Supporting Information for: Dynamics of the particle morphology during the synthesis of waterborne polymer-inorganic hybrids Shaghayegh Hamzehlou; Miren Aguirre; Jose R. Leiza; José M. Asua* POLYMAT, Kimika Aplikatua saila, Kimika Zientzien Fakultatea, University of the Basque Country UPV/EHU, Joxe Mari Korta Zentroa, Tolosa Hiribidea 72, 20018 Donostia-San Sebastián, Spain Corresponding Author *Email: jmasua@ehu.es 1. Size of the CeO 2 nanoparticles
Figure S1.TEM image of a dispersion of CeO2 nanoparticles in mineral spirit. 2- Calculation of number of nanoparticles in aggregates at 100% conversion In order to proof that the CeO2 nanoparticles did not expel from the polymer particles some calculations were carried out. First, the aggregate size (diameter of the aggregate) of the final latex was measured using a commercial Software, Image Pro Plus 7.0. The size of 500 CeO2 aggregates was measured and the volume average was calculated. The CeO2 nanoparticles aggregate size in volume in the final latex was of 22 nm. The total volume of one aggregate of 22 nm is calculated in equation S1: v 4.46 x 10 L S1 At 100%, a hemispherical morphology was achieved, and the CeO2 nanoparticles were completely aggregated in the polymer particle due to the high interfacial tension between the polymer and the CeO2 nanoparticles, and the low interfacial tension between the nanoparticles. However, as they are rigid spheres, there will be voids
between the nanoparticles when they get close to each other, in other words when they are packed. The maximum packing fraction for unimodal particles is φ n =0.639 1. If this maximum packing fraction is considered for the CeO 2 aggregates, the volume that the nanoparticles were filling will be: v 2.85 x 10 L S2 Assuming that this is the volume that the CeO 2 nanoparticles occupied in the 22 nm aggregate and dividing this volume by the volume than a single (3 nm) CeO 2 nanoparticle occupies, this means that there will be 252 nanoparticles in each nanoceria aggregate. v 2.85 x 10 L v 1.131 x 10 252 S3 L On the other hand, the number of monomer droplets and number of individual CeO 2 nanoparticles was calculated before the polymerization was started. In the miniemulsion there were by average 255 CeO 2 nanoparticles per monomer droplet as it is shown in S4. N N 2.54 x 10 255 S4 9.95 x10 This means that the number of CeO 2 nanoparticles at the beginning in the monomer droplets and in the final polymer particles were the same. Therefore, this confirms that there was no leaching of the CeO 2 nanoparticles to the aqueous phase. 2- Relative rates of monomer-polymer interdiffusion and polymerization The relative rates of monomer-polymer interdiffusion and polymerization can be evaluated by comparing the characteristic times for these processes. The characteristic time for interdiffusion is:
5 where is the radius of the particle (6.8 10 m) and the diffusion coefficient of the monomer ( 3.7 10 for the MMA in its polymer at 60 C). 2 The characteristic time for polymerization is: ñ 6 Where V p is the volume of the particle, N A the Avogadro s number, kp the propagation rate coefficient kp 2.67 10 exp. ) 3 and the average number of radicals per particle ( =0.1, this value is the average calculated in the simulation during the polymerization ). Substitution of the values given above in equations S5 and S6, leads to: 9.6 10 1.2 10 7 Namely, the monomer-polymer interdiffusion was much faster than polymerization and therefore, a homogeneous distribution of monomer and polymer in the particles is expected. 3- Generation of TEM-like images In order to obtain TEM-like images from the cluster distributions, the normalized number distributions were transformed to cumulative distributions between zero and 1. One million sampling particles was considered in the algorithm (N). The total numbers of inorganic nanoparticles contained in the equilibrium and non-equilibrium aggregates in N particles are: 8
9 In the same way, the total number of equilibrium and non-equilibrium aggregates are: 10 11 Using the Matlab random number generator, a single uniformly distributed random number in the interval (0,1) was generated and a aggregates size was selected using the cumulative distribution of non-equilibrium clusters (. The selected cluster was placed in a random position among the non-equilibrium positions of the first particle (inside the polymer matrix). The total number of nanoparticles and total number of non-equilibrium aggregates were modified as follows: 12 1 13 This procedure was continued sequentially for the rest of particles until the total nanoparticles in non-equilibrium aggregates be less than and the less than 1. The same algorithm was implemented to distribute the polymer in the equilibrium positions. Later, 10 particles among the one million sampling particles were selected randomly and plotted. First, the morphologies were plotted in 3D and then, a 2D projection of this image was plotted to be comparable to the experimentally obtained TEM images, which are basically 2D projection of the 3D particles. To account for the hairy layer of the nanoparticles and the maximum packing of the nanoparticles in each aggregate (0.64), the nanoparticles were plotted in a random position in a sphere with a bigger volume
comparing to the total volume of the inorganic nanoparticles in each aggregate, if they could coalescence completely in the absence of the hairy layer. The volume of this sphere was multiplied by a factor that changed from 2 to 1.4 during the polymerization to account for the shrinkage of the hairy layer and increasing of the maximum packing factor. As no information about the shape of the aggregates is available from the model, spherical aggregates were used in the TEM-like images. REFERENCES (1) Do Amaral, M.; Van Es, S.; Asua, J. M. Effect of the Particle Size Distribution on the Low Shear Viscosity of High-Solid-Content Latexes. J. Polym. Sci. Part A Polym. Chem. 2004, 42, 3936 3946. (2) Faldi, A.; Tirrell, M.; Lodge, T. P.; Meerwall, E. Von. Monomer Diffusion and the Kinetics of Methyl Methacrylate Radical Polymerization at Intermediate to High Conversion. 1994, 4184 4192. (3) Beuermann, S.; Buback, M.; Davis, T. P.; Gilbert, R. G.; Hutchinson, R. A.; Olaj, O. F.; Russell, G. T.; Schweer, J.; van Herk, A. M. Critically Evaluated Rate Coefficients for Free-Radical Polymerization, 2. Propagation Rate Coefficients for Methyl Methacrylates. Macromol. Chem. Phys. 1997, 198, 1545 1560.