Electrophoretic Behavior of Microgel-Immobilized Polyions

Article pubs.acs.org/Langmuir

Electrophoretic Behavior of Microgel-Immobilized Polyions Etsuo Kokufuta,*,† Seigo Sato,† and Mamoru K. Kokufuta‡ †

Faculty of Life and Environmental Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8572, Japan Mitsui Chemical Analysis and Consulting Service Incorporated, Sodegaura, Chiba 299-0265, Japan

‡

S Supporting Information *

ABSTRACT: Electrophoretic behavior was studied for Nisopropylacrylamide (NIPA) microgels, into which different amounts of poly(acrylic acid) (PAAc) were physically entrapped. Copolymer microgels of NIPA with acrylic acid (AAc) were also studied as a control. Electrophoretic mobility was measured in 0.1 M NaCl solution at 25 °C as a function of pH, using an electrophoretic light scattering technique. The mobility of the copolymer microgel whose COOH groups are fully ionized agreed with that of PAAc when its ionization degree (αn) is close to the mole fraction ( fAAc) of the AAc unit in the copolymer gel. There was good agreement between the mobility values of the copolymer microgel and the linear NIPA/ AAc copolymer when their AAc contents are very close to each other. However, the mobility of the microgel with immobilized PAAc was higher than that of the copolymer microgel, even when there was no difference in the AAc content for both microgels. Moreover, the immobilized PAAc showed a higher mobility than the free PAAc when its αn is equal to fAAc in the immobilized system. No correlation was observed between the mobility and the hydrodynamic radius. These results were discussed in terms of the free draining model (FDM) for the electrophoresis of polyelectrolytes. It became apparent that the mobility difference depending upon whether (i) the PAAc ions are in the cage of the NIPA network or (ii) the AAc units are copolymerized with the network chain is due to the structural difference of the segments considered in the FDM.

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INTRODUCTION Electrophoresis of polyelectrolytes was studied theoretically in the 1950s by Hermans,1 Hermans and Fujita,2 and Overbeek and Stigter,3 and experimentally in the late 1950s and early 1960s by Nagasawa’s group.4,5 The conclusion from both theories and experiments was at first sight surprising, because a macromolecular coil with charges, which behaves in sedimentation or diffusion as impermeable, should behave in electrophoresis as if it were free draining. Thus, the electrophoretic behavior of polyions is different from that of colloid particles generally treated by Smoluchowski’s model6 as well as that of proteins by Henry’s model.7 The free draining model (FDM) for polyelectrolytes has led to renewed interest in the electrophoresis of microgel particles consisting of cross-linked polyelectrolyte chains. When considering polyelectrolyte microgels of various sorts, we must recall the two models other than the FDM, which have been developed to account for the electrophoretic behaviors of N-isopropylacrylamide (NIPA)-based ionic microgels. One is the “charged surface model” (CSM) established by Pelton et al.,8,9 in collaboration with Rowell,8 for understanding the electrophoretic behavior of a NIPA microgel. Charges of the gel particle arise from ionic polymerization initiators bound to many of the end groups of NIPA chains. The other is a model [referred to here as “charged hairy surface-layer model” (CHSLM)] initially proposed by Ohshima10,11 for under© 2013 American Chemical Society

standing the electrophoresis of a NIPA-based microgel consisting of a styrene−NIPA copolymer core with the surface of a NIPA gel layer. Before providing a brief description of these three models, we look at the experimental aspects in the electrophoresis of charged microgel particles. After the first report of CSM8 and CHSLM,10 Nabzar et al.12 measured the electrophoretic mobility as a function of the NaCl concentration for a cationic microgel composed of a polystyrene core with a shell of copolymer of NIPA with aminoethyl methacrylate and claimed that CHSLM did not predict their results. We studied random copolymer microgels of NIPA with acrylic acid (AAc) or 1vinylimidazole (VI) using potentiometric titration and electrophoresis.13 It was demonstrated that FDM was better than CSM in the estimation of charges per particle, yet there was not a good agreement between the results calculated from the mobility and obtained by the titration. On the other hand, Pelton reported in his review9 that there is little difference among the mobility versus temperature curves of NIPA microgels calculated on the basis of the FDM, CSM, and CHSLM with assumed values for a set of parameters (see Figure 15 of ref 9). It appears that because the Hermans−Fujita Received: September 17, 2013 Revised: November 19, 2013 Published: November 20, 2013 15442

dx.doi.org/10.1021/la403597u | Langmuir 2013, 29, 15442−15449

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Table 1. Three Models for Describing the Electrophoretic Mobility (U) of Polyelectrolyte Microgel Particles

Explanation of each term is as follows: For FDM, e, electronic charge; η, viscosity coefficient of the solvent; rs, hydrodynamic radius of a segment in the particle; κ, reciprocal thickness of the ionic atmosphere defined by Debye and Hückel; and b = (6πrsNs)1/2, where Ns is number of the segments per unit volume. For CSM, N, total number of charges per particle; and r, hydrodynamic radius of the particle. For CHSLM, εr, relative permittivity of solution; ε0, permittivity of vacuum; ψ0, potential at the boundary between the hairy surface layer and the surrounding solution; ψDON, Donnan potential of the hairy surface layer; κm, Debye−Hückel parameter; λ, parameter related to the friction exerted on the liquid flow in the hairy surface layer and given as λ = (γ/η)1/2, where γ is the frictional coefficient of the hairy surface layer; and zeN, density of fixed charges within the hairy surface layer (z, valence of fixed charge; N, number density in m−3; and e, electronic charge). a

equation2 and the Ohshima equation10 were based on a twoparameter model, uses of uncertain parameters in the calculations could lead to different conclusions. Taking the above into account, we performed the electrophoretic study using both ampholytic microgels and terpolymers, which have a high similarity in the monomer residue composition of NIPA, AAc, and VI but a big difference in the molar mass.14 A good agreement was found between the mobility values of the microgel and the terpolymer, which were measured at 25 °C over a wide pH range through an isoelectric point (a collapsed state) and at different ionic strengths. This finding strongly suggests that the FDM is adequate for understanding the electrophoretic behavior of our ionic microgels, even when the gel network was in a collapsed state around the isoelectric point. However, we were not able to mention why there is a marked difference between the mobility values obtained experimentally and calculated upon the FDM and CSM theories, without any assumption of the “degree of shielding” for polyion charges. After our publication,14 Femández-Nieves and Márquez15 studied the electrophoresis of ionic microgel particles of poly(2-vinylpridine), which was lightly cross-linked by divinylbenzene. Their conclusion was that the gel particles behave as charged spheres in a deswollen state but as freedraining spherical polyelectrolytes in a swollen state. Then, they claimed that the CHSLM theory is shown to contain the essential physics for describing the experiments, upon adequate consideration of particle swelling behavior and network-solvent friction variations. Since then, there has been continued interest

in the electrophoretic behavior of polyelectrolyte microgels16−22 in connection with CHSLM, as well as with FDM in cases in which gel particles are in a swollen state. Also, several authors23,24 have continued the theoretical understanding of the nature of a polyelectrolyte shell (soft layer) within the gel particle. However, important issues remain unresolved, which prevent comparison of the experimental results and model predictions. For example, one may not determine or predict the effects of charge distributions within the polyelectrolyte microgel particles on their mobility, at least at the present stage of electrophoretic studies. Otherwise, from a historical perspective, we should note that the electrophoretic behavior in aqueous salt solutions of poly(AAc)-coated polystyrene latexes ranging in diameter from 660 to 2000 nm can be accounted for in the FDM theory.25 As a result, there are still difficulties in selecting a suitable model from FDM, CSM, and CHSLM for understanding the electrophoretic behavior of various charged soft particles with and without a core−shell structure. In this study, we attempted to establish an experimental system consisting of polyelectrolyte microgels, which allows us to discuss the electrophoretic results in terms of the FDM theory. The idea is based on the use of two sorts of microgels, in which (i) the charges (as a linear polyion) are caged or immobilized and (ii) the charges (as ionic monomers) are copolymerized. Also, a linear copolymer with the same charge density as both microgels was used as a control sample for comparison. If the FDM is adequate, the mobility of the polyion immobilized within the microgel should be higher than 15443


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change in the “size” of a segment, which is characterized by its hydrodynamic radius rs. (ii) At a high ionic strength, such as 0.1, the U in FDM becomes −e/6πηrs because κ ≫ b (see Table 1); therefore, there is little difference in the mobility among CG, CP, and PE if their segments can be characterized by the same rs; in other words, this means that these three samples have the same number of “neutral” monomer units (NIPA and uncharged AAc) per charge (COO−) for a given solution condition. (iii) In the case of EG (i.e., PE entrapped within the microgel network), however, the segment consisting of one charged monomer unit and the neutral monomer units seems to be spherical in shape, because the charges bound to an immobilized PE chain would be “surrounded” by (but not “linked” with) the neutral monomer units that make up a cagelike microgel network. (iv) In accordance with predictions ii and iii, it seems that the mobility of EG is larger than those of CG, CP, and PE when all of the samples have the same number of neutral monomer units per anion, because of the difference in the shape of a segment: spherical for EG but elliptical for PE, CP, and CG. (v) Prediction iv is not possible based on CSM. (vi) Even when CHSLM becomes identical to FDM under conditions where there is no effect of the hard core on the mobility, the EG particles fall outside the range of CHSLM from which effects arising from an inhomogeneous charge distribution are not clear at present (compare Table 1 to Figure 1).

those of the copolymer microgel and the linear copolymer under conditions where their net charge densities are equal to each other, as will be mentioned later.

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THEORETICAL BACKGROUND Table 1 shows the mathematical expression of FDM, CSM, and CHSLM, together with a schematic illustration to help our understanding of these models. As mentioned in the Introduction, FDM was originally considered to describe the mobility (U) of a polyion coil in aqueous media.1−3 Nevertheless, it may be applied to cross-linked polyelectrolytes because U is given in terms of a segment in the polymer chain with or without cross-linking points. In CSM, the following assumptions were made:8 (i) all of the charges are located on the exterior surface of the gel particle; (ii) the charge density is related to the potential by the Helmholtz equation; (iii) the surface potential is equal to the ζ potential; and (iv) the electrophoretic mobility is related to the ζ potential by the Smoluchowski equation. The equation based on CHSLM10 becomes equivalent to the Smoluchowski equation when the effect of the hair chains is negligible and to the Hermans−Fujita equation when there is no effect of the hard core. Figure 1 shows the schematic illustration of the polyelectrolyte samples studied: a polyelectrolyte-entrapped microgel

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EXPERIMENTAL SECTION

Materials. Table 2 shows the characteristics of our microgel and linear copolymer samples used in this study. Poly(AAc), abbreviated as

Table 2. Charge Density (Dc) and Weight-Average Molecular Weight (M̅ w) of Samples sample

Dc (mmol/g)a

M̅ w (×10−6, g/mol)b

EG-10 EG-30 CG-10 CG-30 CP-30

0.950 3.20 0.931 2.90 2.79

52.4 364 1.47 23.6 0.608

a

Determined by potentiometric titration. bDetermined by the static light scattering method.

PAAc, which was used for the entrapment into NIPA microgels, has a weight-average molar mass (M̅ w) ≈ 450 kDa. Microgels of the NIPA network with entrapped PAAc, gel(PAAc-en-NIPA), simply abbreviated as EG, were synthesized by redox polymerization. Two aqueous feed solutions were used, which contain PAAc at concentrations of 44.4 mmol/L for EG-10 and 171.5 mmol/L for EG-30. The other chemicals added into the PAAc solutions were NIPA (400 mmol/L), N,N′-methylenebisacrylamide (Bis, cross-linker; 3.9 mmol/L), and sodium dodecylbenzene sulfonate (SDBS, surfactant; 10 mmol/L). A 1 L conical flask was used as a reactor, which was equipped with a magnetic stirrer, a thermometer, a nitrogen gas inlet tube, and a reflux condenser with a gas outlet tube at the top. Into 190 mL of the pHcontrolled feed solution in the reactor, 10 mL of aqueous 0.5% (w/v) ammonium persulfate (APS; initiator) solution was added to initiate the polymerization. The reaction was continued at 60 °C for 2 h in a nitrogen atmosphere under stirring (200 rpm) and then terminated by blowing oxygen through the reactor. Also synthesized as the control sample was the microgels of the Bis-cross-linked random copolymer network of NIPA and AAc monomers, gel(AAc-co-NIPA), abbreviated as CG. The procedure was the same as for EG, other than the use of AAc instead of PAAc.

Figure 1. Schematic illustrations of ionic microgels and linear polyions used in this study. EG, microgel of neutral polymer network in which anionic PE is immobilized; PE, polyanion served as a control of EG; CG, microgel of the CP network consisting of anionic and neutral monomer units; and CP, copolymer of anionic and neutral monomers served as a control of CG. In the experiments, NIPA, AAc, and Bis were used as a neutral monomer, an anionic monomer, and a crosslinker, respectively.

(EG), a linear polyelectrolyte (PE, used for the entrapment), a polyelectrolyte copolymer microgel (CG), and a linear polyelectrolyte copolymer (CP). A simple comparison of these samples (in Figure 1) with the models (in Table 1) would lead to the following predictions: (i) In FDM, a segment is defined as a “string” of neutral (or uncharged) monomer units plus one charged monomer unit, so that the mobility varies proportionally to the “net charge” per polyion through a 15444


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The primary factor affecting the purity of EGs should be a trace amount of PAAc that is remaining as the unentrapped free polymer. To remove it from the crude polymer (microgels), which had been precipitated from the reaction mixture with acetone and dried in vacuo, two purification methods were tested. One is centrifugal filtration using a Vivaspin 20 device (Sartorius, Germany) with a polyethersulfone membrane having a molecular weight cutoff of 1000 kDa, through which the PAAc (as sodium salt) dissolved in 0.2 M NaCl solution has been known to be permeable. The other is a repeated precipitation−dissolution method, in which the NIPA-based gel particles were initially precipitated from its aqueous NaOH solution (pH 8) upon heating (45 °C), separated by filtration, and dissolved in the NaOH solution upon cooling (10 °C); these procedures were repeated 3 times. At the final stage of both purification methods, the microgel samples were dissolved in cold water (10 °C), converted into the salt form with NaOH, and dried by lyophilization. To determine the purity of EG and CG preparations, a simple but effective technique was developed, which is based on the polyelectrolyte complex formation of PAAc with polycations, such as poly(diallyldimethylammonium chloride) (PDADMAC). The microgel sample (10 mg) was initially dispersed in a cold HCl solution (pH 3; 5 mL) containing 4 mol/L urea, which can block the formation of hydrogen bonding between the COOH (PAAc) and amide (NIPA) groups.26−28 The dispersion was heated to precipitate microgels and passed through a membrane filter having a pore size of 100 nm. The filtrate (4 mL) was adjusted to pH 8 with a very slight amount of 1 M NaOH solution and mixed with an aqueous PDADMAC solution (2.5 unit mmol/L; 0.1 mL). When PAAc is present in the filtrate, the mixture becomes turbid because of the formation of a water-insoluble PAAc−PDADMAC complex. The detection limit was about 2 mg of PAAc per liter. By this method, the free PAAc was not detected from all of our EG and CG preparations, thus meaning that a guaranteed purity was greater than 99.9%. The obtained EG samples exhibited the cloud point temperature (Tcp) around 32 °C that was independent of pH at pH > 5.5, while the Tcp of the CG samples showed a marked pH dependence (see Figure S1 of the Supporting Information). The stimuli−responsive behavior of the EG particles is very close to that of bulk NIPA gels, into which PAAc was immobilized,27,28 as well as that of PAAc with grafted NIPA site chains,29 thus indicating that the immobilized PAAc has little effect on the thermal response of the NIPA chains in the microgel system at pH > 5.5. In addition to the EG and CG samples, we synthesized a copolymer of AAc and NIPA (abbreviated as CP) and used it as the control for CG. The preparation method is the same as that of CG, except for the use of the monomer solution not containing the cross-linker. Measurements. The overall contents of COOH groups were determined by pH titration at 25 °C and in 0.5 M KCl solution with 0.1 M KOH as a standard titrant. Hydrodynamic radius (Rh) and M̅ w were determined by laser light scattering techniques, using an Otsuka DLS-7000 apparatus equipped with a 75 mW argon ion laser (NEC model GLG-3112). Electrophoretic mobility was measured at 25 °C and at an ionic strength of 0.1 (NaCl) by electrophoretic light scattering (ELS) using an Otsuka ELS-6000 apparatus. We refer to our previous papers14,19 for details on the measurements used here.

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Figure 2. Electrophoretic diagrams of EG samples and their mixtures with PAAc or pure NIPA microgel: (a) mixture of EG-30 (0.01 g/L) and NIPA microgel (0.77 g/L), (b) EG-30 (0.01 g/L), (c) mixture of EG-30 (0.01 g/L) and PAAc (0.5 g/L), (d) EG-10 (0.1 g/L), and (e) mixture of EG-10 (0.1 g/L) and PAAc (1 g/L). All of the samples were prepared with 0.1 M NaCl solution at pH 8.0. Vertical bars show one unit of intensity.

previous study.19 We then assumed that a peak at U ≈ −3.06 × 10−8 m2 V−1 s−1 in diagram b would overlap with the peak of the PAAc released from EG-30. From our preliminary experiments, the detection sensitivity of ELS for the pure NIPA microgel particles was found to be sufficient at the concentrations >0.2 g/L even in the presence of EG-30 (0.01 g/L). Consequently, a peak that appeared at U ≈ −0.67 × 10−8 m2 V−1 s−1 in diagram a is assignable to the pure NIPA gel particles (note that our NIPA microgel has slight negative charges because of the use of APS as a polymerization initiator). Nevertheless, because of a very strong light scattering intensity of EG-30, we might not detect a slight amount of the NIPA microgel from which the entrapped PAAc had been completely released. This means that the above assumption remains valid. Thus, the second control experiments were performed using a mixture of PAAc with EG-10 or EG-30. A considerable amount (0.5 or 1.0 g/L) of PAAc in the mixtures with the EG particles was required for the detection of PAAc by ELS, because of a slight difference in the mobility between both samples (see diagram c), as well as a very low light scattering intensity of PAAc ions. However, there is little difference in the mobility (−2.50 × 10−8 m2 V−1 s−1) of EG-10 between diagrams d and e, as well as of EG-30 (U ≈ −3.06 × 10−8 m2 V−1 s−1) between diagrams b and c. Moreover, the mobility (−3.51 × 10−8 m2 V−1 s−1) of the PAAc ions in the mixture with EG-30 (diagram c) agrees well with that in the mixture with EG-10 (diagram e). As a result, it is obvious that the influence of the released PAAc ions on the mobility of the EG particles is negligible, even though a certain amount of the PAAc ions would be released during the ELS measurements. Another important feature from Figure 2 is that the mobility of EG-30 with M̅ w of 364 MDa is larger than that of EG-10 with M̅ w of 52.4 MDa. The molar mass of EG-30 is 6.95 times that of EG-10, while the charge density (Dc) of EG-30 is 3.37 times that of EG-10 (see Table 2). These facts clearly indicate the

RESULTS

It is of particular importance to examine the release of the entrapped PAAc ions from the EG particles and the influence of the released polyions on the particle mobility during the electrophoresis. For this purpose, we performed two control experiments (see Figure 2). Special attention was then paid to the fact that there is a big difference in the light scattering intensity between each of the microgel samples and also between polyion and ionized microgel, which is due to a difference in the polymer densities rather than particle sizes (e.g., see ref 19). Initially, we compared diagram b for EG-30 with diagram a for a mixture of EG-30 and pure NIPA microgel (Rh = 57 nm), the latter of which is the same as used in our 15445


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solution used in the preparation of EG and CG is less than 1% (see the Experimental Section). This allows us to ignore nBis in eqs 1 and 2. Let us now consider the following relations: nAAc = M̅ wDc and nNIPA = (M̅ w − MAAcnAAc)/MNIPA, where MAAc (≅72 g/mol) and MNIPA (≅113 g/mol) are the molar masses of the AAc and NIPA units, respectively. Moreover, Dc is the charge density in mol/g, which can be determined by the titration of the COOH groups (see Table 2). As a result, fAAc becomes

free draining nature of the PAAc ions entrapped within the NIPA microgel particles in the electrophoresis. Thus, the pH dependence of mobility for each sample in Table 2 and also for PAAc was examined in detail (see Figure 3). For all of the

fAAc ≈

(3)

The calculated results of fAAc for each sample in Table 2 are 0.10 for EG-10, 0.32 for EG-30, 0.10 for CG-10, 0.29 for CG30, and 0.28 for CP-30. Using these fAAc values, the mobility data of EG, CG, and CP were compared to the U versus αn curve of PAAc (see Figure 4). It can be seen that the U values

Figure 3. Change of electrophoretic mobility (U) with pH for each sample shown in the panels. PAAc and CP-30 were used as controls for EG and CG, respectively.

samples examined there is a possibility to form hydrogen bonds between the uncharged AAc and the NIPA units under acidic pH conditions.27−29 From our previous work,30 however, it is strongly suggested that 50% of COOH groups in the EG and CG particles, as well as in PAAc, is neutralized at pH > 5.5 and at ionic strength of 0.1. The significant observations from the U versus pH curves in Figure 3 are as follows: (i) All of the mobility curves leveled off at pH ≥ 6. (ii) Under such pH conditions, the U values of EG-10 and EG-30 are higher than those of the corresponding CG samples. (iii) In particular, at pH ≥ 6, the mobility of EG-30 is close to that of PAAc. (iv) Over the pH range examined, there is a good agreement between the mobility values of CG-30 (microgel) and CP-30 (linear copolymer), both of which have the same charge density but different molar masses. These results are not in conflict with predictions i−iv that were described in the previous section. A full comparison of all of the mobility data in Figure 3 will be made in terms of the FDM theory in the Discussion.

Figure 4. Comparison of mobility data of EG, CG, and CP as a function of fAAc to the U versus αn curve of PAAc.

of the CG and CP agree well with those of PAAc at the corresponding αn values. This clearly indicates the validity of our data analysis. In the case of the EG-10 and EG-30 particles, however, their U values are higher than those of PAAc at the corresponding αn values (0.1 for EG-10 and 0.32 for EG-30). This is of great importance as an “unaccountable” fact according not only to the CSM but also to the CHSLM (see ref 31). Let us try to interpret the above results in terms of the FDM theory. Then, we must consider the “net charge” of a polyion around which counterions are condensed. In the case of PAAc, fortunately, Huizenga et al.32 have accurately measured the degree (dc) of counterion condensation as a function of αn using radioactive Na22 ions as a tracer in their transference experiments. However, there are a few differences in the αn values between ref 32 and our study. Thus, the data dc (socalled “associated Na+ ion fraction” in ref 32) and 1 − dc (free Na+ ion fraction) as a function of αn were subjected to curve fitting by a polynomial of third order. The results of curve fitting are shown in Figure 5, together with the plot of U against (1 − dc)αn that was obtained with our α n and the corresponding 1 − dc. A linear interpolation between U and (1 − dc)αn provides the following “empirical” equation:

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DISCUSSION A description of the electrophoretic behavior of the ionic microgels in Figure 3 was attempted using the FDM theory. At pH values of 7 and 8, the COOH groups in the AAc units in CG-10 and CG-30 (as well as in CP-30) are fully ionized. Therefore, the molar fraction (fAAc) of the AAc monomer unit in CG-10 or CG-30 is comparable to the ratio of charged to uncharged COOH of PAAc; that is, the degree (αn) of ionization of PAAc (it should be noted that, in the FDM theory, the size of a segment becomes a function of αn, as well as of fAAc). This would be the case for EG-10 and EG-30 when we consider the “overall” composition of microgel constituents. The fAAc of all of the microgels can be given by nAAc fAAc = nAAc + nNIPA + nBis (1) where n denotes the mole number of each monomer unit indicated by the subscript. According to the mass balance principle, the M̅ w can be given as M̅ w = nAAcMAAc + nNIPA MNIPA + nBis(MBis /2)

MNIPA Dc 113Dc = (MNIPA − MAAc)Dc + 1 41Dc + 1

(2)

U ≈ −10.4 × 10−8(1 − dc)αn

where M is the molar mass of each monomer unit shown by the subscript. Obviously, nBis = 0 for CP, but nBis ≠ 0 for EG and CG. Nevertheless, the Bis concentration in the monomer

(4)

The term (1 − dc)αn can be regard as the fraction of the polymer-bound COO− ions without the influence of the 15446


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monomer unit, meaning that 35% of all of the COONa groups in NaPAAc contributes to its migration under an applied electric field. Therefore, the experimentally observed U of NaPAAc is found to be about 0.35 times that (−10.4 × 10−8 m2 V−1 s−1) of an “ideal” NaPAAc anion without the influence of counterion condensation. Recalling that a segment in FDM was defined as a string of neutral (or uncharged) monomer units plus one charged monomer unit, we can say that the difference between the ideal and experimental mobilities corresponds to about a 2.9 times increase of f monomer, because the COO− charges are screened by the counterions to increase the number of the uncharged monomer units. Thus, it is of importance to know the fs/f monomer ratio from the mobility data in Figure 4. For this, we used the following relation: ⎛1⎞ fs /fmonomer = −10.4 × 10−8⎜ ⎟ ⎝U ⎠

(5)

The fs/f monomer ratios for PAAc at different αn and for each microgel are shown in Table 3, together with the rs value Table 3. Values of fs/f monomer and rs Calculated from the Mobility (U) and Hydrodynamic Radius (Rh) Obtained by DLS sample

Figure 5. Curve fitting of the (a) plots of the counterion condensation degree (dc) and the free Na+ ion fraction (1 − dc) against the neutralization degree (αn) for the PAAc−NaOH system and (b) dependence of U upon αn(1 − dc). The data in ref 31 was used for the curve fitting, from which the following polynomial equations were obtained with the correlation coefficient (r) of 1.00: dc = −0.128αn3 − 0.480αn2 + 1.242αn − 0.004 and (1 − dc) = 0.128αn3 + 0.480αn2 − 1.242αn + 1.004. A linear interpolation between U and (1 − dc)αn in panel b provided U = (−10.406 × 10−8)(1 − dc)αn + (5 × 10−11) with r = 0.981, which can be approximated as U ≈ −10.4 × 10−8(1 − dc)αn.

EG-10 EG-30 CG-10 CG-30 CP-30 PAAc

αn

fAAc 0.10 0.32 0.10 0.29 0.28

1.0 0.3 0.1

U (×108, m2 V−1 s−1)

fs/f monomer

rs (nm)

Rh (nm)

2.47 3.17 0.93 2.12 2.13 3.51 2.05 0.86

4.21 3.28 11.18 4.91 4.88 2.96 5.07 12.09

0.382 0.298 1.015 0.445 0.443 0.269 0.461 1.098

99 212 48 99 33 23

calculated by rs = −e/6πηU (note that 8.994 × 10−4 kg m−1 s−1 was used for η of aqueous 0.1 M NaCl solution at 25 °C). Also shown in Table 3 is the hydrodynamic radius (Rh) determined by dynamic light scattering (DLS). The most noteworthy results are as follows: (i) The fs/f monomer of EG-10 and EG-30 is smaller than that of the corresponding CG and CP, but in the case of EG-30, its fs/f monomer is close to that of the PAAc at αn = 1 (i.e., NaPAAc). (ii) The fs/f monomer of PAAc at αn = 0.1 and 0.3 is close to that of CG-10 (with fAAc = 0.1) and CG-30 (with fAAc = 0.29), respectively. (iii) The fs/f monomer of CG-30 is almost equivalent to that of CP-30. (iv) There is no correlation between Rh and U (or between Rh and fs/f monomer or rs). These results indicate the structural difference between the electrophoretically migrating segment of the immobilized PAAc and that of the copolymerized AAc chain, both of which are present within the NIPA-based gel particle. An attempt was made to discuss the structure of the segment in the EG and CG particles. As schematically illustrated in Figure 6, a segment in NaPAAc (i.e., PAAc at αn = 1) seems to be composed of one charged unit and two charge-screened (neutral) units because fs/f monomer ≈ 3. A decrease in αn increases the neutral AAc units, leading to the increase of fs/ f monomer. This is the case for CP as well as for CG, as evidenced by results ii and iii from Table 3. Therefore, the segment in the CP or CG particles, which consists of one charged AAc unit (a blue sphere with a minus sign) and several neutral NIPA units (yellow spheres), is expected to be elliptical in shape. In the case of the EG particles, one charged AAc unit is not connected

counterion condensation at a given αn; therefore, eq 4 means a linear dependence of the mobility of a PAAc ion on its net charge. Note that eq 4 gives U ≈ −10.4 × 10−8 m2 V−1 s−1 at αn = 1 and dc = 0, the value of which is between the mobilities of the OH− ion (−20.5 × 10−8 m2 V−1 s−1) and HCO3− ion (−4.61 × 10−8 m2 V−1 s−1) determined by conductometric experiments. This is not a surprising result when we consider the FDM theory, because the mobility of the PAAc ion is based on a monomer unit given as

A question may be raised as to the validity of the above discussion, because the ELS was made at ionic strength 0.1 (NaCl) but the transference experiment32 was performed with PAAc solutions in the absence of added salts (i.e., ionic strength ≈ 0). However, recall that the previous study33 with PAAc has demonstrated little dependence of dc upon the concentration of added salts, such as NaCl. Taking this into account, we have obtained from Figure 5a a relation of 1 − dc = 0.37 at αn = 1. Consequently, U becomes −0.37[e/6πηrs] for the PAAc completely neutralized with NaOH (abbreviated hereafter as NaPAAc) under high ionic strength conditions (see Table 1). This is almost equivalent to eq 6 in ref 25; i.e., U = −0.35e/ f monomer, where f monomer is the frictional coefficient of the 15447


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our microgels are nearly spherical in shape. Thus, parameter b can be calculated from b = (6πrsNs)1/2 using the data in Tables 2 and 3. As a result, we obtained the following f(κ, b): 1.04 for EG-10, 1.08 for EG-30, 1.03 for CG-10, and 1.07 for CG-20. In addition, f(κ, b) = 1.05 was obtained for CP-30 as a linear copolymer. These results support the free draining behavior of NIPA microgel-immobilized PAAc ions in the electrophoresis under a high ionic strength.

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CONCLUSION Our ELS experiments have been demonstrated that the mobilities at pH values of 7.0 and 8.0 and at ionic strength of 0.1 for the EG particles with the immobilized PAAc ion are larger than those for the CG particles consisting of the AAccopolymerized network chains, as well as for a linear CP of AAc and NIPA. However, there was good agreement between the mobilities of the CG and CP particles having the same or very similar fAAc values. The mobility of the CG or CP also agreed with that of the PAAc ions when the fAAc of the former is equal to the αn of the latter. These results are well-interpreted in terms of the FDM theory by considering the structure of an “electrophoretically migrating” segment, thus providing significant insight into the migration mechanism of charged soft particles in electric fields.

Figure 6. Schematic illustrations for segments in the free draining model for the electrophoresis of NIPA microgel-immobilized PAAc ions (EG-10 and EG-30), AAc-copolymerized NIPA microgels (CG10 and CG-30), and poly(AAc-co-NIPA) (CP-30). Also shown in this figure are the free PAAc ions at αn = 0.1, 0.3, and 1.0. Transparent yellow spheres appeared in EG-10 and EG-30 show the NIPA monomer units that surround the segment but do not affect its friction coefficient. The dashed-line circle indicates the size of a hydrodynamically equivalent sphere for each segment.

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with the NIPA units to form a “string of beads” along the backbone but surrounded by the neutral NIPA units of two sorts: one is a constituent of the segment (see a yellow sphere in EG-10), and the other is not a constituent of the segment (see “transparent” yellow spheres in EG-10 and EG-30). The latter have little influence on fs, so that the segment in the EG particles would be spherical (or close to that of NaPAAc). The mobility of such a segment should be larger than that of the elliptical segment having the same number of the neutral units. For comparison, in Figure 6, the size of a hydrodynamically equivalent sphere for each segment was shown by the dashed line circle whose radius was adjusted to be proportional to rs in Table 3. All (or almost all) of the monomer units, which constitute a segment for EG-10 and EG-30, can be seen within the circle. As a result, the discussions of the segment structures allow us to understand why the mobility of the EG particles was higher than that of the CG and CP particles over a wide pH range (Figure 3), as well as that of the PAAc ions under conditions where αn equals fAAc (Figure 4). To support the above discussion, it is significant to confirm that the second parenthesized term in the equation for FDM in Table 1 becomes unity; (3κ3 + 3κ2b + 2κb2 + b3)/(3κ3 + 3κ2b) = f(κ, b) ≅ 1. This is the nature of the FDM theory at a high ionic strength, such as 0.1 (κ ≈ 1.03 × 107 cm−1). As shown in the footnote in Table 1, parameter b is a function of rs and Ns (the number of the segments per unit volume). Here, we calculated Ns from Ns = ρp DcNA ≈

⎛ 3 ⎞⎛ M̅ w ⎞ ⎜ ⎟⎜ ⎟D ⎝ 4π ⎠⎝ R h 3 ⎠ c

ASSOCIATED CONTENT

S Supporting Information *

pH changes of the cloud point temperature for the EG and CG samples (Figure S1). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the Ministry of Education of Japan (Grant 20550183) to Etsuo Kokufuta is gratefully acknowledged.

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REFERENCES

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(6)

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