Rheological Behavior of High Concentrated ...

Soft Materials

ISSN: 1539-445X (Print) 1539-4468 (Online) Journal homepage: http://www.tandfonline.com/loi/lsfm20

Rheological Behavior of High Concentrated Dispersions of Graphite Oxide Ying Liu, Chengmeng Chen, Liyan Liu, Guorui Zhu, Qingqiang Kong, Ranxing Hao & Wei Tan To cite this article: Ying Liu, Chengmeng Chen, Liyan Liu, Guorui Zhu, Qingqiang Kong, Ranxing Hao & Wei Tan (2015) Rheological Behavior of High Concentrated Dispersions of Graphite Oxide, Soft Materials, 13:3, 167-175, DOI: 10.1080/1539445X.2015.1055004 To link to this article: http://dx.doi.org/10.1080/1539445X.2015.1055004

Accepted author version posted online: 09 Jul 2015.

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Date: 29 February 2016, At: 03:56

Soft Materials (2015) 13, 167–175 Copyright © Taylor & Francis Group, LLC ISSN: 1539-445X print / 1539-4468 online DOI: 10.1080/1539445X.2015.1055004

Rheological Behavior of High Concentrated Dispersions of Graphite Oxide YING LIU1, CHENGMENG CHEN1,2, LIYAN LIU1, GUORUI ZHU1, QINGQIANG KONG1,2, RANXING HAO1, and WEI TAN1 * 1

School of Chemical Engineering & Technology, Tianjin University, Tianjin, People’s Republic China Key Laboratory of Carbon Materials, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan, People’s Republic China

2

Downloaded by [Shanghai University] at 03:56 29 February 2016

Received April 14, 2015; accepted May 21, 2015.

The rheological properties of graphite oxide (GO) of high concentrations were studied, which is important for pumping and translating design. Steady test indicated GO displayed shear thinning behaviors at low shear rates. The viscosity and particle increased quickly above certain shear rates. The Herschel–Bulkley model represented flow behavior accurately. Correlations between solid content, temperature, and viscosity were expressed by an exponential equation and a modified Arrhenius type equation, respectively. The dynamic test indicated viscoelasticity of GO decreased remarkably at lower concentrations. Under shearing, network structure of GO broke down gradually, and viscosity decreased with time, causing flow acceleration. Keywords: Graphite oxide, High concentration, Network structure, Rheology, Suspension

Introduction As a new type of extremely thin carbon nanomaterial, graphene has excellent strength, thermal (1), optical, and electrical properties (2), which make it ideal for a wide range of applications. Graphite oxide (GO) is an intermediate product from graphite to graphene obtained by Hummers’ method (3). Rheology plays an important role in characterizing hydrodynamic properties and strongly affects almost all treatment, utilization, and disposal operations, including mixing, pumping, translating, filtrating, and drying. Correctly predicting flow behaviors of engineering hydrodynamic processes requires accurate knowledge of GO rheology. In rheology, there are two types of measurements: steady test and dynamic test. Both tests can provide complete information regarding internal structure of suspension complementarily. Generally, GO and graphene oxide are known as non-Newtonian fluid and usually exhibit thixotropy, solid behavior within shorter time frames, and liquid behavior over longer duration (4). The general models used to describe rheological behavior of GO, are Bingham [Eq. (1)] (5), Power law [Eq. (2)] (6), Herschel-Bulkley [Eq. (3)] (7), and Casson models [Eq. (4)] (8). These models are widely used in the industrial field for pastes, slurries, and suspensions (9).

*Address correspondence to: Wei Tan, School of Chemical Engineering & Technology, Tianjin University, No. 92, Weijin Road, Nankai District, Tianjin 300072, China. Email: [email protected] Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lsfm.

τ = τ0 + kγ˙

(1)

τ = kγ˙ n

(2)

τ = τ0 + kγ˙ n

(3)

τ0.5 = τ0 0.5 + k0.5 γ˙ 0.5

(4)

where τ is shear stress, τ0 is yield stress, γ˙ is shear rate, k is consistency coefficient, and n is flow index (10). In these models, k represents limit viscosity of fluid at an infinite shear rate, whereas flow index n varies from 0 to 1. The fluid properties deviate from Newtonian fluid with the increasing of the flow index. There is some research on the rheology of graphene oxide or GO in the literature. As a function of graphene functionalization, the effect of shear rate and temperature on the rheological, morphological, and electrical properties of graphene/polystyrene nanocomposites has been recently reported (11). The rheological properties of systems such as pristine graphene/polyacrylamide gels (12), thermally reduced graphene oxide (13), and polypyrrole/graphene oxide nanocomposites that were synthesized via in situ polymerization have been investigated. These articles have shown that the rheological properties of graphene systems can be controlled through matrix−filler interactions with different additions. However, the rheological properties of aqueous GO dispersions play an important role in affecting the processing of complex GO/polymer systems. Aqueous dispersions were chosen because water is Newtonian fluid, making the effect of the GO obvious and the dispersions are stable up to high loadings, albeit as a hydrogel at a high volume percent. Such dispersions


168 were described well in the recent work of Tesfai et al. (14), who investigated the rheological properties and intrinsic viscosity of aqueous suspension of graphene and used the measured intrinsic viscosity to determine the aspect ratio of graphene oxide. Dilute suspension of graphene oxide exhibited a shear thinning behavior at low shear rates. The classical Einstein and Batchelor models underestimated the relative viscosity of graphene oxide suspension; Krieger−Dougherty prediction was in a good agreement with the experimental measurement. Recently, Vallés et al. (15) found the aqueous system of graphene oxide behaved as a reversibly flocculated dispersion with linear viscoelastic regions (LVR). Dynamic frequency sweeps conducted within the LVR showed a classic strong-gel spectrum for high concentrations. Herein, we study the effect of GO concentrations, shear rate, and temperature on the rheological properties of aqueous GO suspension. Under different shear rate, the change rate of viscosity is in accord with different models and particle size changes with shear rates. Dynamic tests exhibit the relationship between modulus and frequency. If the structure recovers over a measurable time period, the dispersions are thixotropic. The results obtained for the aqueous dispersion of GO can be correlated with more complex graphite oxide−polymer systems with different interactions between the graphite oxide and matrix.

Experimental Preparation of Graphite Oxide Graphite oxide was prepared from natural graphite using a modified Hummers’ method as described in Chen et al. (16). Aqueous dispersions with concentrations of 0.00625, 0.008, 0.0125, and 0.0167g mL−1 were prepared by dilution from the 0.025 g mL−1 . The weight percentage concentrations of the dispersions were determined by weighing, drying, and re-weighing the samples. The samples were dried at 50◦ C by a dryer until the mass was constant in 2 h. Then, 20-mL dispersions were taken, the quality of watch glass was w0 , the quality after drying was w1 , and the recycled mass was showed by (w1 −w0 ). The weight percentage concentrations can be expressed by (w1 −w0 )/20. Rheological Tests A TA Discovery DHR-2 rheometer with coaxial cylinder geometry (cup diameter, 30.39 mm; bob diameter, 27.98 mm; length, 41.90 mm) was used to analyze the dispersions. After loading, GO was left at rest for 3 min to eliminate the effect of aging history of the sample. This procedure allowed us to obtain reproducible results (17). Steady and dynamic tests were carried out to analyze rheological behaviors of GO with different concentrations. The temperature of the system was controlled at 25◦ C by an advanced Pelletier system unit with a temperature accuracy of 0.1◦ C. The temperature varied from 25◦ C to 65◦ C when measuring its effect on viscosity of GO. To avoid water evaporation during measurement, a plastic ring was fitted around the measuring geometry. Steady Test Steady shear sweep was used to investigate the flow property of the material at different concentrations by recording the shear

Liu et al. stress (σ) and viscosity (η) at increasing shear rates (γ ) from 0.01 to 2000 s−1 . The thixotropy test was used to investigate the dependence of viscosity on time including time sweep at a constant shear rate and stepwise changes in shear rate. For the time sweep, the GOs with different solid contents were sheared at 100 s−1 until steady states were reached. For stepwise changes, shear rate started from 0.1 s−1 , and stepwise increased to 1 s−1 , 10 s−1 ,100 s−1 , and 500 s−1 . Each shear rate was maintained for 2 min. When the shear rate suddenly stepped up, the transient variation of viscosity reflected the changes of GO microstructure. The Peclet number (Pe) was used to scale the obtained data, which exhibited the relative time scales for the hydrodynamic forces on and Brownian motion of the particles. Vallés et al. (15) considered that the graphene oxide was approximated to circular hard discs, such that the Pe is defined by Eq. (5): Pe =

32ηs b3 γ˙ Timescale for convection motion = γ˙ = Timescale for Brownian motion Dr 3kT

(5)

Although graphite oxide had multilayered structure, the aspect ratio of it was very large as observed from Fig. 1. The TEM and AFM images of GO sheets directly dried from the suspension of 0.00625g mL−1 are shown in Fig. 1. GO particle kept the layered structure, and the number of layers was around 10. The thickness distribution of GO particle was concentrated and average thickness was approximately 30 nm. Compared with the lateral dimensions of GO particles, the increased thickness of the GO particles had minimal impact on the simplified model; therefore, we still approximated GO as circular hard discs. The effects of the shape of the particles, aspect ratio, and the concentration on the fluid shear behavior will be researched in our future work. The particle size of GO changes with shear rate, and it does not change obviously lower than 700s−1 , fluctuating around 30 μm. As a result, the value of b was 30 μM and Pe = 1.25 × 104 γ˙ . Therefore, the Brownian motion of the particles was weak and hydrodynamic forces played a leading role on the movement of GO particles. Dynamic Test Dynamic rheological test is a better method for the viscoelastic measurement of GO, by applying sinusoidal stress (τ = τ 0 sin ωt; τ0 , amplitude of applied stress; ω, angular frequency [rad/s]) (18). Dynamic test, including shear strain sweep and frequency sweep, could differentiate the fluid and solid responses. Dynamic strain sweeps are used to find the LVR in which the storage modulus (G’) and the loss modulus (G”) are independent of strain amplitude at a constant frequency of 1 Hz. Dynamic frequency sweeps are conducted at a constant strain of 10% within the LVR to investigate the structure of the dispersions. As shear stress is exerted, viscoelastic material could respond with a combination of fluid and solid behaviors.

Results and Discussion Rheological behaviors of GO can be interpreted from four aspects: liquid characteristic, usually determined by viscosity; solid characteristic, evaluated by yield stress or storage


Rheological Behavior of Graphite Oxide

169

Fig. 1. The TEM and AFM images of GO (0.00625g mL−1 ).

modulus; thixotropic characteristic; and viscoelastic characteristic, described by storage and loss modulus (19).

Steady Shear Properties Liquid characteristic was usually represented by viscosity. Viscosity reflected internal and external interaction forces between the GO flakes and fluids. The value can be determined by ratio of shear stress (σ) to shear rate (γ ). We demonstrated that GO dispersions exhibit unique viscoelastic behavior, wherein the rheological behavior varies considerably with dispersion concentration. As shown in Fig. 2, the GO presented shear-thinning behavior and non-Newtonian characteristics gradually with the increase of solid content. The steady shear behavior could be characterized into three regions depending on the applied shear rate: 1. A first region was observed at low shear rate from 0.01 to 1 s−1 , the stress remained approximately constant with increasing shear rates.

2. A second region was observed at medium shear rates where the linear correlation was significant between shear stress and shear rate. At high concentrations of GO (≥0.025 g mL−1 ), the first region extended until very high shear rates and the dispersions were found not to enter the second region in this work. 3. A third region was observed at high shear rates where the stress significantly increased with increasing shear rates. The lower the concentration, the larger was the increase. The hydrodynamic forces on the particles still dominated over their Brownian motion and the forces were enhanced. At high concentration, the network structure of GO suspensions was compact and there must be larger shear stress to break it. In order to accurately study the difference between the GO with different concentrations, Power law and Herschel−Bulkley models were employed to fit these data. The parameters from the fitting are summarized in Table 1 together with the qualities of the fit. The results indicated that Herschel−Bulkley model fitted the data with different concentrations quite well, which was in accordance with the previous research (15). As shown in Table 1, although the solid content increased from 0.00625 to 0.025 g mL−1 , consistency index (k) increased from 0.0875 to 121.56 mPa s, whereas flow index (n) decreased from 1.63967 to 0.78517, which indicated that non-Newtonian flow characteristics of GO were strengthened at higher solid content. The higher the solid content was, the more viscous and less flowable the fluid was. For the GO, electrostatic and gellike interactions were closely related to non-Newtonian behavior. The oxygenic groups on the surface of GO led to construction of macromolecular colloidal properties with the increase of solid content. Also, the correlation between consistency index (k) and solid content (ϕ) could be expressed by an exponential equation [Eq. (6)], whereas there was no obvious correlation between flow index and solid content. k = 0.000834 ∗ exp (0.1993∅) R2 = 0.99896

Fig. 2. A steady shear rate flow behavior of the GO dispersions at different concentrations.

(6)

Fig. 3 illustrated effects of solid content on viscosity (η) at a shear rate of 100 s−1 and indicated that the viscosity of GO

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Table 1. Parameters obtained from the fitting of the experimental data using different models. Herschel-Bulkley Concentration g/mL


0.00625 0.00800 0.01250 0.01670 0.02500

Power

τ0

k

N

R2

k

n

R2

0.26542 0.20136 0.24193 0.4298 1.14449

8.75E-05 0.00409 0.01104 0.02033 0.12156

1.63967 1.06883 0.98437 0.93661 0.78517

0.99647 0.99980 0.99982 0.99941 0.99927

0.00136 0.01051 0.02125 0.04461 0.24789

1.20869 0.92422 0.88479 0.81768 0.67953

0.98074 0.99684 0.99831 0.99720 0.99720

Fig. 3. The viscosity of the GO dispersions at different concentrations and the fitted curve.

Fig. 4. The particle size of the GO dispersions at different concentrations (the shear rate is 0 to 1000 s−1 ).

increased with the increase of solid content. When the concentration of GO was larger than 0.0167 g mL−1 , the viscosity increased dramatically. At a high concentration of particles, a network of particles was formed due to the strong sheet-sheet and multi-sheet interactions (20). The correlation between viscosity (η) and solid content (ϕ) could be expressed by an exponential equation [Eq. (7)]. The extremely high value of R2 indicated that the correlation between viscosity and solid content could be accurately expressed by the exponential equation. The high exponent value indicated that viscosity of the GO changed much fast with the increasing of solid content.

A dynamic balance state formed in a time period that the particle size of GO was stable at a certain shear rate. However, under high shear rate, the kinetic energy of particles was enhanced, the ability to bind with multi-particles was enhanced, and the particle size increased rapidly. The higher the concentration of GO, the lower the critical value of shear rate and the higher were the change rates of the particle sizes. Tesfai et al. (14) observed that an oblate compact structure of graphene oxide occurred at higher concentrations compared to very thin sheets at lower concentration. With the increase of concentration, the GO particles content of suspension in a certain volume increased, the average distance between particles decreased, and the opportunities for collision were enhanced. There are some oxygen-containing functional groups on the surface of GO particles and some water molecules combine with GO particles. The water molecules may be surrounded by the particles when they agglomerate. The change was conducive to the occurrence of restacking and agglomeration; therefore, the thickness of GO particles increased and the aspect ratio decreased. Understanding the mechanism of GO aggregate formation in aqueous system can enable fine-tuning the microstructure of GO in order to achieve the desired behaviors of GO-based multiphase systems. The evolution of the microstructure of the system is described as follows. When the system was subjected to a weak shear force, part of the GO particles exfoliated between the layers, such that

η = 2.98018 ∗ exp (0.09987∅) R2 = 0.99897

(7)

The particle size of GO had great effect on thermophysical and mechanical properties of nanocomposites. The effect of shear rate on particle size, with a median size value (d0.5), is shown in Fig. 4. The particle size changed inconspicuously under low shear rate and had a significant increase over a critical value. The sizes of the GO particles depend on the competition between the Brownian motion, which forms the flocks, and the shear forces, which break them apart. Under low shear rate, the shear force that acted on the GO particles was weak. Therefore, low shear rate had minimal effect on GO particles size, the existing flocculated network broke down into flocks with decreasing sizes, and the movement fastened as the shear rates increased.


171 solid content are shown in Table 2. The higher the concentration was, the bigger the activation energy was, implying that concentration of the GO network modified the dependence of GO viscosity on temperature. Viscosity is a measure of resistance generated by the movement between two adjacent layers of a fluid. In general, the GO suspension of high concentration contained many GO particles, the crash probability was high and Ea was large; therefore, viscosity was sensitive in regard to temperature.


Dynamic Shear Properties The viscoelasticity of GO can be described by complex modulus (G∗ ); its real part G (storage modulus, ratio of elastic stress over strain); and its imaginary part G (loss modulus, ratio of viscous stress over strain). Complex modulus represents deformation resistance of particle arrangement. Storage modulus expresses the elastic storage capacity during deformation, whereas loss modulus expresses dissipation during deformation. The viscoelastic properties of GO can be investigated by dynamic tests, including the shear strain sweep test and the frequency sweep test.

Fig. 5. Effect of temperature on viscosity at the shear rate of 100 s−1 .

the particle size reduced to a certain extent. Under high shear rate, the kinetic energy of GO particles increased and the chance of combination improved after the collision. The water molecules may be surrounded by the particles when they agglomerate with multi-particles, and, therefore, the particle size would increase. Temperature was another important factor that affected the fluidity of GO, and the relationship between temperature and viscosity is shown in Fig. 5. With the increase of temperature, the mobility of segment was enhanced and the interaction between molecules weakened. The viscosity of the GO suspension decreased with a rise in temperature; however, the reduction speed changed with concentrations. At low concentrations (≤ 0.0125 g mL−1 ), the viscosity fell slowly, whereas at high concentrations (≥ 0.0125 g mL−1 ), the decrease rate of viscosity was enhanced. Thermal motion of particles was more violent at higher temperature, and then the strength among the particles network weakened, which resulted in a decrease of viscosity (21). The influence of temperature on viscosity can be described well by an Arrhenius type equation: η = AeEa /R(T+T0 ) ,

Strain Sweep For the GO with different solid contents, evolution of storage and loss modulus at 1 Hz are shown in Fig. 6. The GO suspensions showed linear viscoelastic behavior under dynamic shear up to a critical strain between 0.1 and 10% depending on the concentration. When the strain was outside the linear viscoelastic region, the structure of the network broke down, which caused rapid decrease of the viscosity and modulus in the system with the increase of strain. With the solid content increasing from 0.00625 to 0.025 g mL−1 , G’ increased from 0.002 to 6 Pa, indicating that colloidal forces and strength of GO network were stronger at higher solid content. 1. At low concentrations (0.00625−0.0167g mL−1 ), there was no crossover between G’ and G”, with G” larger than G’. The phenomenon implied that the interaction forces between sheet and sheet or multi-sheets were weak and GO exhibited liquid characteristics. The GO particles dispersed in water had weak links between each other. The three-dimensional network constructed by GO particles and solvent was easily broken and the system was prone to show fluid properties. 2. At high concentrations (0.0167−0.025 g mL−1 ), G’ and G” intersected, and an intermediate response between fluid behavior and gel behavior was found. At low frequencies, the

(8)

where A is the pre-exponential factor; T is absolute temperature (K); T0 is a temperature constant; R is the universal gas constant (R = 8.3145 × 10−3 kJ K−1 mol−1 ), and Ea is the activation energy of flow (kJ mol−1 ). The values of A and Ea of different

Table 2. Regression model parameters of Eq. (8) of different concentrations. Concentration g mL−1 0.00625 0.00800 0.01250 0.01670 0.02500

A Mpa s

T0 K

Ea kJ mol−1

R2

0.07754 0.03483 0.02648 0.01637 0.06740

463.3341 330.2929 353.0482 270.5043 225.8659

24.742232400 19.207428550 18.074557060 14.820735270 8.490438312

0.98330 0.99728 0.99655 0.99907 0.99849


172

Fig. 6. Stress sweep for GO dispersions of different concentrations at 1 Hz.

phenomenon of G’> G” implied that GO exhibited a gel-like structure. However, at higher frequencies, the phenomenon of G’G ” implied that the solid-like regime had broken down and the GO exhibited a fluid like structure. It should be noticed that the values of G’ and G’’ we measured were lower than that Vallés et al. (15) measured for similar concentrations. The main reason was that the measurement system they used was graphene oxide. Graphene oxide has a large specific surface area, and the oxygen containing functional groups on the surface of graphene oxide was exposed and contacted fully with the solvent; thus, the binding force between graphene oxide particles and solvent was enhanced and a strong threedimensional system was formed. The measurement system we used was graphite oxide, which had multilayered structure. Most of the oxygen containing functional groups hid in the interlayer and could not contact well with the solvent; therefore, the binding force between graphite oxide particles and solvent was poor. As a result, the values of G’ and G’’ we measured were lower. Dynamic Frequency Sweep Fig. 7 illustrates the evolution of storage and loss modulus during a frequency sweep in LVR. The strain amplitude was a constant of 0.1% for aqueous GO dispersions with different concentrations. Within the LVR, the storage modulus could be categorized into three regimes depending on the concentration of GO: 1. The G’ increased with the increasing of frequency at low concentrations (0.00625−0.008g mL−1 ); whereas, the lower the solid content of GO was, the smaller the G’ changed. Part of the network was formed when the concentration was low. The movement of molecule and strength of network was enhanced under oscillation. 2. At medium concentrations (0.008−0.0167g mL-1), G’ was independent of frequency, and the main reason was the formation of a network of GO. The formation of the network was mainly due to attractive electrostatic forces between the graphite oxide flakes. The hydrogen bond interaction also made a difference. The attractive electrostatic forces made the GO particles maintain a balanced state. At the same time, the

Liu et al.

Fig. 7. Frequency sweep for GO dispersions of different concentrations at 0.1%.

water molecules combined with oxygen-containing functional groups on the surface of GO particles through a hydrogen bond and, therefore, the network of GO-water molecule-GO was formed. 3. At high concentrations of GO (0.0167−0.025g mL−1 ), the G’ decreased with increasing frequency because the network that had formed was broken down under oscillation. The higher the concentration was, the higher was the value of G’. The value of G” increased with the increase of oscillation frequency at all the solid contents. The increase amplitude of G” was largely of high concentrations, illustrating that the network broke down under the force of oscillation. The relationships between storage modulus, loss modulus, and frequency can be expressed by Eq. (9): G = a + b × fn

(9)

Parameters in the equation are listed in Table 3, which were obtained by curve-fitting. The higher value of R2 indicated that these equations fitted the experimental data well. As a result, the correlation between G and frequency can be expressed well by a power-low function at a low solid content. The G’ of high solid contents (0.0125−0.025g mL−1 ) could not be expressed by Eq. (9) because the network was complex and unstable under oscillation. The value of n, which was obtained from the fitting, decreased with the increase of concentration. The higher exponent value indicated that the G” of the low solid contents changed much faster than that of high solid contents with the change of frequency. The different results occurred because of different solid contents. As the solid content increased, interactions among particles changed from collision to fraction. Thixotropy Test Thixotropy is defined as the continuous decrease of viscosity with time when a high shear rate is applied on a sample, which is termed shear rejuvenation. Several methods can be used


173

Table 3. Regression model parameters of Eq. (9) of different concentrations. G = a + b × fn Concentration g mL−1


0.00625 0.00800 0.01250 0.01670 0.02500

G = a + b × fn

a

b

n

R2

a

b

N

R2

−0.04400 0.03315

0.07143 0.01688

1.82805 2.24720

0.99949 0.99979

0.07196 0.01951 0.03582 0.36588 1.04467

2.64E-04 0.02525 0.04414 0.12099 0.54484

3.18610 1.65561 1.57261 1.31392 0.96848

0.94658 0.99965 0.99993 0.99541 0.99521

for investigating thixotropy of the GO, including the hysteresis technique, stepwise changes in shear rate, and time sweep at a constant shear rate. The hysteresis loop method is fraught with difficulties due to the presence of particles and flocks. Sedimentation, time effects, shear history prior to experiment start, maximum shear rate, and acceleration rate all could introduce errors. To avoid the drawbacks of the hysteresis loop method, the latter two methods were employed. The functional groups on the surface of GO combined with water molecule tightly. Strong colloidal forces tend to rebuild the solid structure and hydrodynamic forces tend to maintain the broken solid structure. Time Response of Viscosity Sudden changes of shear rate caused instantaneous variation of aggregate shape and orientation. Therefore, evolution of GO viscosity was explored over time at a constant shear rate of 100 s−1 , as shown in Fig. 8. Under shearing, network structure of GO

was broken down gradually, and then viscosity decreased with time, causing flow acceleration due to an avalanche effect (22). The change rate of viscosity with time was small indicating the GO system was stable. GO and water glue together to create a three-dimensional matrix by van der Waals forces, hydrophobic interactions, and bridge via electrostatic binding. Therefore, the network structure and network functional integrity was strong. As a result, the GO needed more energy and more time to cleave the network for achieving a stable state.

Step Analysis of Viscosity The relative change rate of viscosity was calculated by the following formula: RV = (ηs − ηr )/ηs , as shown in Fig. 9, where RV is relative rate of viscosity change, ηs is instantaneous viscosity at initial shear, and ηr is the viscosity at a certain shear rate. For low concentrations, the value of viscosity was unstable with a low shear rate. As a result, the relative change rate of viscosity

Fig. 8. Evolution of viscosity with shear time at shear rate of 100 s−1 of different concentrations.

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samples could be categorized into three regimes depending on the concentration of GO. The relationships between storage modulus, loss modulus, and frequency could be expressed by an exponential equation. 4. Analysis of thixotropic properties illustrated that the network structure broke down quickly at the initial shear. The relative change rate of viscosity decreased with the decrease of concentrations, indicating that the GO of low solid content exhibited a more stable state.

Fig. 9. Relative rate of viscosity change at stepwise shear rate of different concentrations.

was only considered for certain concentrations (0.0125−0.025g mL−1 ). The relative change rate of viscosity decreased with the decrease of concentrations, indicating that the GO of low solid content exhibited a more stable state. As the shear rate increased from 0.1 to 1 s−1 , viscosities of GO (0.025g mL−1 ) and GO (0.0125g mL−1 ) decreased by 97.11% and 80.72% and decreased by 99.15% and 87.33% at 10 s−1 , respectively, which illustrated that flock structure of the two types of GO was broken down at initial shearing and the destruction degree of GO network (0.025g mL−1 ) was greater. Because at high concentration, the contact probability of paddle and particles increased and the destruction degree of GO structure was higher.

Conclusion The rheology properties of high concentrations of GO were investigated by steady and dynamic measurements using a rheometer (DHR-2). The Brownian motion of and the hydrodynamic forces on the particles changed with concentrations. As a result, GO rheological behaviors were altered. Conclusions can be drawn as follows: 1. For GO suspensions, the Herschel−Bulkley model could represent their flow behavior more accurately than other models. The consistency index (k) of GO decreased significantly while flow index (n) increased. The GO suspensions exhibited shear thinning at low shear rates and the viscosity increased quickly when the shear rate was above a certain value. The same rule can also be expressed by particle size. 2. The GO exhibited strong dependence on solid content and temperature. Correlations between solid content, temperature, and viscosity were expressed by an exponential equation and an Arrhenius type equation, respectively. The activation energy of flow increased with the concentrations. 3. Dynamic tests indicated that viscoelastic behavior of GO decreased remarkably with the decrease of concentration. Within the linear viscoelastic regions, the storage modulus of

This research gained a new insight into the rheological behavior of high concentrations of GO and provides reliable flow property parameters to engineers for accurately designing the translated pipe, pump, and heat exchanger. Also, these models can be used to fit hydrodynamic optimization and computational fluid dynamic (CFD) simulation. However, further study will be performed by comparing all the rheological behavior of high concentrations of GO systems with different additions and exploring the microstructure under high shear rates.

Acknowledgments The authors acknowledge the testing support of Shandong Institute of Tianjin University.

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