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Geometrical Characteristics of Polyelectrolyte Nanogel Particles and Their Polyelectrolyte Complexes Studied by Dynamic and Static Light Scattering† Etsuo Kokufuta,*,‡ Kazuyoshi Ogawa,‡ Ryo Doi,‡ Rie Kikuchi,‡ and Raymond S. Farinato§ Graduate School of Life and EnVironmental Sciences, UniVersity of Tsukuba, Tsukuba, Ibaraki 305-8572, Japan, and Kemira Water Solutions, Inc., 1937 West Main Street, Stamford, Connecticut 06904 ReceiVed: January 8, 2007; In Final Form: March 12, 2007
The geometric characteristics of nanogel particles in aqueous solutions were studied by determining their ratios of radius of gyration (mean-square radius; Rg) to hydrodynamic radius (Rh), Rg/Rh, derived from static light scattering and dynamic light scattering experiments, respectively. The various nanogel samples studied included ones composed of lightly cross-linked N-isopropylacrylamide (NIPA) polymer, NIPA-based anionic or cationic copolymers, and amphoteric terpolymers. Polyelectrolyte complexes between anionic or cationic nanogels and oppositely charged polyions or nanogels having opposite charges were also studied. Most NIPA and NIPA-based polyelectrolyte nanogels in a swollen state had Rg/Rh values >0.775, which is the theoretically predicted value for a solid sphere. In a collapsed state, one may expect nanogel particles to be spherical in shape; however, this was not the case for a variety of nanogel samples, either with or without charges. These data were consistent with the idea that the surfaces of these nanogel particles were decorated with attached dangling chains. The Rg/Rh data from polyelectrolyte-nanogel complexes, however, indicated different structures from this. It was found that most of the polyelectrolyte-nanogel complex particles had Rg/Rh ∼ 0.775. This suggested that the complexed nanogel particles were spherical in shape and that there were no dangling surface chains.
Introduction Nanogels (i.e., lightly cross-linked polymer networks) with diameters in the size range of tens to hundreds of nanometers are of broad interest in the fields of colloid and polymer science. A number of studies concerning syntheses, properties, and applications have dealt with nanogel particles, both with and without charges.1 The geometry or shape of nanogels has generally been considered to be that of a spherical particle. Electron microscopic analyses (transmission electron microscopy,2 scanning electron microscopy,3 and environmental scanning electron microscopy)4 of N-isopropylacrylamide (NIPA) polymer nanogels have indicated a spherical shape. This conclusion was obtained from gel particles in the dried state2,3 or at the air/water interface.4 The geometries of colloids and macromolecules in fluids may also be studied by a combination of dynamic light scattering (DLS) and static light scattering (SLS); in particular, by examining the ratio of mean-square radius (Rg) to hydrodynamic radius (Rh). Previous light-scattering studies of nonionic NIPA nanogels,5,6 poly(vinyl alcohol) (PVA) nanogels,7 and NIPAbased polyelectrolyte nanogels8,9 have showed that their Rg/Rh values lie between 1.03 and 0.66, suggesting that these gel particles have roughly a spherical geometry. DLS and SLS studies have also been performed on nanogels obtained by γ-ray irradiation of aqueous PVA solutions having less than the critical gelation concentration7 and with polyampholyte nanogels8,9 † Part of the special issue “International Symposium on Polyelectrolytes (2006)”. * Corresponding author. Fax: 81-298-53-4605. E-mail: kokufuta@ sakura.cc.tsukuba.ac.jp. ‡ University of Tsukuba. § Kemira Water Solutions, Inc.
composed of lightly cross-linked terpolymer chains consisting of NIPA, acrylic acid (AAc), and 1-vinylimidazole (VI). It has been suggested that these gel particles have close to a spherical shape but that attached dangling chains cover their surface. This was further supported by the results of computer simulations.10 Additional support for this picture came from DLS and SLS experiments11 of polyanion-complexed cationic nanogels; that is, polyelectrolyte complexes of potassium poly(vinyl alcohol) sulfate (KPVS) with a cationic terpolymer nanogel composed of NIPA, AAc, and VI. However, it should be noted that these previous conclusions were obtained on the basis of a theory of light scattering from solid particles.12 It was also assumed that the Rayleigh-Gans (R-G) approximation was applicable for determining Rg from SLS data. In order to obtain accurate information about the geometry of nanogel particles from Rg/Rh data, we require appropriate SLS and DLS theories that can be used in determining Rg and Rh for nanosized polymer networks. Burchard has discussed a very elegant theory of the static and dynamic light scattering from branched polymers and copolymers.13 Cascade theory was used to calculate the various multiple sums required for determining the static and dynamic structure factors for a variety of linear and regularly branched chain systems under the assumptions of Gaussian statistics for the subchains connecting any two units in the macrochain and no loops in the chain. On the basis of these calculations, the ratio Rg/Rh was seen to be a useful metric for characterizing branched macromolecules. However, the nanogels discussed in this paper likely have topologies and linkage patterns that are somewhat more complicated than the regular branched systems discussed by Burchard. At the very least, our nanogels very likely contain both loops and cross-links in addition to branches. We distinguish cross-links, which are capable of transferring mechanical
10.1021/jp070147d CCC: $37.00 © 2007 American Chemical Society Published on Web 06/09/2007
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stress in the network, from loops, which are not mechanically active in stress transfer via covalent bonds. A very complete theory that could be used for nanogels of the type studied here might account for the different scattering cross sections of crosslinking junctions compared to linear chain segments, and the effects of linkage patterns that include cross-links and loops. Presently, we have no such theory, and must cautiously apply the general features of the cascade theory for branched systems to our data, especially when attempting to analyze nanogel morphologies that may consist of dangling surface chains attached to an otherwise congested core. Therefore, in this paper, we use a conventional SLS theory to compare Rg/Rh data from a variety of nanogels prepared in different ways and obtained under a variety of conditions. Particular attention has been paid to Rg/Rh values obtained under experimental conditions in which dangling surface chains seemed to be fully collapsed. Under such conditions, we may expect Rg/Rh ∼ 0.775 if the data analysis schemes employed are correct. Theoretical Background Rg and Rh of Solid Bodies. Expressions for the Rg and Rh values of solid spheres, ellipsoids, and rods as a function of the geometrical parameters of these shapes are known (see Table 1).12 The formula for Rh of ellipsoids is taken from Perrin14 and that of rods from Broersma.15 Their formulas are expressed in terms of the ratio of the frictional coefficient of the ellipsoids or the rods to that of a sphere of the same volume. The frictional coefficient of a hard sphere (f0) is given by the well-known Stokes equation,
f0 ) 6πηR
(1)
where R is the radius of a sphere and η is the solvent viscosity, a macroscopic quantity that measures the resistance to flow in the fluid. To define the mean square radius (radius of gyration), Rg, consider a polymer chain (or, for that matter, any other form) as an assembly of mass elements mi, each of identical mass and located a distance ri from the center of mass. Then the formula for the Rg of any shape is expressed by
∑i miri2/∑i mi)1/2
h 2)1/2 ) ( Rg ) (R
(2)
Rayleigh-Gans Approximation in the Determination of Rg from SLS Data. It is generally accepted that the RayleighGans approximation is applicable when 2ka|m - 1| , 1. This is a common approach used when analyzing light-scattering data to estimate the weight-averaged molar mass (Mw) and Rg of macromolecules, for example. The variable k is 2πλ (λ ) 488 nm for an Ar laser and 632.8 nm for a He-Ne laser), a is the particle radius, and m is the relative refractive index of the particle as compared to the medium in which it is surrounded. For nanoparticles composed of a cross-linked polymer network, however, it is not clear whether we should equate a with Rh, Rg, or some other metric. This is because there has not yet been derived an analytical model for light scattering from such complicated particles. However, since the inhomogeneities are likely to be on length scales much smaller than the wavelength of the incident radiation (at least for cases in which dangling surface chains are a very minor mass fraction of the particle) we feel justified in assuming that the R-G approximation is applicable to our system.
TABLE 1: Equation for Mean-Square Radius (Rg) and Hydrodynamic Radius (Rh) as a Function of Shape and Size
a Radius ) R. b Semiaxes a, a, and b (a ) major semiaxis and b ) minor semiaxis). c Semiaxes a, b, and b (a ) major semiaxis and b ) minor semiaxis). d Length ) L and radius ) r.
According to Flory,16 the R-G approach is appropriate for
x
x
macromolecular chains when 0.1 < r2/λ < 1, where r2 is the root-mean-square end-to-end distance of the chain and is
x
related to Rg by Rg ) r2/x6. In addition, according to Tanford,17 the criterion is given by 0.05 e Rg/λ e 0.5. These guidelines mean that the R-G criteria are met when Rg is smaller than 200 nm for an Ar laser (λ ) 488 nm) and 258 nm for a He-Ne laser (λ ) 632.8 nm). In other words, particles whose radii are smaller than ∼260 nm do not need to be treated by a more sophisticated theory, such as the Mie approximation (e.g., see Figure 3 in ref 18). Experimental Section The preparation and measurements of all our nanogel and polymer samples have been reported in detail in refs 7-9, 11, 19, and 20; thus, only a brief description is provided in this paper. Materials. We used two polyampholytic nanogels of N,N′methylenebisacrylamide (MBA)-cross-linked terpolymers composed of NIPA, AAc, and VI, abbreviated as PATNG(1) and PATNG(2) (see Table 2). Several nanogels having different AAc/VI contents were studied. Two MBA-cross-linked polyelectrolyte copolymer nanogels were also studied: One is a cationic polyelectrolyte nanogel (CPENG) consisting of NIPA and VI, and the other is an anionic polyelectrolyte nanogel (APENG) consisting of NIPA and 2-acrylamido-2-methylpropane sulfonic acid (AMPS). We adopted, for the syntheses of these nanogel samples, aqueous reduction-oxidation polymerization initiated by ammonium persulfate (APS) in the presence of sodium dodecylbenzene sulfonate (surfactant) at temperatures above the lower critical solution temperature (LCST; ∼32 °C) of NIPA polymers. As the linear polyanion for complex formation with the cationic nanogel, we used the following two samples: KPVS (Mw, 4.19 × 105 g/mol; charge density, 6.16 mmol/g; Rh and Rg determined in 0.2 M KCl at 25 °C, 16 and 33 nm, respectively); and copoly(NIPA/AMPS) (i.e., random copolymer of NIPA and AMPS) (Mw, 4.05 × 105 g/mol; charge density, 1.34 mmol/g; Rh and Rg determined in 0.2 M KCl at 25 °C, 24 and 49 nm, respectively).
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TABLE 2: Several Nanogel Particles Used for Comparison charge density (mmol/g dry)a sample
preparation
10-7 Mw (mol/g)
NIPANG(1) NIPANG(2) PVANG PATNG(1) PATNG(2) CPENG APENG
APS-initiated aqueous redox polymerization of NIPA and MBA heating of aqueous NIPA polymer solution in the presence of APS γ-ray irradation of aqueous PVA solution APS-initiated aqueous redox polymerization of NIPA, AAc, VI, and MBA ibid APS-initiated aqueous redox polymerization of NIPA, VI, and MBA APS-initiated aqueous redox polymerization of NIPA, AMPS, and MBA
1.35 ( 0.5 2.0 1.0 1.5 5.2 1.2 0.3
anionic
1.36b 0.31b 1.35d
cationic
1.12c 1.15c 1.74c
refs 5 6 7 8,9 8,9 18 18
a Determined by potentiometric titration using fully dried samples. b Based on carboxyl groups. c Based on imidazole groups. d Based on sulfonic groups.
nanogel dispersion (titrant) to either anionic polymer solution or anionic nanogel dispersion (50 mL sample). Light-Scattering Measurements. Samples obtained at different stages of the titrations were examined by DLS and SLS. The DLS measurements were carried out at a scattering angle (θ) of 90° using an Otsuka DLS 7000 apparatus (Osaka, Japan) equipped with a 10 mW He-Ne laser as the light source. We analyzed autocorrelation functions with the CONTIN program. Typical results are shown in Figure1. We note that there was no difference in the DLS data whether the measurements were performed just after or a few days after the titration (i.e., complexation). For SLS measurements, the instrument was calibrated using pure (>99.5%) toluene, and the optical alignment deviated less than (2% over the range of 30° e θ e 140°. We usually determined the Rayleigh ratio (Rθ) as the average of five different measurements of the normalized scattering intensity for each sample. The change in the refractive index with concentration (dn/dc) for nanogel particles and polymer was measured at 25 °C using an electrophotometric differential refractometer (Otsuka model DRM-1021). Measurements were carried out using vertically polarized light from an iodine arc lamp with a spectral filter (λ ) 632.8 nm). The instrument constant was obtained by using a standard KCl solution (0.01481 g/mL) with a known dn/dc value of 0.1344. For the nanogel complexes, the measurements of refractive index increment, (dn/dc)x, was not possible due to their very strong scattering intensities; thus, we calculated (dn/dc)x using the following equation
(dn/dc)x ) {1/(1 + β)}(dn/dc)a + {β/(1 + β)}(dn/dc)b
Figure 1. Typical DLS data for complex formation between anionic and cationic nanogels: (a) APENG and CPENG shown in Table 2, (b) addition of APENG to CPENG, and (c) addition of CPENG to APENG. The composition of both nanogels is indicated by anion/cation ratio (rm) in moles. The function f(Rh) was normalized by the scattered intensity (I ∼ ∫∞o f(Rh) dRh) of the CPENG dispersion at a concentration of 0.025 mg/mL. The data are quoted from Figure 3a and b of ref 19 with modification. Note that there were a few errors in the scale of Rh for Figure 3a of ref 19, which have been corrected in this figure.
Polyelectrolyte complexes composed of cationic nanogels bound with polyanions or complexes of anionic and cationic nanogel particles were formed in a salt-free system at 25 °C by titration using a computer-controlled automatic titrater (Hirama, model ART-3) typically employed in turbidimetric titrations. The solution pH was then adjusted to 3.0 with HCl to completely protonate the imidazole group of the VI segments. Two titration modes were employed: (i) addition of either anionic polymer solution or anionic nanogel dispersion (titrant) to cationic nanogel dispersion (50 mL sample) or (ii) addition of cationic
where subscripts a and b denote the (dn/dc) of a polyion and an ionic nanogel, or of two polyelectrolyte nanogels used in complex formation, and β is the mass ratio of the two polymers in a sample. Typical variation in the measured scattered intensity in many of our DLS and SLS experiments used to determine Rh and Rg for nanogels and polymers under various conditions was at most (7%. This level of experimental error was found when using the present light-scattering apparatus to estimate Rh by analysis of DLS data with the CONTIN program, or when Rg was determined from the angular dependence of Rθ at four or five sample concentrations (i.e., Zimm plot), or at one concentration under assumption of the R-G approximation. Results and Discussion NIPA Nanogels and NIPA-Based Polyelectrolyte Nanogels. Previously, we and others determined DLS and SLS data for NIPA nanogels (NIPANG) and NIPA-based polyelectrolyte nanogels either in a collapsed or swollen state.1-9,11,19 A selection of these samples is shown in Table 2, and a comparison
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TABLE 3: Light-Scattering Data of Several Nanogel Particles Obtained from Previous Studies Rg/Rha sample
measurement conditions
Rh (nm)
Rg (nm)
NIPANG(1) NIPANG(1) NIPANG(2) PVANG PATNG(1) PATNG(2) CPENG APENG
25 °C; in water 40 °C; in water 25 °C; in water 25 °C; in water 25 °C; in 0.1M KCl at pH 5.3 (pI) 25 °C; in 0.1M KCl at pH 6.5 (pI) 25 °C; in 0.2M NaCl at pH 11 25 °C; in 0.2M NaCl
132 50 390 195 ( 13 87 ( 6 132 ( 9 72 ( 5 62 ( 4
87 38 400 191 ( 13 81 ( 5 107 ( 7 86 ( 6 51 ( 3
min
avg
0.851 0.809 0.705 1.038 0.715
0.659 0.760 1.026 0.979 0.931 0.811 1.194 0.823
max
Fb (g/cm3)
1.127 1.071 0.933 1.374 0.946
0.026 0.446 0.013 0.005 0.009 0.009 0.012 0.006
a Minimum Rg/Rh value denotes the rate of minimum Rg to maximum Rh and maximum Rg/Rh value is maximum Rg to minimum Rh. b Polymer density (F) was calculated by F ) Mw/(4/3)πRh3NA, where NA is Avogadro’s number.
of their light-scattering results is given in Table 3. As was mentioned in the Experimental Section, the variation in our DLS and SLS data was at most (7%. Thus, the Rg/Rh data of our samples were evaluated with consideration of this experimental error. In addition, all of the SLS data in Table 3 were obtained from Zimm plots. The second virial coefficients were 1. At this pH, any cationic charge would be fully eliminated. The high value of Rg/Rh suggests a particle surface that is neither smooth nor impenetrable. The two NIPA nanogel samples, that is, NIPANG(1)5 and NIPANG(2),6 prepared by different methods (see Table 2) but both measured in pure water at 25 °C (conditions that should result in a swollen state) had two different Rg/Rh values (0.659 and 1.026). For the NIPANG(2) particle6 with Rg ∼ 400 nm, the R-G approximation used to estimate Rg may not be correct. The NIPANG(1)5 with Rg ∼ 87 nm, for which the R-G approximation is more likely to be correct, had Rg/Rh ∼ 0.659. Values less than that for a solid sphere can arise from particle morphologies having a “corona”-type structure; that is, a denser core surrounded by a less dense layer. An unambiguous morphological characterization is not possible solely on the basis of the Rg/Rh value, since there is more than one mass distribution
that can lead to the same Rg/Rh value. Even for the nanogel particles with Rg/Rh ∼ 0.775, one must be cautious in concluding a spherical geometry with no dangling surface chains. In other words, additional measures of particle morphology are required. Polyelectrolyte Complexes of Ionic Nanogels with Polyions. It is expected that when a suitable amount of polyions bind to polyelectrolyte nanogels to form a complex, the presence of dangling surface chains on Rg may be eliminated. Testing this notion, we compared Rg/Rh data as a function of the degree of polyion binding. We used anion/cation ratio (rm) as a measure of the degree of binding. Three different nanogel complex systems were employed (see Table 4): (i) the KPVS-cationic PATNG(1) system (samples 1-5), in which the complexation was performed by adding KPVS solution into the nanogel dispersion;11 (ii) the copoly(NIPA/AMPS)-CPENG system (samples 6-12), in which the complexation was performed by adding the copolymer solution into the nanogel dispersion;19 and (iii) the same system as ii (samples 6 and 13-17), in which the complexation was performed by adding the nanogel dispersion into the copolymer solution.19 The results are summarized in Table 4. The Rg/Rh data for all the complexes other than samples 7 and 8, which were prepared at low rm, suggest an impenetrable spherical shape. Note that samples 1 and 6 are uncomplexed nanogels. Figure 2 shows Rg-vs-Rh plots based on the data in Table 4. The line in this Figure was obtained from the equations of Rg and Rh for a solid sphere in Table 1. There is a good agreement between the theoretical and experimental results for the complexes other than samples 2, 7, and 8. Samples 2 and 7 were obtained at rm ) 0.25, and sample 8 was at rm ) 0.5. For samples 13-17, however, the experimental data of the complexes obtained at low 1/rm values (i.e., cation/anion ratio), ∼0.1-0.5, agree well with the theoretical line for an impenetrable sphere. This difference in Rg/Rh ratios for similar compositions can be understood by considering the difference in the complexation process due to the mixing method;19 that is, the result of adding of anionic polymer to cationic nanogel (for samples 2-5 and 7-12) differs from the result of adding cationic nanogel to anionic polymer (samples 13-17). We have previously demonstrated that complexes having the same size and molar mass can be obtained by an “all-or-none” process when a nanogel with large number of cationic charges is added to a lesser charged anionic polymer.19 This was the case for samples 13-17; therefore, both Rg and Rh values for samples 13-17 were independent of rm before the aggregation of the resulting complexes began. As a result, we hypothesize that polyelectrolyte nanogel particles complexed with a suitable amount of oppositely charged linear polyions become spherical in shape due to collapse of dangling surface chains. We mean by the term “spherical” that the object has the morphology of an impenetrable sphere. An object with coronal morphology
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TABLE 4: Light Scattering Data of Cationic Nanogel Complexes with Bound Polyanions Measured in Aqueous Salt-Free Solution at pH 3 and at 25 °Ca min
Rg/Rhd avg
max
Fe (g/cm3)
163 ( 11
0.897
1.032
1.187
0.002
158 ( 11 158 ( 11 125 ( 9 67 ( 5
143 ( 10 100 ( 7 82 ( 6 56 ( 4
0.787 0.550 0.570 0.726
0.905 0.633 0.656 0.836
1.041 0.728 0.755 0.962
0.002 0.002 0.004 0.024
1.2
156 ( 11
256 ( 18
1.426
1.641
1.888
0.001
1.5 2.1 2.4 2.3 2.6 2.3
133 ( 9 126 ( 9 122 ( 9 115 ( 8 107 ( 7 107 ( 7
184 ( 13 133 ( 9 96 ( 7 94 ( 7 89 ( 6 88 ( 6
1.202 0.917 0.684 0.710 0.723 0.715
1.383 1.056 0.787 0.817 0.832 0.822
1.592 1.214 0.905 0.940 0.957 0.946
0.003 0.004 0.005 0.006 0.008 0.007
67 ( 5 72 ( 5 67 ( 5 70 ( 5 75 ( 5
53 ( 4 54 ( 4 57 ( 4 55 ( 4 59 ( 4
0.688 0.652 0.739 0.683 0.684
0.791 0.750 0.851 0.786 0.787
0.910 0.863 0.979 0.904 0.905
0.039 0.033 0.040 0.027 0.022
10-7 Mw (mol/g)
Rh (nm)
Rg (nm)
1.5
158 ( 11
0.25 0.50 0.75 1.00
1.6 1.7 1.7 1.8
7 8 9 10 11 12
0.25 0.50 0.75 0.80 0.85 0.90
13 14 15 16 17
0.10 0.15 0.20 0.25 0.50
3.0 3.1 3.1 2.3 2.4
sample
b
c
rm or 1/rm
1 2 3 4 5 6
a SLS data for all the complexes were obtained from angular dependence of R at one concentration, as reported in refs 11 and 19. b Samples 1 θ and 6 show uncomplexed PATNG(1) and CPENG in Table 2, respectively; samples 2-5 and 7-12 were prepared by the addition of KPVS to PATNG(1) and of copoly(NIPA/AMPS) to CPENG, respectively, and samples 13-17 were prepared by the addition of CPENG to copoly(NIPA/ AMPS). c The degree of polyanion binding for samples 2-5 and 7-12 was represented by rm and that for samples 13-17 was by 1/rm. d Minimum and maximum Rg/Rh values were obtained as shown in Table 3. e The F value was calculated as shown in Table 3.
Figure 2. Plots of Rg vs Rh based on the data in Table 4: open triangle, sample 1; open circles, samples 2-5; solid triangle, sample 6; open squares, samples 7-13; and solid squares, samples 1317. Line was obtained on the basis of theory for a solid sphere (see Table 1).
Figure 3. Plots of Rg vs Rh based on the data in Table 5: open triangle, sample 1; open circles, samples 2-5; and solid circles, samples 612. Line was obtained on the basis of theory for a solid sphere (see Table 1).
may have spherical symmetry, but would not be impenetrable in the sense used here. Polyelectrolyte Complexes between Anionic and Cationic Nanogels. Our experimental results reported in the previous section strongly suggest that the polyion-complexed cationic nanogels are spherical in shape. It is now interesting to look at the geometrical characteristics of polyelectrolyte complexes formed from anionic and cationic nanogel particles. Table 5 shows the DLS and SLS data for APENG-CPENG complexes. Note that the number of charges per particle in the CPENG is 4.53 times larger than that in the APENG, as estimated from their charge densities: 1.74 meq/g for the former and 1.35 meq/g for the latter (see Table 2). The nanogel complex was prepared by the addition of the anionic gel dispersion to the cationic gel dispersion (samples 2-5) or vice versa (samples 6-12), as was done in the preparation of the gel-polymer complexes between CPENG and copoly(NIPA/AMPS). On the basis of previous results, we might expect the complexes in samples 2-5 to form according to a random model, whereas the all-or-none model should be appropriate for complex formation in samples 6-12.
Surprisingly, all of the complexes, other than sample 2, exhibited Rg/Rh values suggesting spherical particles within the experimental error ((7% for Rg and Rh). This is supported by the results shown in Figure 3. The results in Table 5 and Figure 3 indicate that the anionic and cationic nanogels, whose individual shapes are not distinctly spherical on the basis of their Rg/Rh values, form spherical polyelectrolyte complexes. We note that the polymer density of individual nanogel particles is very low and that a large network collapse takes place during charge neutralization in the complex formation process. There is still sufficient chain mobility, however, to allow a spherical geometry of the complex to result. A comparison of Figure 2 (the nanogel-polymer complex system) with Figure 3 (the nanogel-nanogel system) supports the notion that there is little difference in the Rg and Rh values between the complexes of CPENG with the linear polymer and with the nanogel particle composed of NIPA and AMPS. We can arrive at a similar picture via a comparison of the F values in Tables 4 and 5. When complexation takes place according to the random model, F values of the nanogel-
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TABLE 5: Light-Scattering Data of Polyelectrolyte Complexes between Anionic and Cationic Nanogels Measured in Aqueous Salt-Free Solution at pH 3 and at 25 °Ca sample 1 2 3 4 5 6 7 8 9 10 11 12
b
rm or 1/rm
10-7 Mw (mol/g)
Rh (nm)
Rg (nm)
0.25 0.5 0.75 0.8 0.10 0.15 0.25 0.35 0.45 0.50 0.55
1.2 1.5 2.1 2.4 2.8 5.7 5.5 5.4 6.0 6.0 5.6 5.3
156 ( 11 150 ( 11 143 ( 10 135 ( 9 122 ( 9 78 ( 5 72 ( 5 78 ( 5 78 ( 5 78 ( 5 85 ( 6 78 ( 5
256 ( 18 141 ( 10 109 ( 8 94 ( 7 93 ( 7 53 ( 4 57 ( 4 59 ( 4 64 ( 4 63 ( 4 70 ( 5 68 ( 5
c
min
Rg/Rhd avg
max
Fe (g/cm3)
1.426 0.817 0.663 0.605 0.663 0.591 0.688 0.657 0.713 0.702 0.716 0.758
1.641 0.940 0.762 0.696 0.762 0.679 0.792 0.756 0.821 0.808 0.824 0.872
1.888 1.082 0.877 0.801 0.877 0.782 0.911 0.870 0.944 0.929 0.948 1.003
0.001 0.002 0.003 0.004 0.006 0.048 0.057 0.045 0.050 0.050 0.037 0.044
a SLS data of all the complexes were obtained from angular dependence of R at one concentration, as reported in ref 19. b Sample 1 is the same θ as sample 6 in Table 4; samples 2-5 were prepared by the addition of APENG to CPENG; and the preparation of samples 6-12 were vice versa. c The degree of the anionic nanogel binding to the cationic nanogel is given by r for samples 2-5, and that of the cationic nanogel to the anionic m nanogel binding is by 1/rm for samples 6-12. d Minimum and maximum Rg/Rh values were obtained as shown in Table 3. e The F value was calculated as shown in Table 3.
Figure 4. Schematic representations for a nanogel particle in a swollen state (a) and a fully collapsed state (b). The degree of collapse pictured is 0.5 in diameter (L). The polymer density (F) was assumed to be constant within the main body (gray circles) of the gel particle; that is, random distribution of cross-linked polymer chains. Rg/Rh > 0.775 (a) and ≈ 0.775 (b).
polymer complexes (samples 7-10 in Table 4) are close to those of the nanogel-nanogel complexes (samples 2-5 in Table 5). In another case in which nanogel-nanogel complexes (samples 6-12 in Table 5) formed according to an “all-or-none” model, the F values are 1.2 times larger than those of nanogel-polymer complexes (samples 13-17 in Table 4). This is because the nanogel-nanogel complexes are not electrically neutral and have an excess of the bound anionic nanogel, in contrast to the polymer-nanogel complexes that form according to 1:1 stoichiometry on the basis of charge neutralization. These results have been obtained from electrophoretic light scattering experiments (see ref 19). General Discussion. Our experimental results of ionic nanogels complexed with oppositely charged polyanions and polyelectrolyte nanogels have demonstrated that their shapes are spherical, since Rg/Rh ∼ 0.775 within the experimental error. In addition, the previously reported NIPA nanogel particles in a fully collapsed state5 were spherical in shape. Several neutral and ionic nanogels in a swollen state had Rg/Rh > 0.775, and a few nanogel particles exhibited Rg/Rh < 0.775. We have
hypothesized that the reason why some nanogels had Rg/Rh > 0.775 is related to significant numbers of dangling chains attached to the nanogel particle surface. When the dangling chains collapse, the particle morphology becomes spherical in shape. This model is schematically shown in Figure 4. For cationic nanogel complexes with different amounts of surfacebound polyanions, this model can help our understanding of their spherical geometry. This is because the complexation process seems to bring about not only network collapse (an increase of F, as shown in Figure 4) but also the collapse of any dangling surface chains (e.g., see the schematic picture in Figure 9 of ref 11). In the case of nanogel-nanogel complexes, however, we have to perform more detailed experiments to provide a good explanation about why a large collapse of both anionic and cationic nanogels during the complexation leads to a spherical particle, as indicated by the results in Table 5 and Figure 3. Although unlikely, we must also consider the possibility that a swollen nanogel particle or its complex might be ellipsoidal in shape. In particular, in the case of sample 2 in Table 5 (i.e., a CPENG-APENG complex obtained at rm ) 0.25), an ellipsoidal shape might result for this complex composed on average of one CPENG and one APENG particle. Considering a simple relation for the molar mass (Mw) of complexes, Mw ) Mw,c + nbMw,a, where Mw,c denotes the molar mass of CPENG, Mw,a is that of APENG, and nb is the number of the binding of APENG to CPENG, we find that nb ∼ 1 for sample 2 in Table 5. If the mechanical strength of the particle networks is great enough, then they may form an aspherical complex. For this situation, we are now working on both the theory and experiment. Conclusions We compared in this study the Rg/Rh values for many nanogel particles with and without charges. The Rg/Rh values of nanogels in a swollen state were greater than 0.775, the theoretical value for a solid sphere. In a fully collapsed state, however, the Rg/ Rh values of the nanogel particles, in particular, of polyelectrolyte nanogel complexes, were close to 0.775, suggesting that the nanogel complexes were spherical in shape, especially under conditions that the presence of any dangling surface chains were fully eliminated. There were only a few Rg/Rh values for nanogel complexes as well as swollen neutral nanogels that were less
8640 J. Phys. Chem. B, Vol. 111, No. 29, 2007 than or greater than 0.775. At the present stage of light scattering theories, we have no good models for a lightly cross-linked nanoparticle consisting of neutral polymers or polyelectrolytes. More detailed studies in both theory and experiment are needed in this regard. Acknowledgment. This work was supported in part by Grant-in-Aids for Scientific Research to E.K. from the Japan Society for the Promotion of Science (Nos. 15350127 and 18655089). References and Notes (1) (2) (3) (4) (5)
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