Phase sensitive molecular dynamics of self-assembly glycolipid thin films: A dielectric spectroscopy investigation T. S. Velayutham, B. K. Ng, W. C. Gan, W. H. Abd. Majid, R. Hashim, N. I. Zahid, and Jitrin Chaiprapa Citation: The Journal of Chemical Physics 141, 085101 (2014); doi: 10.1063/1.4893873 View online: http://dx.doi.org/10.1063/1.4893873 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/141/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Hyperthermal organic thin film growth on surfaces terminated with self-assembled monolayers. I. The dynamics of trapping J. Chem. Phys. 134, 224702 (2011); 10.1063/1.3591965 A molecular simulation study of methylated and hydroxyl sugar-based self-assembled monolayers: Surface hydration and resistance to protein adsorption J. Chem. Phys. 129, 215101 (2008); 10.1063/1.3012563 Influence of alkanethiol self-assembled monolayers with various tail groups on structural and dynamic properties of water films J. Chem. Phys. 129, 154710 (2008); 10.1063/1.2996179 Understanding the nonfouling mechanism of surfaces through molecular simulations of sugar-based selfassembled monolayers J. Chem. Phys. 125, 214704 (2006); 10.1063/1.2397681 Molecular dynamics simulations of a fully hydrated dimyristoylphosphatidylcholine membrane in liquid-crystalline phase J. Chem. Phys. 112, 3437 (2000); 10.1063/1.480924

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THE JOURNAL OF CHEMICAL PHYSICS 141, 085101 (2014)

Phase sensitive molecular dynamics of self-assembly glycolipid thin films: A dielectric spectroscopy investigation T. S. Velayutham,1,a) B. K. Ng,1 W. C. Gan,1 W. H. Abd. Majid,1 R. Hashim,2 N. I. Zahid,2 and Jitrin Chaiprapa3 1

Low Dimensional Materials Research Center, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia 2 Fundamental and Frontier Science of Self-Assembly Center, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia 3 Synchrotron Light Research Institute, Nakhon Ratchasima, Thailand

(Received 5 May 2014; accepted 11 August 2014; published online 28 August 2014) Glycolipid, found commonly in membranes, is also a liquid crystal material which can self-assemble without the presence of a solvent. Here, the dielectric and conductivity properties of three synthetic glycolipid thin films in different thermotropic liquid crystal phases were investigated over a frequency and temperature range of (10−2 –106 Hz) and (303–463 K), respectively. The observed relaxation processes distinguish between the different phases (smectic A, columnar/hexagonal, and bicontinuous cubic Q) and the glycolipid molecular structures. Large dielectric responses were observed in the columnar and bicontinuous cubic phases of the longer branched alkyl chain glycolipids. Glycolipids with the shortest branched alkyl chain experience the most restricted self-assembly dynamic process over the broad temperature range studied compared to the longer ones. A high frequency dielectric absorption (Process I) was observed in all samples. This is related to the dynamics of the hydrogen bond network from the sugar group. An additional low-frequency mechanism (Process II) with a large dielectric strength was observed due to the internal dynamics of the self-assembly organization. Phase sensitive domain heterogeneity in the bicontinuous cubic phase was related to the diffusion of charge carriers. The microscopic features of charge hopping were modelled using the random walk scheme, and two charge carrier hopping lengths were estimated for two glycolipid systems. For Process I, the hopping length is comparable to the hydrogen bond and is related to the dynamics of the hydrogen bond network. Additionally, that for Process II is comparable to the bilayer spacing, hence confirming that this low-frequency mechanism is associated with the internal dynamics within the phase. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4893873] I. INTRODUCTION

A class of glycolipids called glycosides can be found naturally in bio-membranes1 in diverse molecular structures, which seem to suggest they are equally important as other natural phospholipids.2 Glycosides are amphitropic,3 capable of self-assembly in dry conditions as well as when solvated.4 Glycolipids give liquid crystalline properties due to the affinity of the de-mixing of the hydrophilic and hydrophobic parts of the molecules.1 Natural glycolipids usually contain double alkyl chains, which give greater flexibility in self-assembly and enable the formation of various lyotropic phases from simple lamellar to other non-lamellar phases (columnar/hexagonal and cubic),1, 5 which offers a major advantage in biological research.6 In a dry state and driven by temperature (thermotropic), these glycosides can also form self-assembly phases similar to classical lyotropic organizations, but these are referred to using a set of thermotropic nomenclatures such as smectic A (SA ), columnar/hexagonal (Col or H), and cubic phases (Q).7 These phases vary in both their structure and physical properties. In SA , glycolipids exist as a stack of planar molecular a) Author to whom correspondence should be addressed. Electronic mail:

[email protected] 0021-9606/2014/141(8)/085101/11/$30.00

bilayers, with the hydrophilic domain separated from the hydrophobic one. Powder diffraction measurement employed on the glycolipid reveals the formation of the SA , with the measured layer spacing smaller than the length of two molecules.8 This observation suggests that either the long alkyl chain partially overlaps to form interdigitated smectic Ad bilayers with the polar group pointing on the outside,9 or that the molecular arrangement within the layer may be tilted. A bicontinuous cubic phase is a liquid crystal with a cubic structure of some defined space group (usually Im3m, Pn3m, Ia3d), determined from a combination of techniques like X-ray and optical polarizing microscopy (OPM). While in a solvated system these phases are driven by concentration and temperature,10 in the non-solvated system the structure of the molecule (e.g., the branched chain Guerbet glycosides) and temperature support their phase formation.11 Its structure is derived from the bilayer lamellar which curves to form the triply periodic minimal surface (visualization is challenging, see Figure 1) with a zero mean curvature.12 Therefore, a bicontinuous cubic phase is a highly ordered phase and mechanically stiff due to its cubic symmetry, but the overall order is zero since its mean curvature is zero. Finally, the columnar phase is periodic in 2D, and consists of lipid columns where the sugar head group forms the core and the alkyl chains form the continuous phase.

141, 085101-1

© 2014 AIP Publishing LLC

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FIG. 1. (a) Phase behavior of Guerbet maltosides21, 25 with side chain lengths of 8–24. Three of these maltosides are used in the present work, Malto-C8C4, Malto-C12C8, and Malto-C14C10, with chain lengths of 12, 20, and 24, respectively; (b) some possible phases and their structures: (i) smectic A, SA , (ii) the triply periodic minimal surface of bicontinuous cubic, QII with space groups Im3m, Pn3m, and Ia3d, (iii) columnar/hexagonal, Col/H.

Figure 1 illustrates some of the possible organizations, which may be observed in a dry state for some glycolipids (Guerbet maltosides used in the present study). Numerous experimental techniques have been used to study the dynamics of hydrated lipids, such as nuclear magnetic resonance (NMR), quasi-elastic neutron scattering (QENS), dynamics light scattering, and dielectric spectroscopy (Svanberg et al.13 and the references quoted therein). From these studies, different dynamic processes were elucidated such as the diffusion of water and rotation of lipid heads within layers.14 In turn, this information has much advanced our understanding in biology; for example, complex movement of proteins through the lipid matrix is understood from many diffusion studies.15 In contrast, the dynamics study of non-hydrated lipids is scarce and currently is slowly emerging.16 Therefore, dynamic investigation of the anhydrous systems is timely to support the growing scientific interest in the thermotropic lipidic phases from the seminal work of Jeffrey17 and more recently those of Ericsson et al.18 and Auvray et al.19 Considering these points, we have concentrated our efforts on studying the thermotropic glycolipid phases in the absence of a solvent.20, 21 In addition, we have also previously reported on the pyroelectric behavior in dry glycolipids.22 In the ensuing study here, we have investigated the dielectric properties of Guerbet maltosides to establish the diffusion mechanism and the dynamic of the materials without the solvent effect. These Guerbet glycosides, prepared in Ref. 23, can be viewed as Guerbet sugars, along with the other Guerbet materials, including the alcohol, ester, and acid, all of which have been used in many industrial applications.24 The dielectric spectroscopy technique has been extensively applied to the molecular study of polymers,26 glass

formers,27 colloids,28 and other amphitropic systems,16 to probe the dynamic properties of these materials. Hence, the present study aims to characterize the dynamic behavior of thermotropic phases from branched chain glycolipids at molecular and mesoscopic levels using dielectric spectroscopy, and to establish possible relationships between the dynamics and the structure of these compounds. In hydrated glycolipid self-assembly, there are two types of permanent molecular dipoles present. One of these arises from the hydroxyl (OH) units in the head group and the other is from the presence of water around the lipid interface. Water may be regarded as a pair of the OH dipoles that share the oxygen and its dipole is the most mobile permanent dipole and its relaxation frequency occurs at 1–18 GHz.29 However, the relaxation of the free water molecules is not of our interest. Instead, in the present study of anhydrous glycolipids, the slow dynamics of the head group dipole is more relevant and may be related to the in-plane lateral diffusion, undulation and flip-flop which usually occur in milliseconds or in the kHz frequency range. This paper is devoted to the study of the low-frequency dielectric relaxation processes in the range of 0.01 Hz to 1 MHz in different thermotropic phases (SA , HII , and Q) of branched chain glycolipids with different chain lengths.

II. EXPERIMENTAL A. Phase transition studies

Three different branched chain sugar lipids were examined, where the sugar head group is maltose and this is connected via a β-glycosidic linkage. In naming these materials,

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known spacing, i.e., d = 58.38 Å. A sample was heated with a Eurotherm 2216e temperature regulator, with a heating rate of 5 ◦ C/min, and was left in equilibrium for 1 min before recording the diffraction patterns. The SAXSIT program was used to resolve overlapping peaks and determine the peak centers. B. Electrical measurement

FIG. 2. Chemical structure of (a) Malto-C8C4, (b) Malto-C12C8, and (c) Malto-C14C10. (d) Schematic diagram of the Guerbet maltosides.

we used Malto-CmCn, where m and n give the number of carbon atoms in the longer and shorter chains of their tails, respectively. The molecular structure and schematic diagram of the Guebert maltosides used in the study are given in Figure 2. The synthesis and purification method of the materials, among other similar branched lipids, is published in Ref. 23. The phase transition temperature of the sample was studied primarily by a Mettler Toledo differential scanning calorimeter (DSC) 822e equipped with a Haake EK90/MT intercooler. The STARe thermal analysis system software was used for data analysis. The glycolipid was dried over phosphorus pentoxide in a vacuum at 50 ◦ C for 48 h, since it is hygroscopic. The material weighed between 4 and 8 mg in a 40 μl-sized aluminum pan. The experiment was operated at a rate of 5 ◦ C/min for both the heating and cooling cycles. The thermotropic liquid crystalline behavior was characterized using a Mettler Toledo P82HT hot stage, viewed with an Olympus BX51 microscope fitted with crossed polarizing R softfilters, and the image was analyzed using AnalySIS ware. A magnification factor of 20× was used. The heating and cooling was performed at a rate of 2 ◦ C/min to determine the transition temperatures into various liquid crystal phases. In order to identify the phase structure of the materials, especially in the bicontinuous cubic phase, glass capillary tubes were filled with dried glycolipid powder and vacuum sealed. A small angle X-ray scattering (SAXS) experiment was carried out at beamline 2.2 of the Synchrotron Light Research Institute (SLRI), Thailand. A fixed wavelength of 1.55 Å (8 keV) was used. The sample-detector distance was about 0.7 m, which was calibrated using silver behenate with a

For the electrical measurements, the synthesized glycolipids were dissolved in ethanol and immersed in an ultrasonic bath at 60 ◦ C for 40 min to form homogeneous solutions of 0.5 g/ml concentration. Each solution was spin-coated onto glass substrates (which were pre-coated with aluminum electrodes) to form thin films with thicknesses of 1.8 ± 0.2 μm, 2.6 ± 0.4 μm, and 2.0 ± 0.1 μm for Malto-C8C4, MaltoC12C8, and Malto-C14C10, respectively. Top electrodes were deposited on the thin films to produce the metal–insulator– metal (MIM) structure with a 2 mm × 2 mm active area. The prepared samples were dried in a vacuum oven for 3 days prior to dielectric measurement in order to remove any moisture from the samples. The materials are extremely sensitive to the slightest contamination by humidity, etc., and hence the greatest care had to be employed during the preparation of the samples. Thus the measurements were carried out (under an inert gas environment) by varying the temperature from 303 K to 463 K on a hot chuck. The hot chuck was controlled by a STC200 temperature controller. The frequency range of the dielectric study varied from 10−2 Hz to 106 Hz using a combination of two apparatus; a laboratory-made dielectric spectrometer (10−2 –104 Hz)30 and an impedance analyzer (Agilent 4294A) (102 –106 Hz). The results of the measurements were expressed in terms of either the complex permittivity, ε∗ = ε − iε ,

(1)

or the complex conductivity, σ ∗ = σ  − iσ  .

(2)

The complex permittivity, ε∗ , can be converted to the complex conductivity, σ ∗ , through σ ∗ = iωε∗ .(σ  = ωε , σ  = ωε ),

(3)

where ε , ε , σ  , and σ  are the real permittivity (dielectric constant), imaginary permittivity (dielectric loss), real conductivity, and imaginary conductivity, respectively. ω is the angular frequency (2π f) and f is the frequency. The accuracy of measurements of ε and ε within the entire frequency range are ±2% and ±5%, respectively. III. RESULTS AND DISCUSSION A. Phase transition identification

The thermotropic phase transitions of glycolipids were obtained from both DSC and OPM. The phase transition temperatures obtained from these methods compared well with each other (within ±5 ◦ C). The molecular structures and phase transitions of the samples are displayed in Table I. The SAXS results and OPM reveal that Malto-C8C4 yields

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TABLE I. The phase transition temperatures in ◦ C of maltosides upon heating based on DSC and OPM measurements (given in italics). The notations used here are crystal (Cr), smectic A (SA ), bicontinuous cubic (Q), reverse hexagonal (HII ), and isotropic (I). In the DSC measurement, “?” refers to the undetectable temperature, in which a Q phase is expected to exist as detected by the OPM method. Materials Technique DSC OPM

Malto-C8C4

Malto-C12C8

Malto-C14C10

Cr < 25 SA 183 I Cr < 23 SA 183 I

Cr < 25 SA ? Q 209 I Cr < 23 SA 120 Q 204 I

Cr < 25 SA ? Q 140 HII 232 I Cr < 23 SA 78 Q 135 HII 237 I

a different phase sequence from Malto-C12C8 and MaltoC14C10, as a result of shorter alkyl chains. Table I gives the phase sequences of the three lipid compounds. For MaltoC8C4, the crystalline phase (Cr) at low temperatures is followed by the smectic A (SA ) phase and then followed by the isotropic liquid phase (I). For Malto-C12C8 and MaltoC14C10, the crystalline phase (Cr) at low temperatures is followed by the smectic A (SA ) phase. Then, the cubic phase is formed at a higher temperature and followed by the hexagonal columnar (HII ) and isotropic liquid phases in sequence. Strangely, the smectic–bicontinuous cubic phase transition is not visible from the DSC and is only observable in the OPM and SAXS results. The phase sequences of the glycolipids have been reported in Ref. 25, but the space group of the cubic phase has not yet been assigned. Here, indexing of the SAXS patterns of the cubic phase of Malto-C12C8 and Malto-C14C10 is performed, which leads to the Miller index assignments with the space groups shown in Figure 3 and Table II. The ¯ phase (see Figure 3) is chardiffraction patterns of the I a 3d √ √ √ √ acterized by peaks with relative ratios of 6, 8, 14, 16, √ √ √ 20, 22, and 24, corresponding to the diffraction planes (hkl) = (211), (220), (321), (400), (420), (332), and (422), respectively. The strongest peak belongs to the plane (211), while the least strong peak belongs to (220). The higher order

¯ phase peaks are weaker than the first two peaks. For the I a 3d obtained from Malto-C12C8 and Malto-C14C10, the maltose groups form two equivalent continuous interwoven networks which are immersed in the aliphatic matrix, therefore giving rise to an inverse type structure. In thermotropic liquid crys¯ cubic phase is commonly known tals, the bicontinuous I a 3d 31 as the smectic D phase and is frequently encountered in many studies.32

B. Dielectric relaxation phenomena

Figures 4(a) and 4(b) show typical dielectric frequency spectra for Malto-C12C8 heated from 303 K to 433 K with a 10 K temperature step. The plot of the real (dielectric constant) ε and imaginary permittivities (dielectric loss) ε in Figures 4(a) and 4(b) show a significant dependence on temperature in three different frequency regions from which two distinct, thermally activated relaxation processes were extracted and assigned rather prosaically as Processes I and II. Process I exists within the highest frequency window (∼105 – 106 Hz), while Process II occurs in the intermediate frequency range (∼1 kHz) at room temperature. At a sub-Hz frequency window, both the real and imaginary permittivities approached a common permittivity value (∼104 ), which corresponded to a low-frequency dispersion caused by a barrier layer on the electrode.33 Figures 4(c) and 4(d) show the real σ  and imaginary σ  components of the conductive spectra

TABLE II. Measured d spacing and diffraction peaks for the bicontinuous ¯ space group formed by Malto-C12C8 and Maltocubic phase with the I a 3d C14C10. T (◦ C)

Lattice

(hkl)

dhkl (nm)

a (nm)

Malto-C12C8

155

¯ Ia3d

110

¯ Ia3d

3.401 2.945 2.227 2.083 1.863 1.776 1.701 3.780 3.282 2.481 2.328 2.089 1.986

8.33 ± 0.01

Malto-C14C10

(211) (220) (321) (400) (420) (332) (422) (211) (220) (321) (400) (420) (332)

Materials

FIG. 3. SAXS diffraction pattern obtained from a bicontinuous cubic liquid crystalline phase of Malto-C12C8 at 428 K. The scattering curves are also shown on an expanded intensity scale (see inset in the figure) to reveal the higher order Bragg peaks. The positions of the observed reflections matched ¯ crystallographic space group. The cubic cell reflections afforded by the I a 3d lattice parameter obtained for Malto-C12C8 is (8.33 ± 0.01) nm.

9.34 ± 0.03

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FIG. 4. Complex permittivity and conductivity of Malto-C12C8 during the heating from 303 to 433 K with a temperature step of 10 K denoted by the different colored lines: (a) real permittivity (dielectric constant) ε , (b) imaginary permittivity (dielectric loss) ε spectra, (c) real conductivity σ  , and (d) imaginary conductivity σ  .

for Malto-C12C8 during heating from 303 K to 433 K with a 10 K temperature step, respectively. From the plot of σ  , we observed a relatively flat region occurring in the lower frequency window which usually represents the DC conduction. On the other hand, the imaginary conductivity spectrum σ  exhibits two relaxation peaks at intermediate and low-frequency regions. These two peaks are more easily discernible in Figure 6 (see later). Since the isothermal frequency responses (Figure 4) give significant changes, we also give the temperature sweep of the dielectric spectra in Figure 5. Figure 5 shows typical plots of the complex permittivity as a function of temperature (295–433 K) at selected frequencies of 100 Hz, 1 kHz, and 10 kHz for the Malto-C14C10 which gives a clear thermotropic polymorphism of the SA , HII , and Q phases. Using the transition temperatures determined from the OPM and DSC as a guide (refer to Table I), three phase regions are marked on these graphs correspond-

ing to SA below 351 K (78 ◦ C), Q from 351 to 408 K (78– 135 ◦ C) and HII beyond 408 K. From the shape of these plots, in SA the real component gradually increases as the temperature is increased, while in marked contrast to the imaginary component which increases rapidly above 312 K. In Q both components increase rapidly with the temperature, but these plots show a gradual monotonic increase in HII . In both the plots of real and imaginary permittivities over temperature, a distinct discontinuity is observed at around 351 K corresponding to the transition from the SA to the Q phase. This is more pronounced in the lower frequencies spectra (i.e., 100 Hz) compared to the higher 10 kHz spectrum. The observed discontinuity between SA and Q implies a significant change in ordering between these two phases. However, there is only a slight change in the slope at the phase transition between the Q to HII . The phase change involving the Q phase is always thought to be kinetically controlled but the

FIG. 5. The temperature dependence complex permittivity spectra of Malto-C14C10 at 100 Hz, 1 kHz, and 10 kHz. (a) Real permittivity (dielectric constant) ε  and (b) imaginary permittivity (dielectric loss) ε .

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FIG. 6. Observed and fitted spectra of Malto-C12C8 at 373 K during heating (a) complex dielectric ε∗ and (b) complex conductivity σ ∗ . Process I and Process II denote the relaxation phenomena in the system. εI and εII denote the dielectric strength related to Processes I and II, respectively.

discontinuity observed here between SA and Q is rather prominent and such observations have been reported previously for amphotropic systems containing diols16 and carboxylic acids.34 For a quantitative analysis, we reproduced the observed spectra by fitting them to an empirical function,35 ε∗ = ε∞ +

 k

εk σdc (iωτel )γ + , iω 1 + (iωτel )γ [1 + (iωτk )βk ]αk

(4)

where ε∞ is the instantaneous permittivity, ε is the dielectric relaxation strength, and τ is the relaxation time. The α, β, and γ parameters describe the distribution of the relaxation times. The k in εk∗ represents one of the multiple relaxations processes. The plot was converted into complex conductivity, σ ∗ via Eq. (3) using the complex function given by36 εel∗ = εel (iω)γ −1

(5)

and the Havriliak–Negami (HN)37 function for εk∗ , Eq. (4) becomes   1 ∗ σ = σ dc 1 − [1 + (iωτel )δ ]  εk +iω + iωε∞ , (6) k [1 + (iωτ )βk ]αk k where εel∗ is related to electrode polarization. Figure 6 shows exemplary curve fittings of the dielectric and conductive

spectra acquired for Malto-C12C8 at 373 K using Eqs. (4) and (6). The observed spectra (open circles and triangles) are fitted with Eqs. (4) and (6) (solid lines). Upon careful analysis in the dielectric loss ε spectra, the corresponding loss peak can be observed by removing the contribution of DC conductivity and the electrode polarization (represented by a dashed line in Figure 7). The results of the analysis for Processes I and II are presented in Figure 7. Process I is associated with the higher frequency in the range of 10 kHz to 1 MHz. The fitted dielectric strength and relaxation frequency are presented in Figures 7(a) and 7(b) for the three glycolipid systems marked in different colors as a function of temperature. Figure 7(a) shows that in SA for the three glycolipids the dielectric strength, ε, gradually increases with increasing temperature. The averaged magnitudes of the ε extracted from these plots in the SA phase are roughly 3.5, 2, and 1.5 (with errors of about ±0.3) for MaltoC14C10, Malto-C12C8, and Malto-C8C4, respectively. These values agree qualitatively with the dielectric strength obtained for lipid corresponding to head group rotation (ε < 5)38, 39 This suggests Process I is due to the rotation of the permanent dipoles of the hydroxyl groups in the sugar head, as reported previously in the study of the anomalous dispersion of phospholipids at 20 kHz.39 Malto-C14C10 (orange circles) and Malto-C12C8 (black squares) undergo phase transitions between SA and Q at the temperatures as indicated by vertical lines denoted using the same colors. Generally, regardless of the phase, the dielectric strength is the highest for Malto-C14C10. This result is acceptable because it was suggested previously that glycolipids with longer alkyl chains are tilted with respect to the layer normally in SA but the tilt directions are not correlated between the bilayers.40 These tilted glycolipid molecules are electrically polarized thus exhibit higher spontaneous polarization compared to the shorter chain glycolipids. The ε in the Q phase is noticeably reduced compare with SA , indicating that the overall sum of polarization is reduced. Furthermore, in the Q phase the ε is temperature independent. For Malto-C14C10 (orange circles), the ε in HII is not plotted since the relaxation frequency lies outside the frequency window of the experiment. The relaxation time versus reciprocal temperature (1/T) is plotted in Figure 7(b). A slight gradient change is observed in the plot and is consistent with a phase transition (refer to the vertical line in Figure 7(b)) as observed in Figure 5 for Malto-C14C10. The linear behavior of these plots suggests that the process is Arrhenius in nature. However, further confirmation is necessary using the derivativebased analysis.41, 42 While, the Arrhenius-like behavior is rep) ) where Ea is the activation resented by τ (T ) = τo exp( Ea(T RT energy per mole, R is the gas constant, and τ o is the relaxation time, the non-Arrhenius behavior is described by the Vogel–Fulcher–Tammann (VFT) relationship.38 For detecting the cross over dynamic temperature, Stickel et al.43 proposed the derivative analysis of experimental data followed by the linearized plot,44     −1/2 d ln τ −1/2 1 A (7) = Ha =B− , d (1/T ) T T

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FIG. 7. Variation of dielectric strength ε with temperature for (a) Process I and (d) Process II and variation of relaxation time, τ as a function of 1/T for (b) Process I and (e) Process II for Malto-C14C10 (orange), Malto-C12C8 (black), and Malto-C8C4 (dark cyan), respectively. Vertical lines indicate the phase transition. Figures (c) and (f) give the derivative-based transformation of dielectric relaxation data, using Eq. (8) to validate the Arrhenius behaviors in the three glycolipid systems.

where Ha ’ (T) stands for the normalized apparent enthalpy. From the critical like equation,38 Eq. (8) was derived, T2 T −Tc = = AT − B.  H a(T ) φ

(8)

Figure 7(b) shows linear behavior in all the three phases. Moreover, using the derivative-based analysis, i.e., plotting Eq.(8) versus temperature (see Figure 7(c)), we observed a clear non-sloped region in SA for Malto-C8C4 confirming

the Arrhenius behavior, while for Malto-C12C8 and MaltoC14C10 the Arrhenius behavior is less obvious, but we assume it to be the case to within the errors of the calculation. Hence, for Process I the activation energies are calculated for all the glycolipid systems presented in Table III. The dielectric strength and relaxation frequency versus temperature from Process II are presented in Figures 7(d) and 7(e), respectively, for two glycolipids Malto-C12C8 and Malto-C14C10 which are marked in different colors as

TABLE III. Activation parameters of Process I and Process II for the Malto-C8C4, Malto-C12C8, and MaltoC14C10 at the respective phases. Similar results for the thermotropic self-assembly phases are listed for comparison.49, 50

Phases

Process I Ea ± 0.5 (kJ/mol)

Malto-C8C4

SA

229.5

...

Malto-C12C8

SA Q

154.8 102.9

134.9 101.4

Malto-C14C10

SA Q HII

156.1 115.3 ...

134.3 109.2 122.3

N-(2,3-Dihydroxypropyl)-Nmethyl-2,3,4tridodecyloxybenzamide49

HII Q12 I

43 ± 5 38 ± 3

4 -hexadecyloxy-3 -nitro biphenyl carboxyl50

I Q SC

116.9 ± 3 45.6 ± 0.1 51.7 ± 0.1

Materials

Process II Ea ± 0.5 (kJ/mol)

23 ± 6

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before. In Process II, the observed ε are in the range of 400–1600 and these are quite high compared to those from Process I. The relaxation frequency at ∼1 kHz of Process II with high dielectric strength has been reported previously45 and identified with the β dispersion due to the lipid heterogeneous self-assembly structure.45 Furthermore, the high ε may be related to the presence of trace water which is difficult to eliminate due to the hygroscopic nature of the sugar group. In addition, the longer chain Malto-C14C10 exhibits a generally higher dielectric strength compared to Malto-C12C8. In the SA phase, ε increases gradually with temperature, but in the Q phase ε increases initially and it is almost temperature independent thereafter. As for HII phase, ε decreases almost linearly with increase of temperature. Such a linear temperature dependency of ε in the HII phase was reported due to the high conductivity inside the inverse cylindrical structure.16, 46 In the Q phase ε remains almost constant with increasing temperature before its value decreases almost discontinuously at the phase transition into the HII phase (Figure 7(d)). Kresse et al.16 also observed a constant ε in an inverse cubic micellar phase, suggesting that this behavior is related to the isotropic ordering nature of the phase. The change in ε at the phase transition is a result of the variation of dimension, orientation and positional order of the phases before and after the transition.33 The relaxation time of Process II is plotted as a function of the reciprocal temperature in Figure 7(e). Besides, after employing derivative-based analysis (refer to Figure 7(f)) we found that the evolution is Arrhenius in nature for Process II. The activation energies, Ea , were obtained from the Arrhenius expression and are presented in Table III. It was observed that the smectic phase exhibits a significantly larger activation energy compared to the other curve phases, particularly for Malto-C8C4 whose activation energy is 229.5 kJ/mol. This is in accord with the dielectric relaxation measurement performed on other polymeric systems47 with varied side chain length. The stiffening of the chains becomes more effective for shorter chains.47 In the bicontinuous cubic phase the activation barrier is markedly reduced, indicating a reduced overall ordering (isotropic).1 Interestingly, among these phases we found that the Ea of the bicontinuous cubic phase is the smallest. A bicontinuous cubic phase is a highly ordered phase and mechanically stiff, but the overall order is zero, which implies that the phase is isotropic in nature, as observed optically.16, 48 Therefore, the relaxation behavior (hence the activation energy) is expected to be isotropic in nature, reflecting the overall ordering within the phase. Similar results were obtained for other glycolipids reported in the literature25, 40 where the activation energy in the SA phase is always larger than the columnar or bicontinuous cubic phases and, furthermore, shorter alkyl chain length glycosides exhibit higher activation energy compared to longer tail compounds. In Table III, we quote the activation energies from similar measurements conducted for N-(2,3dihydroxypropyl)-N-methyl-2,3,4-tridodecyloxybenzamide49 and 4 -hexadecyloxy-3 -nitro biphenyl carboxyl.50 The first is a diol system, while the second contains a carboxylic group and both are amphitropic self-assembly materials. Comparing our maltoside with eight hydroxyl groups (in SA ) and the

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diol system with two hydroxyl groups (HII ), the activation energy (Ea) of the former is 3–5 times larger than the latter which shows Ea (Process I) is related to the number of the hydroxyl group. The two sets of results are fairly comparable since both have hydroxyl groups, even though these diol materials49 are only remotely similar to ours. C. Diffusion of charge carriers in bicontinuous cubic phase

Generally, in the phase diagram, the bicontinuous cubic phase (Q) is found between the smectic (SA ) and hexagonal (HII ). In addition, Q can be induced by mixing SA and HII .51 It is quite rare to see Q in thermotropic systems from amphiphilic materials, and much less has been studied. Thus, we have focused on the bicontinuous cubic phases for MaltoC12C8 and Malto-C14C10, where they are more prominently observed in the temperature ranges of 393–433 K and 351– 408 K, respectively. Among the quantities determined as bestfit parameters from Eq. (4) are the conductive strength, σ dc , relaxation frequency, fm , and the dielectric strength, ε, in Process I and Process II. Figure 8 shows the plot of σ dc, fm , and ε versus temperature for Malto-C12C8 and MaltoC14C10 in the bicontinuous cubic phase. The temperature dependence properties of Malto-C12C8 and Malto-C14C10 are given in Figures 8(a) and 8(b) for the conducting strength and Figures 8(c) and 8(d) for the relaxation frequency, respectively. Both sets show an increasing trend with temperature. But for the dielectric strength in Figures 8(e) and 8(f), the graphs are almost unvarying with temperature in the Q phase. With respect to these plots, there are several points worth noting which are related to the calculation of the diffusion coefficient in the bicontinuous cubic phase (see later). First, the relaxation frequency, fm , was found to be increasing as a function of temperature (see Figures 8(c) and 8(d)). Second, the values of the dielectric strength, ε, in Processes I and II are independent of temperature in the bicontinuous cubic phase (refer to Figures 8(e) and 8(f)). Finally, the exponent fitting parameter, γ , (defined in Eq. (4)) can be extracted by analyzing the complex function, ε∗ = ε(iω)γ −1 and τ =

1 = 2πfm



ε σdc

 γ1 ,

(9)

given by Furukawa et al.35 and Johnson and Cole,36 respectively, and for the Q phase, it is found to range from 0.90 to 0.95. Different models have been used to describe diffusions in the lyotropic phases of lipids;52 however, to the best of our knowledge, diffusions in anhydrous lipid systems are rarely reported. Thus the dry glycolipid system studied here can serve to study the diffusion process in such a system, in particular the thermotropic bicontinuous cubic phase. Assuming that diffusion of these glycolipids is Brownian and due to charge carriers present within the polar sugar head region, it has a characteristic random walk with a step length λ and a step time τ o. The Einstein–Smoluchowski equation relates λ2 these quantities to the diffusion coefficient, D = 6τ . 0

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FIG. 8. Fitted properties from the Havriliak–Negami (HN)37 function of the bicontinuous cubic phases from Malto-C12C8 and Malto-C14C10 in terms of (a) and (b) conductive strength, σ dc ; (c) and (d) relaxation frequency, fm , and (e) and (f) dielectric strength ε in both Process I and Process II, respectively. The error in the measurement is ±5%.

For a system containing N number of glycolipid molecules with charge q, D is related to the conductive strength, σ dc using Eq. (10), where kB is the Boltzmann constant and T is the absolute temperature, σdc =

N q2 D. kB T

This result supports the view that Process I, which is high frequency motion, is associated with the hydroxyl group dipoles from the sugar head. In addition, in Process II, for MaltoC12C8 and Malto-C14C10, the respective hopping lengths λII were to be (36.0 ± 0.1) Å and (40.0 ± 0.1) Å, which

(10)

In Figure 9, we have plotted in double log the plot of D (value calculated from Eq. (10)), which is related to σ dc , against the relaxation frequency fm from using Eq. (9) and the fitting parameter γ = 0.90−0.95. The plots are linear with a slope approximately equal to 1 (see Figure 9) for both Process I and Process II. Since a normal diffusion gives a slope of unity,39 both processes considered here involve normal diffusion.53 The hopping length, λ, of the conduction process can be evaluated using the Einstein–Smoluchowski equation and by assuming that τ o is proportional to the relaxation frequency, 1/2π fm .54 Consequently, for the two processes the hopping lengths λI and λII are extracted from the intercepts of the plots in Figure 9. For Process I, the hopping length, λI calculated for Malto-C12C8 and Malto-C14C10 is 2.45 ± 0.05 Å and 2.66 ± 0.03 Å, respectively, and these hopping lengths approximate to the hydrogen bond length, which is ∼2−3.5 Å.55

FIG. 9. Double logarithmic plot of diffusion coefficients D of Malto-C12C8 and Malto-C14C10 as a function of the relaxation frequency in Process I and Process II, respectively.

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FIG. 10. Schematic diagram of charge hopping process with hopping length for glycolipids in (a) Malto-C12C8 and (b) Malto-C14C10 for both Process II and Process I (circles represent domain containing disaccharide polar head group only). This model is only applicable in the bicontinuous cubic phase, and thus applies to Malto-C12C8 and Malto-C14C10.

are close to the d spacing length of the strongest peak belonging to the (211) plane (Table II). This suggests Process II involves other dipoles present in the system and related to the bilayer arrangement. Figure 10 provides a depiction of the conduction processes associated with Processes I and II. A similar analysis was undertaken by Furukawa et al.35, 54 who proposed a microscopic conduction mechanism in an ion conducting polymer where ions hop at a rate equaling the segmental relaxation frequency for the monomer length of PPO/LiClO4 . IV. CONCLUSION

We have performed dielectric measurement for three branched chain maltosides in different thermotropic phases, smectic A (SA ), hexagonal (HII ), and cubic bicontinuous (Q). The phases and transition temperatures were assigned for these maltosides using a combination of techniques such as DSC, OPM, and SAXS. In particular, SA were observed in the short chain Malto-C8C4, but the other two longer chains maltosides display thermotropic polymorphism, where MaltoC12C8 gives rise to SA and Q and Malto-C14C10 gives all the three phases (SA , Q, and HII ). From the dielectric spectra, the phase transitions for these materials were found to agree quantitatively with those obtained by the conventional techniques. Dielectric absorptions of Malto-C12C8 and MaltoC14C10 self-assemblies also revealed two main dynamic processes from two frequency regions. One of these is the high frequency relaxation process which is associated with the cooperative motion of hydroxyl dipoles in a hydrogen bond network of the sugar groups. On the other hand, the intermediate frequency relaxation process is related to the collective motion afforded within the self-assembly, such as from a change in the distribution of the molecules in the plane perpendicular to the symmetric axis. Interestingly, the short chain maltoside (Malto-C8C4) exhibits only the high frequency dielectric absorption. Both the dynamic processes are Arrhenius in nature. The dielectric strength is temperature independent in the isotropic Q phase unlike in the other two ordered phases (SA and HII ). The difference between SA and Q phases is further exemplified by an observation that a phase transition of SA –Q is accompanied by a significant change in the dielectric strength, unlike that of the Q–H transition quite unsurprisingly, because this is a phase change between two curved phases. The dynamic nature of the three phases is differentiated by their activation energies, where this is higher in SA

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compared to that in the Q phase. Analyzing the Q phase using the Einstein–Smoluchowski equation and the random walk model, we found the charge carrier hopping is closely related to the molecular motions within the self-assembly system. Two hopping lengths were calculated and one of these (2.4–2.6 Å) is similar to the hydrogen bond length (Process I) while the other (36–40 Å) is similar to the bilayer spacing (Process II).

ACKNOWLEDGMENTS

This work was partially supported by the Higher Ministry of Education under High Impact Research Grant (UM.C/625/1/HIR/MOHE/05), the University of Malaya under the High Impact Research Grant (UM.C/625/1/HIR/041) and the Flagship Grant (FL017-2011). Part of this work was carried out in the Synchrotron Light Research Institute, Thailand at the BL2.2 SAXS beamline, and the help and support of the engineers at the beamline at SLRI is greatly appreciated. The authors wish to thank Professor Takeo Furukawa (Kobayashi Institute of Physical Research, Japan) for his valuable exchanges. 1 R.

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