Collective orientational order and phase behavior of a discotic liquid crystal under nanoscale confinement

The phase behavior and molecular ordering of hexakishexyloxy triphenylene (HAT6) DLCs under cylindrical nanoconfinement are studied utilizing differential scanning calorimetry (DSC) and dielectric spectroscopy (DS), where cylindrical nanoconfinement is established through embedding HAT6 into the nanopores of anodic aluminum oxide (AAO) membranes, and a silica membrane with pore diameters ranging from 161 nm down to 12 nm. Both unmodified and modified pore walls were considered. In the latter case the pore walls of AAO membranes were chemically treated with n-octadecylphosphonic acid (ODPA) resulting in the formation of a 2.2 nm thick layer of grafted alkyl chains. Phase transition enthalpies decrease with decreasing pore size, indicating that a large proportion of the HAT6 molecules within the pores has a disordered structure, which increases with decreasing pore size for both pore walls. In the case of the ODPA-modification, the amount of ordered HAT6 is increased compared to the unmodified case. The pore size dependencies of the phase transition temperatures were approximated using the Gibbs–Thomson equation, where the estimated surface tension is dependent on the molecular ordering of HAT6 molecules within the pores and upon their surface. DS was employed to investigate the molecular ordering of HAT6 within the nanopores. These investigations revealed that with a pore size of around 38 nm, for the samples with the unmodified pore walls, the molecular ordering changes from planar axial to homeotropic radial. However, the planar axial configuration, which is suitable for electronic applications, can be successfully preserved through ODPA-modification for most of the pore sizes.


Introduction
Since the discovery of discotic liquid crystals (DLCs), consisting of molecules having disk-like rigid aromatic cores connected via exible alkyl chains, their intrinsic properties have been extensively investigated to uncover their fundamental properties and potential for applications. 1,2 Research on DLCs over the last few decades has shown that they can be considered promising materials for use in electronic applications as they exhibit one-dimensional high charge mobility along the axis of the column in the columnar mesophase. [3][4][5][6] The hexagonal columnar mesophase is commonly formed by DLCs, between plastic crystalline and isotropic phases as the molecules can self-organize and stack into columns, which is driven by the favorable p-p interaction between the aromatic cores. Hence, the self-assembly results in favorable charge transport along the axis of the column due to the delocalization of p-electrons. As the alkyl chains ll the intercolumnar space and act as an insulator, the columns can be considered as isolated, onedimensional, conducting nanowires. [7][8][9] This makes DLCs promising materials for electronic applications such as in organic eld effect transistors (OFETs), organic light emitting diodes (OLEDs) and organic photovoltaics (OPVs). 3,6,10 DLCs can also be nanoconned into a specic geometry, i.e. as thin lms or in cylindrical nanochannels, in order to optimize their use in electronic applications. Metal oxide membranes with a parallel alignment of cylindrical nanopores and narrow pore size distribution can be produced by electrochemical etching. Conning DLCs into the cylindrical nanopores of metal oxide membranes has gained much interest. This is due to the fact that investigations on such conned systems can address fundamental properties such as phase behavior and glass transition dynamics, whilst also helping to shed light upon the structure-property relationship of so matter under connement. 8,9 Moreover, from an application stand point, it opens up the possibility to prepare nanowires through dissolution of the host membrane. 11 Nanoconnement inuences the properties of DLCs like for other so mater systems 12 which have to be revealed for applications at the nanoscale. The phase behavior under connement and the molecular ordering of DLCs within pore structures are two of the main properties dening their applications in nanotechnology. 3 Hence, several investigations have been carried out to elucidate the phase behavior and molecular ordering of DLCs conned within the nanopores of metal oxide membranes. [7][8][9][13][14][15] Compared to bulk DLCs, a decrease in phase transition temperatures is observed alongside the formation of additional structures under connement that have been reported for pyrene-and triphenylene-based DLCs. 8,9,14 On the other hand, controlling the molecular ordering within pore structures is highly desirable for improving application relevant properties such as conductivity and light harvesting abilities. Hence, aligning the columns of DCLs parallel to the axis of the pores is therefore crucial to their success in specic applications.
Planar (edge-on anchoring) and homeotropic (face-on anchoring) alignments are the two possible types of molecular ordering of DLC molecules with respect to a at surface ( Fig. 1a and b). These two alignments describe the ordering in thin lms of DLCs and DLCs conned between two parallel solid substrates. 16 However, when placed under connement within cylindrical pores, the molecular ordering can become complicated, with conned molecules possessing multiple types of ordering, and thus, describing this ordering within cylindrical pores solely as planar or homeotropic may be insufficient. Hence, additional directional characterization terms such as 'axial' and 'radial' should be used alongside the anchoring type for the clarity. It has been shown that planar axial, planar radial (circular concentric) 17,18 and homeotropic radial (logpile) 19 congurations are the predominant forms of ordering within pore structures (Fig. 1c-f). There is a competition between these congurations, caused by different interfacial tensions observed between air/liquid crystal, liquid crystal/pore walls and liquid crystal/liquid crystal. The dominating type denes the conguration for the overall system.
Among the above-mentioned types of congurations found within the pores, only the axial conguration is suitable for electronic applications. Studies have shown that axial congurations are scarcely observed, whereas homeotropic radial and planar radial congurations are more commonly observed for DLCs conned within the nanopores of metal oxide membranes. 7,14,15,[17][18][19] However, a dominating axial conguration might be obtained through chemical modication of the pore surface. 7 Besides the surface modications changing the hostguest interactions, an appropriate choice of the host pore size with respect to that of the guest DLC can lead to better congurational control. Recently, Zhang et al. 18 reported that the dominating ordering type changes with pore size. 18,19 Furthermore, they observed a transition from a planar radial conguration to an axial conguration with increasing columnar rigidity of the DLC. 18 The column rigidity increases with aromatic core size, and hence, it can be tuned to obtain a desired conguration through an appropriate choice of the DLC.
In this study, the effect of cylindrical connement on the phase behavior and molecular ordering of 2,3,6,7,10,11-hexakis [hexyloxy]triphenylene (HAT6), a triphenylene-based DLC, conned within nanochannels is revealed. Anodic aluminum oxide (AAO) and silica membranes with varying pore diameters, 161 nm down to 12 nm, were used as conning hosts. Some preliminary data for only four pore sizes have been reported for the same system. 8 However, here a broader pore size range is covered, and therefore a better understanding of the connement effect on the phase behavior is obtained. This is also due to the fact that the membranes are characterized in detail. Furthermore, it is aimed to obtain an axial ordering or to increase the degree of axial ordering by chemical modication of the pore walls. The phase behavior was explored by differential scanning calorimetry (DSC) allowing the detection of small changes in the phase behavior. Dielectric spectroscopy was demonstrated as a powerful method to monitor molecular ordering within the pores. 15 Here, we also investigate the collective orientational order, corresponding to dominating molecular conguration, by dielectric spectroscopy.

Experimental section
Materials 2,3,6,7,10,11-Hexakis[hexyloxy]triphenylene (HAT6) was purchased from Synthon Chemicals (Bitterfeld, Germany, CASno.: 70351-86-9) and used as received. The molecular weight was estimated to be 829.24 g mol À1 by MALDI-TOF MS. 31 According to the producer its purity is at least 98%. At room temperature HAT6 appears as white crystals. The chemical structure of HAT6 (sum formula C 54 H 84 O 6 ) and a schematic illustration of its molecular organization and the thermotropic phases for the bulk are shown in Fig. 2. At low temperatures, HAT6 forms a plastic crystalline phases (Cry). Upon further heating the Cry phase, it forms a hexagonal columnar mesophase (Col h ). In the Col h phase, the HAT6 molecules stack up in columns which are arranged in a hexagonal lattice. With further heating the Col h phase, it undergoes a clearing transition to a more or less isotropic liquid state (Iso).
Disk shaped anodic aluminum oxide (AAO) membranes with a variety of pore diameters, thicknesses and porosities were purchased from Smart Membranes GmbH (Halle, Germany) and InRedox (Longmont, USA). Silica membranes having a pore diameter of ca. 12 nm were prepared by electrochemical anodic etching. A highly p-doped h100i silicon wafer with a resistivity of R ¼ 0.01-0.02 U cm was used. As an electrolyte solution a mixture of 40 vol% hydrouoric acid and 60 vol% ethanol was used with an etching current density of 13.3 mA cm À2 applied for 8 h. 21 The porosities and pore diameters of the membranes were characterized by using volumetric N 2 -sorption isotherms at a standard temperature of 77 K. Volumetric N 2 -sorption experiments were carried out by using an Autosorb iQ Quantachrome Instruments gas sorption system. The determined pore sizes and porosities (number of pores per unit area) are given in Table 1 according to the specications of the producers.
The membranes have cylindrical hexagonal ordered pores which are open at both sides. The cylindrical pores are parallel to each other and perpendicular to the surface of the diskshaped membranes. Fig. 3 demonstrates that the pore distribution of the membranes is narrow, and the pores have an almost parallel arrangement.

AAO surface modication
Experiments were carried out on both uncoated and coated pore walls. In the latter case the pore walls of the AAO membranes were chemically modied with n-octadecylphosphonic acid (C 18 H 39 O 3 P; ODPA) following the procedure reported in the literature. 22,23 ODPA was purchased from Alfa Aesar and used as received.
A scheme of the modication process is given in Fig. 4. First, the pore walls of the AAO membranes were activated with 30% aqueous H 2 O 2 solution for 2 h at 45 C, and then dried at 120 C for 15 minutes. The pore wall activated membranes were immersed into a 4 mM solution of ODPA in a n-heptane/isopropyl alcohol solution (volume ratio of 5 : 1) for 48 h at 25 C. The membranes were then washed several times and sonicated Fig. 2 (a) Chemical structure of 2,3,6,7,10,11-hexakis[hexyloxy]triphenylene (HAT6). D HAT6 is the diameter of HAT6 molecules, reported to be ca. 2.1 nm. 20 (b) Phases formed by HAT6 and HAT6 molecules in the hexagonal columnar liquid crystalline phase. a is the hexagonal lattice parameter, reported to be ca. 1.87 nm. 19,31  for 15 minutes with the n-heptane/isopropyl alcohol solution to remove any physically absorbed ODPA. The sonicated samples were then washed several times with the n-heptane/isopropyl alcohol solution, and then with acetone before being le to dry overnight under vacuum at room temperature. The modication of the pore walls was conrmed by FTIR, as given in ESI, Fig. S1. † The long-range ordering of both the unmodied and modied membranes was studied by Small Angle X-ray Scattering (SAXS) in order to estimate the thickness of the ODPA coating. Fig. 5 shows the measured SAXS patterns and corresponding simulations. The simulations are of 2D core-shell cylinders from the SasModels library. 24 Similar models are applied elsewhere. 25,26 The scattering pattern simulations are done with the cylindrical axis parallel to the beam, and using the scattering length densities estimated for bulk ODPA and alumina phases. Simulation trials with different shell parameters (cylinder diameter, shell thickness, and polydispersity) were carried out. The simulation with a shell thickness parameter of 2.2 nm closely approximates the SAXS pattern of the ODPA modied membranes. 27 Hence, it is concluded that the ODPA coating has a thickness of ca. 2.2 AE 0.2 nm. The details of the SAXS measurements and some additional results are given in the ESI. †

Sample preparation
A reproducible pore lling procedure was developed to embed HAT6 into nanochannels. 8 The conned samples were prepared as outlined in ref. 8. In short, the membranes were outgassed in a vacuum of 10 À4 mbar at 473 K for 12 hours, to clean the pores and remove adsorbed water. Then the membranes were transferred under vacuum to an argon-lled glovebox. The amount of material required to ll the membranes completely was calculated from the porosity and the volume of the membranes according to: where F AAO is the porosity, d AAO is the diameter of the diskshaped membrane, l AAO is the thickness of the membrane and r HAT6 is the bulk density of HAT6, found to be 0.92 g cm À3 . 28 The bulk-like density was assumed when HAT6 is conned into nanopores. The calculated amount of the liquid crystal and a small surplus was place on the top of the membrane and heated to 418 K in the isotropic state. At this temperature, the   The lling degree of the membranes with HAT6 was estimated by Thermogravimetric Analysis (TGA). A complete pore lling was obtained for all the samples investigated in this study (see the ESI †).

Differential scanning calorimetry (DSC)
DSC measurements were carried out using a Perkin Elmer DSC 8500 device. The sample (ca. 6-10 mg) was encapsulated in a standard 50 ml aluminum pan and measured in the temperature range from 173 K to 423 K with a heating/cooling rate of 10 K min À1 . Nitrogen was used as a purge gas at a ow rate of 20 ml min À1 . A baseline measurement was conducted by measuring an empty 50 ml aluminum pan under the same conditions. The obtained baseline was subtracted from the data measured for the sample. The second heating and the cooling runs were used to determine the phase transition temperatures and enthalpies. Moreover, the calibration of the machine was checked using an indium standard.

Dielectric spectroscopy (DS)
The dielectric properties of the samples were measured by using a high-resolution ALPHA analyzer (Novocontrol) connected to a sample holder with an active head. The temperature of the sample was controlled by using a Quatro Novocontrol® temperature controller with nitrogen as a heating agent providing a temperature stability better than 0.1 K.
The measurements of HAT6 conned into nanochannels of the membranes were performed in a parallel plate geometry. This means that the disk-shaped samples were placed between two gold-plated brass electrodes with a diameter of 10 mm or 15 mm depending on the outer diameter of the membranes. Spacing between electrodes was dened by the thickness of the membranes. Bulk measurements were conducted using a commercially available liquid crystalline cell. The liquid crystalline cell, having square (10 mm Â 10 mm) patterned ITOcoated electrodes and an average cell gap of 4 mm, was purchased from Instec, Inc. (Colorado, USA). It was capillary lled with HAT6 in the isotropic phase at 383 K by placing a small amount of sample at the front gate of the cell.
The complex dielectric permittivity 3*(f) ¼ 3 0 (f) À i3 00 (f) was measured by temperature scans with a heating and cooling rate of 1 K min À1 at a constant frequency of 35 kHz. Here i ¼ ffiffiffi 1 p symbolizes the imaginary unit and f denotes the frequency where 3 0 and 3 00 are the real and imaginary (loss) parts of the complex dielectric permittivity. More details about BDS can be found in ref. 29.
Three heating/cooling cycles, in the temperature range from 340 K to 383 K for smaller pore sizes (d < 34 nm) and that from 350 K to 383 K for the larger pore sizes (d > 34 nm), were employed to probe all samples. Similarly, three heating/cooling cycles were applied for HAT6 in the liquid crystalline cell in the temperature range from 350 K to 383 K.

Polarizing optical microscopy (POM)
The liquid crystalline texture and the alignment of the columns were investigated by POM for bulk HAT6. The measurements were carried out by using a Zeiss Axioskop Scope A1 optical microscope, with crossed polarizers, connected to a Linkam THMS600 heating stage. The stage was equipped with a liquid nitrogen Dewar allowing a precise control of heating and cooling rates.
The ITO-coated liquid crystalline cell used in the DS measurement was also employed for the POM investigations. The temperature program applied for the DS measurements was also used for the POM measurements.

Mesomorphic properties of bulk
The mesomorphic properties of HAT6 in the bulk state were studied by DSC and POM. DSC thermograms of HAT6 are given for the second heating and cooling runs in Fig. 6. The phase transition temperatures and enthalpies are estimated from the maximum positions of the peaks and the area under the peaks respectively and given in Table 2. Moreover, the Col h -Iso phase transition temperatures were also determined by DS from the rst derivative of 3 0 with respect to temperature. A hysteresis between the cooling and heating cycles was observed where the hysteresis is more pronounced for Cry-Col h transition (DT ¼ 15.9 K) than Col h -Iso transition (DT ¼ 2.8 K).
A step indicating a thermal glass transition was observed in the temperature range between 170 K and 270 K, see the inset of Fig. 6. The mid-step position of the step was taken to determine the thermal glass transition temperature (T thermal g ) of 214 K. The change in the specic heat capacity Dc p was found to be 0.25 J K À1 g À1 . Undergoing a glass transition implies that there are some disordered or amorphous structures within the material. Such disorder, which leads to a glass transition, may be caused by a nanophase separation of the alkyl chains and the aromatic core of HAT6, which is evidenced by the amorphous halo observed in the X-ray pattern of HAT6. 31 Similarly, Yildirim et al. 30 reported a glass transition for HAT6 also detected by DSC. In contrast to our ndings, they found a T thermal g of 186 K. Furthermore, Krause et al. 31 observed a step, which might indicate a glass transition, in the temperature range of 180-220 K upon cooling. They did not observe a glass transition during the heating run. Clarifying these contradicting ndings requires further detailed calorimetric investigations, such as conventional DSC investigations covering temperatures lower than 150 K or Hyper/Flash DSC investigations allowing for higher heating rates. Fig. 7 illustrates the texture and the column alignment of bulk HAT6 obtained by POM. Upon rst heating from room temperature, in the Cry phase at 328 K the texture is very bright under cross polarizers. This indicates a lack of a homeotropic alignment due to tilted columns in the Cry phase (herringbonelike crystal packing 32,33 ) causing a high birefringence. This results in a bright texture with colored crystal domains. 4 A fanshaped texture accompanied by dark areas was observed during the rst heating ramp in the Col h phase at 363 K. The fanshaped texture is typical of a Col h phase of DLCs. It indicates that a column alignment in large spatial regions is not present. As shown in the inset of Fig. 7b, the columns are randomly tilted. 6,34 In addition to the fans, small dark areas were also observed, which indicates that the columns are partially aligned homeotropically among the tilted columns causing a minimal birefringence. However, during the third heating run (aer applying two heating/cooling cycles in the range from 350 K to 383 K) at 363 K, large dark areas are observed (see Fig. 7c), where the columns are mostly aligned homeotropically. The reason for the homeotropic alignment of the columns in large spatial regions compared to the rst heating probably is the temperature program applied due to the self-healing ability of DLCs for the structural defects with thermal annealing. It could also be reasoned that the heating/cooling rate applied, 1 K min À1 , is not slow enough to align the columns during the rst heating due to what is assumed to be slow orientation kinetics.
Phase behavior under connement Fig. 8 depicts the DSC thermograms of bulk HAT6 as well as HAT6 conned into the nanopores of unmodied and ODPA-modied AAO membranes. It is concluded that the conned HAT6 undergoes both phase transitions (Cry-Col h and Col h -Iso) with decreasing pore size for both unmodied and modi-ed pore walls. One exception to this is observed with HAT6 conned within 12 nm pores in a silicon membrane, where the Col h -Iso phase transition is completely suppressed. Such a complete suppression of the phase transition has previously been reported for rod-like LCs. 22 As previously reported for the phase behavior of HAT6 under connement for a limited range of pore sizes, 8 three conclusions can be drawn for both kinds of samples with unmodied and modied pore walls. Firstly, both phase transition temperatures shi to lower temperatures with decreasing pore size. Secondly, both phase transition peaks split into two or three peaks for pore sizes smaller than 95 nm (see Fig. 9). The appearance of the socalled satellite peaks in addition to the main transition peak for the smaller pore sizes was reported for the nanoconned pyrenebased DLC and also for HAT6. 8,9 In a rst interpretation, the  30 Heating Cry, 340.6 K (50.6 J g À1 ); Col h , 371.5 K (5.9 J g À1 ); Iso Ref. 19 Heating Cry, 342.7 K; Col h , 372.7 K; Iso Ref. 31 Heating Cry, 342.0 K (49.9 J g À1 ); Col h , 372.3 K (6.8 J g À1 ); Iso Ref. 8 Heating Cry, 342.0 K (49.9 J g À1 ); Col h , 372.3 K (6.8 J g À1 ); Iso satellite peaks can be due to remaining bulk-like HAT6 located at the surface of the sample although attempts were made to remove it carefully. A similar interpretation is used elsewhere. 35 Secondly, the main and the satellite peaks might be assigned to different congurations of the molecules near the pore walls and the pore center. This conclusion is supported by the observation that the satellite peaks are shied to lower temperatures with respect to the phase transition of the bulk and depend slightly on pore size. For these reasons the second interpretation is favored. However, such assignments can prove to be controversial due to the lack of experimental techniques available to characterize the different structures and their location within the pore space. Thirdly, for both phase transitions the enthalpies decrease with decreasing pore size. However, this conclusion cannot be drawn directly from Fig. 8, as the measured values are normalized to the conned mass of HAT6. This third conclusion is discussed in detail below.
The dependence of phase transition enthalpies normalized to sample mass inside the pores and the phase transition temperatures are shown in Fig. 10. Moreover, the effect of the different host/guest interactions on the phase behavior under nanoconnement is revealed by comparing the behavior of HAT6 conned in both unmodied and ODPA-modied pores. The ODPA modication forms a stable graed alkyl chain monolayer, which results in hydrophobic pore walls with a lower value of the surface energy compared to unmodied pores. 36,37 The thickness of the ODPA coating was reported to be 1.8-2.4 nm on the aluminum oxide surface, 38 which is comparable to the thickness revealed from SAXS investigations. Hence, the modication leads to an observed decrease of the pore diameter of ca. 4.4 nm for the ODPA-modied AAO membranes. The inuence of the decreased pore size should be greater for smaller pores than for larger ones considering inverse pore sizes. Therefore, the dependencies given in Fig. 10 for the sample with the ODPA-modied pore surfaces were drawn considering a 4.4 nm decreased pore size. However, the thickness of the ODPA coating is not known for the pores lled with HAT6. In the ESI, Fig. S4 † shows the dependencies for the nominal pore sizes. When the modied pores are lled with HAT6, the thickness of the coating can, in principle, have a value between 0 nm and 4.4 nm, whereas in reality values tend to lie towards the latter end of this scale.
The dependencies of the phase transition enthalpies of the main peak, normalized to the mass of the conned material, versus inverse pore size are given in Fig. 10a and c for the Cry-Col h and the Col h -Iso transitions respectively. The normalized phase transition enthalpies decrease with decreasing pore size, which provides evidence that a portion of conned HAT6 does not undergo the phase transition. This part of the conned HAT6 should be disordered and may have an amorphous structure. As discussed in ref. 8 and 9, the observed increase in the surface curvature, with decreasing pore size, leads to stronger elastic distortion of the ordered phase, which prevents the molecules from forming an ordered structure and consequently limits the amount of observed ordered phase.  The dependencies of the enthalpies for the Col h -Iso transition reveal that more than half of the material conned in the pore (by volume) is disordered for pore sizes smaller than 47 nm. This is an amount that cannot be neglected in the interpretation of the results for nanoconned HAT6. The spatial location of this disordered portion inside the pore cannot be assigned by methods characterizing the structure such as X-ray diffraction or neutron scattering. As it has been discussed that the disordered portion is likely located at the center of the pore due to the divergence of the excess energies toward the pore center. 7,13,15 A disordered core at the center of the pore was also visualized by molecular dynamics simulations of conned HAT6. 17 The pore size dependencies of the phase transition enthalpies show stronger dependence on pore size for larger pores in comparison to smaller ones. Similar ndings were reported for a series of organic materials conned within nanopores. 39 The surface area of the pores per unit of mass is signicantly higher for smaller pores. This can lead to stronger connement effects on the enthalpies for smaller pores for nanoconned materials, which could explain similar trends observed with different nanoconned materials. In addition, higher values of the transition enthalpies were found for surface modied samples compared to unmodied ones. This means that the amount of ordered HAT6 increases for the samples with the ODPA-modied pore walls even though there is still a considerable amount of disordered material inside the pores, most likely located in the pore center. Fig. 10b and d show the dependencies of the phase transition temperatures on inverse pore size for both phase transitions. It can be seen that the phase transition temperatures decrease with decreasing pore size. In general, the pore size dependence of phase transition temperatures can be well described by the Gibbs-Thomson equation for a variety of materials including liquid crystals. 8,9,40,41 The Gibbs-Thomson equation reads: where T m,bulk is the phase transition temperature of the bulk material, d is the pore diameter, T m (d) is the phase transition temperature of HAT6 within the pores of diameter, d, and s is the surface tension of the interface. DH m,bulk is the phase transition enthalpy of the bulk material.
For the phase transition from the plastic crystalline to the hexagonal ordered phase the data seem to follow the Gibbs-Thomson equation for both types of samples probed. The surface tensions were calculated to be 5.4 mN m À1 and 3.9 mN m À1 from the dependencies of Cry-Col h phase transition temperatures for the samples with unmodied and ODPA- Fig. 10 Dependencies of the phase transition enthalpies for (a) the Cry-Col h transition and (c) the Col h -Iso transition, as well as the dependencies of the phase transition temperatures for (b) the Cry-Col h transition and (d) the Col h -Iso transition versus inverse pore size. Blue squares indicate data for bulk HAT6, black symbols indicate data for HAT6 confined into unmodified membranes and red symbols indicate data for HAT6 confined into ODPA-modified membranes (filled circles: main peak; open symbols: satellite peak). Dashed-dotted lines are a guide for the eye. Solid lines are the fits of eqn (2) to the dependencies. Note that for the samples with modified pore surfaces, the pore diameter was corrected regarding the estimated thickness of the surface layer. modied pore walls, respectively. The ODPA modication makes the pore wall more hydrophobic in comparison to the unmodied pore walls. Therefore, the interfacial tension is lower for the samples with modied pore walls than for unmodied ones. Fig. 10d depicts that the dependence of phase transition temperatures of the Col h -Iso phase transition changes at a pore size of ca. 38 nm for the samples with the unmodied pore walls. Assuming that both pore size dependencies can be described by a Gibbs-Thomson equation for pore sizes larger than 38 nm, the surface tension was calculated to be 2.2 mN m À1 , whilst for pore sizes smaller than 38 nm a value of 0.8 mN m À1 was calculated. As it will be discussed below in more detail this change in the pore size dependence of the phase transition temperature for the Col h -Iso phase transition goes along with a change in the dominating order. It is also important to note that the pore size dependence of the Col h -Iso phase transition observed here is different from that reported in ref. 13. The reason for this is not quite clear and requires additional experiments.
The pore size dependency of the phase transition temperature of the Col h -Iso phase transition for the samples with the modied pore walls can be described with a single Gibbs-Thomson equation where a value of 0.7 mN m À1 was calculated for the surface tension. This value is quite similar to the one obtained for the unmodied pore walls for smaller pore sizes. It might be concluded that the type of dominating anchoring is the same in both cases (see Table 3). Moreover, a study on the effect of orientation on the reduction of the phase transition temperature revealed by specic heat spectroscopy for a conned rod-like liquid crystal 42 demonstrated the stronger decrease of the transition temperatures for a radial conguration. In addition, the favorable interactions between the aromatic core and the polar surface of the unmodied membranes enforce likely face-on anchoring leading to homeotropic radial conguration (logpile). Hence, it can be concluded that the homeotropic radial conguration is the dominant type of ordering found in larger unmodied pores.
Recently, Zhang et al. 19 also found a dominant logpile conguration for HAT6 conned in native nanopores of AAO membranes.
For the smaller unmodied pores and for the modied pores, it was assumed that the dominating type of ordering is a planar axial conguration. The similar values obtained for the surface tensions (s Unmod,2 z s ODPA , Fig. 10d) further support this assumption. The planar conguration is assumed for samples with the modied pore walls due to the similarity between the alkyl chains and the alkyl chains graed to the surface of the modied membranes. In contrast, ndings in the literature for conned HAT6 point out logpile congurations in unmodied small pores 19 and circular concentric (planar radial) congurations in nanopores graed by alkyl chains. 18 Although the calorimetric investigations give a clear picture of the phase behavior under connement, they provide only a limited understanding to predict the dominating conguration in the nanopores based on the pore size dependencies of the phase transition temperatures and enthalpies. These predictions will be reevaluated with respect to the orientational order characterized by DS in the next section.

Collective orientational order
The collective orientational order of HAT6 in the bulk and conned HAT6 was revealed by dielectric spectroscopy. Of course, dielectric spectroscopy is not a tool to estimate the structure directly. Dielectric spectroscopy is sensitive to dipole orientation (dipole vector with respect to the outer electrical eld). Therefore, a change in the orientation at the phase transition can be monitored when a change of the orientation of the dipole moment is involved. Together with a reference measurement on the bulk material where the orientation is known a conclusion based on facts about the orientation can be drawn. The measurements were carried out at a frequency of 35 kHz, where results from the third heating run are provided in Fig. 11. A frequency of 35 kHz was selected for these investigations as no dielectric active processes due to molecular Table 3 The dominating ordering of HAT6 molecules inside the nanopores revealed by means of different techniques. HAT6 confined into the silicon membrane (12 nm) is not presented in the table since the Col h -Iso phase transition is completely suppressed for this sample Fig. 11 Normalized dielectric permittivities as a function of temperature during the third heating run for the bulk, and samples with unmodified and ODPA-modified pore walls as indicated. All measurements were done with a heating/cooling rate of 1 K min À1 at a frequency of 35 kHz. The dashed-dotted lines indicate the Col h -Iso phase transition temperatures determined by DSC. The dashed lines represent the temperature dependencies of 3 0 extrapolated from Col h and Iso phases. The insets on the right-top are the drawings illustrating the measurement geometry used for the dielectric measurement for bulk HAT6 in the cell and the confined HAT6.
uctuations for HAT6 take place in the temperature range from 350 K to 383 K. In this temperature range relaxation processes take place at frequencies between 1.9 MHz and 1.2 GHz (obtained from the extrapolation of the data given in ref. 30). Hence, a measurement frequency of 35 kHz is signicantly lower than the frequency window of the dielectric relaxation processes, and the measurements shown in Fig. 11 correspond to quasi-static dielectric measurements where only the collective orientation of HAT6 contributes to 3 0 , which can be considered as frequency-independent.
In the DS measurements, the cylindrical pores were oriented parallel to the electric eld applied due to the parallel plate geometry (see the inset of Fig. 11). Therefore, the system can be considered as AAO and HAT6 capacitors connected in parallel yielding an additive response. 22 Thus, the absolute value of the permittivity of such a system is related to the porosity of the membrane. For this reason, the measured 3 0 values were normalized with respect to the values of 3 0 at 383 K for each sample.
The excess permittivity (D3) can be dened as the difference between the temperature dependence of 3 0 in the Col h phase, and that of 3 0 extrapolated to the Col h phase from the dependence in the Iso phase. A positive D3 was determined for bulk HAT6, where HAT6 molecules are homeotropically aligned, which was also conrmed by POM. The positive D3 indicates that the columns are perpendicularly aligned to the electrodes. Hence, a positive D3 can be attributed to a dominating axial conguration, whilst a negative D3 corresponds to a dominating radial conguration. In some cases, from the overview given in Fig. 11 it is hard to detect whether D3 is positive or negative. Therefore, enlarged gures are prepared and added to the ESI (see Fig. S6-S10). † For the unmodied pores with diameters smaller than 38 nm, the D3 was estimated to be positive and assigned to a planar axial conguration. For pore sizes greater than 38 nm, a negative D3 was observed and assigned to the homeotropic radial conguration. This is in good agreement with the discussion given above concerning the pore size dependency of the phase transition temperatures. The DSC investigations indicate that a change in the anchoring type occurs at a pore diameter of ca. 38 nm, which was also observed using DS. Conversely, a positive value of D3 was found for samples with modied surfaces, expect for the pore sizes of 73 nm and 161 nm. This has been attributed to the planar axial conguration, where a planar radial conguration was assumed for 73 nm and 161 nm due to the negative value of D3. For the sample with a pore size of 47 nm with modied pore walls, generally a positive value of D3 was found; however it was observed that the phase transition occurs in several steps (see also Fig. S5 in the ESI †). As shown recently with high resolution optical birefringence experiments on HAT6 conned within porous silica and molecular dynamic simulations, 17 such steps can be attributed to a circular concentric (planar radial) conguration. Therefore, it might be concluded that the orientation of HAT6 in 47 nm modied AAO pores also possesses a circular concentric (planar radial) conguration.
In addition to the dielectric investigations the molecular ordering for the samples presented here was also characterized by optical birefringence (OB) measurement and temperature dependent X-ray diffraction (XRD). These measurements will be published elsewhere 43 because they would increase the length of this publication too much. Nevertheless, the results of these measurements are included here in Table 3. Some preliminary results have been already published discussing also the methodology of the measurements (see the ESI of ref. 17). Combining the results of the interpretations based on the DSC investigation and the ordering characterized by DS, OB and XRD, a general picture of the molecular ordering inside the unmodied and ODPA-modied nanopores was obtained (see Table 3). In most cases the results obtained from the DSC and dielectric measurements agree with the data obtained with OB and XRD. A minor difference between DS and OB ndings might be caused by the small differences in the sample preparation. However, it is argued in ref. 15 that the dipolar orientation of the polar ether groups of alkyl chains is sensed by DS, whereas the orientation of the aromatic cores is observed by OB. This may explain the small differences observed in the determined congurations by DS and OB.
According to the above discussions and Table 3, the picture of the molecular ordering of HAT6 inside the unmodied and ODPA-modied nanochannels of AAO membranes can be concluded as follows: a model representing the molecular ordering of HAT6 inside nanopores should include three idealized major layers: a disordered layer probably located at the center of the pore, an axial ordered layer near the center and a radial ordered layer near the pore walls. For HAT6 in the unmodied nanopores, a transition of the dominant conguration from planar axial (Fig. 1d) to homeotropic radial (Fig. 1c) conguration was detected in the pore size range from 24 nm to 38 nm. On the other hand, for HAT6 in the ODPA-modied nanopores the transition from planar axial (Fig. 1f) to planar radial (Fig. 1e) conguration was observed in the pore size range from 73 nm to 95 nm.

Conclusions
The inuence of cylindrical nanoconnement on the phase behavior and molecular orderingtwo main properties determining the applications of a DLC in nanotechnologywas explored by DSC and DS for HAT6 conned into the nanopores of AAO and silica membranes. Pore sizes from 161 nm down to 12 nm were explored. Moreover, the different host/guest interactions and their inuence on the phase behavior as well as molecular ordering were studied by comparing their behavior and ordering in unmodied and ODPA-modied pores. Prior to the investigations, the membranes and the conned samples were well characterized by means of volumetric N 2 -sorption, scanning electron microscopy, FTIR, SAXS and TGA.
The pore size dependencies of the phase transition enthalpies and temperatures were obtained by DSC. It was observed that the phase transition enthalpies decrease with decreasing pore size, which indicates that an increasing fraction of HAT6 does not undergo any phase transitions, and it is thought that this fraction is probably located in the center of the pore. Moreover, the phase transition temperatures decrease with decreasing pore size. These pore size dependencies of the phase transition temperatures were described by the Gibbs-Thomson equation for both transitions. For the Cry-Col h transition, a lower interfacial tension was found for the samples with modied pore walls in comparison to the samples with unmodied pore walls. For the pore size dependency of the Col h -Iso transition temperatures for the samples with unmod-ied pore walls, a change from a stronger to a weaker dependency was observed with a pore size of around 38 nm. Such a change implies that there is an alteration in the dominating order. Therefore, by considering the host-guest interaction it can be concluded that the dominating type of ordering is a homeotropic radial conguration with larger pores (d > 38 nm) and a planar axial conguration for smaller pores (d < 38 nm). However, the dependencies of the Col h -Iso phase transition temperatures for the samples with modied pore walls were approximated by using only one Gibbs-Thomson equation. Similar values for the surface tension for the samples with modied pore walls to those estimated for samples with unmodied pore walls at lower pore sizes (s Unmod,2 z s ODPA ) were found. Hence, it is concluded that for the samples with modied pore walls the dominating type of ordering is also the planar axial conguration.
The collective orientational order of nanoconned HAT6, corresponding to the dominating ordering in the pore, was probed by DS at a constant frequency of 35 kHz. Similar to the DSC ndings, DS investigations revealed that for the unmodi-ed pores a homeotropic radial orientation for the larger pores (d > 38 nm) and a planar axial orientation for the smaller pores (d < 38 nm) were found as dominating forms of ordering. For ODPA-modied pore walls, the planar axial conguration is assigned as the dominating type expect for the pore sizes of 73 nm and 161 nm. Moreover, OB and XRD studies on the samples discussed here mostly agreed the molecular orderings determined by DS.
In summary, we have reported ODPA surface modication as a promising strategy for controlling the molecular ordering of DLCs inside the nanopores of metal oxide membranes. Our results indicate that the dominating planar axial conguration, which is the only conguration suitable for electronic applications, was successfully achieved by ODPA modication for most of the pore sizes probed. Moreover, the higher phase transition enthalpies and temperatures observed for the samples with modied pore walls compared to the unmodied ones imply a signicant improvement in the amount of ordered HAT6 present within the pores.

Conflicts of interest
The authors declare no competing nancial interest.