Introduction

Zwitterionic polyelectrolytes that possess both positive and negative charges can be found in certain natural substances with a high molecular weight, such as poly(amino acid)s, proteins, DNA and cell membrane surfaces. These substances form self-assemblies and nanostructures in aqueous media.1 Various types of polyelectrolyte brushes have been prepared to modify solid surfaces to achieve biocompatibility, switchable wettability and low friction under aqueous conditions.

For example, poly(3-(N-2-methacryloyl-oxyethyl-N,N-dimethyl) ammonatopropanesulfonate) (PMAPS) and poly(2-methacryloyloxyethyl phosphorylcholine) (PMPC) are insoluble and soluble in deionized water at room temperature, respectively. PMAPS is soluble in a solution at a sufficiently higher temperature than the upper critical solubility temperature,2 as well as in an aqueous salt solution because of the strong attractive intermolecular and intramolecular electrostatic interaction between ammonium cations and sulfonyl anions. Huck and co-workers3 prepared a PMAPS brush on gold surfaces by surface-initiated atom transfer radical polymerization, in which they showed that surface wettability changed from hydrophilic to hydrophobic because of the strong interchain and intrachain associations at the upper critical solubility temperature accompanying a change in the thickness of the brushes in an aqueous medium. In addition, excellent lubrication in an aqueous medium was observed on the surface of a PMPC brush.4, 5 The PMPC brush has attracted a great deal of interest because of its excellent biocompatibility6, 7 and characteristics such as its antifouling behavior.8 To understand the mechanism responsible for the excellent biocompatibility and lubrication behavior, it is very important to examine the swollen structure, the conformation of polyelectrolyte brushes in an aqueous solution and the dependence on ionic strength in comparison with the solution properties of unbound, free polyelectrolytes.

In general, high-density polymer brush chains immersed in a good solvent are extended in a perpendicular direction from a substrate because of the osmotic pressure generated by the excluded volume effect.9 Tsujii et al. carried out force curve measurements on a swollen poly(methyl methacrylate) brush on a silicon wafer. They used a silica probe for atomic force microscopy and determined the equilibrium thickness of the brush. The thickness was three times as large as the scaled dry thickness.10 However, it is very difficult to precisely determine the swollen thickness of polyelectrolyte brushes in an aqueous solution. In the case of atomic force microscopy, strong electrostatic attractive or repulsive interactions occur between the polyelectrolyte surface and the probe in an aqueous solution with low ionic strength.

Previously, neutron reflectometry at the polyelectrolyte brushes/deuterium oxide interface was used to characterize the swollen structure of PMAPS11, 12 and PMPC13 brushes. However, the neutron scattering length density profile provided only an ambiguous estimate of the internal structure of the brushes in an aqueous solution with a large molecular weight distribution (MWD) because the average height of the brush increases with polydispersity, whereas the average stretching in the brush decreases.14

In most studies, polyelectrolyte brushes are prepared either by adsorption of block copolymers consisting of a hydrophobic and a polyelectrolyte block on latex particles15 or by surface-initiated polymerization of ionic monomers from hydrophobic polymer latex particles. Polzer et al.16 prepared a PMAPS brush shell on a colloidal particle consisting of a polystyrene gel core, the structure of which was confirmed by cryogenic transmission electron microscopy and dynamic light scattering (DLS) in aqueous NaCl and KCl solutions. However, the interfacial width of the core and shell was unclear, especially in an aqueous salt solution because of the possibility that the polystyrene core might be strained by swollen PMAPS brush chains due to high osmotic pressure. Matsuda et al.17, 18 prepared surface-grafted PMPC on silica nanoparticles by surface-initiated atom transfer radical polymerization to measure DLS in aqueous NaCl solutions. Interestingly, they found that the hydrodynamic radius (RH) and the second virial coefficient (A2) of PMPC were independent of the concentration of NaCl (0–0.5 M), whereas both the RH and the A2 of typical polyampholytes depended strongly on the ionic strength. Unfortunately, there is still a lack of studies at a salt concentration much higher than 1.0 M; such studies are of utmost importance to the full understanding of electrostatic excluded-volume and chain stiffness effects. To the best of our knowledge, previous experimental work on the polyelectrolyte brush state is limited to chain dimension in an aqueous solution. In this paper, we will focus on the dependence of the ionic strength of surface-grafted zwitterionic polyelectrolyte chains attached to the solid on the chain conformation.

In the case of free PMAPS, the dependence of RH and intrinsic viscosity of poly(sulfobetaine)s on ionic strength have been well studied by DLS and viscometry measurements;2, 19, 20, 21, 22, 23 the unique phase behaviors have been known to depend on salt concentration,19, 23, 24 additive salt ion species,25 temperature,2 molecular weight and solvent polarity.20, 26 The z-average, mean-square radius of gyration <S2>z and A2 of PMAPS in an aqueous NaCl solution at 1.0 M and in 2,2,2-trifluoroethanol (TFE) were estimated by Huglin and Radwan,22, 27 who also determined the intrinsic viscosity of PMAPS in a θ-solvent. With increasing salt concentration in an aqueous solution above the θ-concentration, greater chain dimensions of PMAPS were observed in an aqueous solution because the attractive electrostatic interaction among sulfobetaine groups was neutralized by the screening effect of salt ions.28 Kato et al. estimated the <S2>z and θ-concentration of PMAPS in an aqueous NaCl solution at 0.060 M with static light scattering (SLS) for polymers with a weight-average molecular weight (Mw) in the range of 5.4 × 104 to 5.0 × 106. However, the MWD of polymers was not clarified in their report. Polymers with a broad MWD are unfavorable for the estimation of chain dimensions.

In this study, we prepared a well-defined polyelectrolyte brush by surface-initiated atom transfer radical polymerization of MAPS and MPC monomers from SiNPs with a diameter of ∼100 nm. The chain dimensions and intermolecular interactions of surface-grafted and unbound PMAPS and PMPC were estimated in aqueous NaCl solutions at various salt concentrations (Cs) from 0 to 5.0 M by SLS, DLS and synchrotron small-angle X-ray scattering (SAXS). In particular, the effects of salt concentration on the chain conformation of surface-grafted PMAPS and PMPC chains on SiNPs will be discussed.

Experimental procedures

Materials

Copper (I) bromide (CuBr, Wako Pure Chemicals, Osaka, Japan, 99.9%) was purified by successive washing with acetic acid and ethanol and then dried under vacuum. 2-(Dimethylamino)ethyl methacrylate (Wako Pure Chemicals, 98%), 2,2′-dipyridyl (bpy, Wako Pure Chemicals, 99.5%), 1-ethyl-3-methylimidazolium chloride (EMImCl, Merck, KGaA, Darmstadt, Germany, 98%) and 1,3-propane sultone (Aldrich, St Louis, MO, USA, 99%) were used as received. TFE (Tokyo Chemical, 99.0%) was carefully degassed by a freeze-pump-thaw process before dilution of CuBr and bpy. MAPS,29 MPC6 and tris(2-(dimethyl)aminoethyl) amine (Me6TREN)30 were synthesized using previously reported procedures. Deionized water for sample preparation of light scattering and SAXS samples was purified with arium 611UV (Sartorius Stedim Biotech GmbH, Goettingen, Germany, resistivity=18.2 MΩ cm). Silica nanoparticles (SiNPs) with a radius of ∼50 nm dispersed in water (40 wt%) were kindly supplied by Nissan Chemical Industries, Tokyo, Japan. The free PMAPS and PMPC were prepared by free radical homopolymerization of corresponding monomer using 2,2′-azobis(isobutyronitrile) as an initiator in TFE at 60 °C for 24 h. Free polymer samples with a narrow MWD were fractionated by a recycling preparative size-exclusion chromatography system (Japan Analytical Industry, Tokyo, Japan, LC-9104) equipped with an RI detector (JAI RI-7s, Japan) using two columns (JAIGEL GS620-50L, GS320-50L) in an aqueous NaCl solution at Cs=0.2 M as an eluent at a flow rate of 20 ml min−1 at room temperature. The Mw and MWD of the fractionated samples were determined by size-exclusion chromatography measurement using an aqueous NaCl solution at Cs=0.2 M as an eluent calibrated with a series of corresponding polymers as a standard.12 The values of Mw and Mw/Mn of free PMAPS were determined to be 2.47 × 105 g mol−1 and 1.18, respectively. The values of Mw and Mw/Mn of free PMPC were determined to be 2.34 × 105 g mol−1 and 1.12, respectively.

Immobilization of the surface initiator

The surface initiator (2-bromo-2-methyl)propionyloxyhexyltriethoxysilane (BHE)31 was synthesized by hydrosilylation of 5-hexenyl 2-bromoisobutylate treated with triethoxysilane in the presence of the Karstedt catalyst.32 Immobilization of BHE on an SiNP (SiNP-BHE) was accomplished using a previously reported procedure.17, 31 A commercially supplied SiNP suspension (10 ml) was collected in a 500-ml round-bottomed flask and was diluted with 100 ml of ethanol. A mixture of ammonia solution (28% NH3 aqueous solution, 10 ml) and ethanol (180 ml) was added dropwise to the SiNP suspension over 3 h with stirring, and the system was stirred for 2 h at 40 °C. BHE (2 g, 4.8 mmol) diluted with ethanol (10 ml) was added dropwise to the suspension over 15 min, and the reaction mixture was continuously stirred for another 15 h at 40 °C. SiNP-BHE was then cleaned by consecutive centrifugation and redispersion in ethanol. Finally, the SiNP-BHE suspension in ethanol was solvent exchanged to TFE to obtain a 10 wt% suspension in TFE.

Surface-initiated atom transfer radical polymerization of MAPS and MPC from SiNP

Thereafter, MAPS (0.327 mmol), EMImCl (0.65 g), TFE (3.4 g) and 10 wt% SiNP suspension in TFE (2.5 g) were loaded into a well-dried glass tube with a stopcock, degassed three times by the freeze-thaw process and flushed with argon.33 A copper catalyst solution containing CuBr (0.0075 mmol) and bpy (0.015 mmol) diluted with degassed TFE was placed into another glass tube and injected into the mixture suspension. The resulting reaction mixture was again degassed by repeated freeze-thaw cycles to remove the oxygen and then subsequently sealed off under reduced pressure. The polymerization reaction was carried out in a stirring oil bath at 60 °C for 13 h. The reaction was stopped by opening the glass vessel to air at 0 °C. The reaction mixture was poured into methanol, filtered and dried. SiNP-PMAPS was purified by consecutive redispersion in TFE and reprecipitation in methanol to remove the unreacted MAPS and SiNP-BHE and was finally dried under reduced pressure at 60 °C for 12 h.

Thereafter, MPC (1.55 mmol), EMImCl (0.54 g) TFE (20 g) and a 10 wt% SiNP suspension in TFE (0.5 g) were loaded into a well-dried glass tube with a stopcock, degassed three times by the freeze-thaw process and flushed with argon. A copper catalyst solution containing CuBr (0.016 mmol) and bpy (0.032 mmol) diluted with degassed TFE was placed in another glass tube and injected into the mixture suspension. The resulting reaction mixture was again degassed by repeated freeze-thaw cycles to remove the oxygen and then subsequently sealed off under reduced pressure. The polymerization reaction was carried out in a stirring oil bath at 60 °C for 24 h. The reaction was stopped by opening the glass vessel to air at 0 °C. The reaction mixture was cleaned by three cycles of centrifugation and redispersion in methanol to remove the unreacted MPC. Finally, the SiNP-PMPC suspension in methanol was poured into tetrahydrofuran, filtered and dried under reduced pressure at 60 °C for 12 h.

To determine the Mn and Mw/Mn of the surface-grafted polymer on SiNPs, PMAPS and PMPC chains were cleaved from the surface as follows. SiNP-PMAPS and SiNP-PMPC were immersed in a solution mixture of 10 wt% hydrogen fluoride aqueous solution (5 ml) and an aqueous NaCl solution at Cs=0.2 M (10 ml) for 3 days in a plastic vessel and slowly neutralized using a sodium hydrogen carbonate aqueous solution. The resulting solutions were collected in a dialysis membrane tube (Spectra/Por 3, Standard regulated cellulose membrane, Mw=3.50 × 103 g mol−1) and dialyzed in water to remove inorganic salt ions for 3 days and were freeze dried from aqueous solution. The values of Mn and Mw/Mn of the obtained surface-grafted PMAPS and PMPC on an SiNP were determined by size-exclusion chromatography measurement using an aqueous NaCl solution at Cs=0.2 M as an eluent calibrated with a series of corresponding polymers as a standard. The characteristics of SiNP-PMAPS and SiNP-PMPC used in this study are listed in Table 1. The values of weight loss measured by thermogravimetric analysis (Perkin-Elmer Pyris TGA) of SiNP-PMAPS and SiNP-PMPC were determined to be 14.8 and 7.1 wt%, respectively.

Table 1 Characteristics of SiNP-PMAPS and SiNP-PMPC
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Measurements

Both SLS and DLS experiments of the free polymer and surface-grafted polymer on SiNPs in aqueous NaCl solutions at 25 °C were carried out at a scattering angle (θ) ranging from 30 to 150° using a goniometer system (ALV CGS-3-TAC/LSE-5004, Langen, Germany) using a HeNe laser (wavelength λ=632.8 nm) with a power of 22 mW. The Rayleigh ratio at a scattering angle of θ=90° was based on that of pure toluene at a wavelength of 632.8 nm at 25 °C.34 The autocorrelation function was obtained by pseudo-cross-correlation of the signals from two photomultipliers to suppress noise. The samples for SLS and DLS measurements had four different concentrations in aqueous NaCl solutions (Cs=0–5.0 M) contained in 10-mm diameter quartz cells. The scattering vector (q) was defined as 4πnssin(θ/2)/λ, where ns is the refractive index of the solvent.

The densities of aqueous NaCl solutions and polymer solutions were measured at 25 °C using a density meter (Kyoto Electronics Manufacturing DA-505, Kyoto, Japan). The density of an aqueous NaCl solution at 25 °C can be expressed by35

where m and ρ0 are the molal concentration and density (0.99705 g cm−3) of pure water, respectively. The value of m is then converted to Cs (M) by

where M is the molecular weight of NaCl. The values of the refractive index (ns) for aqueous NaCl solutions for Cs from 0 to 5.0 M were measured at 25 °C using a multi-wavelength refractometer (Kyoto Electronics Manufacturing RA-500NW-S, λ=633 nm). The value was found to be expressed by

where n0 is the refractive index (1.3313) of pure water. The viscosity of an aqueous NaCl solution at 25 °C can be expressed as follows:36

Here, η0 is the viscosity (8.902 × 10−3 g cm−1 s−1) of pure water.

The specific refractive index increments (dn/dc) of free polymers in aqueous NaCl solutions for Cs from 0 to 5.0 M were measured using a differential refractometer (Otsuka Electric DRM-1020, Osaka, Japan, λ=633 nm). The values of dn/dc for free PMAPS (Mw=1.36 × 105 g mol−1, Mw/Mn=3.07) in aqueous NaCl solutions at Cs=0.050, 0.10, 0.50, 1.0, 3.0 and 5.0 M were determined to be 0.1347, 0.1343, 0.1300, 0.1251, 0.1124 and 0.1023 g−1 cm3, respectively. The values of dn/dc for free PMPC (Mw=2.43 × 105 g mol−1, Mw/Mn=8.90) in aqueous NaCl solutions at Cs=0, 0.050, 0.50, 1.0, 3.0 and 5.0 M were likewise determined to be 0.1415, 0.1405, 0.1363, 0.1322, 0.1190 and 0.1038 g−1 cm3, respectively. The value of dn/dc for free PMAPS in an aqueous NaCl solution at another unmeasured Cs was also determined to give the same Mw of free PMAPS in an aqueous NaCl solution at Cs=0.10 M.

Small-angle X-ray scattering experiments of surface-grafted polymer chains on SiNPs in aqueous NaCl solutions at room temperature were carried out at the BL03XU37 beamline of SPring-8 at an incident X-ray wavelength λ of 0.1 nm with a sample-to-detector distance of 7994 mm. The scattered intensity was detected using an imaging plate with 3000 × 3000 pixels over a scattering vector range from 0.02 to 0.6 nm−1. The scattering vector (q) as defined by 4π sin(θ)/λ was calibrated by the average of 6 peaks of dry collagen. The samples for SAXS measurements had four different concentrations (Cp=1.0–2.0 mg cm−3) of SiNP-PMAPS and SiNP-PMPC in aqueous NaCl solutions (Cs=0–5.0 M) contained in 2-mm diameter quartz capillaries.

Polymer solutions for scattering experiments were carefully prepared by a gravimetric method. After the free polymer and surface-grafted polymer on SiNPs were sufficiently dried under reduced pressure for >24 h at 60 °C, the samples were dissolved in an aqueous NaCl solution at 40 °C for 12 h. The solutions of surface-grafted polymer on SiNPs were sonicated for 1 h to yield well-dispersed nanoparticle solutions. The resulting solutions were filtered with DISMIC filter units (polytetrafluoroethylene, PTFE, pore size of 0.45 μm) just before the measurements and poured directly into measurement cells in a clean bench. The weight fraction (Wp) was then converted to Cp (g cm−3) by:

where ρs and υp are the densities of solvent and the partial specific volume of the polymer, respectively. The values of υp for free PMAPS in aqueous NaCl solutions at Cs=0.050, 0.10, 0.50, 1.0, 3.0 and 5.0 M were determined to be 0.690, 0.688, 0.682, 0.678, 0.697 and 0.702 cm3 g−1, respectively. The values of υp for free PMPC in the aqueous NaCl solutions at Cs=0, 0.10, 0.50, 1.0, 3.0 and 5.0 M were determined to be 0.729, 0.742, 0.759, 0.763, 0.762 and 0.764 cm3 g−1, respectively.

Results and Discussion

Chain dimensional properties of free PMAPS and PMPC

The values of A2 of free PMAPS and PMPC in aqueous NaCl solutions at Cs=0–5.0 M are summarized in Tables 2 and 3. Details are described in the Supplementary Information. Figure 1 shows a Cs dependence of MwA2 for free PMAPS (○) and PMPC (□) in an aqueous NaCl solution at 25 °C. The MwA2 for PMPC gradually increased with increasing Cs, whereas in the previous study,17 the same parameter was almost constant over the entire Cs region from 0 to 0.5 M (48.8 cm g−1). It is possible that the small difference between our study and the previous one could be attributed to the MWD (Mw/Mn=1.50) of PMPC. However, the MwA2 for PMAPS increased sharply with increasing Cs in the Cs region below 0.5 M and become almost constant in the higher Cs region ∼3.0 M. As A2 reflects the volume exclusion of a polymer chain, Figure 1 suggests that the Cs dependence of the repulsive interaction between PMAPS chains in an aqueous NaCl solution is much stronger than that of PMPC. The value of MwA2 for PMAPS was observed to be 0 in an aqueous NaCl solution at Cs=0.074 M. Therefore, we defined an aqueous NaCl solution at Cs=0.074 M as the θ-concentration (Cs,θ) of PMAPS. Kato et al.28 previously found using SLS that the Cs,θ was 0.060 M for PMAPS at 30 °C is an aqueous NaCl solution. It is possible that the small difference between Cs,θ=0.074 M in our study and Cs,θ=0.060 M in the previous study could be attributed to the MWD of PMAPS and the experimental temperature.

Table 2 Results from SLS and DLS measurements of free PMAPS in aqueous NaCl solutions at Cs=0.050–5.0 M
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Table 3 Results from SLS and DLS measurements of free PMPC in aqueous NaCl solutions at Cs=0–5.0 M
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Figure 1
figure 1

Dependence of MwA2 on Cs for free PMAPS (○) and PMPC (□) in aqueous NaCl solutions. PMAPS, poly[3-(N-2-methacryloyloxyethyl-N,N-dimethyl) ammonatopropanesulfonate]; PMPC, poly(2-methacryloyloxyethyl phosphorylcholine).

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The values of the diffusion coefficient at an infinite dilution (D0), the hydrodynamic radius (RH) and the concentration coefficient of the diffusion coefficient (kD) of free PMAPS and PMPC in aqueous NaCl solutions at Cs=0–5.0 M are summarized in Tables 2 and 3. Details are described in the Supplementary Information. Figure 2 shows the Cs dependence of RH for free PMAPS (○) and PMPC (□) in aqueous NaCl solutions at 25 °C. The RH of PMPC was almost constant regardless of Cs, whereas the RH for PMAPS increased with increasing Cs. The RH values of PMPC in aqueous NaCl solutions were larger than those of PMAPS at all Cs, despite that the weight average degree of polymerization (Nw=792) of PMPC is less than that of PMAPS (Nw=884). Considering that the RH reflects the hydrodynamic dimensions of a polymer chain, the larger RH of PMPC implies that the main chain stiffness of PMPC is higher than that of PMAPS in the solution.

Figure 2
figure 2

Dependence of RH on Cs for free PMAPS (○) and PMPC (□) in aqueous NaCl solutions. PMAPS, poly[3-(N-2-methacryloyloxyethyl-N,N-dimethyl) ammonatopropanesulfonate]; PMPC, poly(2-methacryloyloxyethyl phosphorylcholine).

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The value of kD for flexible polymer chains is defined by the following equation:38

where k′H is a universal constant for free chains irrespective of the kind of polymers and molecular weight. The value of k′H for typical flexible polymers in a good solvent was reported over a range from 4 to 6.38 The value of k′H calculated from the literature data39, 40 for atactic poly(methyl methacrylate) in acetonitrile at 44.0 °C (θ-solvent) is estimated to be approximately 1.3–1.8. The values of k′H for free PMAPS and PMPC were calculated from equation (6) using the measured values of A2, Mw, υp, kD and RH. Figure 3 shows the Cs dependence of k′H for free PMAPS (○) and PMPC (□) in aqueous NaCl solutions at 25 °C, together with that of free poly(styrene sulfonate sodium salt) (NaPSS; Mw=2.56 × 105 g mol−1)41 (Δ) and poly(2-acrylamido-2-methylpropanesulfonate sodium salt) (NaPAMPS; Mw=2.76 × 105 g mol−1)42, 43 (◊) with the same molecular weight. The values of k′H for PMAPS and PMPC in aqueous NaCl solutions were revealed to be 1.5–8, which may be regarded as a θ-state and a good solvent state, indicating the reduction in intramolecular and intermolecular interaction between polymer chains with increasing Cs. However, k′H of the typical polyanions, such as NaPSS, NaPAMPS and sodium carboxylmethyl cellose,44 apparently decreased with increasing Cs until eventually reaching a θ-state and poor solvent state because the intramolecular and intermolecular repulsive interactions between polymer chains were screened by hydrated ions.

Figure 3
figure 3

Dependence of k′H on Cs for free PMAPS (○) and PMPC (□) in aqueous NaCl solutions, together with that of free NaPSS41 (▵) and NaPAMPS42, 43 (◊) with the same molecular weight. PMAPS, poly[3-(N-2-methacryloyloxyethyl-N,N-dimethyl) ammonatopropanesulfonate]; PMPC, poly(2-methacryloyloxyethyl phosphorylcholine).

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Characterization of SiNP-PMAPS and SiNP-PMPC

The scattering form factor (P(q), which is related to ΔI(q)/ΔI(0) (ΔI(q) is the experimental excess scattering intensity) from the SAXS data for SiNP-BHE in TFE, may be compared with the solid sphere model with polydispersity. According to Aragón and Pecora,45 the scattering function for the assumed Schulz-distributed solid spheres with a radius of R is expressed by

and

where α(R), fz(R), z and are the polarizability of the particle, the Schulz distribution function, the width of the distribution and the average radius of the sphere, respectively. α(R) depends on the size through the bulk volume of the particle. Polydispersity (p) for a Schulz distribution can be written as p2=1/(z+1). The experimental data for SiNP-BHE (C=1.38 mg cm−3), which were used for preparation of SiNP-PMAPS, can be described assuming Schulz-distributed spherical particles with a radius of R=55.0 nm and an exponential parameter of z=180, corresponding to a polydispersity of p=0.074, as shown in Figure 4. These values of SiNP-BHE used SiNP-PMPC were determined by the same method to be R=56.0 nm, z=180 and p=0.074.

Figure 4
figure 4

SAXS profiles of SiNP-BHE in TFE. The solid curves represent the theoretical values for the assumed Schulz-distributed spherical particles with a radius of R=55.0 nm and an exponential parameter of z=180. SAXS, small-angle X-ray scattering; SiNP-BHE, immobilization of (2-bromo-2-methyl)propionyloxyhexyltriethoxysilane on a SiNP; TFE, 2,2,2-trifluoroethanol.

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The graft density of a polymer brush on the SiNP surface is expressed by

where ρsilica, w and NA are the density of silica (1.6 g cm−3), the weight loss of a polymer and Avogadro’s number, respectively. The graft densities of PMAPS and PMPC brushes on a SiNP surface were calculated using equation (9) to be 0.129 and 0.065 chains per nm2, respectively. The average numbers of graft PMAPS and PMPC chains per SiNP were estimated to be 4910 and 2590 chains, respectively, assuming the aforementioned graft density and the SiNP surface area. These values of SiNP-PMAPS and SiNP-PMPC are summarized in Table 1.

Dimensions of grafted chains of PMAPS and PMPC on SiNP

The typical autocorrelation function (g2(t)−1) and relaxation spectrum (A(τ)) measured by DLS for SiNP-PMAPS in an aqueous NaCl solution at Cs=5.0 are shown in Figure 5. The concentration of SiNP-PMAPS and the scattering angle were C=0.47 mg cm−3 and θ=90°, respectively. A(τ) at the relaxation time (τ) was calculated from the intensity of g2(t)−1 at time (t) by a CONTIN analysis.46, 47 A(τ) was observed as a single sharp peak. A(τ) of all concentrations and scattering angles for SiNP-PMAPS and SiNP-PMPC solutions showed a unimodal distribution and sharp peak, indicating the homogenous dispersion of SiNP-PMAPS and SiNP-PMPC in aqueous NaCl solutions at various Cs without any aggregations. By extrapolating to q=0 and C=0, the values of D0 and RH for SiNP-PMAPS in an aqueous NaCl solution at Cs=5.0 M were determined to be 1.84 × 10−8 cm2 s−1 and 71.2 nm, respectively. The values of D0 and RH for SiNP-PMAPS and SiNP-PMPC in aqueous NaCl solutions at each Cs were also determined using the same method. The values of D0 and the hydrodynamic radius of a polymer layer (RH,brush) calculated from (RH−Rc)/2 are summarized in Tables 4 and 5.

Figure 5
figure 5

Typical autocorrelation function (○) obtained by DLS for SiNP-PMAPS and relaxation spectrum (□) calculated from the autocorrelation function. The concentration of SiNP-PMAPS in an aqueous NaCl solution at Cs=5.0 M and the scattering angle are Cp=0.47 mg cm−3 and θ=90°. DLS, dynamic light scattering; SiNP-PMAPS, silica nanoparticles immobilized with poly[3-(N-2-methacryloyloxyethyl-N,N-dimethyl) ammonatopropanesulfonate].

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Table 4 Results from DLS and SAXS measurements of SiNP-PMAPS in aqueous NaCl solutions at Cs=0.050–5.0 M
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Table 5 Results from DLS and SAXS measurements of SiNP-PMPC in aqueous NaCl solutions at Cs=0–5.0 M
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Figure 6a shows the SAXS profiles for SiNP-PMAPS in aqueous NaCl solutions for Cs over a range from 0.050 to 5.0 M. The SAXS profiles showed smooth minima in the SiNP-PMAPS form factor, which was slightly shifted to a low-q region, unlike the SiNP-BHE form factor. SiNP-PMAPS in an aqueous NaCl solution is expected to form a core-shell structure, as shown in the inset of Figure 6a. Here, we estimated the radius of gyration of the polymer layer of SiNP-PMAPS from the SAXS profile using a core-shell model analysis, taking the interacting excluded-volume chains into consideration. The scattering form factor for the core-shell model contains four terms as shown below:48

Figure 6
figure 6

(a) SAXS profiles of SiNP-PMAPS in aqueous NaCl solutions at Cs over a range from 0 to 5.0 M. The solid curves represent the values calculated from equations (7), (8) and (10), (11), (12), (13), (14), (15), (16), (17) with the two model parameters. (b) Radial electron density profiles for SiNP-PMAPS in aqueous NaCl solutions at Cs=0.050 (○), 0.074 (□), 0.50 (▵), 1.0 (•), 3.0 (▪) and 5.0 (▴) M estimated from the SAXS profile using a core-shell model analysis. SAXS, small-angle X-ray scattering; SiNP-PMAPS, silica nanoparticles immobilized with poly[3-(N-2-methacryloyloxyethyl-N,N-dimethyl) ammonatopropanesulfonate].

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where N is the number of surface-grafted polymer chains on SiNP, ΔZe the excess electron density, Pcore(q) a scattering function for a rigid sphere assuming Schulz distribution calculated from equations (7) and (8), P′(q) the effective form factor of a chain in the corona chains expressed by the following equations (11) and (12), Score−chain(q) the structure factor between the core and corona chains expressed by equations (13) and (14) and Achain(q) the form-factor amplitude of the chain expressed by equation (14).

and

where PPWC(q), ν and s are the scattering functions for an infinitely thin perturbed wormlike chain,49 parameter-related surface coverage of chains and radius of gyration of the polymer layer, respectively.

and

where Rc and Zchain(r) are the core radius and the average radial electron density profile of the corona chains, respectively.

The excess electron density of the core (ΔZe,core) and chain (ΔZe,chain) are defined as

and

where ne,core and Msilica are the number of electrons and the molecular weight of the silica, respectively, whereas ne,brush and M0,brush are the number of electrons and the molecular weight per repeating unit of the polymer brush, respectively. The density of the polymer brush in the solvent (ρbrush) is defined as (1−υbrushρs)Cbrush+ρs, where the υbrush is the partial specific volume of the polymer brush, which was determined by fitting the experimental data of the SAXS profile with equations (7), (8) and (10), (11), (12), (13), (14), (15), (16), (17) in the low-q region. However, the accurate concentration of the polymer brush (Cbrush) has a distribution along with the distance from the nanoparticle surface to the outer solvent phase due to the swollen brush structure. Therefore, here we used the apparent concentration of the polymer brush in the solvent, Cbrush,app, instead of Cbrush, by calculation using the following expression:

The experimental SAXS profile for SiNP-PMAPS in an aqueous NaCl solution at Cs=0.050 M was close to the theoretical profile obtained from equations (7), (8) and (10), (11), (12), (13), (14), (15), (16), (17) for a core radius Rc=55.0 nm, core polydispersity p=0.074, polymer layer radius s=9.5 nm and υbrush=0.69 g−1 cm3 as shown in the Figure 6a. The values of s and υbrush for SiNP-PMAPS in aqueous NaCl solutions at various Cs values were also estimated using the same method, and these values are listed in Table 4. The solid lines in Figure 6a are values calculated from equations (7), (8) and (10), (11), (12), (13), (14), (15), (16), (17) with the two model parameters. The value of υbrush was close to that of υp of the free PMAPS in an aqueous NaCl solution at a given Cs. The experimental SAXS profiles for SiNP-PMAPS in aqueous NaCl solutions at all Cs values were close to the profiles calculated from equations (7), (8) and (10), (11), (12), (13), (14), (15), (16), (17) with the two model parameters. Figure 6b shows the radial profiles for SiNP-PMAPS in aqueous NaCl solutions at various Cs values estimated from the SAXS profile base on the core-shell model incorporated with interaction among the surface-grafted perturbed wormlike chains, which are the so-called interacting self-avoiding chains.48

Figure 7a shows the SAXS profiles for SiNP-PMPC in aqueous NaCl solutions at Cs values over a range from 0 to 5.0 M. The characteristic parameters of the SiNP-PMPC in aqueous NaCl solutions at various Cs estimated by the procedure mentioned above are summarized in Table 5. The solid lines in Figure 7a are the theoretical curves calculated from equations (7), (8) and (10), (11), (12), (13), (14), (15), (16), (17) with a core radius of Rc=56.0 nm, core polydispersity of p=0.074 and the model parameters listed in Table 5. The scattering factor for SiNP-PMPC in aqueous NaCl solutions is described by the core-shell model, taking into account the interacting self-avoiding chains and assuming a Schulz-distributed core with two fitting parameters. The value of υbrush is close to that of υp of free PMPC in aqueous NaCl solutions for a given Cs, except for Cs=5.0 M. Figure 7b illustrates the radial profiles for SiNP-PMPC in aqueous NaCl solutions at various Cs values estimated from the SAXS profile and the core-shell model containing the interacting self-avoiding chains.

Figure 7
figure 7

(a) SAXS profiles of SiNP-PMPC in the aqueous NaCl solutions at Cs over a range from 0 to 5.0 M. The solid curves represent the values calculated from equations (7), (8) and (10), (11), (12), (13), (14), (15), (16), (17) with the two model parameters. (b) Radial electron density profiles for SiNP-PMPC in aqueous NaCl solutions at Cs=0 (○), 0.050 (□), 0.50 (▵), 1.0 (•), 3.0 (▪) and 5.0 (▴) M estimated from SAXS profile using a core-shell model analysis. SAXS, small-angle X-ray scattering; SiNP-PMAPS, silica nanoparticles immobilized with poly[3-(N-2-methacryloyloxyethyl-N,N-dimethyl) ammonatopropanesulfonate].

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Figure 8 shows the Cs-dependence of RH,brush and s for SiNP-PMAPS (○) and SiNP-PMPC (□) in aqueous NaCl solutions. The RH,brush and s for SiNP-PMPC were constant over the entire Cs region from 0 to 5.0 M. The Cs dependence of RH,brush for SiNP-PMPC is in good agreement with that reported by Matsuda et al., who also did not observe a swelling of the PMPC brush upon addition of up to 0.5 M NaCl.17 These results imply that Cs dependence of the repulsive interaction between polymer chains for SiNP-PMPC in an aqueous NaCl solution is similar to that of the free PMPC. However, the value of s for SiNP-PMAPS increased with increasing Cs, whereas RH,brush for SiNP-PMAPS slightly decreased with increasing Cs in the Cs region below 0.5 M, and that parameter become almost constant in the Cs region above 0.5 M. Polzer et al.16 reported that the RH of PMAPS brush shell on a colloidal particle consisting of a divinylbenzene cross-linked polystyrene core (PS-co-DVB/PMAPS) was almost constant in the Cs region below 0.5 M, but increased with increasing Cs in the Cs region above 0.5 M.16 The RH,brush (7.7 nm) of the PMAPS brush for SiNP-PMAPS in an aqueous NaCl solution at Cs=1.0 M was larger than that (4.0 nm) of the PMAPS brush shell in the previous report at the same Cs, despite that the Mw (3.02 × 104 g mol−1) of the surface-grafted PMAPS chains in our study was smaller than that (Mw=6.96 × 104 g mol−1) of the previous study. It is possible that the difference in the chain dimension of the PMAPS brush between SiNP-PMAPS (σ=0.129 chains per nm2) and PS-co-DVB/PMAPS (σ=0.08 chains per nm2) can be attributed to graft density. These results imply that the Cs dependence of the repulsive interaction between polymer chains for SiNP-PMAPS in an aqueous NaCl solution is similar to that of the PMAPS brush shell for PS-co-DVB/PMAPS and the free PMAPS, except for the Cs-dependence of RH,brush for SiNP-PMAPS.

Figure 8
figure 8

Dependence of s and RH,brush on NaCl concentration for SiNP-PMAPS (○) and SiNP-PMPC (□) in aqueous NaCl solutions at Cs in the range 0–5.0 M. SiNP-PMAPS, silica nanoparticles immobilized with poly[3-(N-2-methacryloyloxyethyl-N,N-dimethyl) ammonatopropanesulfonate].

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The Mw dependence of the z-average, mean-square radius of gyration (〈S2〉z) for the free PMAPS in a θ-state in an aqueous NaCl solution at 0.074 M is given by12

The thickness of the polymer brush layer for SiNP-PMAPS was estimated to be 9.5 nm, which was much larger than the 〈S2〉z1/2=3.1 nm calculated from equation (18) for free PMAPS chains with the same Cs and Mw. The chain dimensions of the polymer brush for SiNP-PMAPS in an aqueous solution were actually larger than the free PMAPS. It is well known that polymer chains in concentrated polymer brushes are extended because of the excluded-volume effect of neighboring polymer chains.10 Thus, significant change seems to have occurred in the chain conformation between the brush and the free polymer.

It is well known that ρ, defined as the ratio of the radius of gyration to the hydrodynamic radius, is a universal constant for free chains almost irrespective of the chemical structure and molecular weight of polymers. The values of ρ estimated from s measured by SAXS and RH,brush measured by DLS of the polymer layer for SiNP-PMAPS and SiNP-PMPC in aqueous NaCl solutions at all Cs are summarized in Tables 4 and 5. The value of ρ for SiNP-PMPC in aqueous NaCl solutions at all Cs was approximately constant (1.19–1.26) and was similar to those of typical flexible polymers in θ-solvent and good solvents (1.2–1.5).50 The ρ for SiNP-PMAPS increased with increasing Cs in the Cs region below 0.5 M and became almost constant in the Cs region above 0.5 M. The values (2.27–2.59) of ρ for SiNP-PMAPS in the Cs region above 0.5 M were larger than those of reference data for PMAPS in an aqueous NaCl solution for Cs in the range 0.06–1.0 M at 30 °C (1.1–1.3)28 and the Gaussian chain limit (1.48).50 Thus, the chain conformation of PMAPS and PMPC brushes on the SiNP surface behaves like a semi-flexible and flexible polymer chain, respectively. It is possible that the difference in the chain conformation between PMAPS and PMPC brushes could be attributed to the broad MWD and low graft density of PMPC because of the following reasons.

de Vos et al.14 reported that the internal structure of the polymer brush by numerical self-consistent field theory is strongly influenced by polydispersity, as shown in Figure 9. Short chains are compressed close to the grafting interface, whereas long chains have a characteristic flower-like conformation. These long chains stretch strongly (forming a stem) when surrounded by shorter chains and decrease their stretching (forming a crown) when only surrounded by longer chains. These findings imply that chain conformation of the PMPC brush with a broad MWD on a SiNP surface behaves like a Gaussian coil. Therefore, our report may be the first experimental report on the crucial difference in the chain conformation between the brush on a SiNP and the free PMAPS with salt concentration dependence.

Figure 9
figure 9

Schematic cross-sectional view of the internal structure of surface-grafted polymer chains with polydispersity on SiNPs. SiNP, silica nanoparticle.

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Conclusions

We performed SLS, DLS and SAXS for PMAPS and PMPC in aqueous NaCl solutions and found that PMPC had a relatively stiff structure in an aqueous NaCl solution for a wide range of Cs (0–5.0 M), unlike PMAPS. This is because the RH of PMPC in aqueous NaCl solutions was larger than that of the PMAPS, whereas the weight average degree of polymerization (Nw=792) of PMPC was less than that of PMAPS (Nw=884). The k′H values of both PMAPS and PMPC in aqueous NaCl solutions were higher than 1.5 in all Cs regions, indicating that the polymers were in the θ-state or good solvent state. The scattering factors for SiNP-PMAPS and SiNP-PMPC in aqueous NaCl solutions at Cs=0–5.0 M were well described by the core-shell model, taking into account interacting self-avoiding chains and assuming a Schulz-distributed core with two fitting parameters. From the ratio of the radius of gyration measured by SAXS to the hydrodynamic radius measured by DLS for the polymer layer for SiNP-PMAPS and SiNP-PMPC in aqueous NaCl solutions at Cs=0–5.0 M, the chain conformations of PMAPS and PMPC brushes on a silica surface resembled semi-flexible and flexible polymer chains, respectively.