Published: February 22, 2011

r 2011 American Chemical Society 2196 dx.doi.org/10.1021/jp111135f | J. Phys. Chem. B 2011, 115, 2196–2204

ARTICLE

pubs.acs.org/JPCB

Dielectric Properties of Micellar Aggregates Due to the Self-Assemblyof Thermoresponsive Diblock CopolymersGiancarlo Masci,† Serena De Santis,† and Cesare Cametti*,‡,§

†Dipartimento di Chimica and ‡Dipartimento di Fisica, Universita' di Roma “La Sapienza”, Rome, Italy§INFM-CNR, CRS-SOFT, Rome, Italy

ABSTRACT: The radiowave dielectric properties of aqueoussolutions of thermosensitive copolymers, consisting of poly(2-acrylamido-2-methylpropanesulfonate) [PAMPS] and poly-(N-isopropylacrylamide) [PNIPAAM] with different blocklengths, have been investigated over a broad temperature andfrequency range. These copolymers PAMPSn-b-PNIPAAMm

form temperature responsive aggregates (micelles) that represent a class of self-assembled structures in water of great interestbecause of their potential use as drug delivery formulations and in diverse biotechnological applications. Copolymers formed byhydrophilic segments covalently attached to a hydrophobic segments are capable of forming a micellar structure as soon as thetemperature is raised above their lower critical solution temperature. We have investigated the dielectric properties of PAMPSn-b-PNIPAAMm diblock copolymers with different lengths of the hydrophilic and hydrophobic segments during the whole aggregationprocess driven by the progressive increase of temperature. The process has been followed by the changes resulting in the dielectricparameters (the dielectric incrementΔε and the relaxation frequency ν0) of the whole aqueous solution. The dielectric response ofthe micelles has been described within the framework of the standard electrokinetic model for charged colloidal particles, and themain characteristic parameters have been evaluated. Subsequent cross-linking of these diblock copolymers by a cationic PEOx-b-PAMPTMAy polyelectrolyte yields hybrid core-shell-corona systems, with the PNIPAAM hydrophobic blocks collapsed in thecore, an interpolyelectrolyte chain complex forming the shell, and the hydrophilic PEO chains as an external corona. In this case too,the dielectric spectra can be appropriately accounted for within the same theoretical framework.

1. INTRODUCTION

Polymer nanoparticles have attracted much attention as poten-tial materials for biomedical applications and devices, particularlyas drug carriers, due to their ability to incorporate both hydrophilicand hydrophobic substances.1-5

In the past few years, much attention has been focused onstable polymeric nanoparticles prepared from a variety ofdiblock copolymers, taking advantage of the fact that, becauseof the worsening of the solvent quality, thermosensitive poly-mers can lead to the formation of assemblies induced by thetemperature.6

Diblock copolymers self-assemble in water because of theopposite interactions of the respective hydrophilic and hydro-phobic parts. These aspects have been extensively investi-gated, revealing the existence of vast and intriguing differentassemblies.7-9

Due to the large number of applications in different fields, rangingfrom nanotechnology to electronics, poly(N-isopropylacril-amide) [PNIPAAM] is a widely investigated thermoresponsivepolymer.10-12 PNIPAAM behaves as a hydrophilic polymer (inwater) below the lower critical solution temperature (LCST),but, due to the increased hydrophobicity with the increase oftemperature, above the LCST the system exhibits a phase transi-tion, and a coil-to-globule transition has been observed. PNI-PAAM exhibits a LCST value of 32 �C.13

We have recently considered dilute solutions of low-molecu-lar-weight asymmetric diblock copolymers, namely, poly(2-acry-lamide-2-methylpropanesulfonate)-block-poly(N-isopropylacryl-amide) [PAMPSn-b-PNIPAAMm], with different lengths of thehydrophilic and hydrophobic blocks, and we have characterizedtheir thermoresponsive properties by means of dynamic lightscattering, nuclear magnetic resonance, and fluorescence spec-troscopy.14

The diblock copolymers in aqueous solution with appro-priate PAMPS/PNIPAAM ratio form spherical core-shelltype micelles, over the whole temperature region above thelower critical solution temperature, where the PNIPAAM block isthe thermosensitive part forming the core of the aggregatewhile the hydrophilic PAMPS part is toward the outside(Figure 1).

The second aspect we are dealing with is the preparation ofshell cross-linked micelles based on the interaction between thePAMPS-b-PNIPAAM micelles with an oppositely charged poly-[(3-acrylamidopropyl)trimethylammonium chloride]-block-poly-(ethylene oxide), PEOx-b-PAMPTMAy, block copolymer. PEOwas chosen as a hydrophilic polymer to stabilize the nanoparticleagainst aggregation, while PAMPTMA polymer strongly interacts

Received: November 22, 2010Revised: January 7, 2011

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with PAMPS polymers to cross-link the shell of the micelle(Figure 1).

We have measured the dielectric and conductometric prop-erties of these diblock copolymers and their shell cross-linkedmicelles in aqueous solution in the temperature range from 20to 50 �C, crossing the lower critical solution temperature(LCST). Copolymers with different lengths of both the hydro-phobic (m = 40, 94) and the hydrophilic (n = 36, 98) part wereinvestigated. Dielectric relaxation measurements have beencarried out in the frequency range from 1 MHz to 2 GHz,where interfacial polarizations, due to the heterogeneity of thesystem, occur.

The paper is organized as follows. In the next section, wepresent the dielectric spectra and preliminarily we discuss indetail their deconvolution, in order to extract the dielectricparameters relevant to the electrical polarizations at the mi-celle-solution interface. Since the spectra are rather complex,reflecting the presence of different relaxation processes, whichpartially overlap with the ones of interest here, this analysisrequires caution. By considering simultaneously the permit-tivity ε0(ω) and the dielectric loss ε00(ω), we are able to obtainthe dielectric parameters of the micelle interfacial polarizationprocess, even if the dc conductivity of the samples investigatedis rather high. In section 3, we present the dielectric modelemployed in light of the standard electrokinetic model, and wediscuss the results obtained. Section 4 contains the concludingremarks.

2. EXPERIMENTAL SECTION

2.1.Materials. PAMPS-b-PNIPAAM and PEO-b-PAMPT-MA block copolymers have been synthesized as describedelsewhere.14,15

2.2. Dynamic Light Scattering Measurements. Dynamiclight scattering data were obtained with a Brookhaven Instru-ments Corp. BI-200SM goniometer equipped with a BI-9000ATdigital correlator using a solid state laser (125 mW, λ = 532 nm).Measurements of the scattered light were made at a scatteringangle of 90�. Before each measurement, the solution was allowedto equilibrate until a stable reading of the intensity was obtained.In order to obtain the micellar size, the measured intensity-intensity autocorrelation functions were analyzed by the cumu-lant method.2.3. Dielectric Measurements. The dielectric and conducto-

metric spectra of PAMPS-b-PNIPAAM polymers in aqueoussolutions (5 mg/mL) at different temperatures from 10 to50 �C have beenmeasured in the frequency range from 1MHz to 2GHzbymeans of a radio frequency impedance analyzer, Hewlett-Packard model 4291A. Details of the dielectric cell and thecalibration procedure have been reported elsewhere.16,17

3. ANALYSIS OF THE DIELECTRIC SPECTRA

A typical dielectric spectrum over the whole frequency rangeinvestigated is shown in Figure 2. As can be seen, the electrodepolarization effect dominates the low-frequency region of thespectrum (panel A), where the apparent permittivity ε0(ω) scaleswith the frequency asω-R (withR = 1.73, in this case). At higherfrequencies, a dielectric dispersion due to the electrical polariza-tion of the counterion atmosphere close to the polymer is wellevidenced, followed by a further relaxation process, at evenhigher frequencies, due to the orientational polarization of thewater molecules. This latter contribution is well evidenced bothin the dielectric loss (Figure 2, panel B) and in the electricalconductivity (Figure 2, panel C).

The dielectric spectra have been described on the basis of aCole-Cole relaxation function18,19 modified by adding a furtherDebye relaxation to take into account the contribution of thedielectric response at higher frequencies (orientational polariza-tion of the aqueous phase) and by adding the contribution of aconstant-phase-angle (CPA) element, to take into account theeffect of the electrode polarization at lower frequencies.20,21 Thecomplete relaxation function reads

ε�ðωÞ ¼ ε0ðωÞ- iε00totðωÞ

¼ AðiωÞ-R þ ε¥ þ Δε

1þ ðiωτÞβþ ΔεW1þ iωτW

þ σ0

iωε0

ð1Þwhere the first term takes into account the scaling law thatdescribes the electrode polarization effect and Δε, ν0 = 1/2πτ,and β are the dielectric increment, the relaxation frequency, andthe spread parameter, respectively, of the intermediate relaxationprocess associated with the micelle interfacial polarization. ΔεWand τW are the dielectric increment and the relaxation time of theaqueous phase, and σ0 is the dc electrical conductivity. In thiscase, the dc electrical conductivity has been measured at afrequency of 1 kHz, well below the frequencies where therelaxation with which we are dealing occurs. For the dielectricparametersΔεW and τW of the aqueous phase relaxation, we haveassumed values corresponding to pure water at the differenttemperatures investigated.22,23

As an example, in Figure 2, panels B, C, and D report thedielectric loss ε00(ω) calculated from the total loss σ(ω)/(ε0ω)by subtracting the dc conductivity contribution σ0/(ε0ω), thetotal electrical conductivity σ(ω), and the Cole-Cole plot,respectively. The deconvolution of the spectra consideringsimultaneously the real ε0(ω) and the imaginary ε00(ω) partshas been carried out on the basis of the Levenberg-Marquardtalgorithm for complex functions,24 and the parameters Δε, ν0,and β have been obtained. The accuracy of the whole fittingprocedure is within 1% for ε0(ω) and within 1-2% for ε00(ω).

Figure 1. Sketch of the formation of shell cross-linked micelles.

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3.1. The Dielectric Behavior of PAMPS-b-PNIPAAM Poly-mer Aqueous Solutions. We have investigated PAMPSn-b-PNIPAAMm polymers with three different values of the couplem and n (n = 36, m = 40; n = 36, m = 94; n = 98, m = 94). Thedielectric spectra have been analyzed on the basis of eq 1, and the

dielectric parameters, the dielectric increment Δε, the relaxationfrequency ν0, and the spread parameter β, have been determined.These dielectric parameters are shown in Figures 3, 4, and 5 as afunction of temperature, in the interval from 20 to 50 �C. As canbe seen, for all the three parameters investigated, close to the

Figure 2. Typical dielectric spectra of PAMPS98-b-PNIPAAM94 aqueous solution (concentration C = 5.0 mg/mL, temperature T = 20 �C) in thefrequency range from 1 MHz to 1 GHz. Panel A: dielectric dispersion characterized by the dielectric increment Δε and relaxation frequency ν0. In thelow-frequency tail of the frequency window investigated, the electrode polarization effect dominates. Panel B: dielectric loss ε00 = (σ(ω)- σ0)/(ε0ω). Inthe high-frequency tail of the frequency window investigated, the beginning of the dielectric loss due to the orientational relaxation of the aqueous phaseappears. Panel C: electrical conductivity σ(ω) as a function of frequency. Panel D: semicircle of the Cole-Cole plot. Deviations on both sides are due tothe contribution of the electrode polarization effect (at low frequencies) and to the losses of the aqueous phase (at higher frequencies).

Figure 3. Dielectric increment Δε of the three different PAMPSn-b-PNIPAAMm diblock copolymers investigated in aqueous solution at theconcentration C = 5.0 mg/mL. Solid symbols: the temperature is increased from 20 to 50 �C. Open symbols: the temperature is decreased from 50 to20 �C.

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LCST, the slope of the temperature dependence changes,indicating that a structural rearrangement takes place. This isparticularly evident in the relaxation frequency ν0 that, as we willdiscuss in the following, can be associated with the typical size ofthe objects in solution.3.2. Dielectric Behavior of Shell Cross-Linking Micellar

Systems. Once a micellar structure was attained at temperaturehigher than the LCST, the addition of a cationic block copoly-mer, PEOx-b-PAMPTMAy in this case, induces the formation ofshell cross-linked micelles. A core-shell-corona system wasformed with the collapsed PNIPAAM chains as the core, theinterpolyelectrolyte complex between PAMPS and PAMPTMAchains as the shell, and the PEO chains as the corona (see sketchof Figure 1). Dynamic light scattering measurements at thetemperature of 50 �C showed that the hydrodynamic radius RHof the PAMPS36-b-PNIPAAM40 micelles increased from about30 nm before shell cross-linking to about 48 nm after shell cross-linking with PEO114-b-PAMPTMA50. This was expected because

the decrease of the size of the interpolyelectrolyte shell withrespect to the PAMPS shell in the PAMPS-b-PNIPAAM micelleshould be smaller than the increase of the size due to the PEOcorona in the shell cross-linked micelle. If shell cross-linking hadnot occurred, dissociation into unimers would be expected uponlowering the solution to 25 �C. However, dynamic light scatter-ing experiments showed that shell cross-linked micelle sizeincreased at room temperature (Figure 6), thus indicating theformation of interpolyelectrolyte cross-linked micelles. This isdue to the rehydration of the PNIPAAM blocks (see sketch ofFigure 1). The process is completely reversible, as the size of theshell cross-linked micelles return to the same value when thetemperature is raised again to 50 �C (Figure 6)From a dielectric point of view, what happens is clearly shown

in Figure 7, where we report the behavior of the permittivityε0(ω) (upper panel) and the dielectric loss ε00(ω) (bottompanel) of PAMPS98-b-PNIPAAM94þ PEO114-b-PAMPTMA100

aqueous solution as a function of frequency, at the temperature of40 �C. As can be seen, due to the addition of polyelectrolyte, thedielectric dispersion reduces its strength and the relaxationfrequency ν0 shifts toward lower values, as a consequence ofthe formation of a complex of larger size and bearing a muchsmaller surface charge.For these aqueous solutions, the shift of the relaxation

region toward lower frequencies, that is, where the electrodepolarization effect dominates, makes the analysis of the di-electric spectra based on the permittivity ε0(ω) harder tomanage. However, these difficulties can be overcame if theanalysis of the dielectric spectra is carried out considering thedielectric loss ε00(ω), derived from the total conductivityσ(ω), subtracting the contribution due to the dc conductivityσ0, according to

ε00ðωÞ ¼ σðωÞ- σ0

ε0ωþ ΔεWðωτWÞ1þ ðωτWÞ2

ð2Þ

A typical example for the PAMPS98-b-PNIPAAM94 þPEO114-b-PAMPTMA100 system is shown in Figure 8.As can be seen, the behavior of the permittivity ε0(ω) does not

allow the evaluation of the dielectric parameters (Δε and ν0) ofthe relaxation because of the presence of the electrode polariza-tion effect. Conversely, the behavior of ε00(ω), once the pureconductivity loss contribution has been subtracted, is such toallow the estimates of both the dielectric increment Δε and therelaxation frequency ν0.

Figure 4. Relaxation frequency ν0 of the three different PAMPSn-b-PNIPAAMm diblock copolymers investigated in aqueous solution at theconcentration C = 5.0 mg/mL. Solid symbols: the temperature isincreased from 20 to 50 �C.Open symbols: the temperature is decreasedfrom 50 to 20 �C.

Figure 5. Spread parameter β of the three different PAMPSn-b-PNI-PAAMm diblock copolymers investigated in aqueous solution at theconcentration C = 5.0 mg/mL. (Circle) PAMPS36-b-PNIPAAM40;(triangle) PAMPS36-b-PNIPAAM94; (square) PAMPS98-b-PNIPAAM94.Solid symbols: the temperature is increased from 20 to 50 �C. Opensymbols: the temperature is decreased from 50 to 20 �C.

Figure 6. Temperature dependence of the hydrodynamic radius DH ofthe PAMPS36-b-PNIPAAM40 þ PEO114-b-PAMPTMA50 shell cross-linked micelles measured by means of dynamic light scattering in 0.001M NaCl aqueous solution.

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In the case shown in Figure 8, the deconvolution of thedielectric loss peak allows us to separate the contributions ofthe aqueous phase and to obtain the dielectric parametersΔε andν0 of the dielectric process of interest here.The effect of addition of a polyelectrolyte to the diblock

copolymer aqueous solution on the dielectric parameters, the

dielectric incrementΔε and the relaxation frequency ν0, is shownin Figure 9, where we report, as a function of temperature, thewhole behavior of the dielectric increment Δε and of therelaxation frequency ν0 for PAMPS98-b-PNIPAAM94 polymeras a function of the temperature, before and after the addition ofthe polyelectrolyte PEO114-b-PAMPTMA100 and the conse-quent formation of shell cross-linked micelles. The addition ofthe PEO-b-PAMPTMA block copolymer provokes a deep re-structuring of the micelle leading to the formation of an inter-polyelectrolyte shell with the release of a significant amount ofcounterions (Naþ and Cl-) from the polyelectrolyte chains andthe formation of a neutral PEO corona surrounding the coacer-vate shell which stabilizes the shell cross-linked micelles. Thisrestructuring is characterized by a dielectric increment Δε of theorder of 10 dielectric units, much smaller than the one of themicelles and, moreover, practically independent of temperature.The same happens for the relaxation frequency ν0 that assumes avalue of the order of about 5 MHz, independent, to a firstapproximation, of the temperature.3.3. Effect of Dialysis. The addition of the cationic block

copolymer to the PAMPS-b-PNIPAAM micelles, and the con-sequent formation of shell cross-linked micelles, provokes therelease in the bulk solutions of a large fraction of counterions. Asa consequence, the electrical conductivity σ(ω) of the solutionincreases. For example, in the case of PAMPS98-b-PNIPAAM94

aqueous solution, starting from the value of 0.14194 mho/m at50 �C, the polyelectrolyte addition leads to a conductivity of0.29025 mho/m, corresponding to a doubling of about the initialvalue. The same happens at lower temperature (T = 20 �C)

Figure 9. Upper panel: dielectric increment Δε of PAMPS98-b-PNI-PAAM94 polymer aqueous solution as a function of temperature. At thetemperature of 50 �C, the addition of PEO114-b-PAMPTMA100

(denoted by E114-A100) induces the formation of shell cross-linkedmicelles. Bottom panel: relaxation frequency ν0 of PAMPS98-b-PNI-PAAM94 polymer aqueous solution as a function of temperature and theeffect of addition at the temperature of 50 �C of PEO114-b-PAMPT-MA100 polyelectrolyte. The arrows mark the LCST values.

Figure 7. Upper panel: permittivity ε0(ω) of PAMPS98-b-PNIPAAM94

aqueous solution (full symbols) and of PAMPS98-b-PNIPAAM94 withthe addition of PEO114-b-PAMPTMA50 (open symbols). The full linesdescribe the calculated values of the permittivity according to eq 1.Bottom panel: dielectric loss ε0 0(ω) of PAMPS98-b-PNIPAAM94 aqu-eous solution (full symbols) and of PAMPS98-b-PNIPAAM94 with theaddition of PEO114-b-PAMPTMA50 (open symbols). The full linesdescribe the calculated values of the permittivity according to eq 1.

Figure 8. Dielectric loss ε0 0(ω) deduced from the total electricalconductivity σ(ω) for the PAMPS98-b-PNIPAAM94 þ PEO114-b-PAMPTMA100 system at the temperature of 40 �C. The full lines arethe calculated values according to eq 1. The inset shows the values of thepermittivity ε0(ω) together with the calculated values on the basis of theparameters deduced from the analysis of the dielectric loss ε00(ω).

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where the conductivity increases from 0.07466 to 0.17311 mho/m.The change of the electrical conductivity is shown in Figure 10.As we have noted above, the increase of the bulk conductivityinduces a shift of the observed dielectric relaxation toward lowerfrequencies, the dielectric effect being much more masked by theelectrode polarization effect. Consequently, we preliminarilyshould ascertain if the reduction of the dielectric increment asa consequence of the polyelectrolyte addition is due to an artifactinduced by the electrode polarization effect or, rather, thisreduction is a consequence of a restructuring of the wholepolymer system.In other words, we must ascertain if, once the bulk electrical

conductivity of the samples under investigation is once morereduced again, the decrease of the dielectric response persists,evidencing therefore its independence from the strength of theionic environment. This can be done by an extensive dialysisagainst deionized water of the polymer aggregates formed afterthe polyelectrolyte addition. Figure 11 shows the permittivityε0(ω) and the dielectric loss ε00(ω) of PAMPS36-b-PNIPAAM40

þ PEO114-b-PAMPTMA50 before and after dialysis.As can be seen, the permittivity spectrum is shifted by an order

of magnitude toward lower frequencies (as expected as a con-sequence of the reduced electrode polarization effect driven bythe reduction of the bulk electrical conductivity). Nevertheless,the observed dielectric increment remains rather small. This factis rather well confirmed by the dielectric loss dependencies inboth the cases, which substantiate the presence of a dielectricdispersion falling at the same frequency (Figure 11, bottompanel).The analysis of the dielectric spectra based on the frequency

dependence of the dielectric loss ε00(ω) furnishes the values ofthe dielectric parameters Δε, ν0, and β and the value of the dcconductivity σ0 (Figure 12). Also in this case, we observe aconstancy of the dielectric increment Δε and the relaxationfrequency ν0 as a function of the temperature.

4. THE DIELECTRIC MODEL

Let us go back to the formation of PAMPS-b-PNIPAAMmicelles as the temperature increases over the LCST (=35 �C).From a dielectric point of view, the micelle can be seen as built upby a spherical core formed by PNIPAAM polymers surrounded

by a concentric shell of PAMPS polymers. In the frequencywindow investigated (1 MHz to 2 GHz), the dielectric behaviorof the micelles in aqueous solution can be described, once theelectrode polarization effects have been removed from the dielectricspectrum, within the framework of the standard electrokinetic

Figure 10. Low-frequency limit of the electrical conductivity σ ofPAMPS98-b-PNIPAAM94 polymer aqueous solution as a function oftemperature before (full symbols) and after the addition of PEO114-b-PAMPTMA100 (denoted by E114-A100) polyelectrolyte solution. Therelease of counterions, as a consequence of the formation of shell cross-linked aggregates, leads to an increase of the bulk conductivity of about adoubling of the preaddition value. Figure 11. Effect of dialysis against deionized water of PAMPS36-b-

PNIPAAM40 þ PEO100-b-PAMPTMA50 (denoted by E100-A50) ag-gregates. Top panel: comparison of the permittivity ε0(ω) of aggregatesbefore dialysis (open symbols) and after dialysis (full symbols). Theinset shows the dc electrical conductivity as a function of the tempera-ture in the two cases. The dialysis induces a decrease of the bulkconductivity of more than 1 order of magnitude. Bottom panels: (left)dielectric loss ε00(ω) of the aggregates in aqueous solution beforedialysis; (right) dielectric loss ε0 0(ω) of the aggregates in aqueoussolution after dialysis.

Figure 12. Dielectric parameters of PAMPS36-b-PNIPAAM40 þPEO114-b-PAMPTMA40 (denoted by E114-A50) aggregates: (A) di-electric increment Δε; (B) relaxation frequency ν0; (C) spread para-meter β; (D) dc electrical conductivity.

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model, extended to take into account the interfacial polarizationof the Maxwell-Wagner effect (should it be necessary to takeinto consideration this contribution too).

The general expression for the complex dielectric constantε*(ω) has been derived by Grosse25 and Grosse et al.,26 and, inthe frequency range here considered, it can be written as the sumof two contiguous relaxation processes named R- and δ-disper-sion, as follows

ε�ðωÞ ¼ ε¥ þΔεRf ðω, τRÞ þ Δεδ1þ iωτδ

þ σ0

iωε0ð3Þ

where ΔεR and Δεδ are the dielectric increments of the relaxa-tions falling at the relaxation times τR and τδ, respectively, ε¥ isthe high-frequency limit of the permittivity, and f(ω,τR) is therelaxation function associated with the R-dispersion. Thesequantities are given by

ΔεR ¼ 94ΦεmðKDRÞ2 ðSþ - S-Þ2

ðSþ þ 2Þ2ðS- þ 2Þ2 ð4Þ

τR ¼ R2

2Dð5Þ

Δεδ ¼ 9Φ½εpσm - εmðσp þ 2λ0=RÞ�2

½εp þ 2εm�½σp þ 2λ0=Rþ 2σm�2ð6Þ

τδ ¼ ε0εp þ 2εm

σp þ 2λ0=Rþ 2σmð7Þ

where KD is the inverse of the Debye screening length and thequantity S( is defined by

S( ¼ 4KDR

exp -zeζ2KBT

� �� �ð8Þ

where D is the diffusion coefficient, ζ is the ζ-potential, and λ0 isthe surface conductivity. The average size of the micelle isdenoted by R, KBT is the thermal energy, and ε0 is the dielectricconstant of free space. In the above model, the micelle isdescribed, to a first approximation, by a homogeneous dielectricparticle characterized by a permittivity εp and an electricalconductivity σp. The external medium (the aqueous phase) ischaracterized by a permittivity εm and an electrical conductivityσm. Φ is the volume fraction of the micelles in the solution.

The frequency νR = 1/(2πτR) of the R-relaxation is indepen-dent of the electrokinetic parameters (eq 5), depending only onthe micellar size R and on the diffusion coefficientD. Assuming adiffusion coefficient D = 2 � 10-9 m2/s and considering atemperature increment coefficient equal to dD/dT = 0.0495 �10-9 m2/(s �C), eq 5 allows us to evaluate the average size of themicelle and its changes with the temperature (should they bepresent) in the whole range of temperature investigated aboveLSCT. We have obtained values of 25, 27, and 30 nm at thetemperature of 35 �C, for PAMPS36-b-PNIPAAM40, PAMPS36-b-PNIPAAM94, and PAMPS98-b-PNIPAAM94, respectively, witha very weak dependence on the temperature. These values agreereasonably well with those determined by dynamic light scatter-ing measurements14 of micelles of PAMPS36-b-PNIPAAM40 andPAMPS36-b-PNIPAAM94 (RH = 30 and 33 nm, respectively).The values determined by dynamic light scattering measurementfor PAMPS98-b-PNIPAAM94 (RH = 47 nm) is higher than the

value determined by our measurements. In this case, it has to beunderlined that, by decreasing the ionic strength, this polymershowed an unusual behavior in dynamic light scattering measure-ments that could be due to aggregation of the micelles or tochange to a vesicular morphology.14

The dielectric increment ΔεR depends on the ζ-potential andon environmental parameters such as the electrical conductivityσm and the permittivity εm of the aqueous phase, besides thefactional volume Φ. As far as this latter parameter is concerned,its value can be evaluated from the polymer molar concentrationCn according to the relationship

Φ ¼ 4π3R3CnN

Nagð9Þ

where Cn is the polymer molar concentration, N the Avogadronumber, and Nag the aggregation number. The values of Φ forthe three different samples investigated are listed in Table 1.

The fitting of eq 4 to the values experimentally observed forthe dielectric incrementΔε (see Figure 3) furnishes the values ofthe ζ-potential. We obtain values between 30 and 60 mV, for thethree different systems investigated, largely independent oftemperature. The observed decrease of ΔεR with the increaseof temperature reflects the decrease of the permittivity εm of theaqueous phase with the increase of the temperature. Both the ζ-potential, which describes the electrical micellar surface, and theradius R, which defines the geometry of the micellar aggregates,do not depend, at least to a first approximation, on the tempera-ture, indicating the formation of rather stable structures.

Equations 6 and 7 predicts that a further relaxation processshould occur at frequencies higher than the ones characteristicsof the R-dispersion. However, for values of the surface conduc-tivity λ0 of the order of λ0 = 10-10 mho, as expected for thesystems under investigation, while the relaxation frequency issome tenth of a megahertz, the dielectric increment is of theorder of one dielectric unit or lower, preventing the possibility ofbeing experimentally observed. This point is illustrated inFigure 13, where we report the two dielectric parameters, thedielectric incrementΔεδ and the relaxation time νδ, as a functionof the surface conductivity λ0. In any case, as can be seen inFigure 13, the strength of this dielectric dispersion is too small toaffect the parameters of the main dispersion.

A final comment is in order. The charge Q at the micellarsurface can be derived from the relationship27

j ¼ KBTze

ln1

6Φ lnð1=ΦÞzeKBT

� �2 Q4πεRH

� �2" #ð10Þ

where ze is the elementary charge and j is the surfacepotential. If we assume the surface potential j equal to the

Table 1. Concentration C, Molecular Weight MW, MolarConcentration Cn, and Fractional Volume Φ, for the ThreeDifferent Polymers Investigateda

sample C (mg/mL) MW (kD) Cn (mol/m3) Φ (%)

A36-N40 5.0 12.7 0.391 3.31

A36-N94 5.0 19.2 0.260 2.93

A98-N94 5.0 33.2 0.151 4.92aThe fractional volumeΦ calculated from eq 9 refers to micelles formedafter the thermal transition. The aggregation number was assumed to beAag = 100. An-Nm stands for PAMPSn-b-PNIPAAMn.

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ζ-potential previously derived from eq 4, eq 10 gives values ofthe surface charge density of the order of 2.5 mC/m2 formicelles of size RH = 20 nm.

Let us consider now the shell cross-linkedmicelles obtained byadding the polyelectrolyte PEO-b-PAMPTMA. Since, in thesestructures, the hydrophilic PEO segments were toward theoutside of the aggregate, the surface charge density is greatlyreduced and the micelles approach the behavior of unchargedobjects dispersed in an electrolyte solution. In these conditions,the restructuring of the aggregates, with the presence of a neutralPEO corona surrounding the coacervate shell, yields a dielectricincrement of aboutΔε = 3.5 and a relaxation frequency ν0 of theorder of 6 MHz (see Figure 12).

The absence or the very low value of a surface charge densitymakes the electrokinetic model no more applicable, and, inparticular, a direct relationship between the size R and therelaxation time τ (eq 5) is no longer valid. This fact justifies that,while the radius of the shell cross-linked micelles increases from44 to 80 nm as the temperature is decreased from 50 to 35 �C, therelaxation frequency remains practically constant at the value ofabout 6 MHz (for sample PAMPS36-b-PNIPAAM40 þ PEO114-b-PAMPTMA40, Figure 6 and Figure 12, panel B).

In these cases, when the R-dispersion is negligibly smallbecause of the overall neutrality of the shell cross-linked micelles,the δ-dispersion becomes important, and the whole dielectricbehavior is described within the Maxwell-Wagner effect forheterogeneous systems. In the presence of a surface conductivityλ0, the dielectric increment Δεδ and the relaxation time τδ aregiven by eqs 6 and 7, which take into account the dielectricrelaxation of uncharged particles dispersed in an electrolytesolution. In these equation, however, the term λ0/R (whichwould depend on the size R of the aggregate) has little effect incomparison to the contribution of the bulk conductivity σm,resulting in Δεδ and νδ = 1/(2πτδ) which are, to a firstapproximation, independent of temperature. In any case, at thetemperature of 35 �C, at the beginning of the shell cross-linkingfor the system PAMPS36-b-PNIPAAM40 þ PEO114-b-PAMPT-MA40, the electrokinetic model (eqs 4 and 5) furnishes a ζ-potential of the order of 2.0 mV and a radius of the shell cross-linked micelle of about 44 nm. This value is in good agreementwith the value measured by dynamic light scattering measure-ment (RH = 48 nm). At higher temperatures, the value of the ζ-potential, practically zero, prevents any evaluation of the aggre-gate size (at least from dielectric measurements).

5. CONCLUSIONS

The well-defined PAMPS-b-PNIPAAM diblock copolymercan self-assemble into PNIPAAM-core micelles as soon as thetemperature is increased above the lower critical solution tem-perature. This assembling process has been monitored by meansof radiowave dielectric spectroscopy measurements in the fre-quency range where the dielectric relaxation associated with thestructure of the micellar interface occurs. The micellizationprocess is fully reversible and is characterized by relaxationfrequencies in the range of some tens of megahertz, to whichcorrespond typical micelle size of the order of 20-30 nm.Dynamic light scattering measurements indicate the presenceof nearly monodisperse micelles of just this size. Novel shellcross-linked micelles in aqueous solution with thermoresponsivePNIPAAM core were then fabricated by cross-linking thePAMPS shell with oppositely charged PEO-b-PAMPTMA blockcopolymers, and their interfacial properties were investigated bydielectric relaxation measurements too. For both systems inves-tigated, the dielectric properties of the micellar phase, at tem-peratures higher than the lower critical solution temperature, canbe appropriately described within the electrokinetic standardmodel for colloidal suspensions.

’AUTHOR INFORMATION

Corresponding Author*E-mail cesare.cametti@roma1.infn.it.

’ACKNOWLEDGMENT

This work was financially supported by MIUR (PRIN 2008).

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Figure 13. Expected dielectric increment Δεδ and the relaxationfrequency νδ of the δ dispersion calculated on the basis of eqs 6 and 7as a function of the surface conductivity λ0. The values of the parametersare R = 30 nm, εm = 75, σm = 0.1 mho/m, and σp = 10� 10-6 mho/m.

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