Aggregate of nanoparticles: rheological and mechanical properties
© Wang et al; licensee Springer. 2011
Received: 21 August 2010
Accepted: 3 February 2011
Published: 3 February 2011
The understanding of the rheological and mechanical properties of nanoparticle aggregates is important for the application of nanofillers in nanocompoistes. In this work, we report a rheological study on the rheological and mechanical properties of nano-silica agglomerates in the form of gel network mainly constructed by hydrogen bonds. The elastic model for rubber is modified to analyze the elastic behavior of the agglomerates. By this modified elastic model, the size of the network mesh can be estimated by the elastic modulus of the network which can be easily obtained by rheology. The stress to destroy the aggregates, i.e., the yield stress (σ y ), and the elastic modulus (G') of the network are found to be depended on the concentration of nano-silica (ϕ, wt.%) with the power of 4.02 and 3.83, respectively. Via this concentration dependent behavior, we can extrapolate two important mechanical parameters for the agglomerates in a dense packing state (ϕ = 1): the shear modulus and the yield stress. Under large deformation (continuous shear flow), the network structure of the aggregates will experience destruction and reconstruction, which gives rise to fluctuations in the viscosity and a shear-thinning behavior.
An important application of nano-fillers is to construct nanocomposites with high performance of mechanical properties or certain functionality . Usually, for their high surface energy, nano-fillers exist in the form of agglomerates. Interestingly, some agglomerates, such as nano-silica and nano-titanium dioxide, can present a chain-like form what is called nanoparticle chain aggregates (NCA) and its dynamic properties have been mainly revealed by the work of Friedlander, Bandyopadhyaya and Rong et. al [2–8]. The ductility of NCA is believed to be related to the sliding/rotation of the primary nanoparticles and the elasticity comes from the effect of the surface energy of nanoparticles [3, 5, 6]. This deformation and elasticity behaviors are very similar to polymer chains as the flexibility of a polymer chain is generated by the rotation of the backbone bonds and the elasticity is driven by the principle of entropy increase.
In fact, the nano- or micro-mechanical properties of the agglomerate are one of the fundamental issues to understand not only the mechanical or the melt rheological properties of nanocomposites, but also the process of the dispersion. However, the work on this area is still seldom reported [7, 9, 10]. For common nanoparticles, the elemental force between the nanoparticles is the Van der Waals force, however, for the nanoparticles with polar groups, such as fumed nano-silica, there is another stronger interaction, hydrogen bonds, owing to the silanol (Si-OH) on the nanoparticle surface . Fumed nano-silica has been widely used as a modifier for rheological properties of coatings  or a reinforcement/functionalization filler in polymer based nanocomposites [13–15]. Certainly, the existence of the hydrogen bonds will affect the dispersion, the nano- or micro-mechanical properties of the nanoparticle agglomerate and finally, the application of nano-silica [15, 16].
Materials, sample preparation and characterizations
For the preparation of nano-silica/tetradecane suspensions, the nanoparticle was firstly dried at 120°C for 12 hs to remove the water adsorbed by the nano-silica. To make the gel network structure more perfect, suspensions were dispersed by ultrasonic treatment for 2 h. Five suspensions with weight fraction (wt.%) of nano-silica from 3 to 7 wt.%, named as ST-3, ST-4, ST-5, ST-6 and ST-7, respectively, were prepared at the same conditions. For the preparation of pure nano-silica disks, the same dried nano-silica (ca. 1 g) was first precompressed in the mold (a hollow column with inner diameter of 25 mm) and then compressed under the pressure of 5 MPa for 5 min at the room temperature. Finally, we obtained a disk with a diameter of 25 mm and about 0.7 mm in height for the rheological tests.
Rheological tests were carried out by a stress-controlled rotational rheometer (AR2000EX, TA instruments, USA) with parallel plates (25 mm in diameter) and at the room temperature 25°C. Because the gel network is very weak, in the process of sample loading and rheological measurements, carefulness and some measures are required to keep the gels intact.
For the gel sample loading, we adopted two measures to reduce the unavoidable destroying of the gels. First, the sample was sucked up carefully and slowly from a plastic tube by a pipette which can accurately control the sample volume (we chose a sample volume of 0.420 ml in our work). Secondly, the speed and the force of the compression process to produce an appropriate gap (0.650 mm) for the rheological tests were strictly controlled by the rheometer. For the rheological tests, we first carried out a strain sweep to determine the upper limit srain (ca. 4%) to keep the gels intact and finally chose a strain of 0.5% to perform the frequency sweep and time sweep. Under these measures, the experimental data were found to be repeatable.
Results and discussion
Dynamic rheological and mechanical properties
where β is a correction factor to consider the difference in the structure between NCA and polymer chain. It is noted that the structure of NCA may change with the concentration of nanoparticles and make β not a constant. For example, a few NCAs may merge into one thick network strand. In this situation, the storage modulus may be different but the length of NCA may be unaltered.
In addition, as also shown in Figure 2 the stability of the gel networks is very conspicuous. For most suspensions of nanoparticles, agglomeration and sedimentation of the nanoparticles are unavoidable and the suspension is commonly unstable [20, 21]. Therefore, it can be concluded that the gel network built by the hydrogen bonds can constantly block the agglomeration process as long as the initial agglomerates have been broken apart. This finding may provide an effective approach to improve or stabilize the dispersion of nano-fillers by introducing some additional interaction among the nano-fillers.
where d is the Euclidean dimension and equals 3, X is the fractal dimension of the backbone of the clusters (i.e., NCA) and it usually takes the value of unity . For the gels investigated here, we have D f = 2.0, lager than 1.78 [20, 21]. This finding indicates that the hydrogen bonds make the fractal more compact [20, 26].
The yield strain as revealed in the inset in Figure 4b reflects the extent for elastic deformation of NCA which mainly relates to the length of NCA and the size of the primary nanoparticles [3, 6]. It is obvious that, for the suspensions in this study, the length of NCA is too short to generate remarkable elastic deformation. This point is embodied by two aspects: (1) The yield strains of all gels are very small (< 5%). (2) The yield strain, on the whole, seems to decrease with the concentration of the nano-silica increasing. For the second finding, it indicates that the mesh of the network becomes shorter as the concentration of the nano-silica increases. However, it was also found that the yield strains of some high-concentration samples seem to rebound, which may be related to a stronger reconstructability of the gel.
Rheological properties under continous shear flow
In practice, such as coating and printing, the suspension is inevitable to experience large deformation or continous shearing. In fact, the flow behaviors of all kinds of suspensions (nano- or micro-fillers with different shapes) are always of great interest in the realm of rheology and shear-thinning and shear-thickening behaviors are not unusual [27–32]. However, the flow behavior of the suspensions here is not simple.
In addition, there are some new characteristics for the continuous shear flow that are worthy to be noted and have been briefly summarized as follows. (1) The periodic time of the fluctuations (T f ) seemed to be only dependent on the shear rate as (Figure 5b), in other words, the product of is a constant, which once again confirm the key role of deformation in understanding of the rheological properties under continous shear flow. (2) The viscosity declined with time on the whole as the density of the network node descends, which may be related to the mesh thickening that results from the agglomeration of the fractured NCAs or fragments as illustrated by the schematic in Figure 6. (3) It can be found in Figure 6 that there is a retarding behavior between the normal force and the viscosity as indicated by the dashed lines. It is reasonable that the response of the structure (such as the viscosity) is always lagged behind the response of the force (take the normal force for example) because the structure evolution is always the result of the effect of the force.
In summary, the rheological and mechanical properties of nanoparticle agglomerates in the form of network structure have been studied by rheology. Hydrogen bond interaction is found to be a key factor to contribute to the properties of the agglomerates. The elastic network model for rubber can be modified to link the mesh size of the network to the dynamic modulus. Furthermore, by rheology, we can define two important parameters, the stack shear modulus and the yield stress of the agglomerate at the DPS, which may be very valuable in nano-science. Under continous shear flow, the structure of the aggregates experiences some repeating process of destruction, reconstruction and agglomeration.
The authors gratefully acknowledge the financial support of National Natural Science Foundation of China (Grant No. 51073110) and the Program for Sichuan Provincial Science Fund for Distinguished Young Scholars (2010JQ0014).
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