Effects of geometry on large-scale tube-shear exfoliation of graphite to multilayer graphene and nanographite in water

Industrially scalable methods for the production of graphene and other nanographites are needed to achieve cost-efficient commercial products. At present, there are several available routes for the production of these materials but few allow large-scale manufacturing and environmentally friendly low-cost solvents are rarely used. We have previously demonstrated a scalable and low-cost industrial route to produce nanographites by tube-shearing in water suspensions. However, for a deeper understanding of the exfoliation mechanism, how and where the actual exfoliation occurs must be known. This study investigates the effect of shear zone geometry, straight and helical coil tubes, on this system based on both numerical simulation and experimental data. The results show that the helical coil tube achieves a more efficient exfoliation with smaller and thinner flakes than the straight version. Furthermore, only the local wall shear stress in the turbulent flow is sufficient for exfoliation since the laminar flow contribution is well below the needed range, indicating that exfoliation occurs at the tube walls. This explains the exfoliation mechanism of water-based tube-shear exfoliation, which is needed to achieve scaling to industrial levels of few-layer graphene with known and consequent quality.


Fluid simulation
The explicit time integration finite element code LS-DYNA (Livermore Software Technology Corporation, USA) was used for the simulation. Two geometries were modeled: a straight tube (S1) of the diameter 2 mm and length 1000 mm and a helical coil tube (S2) with a tube diameter of 2 mm, a helix diameter of 100 mm and a helix pitch of 10 mm.

Viscosity measurements
In order to utilize in the simulation, the dynamic viscosity of 2% graphite suspension was measured on the initial material and after each pass using an Anton Paar Physica MCR 300 Rheometer. In figure 1 viscosity is plotted as a function of shear rate. The shear thinning behavior of the graphite suspension is evident which is attributed to the alignment of particles. At high shear rates (>1000 s -1 ), however, the viscosity becomes relatively constant. After the first pass of shear exfoliation, the suspension becomes thicker probably due to particles entanglement. In figure 1 this behavior is seen in pass_1 curve which is above the curves of other passes at all shear rates. For the simulation a constant fluid viscosity was adopted, i.e., 0.44 mPas which is the viscosity of the 2 % graphite suspension before exfoliation (pass_0) and 2.41 mPa.s which is the viscosity of the 2% graphite suspension after the first run (pass_1) of the exfoliation process. Both values were the average of viscosity values at >1000 s -1 . Figure 2 shows the average pressure at the tubes inlet throughout the simulation time. A steady state is gradually established after about t = 0.02 s. The inlet pressure at the straight tube (S1) is higher than that of the helical coil tube (S2) and proportionally changes with the change of viscosity. The flux at the entrance of the tubes was calculated to be 3.85 l min -1 which is lower than the measured experimental flux, i.e., 4.95 l min -1 . This implies that the constant fluid velocity 26.3 ms -1 may underestimate the flow behavior. The Reynolds number of the four systems were calculated to be 1.6x10 5 and 3x10 4 in S1 and 1.7x10 5 and 3.3x10 4 in S2 respectively for pass_0 and pass_1. Based on the Reynolds number and revealed by the simulation results the flows in the tubes were turbulent.

Figure 2:
Average pressure at tube inlet. S1: straight tube, S2: helical coil tube, pass_0: initial unexfoliated suspension, pass_1: suspension exfoliated once. Figure 3 shows the average fluid velocity gradient for S1 and S2, where the fluid velocity is 6.5 % higher for S2 compared to S1.  Figure 4 shows the fluid velocity vectors in S1 and S2 for the case of pass_0. A distinct difference between S1 and S2 is the swirling flow in S2 which continues throughout the coil. In Figure 5, the contours of average velocity at the central region of the length of S1 is shown at t = 0.1 s for pass_0. In Figure 6, the contours of average velocity at t = 0.1 of S2 is shown at a region far from the tube entrance for pass_0. Comparison of these two figures reveals details of flow pattern in two geometries: on average, the velocity profile gradient in the straight tube is parabolic with a maximum at the centerline of the tube while the velocity profile in the helical coil tube has a maximum close to the tube wall at the side of high helix radius. This results in a preferred shear surface with high wall shear stress in S2 but not in S1.   Figure 7 and 8 show the contours of average shear stress vectors on the surface of S1 and S2 at two times t = 0.1 and t = 0.15 for pass_0. In S1 the distribution of shear vectors do not show any order, however, the pattern remains approximately the same through the time. The distribution of shear vectors in S2, however, reveals a distinct difference between the surface adjacent to the lowest helix radius ( r i ) and the surface adjacent to the highest helix radius ( r o ), i.e, high shear stress toward r o and low shear stress toward r i . In S2 the average surface shear stress pattern is constant through the time. In both S1 and S2, an initial, short length at the entrance side are exempt from the general behavior. Simulation results show that the flow behavior did not get affected significantly by the change of viscosity. Accordingly, the results regarding pass_1 are not discussed.  2 Raman spectroscopy 2.1 Flake thickness determination from Raman Figure 9 shows the ratio I(Si G ) / I(Si 0 ) as a function of flake thickness. The red + markers shows experimental ratio data from Xiao-Li Li et. al [1] as a function on layer number, N, together with a fitted trend line. The blue • markers shows experimental data from tape exfoliated HOPG flakes in our Horiba Xplora plus raman system together with the fitted trend line . 0, 33767 , 4954 y = 0 + 0 9 · e −0,072699·x When plotting the HOPG particle Raman intensity ratio as a function of thickness instead of layer number we obtain an almost identical trend line as the read-out data from Xiao-Li Li et. al. The offset is approximately a factor 3 which fits well with the graphene layer spacing of 0.333 nm. This offset can be due to the use of a different Raman spectroscopy system compared to Xiao-Li Li et. al. and that no instrumental offset has been subtracted in the AFM measurements in this experiment, which gives a higher thickness value. The trend line from HOPG particle Raman intensity ratio was used to determine the flake thickness distribution of the tube exfoliated flakes from both shear zones.

Summary of raman spectrums
The raman intensities for each measured particle is summarized in table 1 for S1 and table 2 for S2. all raman spectrums together with optical images of the particles are shown in section 2.3.  Some flakes were also measured in AFM to check the accuracy of the method. Flake S2-9 1 were measured to be 54.2 nm in Raman and by AFM 55 nm in centre and 27 nm at edges. Flake S2-9 3 were measured to be 35.7 nm in Raman and by AFM 40 nm in centre and 18 nm at edges. Flake S2-9 4 were measured to be 21.8 nm in Raman and by AFM 25 nm in centre and 20 nm at edges. Since the raman value is a mean value of three points across each flake the accuracy of this method can be considered high.

Raman spectra for S1 and S2
This section contains raman spectrums for flakes exfoliated by both S1 and S2. Each diagram shows I(Si G ) as a solid line and I(Si 0 ) as a dotted line. The name of each spectra corresponds to the name of the optical image and flake number found in section 2.2.2. The peak between 900 and 100 cm-1 is a reflection in the system and belongs to the background. This peak shrinks with thicker flakes. Figure 10: Raman spectrums from exfoliated flakes in image S1-1 to S1-6. Figure 11: Raman spectrums from exfoliated flakes in image S1-7 to S1-19.

Optical images of the measured particles in raman
This section contains optical images, achieved from the raman microscope, for flakes exfoliated by both S1 and S2. Each image and flake are numbered and the corresponding spectra is found in section 2.2.1. The magnification is x1000 in all images. Figure 15: Optical images from Raman microscope with 1000x magnification showing images S1-1 to S1-20. The flake size distribution was investigated using a field emission scanning electron microscope (TESCAN MAIA3-2016) at 3 kV. The 1 cm 2 silicon wafer were divided into 9 (3x3 mm) sections (3 rows and 3 columns). To obtain a fair representation of the flakes the center and left center section was imaged. Each section was analyzed with 900 (30x30) images using a view field of 100 μm (magnification: 5537x). The SEM instrumental resolution was 1 nm and the exfoliated material had a flake length and width in the range from approximately 100 nm to 10 μm . The SEM viewfield and image resolution was set to generate a pixel size of 49 nm, which was sufficient to determine the flake size distribution by image analysis. A total amount of 2648 flakes was analyzed. Figure 17 to Figure 19 shows a small selection of the SEM images used for determination of the flake size distribution.

Image analysis
In order to determine the flake size distribution the particles were characterized in size by image analysis using ImageJ software. Contrast and brightness settings during image acquisition of all SEM-images were held constant to simplify the grayscale thresholding. Before thresholding, the images were filtered three times using a Median filter with size 1 pixel. Most flakes were simple to separate from the background due to the substantial difference in intensity values, and the automatic thresholding plugin RenyiEntropy was best suited for our 16-bit images. Some of the flakes that were not thin and flat in the SEM-images had both dark and white area and therefore the grayscale thresholding was insufficient. These flakes were removed from the automated imageJ algorithm and processed manually. For those flakes we used an edge detection procedure instead of grayscale thresholding. Figure 20 shows the difference between the two methods. In ImageJ the function "Find Edges" were used followed by automatic thresholding to obtain a binary image. After image inversion, the edges needed to be dilated to "close" eventual openings, followed by "fill holes" and finally eroding. Since the edge detected was 1 pixel offset, i.e. gave an increased radius with 1 pixel, we used the eroding one additional time to avoid overestimation of the area.

Initial material
The initial material used was thermally expanded graphite from Graphit Kropfmühl in Germany (EXG 9840). To thermally expand graphite the layered structure of graphite is intercalated by sulphur or nitrogen salts followed by rapid heating. Under the influence of heat the layers separate like an accordion, and the graphite flakes expand. Depending on degree of intercalation due to intercalation agent, time heating temperature etc. the expanded graphite gets different fractions of grains in various sizes and crystallinity.
From SEM backscatter images, figure 21, it can be seen that the large EXG 9840 particles contains grains with a size is in the range of 10 to 100 square micrometer and thickness from hundred to a few hundred nanometers.