Enhancement of electrical conductivity, dielectric anisotropy and director relaxation frequency in composites of gold nanoparticle and a weakly polar nematic liquid crystal

Abstract

We report complex permittivity characteristics in composites of gold nanoparticles (GNP) and a weakly polar nematic liquid crystal possessing a low frequency director relaxation. Differential calorimetric measurements show that the inclusion of GNP has a strong influence on the isotropic–nematic (fluid–orientational fluid) transition temperature as well its first order character in terms of the transition entropy. The absolute value of conductivity increases by two to three orders of magnitude with respect to that for the host liquid crystal and its concentration dependence is demonstrated to be described by the percolation scaling law generally observed in composites of metal particles and polymers. However, the obtained exponent is much smaller, possibly owing to thermal fluctuations present in the fluid-like nematic medium. The activation energy governing the temperature dependence of conductivity is much higher in the nematic than in the isotropic phase. The frequency dependence of the ac conductivity exhibits a critical frequency that is concentration-dependent, but the exponents obtained defy Jonscher's Universal Response principle. A surprising feature is the observation of a substantial increase of not only the principal permittivity values, but their anisotropy as well. These studies also constitute the first report on the influence of GNP on the director relaxation mode of nematics. In contrast to the behaviour of the static permittivity, the dynamics of the system as measured using the director relaxation is seen to become faster with the presence of GNP. We provide an explanation for this antagonistic behaviour in terms of the alignment of the liquid crystal molecules in the vicinity of GNP, and the importance of the weak polarity of the liquid crystals used.

---

1. Introduction

Nanocomposites have been attracting substantial attention since the first reports three decades ago.¹ The interest is especially due to the technological importance of percolative composites for the demanding applications requiring high electrical/thermal conductivity or high dielectric constant. Blending the processability of insulating organic materials with high conductivity values of metal particles has been in the forefront of this field.^2,3 Perhaps one of the best examples of these composites are those of liquid crystals (LC) and nanoparticles (NP) showcasing the importance of the judicial combination of soft matter and nanoscience, based on the soft elasticity and field tunability of liquid crystals. Several recent reports exist which demonstrate the importance of the combination of LC and NP.^4–16 Proper realization of the field tunability has been depicted at least in two cases^17,18 with the potential to result in devices in which macroscopic properties can be switched between their anisotropic values along, say, parallel to perpendicular direction with respect to an internal reference axis. In the case of mixtures with carbon nano particles, the frequency dependent conductivity exhibits¹⁸ behaviour similar to the well known feature in disordered solids, qualitatively agreeing with the expectations of the extended pair approximation model.¹⁹

We describe here investigations on composites of gold nanoparticles (GNP) with a weakly polar nematic liquid crystal as the host. In fact, the weak polarity of this host and the absence of any strong longitudinal dipole moment reduce the possibility of build-up of short range ordering in the vicinity of the metal particles, and thus enhance the disordering imparted by the particles. Calorimetric studies show that there is a significant influence of the presence of the particles on the isotropic–nematic (I–N) transition of the host, with both the transition temperature and the transition entropy diminishing significantly. With increasing GNP concentration, while the anisotropic conductivities parallel as well as perpendicular to the director increase exhibiting percolation threshold behaviour, the rate of increase determined using a scaling law, exhibits an exponent that is below the dimension-related universal value. The anisotropy of the conductivity, taken as the ratio of the values in the two orthogonal directions, reduces slightly with increasing GNP concentration. The fact that the host material exhibits a low frequency director relaxation has enabled the first thermal investigations of the mode for the LC–metal particle composites which show strong influence of the concentration of GNP on the relaxation frequency of the mode.

2. Experimental

2.1. Host liquid crystalline material

The liquid crystalline host material was, 4-pentylphenyl 2-chloro-4-(4-pentylbenzoyloxy) benzoate (PCPBB for short), exhibiting the nematic phase over a wide-range of temperatures, through room temperature. PCPBB does not possess any strong dipole moment along the long axis of the molecule, but a weak one along the transverse direction. This feature was the criterion to select it so that the results could be compared with the data available in the literature collected mostly on alkyl/alkoxy cyanobiphenyl (with a strong longitudinal dipole moment) as the host. This compound prepared in our laboratory using the reported methods,²⁰ exhibits the I–N transition at 121.8 °C and the N phase can be supercooled well. An interesting feature of this compound is that it belongs to the class of materials termed as dual frequency materials exhibiting a crossover in the sign of the dielectric anisotropy at a certain frequency. From the point of view of present studies this feature was useful since in such materials, generally, the director relaxation frequency is low.

2.2. Preparation and characterization of nanoparticles

The Brust procedure,²¹ in which GNPs are prepared and capped with alkanethiols in a non-polar organic phase is a popular method, and has been found⁹ to be suitable for the type of studies performed here. The starting materials, hydrogen tetrachloroaurate(III) trihydrate, sodium borohydride, tetraoctylammonium bromide and 1-dodecanethiol were procured from Aldrich Chemical Company and used as received. Ethanol and toluene obtained from a local source were purified following standard procedures. High purity (18 MΩ) water was obtained from Milli-Q ultrapure water system (from Millipore). The deep brown dodecylthio-capped GNPs realized from the Brust procedure were repeatedly (5 times) washed with ethanol. The crude product collected by filtration was quickly dissolved in toluene and again precipitated with ethanol. This process was repeated several times and the pure GNPs were collected by filtration and preserved in the form of a solution in toluene (30%). The general characteristics of the prepared material were found to be consistent with the literature reports.²² The chemical purity of the product was confirmed by ¹H NMR (see ESI†), which showed no indication of any free thiols left over. TEM measurements were carried out to determine the shape as well as the size of the particles (details of the method as well as the TEM image are given in ESI†). The image which showed essentially spherical particles, was analyzed using a digital image analyzer (ImageJ) and yielded a mean particle size of 3.6 ± 0.6 nm. In order to study the surface plasmon resonance (SPR), UV-Vis absorption spectra were recorded in transmission mode in the range 200 to 850 nm with a Perkin Elmer Lambda 20 spectrometer. A clear, single SPR peak at 517 nm supported the spherical nature of the particles. The size of the prepared particles was estimated from the powder Xray diffraction pattern (Panalytical X'Pert Pro equipped with PIXEL detector, Cu K_α radiation, λ = 0.15481 nm) shown in the inset to Fig. 1. The two reflections seen conform to the (111) and (200) reflections of metal with face centred cubic structure. The lattice constant determined from XRD pattern, 0.409 ± 0.001 nm, is in good agreement with the standard diffraction pattern of gold metal (JCPDS Pattern 4-784). The nanoparticles, as one may expect, lack the extended order of usual crystals. This is evident from the fact that the peaks are much broader than one gets for the bulk metal. As is often done, the average GNP size ξ was calculated using the Debye–Scherrer formula,

ξ = Kλ/(β cos θ).

here β is the full width at half maximum, λ and θ are the wavelength of the radiation and the Bragg angle, respectively. The coefficient K is a correction factor that depends on the shape of the domains. For fairly regular shapes it usually varies between 0.8 and 1.0, and is taken to be 0.89 for spherical particles. Using the experimental values for the different parameters the particle size turns out to be 5.4 ± 1 nm, a value comparable to that obtained from TEM. A further support comes from the Porod representation of the low angle Xray data (see Fig. SI-4†), which yields the particle size to 5.3 nm.

Fig. 1 X-ray diffraction profiles for the pure LC (PCPBB) and the X = 0.05 GNP exhibiting two diffuse reflections, Peak 1 and Peak 2, corresponding to the spacing between the molecules along and perpendicular to the director direction. The composite also exhibits a low-intensity peak at wide angles (Peak 3) due to the reflections from the gold nanoparticles. The inset shows the scattering for the nanoparticles as well as the X = 0.05 composite, showing the (111) and (200) peaks characteristic of metallic gold.

To prepare the composites, a colloidal solution of GNP in toluene was added to a previously weighed PCPBB placed in a 5 ml vial. The contents of the vial were subjected mechanical shaking to achieve uniform dispersion. Subsequently the solvent was evaporated and the mixture was dried under reduced pressure. The composite obtained was used for the measurements; the concentration of GNP in the composite is denoted by X in weight fraction, taken as the ratio of weight of GNP to that of LC. Five different compositions were prepared with X = 0.005, 0.01, 0.02, 0.025 and 0.05. Texture photographs obtained with a polarizing optical microscope (Leica DMRXP fitted Optronics digital camera) in the nematic phase for different concentrations of GNP showed that for all composites the GNPs are quite well dispersed without any aggregation.

The Xray diffraction patterns obtained for the pure LC and a representative composite with X = 0.05 are shown in Fig. 1. The two diffuse peaks below 2θ < 30° are characteristic of the nematic scattering, with the low angle peak suggesting the presence of a slight local positional order; The wide angle represents scattering due to the intermolecular distance perpendicular to the nematic director The presence of the peaks at 2θ ∼ 38° and 44° (shown on an enlarged scale in the inset) due to the (111) and (200) reflections arising from gold establishes the presence of GNP in the nematic medium. Although the low concentration of GNP, together with the fact that the dispersing medium is essentially a fluid are responsible for the lowered s/n ratio of these peaks, it is clearly seen that peak positions and widths remain unaltered.

2.3. Measurements

The differential scanning calorimetric measurements were performed with the DSC 7 system of Perkin Elmer. The electrical data were obtained with samples sandwiched between two indium-tin-oxide coated glass plates, very low sheet resistance (<10 Ω □⁻¹). Thin Mylar strips, placed outside the electrically-active area, defined the thickness of the cell. The sample cells were placed inside a copper-block hot stage controlled by an Instec temperature controller. The measurements of the dielectric constant and electrical conductivity were carried out using an impedance analyzer (HP 4194A) or LCR meter (HP4284A) over frequencies in the range 10²–10⁷ Hz.

3. Results and discussion

3.1. Differential scanning calorimetry

Fig. 2 presents the differential scanning calorimeter (DSC) scans taken at a cooling rate of 5 °C min⁻¹ for pure PCPBB and five composites. A qualitatively significant change observed is the weakening of the I–N transition for the composites; the effect becomes more as the concentration of GNP is increased. Additionally the peak also gets broadened for the composites. Both these features can be considered to be arising as an impurity effect, especially since the second constituent (GNP) in the mixtures is a non-LC component. Inset (a) of Fig. 2 shows the influence of X, the GNP concentration, on the thermal parameters, viz., transition temperature (T_IN) and transition entropy (ΔS_IN). When X changes from 0 to 0.05, while the transition temperature diminishes by 10 K, the transition entropy reduces by ∼ 45%. Gorkunov and Osipov²³ have worked out a molecular mean field theory for the composites of nanoparticles with liquid crystals. A special case they consider is that of spherical particles, for which according to the theory the influence on the I–N transition is given by T_IN = (1 − ν)T_INO, where T_INO and T_IN are the transition temperature for the pure LC and the composites, respectively and (1 − ν) represents the contribution of the dilution effect. The term dilution here refers to the feature that inclusion of nanoparticles into the nematic medium diminishes the interaction between the LC molecules, thus diluting the order parameter of the system. In the absence of any explicit expression for the concentration dependence of the parameter ν in the theory, and keeping in view the trend observed in the experiments, we fitted the data in the inset (a) of Fig. 2 to eqn (1)

T_IN = T_INO − AX² (1)

Fig. 2 Differential scanning calorimeter profiles in the vicinity of the isotropic–nematic (I–N) transition for the pure LC (X = 0) and the different composites, with the concentration of GNP indicated against each curve. The drastic reduction in the thermal strength with increasing X is clearly visible. The concentration dependence of the transition temperature (T_IN) and the associated entropy change are shown in inset (a). Inset (b) shows, on an enlarged scale, the double peak profile seen for X = 0.005 composite, with the position of the weaker peak indicated by the arrow corresponding to the surface I–N transition, discussed in the text.

and find the fitting is quite good, which shows that the dilution effect is quite strong for the present system. The weakening of the thermal signature of the transition with increasing GNP concentration is evident from the DSC scans. To quantify the weakening, we determined the entropy (ΔS) associated with the transition using the area under the peak. Inset (a) of Fig. 2 shows that ΔS decreases significantly with X, a feature in general agreement with the dilution theory.²³ A further argument can be made by keeping in mind that the I–N transition for the pure LC is a weak first order transition with a jump in the order parameter. The observed behavior of ΔS suggests that the presence of the particles drives the transition towards a second order transition region through a tricritical point.²⁴

Another feature that was observed for X = 0.005 and 0.01 composites is the existence of a small peak just below the main peak (seen clearly on an enlarged scale shown in the inset (b) of Fig. 2 for X = 0.005). Optical microscopy observations show that there is no textural change across the small peak, with the material remaining in the nematic phase. The separation between the twin peaks decreases for X = 0.01 composite, and for higher concentration materials it is difficult to discern such a feature, even if present owing to the fact that the overall strength diminishes. A twin peak profile for the isotropic–nematic transition, absent in the pure LC material, has been observed in both specific heat and DSC profiles for composites of LC with aerosil.^25,26 Analyzing high resolution calorimetric, light scattering and microscopy techniques, Caggioni et al.²⁶ propose that in the LC–aerosil systems the nematic order develops from the isotropic phase through a two-step process and explain in terms of a system exhibiting temperature dependent disorder strength, and due to a crossover from a random-dilution regime where the silica gel couples to the scalar part of the nematic order parameter, to a low-temperature random-field regime where the coupling induces distortions in the director field. A similar crossover phenomenon has been found in disordered antiferromagnets.²⁷ As it happens in these systems also, the presently studied materials show that the high-temperature peak is much sharper compared to the low-temperature peak. While the random field crossover phenomenon mentioned above is possible in the present case also, the observed double peak profile here can also be viewed in terms of a surface transition separated from a bulk transition. The bulk transition is caused by molecules which are away from the GNP surfaces and are not influenced by the particles. The second transition is due to the molecules which are attached to, or in the immediate vicinity of GNP. Such “surface” LC molecules bind to GNP (through chain–chain interaction of the hydrophobic chain on the LC molecule and the capping agent of the particle) with an orientation that is locally perpendicular to the particle surface creating a region of higher disorder in comparison to the bulk region. The reduced order of the surface molecules would also lower their transition temperature. If the surface effects become strong, then there can be a bifurcation of the temperature at which the bulk and the surface molecules undergo the transition resulting in doubling of the peaks. With increasing concentration of GNP, the proximity of the particles reduces the unaffected bulk regions thus weakening the thermal signal at the transition, and consequently diminishing the ability to detect the surface transition.

Electrical conductivity. Fig. 3(a) and (b) show the conductivity along (σ_||) and perpendicular (σ_⊥) to the nematic director (n̂) obtained at 1 kHz by having a small probing voltage (0.5 V) parallel and normal to n̂, respectively, whose direction is fixed by imposing an orienting magnetic field of magnitude 1 T. In order to avoid the effects of the sample pre-history and any transient processes, the samples were first heated to the isotropic phase and the data were collected in the cooling mode. Even at a cursory level, the data presented are consistent with the percolation model, i.e., the σ values, which for the pure LC are typical of insulators, increase by more than an order of magnitude even for the lowest concentration studied, viz., X = 0.005. With further increase in concentration there is a steady increase in the value resulting in an overall increase of ∼ two orders of magnitude for X = 0.05. Two other features seen in Fig. 3(a) and (b) are: (i) σ_|| for pure LC exhibits an anomalous increase at low temperatures (high 1/T). As we shall see later this is an artefact resulting from the dielectric relaxation of the medium. (ii) For all concentrations, the I–N transition is marked by a step or change in the slope of the temperature dependence of σ, although the effect gets smoothened for higher concentrations.

Fig. 3 Thermal dependence of the electrical conductivity at 1 kHz on a semi-logarithmic scale (a) along, and (b) perpendicular to the nematic director direction for the pure LC and the different composites, with the concentration of GNP indicated against each data set. The step like change seen in each set corresponds to the I–N transition.

The concentration dependence of σ_Iso, the value in the isotropic phase just at the I–N transition, and σ_⊥ in the nematic phase taken at two fixed relative temperatures of T_IN – T = 10 K and T_IN – T = 70 K are shown in Fig. 4. The data sets exhibit transition to a reasonably high conducting state at concentrations of GNP exceeding X = 0.005, and the behaviour is again typical of systems showing a percolation threshold,²⁸ which can be explained as follows. With the increase in the content of GNP in the composite, the interactions between individual GNPs become important, and at the percolation threshold, defined as content of GNP necessary for building a continuous conductive path inside the isolative matrix, a transition from the nonconductive to the conductive state occurs.²⁹ After the drastic increase at the threshold, σ develops a much weaker dependence on further increase in the concentration of GNP. The abrupt increase at the threshold followed by a weaker increase can be described by a percolation scaling law of the type

σ ∝ (X − X_c)^t (2)

here X_c is the threshold concentration and t is a characteristic exponent. Fitting the data presented in Fig. 4 to eqn (2) yields exponent values which are essentially the same, being t = 0.63 ± 0.03 and 0.71 ± 0.05 in the nematic (at T_IN – 10 K) and isotropic phases respectively. It should however be noted that these values are much lower than found in a large number of insulating systems,³⁰ in which the conducting state is induced by the addition of particles such as carbon nanotubes (CNT). In such polymer–CNT complexes, the value of the exponent t is dependent on the dimensionality d of the system: t = 1.1–1.3 for d = 2, and 1.6–2.0 for d = 3. Thus the exponent values for the currently studied composites, are much lower than these expectations. The experimental values are rather closer to those expected in the pre-percolation regime, which definitely is not true in the present scenario. But it may be recalled that deviations are often found in conductive composites containing dispersed fillers, and attributed³¹ to many peculiarities associated with such systems, such as, host–filler interaction and existence of contact phenomena on the particle–particle boundary. In the case of liquid crystal hosts, a further parameter that may have to be included is the influence of thermal fluctuations on the fluid environment, and consequently on the connectivity of the metal particles with their organic capping unable to maintain a time-independent contact. This requirement is perhaps supported by our observation that the exponent increases from 0.63 to 0.99 when the lowest temperature data (at T_IN – 70 K) in the nematic phase are considered.

Fig. 4 GNP concentration of σ at the isotropic-nematic transition (T_IN set), and in the nematic phase, not too far from the transition (T_IN − 10 K set) and deep in the nematic phase (T_IN − 70 K set). The lines represent the fit to the percolation model (eqn (2)). Error bars are smaller than the symbol size used.

For an anisotropic system, the behaviour in different directions is an important feature. Fig. 5 shows the concentration-dependence of the conductivity anisotropy, defined as R = σ_||/σ_⊥, exhibiting a gentle decrease of about 15% from X = 0 to X = 0.05 and suggesting that the charge transport becomes more isotropic. This could be arguably due to the network becoming more 3D-like, as the GNP concentration is increased. Employment of anisotropic metal particles perhaps reduces this tendency to form a 3D network, and thus help to retain the conductivity anisotropy ratio unaltered.¹⁰

Fig. 5 Concentration dependence of the anisotropy of conductivity σ_a (= σ_||/σ_⊥) and permittivity ε_a (= ε_|| − ε_⊥) at a relative temperature of T_IN − 10 K. The lines are just guides to the eye.

3.2 Arrhenius behavaiour of conductivity

Both the anisotropic conductivities, σ_|| and σ_⊥ (in the nematic phase), and of σ_Iso in the isotropic exhibit significant temperature dependence. Owing to the influence of the low frequency director relaxation on σ_||, mentioned above, we use the σ_⊥ data for analysis in the nematic phase. In the semi-logarithmic depiction in Fig. 3(b), σ is seen to vary linearly with inverse temperature. Therefore we fitted the data in the two phases (except in the vicinity of the transition) to the Arrhenius law

This equation is derived to describe the change of the electrical conductivity with temperature for the general case of non-metallic thermally-driven conductors, with E_s denoting the thermal activation energy of electrical conduction that depends on the nature of the conductor, the prefactor (σ₀) being the conductivity when the reciprocal temperature approaches zero and k_B, the Boltzmann constant. It should however be mentioned that the quality of fitting improves slightly if instead of the Arrhenius law, the Vogel–Fulcher–Tammann (VFT) expression

σ(T) = σ₀ exp[−B/(T − T_g)]

with T_g as the glass transition temperature, is employed. However, since experiments could not be carried out at temperatures which are close to the possible T_g we limited the analysis to the Arrhenius law. The E_s values obtained by a least-squares fit of the data to eqn (3) for the different concentrations in the nematic and isotropic phases are listed in Table 1 and also presented in Fig. 6. Interestingly, the activation energy values in the isotropic phases are about half of those in the nematic phases indicating that the charge transport is influenced by the underlying orientational order, although the conducting particles are themselves isotropic. It may be mentioned that the activation energy values obtained from the σ_|| data set (by considering the region away from the relaxation frequency artefact mentioned above) is marginally different from those for the σ_⊥ data.

Table 1 Activation energies (in kJ mol⁻¹) for the thermal behaviour of the conductivity (E_s) and dielectric relaxation frequency (E_d) as a function of GNP concentration in the composite

X	Es		Ed
	Nematic	Isotropic	Nematic
0	36.3 ± 0.05	23.9 ± 0.07	78.7 ± 0.20
0.005	36.9 ± 0.05	21.3 ± 0.06	74.6 ± 0.08
0.01	38.5 ± 0.02	22.7 ± 0.02	76.2 ± 0.10
0.02	35.7 ± 0.02	21.5 ± 0.02	74.4 ± 0.08
0.025	35.7 ± 0.03	21.5 ± 0.02	74.4 ± 0.08
0.05	36.8 ± 0.04	22.1 ± 0.03	74.3 ± 0.08

---

Fig. 6 Influence of GNP concentration on the activation energy values associated with the thermal dependence of conductivity (E_s) and the dielectric relaxation frequency (E_d). The lines are merely guides to the eye. The error bars are contained inside the symbols used, as can be seen from Table 1.

3.3 Frequency dependence of conductivity

The frequency-dispersion of conductivity is an important characteristic of conductors formed by particle-doped insulators. A wide variety of materials including glasses, polycrystalline semiconductors, polymers, transition metal oxides, organic–inorganic composites, ceramics, etc., exhibit a similar frequency dependent conductivity, often termed Jonscher's Universal Response.³² In such materials, at low frequencies, one observes a constant conductivity while at higher frequencies the conductivity becomes strongly frequency-dependent. Therefore it is customary to express the conductivity σ(f) measured at a finite frequency f as

σ(f) = σ_DC + σ_AC

where σ_DC and σ_AC are the zero-frequency DC component, and AC contributions, respectively. The Jonscher's universal description considers a distribution of hopping probabilities between sites distributed randomly in space and in energy and uses the following explicit expression for σ(f)

σ(f) = σ_DC(1 + k(f/f_c)ⁿ) (4)

where k is a constant and in disordered solids, 0 < n < 1. The critical frequency f_c marks the onset of the conductivity relaxation, and the transformation from long range hopping to the short range motions. Fig. 7 presents the frequency-dependent σ_⊥ data for pure LC and composites, with X = 0.02, with the observed behaviour consistent with other such conducting systems. The solid lines depict the fitting to eqn (4) showing that the expression describes the data well. For all the two materials the fitted values of the exponent, n = 1.45 ± 0.01 and 1.26 ± 0.02 for X = 0, 0.02 composites respectively, fail the universal expectation that the exponent should be <1. The reason for this discrepancy is not clear to us, although it must be mentioned that the model, which is meant for disordered solids does not obviously consider thermal fluctuations, a feature that is invariably present in the nematic phase, and cannot be ignored. It may, however, be pointed out that discussing a jump relaxation model Funke³³ suggested that a value of n > 1 could actually be suggesting a physical situation wherein the motion involved is a short hopping of the species localized to the neighbourhood. More recently Papathanassiou et al.³⁴ highlighted the experimental observations in certain glassy materials³⁵ and proposed a model stating that there is no physical argument to restrict the value of n below 1. According to them while a qualitative universal behaviour of the AC conductivity in disordered media is envisaged, there need not be a universal fractional power law. More liquid crystalline systems have to be investigated to test the application of this idea in soft systems. The critical frequency f_c is seen to increase with increasing concentration, a behaviour consistent with that seen for insulating polymers incorporated with conducting particles.³⁶

Fig. 7 Probing frequency dependence of the conductivity for the pure LC and the X = 0.02 composite at a relative temperature of T_IN − 70 K. The lines represent the fit to eqn (4).

Dielectric permittivity. The temperature dependence of the permittivity along (ε_||) and perpendicular (ε_⊥) to the nematic director determined at a fixed frequency of 1 kHz for the pure LC and three composites, X = 0.01,0.02 and 0.05 are shown in Fig. 8. In all the three sets the abrupt change in the data marks the I–N transition. Several interesting features are seen: (i) the composites retain the positive dielectric anisotropy of the pure LC, (ii) both the anisotropic permittivities (ε_|| and ε_⊥), as well as the value in the isotropic phase (ε_iso) increase with increasing GNP concentration, (iii) the difference between ε_|| and ε_⊥ appears to increase as X increases. These features suggest that there is an additional dipolar contribution from the metal particle network to the overall permittivity of the medium, which increases with the concentration of GNP. The increase in ε′ for the composite is also possibly due to the creation of an increased number of GNP–LC–GNP capacitors. A better explanation perhaps is the following. An increase in dielectric constant in polymeric systems with metal nanoparticles has been attributed to the phenomenon of coulombic blockade.³⁷ This phenomenon, which has found applications in single electron transistors³⁸ and thermometers³⁹ etc., occurs in systems having tunnel barriers separating conducting islands from one another and the electrodes, resulting in an enhancement of the permittivity. Such a blockade also leads to a lowering of the dielectric dissipation factor. This could not be checked in the present system owing to the presence of a low frequency relaxation, to be discussed below.

Fig. 8 Thermal variation of the permittivity in the isotropic and nematic phases measured at 1 kHz along and perpendicular to the director for the pure LC and composites. In each case the temperature at which there is a step-like change in the value, marks the transition between the two phases. The significant increase in the values with increasing concentration of GNP is evident.

The anisotropy ε_a (= ε_|| – ε_⊥) at T_IN − 10 K, shown in Fig. 5, exhibits a marked increase of 28%. It may be recalled here that the qualitative behaviour of ε_a seen for the present system is quite similar to that for composites with a strongly polar nematic liquid crystal having spherical⁴⁰ as well as rod-like GNP,⁴¹ and thus is perhaps a general feature of GNP–LC systems. In liquid crystalline materials an enhancement in ε_a is associated with an increase in the orientational order. However, the lowering of σ_a the discussed earlier, and the director relaxation behaviour (vide infra), indicate the opposite, i.e., a reduction in nematic order with increasing GNP concentration. In view of this antagonistic requirement we tend to think that the increase in the dielectric anisotropy to be arising from the polarisability of the GNPs.

Dielectric relaxation spectroscopy. Fig. 9(a) and (b) show spectra for the real (ε′) and imaginary (ε′′) parts of the permittivity for the pure LC and composites with X = 0.05 at a fixed relative temperature of T_IN − 70 K. While the increase in ε′ could be because of reasons mentioned above, the enhancement of ε′′ could be either due to an increased electrical conductivity (described below) or associated with GNP–LC interfacial regions. More than the absolute values of the permittivity, it is the presence of a relaxation – clearly visible in the ε_|| data for both the pure LC and composite samples (the governing relaxation frequency of the mode being approximately the midpoint of the step in ε′ and peak point in ε′′ data) – that is important. The single relaxation is associated with the director relaxation, and it is notable that the relaxation frequency appears to be shifting to higher values with increasing X; nearly doubling in the value from X = 0 to 0.05. We will discuss this feature below.

Fig. 9 Dielectric relaxation spectra in the nematic phase (T_IN − 70 K) for the pure LC and a representative composite X = 0.05 exhibiting a clear relaxation process in both the (a) real and (b) imaginary components of the permittivity. The large increase in ε′′ at low frequencies is due to the conductivity of the system, by subtracting which the relaxation curves stand out as shown in the inset of the bottom panel. The lines stand for the fit of the data to eqn (5). The inset in the upper panel presents the anisotropy in the permittivity below (+ε_a) and above (−ε_a) the crossover frequency that lies very close to the relaxation frequency. The error bars are smaller than the symbol size used.

Especially for the composite in the vicinity of the relaxation, the data of the imaginary component (ε′′), is partially masked by the large frequency dependence of ionic current contribution extending from the lowest frequency. However, quantitative description of the data using a standard Havriliak–Negami (HN) expression,⁴² given below, clearly brings about the relaxation phenomenon in the composite also.

Here ε*(f) is the complex capacitance at a frequency f, and ε_∞ associated with the dielectric strengths of all the high frequency modes other than the one under consideration. Δε and f_R are the strength and frequency of the relaxation mode. The parameter α characterizes the distribution of the relaxation times while β is a measure of the asymmetry of the distribution. The RHS of eqn (5) contains, in addition to the HN contribution (2^nd term), a term to account for the DC conductivity (σ_o) contribution to ε^′′, and a part (the last term in eqn (5)) to explain the cell relaxation time arising from the finite sheet resistance of the ITO-coated glass plates used. For both the pure LC and the mixtures the frequency-dependent data are well described by eqn (5). The HN parameter β was found to be equal to 1 for the pure LC as well as the mixtures, indicating a symmetric relaxation profile. The other parameter, α, also turned out to be equal to 1 for the pure LC indicating a Debye relaxation; for the LC–GNP dispersion, however, 0.93 < α < 1 indicating a slight distribution of the relaxation times.

As stated earlier, the large conductivity masks the existence of the relaxation for the composite. But the subtraction of the conductivity contribution estimated from the third term of eqn (5) brings out the dielectric features in the imaginary part of the permittivity also (see Fig. 9(b)). In fact, the observed features in ε′′ are in conformity with those seen for the ε′ vs. frequency data.

In the frequency range studied ε_⊥, the permittivity in the plane perpendicular to the nematic director, has hardly any frequency dependence, while ε_|| exhibits a relaxation. For the material under study, the relaxation creates a situation wherein at a particular frequency, referred to as the crossover frequency (f_cr), ε_⊥ cuts through the ε′_|| data. This causes ε_a to be positive below f_cr, and negative, above f_cr; invariably, f_cr lies in the close proximity of f_R. Inset of Fig. 9(a) shows the GNP concentration (X) dependence of the dielectric anisotropy below (+ε_a) and above (−ε_a) f_cr, and it is seen that both the parameters have a very weak dependence on X.

The temperature dependence of the relaxation frequency f_R for the pure LC and different composites are shown in Fig. 10. The presence of the nanoparticles is seen to have a substantial influence on the magnitude of relaxation frequency: f_R increases with increasing X, as shown in the inset to Fig. 10 presenting the concentration dependence of the relaxation frequency at a constant temperature of T = 50 °C. An increase in f_R for the observed director relaxation mode can be associated with a reduction in the orientational order. In fact, such an increase in the relaxation frequency is also seen in a non-conducting nanoparticle–LC system,²⁵ such as, for example, in composites of nematic with aerosil particles. However, the effect is much weaker in the case of aerosil systems. For example, with the same host LC and a particle concentration of 5%, the increase in f_R is only ∼20% for the aerosil composites, whereas the presently studied GNP composites exhibit a doubling of the value. This is indicative of the stronger reduction in the order parameter for the GNP composites than for the aerosil mixtures. Of course, a feature of the aerosil system that should be borne in mind is that the hydroxyl groups decorating the particles create a hydrogen bonded network that perhaps is responsible for diminishing the influence of the particles on the order parameter of the system.

Fig. 10 Temperature dependence of the dielectric relaxation process in the nematic phase of the pure LC (a), and the composites X = 0.01, 0.02 and 0.05 (b,c and d) exhibiting Arrhenius behaviour, the activation energy (E_d) of which is shown in Fig. 6. The inset shows the strong influence of GNP concentration on the relaxation frequency at T = 50 °C presented on a semilogarithmic scale. The line is merely a guide to the eye.

For the pure LC and the composites as well f_R has a linear dependence (except in the vicinity of T_IN) with reciprocal temperature in the semi-logarithmic representation shown in Fig. 10. As mentioned in the conductivity case, such a feature indicates Arrhenius behaviour. Accordingly we fitted the data to

The E_d values obtained by a least-squares fit of the data for the different concentrations in the nematic phase are given in Table 1 and also graphically represented in Fig. 6. Unlike the concentration-independence of E_s, the activation energy for the conducting process, E_d exhibits a small decrease with X. These two features suggest that despite the large changes in the magnitude to the parameters of σ and f_R, the activation energies are not altered much by the presence of the metal particles. Further E_d values are much higher than the corresponding E_s values indicating that different mechanisms control the two processes.

Finally, we consider the importance of the host PCPBB LC molecule used in the presence of study. As already stated the molecule does not possess a strong dipole moment along the long axis of the molecule, but has a weak one (Cl) along the transverse direction. Since there is no basis to expect the interaction between the PCPBB molecule and the metal particle surface (the dodecane thiol shell rather than the bare particle) to be dipolar in nature, we consider such an interaction to be hydrophobic – between the terminal chains of PCPBB and the dodecane chain of GNP. Maximizing such an interaction would then make the LC molecular arrangement in the vicinity of GNP to radiate out resembling a pin-cushion, and lowering the order parameter of the region. However, the resulting elastic deformation of the director profile would not allow the radiating pattern to extend over long distances away from GNP. With an increasing concentration of GNP the regions around the particles also start interacting diminishing the overall order parameter of the medium. These features are schematically shown in Fig. 11.

Fig. 11 Schematic illustration to show the disruption of the orientational ordering of the liquid crystal molecules in the vicinity of GNP: The dodecane thiol chains involved in the capping of the particle are shown in wiggles in cyan, and the LC molecules as blue ellipses with two hydrocarbon chains (shown as black wiggles) on either side the molecule. Moving away from the centre of the particle, the orientational ordering increases towards the value dictated by the surrounding nematic. This feature is colour coded such that lighter the colouring, higher is the orientational ordering. When the particles are far apart the ordering of the intervening region is comparable (light yellow) to that of the bulk nematic, as shown in (b). When the particles come nearer as would happen with higher concentration of GNP, the disordering increases shown with deeper yellow in (c).

4. Summary

We have presented results of the first detailed calorimetric, frequency-dependent anisotropic conductivity and permittivity measurements in composites of gold nanoparticles (GNP) and a weakly-polar nematic liquid crystal possessing a low frequency director relaxation. The presence of the nanoparticles substantially lowers the nematic–isotropic transition temperature and also the associated transition entropy. The conductivity of the composites is enhanced by two orders of magnitude, with a concentration dependence described by a percolation scaling law usually observed in mixtures of metal particles and polymers. The exponent determined is much smaller, which could be due to the presence of thermal fluctuations characteristic of the fluid-like nematic medium. The frequency dependence of the AC conductivity exhibits a critical frequency that increases with concentration of GNP; the high frequency response is not in agreement with Jonscher's Universal Response principle. The low frequency of the director relaxation mode enabled detailed dielectric relaxation spectroscopy studies, the first of its kind. While the value of the relaxation frequency depends strongly on the concentration of GNP, the activation energy remains essentially the same. We compare the observations with those predicted by the dilution theory, and find a general agreement. Experiments are underway to replace the spherical particles used here with anisotropic particles to further test the predictions of the theory and also to explore the behaviour of the anisotropic charge transport and permittivity along and perpendicular symmetry-breaking directions.

Acknowledgements

The authors express their gratitude to Prof. C.N. R. Rao and Ms. G. Usha Tumkurkar of JNCASR, Bangalore, for kindly providing the TEM images. They also thank Dr Uma Hiremath, CSMR, Bangalore for her help in the preparation of the nanoparticles. SKP and TS gratefully acknowledge the financial support by the Department of Science and Technology, New Delhi, under a SERC project.

References

1. K. I. Winey and R. A. Vaia, MRS Bull., 2007, 32, 314.
2. A. Heilmann, Polymer Films with Embedded Metal Nanoparticles, Springer-Verlag, Berlin, 2003.
3. D. Bloor, A. Graham, E. J. Williams, P. J. Laughlin and D. Lussey, Appl. Phys. Lett., 2006, 88, 102103.
4. O. Stamatoiu, J. Mirzaei, X. Feng and T. Hegmann, in Liquid Crystals Materials Design and Self-Assembly, ed. C. Tschierske, Springer-Verlag, Heidelberg, Top. Curr. Chem, 2012, 318, 331.
5. Yu. M. Yevdokimov, V. I. Salyanov, E. I. Katz and S. Skuridin, Acta Nat., 2012, 4, 78.
6. K. K. Vardanyan, D. M. Sita, R. D. Walton, W. M. Saidel and K. M. Jones, RSC Adv., 2013, 3, 259.
7. P. Goel, G. Singh, R. P. Pant and A. M. Biradar, Liq. Cryst., 2012, 39, 927.
8. M. Draper, I. M. Saez, S. J. Cowling, P. Gai, B. Heinrich, B. Donnio, D. Guillon and J. W. Goodby, Adv. Funct. Mater., 2011, 21, 1260.
9. S. K. Prasad, K. L. Sandhya, G. G. Nair, U. S. Hiremath, C. V. Yelamaggad and S. Sampath, Liq. Cryst., 2006, 33, 1121.
10. S. Sridevi, S. Krishna Prasad, G. G. Nair, V. D'Britto and B. L. V. Prasad, Appl. Phys. Lett., 2010, 97, 151913.
11. Neeraj and K. K. Raina, Opt. Mater., 2013, 35, 531.
12. J. Mirzaei, R. Sawatzky, A. Sharma, M. Urbanski, K. Yu, H. S. Kitzerow and T. Hegmann, Proc. SPIE 8279, Emerging Liquid Crystal Technologies VII, 2012, p. 8279; Y. A. Garbovskiy and A. V. Gluscchenko, in Solid State Physics, vol. 62, ed. R. E. Camley and R. L. Stamps, Academic Press, 2011.
13. U. B. Singh, R. Dhar, R. Dabrowski and M. B. Pandey, Liq. Cryst., 2012, 40, 774.
14. P. K. Tripathi, A. K. Misra, S. Manohar, S. K. Gupta and R. Manohar, J. Mol. Struct., 2013, 1035, 371.
15. W. Haase, A. Lapanik and M. Ottinger, Proceedings of SPIE 8114, Liquid Crystals XV, 2011, p. 81140H.
16. J. P. F. Lagerwall and F. Scalia, Curr. Appl. Phys., 2012, 12, 1387; E. R. Soulé, J. Milette, L. Reven and A. D. Rey, Soft Matter, 2012, 8, 2860.
17. H. Qi, B. Kinkead and T. Hegmann, Adv. Funct. Mater., 2008, 18, 212.
18. S. Krishna Prasad, M. Vijay Kumar and C. V. Yelamaggad, Carbon, 2013, 59, 51.
19. B. E. Kilbride, J. N. Coleman, J. Fraysse, P. Fournet, M. Cadek, A. Drury, S. Hutzler, S. Roth and W. J. Blau, J. Appl. Phys., 2002, 92, 4024.
20. J. P. Van Meter and B. H. Klanderman, Mol. Cryst. Liq. Cryst., 1973, 22, 285.
21. M. Brust, M. Walker, D. Bethell, D. J. Schiffrin and R. Whyman, J. Chem. Soc., Chem. Commun., 1994, 801.
22. M. J. Hostetler, J. E. Wingate, C. J. Zhong, J. E. Harris, R. W. Vachet, M. R. Clark, J. D. Londono, S. J. Green, J. J. Stokes, G. D. Wignall, G. L. Glish, M. D. Porter, N. D. Evans and R. W. Murray, Langmuir, 1998, 14, 17.
23. M. V. Gorkunov and M. A. Osipov, Soft Matter, 2011, 7, 4348–4356; M. V. Gorkunov, G. A. Shandryuk, M. S. Alina, Y. K. Irina, S. M. Alexey, V. K. Yaroslav, V. T. Raisa and A. O. Mikhail, Soft Matter, 2013, 9, 3578.
24. P. K. Mukherjee, Int. J. Mod. Phys. B, 1998, 12, 1589; V. M. Lenart, S. L. Gómez, I. H. Bechtold, A. M. Figueiredo Neto and S. R. Salinas, Eur. Phys. J. E: Soft Matter Biol. Phys., 2012, 35, 4; J. S. Rzoska and A. Drozd-Rzoska, Nato Science Series II, ed. A. R. Imre, H. J. Maris and P. R. Williams, 2002, 84, p. 117; M. S. Ishtiaque, P. Virgi, G. P. Rolfe and C. Rosenblatt, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2003, 67, 011704.
25. V. Jayalakshmi, G. G. Nair and S. Krishna Prasad, J. Phys.: Condens. Matter, 2007, 19, 226213.
26. M. Caggioni, A. Roshi, S. Barjami, F. Mantegazza, G. S. Iannacchione and T. Bellini, Phys. Rev. Lett., 2004, 93, 127801.
27. See e.g., D. P. Belanger, Braz. J. Phys., 2000, 30, 682.
28. See e.g., Y. Pan, G. J. Weng, S. A. Meguid, W. S. Bao, Z.-H. Zhu and A. M. S. Hamouda, J. Appl. Phys., 2011, 110, 123715.
29. D. Stauffer, A. Aharony, Introduction to Percolation Theory, Taylor & Francis, London, 1994.
30. See e.g., C.-W. Nan, Y. Shen and J. Ma, Annu. Rev. Mater. Res., 2010, 40, 131.
31. Ye. P. Mamunya, V. V. Davydenko, P. Pissis and E. V. Lebedev, Eur. Polym. J., 2002, 38, 1887.
32. A. K. Jonscher, Nature, 1977, 267, 673; J. C. Dyre and T. B. Schrbder, Rev. Mod. Phys., 2000, 72, 873; D. L. Sidebottom, B. Roling and K. Funke, Phys. Rev. B: Condens. Matter Mater. Phys., 2001, 63, 5068.
33. K. Funke, Prog. Solid State Chem., 1993, 22, 111.
34. A. N. Papathanassiou, I. Sakellis and J. Grammatikakis, Appl. Phys. Lett., 2007, 91, 122911.
35. C. Cramer, S. Brunklaus, E. Ratai and Y. Gao, Phys. Rev. Lett., 2003, 91, 266601.
36. S. Barrau, P. Demont, A. Peigney, C. Laurent and C. Lacabanne, Macromolecules, 2003, 36, 5187.
37. See e.g., J. Lu, K.-S. Moon, J. Xu and C. P. Wong, J. Mater. Chem., 2006, 16, 1543.
38. M. A. Kastner, Rev. Mod. Phys., 1992, 64, 849.
39. J. P. Pekola, K. P. Hirvi, J. P. Kauppinen and M. A. Paalanen, Phys. Rev. Lett., 1994, 73, 2903.
40. S. Krishna Prasad, K. L. Sandhya, G. G. Nair, U. S. Hiremath, C. V. Yelamaggad and S. Sampath, Liq. Cryst., 2006, 33, 1121.
41. S. Sridevi, S. Krishna Prasad, G. G. Nair, V. D'Britto and B. L. V. Prasad, Appl. Phys. Lett., 2010, 97, 151913.
42. S. Havriliak and S. Negami., Polymer, 1967, 8, 161.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c3ra45761c

---