Cadmium selenide quantum dots for the amelioration of the properties of a room temperature discotic liquid crystalline material

Abstract

The effect of cadmium selenide quantum dots on a room temperature discotic liquid crystalline material has been studied. These composites were characterized using differential scanning calorimetry, polarizing optical microscopy, impedance spectroscopy and small angle X-ray scattering. It was found that the composite with the lowest concentration of quantum dots enhanced the quasi one-dimensional conductivity of the discotic liquid crystal by five orders of magnitude without altering the columnar hexagonal phase. X-ray scattering results reveal that a decrement in the core–core distance is brought about by the intercalation of quantum dots in between the columns of the discotic liquid crystal matrix. Dielectric spectroscopy shows a relaxation mode in the high frequency region of the pure discotic material as well as in the composites.

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1. Introduction

1,2,3,5,6,7-Hexahydroxy-9,10-anthraquinone, generally called rufigallol is known to act as a core fragment in a variety of discotic liquid crystals (DLCs).¹ DLCs are self-assembled materials where noncovalent intermolecular interactions drive the self-assembly.² Rufigallol derivatives made of disc shaped molecules consist of an elongated core with a twofold symmetry axis which is substituted by flexible aliphatic side chains. These side chains lead to enhanced solubility, processability, and rich thermotropic behavior.³ Furthermore, because of their liquid-character, they possess the capacity to self-heal structural defects such as grain boundaries.⁴ They are one of the primitive systems to display columnar mesophases.^5,6 The columnar hexagonal phase exhibited by most of the rufigallol derivatives has strong anisotropic electronic transport properties that are related to unidirectional intermolecular coupling along the column axis.^7,8 Shape anisotropy, micro segregation between the rigid core and flexible chains and core–core van der Waals attractions are the driving forces for the formation of columnar hexagonal mesophases. These smart materials show polymorphism, have high diffusion lengths, and are thermally stable and colored. These characteristics make them promising candidates for applications in molecular electronics and high efficiency photoconductive switches, solar cells and organic light emitting diodes.^9,10 However, the conductivity of these LCs is low. Doping them with nanomaterials can help increase their conductivity and make them more viable for use in technological applications.¹¹

Merging the interesting self-organizing propensity of these rufigallol derivatives with the exceptional, readily tailored features of zero dimensional nanomaterials such as quantum dots (QDs) can be challenging and useful from the applications point of view. The three dimensional quantum confinement effect i.e. the strong confinement of electrons and holes where the radius of a particle is below the exciton Bohr radius of the material is responsible for their unique size and shape dependent electronic properties differing from the bulk counterparts.^12,13 Their band gap is tunable to different wavelengths of light, allowing them to harness energy from the visible to the infrared regions. Their photochemical stability and small size makes them viable for the manufacture of novel biological sensors, lasers, resonators, and photovoltaic solar cells.^14–17 Kumar and co-workers presented data on DLC nanocomposites which show that QDs increase the electrical conductivity of the DLC host by two orders of magnitude.¹⁸ Basu et al. demonstrated the formation of one dimensional chain like arrays and a larger dielectric constant by doping CdS QDs into nematic LCs.¹⁹ Biradar et al. achieved a good memory effect by tuning CdTe QDs in ferroelectric LCs that can be utilized in future zero power displays.²⁰ Hegmann and co-workers have worked extensively on LC nanocomposites and reported beneficial effects.^21,22

In this report, we use 1,5-dihydroxy-2,3,6,7-tetrakis(3,7-dimethyloctyloxy)-9,10-anthraquinone (RTAQ) as a host to incorporate CdSe QDs. RTAQ has the widest columnar hexagonal room temperature mesophase and is a difunctional molecule. The dielectric properties of DLCs in general and RTAQ in particular are the least understood. Frequency and temperature dependent dielectric spectroscopy of RTAQ is not yet reported. In the present work, we have carried out dielectric spectroscopy on RTAQ and its composite with CdSe QDs. Our aim is to see how various dielectric parameters such as permittivity, conductivity, relaxation frequency (if any mode exists) and its strength are affected in the presence of QDs. These DLC + QDs composites may potentially possess versatile applications in electronic and optical nano-devices.

2. Experimental details

2.1. Materials

The RTAQ molecule has two hydrogen bonds. It is deep orange in color. It was synthesized in the same manner as reported earlier by Kumar et al.²³ It shows a columnar hexagonal phase confirmed by X-ray diffraction studies as well as POM.⁵¹ CdSe QDs are essentially monodisperse and have an average diameter of 3.5 nm. They are highly soluble in non-polar solvents such as hexane, toluene, and chloroform. Details on the preparation and the characterization of the CdSe nanoparticles have been described elsewhere.^24,25

2.2. Preparation of composites

To prepare the composites, a solution of CdSe QDs in chloroform was added to a previously weighed RTAQ sample placed in a vial. The contents of the vial were subjected to ultrasonication for five hours to ensure uniform dispersion. The chloroform was evaporated slowly (within ∼24 hours) leaving behind the RTAQ + QDs mixture. However, before taking the material for various measurements, it is once again mixed in its isotropic liquid phase (for about 30 minutes) with the help of a magnetic stirrer. This process was repeated to prepare three composites viz., 0.5QDAQ, 1QDAQ, and 5QDAQ having 0.5 wt%, 1 wt% and 5 wt% QDs respectively, in RTAQ.

2.3. Sample characterization

The differential scanning calorimetry measurements were performed on pure and dispersed samples with the help of a differential scanning calorimeter (DSC), NETZSCH model DSC-200-F3-Maia. The peak transition temperature (T_p in °C) and associated transition enthalpy (ΔH in J g⁻¹) for various transitions were measured from −30 °C to isotropic temperatures at scanning rates of 15, 12.5, 10, 7.5 and 5 °C min⁻¹ during the heating and cooling cycles. Polarised optical microscopy (POM) images were taken using a polarized microscope coupled with an Instec mK 1000 heating stage. The dielectric studies of the samples were carried out under homeotropic geometry wherein the plane of discotic molecules is parallel to the electrode’s surfaces. The sandwiched type (capacitors) cells were made using two glass substrates coated with indium tin oxide (ITO) layers. The thickness of the cell was defined by placing two Mylar spacers (thickness 10 μm) between the glass plates. These cells have been used for optical texture studies as well. The samples were introduced via capillary action by heating to the isotropic liquid phase. In order to achieve homeotropic alignment, the samples were slowly cooled at the rate of 0.1 °C min⁻¹ from the isotropic phase without any chemical treatment. This usually adopted process yields a reasonably good quality of homeotropic alignment due to the minimum energy configuration of the discotic molecules. For all POM imaging and electrical measurements, the LC mixtures were heated above the phase transition temperature and cooled at a rate of 0.1 °C min⁻¹. The temperature of the sample has been controlled with the help of a hot stage (Instec model HCS 302) joined with a temperature controller (Instec model mK 1000). The sample temperature has been determined by measuring the thermo-emf of a copper–constantan thermocouple with the help of a six and half-digit multi meter from Agilent (model-34410A) with the accuracy of ±0.1 °C. Dielectric data have been acquired using a Newton’s Phase Sensitive Multi meter (model-1735) coupled with an IAI (model-1257) in the frequency range of 1 Hz to 35 MHz. A measuring electric field of magnitude 500 mV_rms was applied normal to the electrode surfaces while acquiring the electrical data. POM and dielectric studies have been carried out during the cooling cycles where better alignment is expected than in the heating cycle. Detailed methodology and the necessary mathematical equations to obtain the permittivity (ε′), loss (ε′′) and conductivity (σ) of the materials are reported elsewhere.^26,27 Small angle X-ray scattering (SAXS) studies were carried out using an X-ray diffractometer (Rigaku, UltraX 18) operating at 50 kV and 80 mA current having Cu-Kα radiation of the wavelength of 1.54 Å.

3. Results and discussion

3.1. DSC studies

The mesophase behavior of pure RTAQ and its composites has been studied using DSC. Fig. 1 presents the DSC thermograms taken during heating and cooling at the scan rate of 5 °C min⁻¹ for pure RTAQ and the three composites. The pure sample and the composites on heating and cooling show peaks signifying columnar hexagonal-isotropic (Col_h-I) and isotropic-columnar hexagonal (I-Col_h) transitions respectively. In general, these two transitions are expected at the same temperature under the condition of thermodynamic equilibrium. However, in the case of the dynamic process (scan rate 5.0 °C min⁻¹), thermodynamic equilibrium is not achieved and hence these two transitions occur at different temperatures. During the heating cycle, the detected transition temperature is higher whereas during the cooling it is lower than the actual transition temperature. As the scan rate increases, the system moves away from the condition of thermodynamic equilibrium due to thermal inertia and hence the above difference increases.^28,29 It has been observed that transition temperatures vary linearly with the scanning rate with opposite slopes in the heating (positive) and cooling (negative) cycles as also reported earlier.^28,29 However, extrapolated transition temperatures at the (hypothetical) scanning rate of 0 °C min⁻¹ agree for the heating and cooling cycles of the enantiotropic phase transitions except when there is some super cooling effect.^28,29 Extrapolated transition temperatures thus obtained are given in Table 1 and are the same for Col_h-I and I-Col_h transitions. Thus Col_h-I and I-Col_h transitions are equivalent and hence forth we will call them both I-Col_h transitions as most of the other experiments have been performed during the cooling cycle. A significant effect observed is the decrease of the I-Col_h transition temperatures for the composites (see Table 1) as compared to the pure sample; the effect becomes more pronounced as the concentration of QDs is increased. This is expected to be due to an impurity effect, since QDs in the composites are non-liquid crystalline components. QDs tend to intercalate between the columns, weakening the inter columnar interaction. However, another interesting result obtained for 0.5QDAQ is that the enthalpy of this transition (refer to Table 1) increases by 17% as compared to that of pure RTAQ which indicates that the stability of the Col_h has enhanced in the case of 0.5QDAQ. Also, the peak for the Col_h-I/I-Col_h transition is almost symmetric as in the case of pure RTAQ. At the clearing temperature, the unstacking of molecular cores takes place. When the concentration is low, QDs are packed between flexible chains and resist the unstacking of molecular cores. All these suggest that the ordering of the molecular discs inside a column increases. For 1QDAQ and 5QDAQ, the peaks become highly asymmetric with a decrease in height of 90% and 88% respectively (with respect to the pure sample) indicating that a higher concentration of QDs slows down the transition process. Here it is important to point out that the peak height represents the maximum rate of heat flow with time. When the concentration of QDs is increased above 0.5 wt%, they tend to disrupt the columns and induce defects in them. The large size of the aggregated QDs disturbs the packing of the molecular discs as they cannot be accomodated between the flexible chains without disturbing the columns. This leads to a decrease in the enthalpy of the Col_h-I transition. On the basis of the thermodynamic results, we have an indication that a low concentration of QDs (0.5 wt%) is uniformly miscible with RTAQ but as the concentration increases, the miscibility decreases. This result is in agreement with those obtained from the optical microscopic and dielectric studies discussed in the forthcoming sections. Immiscibility and phase separation at higher concentrations has been reported by other workers as well.³⁰ As long as there is good miscibility, QDs act as an impurity and the I-Col_h transition temperature decreases according to the general rule. With an increasing concentration of QDs, when the miscibility becomes poor (5 wt%), there seems to be phase separation like behavior and the I-Col_h transition temperature tries to return towards the original value for RTAQ.

Fig. 1 DSC curves taken during heating and cooling for (1) pure RTAQ, (2) 0.5QDAQ, (3) 1QDAQ and (4) 5QDAQ.

Table 1 Transition temperatures (T_I-Colh in °C) obtained from DSC as well as POM and dielectric studies, corresponding enthalpies (ΔH in J g⁻¹) obtained from DSC, relaxation frequencies (f_R in kHz), and strengths of the relaxation mode (δε) obtained by fitting dielectric spectra to eqn (3) at 30.5 °C for pure and composite systems

System	TI-Colh		ΔH	fR	δε
	DSC	POM/dielectric studies
RTAQ	112.2	112.4	5.8	408	1.12
0.5QDAQ	110.1	110.6	6.8	394	1.12
1QDAQ	99.4	99.6	4.2	359	1.11
5QDAQ	102.5	102.8	4.8	363	0.97

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3.2. Optical studies

POM under the crossed polarizer condition is used to image the spatial variation in the director orientation, as LCs are optically anisotropic. Phase transitions for all the samples are clearly visible under POM. The I-Col_h transition temperatures obtained from POM are slightly higher than those obtained from DSC (see Table 1). This is because the transition temperatures obtained from DSC are peak temperatures (where the process of the transition is at a maximum) whereas in the case of POM studies, these are onset (i.e. the start of the transition) temperatures. The environment around the sample is also different in the two cases. In the case of DSC, the sample is under an inert atmosphere whereas in the case of POM it is under a normal atmosphere. The colour and area of the domains changes with temperature also. Fig. 2a and b show the optical textures of pure RTAQ. These textures reveal some dark areas which show that the columns get easily aligned homeotropically (i.e. the column axis is perpendicular to the glass substrates) on untreated glass substrates when cooled slowly i.e. at rate of 0.1 °C min⁻¹ from the isotropic phase.³¹ Some bright domains can also be seen which indicate areas where molecular planes may be minutely tilted with respect to the substrates. These are π disclinations or defects.³² The POM images of 0.5QDAQ are shown in Fig. 2c and d. Here the entire field of view became dark when the sample was completely in the mesophase (Fig. 2d). This suggests that the addition of QDs leads to a decrease in π disclinations or defects. QDs help to align the disk shaped molecules inside a column, leading to a better homeotropic arrangement of columns on the glass substrates. It is known that the rigid cores of the discotic molecules are translationally disordered within the columns.³³ Microscopic observations on 1QDAQ (shown in Fig. 3a–d) show an increased number of π disclination like regions. This shows that as the concentration of QDs is increased, they tend to tilt the molecular disks inside the columns slightly. Prasad et al. have previously described such textures of the columnar hexagonal phase of a novel series of anthraquinone based DLCs with bulky substituents.³² Highly bright textures were observed for 5QDAQ as shown in Fig. 3e–h which are completely distinct from those in Fig. 3a–d. While cooling in the columnar phase, the textures show continuous changes with the appearance of defect like regions. Large domains increase in size while cooling from the isotropic phase at about 84.3 °C. On further cooling at about 82.6 °C (see Fig. 3g), a number of defects appear on the domain and this number tends to rise with cooling. Aggregation of QDs may lead to the development of such defects in DLCs. Several reports state that after a certain concentration, nanoparticles have a tendency to aggregate.³⁴ Kinkead and Hegmann have also reported the tendency of CdSe QDs to aggregate above 1 wt% when doped in a nematic liquid crystal.²² However, aggregates that may eventually form at a higher concentration are not directly visible at magnifications up to 100×. There is no sign of crystallization in the case of the pure sample or the composites while cooling the samples to room temperature which confirms the results obtained from DSC.

Fig. 2 POM images (a) for pure RTAQ at 112.4 °C during the transition, (b) for pure RTAQ at 49.1 °C in the complete Col_h phase, (c) for 0.5QDAQ at 110.6 °C during the transition, (d) for 0.5QDAQ at 68.9 °C in the complete Col_h phase.

Fig. 3 POM images taken while cooling (a–d) for 1QDAQ (a) at the transition at 99.3 °C, (b) at 88.2 °C, (c) at 82.6 °C and (d) at 30.5 °C in the complete Col_h phase. (e–h) for 5QDAQ (e) at the transition at 102.8 °C, (f) at 84.3 °C (here in each domain columns are aligned unidirectionally), (g) at 82.6 °C (one can note here the appearance of defects on the domains) and (h) at 30.5 °C where defects further dominate.

3.3. Dielectric studies

Conductivity measurements were carried out on pure RTAQ and its composites to evaluate the effect of the QD dispersion on the electrical properties of DLCs. Fig. 4 shows the temperature variation of DC conductivity for the pure sample and the composites. The conductivity of virgin RTAQ is of the order of 10⁻¹⁰ S m⁻¹. An enhancement in conductivity by five orders of magnitude is observed in the case of the lowest concentration i.e. 0.5 wt% of QDs in the pure DLC. The conductivity of 0.5QDAQ has been found to be 6 × 10⁻⁹ S m⁻¹ in the isotropic phase. It increases with the decrease in temperature, becoming 8.95 × 10⁻⁶ S m⁻¹ at 86.2 °C and finally reaching a value of 2.05 × 10⁻⁵ S m⁻¹ at 30.5 °C. The drastic increment in conductivity can be attributed to the ordered arrangement of the discotic molecules and QDs as evidenced by the optical texture (see Fig. 2d) discussed in the previous section. Based on the Marcus equation, the theoretical description of the electron hopping rate between adjacent discs is explained by the transfer integral which is a function of the LUMO (HOMO) of adjacent molecules for electron (hole) transport and the internal reorganization energy.³⁵ Charge transport in the bulk material depends on the degree of order within the columnar stack and thus on the overlap between the π-orbitals.³⁶ Chandrashekhar et al. have asserted that the rigid core of DLCs are ordered, with the orientational order parameter S, defined as where θ = the angle which the molecular symmetry axis makes with the director or the column axis.³⁷ The core is not normal to the column axis but is inclined in columnar mesophases. It is established that the tilt of the molecular core persists in the columnar hexagonal phase as well.³⁸ Also, mobility is more dependent on the intracolumnar order than on the intercolumnar ordering.³⁹ Based on these facts, it can be inferred that the increase in the orientational order of the rigid cores arises from the doping of QDs into the DLC matrix. The overlap of the π-orbitals of the cores increases which in turn leads to an increase in the mobility along the columns. The QDs act as a conductive filler which bridges the defects within the columnar matrix. Thus, high mobility along the columns leads to a very high conductivity for 0.5QDAQ. These experiments were repeated in order to validate the results obtained. X-ray diffraction studies (discussed in the forthcoming section) also explain the increase in conductivity.

Fig. 4 Temperature dependence of DC conductivity: curve (1) pure RTAQ, (2) 0.5QDAQ, (3) 1QDAQ and (4) 5QDAQ. The lines are guides to the eyes.

When the concentration of QDs in the DLC is increased, the conductivity tends to decrease with respect to that for 0.5QDAQ. For 1QDAQ, the conductivity is of the order of 10⁻⁹ S m⁻¹ in the isotropic liquid phase, it increases to 2.0 × 10⁻⁷ S m⁻¹ at 78.3 °C and 1.28 × 10⁻⁶ S m⁻¹ at 39.4 °C. In the case of 5QDAQ, the conductivity increases from 1.32 × 10⁻⁹ S m⁻¹at 114.0 °C (isotropic liquid phase), reaching a maximum of 4.07 × 10⁻⁷ S m⁻¹ at 84.3 °C. At 82.6 °C, it abruptly decreases to 2.18 × 10⁻⁸ S m⁻¹ and continues to do so until 60.0 °C. It is important to note that this is the same temperature where optical textures also show the growth of some defects (refer to Fig. 3g). On further cooling, it shows an increasing trend. In this case when the material is transferred to the columnar mesophase (from the isotropic liquid phase), initially the conductivity is high when the alignment is good. However, when the temperature further decreases, perhaps due to the aggregation of QDs, the alignment deteriorates and hence the conductivity decreases. Again when the settlement of the discs improves with the decrease in temperature, the conductivity slowly increases. Such competition may occur during the whole cooling process. In other words, it is apparent that the columns of the mesophase are not properly ordered (unidirectional) when aggregation occurs. This tendency increases with the increase in the concentration of the QDs leading to the creation of more defects. Further, due to the aggregation of the QDs, the DLC takes time to settle down properly in its mesophase as revealed by POM and DSC. This also causes the asymmetry of the I-Col_h peaks observed using DSC. Results obtained by Wood et al. also illustrate that colloidal particles incorporated in LCs decrease the orientational order, generating defect lines called disclinations.⁴⁰

Interestingly, the conductivity of all composites is higher in the Col_h mesophase compared to that in the isotropic phase which is important from the applications point of view. The aligned sample provides a facile electron transport route as compared to the unaligned sample.

A significant parameter for conductors formed by particle doped insulators is the frequency dependence of the conductivity. Jonscher’s universal response is used to define the frequency dependent conductivity in such types of materials including polymers, glasses, organic–inorganic composites etc.⁴¹ At low frequencies, the random diffusion of the ionic charge carriers via activated hopping gives rise to a frequency-independent conductivity. Whereas, at higher frequencies conductivity increases in a power-law fashion roughly exhibiting dispersion. So, the total conductivity σ(f) measured at a finite frequency f is expressed as:

σ(f) = σ_DC + σ_AC (1)

where σ_DC and σ_AC are the DC component and the AC contribution to the conductivity. Jonscher’s universal description considers a distribution of hopping probabilities between sites distributed randomly in space and in energy. The expression used for σ(f) in Jonscher’s universal description is:

σ(f) = σ_DC(1 + k(f|f_c)ⁿ) (2)

where k and n are constants, (0 < n < 1) for disordered solids. The onset of the conductivity relaxation and the transformation from long range hopping to short range motion is marked by the critical frequency (f_c). Fig. 5 represents the variation of log(σ) with frequency for the pure sample and the composites. The experimental data fit eqn (2) well except for the pure sample because the conductivity measurements are not within the range of the used bridge. The critical frequency for all composites viz., 0.5QDAQ, 1QDAQ and 5QDAQ are 236.07 kHz, 137.54 kHz and 42.23 kHz respectively which are higher than that for the pure material (6.6 kHz). This indicates that QDs extend the long range hopping to a wider frequency range. The values of n as obtained by fitting for the pure sample and the composites are 1.96, 1.25, 1.44 and 1.65 respectively. The value of n is not between 0 and 1 as predicted by Jonscher. Papathanassiou et al. have proposed a model stating that there is no physical argument to restrict the value of n to below 1.⁴² According to the authors, there does not exist a ‘universal fractional power law’. They found a lot of inaccuracies about the validity of the universal power law such as the fact that n is frequency dependent, n is greater than 1 for glassy 0.3(xLi₂O·(1 − x)Li₂O)·0.7B₂O₃ etc.⁴³ Recently, Prasad et al. have found some surprising results in liquid crystal gold nanocomposites formed by a gel network of aerosol particles.⁴⁴ The value of n for the pure LC obtained by them was 1.95. The authors further averred that the addition of nanoparticles in LCs reduces the value of the exponent n to such an extent that the composite has values which are within the Jonscher limit.⁴⁴

Fig. 5 Frequency dependence of the total conductivity (σ), curve (1) pure RTAQ, (2) 0.5QDAQ, (3) 1QDAQ and (4) 5QDAQ at 49.0 °C. The open symbols represent the fit to eqn (2). The arrow indicates a slight deviation from eqn (2) due to the presence of a relaxation mode in this frequency region.

The temperature dependent permittivity (ε′) plots for pure RTAQ and its three composites determined at a fixed frequency of 100 kHz are shown in Fig. 6. All the plots show an abrupt jump in the value of the permittivity at the I-Col_h transition. The value of the permittivity in the isotropic phase increases with the increase in concentration of QDs. This feature suggests that there is an additional dipolar contribution from the semiconducting nanoparticles to the total permittivity of the medium. CdSe QDs possess a dipole moment.⁴⁵ The creation of an increased number of QD-DLC-QD capacitors may lead to the increase in the permittivity of the composites. However, in liquid crystalline materials, an increment in ε′ is associated with an increase in orientational ordering. But in our case, the results are contradictory. Increasing the concentration of the QDs in the columnar matrix causes a decrease in the order of the DLC as confirmed by the conductivity studies. So, the polarisability of the QDs could be the reason for the enhancement in ε′. At low temperatures, a decrement in ε′ is seen for the pure sample as well as the composites. This is due to the lowering of the relaxation frequency so much so that the frequency of the measurement lies in the dispersion region to be discussed subsequently.

Fig. 6 Thermal variation of permittivity (ε′) in the isotropic and Col_h phases measured at 100 kHz for pure (1), 0.5QDAQ (2), 1QDAQ (3), and 5QDAQ (4). In each case there is a step change at the transition between the phases.

Fig. 7 shows the spectra for the real (ε′) and imaginary (ε′′) parts of the permittivity for the pure DLC at various temperatures. It demonstrates that the DLC used here has a higher value of permittivity than other discotics. Each RTAQ molecule is composed of two hydrogen bonds which provide stability to the mesophase. The data were processed by fitting the Cole–Cole equation⁴⁶ because there is very good evidence for a dielectric spectrum of the Cole–Cole type (see Fig. 9):

where δε = ε(0) − ε(∞) is the dielectric strength of the relaxation mode with ε(0) and ε(∞) being the low and high frequency limiting values of the relative permittivity, respectively, and τ is the relaxation time. The parameter α corresponds to the symmetric distribution of the relaxation times with a value in the range (0 < α < 1). The third and fourth terms on the R.H.S. of eqn (3) represent the contributions of the electrode polarization capacitance and DC conductivity at low frequencies. The fifth imaginary term Bω^m is included in eqn (3) to partially account for the finite sheet resistance of the ITO coated glass sheets used. A prominent dielectric relaxation is clearly visible in the 340 kHz to 2 MHz region in the Col_h phase only which starts appearing at 74 °C. It is important to note that the relaxation frequency (f_R) of the mode lies approximately at the midpoint of the step of ε′ (i.e. the point of inflexion) which corresponds to the peak point of the ε′′ data (see Fig. 7). f_R decreases (due to the increase of viscosity which opposes the motion of the molecules) while δε increases (due to the improvement of the alignment) with a decrease in temperature (refer to Fig. 7). The temperature dependence of f_R follows the Arrhenius equation (Fig. 8):where E_A denotes the activation energy and R is the ideal gas constant. The activation energy is estimated to be 42.67 kJ mol⁻¹. It is elucidated that the observed relaxation is a Debye process from the value of the distribution parameter α = 0.06 obtained by fitting the experimental data as well as the Cole–Cole plot (Fig. 9). The composites also repeat the same features as the pure sample (refer to Fig. 10) but with appreciable changes in f_R and δε (see Table 1). Table 1 shows that f_R decreases with the increase in the concentration of the QDs. With the increasing concentration of QDs, δε is almost constant for RTAQ, 0.5QDAQ and 1QDAQ but it has appreciably decreased in the case of 5QDAQ (see Table 1).

Fig. 7 Variation of permittivity (ε′) and loss (ε′′) with frequency for pure RTAQ.

Fig. 8 Temperature dependence of the relaxation frequency for pure RTAQ following Arrhenius behavior.

Fig. 9 Cole–Cole plots showing the variation of the dielectric loss with relative permittivity for the pure sample (curve 1 for measured data and curve 2 for corrected data).

Fig. 10 Dielectric relaxation spectra in the Col_h phase exhibiting a prominent relaxation process in the real (ε′) and imaginary (ε′′) components of the permittivity. Curves 1 and 4 show the measured value of ε′ and ε′′. Curves 3 and 6 show the generated data for ε′ and ε′′ by fitting to eqn (3). Curves 2 and 5 represent the corrected data of ε′ and ε′′ obtained after subtracting the low and high frequency parasitic effects from the measured data. (a) Pure RTAQ, (b) 0.5QDAQ, (c) 1QDAQ, and (d) 5QDAQ. In the case of 0.5QDAQ, the relaxation mode is not seen in the loss data due to high conductivity.

For other DLCs a similar relaxation process is observed. A value of 23 kJ mol⁻¹ was found for the E_A of relaxation in a triphenylene derivative with five CH₂ groups.⁴⁷ For a pyrene derivative a relatively low value of 10 kJ mol⁻¹ was reported.⁴⁸ The authors assigned it to the localized fluctuations of the methylene groups. Discotic liquid crystalline hexabenzocoronene derivatives have an activation energy of 50 kJ mol⁻¹.⁴⁹ Such obtained values of activation energy are comparable to those identified for the localized molecular motions perceived in polyethylene.⁵⁰ Hence, it is reasonable to accept that the relaxation mode observed here is due to the local fluctuations of the side chains of the discotic molecules. The decrease of f_R is due to the increase in the concentration of the QDs as the QDs (trapped between the chains) increase the inertia of the fluctuating chains. Further, due to the better packing, as free space for the movement of the chains decreases, the relaxation frequency decreases. However, in the case of 5QDAQ, one can notice a marginal increase in the relaxation frequency. It has happened due to the dominating additional free space developed due to the heavy aggregation of the QDs.

With the increasing concentration of QDs, δε is almost constant for RTAQ, 0.5QDAQ and 1QDAQ (slight decrease in this case, although within error of measurement) but it appreciably decreases in the case of 5QDAQ. The latter has occurred due to the disorder produced in the system due to the aggregation of the QDs in between the flexible chains (and hence the poor alignment of the molecules) as discussed in previous sections. It is imperative to say that no such kind of relaxation has been reported earlier in anthraquinone derivatives.

3.4. SAXS studies

X-ray diffraction studies were performed in order to investigate the mesophase structure of the dispersed samples. A typical diffraction pattern is shown in Fig. 11 for 0.5QDAQ. Here, in the small angle region, two sharp peaks, one strong and one weak reflection can be seen whose d-spacings are in the ratio of 1 : 1/√3 as in the case of RTAQ. This suggests that the two-dimensional hexagonal lattice structure of RTAQ is not disturbed due to addition of QDs. In the wide angle region, the broad peak corresponds to that of alkyl chains and another sharp peak shows the reflection due to (01) plane corresponding to the core–core separation. X-ray studies confirm that the composites also show a columnar hexagonal phase. For the pure material, the intercolumnar distance is 22.4 Å and the core–core separation is 3.43 Å at 25.0 °C.⁵¹ QDs being 3.5 nm in size easily embed themselves between the columns, increasing the intercolumnar distances slightly. The average stacking distance (core–core separation) decreases to 3.38 Å for 0.5 wt% QDs at 80.0 °C. The decrease in the core–core separation leads to better overlap between π orbitals, increasing the conductivity in the case of 0.5QDAQ. However, once the concentration of QDs is increased above 0.5 wt%, the onset of the aggregation of the QDs probably minimizes the packing effects and the lattice tends to relax back to values of the pure host material. For all the composites the core–core separation decreases as the temperature decreases (refer to Table 2). At 105.0 °C, the core–core separation could not be calculated because the peak was not discernable due to the sample being in the isotropic phase for 5QDAQ.

Fig. 11 1-dimensional intensity versus 2θ profile for the 0.5QDAQ composite. The inset shows an enlarged view to show peaks of low intensity at 60.0 °C.

Table 2 Intercolumnar distance (d_inter in Å) and average stacking distance (core–core separation in Å) of composites derived from the diffraction patterns at different temperatures

System	T (°C)	d-Spacing (Å)	dinter	Core–core separation
0.5QDAQ	105	19.703	22.752	3.428
	80	19.588	22.612	3.381
	60	19.588	22.612	3.374
1QDAQ	105	19.782	22.843	—
	85	19.900	22.979	3.397
	70	19.900	22.979	3.377
5QDAQ	105	19.782	22.843	—
	85	19.900	22.979	3.407
	70	19.781	22.842	3.380

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4. Conclusion

The effect of the dispersion of CdSe QDs on RTAQ shows that the dispersion at low concentrations is uniform but at higher concentrations shows aggregation. For low concentrations when the dispersion is uniform, the stability of the columnar mesophase is enhanced. However, for high concentrations, when the QDs tend to aggregate, the stability of the mesophase decreases. The conductivity is enhanced by five orders of magnitude in the case of lowest concentration of QDs (i.e. 0.5 wt%) doped in RTAQ. For higher concentrations, the conductivity enhancement is poor. Jonscher’s universal response principle has been used to determine the critical frequency above which the conductivity becomes frequency dependent. The critical frequency has been found to be high for the composites suggesting that the QDs increase the long range hopping. Dielectric spectroscopy of RTAQ shows a relaxation mode in the frequency range of a few hundreds of kHz to MHz which arises due to the local fluctuations of the side chains of the discotic molecules, the first of its kind found in anthraquinone derivatives. The dynamics of the system as measured using the relaxation mechanism is seen to become slower in the presence of the QDs. On the basis of these studies it is concluded that a low concentration of QDs in a pure DLC with uniform dispersion may be advantageous in bulk heterojunctions as well as in dye sensitized solar cells.

Acknowledgements

This work is financially supported by Department of Electronics and Information Technology (DEITY) under a research project no. 12(6)/2011-EMCD. One of us (NY) thanks DEITY for fellowship under the project.

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