Introduction In the last few years an intense research activity on hybrid sol-gel derived materials has been developed [1-3]. This type of materials combines the complementary properties of the inorganic and organic materials which constitute them to obtain composite materials with reinforced properties. Actually the possibility to obtain a wide variety of hybrid sol gel derived materials has increased because the availability of a great number of precursors for the inorganic component through metal alkoxides, organo(alkoxi)silanes and nanoparticles and their compatibility to the incorporation of polymerizable groups such as methacryloxy, vinil and epoxy groups. Hybrid materials consist of a dual polymer network, in which cluster or polymer type inorganic structures are linked to organic groups or polymer fragments and they can be divided into two general classes. Class I hybrid systems consists in organic molecules, oligomers, or low molecular weight organic polymers, which are simply embedded in an inorganic matrix. Both components exchange rather weak bonds, mainly through van der Waals, hydrogen, or ionic interactions. Class II hybrid systems are compounds where organic and inorganic components are bonded through stronger covalent or ionic- covalent chemical bonds. A lot of novel and multifunctional hybrid materials can be designed by selecting adequately the inorganic and organic components with the adequate composition. The applications of hybrid materials are numerous and they include anticorrosion coatings for metals, scratch and abrasion resistant coatings for plastics, antistatic films, colour decorative coatings for glasses and plastics, etc. [3-5]. Among the applications of hybrid coatings, the reinforcement of the mechanical properties of plastic materials like polymethylmethacrylate (PMMA) by means of mixing with harder inorganic materials like for example SiO2 can be emphasised. For this specific application, reliable experimental techniques for monitoring mechanical properties like hardness of hybrid films are needed. Among these, depth sensing indentation (DSI) plays a fundamental role since it is practically the unique and cost-effective tool for evaluation of mechanical response of mono or multilayer thin film–substrate systems. This technique is very useful in the process of selection and optimization of coatings for particular applications. The interpretation of the indentation data obtained from coated systems is complex due to the fact that the response of the system depends significantly on the scale of contact, being dominated by the film hardness at small scales in comparison with the coating thickness and by the substrate hardness at large scales [6, 7]. Both film and substrate hardness themselves could also be dependent on the scale of contact, giving rise to an indentation size effect (ISE) in both materials [8]. Few reports can be found in the literature based on the hardness measurement of thin films and none on hardness quantification using a Nanoscope depth sensing indentation system. This is probably due to the fact that in the Nanoscope system a small extra sharp diamond indenter of unconventional geometry is used. On the other hand, this extra sharp tip allows hardness quantification of films using extra low loads (100 μN), permissible in the cantilever system of the atomic force microscope (AFM). To determine the hardness of thin films from DSI tests a number of models have been developed in the last few years, where the work of indentation model is probably one of the most useful since it has been developed on the basis of considering the way that the work of indentation can be changed by the presence of the coating, as a function of contact scale [6, 9-10]. In this paper we applied two DSI systems, each one using indenters with different geometry and size, to analyze the mechanical behaviour of hybrid coatings of SiO2-PMMA with different molar ratios. Applying the work of indentation model, the absolute hardness of the coatings was evaluated with both systems as a function of the PMMA content of the hybrid films. The hardness quantification on materials using a Nanoscope IV depth sensing indentation system is reported for the first time. Experimental Hybrid thin films were deposited on Corning glass substrates by dip-coating. The precursor solution was prepared adding 3-(trimethoxysilyl) propyl methacrylate (MPS) to a pre-polymerized solution of tetraethilorthosilicate (TEOS) in ethanol, then water with a diluted solution of HCl (pH=2) was added drop wise while agitating for 1 h at room temperature. On the other hand, the monomer methyl methacrylate was initiated using benzoil peroxide (BPO) agitating for 1hr. The two solutions were mixed and stirred at room temperature for 24 h. After the deposition the samples were heated at 70ºC for 24 h. Several samples were prepared using different molar relationships, namely 1.0:0.0, 1.0:0.25, 1.0:0.50, 1.0:0.75, 1.0:1.0, 1.0:1.50 y 1.0:2, for TEOS:MMA, respectively keeping constant the MPS molar content at 0.5. All the obtained hybrid films were studied by Fourier transform infrared (FTIR) spectroscopy measurements performed with a Nicolet Avantar 360 FTIR spectrometer. The mechanical properties of the hybrid thin films were assessed by two nanoindentation systems: the Triboscope indenter (Hysitron Inc.) equipped with a Berkovich pyramid and an AFM Nanoscope IV Dimension 3100. With the Triboscope indenter the applied loads were from 500 µN to 7 mN. For each load, the hardness was obtained from ten indentations. The calibration procedure suggested by Oliver and Pharr [11] was used to correct for the load frame compliance of the apparatus and the imperfect shape of the indenter tip. The area function of the Berkovich indenter was calibrated using fused quartz. The second system is the commercial module of the same AFM in which ultra low load indentation (Pmax 100 µN) can be applied through a three sided diamond pyramid mounted on a steel cantilever, as delivered by the same provider of the AFM. In this system, loads from 13 to 98 μN with loading rates of 2 Hz in a single step were used. The system was calibrated using two standard materials: sapphire (0001) single crystal (rigid elastic) and gold (rigid plastic). The former standard to determine the parameters for the construction of the load versus displacement curve and the latter one for the determination of the area function. The DSI Nanoscope IV showed a non conventional indenter geometry, having an area function of A=2.877 hc2, as determined experimentally using a gold standard sample. Other method to determine the projected area of the indenter at different applied loads was the measurement of the angles from the remnant indentation on the rigid plastic material, since no elastic recovery is expected. This calibration was performed always before the indentation procedure in all the range of loads, taking care of the very small loads, which allows the minimization of indentation size effect at small penetration depths. The load-displacement curves were analyzed using the method proposed by Oliver and Pharr [11], yielding to the elastic modulus and the hardness. The results of the composite hardness measured with both systems were analyzed using the work-of-indentation approach [6] for the hardness of coated systems. Results and Discussion FTIR Characterization Figure 1 shows the infrared spectra of the hybrid films with 1:0, 1:0.5, 1:1 and 1:2 molar ratio for TEOS:MMA. All the spectra are very similar to those of hybrid films reported in literature [12-15], where intense absorption peaks at about 954, 1080, 1170 cm-1, and a broad band between 3100 and 3600 cm-1, associated with the absorption of the Si-OH group are displayed. Also observed are transversal optic (TO) Si-O-Si asymmetric stretching and longitudinal optic (LO) Si-O-Si asymmetric stretching and hydroxyl groups, respectively. Furthermore, a weak signal is observed at about 800 cm-1, which is related to the absorption by Si-O-Si symmetric stretching. The appearance of the first peak, at 954 cm-1, shows an incomplete condensation of the Si-OH bond in the hybrid matrix. The peaks due to the Si-O-Si asymmetric and symmetric stretching indicates the formation of the silica network produced by the sol-gel process. It has been reported that the organic-inorganic interfacial interaction is given through the formation of hydrogen bonds [12,13]. For the case of our hybrid films, the residual silanol groups in the silica structure are capable to form hydrogen bond and their presence is evidenced in the hybrid films by the absorption peak at 954 cm-1 and the broad absorption band due to the hydroxyl groups in the FTIR spectra of all the hybrid films. Therefore, the FTIR results are compatible with the formation of hybrid films with a homogeneous matrix constituted by both organic PMMA and inorganic SiO2 components. 
Figure 1. FTIR spectra of the hybrid coatings with molar ratio 1:0, 1:0.5, 1:1 and 1:2 for TEOS:PMMA Mechanical Properties by DSI Figure 2 shows typical graphics hardness versus contact depth from where composite hardness was obtained using both indentation systems, a) triboscope and b) nanoscope IV. The data are plotted for hybrid coatings with three different molar ratios for TEOS:MMA and for comparison the data was also plotted for bulk acrylic. In Figure 2 a), the experimental data obtained show two behaviours patterns for the composite hardness as a function of contact depth separated by a minimum in the hardness values at about 180 nm. To the right of this minimum an increasing tendency with higher penetration depths with the indenter is observed, which is attributed to a transient region resulting from the contribution to the composite hardness of the Corning glass substrate (6.7 GPa). Interesting to note is the measured minimum and the values of hardness at lower penetration depths because these are directly correlated with the mechanical properties of the hybrid coating. In many materials, ISE are observed where hardness increases as the load and hence the contact size is reduced. In this particular case, the higher hardness values at very low indentation depth could be due to the ISE, a mixed effect of a geometric factor (surface roughness) and of genuine property gradients of hardness enhancement at the surface. However, the influence of the ISE was ignored in the analysis because no effect was measured at this penetration depth on several materials such as the Corning glass substrate, acrylic bulk material and fused quartz. Thus, according to the results of Figure 2 a), we propose that the hybrid coating presented a self assembly mechanism yielding to a hardness enhancement at the surface, higher than in the intermediate part of the film. This behaviour is observed in both indentation systems but in different magnitudes. Further on, the behaviour of the whole coating-substrate system can be approximated to a system of two layers of materials with different hardness on a glass substrate. It is known that at penetration depths larger than 10% of film thickness, the substrate has a proportional effect to the indentation. We conclude that the observed increase of hardness at penetration depths up to 180 nm is due to this phenomenon. On the other hand, the results obtained with Nanoscope IV Dimension 3100 system, plotted in Figure 2 b), show that hardness decreases proportionally with penetration depth, which agrees with the results obtained by the triboscope (Figure 2a) ). It is also clear that our hybrid films attained higher hardness than PMMA [16] even in the intermediate layer of the coating, which is much softer than the surface layer. 
Figure 2. Hardness versus contact depth for several hybrid coatings measured with the Hysitron Triboscope (a) and Nanoscope IV Dimension 3100 (b). The data for bulk acrylic are included in this graph for comparison. The work of indentation model presented by Korsunsky has been successfully used for the determination of effective hardness of thin films. The results of hardness in both systems were analyzed with this model, considering the system of the deposited film as two layers. The hardened material on the surface as a hard film on a soft substrate (layer 1) and the less reinforced material as a soft film on a hard substrate (layer 2). The models applied to each layer system are the next:  
were H1 y H2 are the composite hardness of the materials from the outer layer (1) and the inner layer (2) of the coating, Hm and He are the intrinsic hardness of the inner and outer layers, respectively and Hg is the hardness of glass. k1 and k2 are parameters related with the mechanical behaviour of the coating-substrate system during indentation. Further on, β1=hc/t1 and β2= hc/t2 are the relative penetration depths to the systems 1 and 2, respectively. Finally, t1 and t2 are the thicknesses of the different coating layers. The main challenge in the application of the work of indentation model in this system of two layers is that the thickness of the coating single layers is unknown. In this case, the model implies three unknown variables, film hardness, the mentioned thickness of the coating single layers, as well as the fitting parameter k. To solve this problem, we considered first the hardness of the Corning glass Hg and the thickness of the whole coating to calculate the hardness of the coating, which would correspond to that of the inner layer Hm. Knowing Hm the value of He (surface hardness of the coating) can be computed using again the work of indentation model, where the thickness of the outer layer is approximated to that of the measured minimum of the composite hardness. The best fitting of the work of indentation model to the hardness measurements of several hybrid coatings with different TEOS:MMA molar ratios are shown in Figure 3 for low (3a) and high (3b) loads. The measurements were obtained with the Triboscope indenter. From these graphs, it is clear that the composite hardness changes with the penetration depth. At low penetration depths, the DSI systems mainly detects the hardness of the surface irrespective of the influence of the glass substrate leading to higher values of the hardness surface of about 4 GPa. The work of indentation model was also applied to the results of Figure 2b (not shown here), obtained with the Nanoscope indenter. To do this, the thickness of the outer layer of the hybrid coating was the same as for the fitting procedure of the Triboscope results. Due to the considerably higher values of the composite hardness at very low penetration depths, the fitting results lead to higher values of He compared with those computed for the Triboscope system. 
Figure 3. a) Low loads and b) high loads composite hardness plotted against relative indentation depth for several hybrid coatings measured with the Triboscope. The solid lines correspond to the best fitting of the experimental data to the work of indentation model. There are several important aspects that must be discussed regarding comparison of composite hardness measured with different nanoindenter sizes and geometries. In the first place, considering the basic assumption of the change in the composite hardness as a function of the penetration depth, the question is at which fraction of the film thickness the contribution of the substrate to the composite hardness starts to be effective. According to Jonsson and Hogmark [10], the fraction of the film thickness from which the substrate begins to contribute to the composite hardness varies between approximately 0.07 and 0.2, where the most unfavourable case is that of a hard coating on a softer substrate. Also, according to the data presented by Korsunsky et al., this fraction could be of the order of 0.1 or less. For the Nanoscope system, when performing nanoindentation at ultra low loads, only very shallow indents were obtained, so that the response of the hybrid coating can be considered as free of the contribution of the glass substrate, but not of the intermediate softer section of the hybrid coating. Furthermore, the geometry of the indenter used in both systems is quite different, being sharper for the Nanoscope indenter, with an experimentally determined area function of Ac=2.88 hc2. Considering that the hardness is related with the inverse of the contact area, and comparing the cross point of both curves, where the composite hardness are equal of approximately 600 MPa at the same penetration depth (~100 nm), the loads to reach this values are six times and a projected contact of eight times higher in the Hysitron indenter (~229 µN). 
Figure 4. Comparison of composite hardness results for a 0.5 mol of PMMA hybrid coating on glass substrate system measured with both nanoindentation systems. Schematic representation of the indenter geometries is also shown. As mentioned above, for homogeneous coatings it is expected that at penetration depths lower than 10% of the coating thickness the composite hardness behaves constant. Both systems are sensible to the hardness enhancement at the surface, but the Nanoscope reports higher values, which can be explained based on an absence of the substrate influence, at these penetration depths. Thus, very reliable hardness measurements in thin films can be performed under conditions of low loads and very small indenter diagonal sizes, in such a way that the penetration depth does not reach the 10% of the film thickness. These results support our proposed mechanism of self assembly formation of a hard surface on a softer matrix present in the prepared hybrid coatings, possibly due to a higher concentration of SiO2 particles at the surface of the film. We think that the rich SiO2 harder external layer is originated at the beginning of the drying process because of some evaporation of the monomer MMA. The escape of monomer from the hybrid coating stops when this external layer attains the appropriate thickness to work as a diffusion barrier for the monomer. Figure 5 shows the calculated surface- and intermediate-coating hardness as function of the PMMA molar content. The behaviour in both, surface and intermediate coating hardness is in a non-linear decreasing as the PMMA contents increase. This tendency is not surprising, since PMMA shows hardness values much lower than SiO2. Considering these results, hybrid coatings can be produced with tailored mechanical properties. 
Figure 5. Coating hardness of the surface and intermediate layer as a function of PMMA concentration measured with Nanoscope IV. Conclusions Hybrid SiO2-PMMA coatings were successfully prepared by the sol-gel method. The mechanical behavior of the whole hybrid coating-substrate system can be appropriately described by a system of two layers of materials with different hardness on a glass substrate and analyzed separately by the indentation method. Analysis of the mechanical behaviour of the two layers as a function of penetration depth in the prepared hybrid coatings showed a hardness enhancement mechanism, because the formation of a SiO2 rich layer at the surface of the coatings during the drying process. This hardness enhancement effect is as high as one order of magnitude compared to the PMMA hardness. The hardness behavior of the hybrid coatings as a function of the TEOS:PMMA ratio is in a non-linear decrease as the PMMA contents increase. References 1. 1. U. Schubert, N. Hüsing and A. Lorenz, “Hybrid Inorganic-Organic Materials by Sol-Gel Processing of Organofunctional Metal Alkoxides”, Chem. Mater., 7 (1995) 2010-2027. 2. 2. C. Sanchez and F. Ribbot, “Design of hybrid organic-inorganic materials synthesized via sol-gel chemistry”, New J. of Chem., 18 (1994) 1007-1047. 3. 3. J. Wen and G. L. Wilkes, “Organic/Inorganic Hybrid Network Materials by the Sol–Gel Approach”, Chem. Mater., 8 (1996) 1667-1681. 4. 4. P. Judeinstein and C. Sanchez, “Hybrid organic-inorganic materials: a land of multidiciplinarity”, J. Mater. Chem., 6 (1996) 511-525. 5. 5. P. F. W. Simon, R. Ulrich, H. W. Sleps and Ulrich Wiesner, “Block Copolymer-Ceramic Hybrid Materials from Organically Modified Ceramic Precursors”, Chem. Mater., 13 (2001) 3464-3486. 6. 6. A. M. Korsunsky, M. R. McGurk, S. J. Bull and T. F. Page, “On the hardness of coated systems” Surf. Coat. Technol., 99 (1998) 171-183. 7. 7. A. Hurtado Macías, J. González Hernández, J. Muñoz Saldaña, P. Herrera Fierro, P. García Jiménez, J. Espinoza Beltrán, T. Scholz and G. A. Schneider, “Mechanical characterization or thin amorfous tungsten-carbon (WxCy) films prepared by DC-cosputtering”, Vacuum, 76 (2004) 173-176. 8. 8. P.J. Burnett and D.S. Rickerby, “The mechanical properties of wear-resistant coatings”, Thin Solid Films, 148 (1987) 51-65. 9. 9. J. R. Tuck, A. M. Korsunsky, D.G. Bhat and S.J. Bull, “Indentation hardness evaluation of cathodic arc deposited thin hard coatings”, Surface and Coatings Technology, 139 (1998) 63-74. 10. 10. B. Jonsson and S. Hogmark, “Hardness measurements of thin films” Thin Solid Films, 114 (1984) 257-269. 11. 11. W.C. Oliver and G.M. Pharr, “An improved technique for determining hardness and elastic modulus using load a displacement sensing indentation experiments”, J. Mater, Res., 7 (1992) 1564-1583. 12. 12. Z.H. Huang and K.Y. Qiu, “The effects of interactions on the properties of acrylic polymers/silica hybrid materials prepared by the in situ sol-gel process”, Polymer, 38 (1997) 521-526. 13. 13. C.K. Chan, S.L. Peng, I.M. Chu and S.C. Ni, “Effects of heat treatment on the properties of poly(methyl methacrylate)/silica hybrid materials prepared by sol-gel process”, Polymer, 42 (2001) 4189-4196. 14. 14. J. Gallardo, A. Duran, D. Di Martino and R.M. Almeida, “Structure of inorganic and hybrid SiO2 sol-gel coatings studied by variable incidence infrared spectroscopy”, J. Non-Cryst. Solids, 298 (2002) 219-225. 15. 15. A. Fidalgo and L.M. Ilharco, “Thickness, Morphology and Structure of Sol-Gel Hybrid Films: I-The Role of Precursor Solution’s Ageing”, J. Sol-Gel Science and Technology, 26 (2003) 363-367. 16. 16 Y. Zhang and M. Wang, “Mechanical characterization and optical properties analysis of organically modified silicates”, J. Non-Cryst. Solids, 271 (2000) 88-93. Contact Details | J.L. Almaral-Sanchez Universidad Autonoma de Sinaloa, Fuente de Poseidon y Prol. Angel Flores, S.N., C.P. 81223
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