion
In combination with our previous work of dimers T4Dn based on HAT4, [18,20] a detail comparison of phase behaviours and charge-carrier mobilities among dimers T3D6-T3D12, T4D6-T4D12 and T5D6-T5D11 was made and the results illustrated the significant role of different length of alkyl side chains and linkages in promoting their different packing structures during LC phase. T3D5 with short linkage formed a rectangular columnar plastic phase. Both of the triphenylene units in dimer T3D5 were unlikely to be coplanar which led to these units tilting with respect to their columnar axis for steric crowding when forming the columnar phase. Columns with tilted cores contributed to the presence of elliptical cross-section which was suit for the rectangular lattice. [20,[31][32][33] T5D12 with a O(CH 2 ) 12 O linkage, also formed a rectangular lattice.
The triphenylene units in T5D12 were also unlikely to be coplanar for the large steric perturbations introduced by long linkage.
Dimers T3D6-T3D12 (6-12) formed a highly ordered hexagonal columnar plastic phase and dimers T5D6-T5D11 (n = 6-11) formed a hexagonal columnar phase. Dimers T4Dn (n = 6, 7, 11, 12) showed a highly ordered col hp phase in the relatively low-temperature range and a col h phase in the higher temperature range. Dimers T4Dn (n = 8, 9, 10) formed a single col hp phase. Compared to the mesomorphism of these dimers, dimers T3Dn, T4Dn and T5Dn exhibited a transition from col hp phase to a col h phase, which attributed to the different degree of steric repulsion induced by alkyl side chains. Steric repulsion leads to lateral libration of aromatic cores in adjacent columns, prevents them from getting closer and eventually the degree of the stacking order decreases. And the steric repulsion increases with the length of alkyl side chains increasing, which leads to intracolumnar packing more disorder. [34,35] The length of side chains in T4Dn was longer than that of T3Dn and shorter than that of T5Dn. So dimers T3Dn, T4Dn and T5Dn exhibited a transition from col hp phase to a col h phase.
Dimers T4Dn showed a phase competition between col h phase and col hp phase [ Figure 3(a)]. The perturbation induced by linkage gave a reasonable explanation for the  phase competition. It first decreased and then increased with linkage length increasing, resulting different degrees of lateral fluctuation. [11] The smallest perturbation occurred at linkage length was twice that of side chains. When linkage length was too short or too long, it need lower temperature to supress the lateral fluctuation and formed columnar plastic phase. Dimers T4D8, T4D9 and T4D10 with linkage length being or close to twice that of side chains had the smallest perturbation, formed a single highly ordered columnar plastic phase and owned the largest and comparable temperature range of columnar plastic phase. The enthalpies of mesophase-isotropic phase transition are corresponding to break their supramolecular structure. A highly ordered mesophase should own large enthalpies of mesophase-isotropic phase transition, which allow the estimation mesophase ordering. [24,[36][37][38] The enthalpies of T4D8 were quite larger than those of T4D6 and T4D7 [ Figure 3(b)]. When linkage length was larger than 8, the enthalpies of corresponding dimer T4D9-T4D12 decreased with linkage length increasing. The result was not consistent with the fact that enthalpies of mesophase-isotropic phase transition showed a positive linear relationship with molecular mass. [39][40][41] The decrease in degree of stacking order gave a reasonable explanation for the decrease in enthalpies of T4D9-T4D12. The result indicated that T4D8 formed the most highly ordered phase among their homologues. The enthalpies of T5D10 were quite larger than those of T5D6-T5D9 and slightly larger than those of T5D11 [ Figure 3(b)], which indicated T5D10 formed the most highly ordered phase among their homologues. The enthalpies of T3D6 were comparable to those of T3D8 and T3D9 but larger than those of T3D7 [ Figure 3(b)]. When linkage length was larger than 9, the enthalpies of corresponding dimer T3D9-T3D12 decreased with linkage length increasing. The only explanation for this unusual phenomenon was that T3D6 formed the most highly ordered phase among their homologues and the degree of stacking order of T3D9-T3D12 decreased as linkage length increased.
In the wide angle region of XRD pattern, d spacing of (001) reflection for ordinary columnar phase and (002) reflection for highly ordered columnar plastic phase stands for the average intracolumnar distance of aromatic cores.
The full-width at half-maximum (FWHM) is related to the length scale over which the positions of molecules are correlated, or the periodic arrangement of molecules. So the core-core distance, the shape of (001) reflection peak and (002) reflection peak can estimate the degree of stacking order in mesophase. [8,24] In the XRD patterns of T4D6-T4D12 [ Figure 4(a)], their d spacings of (002) reflections first decreased, and then increased with linkage length increasing, which obviously indicated that degree of stacking order first increased, and then decreased. T4D8 and T4D9 owned the smallest d spacing of intracolumnar distance of aromatic cores and formed the most highly ordered phase among their homologues. The (001) reflection peaks of T5D6-T5D11 became narrower and their calculated d spacings decreased as linkage length increased [ Figure 4(b)]. T5D10 and T5D11 owned the highest packing order for their narrowest (001) reflections and smallest d spacing. In the XRD patterns of T3D6-T3D12 [ Figure 4(c)], their d spacing of (002) reflections did not show obvious and regular change. An additional weak peak of T3D6-T3D9 and T3D11 appeared which came from π-π stacking of the adjacent aromatic cores, and their d spacing increased with linkage length increasing. The results indicated that their π-π interaction decreased as well as their intracolumnar order degree and dimer T3D6 formed the most highly ordered phase among its homologues.
To further investigate their degree of stacking order, charge-carrier mobilities of compounds T3D6-T3D12 and T5D6-T5D11 were measured by a time-of-flight (TOF) method at 40°C [ Figure 5(a,b,e,f)]. The charge-carrier mobility of T4D6-T4D12 has been reported in our previous work [ Figure 5(c,d)]. [20] These purified compounds were capillary-filled into LC cells consisting of two ITO-coated glass surfaces at their isotropic temperatures, and then slowly cooled to their mesophase at a rate of 0.5°C min −1 to obtain a well-defined homeotropic alignment. The cells were illuminated by a nitrogen gas laser T5D6-T5D11 (f) at 40°C (applied electric field E = 6.7 × 10 3 V cm −1 ); typical TOF transits for T4D6-T4D12 (c) and hole mobilities of T4D6-T4D12 (d) at 40°C (applied electric field E = 2 × 10 4 V cm −1 ).
(λ = 337) pulse with 10 ns intervals. The photocurrent was recorded as a function of time using a digital oscilloscope and analysed in liner and double logarithmic plots. The transit time t T was determined from the kink point in the transient photocurrent curves. The charge-carrier mobility μ is calculated according to Equation (3), where V is the applied voltage and d is the sample thickness.
Dispersive transient photocurrents for holes were observed in T3D6-T3D12 and T5D6-T5D11, respectively. Figure 4(a,b) exhibits the transient photocurrent curves for holes at 40°C. The relationship between hole mobilities and linkage length is shown in Figure 4(c,d).
The hole mobilities of dimers T3D6 and T5D10 were calculated to be 5.45 × 10 −2 and 1.94 × 10 −3 cm 2 V −1 s −1 , respectively, which were the highest charge-carrier mobility among their homologues. And their charge-carrier mobilities decreased regularly with linkage length becoming shorter or longer than twice that of side chains. The results were highly consistent with the results of DSC and XRD described earlier, which was also an evidence for the fact that the degree of stacking order decreased regularly with the linkage length becoming shorter or longer than twice that of side chain. [42,43] In combination with the thermal data, XRD data and charge-carrier mobilities of dimers T3D6-T3D12, T4D6-T4D12 and T5D6-T5D11, a conclusion was made that perfect twins T3D6, T4D8 and T5D10 owned the largest enthalpies, the smallest intracolumnar spacings, the highest charge-carrier mobilities and formed the most highly ordered phase among their homologues, respectively. When linkage length was shorter or longer than twice that of side chains, the degree of stacking order decreased. The steric perturbations, induced by flexible linkages of discotic dimers, contributed to this regular. It first decreased, and then increased with linkage length increasing, which resulted in different degree of intracolumnar disorder. When linkage length was twice that of side chains, the corresponding dimer owned the perfect twin structure and formed the most highly ordered phase among its homologues.
A comparison of phase behaviours and charge-carrier mobilities between the perfect twins of T3D6, T4D8, T5D10 and their monomers HAT3, HAT4, HAT5 was based on our measurement results and the previous works (Table 3). Although their LC temperature ranges of T4D8 andT5D10 were somewhat larger than their monomers and that of T3D6 was slightly smaller than its monomer, perfect twins of T3D6, T4D8 and T5D10 exhibited the same mesophase to their corresponding monomers. The charge-carrier mobilities of perfect twins of T3D6, T4D8 and T5D10 were not only comparable to their corresponding monomers but also slightly larger than those of their monomers. For T3D6, T4D8 and T5D10, with the structures of perfect twins, the perturbations were minimised for the mesophase structures being regarded as columns consisting of stacked separated monomers, the planar motions in perfect twins were limited by the linkages of the dimers and many times smaller than those of the corresponding monomers, ultimately, the degree of stacking order increased which made a slight increase of chargecarrier mobility in perfect twins compared to their monomers. [44]

Conclusion
In this paper, two series triphenylene-based dimers T3Dn and T5Dn were synthesised by us. Based on T3Dn, T5Dn and T4Dn reported in our previous work, a systematic investigation of structure-properties relationship was carried out. The results of XRD, enthalpy and charge-carrier mobility all showed their packing order first increased, and then decreased. Those dimers in which linkage lengths were twice those of side chains showed the largest enthalpies, the smallest intracolumnar spacings and the highest charge-carrier mobilities among their homologues, respectively, which implied that they formed the most highly ordered phase among their homologues. In contrast with their corresponding monomers, steric perturbations, induced by flexible linkages in discotic dimers, first decreased, and then increased with their linkage length increasing which resulted in different degree of intracolumnar disorder. When their linkage lengths were twice that of side chains, the structure of mesophase can be regarded as two corresponding monomers HATn stacking in adjacent columns, the perturbation was minimised, they formed the most highly ordered phase among their homologues, owned a similar mesophase to its monomer and their charge-carrier mobilities were maintained. This work first elucidates the structure-relationship in discotic dimers with different linkage lengths and side chain lengths, and gives a molecular design strategy for discotic LC polymers, which can provide a clue for how to manipulate discotic LCs to obtain good performances of electronic devices.