Colloid Polym Sci DOI 10.1007/s00396-013-2923-z
ORIGINAL CONTRIBUTION
Synthesis and characterization of polystyrene chains on the surface of silica nanoparticles: comparison of SANS, SAXS, and DLS results Polystyrene chains on silica nanoparticle Chang J. Kim · Katrin Sondergeld · Markus Mazurowski · Markus Gallei · Matthias Rehahn · Tinka Spehr · Henrich Frielinghaus · Bernd Stuhn ¨ Received: 15 January 2013 / Accepted: 6 February 2013 © Springer-Verlag Berlin Heidelberg 2013
Abstract An extensive characterization of well-defined polystyrene (PS)-grafted silica nanoparticles is reported. Bare SiO2 particles (diameter 50 nm) were functionalized with a suitable initiator for the surface-initiated anionic polymerization of styrene. Both grafted and free PS chains were characterized and compared by size-exclusion chromatography (SEC). PS-grafted particles were characterized by transmission electron microscopy (TEM), thermogravimetric analysis (TGA), small-angle x-ray scattering (SAXS), small-angle neutron scattering (SANS), and dynamic light scattering (DLS). The thickness of the grafted PS chains was obtained by SANS and DLS and scaled with Mw0.6 displaying similar behavior with free PS chains in the same solvent used, tetrahydrofuran (THF). Grafting densities obtained from SANS data and TGA were found to be small, and the thickness of the grafted PS chains determined by SANS was found to be similar to 2Rg of free PS chains in THF. Both results are consistent with a “coil-like” conformation of the grafted PS chains. Keywords Small angle scattering · Light scattering · Nanoparticle · Grafting · Polymer conformation C. J.Kim () · B. St¨uhn · T. Spehr Institut f¨ur Festk¨orperphysik, Technische Universit¨at Darmstadt, Hochschulstrasse 6, 64289 Darmstadt, Germany e-mail:
[email protected] K. Sondergeld · M. Mazurowski · M. Gallei · M. Rehahn () Ernst-Berl-Institut f¨ur Technische und Makromolekulare Chemie, Technische Universit¨at Darmstadt, Petersenstrasse 22, 64287 Darmstadt, Germany e-mail:
[email protected] H. Frielinghaus J¨ulich Centre for Neutron Science, Lichtenbergstrasse 1, 85747 Garching, Germany
Introduction Polymer chains on solid surfaces are compelled to assume conformation features that differ considerably from those in the unperturbed bulk state, and their physical properties may differ quite severely as well [1, 2]. Conformational perturbations of polymer chains even may justify, considering the “surface-constrained” material as an individual phase, sometimes called “interphase.” However, we are far away from understanding these interphases profoundly, and this knowledge might help in explaining and tailoring the property profiles of interphase-dominated polymeric systems like nanocomposites or thin films and layers, for example. Recently, polymer chains on spherical nanoparticles attracted much attention due to their wide applications including stabilization of colloidal suspensions [3, 4], enhancement of physical properties in polymer nanoparticle composites [5–7], and their potential use in electronics, optics, and sensors [8–12]. These applications depend on the dispersion state of individual nanoparticles. Dispersion is affected by the interaction between chains on each of the attached sites and that between chains and surrounding media such as solvent molecules and polymer matrices. One important issue then is the profound analysis of well-defined model interphases consisting of polymer chains having defined length, polydispersity, and architecture, which are immobilized by covalent bonds and with a defined grafting density at solid surfaces. Such an analysis moreover requires a systematic variation of all parameters contributing to the interphase as well as for selective visualization of the surface-anchored chains by appropriate analytical techniques. Relevant parameters affecting the conformation of polymer chains on the spherical substrate are known to be grafting density, molar mass of the grafted polymer chains, and curvature of the nanoparticles.
Colloid Polym Sci
Numerous studies were made to characterize the structure of the grafted polymer chains on the nanoparticles using dynamic light scattering (DLS) [13–16] and smallangle neutron scattering (SANS) [17–20]. Some works focused on the scaling of the thickness (H) with molar mass (Mw ) and grafting densities (σ ) of the grafted polymer layers [14–16]. Scaling relations between H and Mw were reported based on DLS studies, and the main factors governing polymer conformation were found to be the size of the core of the spherical particles, the grafting density, and the molar mass of the grafted chains. We note that DLS probes the hydrodynamic size of the particles. SANS, on the other hand, provides direct access to the static structure of the polymer layer. In SANS studies, grafted polymer chains were characterized via contrast matching of core and solvent to access the structure of the grafted polymer layer. Such measurements are also possible for grafted particles in a polymer matrix. Chevigny et al. [17] reported that the thickness of the grafted chains obtained from SANS measurements were consistent with two times the radius of gyration (Rg ) of the grafted polymer. In the present paper, we selected silica nanoparticles with a diameter of ∼ 50 nm as supports for our investigations and decorated those particles with PS. We functionalized bare silica nanoparticles with (3-chloropropyl) triethoxysilane to obtain a thin initiator shell, which is suitable for surface-initiated anionic polymerization of styrene via halogen-metal exchange with, e.g., butyllithium compounds. By this methodology, we were able to obtain defined surface-anchored PS with low polydispersities, adjustable molar masses, and different grafting densities. Nevertheless, we are aware of the fact that successful living anionic polymerization of styrene nearby surfaces of silica nanoparticles is a great challenge: these particles are known to contain SiOH functions, ethanol, water, and other contaminants, which severely interfere with carbanionic centers, and effective concepts were requested to eliminate the influence of those groups reliably [21–23]. In the following, we describe how we immobilized appropriate precursor groups on the silica surfaces, how we deactivated disturbing protic groups, how we activated subsequently surface-immobilized initiator functions, and finally how we polymerized styrene from the silica surfaces. Both “free” PS, which could be obtained by adding additional initiator for the anionic polymerization and surface-attached PS were characterized by size-exclusion chromatography (SEC). In the latter case, the polymers could be detached from the surface by etching the silica particles with hydrofluoric acid. The grafted particles were additionally studied by transmission electron microscopy (TEM). Three samples of PS-grafted silica particles differing in molar masses and grafting
densities were synthesized and used for a structural characterization. DLS, SAXS, and finally SANS were applied as complementary tools, and their results will be compared.
Experimental section Materials and methods All solvents and reagents were purchased from Alfa Aesar, Sigma Aldrich, Fisher Scientific, and ABCR and used as received unless otherwise stated. Tetrahydrofuran (THF), toluene, and cyclohexane were distilled from sodium/benzophenone under reduced pressure (cryotransfer) prior to the addition of 1,1-diphenylethylene and n-butyllithium (n-BuLi) as well as a second cryotransfer. 1,1-Diphenylethylene (DPE) was dried by titration with n-BuLi and distilled after a deep red color was achieved. Ethanol was dried with magnesium and then distilled. Styrene was dried over calcium hydride (CaH2 ) and freshly distilled prior to use. Zellu Trans 6.0 for dialysis was purchased from Roth. All syntheses were carried out under an atmosphere of nitrogen or argon using Schlenk technique or a glove box equipped with a Coldwell apparatus. The silica particle dispersion was received from Merck. Synthesis Functionalization and drying procedure of silica particles 10 g bare silica particles (average diameter of 50 nm) received as dispersion in a mixture of ethanol and water (vol% 7/3) were treated with 1.204 g (3-chloropropyl) triethoxysilane (5 mmol). The mixture was stirred at room temperature for 1 h followed by stirring for 12 h at 60 ◦ C. After that time, 900 mL ethanol was added successively whilst removing the ethanol/water mixture by azeotropic vacuum distillation. Afterwards, 2.229 g methyltriethoxysilane (12.5 mmol) and 0.25 mL ammonia were added at room temperature and stirred for 1 h before heating the dispersion to 60 ◦ C. Stirring was continued for further 12 h. The dispersion was dialyzed against ethanol for 20 h including two times of solvent exchange. For transferring in a nonpolar and nonprotic solvent, 1.6 L toluene was added continuously while ethanol was removed by vacuum distillation. After the silica dispersion in toluene was carefully concentrated to approximately 25–30 vol% of its original volume, it was set under an atmosphere of nitrogen and diluted to the threefold volume by adding dry cyclohexane. The dispersion was stored in a glove box for further usage.
Colloid Polym Sci
Surface-initiated anionic polymerization of styrene Necessary amount of n-BuLi both for halogen–metal exchange and, hence, for anionic polymerization as well as scavenger to get rid of all residual protic impurities was determinated by previous titration of an aliquot of the prepared functionalized silica dispersion. For a preceding titration, a solution of 2.5 mL THF, 0.5 mL n-BuLi (c = 2.5 M, 1.25 mmol), and 0.44 mL 1,1-diphenylethylene (DPE) (2.5 mmol) was prepared. The intensely red-colored diphenylhexyllithium solution was added with a microliter syringe to a representative 1-mL sample of the silica dispersion diluted with 5 mL THF until a slightly red color remained. In the next step, the functionalized particles were activated via halogen–metal exchange by adding 0.56 mL nBuLi to 800 mg of the functionalized particles in additional 30 mL cyclohexane. The dispersion was stirred at room temperature for 12 h. The indicated amount of styrene was added (sample 1, 4.8 mL; sample 2, 13.8 mL; and sample 3, 15.9 mL), and the mixture was stirred for further 2 h before methanol was added to terminate the active PS chains. Free PS was removed by nanofiltration using an Anodisc 47 membrane (0.02 µm) from Whatman in cyclohexane (3.5 L; 0.8 bar pressure). For characterization of surface-grafted PS, 120 mg of the grafted particles in 10 mL toluene was treated with 10 mL of 20 vol% HF in water. After stirring for 12 h at room temperature, the aqueous layer was removed with a separation funnel, and the organic layer was extracted three times with 10 mL of water. The solvent was removed, and the residual polymer dried in vacuo.
where is the decay rate and τ is the correlation time. μ2 is the variance, and μ3 is the skewness or asymmetry of the particle size distribution. B is the baseline factor which is approximately equal to one. We focus on the hydrodynamic radius (Rh ) which is obtained from using, = Dq 2
(2)
For low concentration, D is the translational diffusion coefficient of the particle. q denotes the modulus of the scattering vector and it is defined as
q=
4πn sin (θ) λ
(3)
Here, n is the refractive index of the solvent, λ is the wavelength of the laser, and 2θ is the scattering angle. The Stokes–Einstein relation finally allows to calculate the hydrodynamic radius as Rh =
kB T 6πηD
(4)
where kB is the Boltzmann constant, T is the absolute temperature, and η is the viscosity of the solvent. Standard deviation of hydrodynamic radius (polydispersity index, p.d. is given by [25, 26], p.d. =
μ2 2
(5)
Experimental
Small-angle x-ray scattering (SAXS)
Dynamic light scattering (DLS)
SAXS measurements were performed using a pinhole SAXS system with a two-dimensional detector (Molecular ˚ metrology). The x-ray beam from a Cu anode (λ = 1.54 A) passes an x-ray mirror and is further collimated with three pinholes. The scattering vector is related to wavelength and scattering angle according to Eq. (3) with n = 1. The detector is located at a distance of 150 cm from the sample holder ˚ −1 . The sample is to provide a q range from 0.008 to 0.25 A placed in a 1.5 mm Mark capillary and kept in an evacuated sample chamber at room temperature. The two-dimensional scattering pattern is azimuthally averaged to result in the intensity I (q).
DLS measurements were carried out at room temperature. The setup consists of a He–Ne laser (wavelength λ = 632.8 nm) and an ALV-5000 correlator. The scattered beam is not analyzed with respect to its polarization. Samples were filtered using 0.2-µm teflon filters. They were placed in a cylindrical glass cuvette (Hellma) with 10-mm diameter. In most cases, a series of concentration is studied, and the results reported correspond to the extrapolated value at zero concentration. The scattering intensity was measured in a range of scattering angles 2θ from 50◦ to 130◦ . The autocorrelation function of the intensity g2 (τ ) is, thus, obtained. For the scattering from particles with a narrow size distribution, it can be described by a cumulant expansion [24–26], μ2 2 μ3 3 g2 (τ ) = B + β exp(−2τ ) 1 + τ − τ ··· 2! 3!
(1)
Small-angle neutron scattering (SANS) SANS measurements were performed at the KWS-2 beamline at FRM 2 (Munich). The neutron beam was monochromatized with a mechanical velocity selector set to a wavelength spread λ/λ = 0.2. To cover a q range ˚ −1 , two different sample-to-detector from 0.005 to 0.3 A
Colloid Polym Sci
distances (8 and 2 m) and a collimation distance (8 m) at ˚ was used. In order to check samples a wavelength 4.5 A for possible aggregation for some samples, a q value as ˚ −1 was reached. This measurement needs small as 0.002 A a sample-to-detector distance of 8 m and a collimation dis˚ The samples were tance of 8 m at a wavelength 12 A. placed in Hellma cuvettes with sample thickness of 1 mm. The raw data obtained were treated with correction for electronic background, empty cell scattering, and absorption. Polymethylmethacrylate was used as a standard to obtain absolute intensity. TEM TEM experiments were carried out on a Zeiss EM 10 electron microscope operating at 80 kV. All images shown were recorded with a slow-scan CCD camera obtained from TRS (Tr¨ondle) in bright field mode. Camera control was computer-aided using the ImageSP software from TRS. SEC SEC was performed with THF as the mobile phase (flow rate 1 mL min−1 ) with a styrene-divinylbenzene (SDV) column set from Polymer Standard Service (PSS) (SDV 1,000; SDV 100,000; SDV 1,000,000) at 30 ◦ C. Calibration was carried out using PS standards from PSS, Mainz. TGA For thermogravimetric analysis (TGA), a TA Instruments TGA Q-500 was used, and a temperature range from 35 to 750 ◦ C and a heating rate of 10 K min−1 under oxygen atmosphere was applied.
Results and discussion Characterization of bare and surface-modified silica nanoparticles We start with the characterization of bare and surfacemodified silica particles with SAXS, SANS, DLS, and TEM. This also allows a comparison of the results of the different experimental approaches. DLS determines the hydrodynamic radius of the bare and surface-modified particles. Therefore, the particles were dissolved in an ethanol/water mixture (7:3 volume ratio). A series of concentrations was prepared, and the correlation function was measured in a range of scattering angles. Figure 1 shows representative results for a concentration of c = 0.08 wt%. The correlation functions are found to
(b)
Fig. 1 a Intensity autocorrelation function of bare silica particle in ethanol/water mixture (0.08 wt%) at selected scattering angles as an example. Solid line presents fits using a cumulant analysis. b q 2 dependence of to determine diffusion coefficient for bare silica particle (square) and surface-modified silica particle (circle). Solid and dotted line present the linear fit to obtain D
be very close to single exponentials. For each q, we use Eq. (1) to determine the relaxation rate and the variance μ2 . In Fig. 1b, the variation of is shown in dependence on q 2 . The data follow the expectation for particle diffusion Eq. (2) and, thus, allow the determination of a diffusion coefficient and a hydrodynamic radius. For each concentration, we can, thus, determine an effective hydrodynamic radius and extrapolate to zero concentration. The extrapolated value is RH = (38.3 ± 1.1) nm for the data shown in Fig. 1. In a next step, the silica particles were surface-modified with (3-chloropropyl) triethoxysilane to yield the precursor groups, and particles were dispersed in the same ethanol/water mixture. Here, the hydrodynamic radius determined by DLS was found to be RH = (35 ± 0.8) nm. It is, thus, smaller than the RH of the unmodified particles. The variation of with q 2 is included in Fig. 1b. The
Colloid Polym Sci
difference between RH of the bare particle and that of the surface-modified particle may be attributed to the different surface structure. The smaller number of OH bonds on the surface of the modified particles results in a faster diffusion and, thus, in a smaller RH . Close inspection of the data in Fig. 1b shows that data deviate from the straight line at small q. This may be caused by the slightly non-spherical shape of the particles which is also observed in TEM (see Fig. 3). The same bare and surface-modified silica particles dispersed in ethanol and water mixture at a concentration of 0.2 wt% were also analyzed by SAXS. Figure 2a compares these results for both systems in ethanol/water. It is obvious that the scattering pattern for both samples is very similar. It shows the features of single particle scattering with a shoulder in I (q) resulting from intraparticle interference.
We, therefore, used a single particle scattering function to fit the data. The total intensity is then given as I (q) = k F (q, R)2 + Ib
The patterns are well described using a model of a solid spherical particle with a form factor F (q). The intensity is scaled with k, and a flat background is taken into account with the parameter Ib . Details concerning the structure of the scattering particle are contained in the form factor F (q) which is the Fourier transform of the scattering length density distribution of the particle. For a solid spherical particle, F (q) is given as F (q, R) = Vparticle 3
(a)
(b)
Fig. 2 a SAXS data of bare (lower) and surface-modified silica (upper) dissolved in 0.2 wt% ethanol/water mixture. Solid lines are fits with the spherical form factor. The curve of surface-modified silica was shifted for clarity. Open symbols indicate those that were not taken into account to data analysis. b SAXS (lower) and SANS (upper) data from surface-modified silica dissolved in 0.5 wt% deuterated THF. Solid lines are fits with Eq. (6) including the term Cq −α . Open symbols were not taken into account to fit the data
(6)
sin(qR) − qR cos(qR) (qR)3
(7)
where R is the core radius, q the scattering vector, and Vparticle the volume of the particle. The brackets ... in Eq. (6) denote an average with respect to the particle size distribution. This is carried out in the fits using a Schultz distribution of particle radii. In Fig. 2a, we include the fit of Eq. (6) as a line. It is seen that the model of a spherical particle describes our data very well. As a result of the fits, we find the average radius for both samples to be ∼ 26 nm. The width of the size distribution is ∼ 18 %. The width of the size distributions is, thus, very similar to the result obtained from DLS. The absolute value of the particle radius, however, is significantly lower. The polystyrene grafted particles will be characterized in THF. Therefore, we also investigate the structure of surface-modified particles in the same solvent. Here, we also compare results from two static scattering techniques: SAXS and SANS. SAXS and SANS measurements were done on particles dissolved in deuterated THF. Figure 2b compares the results from SANS and SAXS for surface-modified particles at c = 0.5 wt%. Data from SANS extend to much lower q and reveal the existence of aggregates in the sample. The scattering curve from the SAXS measurement clearly shows a better resolution as is seen in the more pronounced shoulder in I (q) compared to that from the SANS measurement. At small q, a contribution of scattering from aggregates is seen in particular in the SANS data. In order to account for this additional scattering in the low q range, we add a term Cq −α to Eq. (6). It is then possible to obtain a good fit within a wide q range as is demonstrated by the lines included in Fig. 2b. Porod’s law for the scattering from large particles would result in an exponent α = 4. Fitted values are α ≈ 3.6 for SAXS and α ≈ 3.4 for SANS. The particle sizes obtained from the fits are ∼ 25.6 nm for SAXS and ∼ 23.3 nm for SANS. The SAXS value is consistent with the result obtained in ethanol/water. The slightly smaller value obtained in the
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SANS experiment may be caused by the rather wide wavelength distribution of KWS-2 [27]. We do not attempt to correct for this effect, but we will use the value obtained here for the surface-modified silica particles in the modeling of data for the grafted particles. TEM investigations both of the bare and the polymerfunctionalized nanoparticles are shown in Fig. 3 and clearly reveal a shell for the PS-grafted silica nanoparticles compared to the bare particles. Grafted particles are well dispersible in common organic solvents and tend to form films during the drying process of the TEM sample preparation. Investigation of the conformation of grafted PS chains on silica nanoparticles We now turn to the determination of the polymer structure grafted on silica particles. In particular, we aim to determine the conformation of polymer chains in the grafted layer. Prior to these characterizations, free PS and graftedPS chains were investigated by SEC. We note that the molar mass of “free PS” was taken from freely formed
Fig. 3 TEM images of bare silica nanoparticles (upper images) and the PS-grafted silica nanoparticles (images below) prepared by using the drop-cast method of their dispersions on carbon-coated copper grids
bulk PS by sacrificial initiator and that of grafted PS was from PS detached from silica core with hydrofluoric acid. Results are shown in Table 1. In Table 1, it can be concluded that molar masses of chains are slightly lower than those of freely grown chains and additionally show higher polydispersities similar to work of Zhou et al. [28]. In the case of SEC measurements of the surface-detached PS after etching, a shoulder in the molecular weight distributions appeared. The maxima of the curves agree quite well with maxima obtained from SEC measurements for the free PS chains. An overlay for samples 2 and 3 is shown in Fig. 4. The first possible explanation was that preliminarily purified particles still contain free PS, which is not attached to the particle’s surface and generated by free living anionic polymerization initiated by sacrificial initiator. Hence, an exemplary sample was, additionally, after the before described purification steps involving nanofiltration treated in the following way by ultracentrifugation. Ultracentrifugation of the polymer-grafted particle aliquot dispersed in THF was performed with an Avanti J-30I from Beckman Coulter for half an hour with a speed of 17,000 rpm. The
Colloid Polym Sci Table 1 Molar masses were determined with SEC Sample
Mw,grafted [g mol−1 ]
PDIgrafted
Mw,free [g mol−1 ]
PDIfree
Grafting density a [chains nm−2 ]
1 2 3
– 25,400 42,000
– 1.23 1.29
17,200 31,800 55,200
1.13 1.08 1.12
– 0.032 0.015
In case of surface-grafted PS, the chains were detached via etching the SiO2 particles with hydrofluoric acid. For sample 1, no grafted PS chains could be obtained after etching due to a very low grafting density a Grafting density determined by TGA compared with initiator functionalized silica nanoparticle. The weight loss used was estimated in the temperature range between 260 to 750 ◦ C
Fig. 4 Overlay molecular weight SEC measurements for sample 2 (top) and sample 3 (bottom) obtained vs PS standards. The broader bimodally distributed curves (dotted) correspond to the surfaceattached PS, which have been detached by etching. The narrow monomodal distributions (lined) correspond to free PS, which was initiated by sacrificial initiator in solution
supernatant THF was concentrated and investigated via SEC measurements. That step was repeated for 12 times and in no case that free polymer could be observed. It can be, therefore, assumed that the bimodal distribution is proved to be of the origin of definitely surface-attached PS chains. Due to the low grafting densities of the herein characterized polymers on the particles, which have been generated by the grafting-from approach yielding lower molar masses and broader molecular weight distributions, it turns out that freely polymerized styrene (higher molar masses, narrow molecular weight distribution) is able to attach by a subsequent grafting-onto process to the particle’ s surface. This would explain the bimodal distributions and, additionally, the difference in their shape, as surface-initiated anionic polymerizations typically reveal less defined polymers. Nevertheless, both—still narrowly distributed—polymers are covalently surface-attached, and all values obtained by following characterization methods can be attributed to surface-attached PS chains. For silica nanoparticles, Prucker and R¨uhe [29, 30] and B¨ottcher et al. [31] reported that TGA is a reliable method to determine the amount of surface-attached initiators and polymers. Therefore, the weight loss in the range from 260 to 750 ◦ C was taken for calculation. As in the case of the bare and surface-modified particles, we applied DLS and SAXS for characterization of the grafted particles. In order to obtain more detailed information on the structure of the polymer layer, we make use of SANS. Using deuterated THF as a solvent, the contrast between polymer layer and solvent is enhanced. The difference in contrast for SAXS and SANS experiments is seen directly by comparing the scattering length densities or electron densities given in Table 2. In order to calculate the electron density and scattering length density, the mass density of silica was taken to be 1.85 g/ml [32]. The scattering length densities will be used for the fit of SANS, and the electron densities for SAXS data are to be discussed below. The electron density of PS is significantly closer to that of THF than to the silica core. Therefore, a SAXS experiment will be more sensitive to the silica core. The SANS experiment, however, will have
Colloid Polym Sci Table 2 Scattering length densities and electron densities used for data fitting Compound
Scattering length density (10−4 nm−2 )
Electron density (nm−3 )
SiO2 PS d-THF
2.92 1.41 6.35
556 340 296
stronger contrast between the polymer and the surrounding matrix. In Fig. 5a, b, we compare the results obtained from both types of small-angle scattering experiments. Just as in the case of the surface-modified particles, we find the SAXS data to be compatible with the model of spherical particles. THF as a good solvent apparently mixes so well with the grafted polymer layer, that a contrast between the swollen layer and the solvent is not seen in SAXS. That THF can be assigned as a very good solvent for PS can also be pointed out from the Hansen solubility parameters, whose values are very similar (PS, 18.6 MPa0.5 ; THF, 20.3 MPa0.5 ) [33, 34]. Fits of this model are included as full lines in Fig. 5a. We, thus, determine the core radius of the grafted particle, making use of the particular scattering contrast of SAXS to be 26.2 ± 0.07 nm, which is in good agreement with the value found for the bare particle. The SANS data shown in Fig. 5b display a variation of intensity with q that differs clearly from the SAXS data. A steep decrease of intensity at low q is followed by a variation ∼ 1/q 2 at larger q. This is a strong indication for the existence of a polymer layer on the outside of the silica particle. Indeed, a detailed fit of the data is no longer possible with the model of a simple sphere with homogeneous scattering length density. Also, the extension of this model to core–shell particles with a shell of constant density fails to describe the data adequately. This model would not be able to account for the ∼ 1/q 2 variation of intensity at large q. We are, therefore, led to apply a more detailed model for the variation of scattering length density within the polymer layer that takes the conformation of the polymer chain into account. The problem of scattering from Gaussian polymer chains attached to a spherical particle has been treated by Pedersen [35, 36]. This model is composed of a spherical dense core and a shell of Gaussian polymer chains grafted to the surface. As is shown in Fig. 5c, the form factor based on this approach describes our data only approximately. There are clear deviations in the intermediate q range (0.2 nm−1 < q < 0.35 nm−1 ) and high q range (q > 0.4 nm−1 ). Moreover, the fitting parameters obtained from this fit were unphysical. For example, the thickness was found to be significantly smaller than the radius of gyration of PS chain in the same solvent, THF. Chevigny
(a)
(b)
(c)
Fig. 5 SAXS (a) and SANS (b) data for PS-grafted silica dissolved in d-THF (c = 0.2 wt%). The full curves are fits using the linear profile model (see text) for SANS data and the solid sphere model for SAXS data. Square, sample 1; circle, sample 2; triangle, sample 3. Straight lines demonstrate q −4 dependence for low q and q −2 for high q regime. Open symbols indicate those that were not considered to data analysis. SANS data have been corrected for the flat incoherent background. The curves of samples 2 and 3 were shifted for clarity. c A scattering curve of sample 2 in d-THF (0.2 wt%) analyzed by the Pedersen model
Colloid Polym Sci
et al. [17] applied this model for the case of PS-grafted silica particles dispersed in a theta solvent. They could well describe the shell structure for the protonated PS shell but not for the deuterated PS shell. F¨orster et al. [37, 38] introduced a power law type r −α density profile to analyze the scattering from polymer chains on the spherical dense core. This model was inspired by the work of Daoud and Cotton [39] who further developed a model for star-like polymer which has a power law type of density profile, ρ(r) = r −α . They found that the exponent α obtained by their fit results was consistent with the argument by Daoud and Cotton who claimed that the exponent should lie in the range between 1 and 1.34. But data were not taken to the high q range. Won et al. [40] used a Fermi–Dirac-type density profile to describe the polymeric shell on the spherical core. The advantage of this model is its ability to describe the density profile spanning from the typical step-like core–shell structure throughout the parabolic and the hyperbolic (power law) like shell structure. The model, however, did not fit our data at high q. In an attempt to describe the full q range of our data with a simple model for the variation of scattering length density, we have, therefore, chosen to superimpose two scattering components. The variation of density within the polymer layer is described by a concentration profile ρ(r). It is implemented in the fitting procedure as a multishell model consisting of n partial shells adding up to a total shell thickness .
Fig. 6 Schematic representation of a radial density profile. Scattering length density ρ(r) is constant in the core (r < Rc ) and depends on r in the layer regime. (Rc < r < Rc + )
Rg is a radius of gyration of the polymer. Clearly, the restricted range of q does not allow us to fit Rg . We, therefore, use a fixed value calculated on the basis of ref. [43] that was determined for PS in a good solvent: Rg = (0.0125)Mw0.595(nm)
1 Fmultishell = (ρcore − ρsh ) · Fcore (Rc )
n k·
k+1 k + ρsh − ρsh · Fcore Rc + n
(10)
As an example for the quality of fit provided by this model, Fig. 7 shows data obtained for sample 2 with curves displaying the contribution from both components in our
k=1
(8)
Here, F (qR) is the form factor of a spherical particle given k in Eq. (7). ρsh is the scattering length density of partial 1 that of first partial shell. ρ n+1 corresponds shell k and ρsh sh with ρsol . In order to keep the number of parameters small, we have restricted the number of shells to one. The resulting scattering length density profile then is just linear and sketched in Fig. 6. Obviously at large q, the detailed conformation of the grafted polymer chains becomes relevant. This contribution has been found for grafted chains in good solvents [17, 18, 41, 42]. We approximate this component by an additional Debye function:
Pdebye (q) = 2
exp −q 2 Rg2 − 1 + q 2 Rg2 q 4 Rg4
(9)
Fig. 7 Two contributions of the fit function are presented. Data are from sample 2. Dotted line, contribution from radial density profile; dashed dotted line, Debye term described in Eq. (9); full line, total fit function
Colloid Polym Sci Table 3 Structural parameters derived from SAXS, SANS, DLS Sample
Sample 1 Sample 2 Sample 3
SAXS
SANS
DLS
Rc (nm)
p.d.
Rc (nm)
(nm)
p.d.
Rg (nm)
s.l.d.(10−4 nm−2 )
Dh (nm)
p.d.
27 ± 0.2 26.2 ± 0.1 25.8 ± 0.1
0.18 0.18 0.18
23.3 23.3 23.3
8.4 ± 0.3 13.4 ± 0.03 17.4 ± 0.06
0.21 0.21 0.21
4.2 5.2 7.0
5.96 ± 0.07 5.87 ± 0.01 6.11 ± 0.01
15.3 ± 1.5 20.9 ± 1.1 25.8 ± 1
0.16 0.14 0.16
Rc : particle core radius; : thickness of grafted polymer layer from SANS; s.l.d: scattering length density of the interface between the core and the shell; Rg : radius of gyration of free PS chain obtained from Eq. (10)
model. The linear model obviously provides a very good description of the experimental data. The core radius was fixed to the value obtained for the surface-modified particle in d-THF. Results of these fits are compiled in Table 3. It is seen that the layer thickness increases with molar mass of the grafted polymer. The scattering length den1 appears to be independent of molar mass. Its value sity ρsh is only slightly below that of d-THF, indicating a strong swelling of the polymer layer in the used solvent THF. The remaining small contrast between the polymer layer and the solvent obviously does not allow determining fine variations of density. The use of the simple linear model is therefore adequate. We can use the scattering length density profile to estimate the grafting density of the polymer chains. Let
PS (r) denote the volume fraction of PS segments at distance r from the particle center. Then ρ(r), the scattering length density, is ρ(r) = ρPS · PS (r) + ρd−THF · 1 − PS (r)
for one sample. Relaxation functions are again very close to single exponentials, and we use Eq. (1) to determine relaxation rates for each q. Figure 8b shows that, for all samples, we find a simple diffusive behavior, and we are, thus, able to obtain the diffusion coefficient D. Table 3 compiles the results from three experimental methods used to characterize the structure of the grafted
(11)
Using the linear variation of ρ(r) expressed in the parameters of our model, one obtains for PS (r)
PS (r) =
1 ρsol − ρsh (r − Rc − )
· (ρPS − ρsol )
(12)
Integrating PS (r) over the shell volume, one can obtain the volume occupied by polymer, and, furthermore, using the molar masses of grafted PS allows calculating the number σ of chains grafted per unit area. The grafting densities obtained by this method are 15(±3)10−3 chains per nm2 for sample 1, 20(±0.3)10−3 chains per nm2 for sample 2, and 10(±0.2)10−3 chains per nm2 for sample 3. We note that the grafting densities of samples 2 and 3 are compatible with those from TGA. We now turn to the determination of the polymer layer thickness using DLS. As we have determined hydrodynamic radii of the particles before the grafting process, we can now apply the same measurement to obtain these values for the PS-grafted system. In Fig. 8, we show representative results
(b)
Fig. 8 a Intensity autocorrelation function for sample 2 in THF at selected scattering angles. Solid line represents fit using Eq. (1). b Relaxation rate vs. q 2 to obtain diffusion coefficient D of sample 1 (square), sample 2 (circle), and sample 3 (triangle) in THF (concentration used 0.02 wt%). Solid, dashed, and dotted lines represent the linear fit to obtain D for samples 1, 2, and 3
Colloid Polym Sci
particles in d-THF. The radius of the silica core is systematically found to be larger in the SAXS than in the SANS experiments. This may be caused by the rather large width of the wavelength distribution in the SANS measurement. This spread also contributes to the apparent size distribution which is larger in the SANS than in the SAXS measurement. Lowest values for polydispersity are obtained from DLS. It should be noted that with this method, the weighting of particle size is different from that in static scattering methods. The table provides a layer thickness as obtained from SANS. Moreover, the difference in hydrodynamic radii before and after grafting Dh is a measure for polymer layer thickness. We also include this result for our grafted particles in Table 3. It is seen that the measures of the layer thickness, thus, determined clearly are of the same order of magnitude as the radius of the supporting particle. We now compare the results for the apparent thickness of the polymer layer on the silica particle. Results from DLS provide a measure of the thickness as the difference in the hydrodynamic radii of surface-modified and -grafted particle. On the other hand, SANS allows deriving the thickness as a static quantity, and we used the parameter introduced above. In Fig. 9, we collected these results. The molar masses of samples 2 and 3 were taken from those of the grafted chains shown in Table 1. The molar mass for sample 1 was, on the other hand, that of the free chain. It is observed in Fig. 9 that the DLS results are 1.5 times larger than the SANS results. However, their variation with molar mass follows the same law. For the surface-modified particle, we had also observed a factor of 1.5 between the results from DLS and SAXS. The difference is in part caused by the adherence of solvent
Fig. 9 Variation of the apparent thickness (dapp ) of the grafted PS layer on the surface of spherical silica particle in THF, obtained by SANS (circle) and by DLS (square) with molar mass. The solid line is dapp as calculated for PS in toluene (see Eq. (10)). Dotted and dashdotted lines are fits of dapp obtained from DLS and SANS, respectively. The open symbol is used for sample 1 as its molar mass was not taken from that of the grafted chain
molecules to the particle, thus decreasing its diffusion coefficient [44]. A possible deviation of the particle shape from a sphere may also contribute to this discrepancy. Such deviations of the particle shape are indeed seen in TEM images as shown in Fig. 3. The DLS data given in ref. [15] also show the difference of the apparent thickness from DLS and the calculation at a low grafting density. In order to compare the layer thickness with the size of the grafted polymer chains, we calculated the radii of gyration of free PS chains as introduced previously. 2Rg was taken to be dapp for comparison with dapp from SANS and DLS measurement. In Fig. 9, we plot the results for dapp from SANS ( ), DLS (Dh ), and 2Rg from Eq. (10) as a function of the molar mass of the grafted PS chains. Both experimental methods result in a variation of size with molar mass compatible with dapp ∝ Mw0.6 . This is also observed for free PS chains in good solvents as it is demonstrated by the lines drawn in Fig. 9. The deviation for the sample 1 may be attributed to the molar mass taken from the free polymer chain, which tends to be larger than that of the grafted chain. Therefore, within the range of the molar masses investigated in our study, the PS chains are swollen by the good solvent. Their size scales with molar mass just as for free chains in a good solvent. The thickness and the conformation of the grafted polymer layer on the flat substrate are known to depend on grafting density. At a low grafting density, individual chains are separated, and they do not interact. This results in a “mushroom-like” conformation. The measured thickness in this case was determined to be ∼ 2Rg [45, 46]. Wu et al. [45, 46] reported that the crossover from a “mushroom” to a “brush” regime depends on the grafting density and occurred at a grafting density of approximately σ ≈ 0.065 chains nm−2 . The grafting densities for our particles are below this value. A curved substrate as in the case of nanoparticles supports polymer coil conformations that may depend on the radius. In the limit of strong curvature, the system should be similar to a star polymer. A theoretical description of the conformation has been given in the literature [13, 47, 48]. At fixed curvature a brush-like behavior of the grafted polymer chains is expected for densely grafted polymers and a “coil-like behavior” for the polymers with a low grafting density. Lo Verso et al. [47] investigated the conformation of the grafted polymer chains on the spherical surface by a coarsegrained model, and they observed the increase of the radius of gyration of the grafted chains in the radial direction as the grafting density is increased. It represents the increase of the stretching of the grafted chains with increasing grafting density. The above-mentioned theoretical consideration could be applied to our experimental observation. The thickness determined by SANS was similar to 2Rg of free PS chain in the same solvent, and the grafting density of our
Colloid Polym Sci
PS-grafted silica particles was low. This demonstrates that PS chains studied in our experiment have a “coil-like” conformation. A more general scaling concept was introduced by Lo Verso et al. [47]. It includes not only the effect of the length of the grafted chains and the grafting density but also that of the curvature of the particle on the size of the grafted chains. The scaling law of the thickness of the grafted layer H with the length of the grafted chains, grafting density, and size of the core for the spherical surface is then given by H ∝ σ 0.2 N 0.6 Rc 0.4
(13)
where N is the degree of the polymerization and Rc the radius of the core. The scaling law introduced in Eq. (13) is expected to correct the deviation from power law fit shown in Fig. 9 due to the multiplication of σ 0.2 on the molar mass. However, we did not attempt to plot the result using Eq. (13) because only two molar masses for samples 2 and 3 were available.
Conclusion We described a method to prepare spherical core/shell silica nanoparticles grafted with PS by surface-initiated anionic polymerization. Therefore, an initiator shell on the surface of silica particles has been successfully generated, and the anionic polymerization was initiated via halogen–metal exchange with organolithium compounds. Three samples were prepared with differences regarding to their grafting density and molar masses of the PS chains. Samples were characterized by SAXS, DLS, TEM, and SANS. Free PS and surface-anchored PS, which were detached by etching with hydrofluoric acid, have been characterized by using SEC measurements. It became clear that after extensive and careful purification procedures for the grafted particles by using nanofiltration and additionally repeated ultracentrifugation, molecular weight distributions were bimodal. Overall, molecular weights were still narrowly distributed due to the living polymerization methodology used. In fact, all generated PS chains were surface-attached, but we assume a grafting-from as well as a subsequent graftingonto approach of the living polystyrene macro-anions. All received results can, therefore, be attributed to surfaceattached PS chains. An enhanced contrast between PS chains and solvent was achieved by SANS being used for the study of the layer of PS chains on top of the particles. In order to describe the form factor of the shell of PS-grafted silica particles, a simple density profile was found to adequately describe the low q regime. Additional scattering at high q was attributed to the coil structure of the polymer chain. Our measurements from DLS and SANS revealed that the thickness of PS chains in good solvent, THF, scales
with Mw 0.6 displaying a similar behavior with free polymer chains in the same solvent. Grafting densities were determined from SANS and TGA. They were found to be low (less than 0.1 chains nm−2 ). The thickness of the grafted PS layers determined by DLS and SANS was comparable with the size of the free polymer chain. Both results demonstrate that the grafted PS chain have a “coil-like” conformation. Work is in progress to extend our study to probe the effect of variation of molar mass of PS matrices when PS-grafted silica particles are dispersed in PS matrices at a constant grafting density and molar mass of grafted PS. Acknowledgments The authors would like to thank the Deutsche Forschungsgemeinschaft (DFG SPP-1369) for financial support of this work. Marion Trautmann and Matthias Wittemann are acknowledged for SEC measurements.
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