Dynamics of Hybrid Poly(acrylamide-co-N,N-dimethylacrylamide

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Dynamics of Hybrid Poly(acrylamide-co-N,N‑dimethylacrylamide) Hydrogels Containing Silica Nanoparticles Studied by Dynamic Light Scattering Séverine Rose, Alba Marcellan, Dominique Hourdet, and Tetsuharu Narita* Laboratoire SIMM-PPMD, UMR7615, UPMC-ESPCI ParisTech-CNRS, 10 Rue Vauquelin, 75231 Paris Cedex 05, France ABSTRACT: Nanohybrid gels based on poly(acrylamide-coN,N-dimethylacrylamide), P(AAm-co-DMA), and colloidal silica nanoparticles were synthesized by radical polymerization, and the influence of hydrogen bonding between DMA and silica nanoparticles on the dynamics of the network and the nanoparticles were studied by dynamic light scattering. As previously reported, in the case of polyacrylamide homopolymer, PAAm, which have no hydrogen bonding with silica, we observed two decay modes in the hybrid gels, a gel mode and a Brownian diffusion mode of silica nanoparticles. When we increased the DMA weight fraction (or physical cross-link density), we observed (1) a higher scattered light intensity than the silica suspension and the gel without silica, (2) an increased plateau value of the autocorrelation function, (3) a slowing down of the silica diffusion mode, and (4) no influence on the gel mode. These results, compared with those of the mixtures of the linear PDMA and silica nanoparticles in solution (showing an increase in the scattered light intensity and in the hydrodynamic radius), indicate that the P(AAm-co-DMA) hybrid gels have a more heterogeneous structure due to the adsorption of the polymer on the silica nanoparticles, and that the silica nanoparticles, trapped in the network due to the adsorption of the polymer, show a cage dynamics in the network. The local viscoelastic properties probed by the bound nanoparticles are discussed.

1. INTRODUCTION Hydrogels are cross-linked polymers forming a three-dimensional network highly swollen by an aqueous medium. From a macroscopic point of view, if the lifetime of the polymer crosslinks is long enough compared to the experimental time, hydrogels behave like solids; they have a defined geometry and they do not flow like liquids on the corresponding time scale. Simultaneously, these macromolecular reservoirs are similar to real solutions as solute diffusion can occur through hydrogels, with diffusion coefficients depending on the mesh size of the network and on the level of interactions. Since the beginning of the 1980s, hydrogels have had a continuous development, leading to many biomedical applications such as drug delivery systems, superabsorbent or contact lenses, etc.1−4 The high water content of synthetic hydrogels is at the origin of their dominating brittleness, limiting their applications: they break often under a few kPa of stress. The reinforcement of their poor mechanical properties is actually a fundamental challenge for a lot of research groups, motivated by the numerous future applications of toughened hydrogels. Over the past ten years, several reinforcement strategies have been developed all over the world, such as the elaboration of ideal networks,5,6 the design of highly heterogeneous double networks,7,8 and the combination of organic and inorganic components in nanocomposite hydrogels. This last strategy has been largely studied by Haraguchi et al.9−11 This strategy aims © XXXX American Chemical Society

at mixing chemical and reversible interactions by introducing inorganic nanoparticles in the polymer network. The mechanical properties of a system based on poly(Nalkylacrylamide) hydrogels with silica nanoparticles have been widely studied.12,13 Reinforcement due to strong but reversible adsorption of polymer chains onto the surface of silica nanoparticles has been demonstrated, leading to a simultaneous enhancement of elasticity and strain at failure. In these nanocomposite gels, prepared with and without chemical cross-linker (such as N,N′-methylenebis(acrylamide)), inorganic particles behave as physical multiple cross-linking points. Mechanisms for forming the unique network structure have been proposed. Haraguchi et al. proposed the formation of “clay-brush particles”.14 As a matter of fact, the interactions between clay surfaces and a mixture of N-isopropylacrylamide monomer, potassium persulfate and a common catalyst (TEMED) lead to the growth of polymer brushes grafted on the exfoliated clay platelets. With this specific grafting, occurring during the first steps of polymerization, the obtained hybrid hydrogels are heterogeneous regarding the spatial organization of cross-linking points. Abdurrahmanoglu et al. proposed a mechanisms of adsorption of N-alkylacrylamide Received: May 2, 2013 Revised: June 5, 2013

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nanoparticles, using thermal dissociation of KPS as initiator, at 80 °C. For all the syntheses the polymer concentration was set equal to 6 wt %. Aqueous solutions were initially prepared with the following concentrations: 10 wt % of AAm, 2.5 wt % of DMA, 1 wt % of MBA, 1 wt % of KPS, and 10 wt % of silica nanoparticles. The aqueous solutions were introduced in a vessel in this order: AAm, DMA, MBA, KPS, silica nanoparticles and distilled water. After stirring, the obtained mixture was introduced in test tubes of 10 mm diameter through syringe filters of 0.8 μm. The sealed test tubes were placed in an oven at 80 °C for 12 h. The weight fraction of the DMA monomer to the total monomer content, ωDMA was varied from 0 to 0.1. Since the total monomer concentration was kept to 6 wt %, the DMA concentration to the total gel weight is 6ωDMA (wt %). We did not adjust pH or ionic strength. For pregel solutions containing 1% of silica nanoparticles the value of pH was measured to be 9.4. The solutions contain 8.5 mM of KPS. 2.3. Dynamic Light Scattering Measurements. Dynamic light scattering measurements were performed with an ALV CGS-3 goniometer system (ALV, Langen, Germany), equipped with a cuvette rotation/translation unit (CRTU) and a He−Ne laser (22 mW at λ = 632.8 nm). The system measures the time-averaged autocorrelation function of the scattered light intensity at a scattering vector q. In order to circumvent the nonergodicity associated with the presence of frozen disorder in chemically cross-linked gels, the sample cell was vertically translated steadily while time-averaging. Thus, g(2) coincides with the ensemble-averaged autocorrelation function, up to a cutoff delay time fixed by the sample rotation speed. For this study this cutoff decay time was found to be about 100 s, independent of q. The averaging duration was more than 3600 s depending on the slowest relaxation modes found in the autocorrelation functions. Gels samples for DLS measurements were prepared in test tubes (10 mm in diameter), filtered by a syringe filter of 0.45 μm. 2.4. Hydrogels Synthesis for Mechanical Measurements. Hydrogels were prepared at 25 °C by free-radical polymerization of DMA and AAm in an aqueous suspension of silica nanoparticles using KPS and TEMED as redox initiatiors. For all syntheses, the (DMA)/ (KPS) and (DMA)/(TEMED) molar ratio were fixed equal to 100. The cross-linking density was also kept constant, using a cross-linker/ monomer molar ratio (MBA/DMA) equal to 0.1 mol %. The amount of silica nanoparticles was varied, keeping constant the matrix composition, i.e. the water/polymer ratio, corresponding to a concentration of 12.5 wt %. Two aqueous solutions were prepared: KPS at 4.5 wt % and MBA at 1.2 wt %. First, the MBA solution and the DMA and/or AAm were dissolved at 25 °C in an aqueous suspension of silica particles. The homogeneous suspension was purged with nitrogen during 15 min under magnetic stirring. At the same time, the aqueous solution of KPS was prepared and deoxygenated with nitrogen bubbling. The KPS solution and TEMED were then rapidly added into the suspension under vigorous stirring. Finally, the mixture was transferred, under nitrogen atmosphere, into appropriate laboratory-made molds. The samples were left for 24 h in a closed vessel under nitrogen atmosphere before use. 2.5. Mechanical Measurements. Mechanical tests were performed on a tensile Instron machine (model 5565) equipped with a 10N load cell (with a relative uncertainty of 0.16% in the range from 0 to 0.1 N) and a video extensometer (with a relative uncertainty of 0.11% at full scale of 120 mm). The nominal strain was kept equal to 0.06 s−1. Sample geometry was kept constant: the gauge length L0 ≈ 20−25 mm, the width w = 5 mm and the thickness t = 2 mm. In order to avoid any change in hydrogel composition, induced by swelling or drying during the experiment, samples were stored into paraffin oil until mechanical testing.

monomers on the clay particle surfaces, leading to depletioninduced particle aggregates.15 Recently, we studied the dynamic behaviors of these chemically and physically cross-linked networks and of the nanoparticles, that had not been systematically studied in the literature.16 The nature and the quality of the interactions occurring between the polymeric matrix and the nanoparticles clearly affect the dynamics of the system. Working on the dynamics of hybrid polyacrylamide hydrogels containing colloidal silica particles, we explored the effects of chemical cross-links, physical cross-links and radical polymerization separately. Different from the poly(N-alkylacrylamides) which are known to be able to form hydrogen-bonds with silica, polyacrylamide shows less interaction since it is simultaneously hydrogen-bonding donor and acceptor.17 In fact the hybrid polyacrylamide hydrogels do not show any reinforced properties when synthesized in presence of silica nanoparticles.12 More experimental results showing the difference in affinity with silica between PDMA and PAAm can be found in the literature, such as the study of adsorption of grafted copolymers onto silica, in which Cohen-Stuart and coauthors demonstrated the poor affinity between polyacrylamide and silica surface.18 In our previous study,16 the silica nanoparticles acted as diffusion tracer probing the microenvironment in the polyacrylamide hydrogel. We demonstrated that a transfer of radicals from the persulfate used, to the surface of the silica nanoparticles was at the origin of a polyacrylamide chain growth from the silica surface: a grafting polymerization of acrylamide occurs, giving rise to heterogeneous network structures. In the present study, we report a dynamic light scattering study of the dynamics of silica nanoparticles in poly(acrylamide-co-N,N-dimethylacrylamide) hybrid gels (P(AAmco-DMA) gels). The physical interactions between DMA and silica nanoparticles is controlled by changing the monomer composition. We show that the addition of the hydrogen bonding comonomer DMA, changes dramatically the dynamics of silica nanoparticles in the gels compared with the gels without specific interactions. The physical interactions trap the silica nanoparticles in the gel, showing a cage dynamic behavior. We also try to correlate these differences in local dynamics with the significant differences in mechanical properties previously observed12,13 between poly(AAm-co-DMA) and PAAm hybrid gels. It was shown that the first polymer PAAm does not lead to any mechanical reinforcement, while the second one PDMA clearly increases the initial stiffness and the strain at failure of the gel in the presence of silica nanoparticles.

2. EXPERIMENTAL SECTION 2.1. Materials. N,N-Dimethylacrylamide (DMA, 99%, SigmaAldrich), acrylamide (AAm, 99%, Sigma-Aldrich), N,N′-methylenebis(acrylamide) (MBA, Fluka), potassium persulfate (KPS, Acros Organics), poly(N,N-dimethylacrylamide) (PDMA, Mw = 100000 g/ mol, Scientific Polymer Products), and urea (Sigma-Aldrich) were used as received without further purification. The silica particles suspension (Ludox TM-50) were purchased from Aldrich and used as received (52 wt % of silica in water). They were characterized by dynamic light scattering using an ALV/CGS-3 compact goniometer (ALV, Langen, Germany) in dilute conditions giving an average hydrodynamic radius Rh = 17 nm. A specific area Sspe = (3/ρSiR) = 100 m2/g, using ρSi = 2.3 × 106 g/m3 for the density of pure silica. 2.2. Hydrogels Synthesis for DLS Measurements. Hybrid hydrogels were prepared by free-radical copolymerization of DMA and AAm monomers and MBA in an aqueous suspension of silica

3. RESULTS AND DISCUSSION In order to clearly discuss the dynamics of P(AAm-co-DMA) hybrid gels, we characterized first a reference network composed of cross-linked P(AAm-co-DMA) without silica nanoparticles. The chemical cross-linking ratio was fixed at B

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hybrid gels, and the field autocorrelation function can be well fit with the following equation:

0.1 mol %, sufficient to obtain a well-defined plateau in the autocorrelation function, low enough to allow the particles to show mobility detectable by DLS. Figure 1 shows a comparison

(1)

g (t ) = Agel + g(1)(∞)

⎡ ⎛ ⎞γ ⎤ ⎡ ⎛ t ⎞γSi ⎤ t exp⎢ −⎜⎜ ⎟⎟ ⎥ + ASi exp⎢ −⎜ ⎟ ⎥ ⎢⎣ ⎝ τgel ⎠ ⎥⎦ ⎢⎣ ⎝ τSi ⎠ ⎥⎦ (1)

Here A is the amplitude of each mode, τ is its characteristic relaxation time, the exponent γ which takes into account the slight polydispersity. g(1)(∞) which is equal to 1 − Agel − ASi indicates the amplitude of the plateau. Note that the autocorrelation function contains the decorrelation due to the translation of the sample for ensemble averaging at the longer time range. The plateau value was taken as the amplitude of this decorrelation which has no physical meaning of the gel. The introduction of the DMA comonomer in the acrylamide network leads to practically no effect on the gel mode even in the presence of the silica nanoparticles. At given silica concentration, the characteristic relaxation time of the gel mode does not change with DMA concentration as shown in the inset of Figure 2. On the other hand, a pronounced change in the silica dynamics was observed: increasing the DMA content apparently results in (1) an increase in the characteristic time of the silica nanoparticles dynamics and (2) an increase in the amplitude of the plateau. The characteristic times τSi of the silica nanoparticles dynamics are plotted as a function of the scattering vector q in Figure 3. We observed that τSi increased with increase in the

Figure 1. Normalized field autocorrelation functions for PAAm gel (solid line) and P(AAm-co-DMA) gel (dashed line). The weight fraction of DMA monomer was 0.05. Inset: collective diffusion coefficient and normalized intensity of P(AAm-co-DMA) chemical gels as a function of DMA weight fraction.

of the normalized field autocorrelation functions of a PAAm hydrogel with a P(AAm-co-DMA) hydrogel (with a weight fraction of DMA to the total monomer content equal to ωDMA = 0.05) without silica nanoparticles. We found no difference between the two gels: for both hydrogels, a decorrelation corresponding to the gel mode characteristic of the collective diffusion of the cross-linked network, is followed by a plateau, the amplitude of which corresponds to the nonfluctuating concentration gradient of the gel. The addition of DMA monomer does not influence the dynamics of the gel presumably due to the physicochemical similarities between the two monomers and the small amount of added DMA. For all the gels studied in this work we found a q−2 dependence of the characteristic time of the gel mode (no data shown). The diffusion coefficient, D, is defined as τ = 1/(Dq2). The effects of the silica nanoparticles added into the polymeric network on its dynamic properties were studied. Here the reference hybrid hydrogel is composed of a pure PAAm network chemically cross-linked by 0.1 mol % of MBA and containing 1% of silica nanoparticles (gray line in Figure 2). This hybrid hydrogel shows a first decorrelation mode at about 10−4 s (gel mode) and a second one at about 0.1 s corresponding to the silica nanoparticles dynamics as previously reported.16 As previously reported, 16 the second slow mode was attributed to the dynamics of silica nanoparticles in the

Figure 3. Characteristic times of gel mode and silica nanoparticle diffusive mode in P(AAm-co-DMA) hybrid gels having various DMA weight fraction.

DMA weight fraction showing a q−2 dependence at high q values. At low q values τSi is independent of q, τ = 0.5 (sec) for ωDMA = 0.0075, and τ = 1.5 (sec) for ωDMA = 0.025. This q independent dynamics can be interpreted as the dynamics of particles in a “cage”: the particles are bound to the polymer or trapped in the network and show a limited displacement in a cage. Thus, at the length scale of observation 1/q larger than the cage size δ, τSi is independent of q. And at 1/q < δ, diffusive movement inside the cage can be observed and τSi shows a q−2 dependence. The transition from the q−2 to the q0 dependence occurs at qcage = 1/δ = 1.3 × 107 m−1 for ωDMA = 0.0075 (thus δ = 77 nm) and at qcage = 1/δ = 1.9 × 107 m−1 for ωDMA = 0.025 (δ = 52 nm). Although the dispersion of data points is rather large, we can reasonably observe that the cage size δ decreased with an increase in the DMA concentration. Figure 4 shows the logarithmic value of the normalized field autocorrelation function at the plateau as a function of q2. For

Figure 2. Normalized field autocorrelation functions of P(AAm-coDMA) hybrid gels containing 1% silica nanoparticles. Inset: q dependence of the gel mode characteristic time. C

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Figure 4. q2 dependence of ln g(1) at the plateau. Figure 5. Normalized scattering light intensity as a function of DMA weight fraction in P(AAm-co-DMA) hybrid gels containing 1% of silica nanoparticles. The gray dashed line indicates the value for silica nanoparticle suspension at the same concentration (without gel).

the reference hybrid PAAm gel (ωDMA = 0), we observed that the plateau value was independent of q2. For the hybrid gels containing DMA, we observed that the value of ln g(1)(∞) was constant at high q value while at low q value it increases to 0 with decrease in q. Although the uncerainty is rather important, the change in the slope occurs practically at the same value of q as that for τSi in Figure 3, indicating the transition from the cage dynamics to diffusive motion. The arrows in Figure 4 indicate 1/δ2. It should be noted that when the value of τSi is close to the decay time of translation (about 100 s), the two modes start to overlap and the accuracy of the estimation of ASi thus ln g(1)(∞) and τSi decreases. We found that for the DMA fraction higher than 0.03, the transition point 1/q = δ does not match for τSi and ln g(1)(∞). For ωDMA less than 0.025, they matched reasonably despite the relatively large data dispersion. We will discuss qualitatively the interpretation of this dependence later in this article. For the system having caged particles, the asymptotic value at the plateau is related to the cage size δ:19

estimated from the cage dynamics, giving a lower value of the slope and thus of δ. This situation is different from that explained by eq 2, and has not been well studied, since in the typical microrheological experiments, “probe” particles are not supposed to change the probed network structure. The effects of the DMA−silica physical interaction on the scattering intensity are further studied. In order to evaluate the stoichiometry of the interaction, the influence of the silica nanoparticle concentration on the scattered light intensity was studied. Figure 6 shows the scattered light intensity of the

g(1)(q , ∞) = exp( −q2δ 2), ln g(1)(q , ∞) = −q2δ 2

(2) (1)

As shown in Figure 4, at lower q values, ln g (∞) is proportional to q2, with the slope expected to be equal to −δ2. The two values of δ, one estimated from the transition point of q0 to q−2 dependence in Figure 3, the other from the slope of the plateau value of ln g(1) in Figure 4 were compared. We found a smaller value of δ for the second estimate (from the slope). For example, for ωDMA = 0.0075, we found δ = 77 nm from the transition point and 51 nm from this slope. In order to understand this discrepancy, it is necessary to take into account of the total scattering light intensity, because the amplitude of each relaxation mode and that of the plateau value are related to the scattered light intensity of the corresponding mode, and the plateau value is correlated also to the frozen-in component of the scattered light deriving from the static concentration gradient of the network. Figure 5 shows the normalized scattered light intensity as a function of DMA weight fraction. At low DMA fractions (from 1 × 10−3 to 3 × 10−3), the intensity is the same as that of silica nanoparticles in suspension (I/Itol = 450), and much bigger than that of the gel without silica nanoparticle (I/Itol = 11). At ωDMA = 0.004, the intensity suddenly increases up to about 900, showing no particular DMA fraction dependence at higher concentration. These results indicate that the structure of the network and/or silica dispersion in the gel was modified by the presence of DMA. Thus, the plateau value of the network is higher than that

Figure 6. Scattered light intensity of P(AAm-co-DMA) hybrid gel normalized by that of the silica nanoparticles suspensions of the same concentration as a function of the weight ratio of DMA to silica nanoparticles.

hybrid gels normalized by that of the corresponding silica suspension as a function of the weight ratio of DMA to silica nanoparticles. We found that the intensity increases dramatically at a certain weight ratio, 0.12 g/g, for all the studied silica nanoparticles concentrations. Using this value and that of the specific surface area (100 m2/g),20 the amount of the DMA (incorporated in the P(AAm-co-DMA) copolymer) adsorbed onto the silica surface is estimated to be 1.2 mg/m2. This value is close to the literature value for the adsorption of the linear PDMA polymer in solution (0.95 mg/m2),20 suggesting that the adsorption of radically polymerized P(AAm-co-DMA) polymer starts from this weight ratio of 0.12. The scattered light intensity from P(AAm-co-DMA) hybrid gels (Figure 5) was compared with that from the mixture of the linear PDMA polymer and the silica nanoparticles in solution. A commercially available PDMA polymer was used, and no radical polymerization in the presence of silica particles was performed. In Figure 7a, the scattered light intensity normalized by that of toluene at 90° is plotted as a function of the PDMA D

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Figure 8. Schematic illustration of dynamics of silica nanoparticles in PAAm gel and P(AAm-co-DMA) gel. For PAAm gel without DMA (left), no polymer adsorption occurs, thus hindered diffusion of silica nanoparticles passing through the mesh of the gel is observed (τSi ∼ q−2). For P(AAm-co-DMA) gel (right), the polymer adsorption entraps the silica nanoparticles; thus, the cage dynamics is observed for the length scale 1/q longer than the cage size δ (τSi ∼ q0).

Figure 7. Hydrodynamic thickness of adsorbed PDMA polymer on silica nanoparticle surface in solution as a function of DMA weight fraction without (filled triangles) and with (open triangles) urea.

concentration. The silica nanoparticles concentration is 1% for the both systems. We observed a gradual increase in the intensity from as low PDMA concentration as 0.02%. The intensity leveled off at about I/Itol = 700. At the same time the hydrodynamic radius of the silica nanoparticles was measured. The increase in the hydrodynamic radius, attributed to the adsorbed polymer layer, was calculated with the measured values of the diffusion coefficient and viscosity. By using the diffusion coefficient of the particles in water D0 and in the polymer solution D, and the viscosity of water η0 and of the polymer solution η, the hydrodynamic thickness of the adsorbed polymer layer, e, can be estimated from: D0 =

kBT , 6πη0R

D=

kBT , 6πη(R + e)

linear PDMA adsorption in solution (Figure 7), the adsorbed polymer layer thickness e in a P(AAm-co-DMA) gel is expected to be several nm. The maximum displacement of the nanoparticles with their adsorbed polymer layer is the cage size δ. The silica nanoparticles bound to the network show diffusive motion in the cage when observed at the length scale of observation 1/q < δ. In order to qualitatively discuss the effects of DMA concentration on the cage dynamics, the value of δ is discussed. The values of δ determined from the transition points in Figure 3 and 4 were plotted as a function of ωDMA in the inset of Figure 9. δ deceases monotonously with increase in ωDMA. The

Dη R = R+e D0η0 (3)

Figure 7b shows the hydrodynamic adsorbed polymer layer thickness e as a function of the polymer concentration. The value of e increased gradually with the PDMA concentration up to 10 nm. This value is comparable with that of poly(ethylene oxide) having the same molecular weight, which adsorbs also onto the silica surface by hydrogen bonding.21 We found also that the addition of urea in the solution decreased the absorbed polymer thickness, indicating that the DMA − silica interaction is due to hydrogen bonding. Comparing Figure 5 and Figure 7a, the critical increase in the intensity for the P(AAm-co-DMA) hybrid gel is presumably due to the free radical copolymerization. The DMA fraction in the copolymer might become higher at the silica surface during the polymerization. We do not have however any experimental proof of monomer adsorption. From these experimental results we schematically illustrate the dynamics of the silica nanoparticles in the hybrid gels with and without DMA (Figure 8). For 1% of nanoparticles having a hydrodynamic radius of 17 nm, the average interparticle centerto-center distance is predicted to be 168 nm. Without DMA, or in chemically cross-linked PAAm gels, there are no interactions between the network and the silica nanoparticles, and the nanoparticles show diffusive motion in the network. Although the average hydrodynamic correlation length is smaller than the particle radius, the network structure is very heterogeneous for this polymer concentration and the low level of chemical crosslinking, thus the particles can be diffusive.16 With a sufficient amount of DMA (DMA/Si > 0.12), the P(AAm-co-DMA) is partly adsorbed onto the silica surface by hydrogen bonding, hindering diffusive motion of the silica nanoparticles. Although we do not have any direct proof, from the comparison with the

Figure 9. Local shear modulus μ probed by the silica nanoparticles as a function of weight fraction of DMA monomer in P(AAm-co-DMA) gels. Inset: cage size δ as a function of ωDMA determined by the transition points of τSi in Figure 3 (filled circle) and of ln g(1)(∞) in Figure 4 (open square).

values determined from τSi in Figure 3 showed a good agreement with those determined from ln g(1) in Figure 4, though the dispersion is larger for the latter. The values estimated from the transition point of τSi in Figure 3, are used for further discussion. The local shear modulus μ probed by the silica nanoparticles can be calculated from μ=

kBT 6πRδ 2

(4)

μ is plotted as a function of ωDMA in Figure 9. The local shear modulus, which is of the order of a few Pa, increases monotonously with the DMA concentration. The shear modulus measured by polystyrene particles much bigger than the mesh size (250 nm in radius) is about 200 Pa.16 This result suggests that the silica nanoparticles having a size comparable E

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with the mesh of the network do not probe the viscoelasticity of the bulk network as do the bigger polystyrene particles. We believe that the local shear modulus probed by the silica particles corresponds to the elasticity of the polymer chains adsorbed by hydrogen bonding between DMA and silica, connecting the silica particles to the network. Since the polymer chains adsorbed by hydrogen bonding could reversibly dissociate and reassociate, and they are expected to be connected to the network, it is not clear how the movement of the silica nanoparticles is coupled with that of the adsorbed polymer layer. Still the impact of the adsorbed polymer layer thickness e on the estimation of the local shear modulus is not high: in eq 4 R = 17 nm is simply replaced by R + e = 27 nm, the difference of the modulus is of a factor of 17/27 = 0.63. It does not influence the following discussion. The increase in the local modulus with increase in the DMA fraction in the polymer network was further investigated. Since the local modulus measured here is entropic, it should be proportional to the density of elastic active chains, G′ = (N/V) kBT, where N is the number of elastically active chains in the considered volume V. If we only consider chemical cross-links, in the volume corresponding to the dynamic cage, V = (4π/ 3)δ3, the value of N is almost 1 for all the data in Figure 9, suggesting that the increase in μ observed in Figure 9 is not due to the increased number of elastically active chains. From the bulk modulus, we calculated the length of the elastically active chain between two chemical cross-links, ξ to be 27 nm (G′ = (kBT/ξ3). With the values of the Kuhn length (b = 0.6 nm) and the exponent of Marks-Houwink relation (α = 0.75) of polyacrylamide in water found in the literature, the number of monomers in an elastically active chain, n, was estimated to be 680 (ξ = bn(α + 1)/3)). For a random copolymerization of the given DMA amounts ωDMA between 0.0075 and 0.025, 5 to 17 DMA units should be copolymerized in the chain. Since the chain adsorbs onto the silica surface by the DMA units, these DMA/silica interactions decrease the effective number of monomers neff of the elastically active chain as neff ∼ (n/ωDMA). The finite extensibility of the chain should scale with neff/neff0.58 = neff0.42 and controls δ. Thus, we expect that the extensibility of the adsorbed chain plays an important role on the measured local modulus: the more DMA in the copolymer, the less the adsorbed polymer chains can stretch, thus μ increases with ωDMA. The local friction coefficient ν probed by the nanoparticles can be estimated from the characteristic time of the cage τcage (the value of τSi independent of q at q < 1/δ) and the cage size δ: ν = μτcage =

Figure 10. Local friction coefficient ν probed by the silica nanoparticles as a function of weight fraction of DMA monomer in P(AAm-co-DMA) gels. Closed squares: calculated from the cage size and characteristic time. Open squares: calculated from Stokes− Einstein relation in the cage. Inset: characteristic time of the cage τcage as a function of ωDMA.

the binding sites, slowing down the relaxation process of the surrounding polymer matrix. The diffusive mechanisms occurring in the hybrid network can be separated and analyzed in terms of a collective diffusion coefficient and a diffusion coefficient of the silica nanoparticles. Figure 11a shows the DMA weight fraction dependence of the

Figure 11. (a) Collective diffusion coefficient and (b) diffusion coefficient of silica nanoparticles (in the cage) as a function of DMA weight fraction in P(AAm-co-DMA) hybrid gels. The gray dashed line indicates the value for ωDMA = 0 (PAAm gel).

collective diffusion coefficient. It is clear that the DMA has no effect on this collective diffusion coefficient at the given DMA and silica concentrations. Concerning the silica nanoparticles diffusion, increasing the DMA weight fraction strongly decreases their diffusion coefficient which is inversely proportional to ν, as shown in Figure 11b. Note that a very small amount of DMA is sufficient to decrease considerably the diffusion coefficient. With our DLS setup it is practically impossible to detect the silica dynamics when ωDMA > 0.03. Before concluding this paper, let us discuss the effect of copolymerization on the macroscopic mechanical properties. A comparison between the information obtained at a microstructural level can be done with the macroscopic mechanical behavior of hybrid hydrogels that have been studied in terms of Young’s modulus as a function of the silica volume fraction. The results are presented in Figure 12. For hybrid hydrogels of pure PDMA matrix, an enhancement of the initial stiffness is obvious by increasing the silica content and can be explained

kBTτcage 6πRδ 2

(5)

This relation is essentially a Stokes−Einstein relation; thus, ν can also be estimated from the diffusive motion in the q−2 dependent regime: D=

kBT 1 = 2, 6πvR τq

thus v =

kBTτ 6πRq−2

(6)

As shown in Figure 10, we found that the value of ν increased with the DMA concentration. The value is between 0.3 and 8 Pa·s within the studied range of DMA concentration. Nisato et al. found about 2 Pa·s for chemically cross-linked PAAm gels, independent of the chemical cross-linking ratio.22 Here increasing the DMA concentration results in an increase in F

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described in the Experimental Section but incorporating also urea in water with a fixed amount of urea for each gel (10%). We observed that the initial modulus of the hydrogels with urea (open circles) is far below the reference hybrid hydrogels without urea (filled circles). Similarly to the result shown in Figure 7b, the presence of urea reduces the hydrogen bonding between the PDMA and silica nanoparticles, decreases the polymer adsorption and thus the mechanical reinforcement.

4. CONCLUSIONS The dynamics of hybrid P(AAm-co-DMA) hydrogels with various weight ratios of AAm and DMA, containing silica nanoparticles have been studied by dynamic light scattering. We observed and explained the effects of the presence of silica nanoparticles, having interactions (hydrogen bonding) with DMA but not with AAm, on the dynamics of the network and of the nanoparticles in the polymeric network. When the amount of DMA is progressively increased in P(AAm-co-DMA) hybrid hydrogels, a trapping of the silica nanoparticles is observed due to the strong physical interactions with DMA, clearly demonstrated by the q-dependence of the characteristic time of the silica nanoparticles dynamics. Microrheological properties of the hybrid gels probed directly by the silica nanoparticles with adsorbed polymer network were studied. The local shear modulus and the local friction coefficient increased with an increase in the amount of DMA monomer. These values are not comparable with those of the bulk network, suggesting that the local motion of the nanoparticles inside the network is sensitive to the adsorbed polymer layer and to the immediately surrounding polymer structure, which may be different from that of the bulk which is also shown as an increase in the total scattering intensity from the hybrid gels. It is suggested that the extensibility of the adsorbed elastically active chain contributed to the increase in the local modulus with increase in DMA concentration. The physical adsorption of PDMA units onto the silica nanoparticles surface leads to an enhancement of the mechanical properties of the hydrogels: the initial stiffness and the strain at failure increased with the silica content. This improvement can be controlled and reversed by introducing a hydrogen bonding competitor, such as urea, leading to a dramatic decrease of the mechanical properties.

Figure 12. Modulus of P(AAm-co-DMA) hybrid gels as a function of volume fraction of silica nanoparticles. Key: filled circles, ωDMA = 1; open squares, ωDMA = 0.3; filled triangle, ωDMA = 0.1; open triangle, ωDMA = 0.01; open circles, ωDMA = 1 with 10% of urea. The black dashed line is the guide for the eye. The gray solid line gives predicted values of the modulus calculated from the Guth−Gold model. Inset: Modulus of P(AAm-co-DMA) hybrid gels containing ϕSi = 0.21 of silica nanoparticles as a function of volume fraction of the weight ratio of DMA to silica nanoparticles.

thanks to the specific interactions between PDMA and the silica nanoparticles (black dots). This improvement has been studied and reported in detail previously,12,13 and contrary to most hybrid hydrogels, the mechanical properties are enhanced not only in terms of initial stiffness but also in terms of strain at failure. The reinforcement effect can be compared to the classical model of Guth, Gold, and Simha developed in order to study the impact of filler content on the properties of a rubbery matrix (gray line).23,24 The conditions of use of this model are: an incompressible matrix and hard spherical particles without specific interactions with the matrix. This model can be used for low volume fractions of filler (typically lower than 0.2) and the Young’s modulus of the reinforced material E is then E = E0(1 + 2.5ϕ + 14.1ϕ2)

(7)

with E0 the Young’s modulus of the unfilled matrix. As represented in Figure 12, the model of Guth and Gold is far below the experimental values of the initial modulus, revealing macroscopically the strong interactions taking place between the PDMA swollen matrix and the silica nanoparticles. The reinforcement is essentially visible at high silica contents (especially for silica volume fractions higher than 0.1), corresponding to a weight ratio DMA/Si values varying from 0.2 to 0.5. Introducing the non-hydrogen bonding monomer AAm into the PDMA network directly leads to a decrease in modulus compared to the pure PDMA system. The progressive loss of stiffness exactly follows the progressive incorporation of AAm monomer into the network: from ωDMA = 1 to 0.01 in the polymer matrix, the initial modulus decreases from 102 to 20 kPa at a fixed silica volume fraction of 0.21, as represented in Figure 12. In the inset, the modulus is plotted as a function of the weight ratio DMA/Si. It is shown that a certain amount of DMA, more than DMA/Si = 0.1, is required for the mechanical reinforcement by the DMA adsorption. The result in Figure 6 which indicates that DMA/Si > 0.12 is the condition for P(AAm-co-DMA) adsorption, qualitatively agrees with that of the inset in Figure 12. The physical adsorption of the PDMA chains onto the silica surface can be annihilated in the presence of a hydrogen bonding competitor, such as urea. For that purpose, hybrid hydrogels were prepared following the same protocols as

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AUTHOR INFORMATION

Corresponding Author

*(T.N.) Fax: +33(0)1 40 79 46 86. Telephone: +33 (0)1 40 79 47 42. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partly founded by the grant “Dynagel” of the Agence Nationale de la Recherche (ANR 2010 JCJC 0808) and also by the Ministère de la Recherche of France. The authors thank Jean-Pierre Munch, Pascal Hébraud and Costantino Creton for helpful discussion.

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