High Dielectric Constant and Relaxation Mechanism of Water with

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High Dielectric Constant and Relaxation Mechanism of Water with Hydrated Copper(II) Ions in a Cucurbit[8]uril-Based Supramolecular Architecture Hai-Xia Zhao,† Jing-Xin Liu,† La-Sheng Long,*,† Alexei A. Bokov,‡ Zuo-Guang Ye,*,‡ Rong-Bin Huang,† and Lan-Sun Zheng† †

State Key Laboratory for Physical Chemistry of Solid Surfaces, Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China ‡ Department of Chemistry and 4D LABS, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada ABSTRACT: The dielectric properties of water confined in nanochannels of a cucurbit[8]uril-based supramolecular architecture containing water and hydrated copper(II) ions were investigated in the frequency range of 102 to 5 × 107 Hz at various temperatures around room temperature. Two relaxation processes were revealed and studied. The low-frequency dispersion described by the fractional power law is related to the relaxation of hopping charge carriers. The second orientational polarization contribution follows the Kohlrausch−Williams−Watts relaxation law with the characteristic relaxation time almost independent of temperature and gives rise to an exceptionally large static dielectric constant (∼500). The data suggest the existence of a third relaxation process with the characteristic frequency significantly larger than the measurement frequencies used in this work.

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INTRODUCTION Water confined in nanopores or nanochannels is very common in biological systems and often exhibits unique properties drastically different from those of bulk water.1−4 More importantly, these unusual properties of the confined water can significantly affect the energy in biological cells, the enzymatic activity of proteins, the function of membranes, and the transport through ion channels.5−7 Hence, investigation of the properties of confined water in diverse environments is of key importance for our understanding of the complex behavior of water and its role in life processes.1−4,8−20 Supramolecular architectures, featuring structural diversity and adjustability, are important systems for the investigation of the properties of confined water,3,4,21−25 because they allow us not only to facilely obtain different water species, but also to study the water species in diverse environments. Although many water species have been obtained on the basis of supramolecular architectures,3,4,21−35 their properties have been seldom investigated.3,4,21−25 Especially, the properties of confined water containing hydrated metal ions have not been studied in supramolecular architectures so far, despite such a kind of water playing a key role in many biological processes.8−12,15−20 Here we report the dielectric study of the dynamic process of confined water containing hydrated copper(II) ions within a cucurbit[8]uril-based supramolecular architecture.

CuCl2·6H2O and Q[8] in water. Q[8] was synthesized by following published procedures.36 Other reagents were all of commercial origin. The thermogravimetric analyses were carried out with NETZSCH STA 449C, and X-ray powder diffraction was performed on a PANalytical X’Pert PRO diffractometer with Cu Kα radiation. Synthesis of Complex 1. Q[8] (0.064 g, 0.05 mmol), CuCl2·6H2O (0.243 g, 1.0 mmol), and H2O (10 mL) were mixed and then transferred and sealed in a 25 mL Teflon-lined stainless steel container. The container was heated to 150 °C and held at that temperature for 40 h and then cooled to 100 °C at a rate of 3 °C·h−1 and held for 16 h, followed by further cooling to 30 °C at a rate of 5 °C·h−1. Green-blue crystals of 1 were collected by filtration and air-dried in 30% yield based on Q[8]. Anal. Calcd (Found) for 1: C, 29.15 (28.98); N, 22.67 (23.00); H, 6.07 (5.38). IR (KBr): 3348.3 (s), 2926.5 (w), 1727.7 (s), 1473.2 (s), 1424.8 (m), 1375.6 (m), 1318.5 (m), 1232.3 (m), 1192.6 (m), 1156.6 (w), 1077.2 (w), 969.8 (s), 807.7 (s), 759.6 (m), 674.1 (m) cm−1. Single-Crystal Structure Determination. Data were collected on a Bruker SMART Apex charge-coupled device (CCD) diffractometer at 173 K. Absorption corrections were applied using the multiscan program SADABS.37 The structures were solved by direct methods, and the non-hydrogen atoms were refined anisotropically by the least-squares method on F2 using the SHELXTL program.38 The hydrogen atoms of the

EXPERIMENTAL SECTION The complex Q[8](CuCl2)0.75·30(H2O) (Q[8] = cucurbit[8]uril) (1) was prepared through the hydrothermal reaction of

Received: February 24, 2012 Revised: May 14, 2012 Published: June 12, 2012

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© 2012 American Chemical Society

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organic ligand were generated geometrically (C−H = 0.96 Å). All the guest molecules (water and CuCl2) were omitted by SQUEEZE during the refinement of the structure. CCDC678276 for 1 containing the supplementary crystallographic data for this paper can be obtained from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_ request/cif. Dielectric Measurements. All the dielectric measurements were made on the single crystals with gold paste. The real and imaginary parts of the dielectric constant were measured with a Wayne Kerr (6550B) precision impendence analyzer in conjunction with an Oxford low-temperature system. The humidity dependences of current−voltage curves were measured by the two-probe dc method along different directions of the single crystals. Various humidities were realized in different concentrated solutions of sulfuric acid. Gold paste (Tokuriki 8560) was used to contact gold wires (25 μm diameter) to the single crystals (0.6 × 0.4 × 0.4 mm).

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Figure 2. (a) TG−DSC curves for 1. (b) Color of 1 in the presence and absence of guest water molecules. (c) EPR of 1 at different temperatures. (d) Powder X-ray diffraction pattern of 1 at different conditions.

RESULTS AND DISCUSSION The single-crystal structure39 reveals that its unit cell consists of 0.5 Q[8] and 15 water molecules (the number of water molecules is obtained from elemental analysis). However, the atomic absorption spectrum shows that 1 mol of 1 contains about 0.75 mol of CuCl2. This discrepancy between the composition deduced from the crystal structure and that from atomic absorption is due to the disorder of copper(II) and chloride ions. A similar phenomenon was also observed in FevHw[Mo12O46(AsC6H4-4-OH)4]·xH2O·yDMSO,40 in which the Fe3+ ion was not detected from its crystal structure. Each Q[8] is connected to four other Q[8] molecules through its two portal C−H···O interactions and its two waist C−H···O interactions, generating a subunit of (Q[8])5 (Figure 1a). The

air, the color recovers slowly, indicating that the dehydration and rehydration are reversible. However, the rehydration process results in a bad crystal surface, so the color is appreciably lighter. The reversible rehydration and dehydration process, as well as the capability of retaining crystallinity when water molecules are fully removed, is further demonstrated from the X-ray powder diffraction patterns at different temperatures (Figure 2d). Figure 3 illustrates the dielectric properties of 1 measured at various frequencies and temperatures. At high temperatures, the

Figure 1. (a) Structure of the (Q[8])5 unit. (b) 3D crystal structure of 1.

Figure 3. Frequency dependences of the real part of the permittivity (ε′) (a) and tan δ (b) of 1 measured at various temperatures. Frequency dependences of the room-temperature dielectric constant (ε′).

3D structure of 1 can be viewed as an extension of the subunit of (Q[8])5 with each Q[8] surrounded by four other Q[8] molecules (Figure 1b), much different from the metal-free Q[8]-based architectures.41 Water and CuCl2 molecules fill the pores. From Figure 2a, 1 begins to lose its guest water molecules gradually from 296 K. At 368 K, it loses all the guest water molecules and becomes dehydrated. Although 1 is constructed from organic ligands, it is stable up to 590 K (Figure 2a). Significantly, 1 retains its crystallinity throughout the color change (Figure 2b). The color change indicates that 1 contains hydrated copper(II) ions, which is confirmed by its electron paramagnetic resonance (EPR) spectrum (Figure 2c), since the g value for copper(II) ions at 348 K is slightly different from that at room temperature. The hyperfine line width of the spectrum broadens, and its intensity decreases; meanwhile, some of the peaks split faintly to some extent. Upon cooling in

real part of the permittivity drops steeply to about 500 with the frequency increasing to 10 kHz, showing clearly a strong dielectric dispersion in this frequency range. A further increase in the frequency from 10 kHz to 50 MHz results in the real part of the permittivity decreasing to ∼200, indicating a second dispersion region. At 280 K, the real part of the permittivity almost remains constant at 300 with the frequency increasing from 0.2 to 100 kHz and decreases from 300 to 100 with the frequency increasing from 100 kHz to 50 MHz, indicating that only one relaxation process remains in the measured frequency window at low temperatures. The frequency-dependent dielectric loss tangent (tan δ) at various temperatures is shown in Figure 3b. Since the dielectric constant of dehydrated 1 is almost frequency-independent (Figure 4) at room 14200

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χ*U1 and χ*U2 are expressed by the “universal” relaxation law42 to describe the linear dependence between the real and imaginary parts of the susceptibility observed in Figure 5 at low frequencies:

temperature, the temperature- and frequency-dependent permittivity is thus attributed to the guest molecules.

χ″Uk = Ak f nk − 1

(k = 1, 2)

χ ′Uk = tan(nk π /2)χ ″Uk

(k = 1, 2)

(3) (4)

ε∞ describes the possible contributions of some other polarization mechanisms for which the dielectric dispersion is observed at very high frequencies inaccessible in our experiments. To determine the frequency-independent relaxation parameters χ0, f 0, α, γ, A1, n1, A2, n2, and ε∞, we perform nonlinear least-squares fitting of the real and imaginary parts of the dielectric spectra at several fixed temperatures to eq 1 with the terms expressed by eqs 2−4. To reduce the number of independent adjustable parameters, we apply the following procedure as a step preceding the final fitting. The highfrequency parts of the measured ε″(f) curves are analyzed, taking into account that only single HN relaxation significantly contributes here to the loss (i.e., ε″ ≅ χ″Hf). It is known42 that the high-frequency slope of the HN function can be expressed by the power law χ″ ∝ f −αγ. Note that this dependence becomes linear in the double logarithmic presentation. Indeed, our experimental ε″(f) curves presented in this manner in Figure 6 are nearly straight lines at f > 5 MHz. Therefore, it is

Figure 4. Dielectric constant (real parts) at different frequencies for hydrated and dehydrated 1 measured at room temperature.

Figure 5 shows the Cole−Cole plot of 1. The plot consists of a semicircle and a spike, confirming the existence of two

Figure 5. Cole−Cole plots at different temperatures for 1.

relaxation processes contributing to the dielectric response. Note the change of the slope of the linear ε″ (ε′) dependence observed on the 297.4 K curve at ε′ ≈ 1500. This may signify the presence of a third contribution which becomes significant in the measured frequency range at high temperatures. Therefore, we analyze the dielectric spectra by considering the above-mentioned three possible relaxation contributions, with the complex dielectric susceptibilities designated as χ*Hf, χ*U1, and χ*U2, respectively, so that the total relative dielectric permittivity is expressed as

Figure 6. Temperature dependences of the real (a, c) and imaginary (b, d) parts of the relative dielectric permittivity in 1 at selected temperatures of 297 K (a, b) and 286 K (c, d). Experimental data (dots) and fitting (solid) curves are presented for comparison. Dashed lines show the calculated contributions of two relaxation mechanisms and dc conductance.

ε*(f ) = ε′(f ) − iε″(f ) = χ *Hf (f ) + χ *U1(f ) + χ *U2 (f ) + ε∞

(1)

possible to determine the values of αγ from the slopes of these lines. It is found that αγ ≈ 0.38 for all temperatures. Thus, αγ is forced to be 0.38 in the course of the subsequent final nonlinear least-squares fitting, while all other relaxation parameters are considered to be the independently adjustable parameters. The results of fitting at two selected temperatures are represented in Figure 6. Similar results are obtained for other temperatures.

In eq 1, χ*Hf(f) stands for the high-frequency relaxation process (semicircle in Figure 5), and its frequency dependence is analyzed with the most general relaxation formula, namely, the Havriliak−Negami (HN) relationship:42 χ *Hf = χ0 [1 + (if /f0 )α ]−γ

(2) 14201

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The value of n2 is found to be zero at all temperatures, and according to eq 4, χ′U2 is also zero. This means that the contribution of χ*U2 to the dielectric spectrum contains only the imaginary part; i.e., it is related to dc conductance.42 Subsequently, the dc conductivity can be calculated as σdc = 2πε0fχ ″U2 = 2ε0πA 2

water it contains corresponds to a humidity level of 65%. The strong dependence of conductivity on humidity indicates that water provides a key contribution to the conductivity of 1. Significant variation of weight observed even around room temperature in the thermogravimetry−differential scanning calorimetry (TG−DSC) curves (Figure 2a) suggests that the water content in our sample may vary during measurements and the nonlinear increase of log σdc with decreasing 1/T may be related, at least partially, to the loss of water molecules from the host. The relaxation process responsible for the χ*U1 dielectric contribution is characterized by the real and imaginary parts that diverge toward low frequencies according to eqs 3 and 4 with the exponent n1 increasing upon cooling (Figure 7b). This behavior is characteristic of the so-called low-frequency dispersion which is observed in many dielectrics and semiconductors42 and typically attributed to the hopping charge carriers. The temperature dependence of χ′U1 calculated for 100 Hz is shown in Figure 7a. One can see that the susceptibility increases exponentially with increasing temperature at a rate close to the rate of the dc conductivity increase, suggesting that the same charge carriers are responsible for the dc conductance and for the low-frequency dispersion. The parameters α and γ which determine the shape of the χHf(f) dependences are practically independent of temperature (Figure 7b). Remarkably, on the basis of γ = 0.489 ± 0.017 and α = 0.78 ± 0.03 found in our work (averaged over all temperatures), we may conclude that the corresponding relaxation actually follows (in the time domain) the Kohlrausch−Williams−Watts (KWW) function, exp[−(t/ τKWW)β]. Indeed, these values agree well with those which should be obtained when the HN relation is fitted to the KWW function with the shape parameter β = 0.47.44 The characteristic KWW relaxation time is calculated from the fitted f 0 values using the relation44

(5)

where ε0 is the permittivity of free space. The calculated σdc is shown in Figure 7a as a function of 1/T. Although the conductivity of 1 increases with increasing temperature, the increase is nonlinear, similar to what is found in DNA.43

Figure 7. Temperature dependences of the relaxation parameters for 1: (a) dc conductivity (squares), KWW characteristic relaxation time (dots), and real part of the low-frequency susceptibility at 100 Hz (triangles); (b) HN shape parameters α (dots) and γ (squares) and low-frequency relaxation exponent n1 (triangles); (c) dielectric strength of high-frequency (KWW) relaxation (squares) and highfrequency limit of permittivity (triangles).

τKWW = exp[− ln(2πf0 ) − 2.6(1 − β)0.5 exp(− 3β )]

(6)

and presented in Figure 7a as a function of 1/T. It was noted that although the temperature-dependent relaxation time in 1 is significantly different from that of the universal feature of confined water,13 it is similar to that found in DNA with an ion strength larger than 1.0 mM.45 The value of χ0 which represents the dielectric increment shows a significant increase with increasing temperature and remains much larger than the temperature-independent highfrequency permittivity limit ε∞ ≈ 50 (Figure 7c). It was recently reported that the largest dielectric constant observed so far in nonferroelectric materials is on the order of 100,46 so the value of χ0 ≈ 500 found in 1 is exceptionally large. The high dielectric constant in most, if not all, nonferroelectric materials is extrinsic in nature and can be attributed to the Maxwell− Wagner (space charge) contribution when the free charge carriers responsible for the dc conduction are blocked at internal interfaces, forming space charges and thereby increasing the measured dielectric constant.46 However, the shape as well as the temperature evolution of the dielectric spectrum we observed is incompatible with the Maxwell− Wagner relaxation. Indeed, its spectral shape is described by the Debye function,47 which corresponds to the (nonstretched) exponential dependence in the time domain, in other words, to the KWW dependence with β = 1. We observed β = 0.47. Besides, the relaxation time of the Maxwell−Wagner process

To reveal the possible reason for the nonlinear increase of log σdc with decreasing 1/T, the humidity-dependent I−V curves of 1 are obtained. As shown in Figure 8, when the humidity changed from 20% to 80%, the conductivity changed from 1.5 × 10−9 to 1.6 × 10−6 S·cm−1. By comparing these data with the room-temperature conductivity of 3 × 10−7 S·cm−1 observed in the sample in which the dielectric spectra were measured (Figure 7a), we can estimate that the amount of

Figure 8. I−V curves under different humidities for 1. 14202

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must be proportional to (σdc)−1. In contrast, the characteristic time τKWW in 1 does not correlate with (σdc)−1 in such a manner (Figure 7a). Furthermore, the dielectric increment in the case of the Maxwell−Wagner relaxation is typically almost independent of temperature, while we have observed dramatic temperature variation. The temperature dependence of the dielectric increment in 1 is consistent with that in DNA in solutions of various ionic strengths.45 On the other hand, in the case of intrinsic dielectric response related to the reorientation of dipole moments of individual molecules or groups of molecules, an increase as well as a decrease of the dielectric increment and relaxation time with temperature can be observed depending on the material structure.47 Therefore, our data suggest that the KWW (high-frequency) relaxation process in 1 is intrinsic in nature. The high-frequency permittivity limit of ε∞ ≈ 50 we determined is much larger than the permittivity of ∼2 related to the vibrational modes of water48 and the permittivity of the dehydrated 1 (Figure 4). This means that one more relaxation process exists with the relaxation frequency significantly higher than the upper measurement frequency of 50 MHz. Let us now discuss the possible mechanisms of the KWW relaxation we observed. The absence of this relaxation in the dehydrated samples (Figure 4) strongly suggests that the water molecules are involved. In the temperature range we studied, the characteristic relaxation frequency in the pure bulk water is about 2 GHz, the dielectric spectrum can be well represented by a Debye relaxation pattern49 (which is a special case of the KWW pattern with β = 1), and the static permittivity (around 80) slightly changes with temperature.50 The decreased relaxation frequency (∼1 MHz in our experiments) is a wellknown property of bound water related to the increased activation enthalpy for the reorientations of water molecules.49 The reorientation of the molecule is possible if some bonds it forms with neighboring molecules are broken. In pure liquid water these are weak hydrogen bonds. In solutions, interactions with foreign molecules can change the activation enthalpy dramatically, thereby affecting the relaxation behavior. Similar effects are observed in the case of geometric confinement of liquid in spaces several nanometers in diameter. The size of the cucurbit[8]uril cavity is about 1 nm, and the intermolecular pores are somewhat larger. Besides, guest molecules of hydrated copper(II) ions may be present in the solution. Therefore, the water molecules in 1 (or a large portion of them) are expected to be bound. The reduction of stretching exponent β due to confinement of water is also expected. Molecular dynamics simulations of the mobile portion of water confined in the nanometer-sized pores revealed51 a value of β ≈ 0.5 almost independent of temperature (at 190−300 K), in good agreement with our observations. Furthermore, the same simulations demonstrate that the relaxation time below room temperature obeys the Vogel−Fulcher−Taman law, which prescribes a very slow temperature variation of the relaxation time in the temperature interval in which our measurements were performed, again in agreement with our results. On the other hand, both molecular dynamics simulations51 and experimental observations52 suggest that the liquid geometrically confined in a rigid matrix (as in our case) is characterized by a significant gradient of relaxation properties. At the center of the nanosized cavity, the water molecules are free (unbound) and possess practically the same relaxation time as the bulk water (however, the value of β is smaller). The

molecules located close to the surface (pore boundaries) are bound, and according to simulations, their relaxation time is about 2 orders of magnitude smaller than in the bulk water.53 The KWW process we observed can originate from the relaxation of these molecules. Free water molecules can give rise to the relaxation process found at high frequencies outside the measurement frequency window.

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CONCLUSIONS We have investigated the dielectric properties of water and hydrated metal ions in a 3D cucurbit[8]uril-based supramolecular architecture. Although the structural information on the confined water and hydrated copper(II) ions is unclear due to the large disorder of water and hydrated copper(II) ions, the dielectric spectra at different temperatures and frequencies clearly reveal the existence of two relaxation processes. The low-frequency dispersion described by the fractional power law is related to the relaxation of hopping charge carriers. The second relaxation contribution gives rise to an exceptionally large dielectric constant and follows the Kohlrausch−Williams− Watts relaxation law with the characteristic relaxation time almost independent of temperature. This process is attributed to bound water molecules. The third relaxation process should also exist at higher frequencies, which is presumably related to the relaxation of free water molecules.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected](L.-S.L.); [email protected] (Z.-G.Y.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the National Natural Science Foundation of China (Grants 20825103, 90922031, 21001089, and 21021061), the 973 Project from the Ministry of Science and Technology of China (Grant 2012CB821704), the Minjiang Scholar Program, and the Natural Science and Engineering Research Council of Canada for support.

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