Electric Properties and Cross-Linking

Jul 19, 2012 - Yun Xia Guo , Ying Dan Liu , Riping Liu , Yongjun Tian , Ke Chen , Li-Min ... of cross-linking density distribution on the volume phase...
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Article pubs.acs.org/Macromolecules

Correlation between Dielectric/Electric Properties and Cross-Linking/ Charge Density Distributions of Thermally Sensitive Spherical PNIPAM Microgels Jianfeng Zhou,§ Jingjing Wei,‡ To Ngai,‡ Li Wang,§ Dan Zhu,*,† and Jian Shen*,† †

Jiangsu Key Laboratory of Biofunctional Materials, College of Chemistry and Material Science, Nanjing Normal University, Nanjing 210097, P. R. China ‡ Department of Chemistry, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong § Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, P. R. China S Supporting Information *

ABSTRACT: Thermally sensitive poly(N-isopropylacrylamide) (PNIPAM) spherical microgels with different charge distribution were prepared by different monomer and comonomer feeding methods. The frequency ( f, 10−2−107 Hz) and temperature (T, 5−50 °C) dependent complex dielectric/electric properties of these microgels were analyzed by dielectric relaxation spectroscopy. Each microgel can be treated as a large multicharged macroion surrounded by many small counterions, and the relative displacement and the diffusion of counterions contribute to the permittivity and conductivity of the microgel dispersion. Both the dielectric permittivity at f > 103 Hz and the conductivity at f > 106 Hz decrease when the microgels shrink at temperatures higher than the lower critical solution temperature (LCST) of PNIPAM due to the shrink-induced counterion dissociation. The variation of either permittivity or conductivity with temperature reveals a sharper transition for the microgels or the microgel shell with a more uniform charge distribution than those with an inhomogeneous dense core−loose shell structure, indicating a more gradual chain shrinkage for the latter. By detecting the counterions’ behaviors, we can use dielectric relaxation spectroscopy to probe the microscopic structural and dynamic heterogeneities of PNIPAM microgel dispersions.

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INTRODUCTION Poly(N-isopropylacrylamide) (PNIPAM) is a thermally sensitive polymer with a lower critical solution temperature (LCST) of ∼32 °C in water.1 The phase transitions of individual linear PNIPAM chains and PNIPAM related gels have been extensively investigated in the past two decades.2 Especially, the coil-to-globule transition of individual PNIPAM linear chains is related to a fundamental problem in polymer physics, while the shrinking−swelling volume transition of PNIPAM gel networks around its LCST leads to a new research field of environmentally sensitive or stimuli-responsive polymer gels because of their potential applications in controlled release, sensors, or energy transducers. Apparently, these two phenomena are different but they are microscopically connected.3 Namely, it is the coil-to-globule transition of topologically constrained subchains between two neighboring cross-linking points that leads to the shrinkage of a polymer gel. In theory, the expansion or collapse of subchains with different lengths should occur at different LCSTs. For individual free chains, one can prepare narrowly distributed (Mw/Mn < 1.1) and high molar mass (∼107 g/mol) chains and study the coilto-globule transition with laser light scattering,3,4 while for a polymer gel network, it is rather difficult to determine the internal structures and their changes in the coil-to-globule © 2012 American Chemical Society

transition. Such difficulties lie in two reasons: one is the lack of perfect samples with the topologically restrained subchains of uniform length, and they are uniformly distributed; the other is the lack of precise and fast detecting techniques. The problems of broad length distribution of topologically restrained subchains and their uneven distribution, i.e., heterogeneous chain density, come from the different reactivity ratios of the comonomers, including cross-linking agents, during the polymerization.5 Therefore, a PNIPAM bulk gel normally contains unevenly distributed compositions; i.e., there are denser and looser microstructures or microdomains inside. The problem is getting worse when PNIPAM microgels are prepared by the microprecipitation method at higher temperatures because more reactive cross-linking agent, N,N′methylenebis(acrylamide) (BIS), reacts first together with some N-isopropylacrylamide (NIPAM) monomer to result in a relatively dense core surrounded by a loose PNIPAM shell that is made of loosely interconnected PNIPAM chains or even dangling PNIPAM brushes. Such a core−shell structure sometimes leads to a shrinkage with several stages.6 A great Received: March 5, 2012 Revised: June 8, 2012 Published: July 19, 2012 6158

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induced by thermal motions in a broad range of spatial and temporal scales.22,23 Additional advantages of dielectric relaxation spectroscopy are attributed to its quick, easy, noninvasive, and sensitive measurement of electrical properties of a given material.22 In a complicated heterogeneous system, such as polymer composites, blends with microphase separation, homopolymers but with crystalline and amorphous domains, and colloidal dispersions, some interfacial phenomena and dynamics are related to Maxwell−Wagner or interfacial polarization process,22,24 so we can use dielectric relaxation method to probe interfacial structure and dynamics, local motion of counterions, and microstructures. To connect dielectric properties of counterions to a gel network, one has to first prepare polymer gel networks with desired and defined charge distributions. In order to increase the signal-to-noise ratio, we have decided to use PNIPAM microgels because they have a much larger interfacial area in comparison with a bulk gel and their thermal sensitivity offers us another parameter to adjust their charge distribution. In a typical microprecipitation method, PNIPAM microgels are prepared at 60 °C or higher temperatures using ionic KPS initiator, BIS as cross-linker, and sometimes acrylic acid as comonomer. NIPAM monomer is soluble in water at higher temperatures but not PNIPAM. As discussed before, BIS is more reactive so that resultant cross-linked PNIPAM chains collapse to form a dense core with those lightly connected/ branched or linear dangling chains on its periphery, as schematically shown in Figure 1a. In the current study, we

amount of effort has been spent on the synthesis that PNIPAM microgels with uniform cross-linking, among which Varga7 and Ngai8 have developed a programmed synthesis on feeding and temperature ramp that allows the preparation of microgels with controlled spatial distribution of chain density or functional groups. Optical appearance and microscopy using dye labeling have been used to characterize the structural heterogeneity, but the visual technique is powerless in dealing with the structural dynamics. A great amount of effort has been spent on the development and study of PNIPAM gels. First, it is focused on gels with small volume, i.e., microgels. Tanaka et al. have reported that the swelling or shrinking time of a spherical gel is proportional to the square of its radius;9 i.e., small microgels with a size of ∼102 nm swell and shrink much faster than bulk gels. By taking care of their preparation, microgels can maintain some physical properties of bulk gels and also homogeneity at some degree. Though there are some experimental methods, such as light scattering,10,11 electrophoresis,12 and viscoelastic or dielectric relaxations,13 that have been used to investigate the translational behavior, chain density fluctuation, microstructures, and viscoelastic and dielectric properties of polymers, the dynamics and kinetics of the PNIPAM microgels with a submicrometer size have not been extensively studied. It is presumably because we nowadays still lack an effective tool to probe microstructures of a given polymer gel network because it is soft, random, and filled with more than 95% of water. Specially, their dielectric measurements often exhibit some broad, non-Debye-type relaxation modes, presumably due to the dipolar−dipolar interaction.14 The chain and network dynamics are interconnected and mixed together. We have noted that in the preparation of PNIPAM microgels one often introduces ionic groups on them with or without intention, i.e., from initiator (e.g., KPS) or from comonomer (e.g., acrylic acid and its salts), which possibly leads to another kind of structural heterogeneity. These ionic groups dissociate in aqueous or polar organic solvent to release counterions and form loosely bound ionic cloud around polymer chains15,16 and screen the charges on the polymer chains inside a microgel which can be considered as a large macroion. Besides the temperature, these counterions together with or without some additional salts can also lead to the gel swelling and shrinking.17−19 Nevertheless, long-range electrostatic interaction among subchains makes the problem more complex.20,21 However, we should not forget one principle that polyelectrolytes physics is always closely related to counterions. Many of the macroscopic properties or behaviors of polyelectrolytes are driven by entropy gained or lost due to those counterions that are closely associated with or somewhat isolated from the polymer chains, especially when no additional salts exist. Therefore, a probe of these counterions, their distribution, fluctuation, and displacement can lead to an insight into polymer chains or gel networks. Dielectric or electric analysis is an old but robust tool in studying chemical or physical natures of materials, based on the interactions between electromagnetic radiation and molecules inside a material, since electrons or charges characteristically respond to an applied electric field to result in macroscopic electrical or dielectric behaviors. Those behaviors not only are important to the evaluations and the applications of a specific material in electrical engineering but also provide abundant information on the movement, the distribution and the fluctuation of charges, and the dipolar and ionic relaxation

Figure 1. Schematic of three PNIPAM microgels in swollen state with different chain density and charge distributions: (A) microgels with a dense core and a loose and charged shell, (B) microgels with a loose core and a dense and charged shell, and (C) microgels with a uniform chain density and charge distribution. The blue grid represents the condensed polymer, the darker the color, the higher the cross-linking degree or chain density, and the red dot represents the counterions associated with the polymer chains.

have prepared another two kinds of PNIPAM microgels with different charge distribution by adding ionic comonomer and adjusting BIS at different polymerization stages with controlled feeding and heating. The confocal laser scanning microscopy has been used to characterize the distribution of the functional group of −COOH after labeling the microgel with Rhodamine B, and the spatial distributions of the functional groups and cross-linkers are recorded or deduced.8 Figures 1b and 1c schematically show their structures, namely, microgels with a loose core and a dense and charged shell and with a uniform chain density and charge distribution. The main purpose of the current study is to find dielectric signatures of different gel networks for future research.

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EXPERIMENTAL SECTION

Materials and Samples Preparation. N-Isopropylacrylamide (NIPAM, Fluka) was recrystallized from a toluene/n-hexane mixture. 6159

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Potassium persulfate (KPS, Riedel de Haen) was recrystallized from water. N,N′-Methylenebis-acrylamide (BIS, Fluka) and acrylic acid (AA, Farco) were used as received. All the PNIPAM-co-AA microgel particles of different morphologies were prepared through surfactantfree emulsion polymerization. All the resultant microgels were centrifuged at 18 000 rcf three times to remove the remove residual monomer and the un-cross-linked linear polymer fractions. All the microgels were dispersed in deionized water. The details of the polymerization of NIPAM into linear chains with narrowly distributed molecular weight or gel networks have been described elsewhere.25,26 Here we only outline how to prepare three different kinds of microgels. Microgels with a Dense Core and a Loose and Charged Shell. For traditional dense-core−loose-shell microgels, 0.7638 g of NIPAM, 0.0336 g of AA, and 0.0302 g of BIS in 45 mL of deionized water were preheated to 70 °C and purged with nitrogen gas for 30 min. After this, KPS (0.0500 g) dissolved in 5 mL of water was introduced to initiate the polymerization. The reaction mixture was kept at 70 °C for 8 h. Microgels with a Loose Core and a Dense and Charged Shell. For the loose-core−dense-shell microgels, 0.3849 g of NIPAM in 35 mL of deionized water was preheated to 70 °C and purged with nitrogen gas for 30 min. After this, 0.0519 g of KPS dissolved in 5 mL of water was introduced to initiate the polymerization. Note that no cross-linker was added in this stage of the polymerization. After 110 min, 0.3837 g of NIPAM, 0.034 g of AA, and 0.0294 g of BIS dissolved in 10 mL of water was fed into the cross-linker-free reaction mixture with a feeding rate of 4 mL/h by means of a syringe pump. Microgels with a Uniform Chain Density and Charge Distribution. For the homogeneous microgels, 0.6186 g of NIPAM, 0.0043 g of AA, and 0.0045 g of BIS in 50 mL of deionized water was preheated to 70 °C and purged with nitrogen gas for 30 min. After this, 0.0165 g of KPS dissolved in 5 mL of water was introduced to initiate the polymerization. Immediately, 0.0217 g of AA and 0.0233 g of BIS dissolved in 5 mL of water were fed into the reaction mixture with a feeding rate of 10 mL/h by means of a syringe pump. Laser Light Scattering. A commercial LLS spectrometer (ALV/ DLS/SLS-5022F) equipped with a multi-τ digital time correlation (ALV5000) and a cylindrical 22 mW He−Ne laser light source (632 nm, UNIPHASE) has been used to determine the gyration radius (Rg) and hydrodynamic radius (Rh) of the PNIPAM microgels at different temperatures. In dynamic LLS, the Laplace inversion (the CONTIN method in the correlator) of each measured intensity−intensity time correlation function G(2)(q,t) in the self-beating mode can derive an accurate determination of the average line width ⟨Γ⟩. For a diffusive relaxation, ⟨Γ⟩ is related to the translational diffusion coefficient ⟨D⟩ by (⟨Γ⟩/q2)q→0,C→0. Therefore, a hydrodynamic radius ⟨Rh⟩ can be obtained via the Stokes−Einstein equation, ⟨Rh⟩ = kBT/(6πη⟨D⟩), where kB, T, and η are the Boltzmann constant, the absolute temperature, and the solvent viscosity, respectively. In this study, we have measured the value of ⟨Γ⟩ at different scattering angles at each temperature. The solutions are clarified with 0.45 μm Millipore MillexLCR filters to remove the dust. Particle sizer (Zetasizer Nano ZS90) from Malvern on the same dynamic LLS principle but at only one scattering angle (90°) is also used to quickly estimate the size distribution of the microgels studied. Dielectric Relaxation Spectrometer. A broadband dielectric spectrometer (Novocontrol BDS40) with a ZGS extension test interface was used to characterize dielectric and electric behaviors of the PNIPAM microgels. The applied filed is ac voltage 1.5 V rms, namely electric filed 250 V rms/m when we use the sample cell with thickness of 6 mm, frequency range is from 10−2 to 20 MHz, and the temperature is adjusted with a temperature-control water bath and circulating system with range of 0−60 °C and accuracy of ±0.05 °C. Figure 2 schematically shows the dielectric measurement of PNIPAM microgels under two different temperatures below and above LCST. The self-made sample cell is constituted of a Teflon cylinder with different heights (2−10 mm) and two gold-coated copper electrodes. The sample cell is put into the cylindrical copper jacket with a water-circulating path so that the cell temperature can be

Figure 2. Schematic of dielectric measurement of PNIPAM microgels dispersed in water, where (a) swollen microgels below the LCST of PNIPAM and (b) shrunk microgels above LCST. well controlled between 5 and 50 ± 0.05 °C by a thermostat. The temperature inside the cell is monitored by a calibrated Pt100 thermal sensor placed inside the Teflon cylinder and close to the lower electrode. A small hole through the upper electrode is designed to expel the air and the excessive liquid from the cell during the sample loading. The space between the two electrodes can be adjusted by different Teflon cylinders. Note that PNIPAM microgels dispersed in water is a complex system with both dipolar and ionic response to an applied field. As schematically shown in Figure 3a, small free ions marked with triangles

Figure 3. (a) Schematics of the microscopic dipolar and ionic response of PNIPAM microgels dispersion in water to an applied field. (b) Vector diagram of an applied voltage and its induced currents in a plural plane.

in Figure 3a move to the oppositely charged electrode when an alternative electric potential is applied by a constant-voltage supplier, resulting in a conductive current. When they reach the electrodes and take or release electrons, the power supplier must move more electrons to the electrodes to maintain the applied voltage so that a current (IG) is detected in the outside circuit, in phase with the applied voltage, and its value equals to the inner conductive current. The polarization at the interface of two electrodes and the microgel/water interface is another response. The accumulation of dipoles (marked with ellipse) or ions (circle) with a total charge Q′ at the electrode interface establishes an internal potential that is opposite to the applied one so that the power supplier must also supply extra charges to the electrodes to maintain the applied voltage, resulting in another outside current (IC), which is related to the charging quantity Q on the electrode varying with time, IC= dQ/dt. Note that the phase of IC is π/ 2 ahead of that of the applied voltage. The relation among the applied field, the conduction current, the polarization current, and the total current are shown in the vector diagram in Figure 3b. The principle of dielectric or electric relaxation spectroscopy is based on the impedance measurement. Figure 3b shows that when an alternative field U* = U0eiωt with a frequency of f or an angular frequency of ω is applied onto a sample, the phase of the detected output current I* = I0ei(ωt+φ) usually shifts φ from that of the applied field. The two components of I* are IG and IC. The real and imaginary parts (σ′ and σ″) of the complex conductivity can be deduced from IG and IC as 6160

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σ′ =

IG d I d I d = 0 cos φ = 0 sin δ U0 S U0 S U0 S

σ″ =

IC d I d I d = 0 sin φ = 0 cos δ U0 S U0 S U0 S

have measured the average radius of gyration (⟨Rg⟩) of these microgels from the angular dependent scattered light intensity. The ⟨Rg⟩/⟨Rh⟩ ratio reflects the chain density spatial distribution. For the uniform nondraining sphere, ⟨Rg⟩/⟨Rh⟩ = 0.774. The lower ⟨Rg⟩/⟨Rh⟩ ratio reveals the dense-core− loose-shell structure because the loose shell contributes less to ⟨Rg⟩ so that it becomes smaller in comparison with a uniform sphere with an identical ⟨Rh⟩. For microgels B and C, their sizes are independent of the ultrasonic treatment. Presumably, it is those loosely dangling chains on the periphery that lead to the interparticle aggregation at a relatively concentrated dispersion (∼0.5 wt %). Besides the ⟨Rg⟩, ⟨Rh⟩, and ⟨Rg⟩/⟨Rh⟩ ratio for PNIPAM microgels obtained, their molar weight (Mw) is determined by SLS and listed in Table 1. The cross-linking density and average charge of each microgel are estimated from the Mw and the original ingredients in synthesizing samples A, B, and C. However, it is difficult to precisely estimate how many average charges are actually on each microgel because some of added charged monomers might form soluble chains inside the reaction mixture and washed out during the purification and some of charges are embedded inside the microgel. Figure 4 shows the temperature dependence of ⟨Rg⟩ and ⟨Rh⟩ of PNIPAM microgels A, B, and C. As the dispersion

(1)

where d is the distance between two electrodes, S is the surface area of one electrode, and sin δ/cos δ = tan δ is the loss tangent. The real and imaginary parts (ε′ and ε″) of the complex permittivity can also be deduced as ε′ = − ε″ =

σ″ ωε0

σ′ ωε0

(2)

Therefore, at a certain temperature, the real and imaginary parts of the complex permittivity and conductivity as well as the loss tangent tan δ are shown as a function of ω.

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RESULTS AND DISCUSSION First, we use laser light scattering (LLS) to characterize the average radius of gyration (⟨Rg⟩) and hydrodynamic radius (⟨Rh⟩) of these three kinds of PNIPAM microgels with different chain density and charge distributions. The normal PNIPAM microgels with a dense core and a loose and charged shell are prepared by adding BIS together with NIPAM monomer at one shot, and the reaction temperature is kept at 56 °C. Previous studies show that both the chain density and charge distributions of such prepared microgels are uneven, most of BIS are cross-linked and concentrated in the core, and most of charged groups from KPS are located at the periphery to form a loose and charged shell made of lightly cross-linked or branched or even grafted linear chains because they are hydrophilic.27−29 As the temperature increases, subchains in the core shrink first, transiting from a random coil to a collapsed globule,28 reducing its surface so that the more hydrophilic chains in the shell are pushed to extend and undergo a mushroom−pancake−brush conformational change. Further increase of the temperature finally leads to the collapse of chains at the shell.30 The temperature-dependent swelling of microgels with a dense and charged shell and with a uniform chain density and charge distribution are not so eventful. Table 1 shows that microgels A with a dense core and a loose and charged shell have a much large average hydrodynamic

Figure 4. Average hydrodynamic radius (⟨Rh⟩, filled symbols) and average radius of gyration (⟨Rg⟩, hollow symbols) of PNIPAM microgels, where “circles” represent PNIPAM microgels A, “squares” represent B, and “triangles” represent C.

temperature increases, their sizes shrink about 3 times. As expected, both ⟨Rg⟩ and ⟨Rh⟩ abruptly change at ∼32 °C. Further increase of temperature has no obvious effect on their sizes, indicating they are stable at higher temperatures. As discussed before, such a sharp change in both ⟨Rg⟩ and ⟨Rh⟩ is due to the conformational change of individual subchains between two neighboring cross-linking points. Namely, PNIPAM is soluble in water at T < 32 °C so that PNIPAM microgels swell in the dispersion. It has been shown that PNIPAM chains collapse in water at higher temperatures are related to the release of some associated water molecules from their hydrophobic isopropyl domains. However, it should be noted that even in their fully collapsed and insoluble state at higher temperatures, PNIPAM microgels still contain more than 80 wt % of water inside. The permittivity spectroscopy at the indicated temperatures is shown in Figure 5. All the measured permittivity have been calibrated with the stray capacitance from the sample cell, which is in parallel circuit with the sample, and considered constant in the testing temperature range. The calibration details are referred in the manual of Cylindrical Liquid Sample Cell BDS 1307, Novocontrol. An alternative field of U* =

Table 1. Size and the Polydispersity Index (PDI) of PNIPAM Microgels zetasizer

LLS results

microgels

⟨Rh⟩/nm

PDI

⟨Rg⟩/nm

⟨Rg⟩/⟨Rh⟩

Mw/(g/mol)

A

2.5 × 102 before ultrasonic 1.8 × 102 after ultrasonic 2.4 × 102 1.3 × 102

0.20

3.0 × 102

0.65

3.49 × 108

1.7 × 102 1.5 × 102

0.68 0.78

6.43 × 107 1.24 × 108

B C

0.26 0.05 0.10

radius ∼250 nm and are broadly distributed in size. A comparison with the results from ALV spectrometer, where the dispersion has been filtered before each LLS measurement, reveals possible interparticle aggregation. We redispersed them by an ultrasonic treatment of 30 min, resulting in a decrease of ⟨Rh⟩ to ∼185 nm, which confirms our assumption. We also 6161

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Figure 5. Frequency dependence of real and derivative imaginary parts of complex permittivity (ε′ and ε″der) of PNIPAM microgels A, B, and C, where insets show the enlarged spectrum of ε′ over a signature frequency range.

U0eiωt with different frequencies is applied to the dispersion at a given temperature. The complex permittivity and conductivity were calculated on the basis of eqs 1 and 2 from the measured current and phase angle. It is observed from the spectroscopy that the real part (ε′) increases with the decreasing frequencies. When frequency is lower than 1 kHz, there occurs a rapid increasing in ε′ with the decreasing frequency, which is attributed to the charge accumulation or depletion at the electrode−sample interface, termed as electrode polarization.22,31 In such an ionic conductive microgel dispersion, the ohmic conduction loss dominates the imaginary part of permittivity, so the logarithmic ε″ decreases linearly with the increasing of logarithmic frequency; namely, ε″ is linear to the reciprocal of angular frequency in the double-logarithmic plot, following the relation of ε″ = σ0/ωε0, in which ε0 is the dielectric constant of vacuum, while σ0 is the dc conductivity. Normally we judge the microscopic polarization relaxation from the position and strength of the permittivity loss peak in the spectroscopy; the relaxation time can be calculated from the peak position f max, which is τ = 1/ω = 1/(2πf max). In the conductive condition that the conduction loss totally covers the relaxation process, we usually use an effective method to deduce ε″ from ε′ with the Kramers−Kronig relation,32 which is described in eqs 3 and 4, the derivated permittivity loss, marked as ε″der, is shown in Figure 5. ε″(ω) =

σdc 2 + ωε0 π

∫0

∞

ε′(ω)

ω dω′ ω′ − ω 2 2

ε″der ≈ −

π ∂ε′(ω) 2 ∂ ln ω

(4)

In Figure 5, there are two relaxations that can be observed in the PNIPAM microgels below LCST: one is around MHz; another is at 10 kHz. In aqueous colloidal dispersions, the dielectric dispersion typically in the range of MHz is determined by the Maxwell−Wagner−O’Konski relaxation,22 also termed as δ-dispersion, which is caused by the unmatched permittivity and conductivity of the particle and the surrounding medium. It is the density distribution or fluctuation of the charges with accumulation and depletion at the interface of the particle, i.e., the deformation of the counterion cloud around the macroion of the PNIPAM colloid particle, due to the different statistical response of the whole particle and the medium at the same applied field. The αdispersion at the low frequency of kHz, though being the featured characteristic phenomenon in electric permittivity of suspensions, it has not been clearly confirmed. There are several hypotheses, one of which is the concentration polarization,33 which is originated in the asymmetry of these systems with respect to the ion signs, namely to the fixed charge of the suspended particles; the behavior of counterions and coion is different under an applied field at very low frequencies, and another report attributes it to the movement of the polyelectrolyte chains.34 In our opinion, it is the translocation of the overall counterions around the particle, compared with the deformation of the counterion cloud, so that its relaxation time is relevant with the hydrodynamic diameter of the colloidal particle. So both the two relaxations at MHz and kHz

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Figure 6. Temperature dependence of real part (ε′) of complex permittivity of PNIPAM microgels A, B, and C measured at the indicated frequencies, where smaller figures on the right enlarge ε′ vs T at a few frequencies higher than 104 Hz to illustrate its temperature dependence.

mole of each ion present in a dilute solution. The λ0 values are tabulated in the CRC Handbook of Chemistry and Physics, and that of H+ and K+ is 349.6 and 73.5 S cm2/mol, respectively.36 Considering the anion is the macroion of PNIPAM microgel, whose mobility is tiny, and its λ0− is very small, so the second term in calculating the limiting molar conductivity can be omitted, and along the above description back, the diffusion coefficient of counterions, about 9.3 × 10−5 and 2.0 × 10−5 cm2/s for H+ and K+ respectively, can be obtained. From the relaxation time determined from the dielectric relaxation spectroscopy, the length scales of the ion movement can be determined from Einstein equation; that is, the MHz relaxation corresponds to 40−70 nm, while the kHz to ∼200− 500 nm for the samples ( f max ∼ (2−3) × 104 Hz). The former can be considered as the thickness of the double layer at the interface of PNIPAM microgels, while the latter is in consistent with the hydrodynamic diameter of the each microgel, which has been confirmed by the light scattering results in Table 1. Namely from Figure 5, the above two relaxation modes are more observable in swollen microgels, and their peak positions shift toward higher frequencies as temperature increases because the diffusion coefficient of the counterions becomes larger. For shrunken microgels, the slow mode becomes less distinctive because of the dissociation of counterions as temperature increases above LCST of PNIPAM; we will launch a detailed discussion on that point thereafter. Meanwhile, the

are resulted from the displacement or diffusion behaviors of counterions, and their relaxation time, according to the Einstein equation, the MHz relaxation is relevant with the Debye length, τMHz = LD2/2D, while the kHz relaxation is corresponding to the hydrodynamic radius of the colloidal particles, τkHz = Rh2/ 2D, in which τ is the relaxation time, LD is the Debye length, or as usually understood, the thickness of electric double layer of the particle in aqueous medium, Rh is the hydrodynamic radius of the particle, and D is the diffusion coefficient of the counterions. In our case of PNIPAM microgels, the counterions are mostly hydrogen H+ and the potassium ion, introduced by the comonomer of acrylic acid and the initiator of KPS in the polymerization. The diffusion coefficient should be experimentally determined by the molar conductivity,35 D = ΛRT/Z2F2, in which, Λ is the molar conductivity, R is the universal gas constant, T is temperature, Z is the covalent number of the ion, and F is the Faraday constant. When the concentration of the ion approaches to zero, the molar conductivity nearly equals to limiting molar conductivity, Λ0, according to Kohlrausch’s law. The limiting molar conductivity is calculated by Kohlrausch’s law of the independent migration of ions, Λ0 = υ+λ0+ + υ−λ0−, in which υ+ and υ− represent stoichiometric coefficients for the cation and anion in the electrolyte, respectively, and λ0+ and λ0− are limiting ionic molar conductivities, representing the contributions to the total solution conductivity made per 6163

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counterions around each microgel, which should occur at lower frequencies, involving the movement of counterions over a diameter distance of one microgel, as shown in Figure 7c. Note that the dipolar moment (M) is the product of the number of electric charges (q) and the distance between the centers of gravity of negative and positive charges (d). Let us examine the results in Figures 5 and 6. For a given temperature, ε′ always decreases as the frequency increases because counterions move a shorter distance under a quicker alternative electric field. For a given frequency, the temperature dependence of ε′ is very complicated, varying with both the frequency and microgel structure. We will focus on three frequencies of 2.95 × 102 Hz (low), 1.19 × 104 Hz (middle), and 1.33 × 106 Hz (high). At the low frequency, ε′ increases with temperature (i.e., as the microgel shrinks). Note that at such low frequency electrode polarization dominates ε′. As the temperature increases, ions mobility increases, and when T > LCST, counterion dissociate, so there are more and more mobile charges accumulate near the electrode. At the high frequency, ε′ gradually decreases as the temperature increases, which is perfectly understandable because random thermal motion disturbs the bulk polarization at the applied field. At the middle frequency, the microgel structure plays an important role. For microgels A, ε′ slowly increases before the temperature reaches the LCST because the shrinkage of the core makes the chains in the shell extended away from the periphery so that counterions are less trapped and move fast over a longer distance. The decrease of ε′ at higher temperatures is surely attributed to the collapse of the loose shell. As expected, microgels B and C shrink as the temperature increases so that counterions dissociate, leading to a low q referred in Figure 7, and the remaining counterions are more entrapped inside with a more confined movement over a shorter distance, so that M decreases for each dipole. Since the measured polarizability or permittivity is proportional to the strength and the number of all kinds of induced dipoles, with the temperature increasing above the LCST of PNIPM, the slow mode becomes less distinctive in Figure 5 and ε′ decreases in Figure 6. However, the decrease of ε′ for microgels B is sharper around the LCST, which is presumably attributed to a shaper collapse of the shell wherein counterions are located. A more quantitative evaluation is as follows. Assuming the applied field pulls counterions with a collective positive charge +q to a new position, a distance of d away from their original position, until the electric potential of such an induced dipole balances the local electric field (E) exerted on each microgel with a radius of r, we have, according to Gauss’ law: qE = (q/4πεd2)(d3/r3)q or d = (4πεr3E)/q. It is also known that the induced dipole has a moment of M = qd = 4πεr3E. The polarizability is defined as the induced dipolar moment per unit field strength, so that the polarizability of a microgel is a = 4πεr3. On the other hand, for N microgels, the bulk polarizability (P = NaE) is proportional to the bulk permittivity. Therefore, the measured bulk permittivity due to the displacement of counterions quickly decreases as the microgel shrinks. Figure 8 schematically summarizes how microgels A, B, and C shrink during the heating. Note that in the frequency range studied the measured permittivity or conductivity reflects the movement of ions, especially counterions, around PNIPAM microgels. The difference is that the permittivity is related to the moving distance, while the conductivity is linked to the diffusion (hopping) of charges.38 The measured conductivity is directly

fast mode becomes more visible and more narrowly distributed because the microgel/water interface becomes more clear. Figure 6 displays the dielectric permittivity of PNIPAM microgels versus temperature variation. At low frequencies ( 32 °C, which is due to the electrode polarization, as discussed above. When the frequency is higher than 3 kHz, as shown in the insets, ε′ decreases as the temperature increases in the range 30 °C < T < 40 °C for microgels A. However, real permittivity ε′ abruptly decreases around 32 °C for microgels B and C, indicating some microstructure related changes of charge distribution. As discussed before, relative dielectric permittivity is a macroscopically collective sum of all the microscopic polarizations of a material under an applied filed, namely an average over all the microscopic polarization modes; the measured polarizability or permittivity increases with the strength and the number of all kinds of induced dipoles in a system. In order to find different contributions, we must know different microscopic polarization modes in a complex dispersion and find which one is dominant in our frequency range. Here we can neglect electronic and atomic polarizations and orientation polarization of small molecules (e.g., water) because they occur at frequencies higher than GHz. Therefore, it should be the polarization of individual microgels themselves that dominates the permittivity in the measured frequency range, especially when no additional salt is added. Some of the free small ions introduced in the microgel preparation also lead to the second kind of polarization. Previous studies of NIPAM copolymerized with charged comonomer have shown that its first-order-like coil-to-globule transition is related to the cooperative dissociation of counterions association.25,37 A microgel can be considered as a large multicharged macroion surrounded by an equal amount of small counterions at each moment. Their collective (averaged) charge centers overlap with each other, as schematically shown in Figure 7a.

Figure 7. Schematics of (a) a spherical microgel (a large macroion) and its small counterions and an induced dipole due to (b) counterion shift and (c) counterion redistribution around a microgel at an external electric field (E).

When an electric field is applied to the microgel dispersion, small counterions shift toward the oppositely charged electrode and each microgel slightly moves to an opposite direction, as shown in Figure 7b, which should occur in the range 103−106 Hz. The distance between two charge centers is only over a scale of the Debye length. The second important contribution to the polarization should be related to the redistribution of 6164

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counterions, especially how the surrounding polymer network and chains on the periphery affect their diffusion under an applied field, we measured the frequency and temperature dependence of the ac conductivity, i.e., the real part of the complex conductivity (σ′), as shown in Figure 9. Figure 9 shows that for PNIPAM microgels σ′ quickly decreases with frequency in the low frequency range f *, σ′ increases with frequency, implying that the mean-square displacement ⟨r2(t)⟩ of counterions increases with time, but not linearly, in the range t < 1/(2πf *); in other words, within a short time or moving distance, the counterion movement is subdiffusive. It is reasonable to assume that within a short time the hopping movements of one ion should be less affected by other ions, only reflecting its local confinement (environment). When f < f *, σ′ is nearly independent of f, usually identified as the dc conductivity (σdc), indicating that when time is longer than 1/(2πf *), the motions of counterions are driven by thermal fluctuation and become diffusive, i.e., ⟨r2(t)⟩ increases linearly with time. Namely

Figure 8. Schematic of temperature-induced conformation change for PNIPAM microgels A, B, and C as temperature increases higher than 32 °C.

related to the product of number and mobility of charge carriers and electric charges per carrier. It is expected that small and free ions can follow the applied alternative field at frequencies higher than 106 Hz so that they contribute a constant background at lower frequencies. Since counterions are condensed inside the microgel network, their movements must be slower, characteristically responding at lower frequencies, which are affected by their individual local environments. In order to figure out the movement of

⎧ f < f* ⎪t ⟨r 2(t )⟩ ∝ ⎨ ⎪ β ⎩t f > f *

(5)

Further, let us examine the temperature effect on σ′. Figure 9 shows a common feature: σ′ increases with temperature for

Figure 9. Frequency and temperature dependence of ac conductivity of PNIPAM microgels A, B, and C. 6165

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both swollen (T ≪ LCST) and shrunk (T ≫ LCST) microgels because the ion mobility increases with temperature. At each T, the ac conductivity is contributed by the movement of both the free counterions and condensed counterions. At frequencies lower than ∼106 Hz, the contribution from the free ions dominates, and the ac conductivity will increase monotonically with the increasing temperatures. While at high frequencies, the local motion of the associated counterions account more proportion, so that there shows a decrease in the conductivity when T > LCST, due to the dissociation of the counterions. Those associated counterions, which contribute more to the high frequency ac conductivity, are featured in subdiffusive motion, reflecting their local confinement (environment) of the chain, so they reflect the structural change for chains or gel network. Interestingly, the variation of σ′ with temperature at T ∼ LCST depends on the microgel structure. For microgels A at higher frequencies, σ′ decreases as the temperature increases in the range T > LCST, indicating that the collapse of the loose shell entrapped more counterions inside so that there are less number of mobile counterions. For microgels B, the decrease of σ′ is smaller, while for microgels C, it seems that the decrease of σ′ is offset by the temperature-induced increase of σ′ so that the increasing rate of σ′ becomes lower before the microgels are fully collapsed at ∼34 °C.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support of the National Natural Science Foundation of China (Grant 21074056) and the Priority Academic Program Development of Jiangsu Higher Education Institutions is gratefully acknowledged. We also express our gratitude to Professor Chi Wu in the Chinese University of Hong Kong for some of his valuable suggestions.

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CONCLUSIONS By introducing ionic comonomer and cross-linking agent at different polymerization stages, we are able to prepare thermally sensitive spherical poly(N-isopropylacrylamide) (PNIPAM) microgels with different charge distributions and structures, including (A) a densely cross-linked core and a loose and charged shell, (B) a lightly cross-linked core and a dense and charged shell, and (C) uniform cross-linking and charge distribution. The frequency and temperature dependent dielectric/electric spectrum reveal two relaxation modes, located at ∼103 and ∼106 Hz, respectively. The slow mode can be assigned to the α-dispersion, i.e., the external electric field induced concentration polarization, involving the diffusion of counterions over a length scale of ∼102−103 nm, similar to the microgel size, so that it can be used to monitor the thermally induced shrinking and swelling of microgels. The fast mode is the δ-dispersion (Maxwell−Wagner−O’Konski polarization), which is related to distortion of the cloud of counterions around each microgel (the Debye double layer at the microgel/water interface), involving in the diffusion of counterions over a length scale of ∼101−102 nm, close to the Debye length, so that it can be used to differentiate different structures of microgels. We have established some correlations between macroscopically measured dielectric/electric properties (permittivity and conductivity) and microscopic structures, which makes dielectric relaxation spectrometry a useful new tool in the study of colloidal particles in dispersion.

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ASSOCIATED CONTENT

S Supporting Information *

Figures 1s and 2s; Table 1s. This material is available free of charge via the Internet at http://pubs.acs.org.

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*Tel +86 25 85891767; e-mail [email protected] (D.Z.), [email protected] (J.S.). 6166

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