## 3 Results and Discussion
### Nanoparticle Incorporation into PDMS Matrix  
PDMS is a cross-linkable polymer widely used in microfluidics. Magnetic PDMS is intended to be used in pumping or actuating systems in micro-systems [2; 6; 14; 15; 32]. The main PDMS used in microfluidics is the Sylgard 184, which allows good elasticity and mechanical stability. This polymer can be crosslinked by the mixture of two components in a ratio 10:1. Studies have shown that polymer chains grafted onto nanoparticles should be longer than the matrix chains in order to have a good dispersion with a swollen corona [20; 33]. In the case of Sylgard 184, a mixture of almost six components complicates the interpretation in terms of particle distribution in the matrix. The crosslinking reaction is achieved with platinum catalyst that allows the reaction between Si-H bound and carbon-carbon double bounds. The PDMS-_co_-APMS copolymer used in this study contained no such chemical function. As a consequence, nanoparticles will not interact with the chemical backbone of the PDMS matrix. For this reason, two cases can be considered. First, NPPDMS are smaller than the reticulated matrix mesh size, and the reticulation should not be changed, leading to no change in elastic modulus of the loaded Sylgard 184. Secondly, NPPDMS are larger than the matrix mesh size. In this case, the reticulation process should be impeached by the nanoparticles. The more particles, the smaller the elastic modulus should be. We achieved experiments with Sylgard 184 and its crosslinker in the ratio 10:1, adding 4%, 9%, and 24% by weight of magnetic nanoparticles coated with 4-5% PDMS-_co_-APMS. Dynamic viscosity was measured _versus_ time by rheometry at 70 \({}^{\circ}\)C on a plane-plane rheometer (rheooptical rheometer, Thermo-Haake) by oscillations at 10 Hz with a strain fixed at 10 Pa during reticulation (Figure 4). Figure 4: Dynamic viscosity _versus_ time for Sylgard 184 reticulation without and with 4 wt %, 9 wt %, and 24 wt% of magnetic nanoparticles coated with 4–5% PDMS-_co_-APMS. The viscosity plateau is expected when complete reticulation is reached. This appeared for pristine Sylgard in 15,000 s with a plateau at 10\({}^{4}\) Pa\(\cdot\)s. For the PDMS mixtures containing magnetic nanoparticles, two observations are noticed. Firstly, the reticulation appeared at shorter times. This could be due to a catalytic effect of the nanoparticles in the matrix. Secondly, the higher the proportion of nanoparticles, the lower the viscosity at the plateau. As an example, the plateau dynamic viscosity decreased from 10\({}^{4}\) Pa\(\cdot\)s for unloaded matrix to 500 Pa\(\cdot\)s for the PDMS matrix loaded with 24 wt.% of nanoparticles. NPPDMS clearly induced a decrease of the mechanical properties of the reticulated Sylgard 184 matrix. To overcome this diminution of mechanical properties, we made different formulations with copolymers that contain Si-H and carbon-carbon double bounds. They acted as a crosslink in the matrix. Two copolymers were selected, which are poly(hydromethylsiloxane-_co_-dimethylsiloxane) with 7-8 % (HPDMS) of Si-H functions copolymer and poly(vinylmethylsiloxane-_co_-dimethylsiloxane) copolymer with 7-8 % of vinyl functions (VPDMS). An optimization of the formulation, which is not detailed here, gave the best results in terms of elasticity and non-stickiness for one part by mass of Sylgard 184 10:1 mixed with 0.8 part by mass of the mixture VPDMS/HPDMS in the ratio 1:1. Same experiments as the one presented in Figure 4 were performed with this formulation (Figure 5). The reticulation of the Sylgard and the VPDMS/HPDMS mixture is very slow, even compared to the pure Sylgard matrix reticulation. However, the same viscosity plateau is reached for those two matrixes. As shown for the Sylgard matrix, nanoparticles increased the reticulation rate, compared to the matrix.