A Differential Dielectric Spectroscopy Setup to Measure the Electric Dipole Moment and Net Charge of Colloidal Quantum Dots R

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A differential dielectric spectroscopy setup to measure the electric dipole moment and net charge of colloidal quantum dots R. J. Kortschot, I. A. Bakelaar, B. H. Erné, and B. W. M. Kuipers

Citation: Review of Scientific Instruments 85, 033903 (2014); doi: 10.1063/1.4867666 View online: http://dx.doi.org/10.1063/1.4867666 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/3?ver=pdfcov Published by the AIP Publishing

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This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 131.211.104.187 On: Thu, 08 Jan 2015 14:01:16 REVIEW OF SCIENTIFIC INSTRUMENTS 85, 033903 (2014)

A differential dielectric spectroscopy setup to measure the electric dipole moment and net charge of colloidal quantum dots R. J. Kortschot, I. A. Bakelaar, B. H. Erné, and B. W. M. Kuipersa) Van ’t Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute for Nanomaterials Science, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands (Received 4 December 2013; accepted 23 February 2014; published online 13 March 2014) A sensitive dielectric spectroscopy setup is built to measure the response of nanoparticles dispersed in a liquid to an alternating electric ﬁeld over a frequency range from 10−2 to 107 Hz. The measured complex permittivity spectrum records both the rotational dynamics due to a permanent electric dipole moment and the translational dynamics due to net charges. The setup consists of a half- transparent capacitor connected in a bridge circuit, which is balanced on pure solvent only, using a software-controlled compensating voltage. In this way, the measured signal is dominated by the contributions of the nanoparticles rather than by the solvent. We demonstrate the performance of the setup with measurements on a dispersion of colloidal CdSe quantum dots in the apolar liquid decalin. © 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4867666]

I. INTRODUCTION mittivity spectrum from 10−2 to 107 Hz using a transparent capacitor, we want to make it possible to measure both the net Two essential electric properties of colloidal semicon- charge and permanent dipole moment in the dark and under ductor nanoparticles, so-called quantum dots, are their net illumination in a single setup. charge and permanent electric dipole moment. They affect Dielectric spectroscopy is well-known in soft matter sci- their optical properties1 and colloidal interactions,2, 3 for in- ence and has been applied to many materials, for instance, stance, enabling controlled assembly of particles on a sub- polymers,13 proteins,14 and colloids.15 Commercial analyz- strate using electric fields.4 The electric properties can be de- ers for dielectric spectroscopy generally include automatic termined from the complex permittivity spectrum when the balancing bridges and frequency response analysis.16, 17 The particles are dispersed in a liquid.5, 6 Dilute dispersions have bridge achieves balance by automatically adjusting capac- the advantage of avoiding interparticle interactions and of itive and resistive components,18–20 and the permittivity at limiting the required amount of precious particles, but the a particular frequency is calculated from the circuit com- relative contribution of the nanoparticle dipole moments to ponents in the balanced situation. Phase-dependent voltages the permittivity spectrum is weak. To optimize sensitivity, we are measured using gain-phase analyzers, vector voltmeters, built a complex dielectric spectroscopy setup whose output or lock-in amplifiers (LIA). A broad frequency range can signal can be nullified in the absence of nanoparticles, so that be accessed thanks to measurement resistors whose values after they are added to the liquid, their contribution dominates can be selected on a logarithmic scale.21 The end result is the measured signal. the total permittivity of the sample. Our own objective is to Both dipole moment and charge of colloidal quantum measure directly the excess permittivity from the differen- dots can be determined by dielectric spectroscopy. The per- tial signal of a bridge circuit. Background signal is removed manent electric dipole moment of particles with a hydrody- using a software-controlled phase-dependent compensating namic radius on the order of 2–8 nm dispersed in a liquid with voltage.22–24 The bridge is balanced on pure solvent, and upon a viscosity of about 1 mPa s is observable in the permittivity addition of colloidal nanoparticles, the complex excess per- spectrum as a Debye relaxation in the 105–107 Hz frequency mittivity is measured at the highest possible sensitivity of the range.5, 6 Net charge on the particles gives rise to conductivity lock-in amplifier. of the dispersion and polarization of the electrodes,6, 7 with a − This paper is organized as follows: the experimental relaxation frequency of typically 10 1–103 Hz, a function of setup is presented in Sec. II, followed by its characterization cell geometry, ion concentration, and mobility of the charged and calibration in Sec. III. Permittivity spectra are shown in particles. Both the dipole moment and the net charge can Sec. IV, and conclusions are drawn in Sec. V. also be measured by other techniques. Dipole moments have been measured using optical spectroscopy8 or with transient 9 electric birefringence (for rod-like particles). Net charges II. EXPERIMENTAL SETUP have been determined by transient current analysis10 and laser Doppler electrophoresis.11 Additionally, it has been shown by A. General principle electrostatic force microscopy that quantum dots can acquire The setup consists of a differential impedance bridge in 12 a net charge upon illumination. Here, by measuring the per- which two capacitors are compared (Fig. 1) to measure the complex excess permittivity ex(ω) a)Author to whom correspondence should be addressed. Electronic mail: ex [email protected] (ω) = (ω) − s , (1)

(a) (b)

FIG. 1. Schematic diagrams of (a) the differential permittivity measurement circuit and (b) the transparent sample capacitor.

where (ω) is the permittivity of the colloidal dispersion, s measured separately, providing magnitude and phase of the is the permittivity of the solvent, and ω = 2πf is the angular voltage over the reference capacitor. frequency. Capacitor CA is a reference capacitor with capac- The transparent capacitor consists of one gold-plated itance CA or C, and capacitor CB contains either dispersion electrode (25 mm × 25 mm × 7.5 mm) and one ITO coated or solvent and has capacitance CB. The voltage VA−B is pro- glass electrode (25 mm × 25 mm × 1.1 mm, surface re- portional to the difference C in capacitance between sam- sistivity 8–12 /sq, Sigma Aldrich). Both square electrodes ple and reference capacitors. Ideally, the reference capacity is are glued together on the edges with adhesive (Araldite, such that C is zero at each frequency for a background mea- AW2101/HW2951), through which 75 μm diameter glass surement (Cbg), i.e., the sample capacitor filled with pure spacer beads (Sigma Aldrich) are mixed. Two polytetraflu- solvent. Then, the excess complex capacitance or permittiv- oroethylene syringe tubes (Sigma Aldrich) are glued in two ity can be measured with a sample measurement (Cs), i.e., holes (diameter = 1 mm) through the gold electrode to the sample capacitor filled with a dispersion. In practice, the fill the capacitor with dispersion. Conductive silver epoxy bridge is never exactly balanced and Cbg is neither zero nor (SPI, #05062) is used for electrical contact with the ITO frequency independent. To measure at the highest sensitivity, electrode. not limited by any offset, a compensating voltage Vcomp is ap- An adjustable capacitor with aluminum electrodes and plied in both the sample and the background measurements. Teflon spacer was used as reference capacitor. The spacing This is similar to the approach that we followed to develop a could be adjusted by varying the distance between the elec- differential magnetic susceptibility setup.22 A sample capaci- trodes using screws. The reference capacitor was set equal tor with one transparent indium tin oxide (ITO) electrode was roughly to the high frequency capacitance of the sample ca- constructed to allow measurements under illumination. pacitor. Both capacitors were measured independently with an HP4192A impedance analyzer. The circuit was placed in an B. Hardware electrically grounded and thermally insulated box with inter- nal copper walls in contact with copper tubing thermostatized The electronics of the setup are a Zurich Instruments using liquid pumped from a Julabo F25 thermostatic bath HF2LI differential LIA and two external Zurich Instruments (± 0.01 ◦C). HF2CA current pre-amplifiers (AMP1/AMP2). The LIA has two synchronized oscillation outputs (OSC1/OSC2) and two C. Measurement procedure phase sensitive detectors (PSD). ex The signals of the reference and sample branches, VA Determination of the excess capacitance C requires and VB, respectively, are measured with the two independent measurement of Vdiff and VA, both for a sample measurement amplification channels of the first amplifier (AMP1), which on dispersion and a background measurement on pure solvent. has a 101–106 selectable measurement resistor. These sig- Additionally, the nullification procedure is necessary to deter- nals are subtracted using the second amplifier (AMP2), yield- mine and to apply a compensating voltage Vcomp. All measure- ing VA−B. A second output (OSC2) is used to apply a com- ment procedures were implemented on a PC using LABVIEW plex compensating voltage (Vcomp), to reduce any offset if the software. impedance bridge is not perfectly balanced at a particular fre- The measurement procedure is as follows. First, the ca- quency. This voltage is subtracted from VA−B by the LIA, pacitor is filled with a sample and the voltage VA−B is mea- yielding Vdiff. The voltage of the reference branch VA is also sured directly without compensating voltage, starting with the This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 131.211.104.187 On: Thu, 08 Jan 2015 14:01:16 033903-3 Kortschot et al. Rev. Sci. Instrum. 85, 033903 (2014)

least sensitive range of the LIA, and switching successively The nullification procedure applies a compensating volt- to more sensitive ranges if no overload is expected.22 Second, age to cancel any remaining signal, which is required in the a compensating voltage Vcomp is applied, which is set equal case that the sample signal is smaller than the additional ca- to the measured voltage VA−B, and the remnant signal Vdiff pacitance due to an imperfectly balanced bridge. In this case, ex is measured. Third, since Vdiff is not necessarily zero, Vcomp one measures Vdiff = VA−B − Vcomp and C is determined is adjusted by an iterative procedure as discussed below, to from further reduce Vdiff. Finally, the capacitor is filled with pure V s V bg solvent and, while the optimal Vcomp is maintained, Vdiff is Cex =−C diff − diff (5) V s bg measured at the highest sensitivity. Independently from this A VA nullification procedure, the voltage V is measured. A · The compensating voltage V necessary to nullify provided that ωRC 1 and ωRC Vdiff/VA 1. comp Measurements of electrode polarization at lower frequen- Vdiff, in order to reduce any offset, was determined by an iterative nullification procedure that we developed for this cies require less sensitivity, and alternatively, VB can be mea- setup.24 This procedure rapidly converges to the noise-limited sured directly. In this case, the reference branch is discon- minimum by taking into account the instrumental damping nected, and CB is obtained from and phase shifting of V in terms of an empirical complex comp = VB constantα ˜ . According to this procedure, the output of the CB (6) iωRVapp n circuit is determined in the nth step of the iteration by Vdiff = − n n with Vapp the applied voltage. VA−B α˜ Vcomp. After the initializing step, in which 0 The complex excess relative permittivity due to the V = V − , the compensating voltage is then determined comp A B ex by nanoparticles is given by

n ex ex A ex + VA−B Vcomp C = K ≈ (7) V n 1 = = . (2) c 0 comp n − n d α˜ 1 Vdiff VA−B with Kc the cell constant of the capacitor, A the surface area As explained in Ref. 22, it is preferred to perform the of the capacitor, d the spacing between the capacitor plates, nulliﬁcation procedure during the sample measurement and and 0 the vacuum permittivity. to apply the same compensating voltage again during the background measurement, instead of the other way around. The selectable measurement resistors of AMP1 are cho- III. CHARACTERIZATION AND CALIBRATION sen to be as large as possible, but with the restriction ωRC The setup is characterized and calibrated with organic < 0.015, where R is the measurement resistance. AC cou- solvents of known permittivity and low conductivity. The re- pling is selected for AMP1 and AMP2 at frequencies above sults are used to determine the cell constant of the capacitor. 100 kHz. An oscillating voltage of 1 V was applied, unless The impedance spectra of the transparent capacitor with stated otherwise. Usually, 10 data points are averaged at each ◦ different solvents (Fig. 2(a)) resemble that of a capacitor frequency. Calibration of the setup was performed at 22.0 C and resistor in parallel, though not perfectly. When measured with toluene (J.T. Baker), cyclohexane (Interchema), and di- with the differential setup in the 102–107 Hz frequency range ethyl ether (Biosolve). Tertbutylammonium tertphenylborate with a reference capacitor of 185.4 pF, it becomes clear that (Fluka) was dissolved in hexanol (Sigma-Aldrich). Re(C), the component of C that is in phase with the reference capacitor, is not constant (Fig. 2(b)), but it decreases approximately linearly with the logarithm of frequency. Con- D. Calculation of the permittivity currently, the out-of-phase component Im(C) is nonzero The electric circuit allows calculation of the difference (Fig. 2(c)). Despite this nonideal behavior, which we ascribe between capacitances, C = CB − C, by measuring the volt- to dissipation of the glue spacer which has an impedance par- age over the reference resistor, VA, and the voltage difference allel to the sample impedance, accurate measurements are between the two resistors, VA−B. In the case of ωRC 1, possible. Empirically we ﬁnd, when calculating the excess capacity Cex compared to toluene, that the capacity scales lin- V − C =−C A B . (3) early with the permittivity of the solvents (Fig. 2(d)). Im(Cex) VA shows effects of nonzero conductivity and approaches zero at To exclude any additional capacitance resulting from an higher frequencies (Fig. 2(e)), while above 1 MHz inductive imperfectly balanced bridge, the increment in capacitance due effects become visible, proportional to Re(Cex). To calibrate to the sample is determined from a sample measurement (s, the setup and to determine the cell constant of the capacitor, with sample) and a background measurement (bg, without Re(Cex) is averaged over the 103–106 Hz frequency range for sample) each solvent and plotted against the relative permittivity of the solvent, known from literature25 (Fig. 2(f)). The slope in s bg V − V − this plot is equal to the cell constant K = 28.70 ± 0.10 pF. Cex = Cs − Cbg =−C A B − A B (4) c s bg The surface area of the capacitor was determined from a VA V A digital photograph of the capacitor (A = 3.07 cm2). Using provided that ωRC 1 and ωRC · VA−B/VA 1. Eq. (7), the distance between the electrodes is estimated to be This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 131.211.104.187 On: Thu, 08 Jan 2015 14:01:16 033903-4 Kortschot et al. Rev. Sci. Instrum. 85, 033903 (2014)

(a) (b) 5 100 ] 4 8 50 0

3 C) [pF]

Z’’ [1 0

2 Re( 1 -50 0 -100 02468 10 102 103 104 105 106 107 8 Z’ [10 ] Frequency [Hz] (c) (d) 90 0 60 ) [pF] C) [pF] ex

-20 C 30 Im(

Re( 0 -40 -30 -60 -60 102 103 104 105 106 107 102 103 104 105 106 107 Frequency [Hz] Frequency [Hz] (e) (f)

0 60 Kc = 28.70 ± 0.10 pF ) [pF] ) [pF] ex ex 30

-20 C Im(C

Re( 0 -40 -30

-60 -60 102 103 104 105 106 107 012345 Frequency [Hz] Dielectric constant

FIG. 2. Calibration in the 102–107 Hz range with different solvents (diethyl ether •, toluene , cyclohexane ) and air (◦): (a) Impedance spectrum Z = Z − iZ,(b)Re(C), (c) Im(C), (d) Re(Cex), and (e) Im(Cex) as a function of frequency, and (f) Re(Cex) as a function of solvent permittivity to determine the cell constant Kc.

d = 94.6 μm, slightly larger than the average diameter of the IV. PERMITTIVITY SPECTRA silica glass beads (75 μm) used as spacer. As a demonstration of the setup, the excess complex At lower frequencies (10−2–102 Hz), Cex goes up dra- permittivity spectrum (Fig. 5) was measured of a dilute matically (Figs. 3(a) and 3(b)), due to electrode polarization. (5.5 μM/0.1 vol. % including surfactant shell) dispersion of Apparently, charged impurities are present in the solvents, be CdSe quantum dots with a 4.0 nm core diameter dispersed in it at very low concentrations (∼nM for diethyl ether,

ex (a) |C | [pF] |εex| 3 10x10 101 8x103 10-1 ) [pF] 6x103 100 ex -2 4x103 10 10-1 Re(C 2x103 10-3 0 10-2 -2x103 10-4 10-2 10-1 100 101 102 10-3 102 103 104 105 106 107 Frequency [Hz] Frequency [Hz] (b) 3 5x10 FIG. 4. Differential measurement between two aliquots of toluene.

) [pF] 0

ex -5x103 agreement with the dimensions of the nanoparticle covered with a 2.3 nm oleic acid shell. The magnitude of the relaxation Im(C -10x103 d = 0.00097 yields a dipole moment μ = 53 D, which is 5, 6 -15x103 close to previously reported values. The ﬁnite conductivity indicates the presence of charged 3 -20x10 species, which, at low frequencies, leads to electric double -2 -1 0 1 2 10 10 10 10 10 layers at the electrodes. The relaxation of these double layers Frequency [Hz] is described by the following function:26, 27 (c) (ω) = EP (10) 1200 EP −α ex (iωτ∞)1 + iωτ Re(C )

C) [pF] 900 in which EP = sκd/2 is the relaxation magnitude, d = 600 is the distance between the electrodes, τ d/(2Dκ)is 2 the double layer relaxation time, τ ∞ = 1/(Dκ )isthe ex 300 Im(C ) Maxwell-Wagner relaxation time, and α is an empirical con- C) , Im( 0 stant. The translation diffusion coefficient of the charged D = kT πηa κ−1 Re( species is /(6 H), and the Debye length is -300 2 1/2 = [0skT/(2nq )] , where q is the magnitude of the posi- -2 -1 0 1 2 10 10 10 10 10 tive and negative charges and 2n their total number density. Frequency [Hz] Here, a fit of the electrode polarization yields that a fraction of 1.2% of the nanoparticles carries a net charge of ±1e, while −2 2 FIG. 3. Calibration in the 10 –10 Hz range with different solvents (diethyl the other nanoparticles are charge-neutral. ether •, toluene , cyclohexane ) and air (◦): (a) Re(Cex) and (b) Im(Cex)as a function of frequency, and (c) calibration with an air capacitor (Cex = 900 After fitting of the electrode polarization and the dipolar pF). The error bars indicate the standard deviation of ten measurements at relaxation, a small shoulder is observed in the real part of the each frequency. permittivity in the 102–104 Hz frequency range. This shoulder is likely an artifact. Exactly in this frequency range the ratio / is the smallest (/ < 0.01), hence is the most

(a) (b) 3 10 ε 0.005 ε’ ’ 102 conductivity ε’’ 0.004 dipolar 101 relaxation 100 0.003

-1 10 0.002 10-2 electrode 0.001 10-3 polarization 10-4 0.000 100 101 102 103 104 105 106 107 103 104 105 106 107 Frequency [Hz] Frequency [Hz]

FIG. 5. Excess permittivity (: •, : ◦) of a dilute dispersion of CdSe quantum dots in decalin (0.1 vol. %): (a) total spectrum and (b) a close-up of the dipolar relaxation. Solid lines are ﬁts using Eqs. (8) and (10).

(a) on a dilute dispersion of CdSe quantum dots demonstrates 103 sufﬁcient sensitivity to measure the dipolar relaxation due to a ε ε ’ , ’’ ε’’ permanent dipole moment and the conductivity and electrode 102 polarization due to particles with a net charge.

1 10 ACKNOWLEDGMENTS ε ’ CdSe quantum dots were kindly provided by Relinde van 100 Dijk-Moes. Ernst van Faassen and Casper van der Wel are acknowledged for useful discussions, and the latter also for -1 10 providing Fig. 1(b). This work was supported by The Nether- lands Organisation for Scientific Research (NWO). 10-2 102 103 104 105 106 1S. A. Empedocles and M. G. Bawendi, Science 278, 2114 (1997). 2M. Klokkenburg, A. J. Houtepen, R. Koole, J. W. J. de Folter, B. H. Erné, Frequency [Hz] E. van Faassen, and D. Vanmaekelbergh, Nano Lett. 7, 2931 (2007). (b) 3J. van Rijssel, B. H. Erné, J. D. Meeldijk, M. Casavola, D. Vanmaekel- bergh, A. Meijerink, and A. P. Philipse, Phys. Chem. Chem. Phys. 13, ε’/ε’’ 12770 (2011). 4 -1 S. Ahmed and K. M. Ryan, Chem. Commun. 2009, 6421. 10 5S. A. Blanton, R. L. Leheny, M. A. Hines, and P. Guyot-Sionnest, Phys. Rev. Lett. 79, 865 (1997). 6M. Shim and P. Guyot-Sionnest, J. Chem. Phys. 111, 6955 (1999). 7A. D. Hollingsworth and D. A. Saville, J. Colloid Interface Sci. 257,65 (2003). 8 10-2 V. L. Colvin and A. P. Alivisatos, J. Chem. Phys. 97, 730 (1992). 9L. S. Li and A. P. Alivisatos, Phys. Rev. Lett. 90, 097402 (2003). 10M. Cirillo, F. Strubbe, K. Neyts, and Z. Hens, ACS Nano 5, 1345 (2011). 11E. V. Shevchenko, D. V. Talapin, N. A. Kotov, S. O’Brien, and C. B. Murray, Nature (London) 439, 55 (2006). 12T. D. Krauss and L. E. Brus, Phys. Rev. Lett. 83, 4840 (1999). 10-3 13J. P. Runt and J. J. Fitzgerald, Dielectric Spectroscopy of Polymeric Mate- 102 103 104 105 rials (American Chemical Society, 1997). 14R. Pethig, Annu. Rev. Phys. Chem. 43, 177 (1992). Frequency [Hz] 15A. D. Hollingsworth and D. A. Saville, J. Colloid Interface Sci. 272, 235 (2004). FIG. 6. Permittivity spectrum of tertbutylammonium tertphenylborate salt in 16F. Kremer and M. Arndt, Broadband Dielectric Measurement Techniques hexanol and fitted for electrode polarization. The part of the real permittivity (American Chemical Society, 1997), pp. 67–79. in (a) that is not fitted well, as indicated by the arrow, corresponds to the 17P. Hedvig, Dielectric Spectroscopy of Polymers (Adam Hilger Ltd., Bristol, frequency range where the ratio / in (b) is the smallest. 1977). 18L. Callegaro, Instrumentation 54, 529 (2005). 19M. Dutta, A. Chatterjee, and A. Rakshit, Measurement 39, 884 (2006). susceptible for, for instance, a small systematic error in the 20N. K. Das, T. Jayakumar, and B. Raj, IEEE Trans. Instrum. Meas. 59, 3058 phase angle in the measured impedance. As indicated in (2010). 21 Fig. 6, this shoulder is also observed in the permittivity spec- R. Richert, Rev. Sci. Instrum. 67, 3217 (1996). 22B. W. M. Kuipers, I. A. Bakelaar, M. Klokkenburg, and B. H. Erné, Rev. trum of tertbutylammonium tertphenylborate salt in hexanol, Sci. Instrum. 79, 013901 (2008). which does show electrode polarization as well. This shoulder 23“Input offset reduction using the model 7265/7260/7225/7220 synchronous does not obstruct the observation of the dipolar relaxation. oscillator/demodulator monitor output,” Signal Recovery, Technical Report No. AN 1001, 2008. 24C. M. van der Wel, R. J. Kortschot, I. A. Bakelaar, B. H. Erné, and B. W. V. CONCLUSIONS M. Kuipers, Rev. Sci. Instrum. 84, 036109 (2013). 25“Permittivity (dielectric constant) of liquids,” CRC Handbook of Chemistry The described setup successfully measures the complex and Physics, 93rd ed. 2012–2013 (http://www.hbcpnetbase.com/, accessed excess permittivity of liquid dispersions of colloidal quantum 2012). 26Details of the CdSe quantum dots and further analysis will be presented in −2 7 dots in the 10 –10 Hz frequency range, using a differential a future publication. circuit with background compensating voltage. Measurement 27J. R. Macdonald, J. Phys.: Condens. Matter 22, 495101 (2010).