J. Cent. South Univ. Technol. (2007)06-0737-05 

DOI: 10.1007/s11771-007-0140-y 

Viscoelastic properties of monodisperse spherical silica suspension

WU Qiu-mei(伍秋美), RUAN Jian-ming(阮建明), HUANG Bai-yun(黄伯云),

ZHOU Zhong-cheng(周忠诚), ZOU Jian-peng(邹俭鹏)

(State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China)

Key words:

viscoelasticity; monodisperse silica; suspension; shear thickening；

  1 Introduction

Many colloidal suspensions, such as paints, coatings, and lubricants, are subjected to rapid shearing during processing. In some instances the shear force can be strong enough to drive shear thickening, which is marked by a rapid, sometimes discontinuous increase in viscosity with small increase in shear rate. This behavior can induce dramatic changes in the suspension microstructure such as driving irreversible flocculation and particle aggregation and damage processing equipment. The change in microstructure leads to poor fluid and coating qualities. Thereby a number of documents have been addressed about the factors that influence the shear thickening degree. For example, the volume fraction of the particles has no influence on the critical stress where shear thickening takes place^[1-2], the increasing particle size and the lower temperature make the shear thickening behavior take place at lower shear stress and shear rate, and the increase in the polydispersity of the particles decreases the severity of the shear thickening^[1-3].

On the other hand, this shear thickening behavior could be exploited in the design of damping and control devices, whereby the fluid can limit the maximum rate of flow through a highly nonlinear response^[4]. LEE et al^[5] and TAN et al^[6] used the shear-thickening properties of the silica suspensions in ethylene glycol, polyethylene glycol (PEG) and water to make advanced body armor materials. These materials can offer equivalent ballistic performance of existing body armor materials, but with significantly more compactness and flexibility. Despite a lot of documents have reported the rheological properties of the shear thickening suspensions^[7-9], there is little information addressing the viscoelastic properties of this suspension in detail. In this work, the controlled stress rheometer was used to study the viscoelastic properties of the monodisperse spherical silica suspension in PEG and the energy dissipated in the stress shear was calculated.

2 Experimental

2.1 Materials

The monodisperse spherical silica was produced by hydrolysis of tetraethoxysilane in alcohol solvent using ammonia as a catalyst^[10-11]. The silica produced by these means is hydrophilic due to the presence of hydroxyl groups (Si-OH) on the surface^[12].

A polar liquid, polyethylene glycol(PEG), with average relative molecular mass of 200 provided by Sinopharm Chemical Reagent Co Ltd was used as the continuous phase. It is a Newtonian liquid with low viscosity of 0.03 Pa·s at 25 ℃.

2.2 Morphology of silica

The morphology of silica was observed on H-800 transmission electron microscope(TEM) after silica was dispersed in ethanol by ultrasonic treatment for 30 min and then placed on copper foil for drying.

2.3 Sample preparation

The suspension with the volume fraction of SiO₂ of 51% was prepared by adding the silica powder into the liquid in a blender and stirring for approximately 30 min. The samples were placed under vacuum at room temperature for 24 h to remove air bubbles. When the silica powder was dispersed in polar suspending fluid, the hydroxyl groups of the silica preferentially interacted with suspending molecules through hydrogen bonds, leading to nonflocculated suspension^[12]. The volume fraction of the silica in the suspension was calculated from the mass fraction, the density of the silica and PEG. Here, the silica density was calculated from solution densimetry measurements using a volumetric balance assuming ideal mixing.

2.4 Viscoelastic behavior measurements

The viscoelastic behavior measurements were conducted on a stress-controlled rheometer AR2000 (TA Company, USA). Experiments were conducted under oscillatory stress shear at 25 ℃, and the frequency was fixed at 20 rad/s and the shear stress was in the range from 0.01 to 1 000 Pa. In all the experiments, cone-plate fixture (diameter of 40 mm, angle of 2?) was used.

3 Results and discussion

3.1 Morphology of silica

The morphology image of silica observed by H-800 transmission electron microscope (TEM) is shown in Fig.1. TEM measurement demonstrates that the particles are nearly monodisperse, spherical ones with the average diameter of 500 nm.

Fig.1 TEM image of silica

3.2 Dynamic rheological behavior

The dependence of the complex viscosity (η*) on the shear stress (σ) for the silica suspension at the frequency of 20 rad/s is presented in Fig.2. As can be observed that at low amplitude of σ, η* almost remains unchanged with increasing σ (RegionⅠ), and then η* decreases (RegionⅡ). After reaching a minimum value, η* starts to increase (Region Ⅲ). The point where η* is the minimum is defined as the critical point and the stress at this point is denoted as the critical shear stress (σ_c).

Fig.2 Complex viscosity (η*) as function of oscillation stress (σ) for SiO₂/PEG suspension

The change in the viscosity of the silica suspension is assumed to be the result of the microstructure change. At small stress amplitude, Brownian motion and the interparticle forces are able to restore the structure to the equilibrium state during the oscillatory, therefore the viscosity almost remains unchanged. When the stress increases further, the structure breakdown caused by the stress shear becomes significant and Brownian motion and the interparticle forces are no longer capable of restoring the microstructure, so the viscosity decreases. Certainly, the relaxation of the molecular chain of the PEG has contribution to the decrease in the viscosity. At the critical point, the hydrodynamic forces equal the repulsive interactions, after that the hydrodynamic forces exceed the repulsive interactions, and the temporary clusters of the silica particles form^[4,13-14]. These clusters are separated by a thin solvent layer and play an important role in blocking the flow of the fluid, which makes η* increase as the shear stress increases.

To confirm the reversibility of these shear thinning and shear thickening behaviors, η* was measured for both ascending and descending stress sweeps, as shown in Fig.2. The good agreement except some hysteresis of η* under the low stress for the descending plot shows that the “clusters” can decompose and disperse into the suspending fluids again when the shear stress decreases. This indicates that the shear-thinning and shear- thickening behaviors are reversible.

3.3 Storage modulus and loss modulus

The dependence of storage modulus (G′) and loss modulus (G″) on the oscillatory stress (σ) for SiO₂/PEG suspension is shown in Fig.3. The experimental conditions are the same as those in Fig.2. It is clear that the system also shows linear viscoelastic (RegionⅠ), shear thinning (RegionⅡ) and shear thickening (Region Ⅲ) behavior as increasing σ, and the magnitude of G″ is larger than that of G′ in all the stress ranges studied. According to the viscoelastic theory^[15]，elasticity is considered to be the behavior of solid, whereas viscidity is the behavior of fluid. The values of storage modulus G′ and loss modulus G″ represent the intensity of elasticity and viscidity, respectively, and the complex viscosity η* is composed of elastic-like viscosity (G′/ω) and the viscous-like viscosity (G″/ω). In this system, the larger G″ over G′ in the entire range of the stress indicates the suspension possesses the viscous property predominantly, and the portion of the energy dissipated by viscous forces is larger than that stored in the structure of the suspension for this system.

Fig.3 Storage modulus (G′) and loss modulus (G″) as functions of oscillation stress (σ) for SiO₂ /PEG suspension

It can be observed that the plot of G′ in Fig.3 has obvious decrease, while the plot of G″ only shows slight decrease in region II. These phenomena were also observed by BENDER and WAGNER^[16] and KAFFASHI et al^[17]. The stress-optical relationship shows that the shear thinning of those hard-sphere silica suspensions is due to the changes in the thermodynamic contribution to the viscosity, while the hydrodynamic contribution remains relatively constant throughout the shear thinning regime, and BENDER and WAGNER^[16] also provided evidence that shear-thickening was attributed to the increased hydrodynamic interactions. In the experiments of KAFFASHI et al^[17], the shear rate appears to be too low for the shear thickening to occur, while in the the shear thinning region, they observed that the elastic-like viscosity introduced by the Brownian motion was contributed to the shear- thinning and appeared to be sensitive to structure changes in the sheared suspension, conversely the viscous-like viscosity, due to hydrodynamics, was approximately independent of the shear rate.

3.4 Lissajous plot

To further understand the viscoelastic properties of the suspension, the dissipated energy under stress shear can be obtained by integrating the area contained in a plot of stress vs strain (Lissajous plot) for a cycle stress shear^[18-19]. During oscillatory shear, for every stress point σ, sine stress wave: σ=σ_maxsin(ωt) will be exerted on the suspension with σ being the maximum stress σ_max. When one cycle shearing of sine stress wave is performed, there will be a maximum strain γ_max. The area circled by the Lissajous plot is the energy dissipated for one cycle shearing of sine stress wave. The Lissajous plots of the SiO₂/PEG suspension at 0.1, 2.0, 500.0 Pa in linear viscoelastic, shear thinning and shear thickening ranges respectively at the frequency of 20 rad/s are shown in Fig.4. Comparing these figures, it is clear that as increasing the stress, the area circled by the plots becomes larger, which means the dissipated energy becomes more.

Fig.4 Lissajous plots for SiO₂/PEG suspension of different stress amplitudes

 (a) σ_max=0.1 Pa; (b) σ_max=2.0 Pa; (c) σ_max=500.0 Pa

It is clear that the larger the shear stress is, the more the energy will be dissipated, but the shapes of Lissajous plots are different in Fig.4. The normalized strain (γ/γ_max) as a function of normalized applied stress (σ/σ_max) when the stress is 0.1, 0.5, 2.0, 5.0, 40.0, 100.0, 250.0 and 500.0 Pa (sinusoidal frequency ω=20 rad/s) for the SiO₂/PEG suspension is shown in Fig.5. For the sake of comparing the suspension with the suspending fluid PEG (Newtonian fluid), the same experiment was performed on PEG, as shown in Fig.5. For the Newtonian fluid PEG, the scaled Lissajous plot is nearly a superposed line, whereas the scaled Lissajous plots for suspension deviate from a superposed line and take on elliptic forms. The more closely the shear stress approaches the critical stress, the more similar the shape of Lissajous plot is to that of the curve of PEG. Compared with Fig.3, when σ=σ_c=5.0 Pa for the SiO₂/PEG suspension, G′ being the minimum, the portion of G″ in G* is larger than that of any other points, that is, the system takes on fluid property the most obviously, so the plot is the most similar to that of PEG.

Fig.5 Scaled Lissajous plots for PEG（★）and SiO₂/PEG suspension at stress amplitudes

3.5 Dissipated energy

Through the mathematical treatment, the relation between the dissipated energy (E_d) and the maximum strain (γ_max) during one cycle shear can be obtained from the relation^[18-20]:

            (1)

It is clear that when G″ is constant, E_d is a quadratic function of γ_max, and when G″ is variable, E_d is affected by both of γ_max and G″.

Fig.6 shows the relation between the dissipated energy E_d and the maximum strain γ_max for SiO₂/PEG suspension when σ is 0.1, 0.5, 2.0, 5.0, 40.0, 100.0, 250.0 and 500.0 Pa, respectively. It can be seen that under low stress shear (before shear thickening), G″ nearly remains constant as increasing shear stress, the slope of E_d vs γ_max obtained on the log-log plot for SiO₂/PEG suspension is 1.92, approximating to two, as anticipated by Eqn.(1). However, in the shear thickening region, G″ increases as the shear stress increasing, E_d of SiO₂/PEG suspension is proportional to γ_max rising with the exponent about 5, that is to say, G″ increases proportionally to γ_max with the power law relation in the shear thickening region.

Fig.6 Energy dissipated (E_d) as function of measured maximum strain (γ_max) for SiO₂ /PEG suspension

4 Conclusions

1) The monodisperse spherical silica suspension in PEG shows reversible shear thinning and shear thickening behaviors. During shear thinning region, G″ almost remains unchanged, whereas η* and G′ decrease. During shear thickening region, all of η*, G′ and G″ increase at the same time due to the formation of the temporary and flow-induced clusters.

2) The viscoelastic measurements indicate that in the entire range of stress studied, G″ is larger than G′, indicating that the portion of the energy dissipated is more than that stored, and the suspension shows viscous behavior predominantly.

3) The slope of energy dissipated (E_d) vs maximum strain（γ_max）on the log-log plots approach to 2 under low shear stress. However, in the shear thickening region, E_d of SiO₂/PEG suspension is proportional to γ_max rising with the exponent of about 5.

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(Edited by CHEN Wei-ping)

Received date: 2007-03-07; Accepted date: 2007-05-20

Corresponding author: RUAN Jian-ming, PhD, Professor; Tel:+86-731-8876644; E-mail: jianming@mail.csu.edu.cn