Tailored Colloidal Stability and Rheological Properties of Graphene

5 days ago - Graphene oxide liquid crystallinity (GO LC) has been widely exploited for high-performance graphene-based applications. In this regard ...
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Tailored Colloidal Stability and Rheological Properties of Graphene Oxide Liquid Crystals with Polymer Induced Depletion Attractions Yul Hui Shim, Kyung Eun Lee, Tae Joo Shin, Sang Ouk Kim, and So Youn Kim ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b06320 • Publication Date (Web): 08 Nov 2018 Downloaded from http://pubs.acs.org on November 9, 2018

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Tailored Colloidal Stability and Rheological Properties of Graphene Oxide Liquid Crystals with Polymer Induced Depletion Attractions

Yul Hui Shim†, Kyung Eun Lee‡, Tae Joo Shin#, Sang Ouk Kim‡ and So Youn Kim†,* †School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan, 44919, Republic of Korea ‡National Creative Research Initiative Center for Multi-Dimensional Directed Nanoscale Assembly, Department of Materials Science & Engineering, KAIST, Daejeon, 34141, Republic of Korea, # UNIST Central Research Facilities & School of Natural Science, Ulsan National Institute of Science and Technology (UNIST), Ulsan, 44919, Republic of Korea Corresponding Author * E-mail [email protected] (S. Y. K.); +82 52 217 2558

KEYWORDS. graphene oxide, polymer, molecular weight, liquid crystal, viscosity, rheology

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ABSTRACT.

Graphene oxide liquid crystallinity (GO LC) has been widely exploited for high performance graphene based applications. In this regard, colloidal stability of GO LC suspension is a crucial requirement, particularly while polymers are often added to the GO LC. Unfortunately, current level of knowledge on how polymers influence on the structure and properties of GO LC is not sufficient to systematically guide the development of applications. Here, we investigate the microstructure and rheological properties of GO LC suspensions in the presence of polymer additives with different molecular weights and concentrations. Similar to conventional colloidal systems, non-negligible polymer-induced interactions are found in GO LC suspensions, which can effectively modulate the interaction among GO platelets and the relevant physical properties. Based on extensive small angle x-ray scattering and rheological measurements, we demonstrate that, contrary to the general perception, polymer-induced depletion attraction can increase the colloidal stability of GO, while also preventing the vitrification of GO LC. In addition, a proper level of polymer additive can reduce the viscosity of GO LC suspensions by orders of magnitude, providing an effective route to GO LC based solution processing. After all, the colloidal stability and rheological properties of GO can significantly impact on the quality of GO. Therefore, we believe that our findings will be of great interest in the field of graphene based applications as it presents effective strategies for improving properties.

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Graphene oxide (GO), a representative of two-dimensional materials has brought tremendous attention in material science based on its extraordinary mechanical, electrical and thermal properties.1-9 The use of GO is often more advantageous than pristine graphene due to the easy synthesis, process scalability and manageability.10-12 GO can be readily dispersed in polar solvents including water and exhibit nematic liquid crystallinity (LC),13-19 and thereby enables solution processing of highly ordered graphene based fibers and films.20-24 In these applications, polymer additives have been frequently employed and often led to improved performances compared to neat GO LC based counterparts.25-27 Therefore, a systematic understanding on the exact role of polymers at GO interface and the resultant modulation of structure and dynamics of GO LC is highly desired for further advanced applications.28 Nonetheless, most of previous studies on GO LC based application have primarily focused on the characterization of physical properties in a macroscopic level without detailed concerns in terms of the interaction among polymer molecules and GO sheets.29-34 Moreover, the discussions on colloidal interactions of GOs in the preparation step of GO LC are often missing, thus how polymer induced interactions can change the GO-GO interactions has not been answered. In colloidal science, polymers are frequently employed as they can change the interparticle interactions driving depletion attractions or steric repulsions.35-37 While adding non-adsorbing polymers bring purely entropic depletion attractions, adding adsorbing polymers often accompany complicated depletion attractions and steric repulsions.38-40 Likewise, the addition of polymer in the GO suspension can also have an equivalent effect on GO-GO interaction

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as in conventional colloidal solutions. In this study, the microstructure and rheological property of GO aqueous suspensions were investigated in the presence of polymers with varying polymer molecular weights and concentrations. Depending on the polymer molecular weight, the addition of polymers could dramatically change the rheological property of GO LC as it changes the GOGO interactions, suggesting an effective strategy to ensure a good processability of GO LC. Small angle X-ray scatterings (SAXS) and polarized optical microscopy (POM) are employed to examine the microstructure of GO LC and the oscillatory rheometry experiment is provided for more quantitative comparison of colloidal property of GO LC. Result and Discussion GO with typical lateral dimension of 1 m was prepared from the modified Hummers’ method.25 Then aqueous GO suspension was carefully purified to remove ionic impurities, and was mixed with a desired amount of polymer. Poly(ethylene glycol) (PEG, Mn = 400, 1000, 3350, 6000, and 10000 g/mol) was chosen based on the good solubility in water and adsorption ability onto GO surface via hydrogen bonding.41, 42 We first performed SAXS experiment to observe the change of microstructure of GO suspension at initial state (see Methods for experimental details). The stretched 2D SAXS patterns (Figure 1a) and POM images (Figure S1) show that GO readily form nematic LC phase in polymer solutions as confirmed previously.41 The 1D scattering intensity was averaged with a mask aligning along the stretched direction. In Figure 1b, the correlation peak of GO is found in the 360° azimuthal-averaged scattering data and it is more distinctive in the stretched direction, implying that GOs are aligned parallel to the long axis of the sample cell. Figure 1c shows the normalized scattering intensity of GO in 30 wt PEG solutions at different polymer molecular weights (MWs)

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where the intensity was normalized by multiplying q2 considering the typical scattering behavior of two-dimensional material. The scattering intensity (I(q)) averaged in the stretched direction vs. q-vector is shown in the inset of Figure 1c and Figure S2. The scattering profiles show prominent peaks at q*, which can be converted to the average plane-to-plane distance, davg (=2π/q*) where q* is the position of peaks. davg is analyzed at a fixed GO concentration (GO), with varying PEG concentrations (cp) and MWs as shown in Figure 1d. davg decreases with increasing cp in all PEG MW systems. The decreasing davg results from the reduced repulsions between GOs with adding polymers.41, 43, 44 Therefore, it is not new that davg decreases with cp in all MWs. However, it is worth noting that the davg is decreased more with higher PEG MW at a same cp in the range of cp≤10 wt. In other words, increasing PEG MW is more effective to reduce the repulsive nature of GOs, which implies the existence of MW dependent polymer induced interactions. One should note that the scattering intensity was obtained within a few days after the sample preparation. Thus, the ultimate aggregation of GO induced by the depletion attractions was not seen while the decreasing davg with cp clearly confirmed the reduced electrostatic repulsions. The davg can be decreased further with time.41 No upturns at low q range from all samples also suggest that GO are dispersed nicely without agglomeration at initial state. The detailed discussion will be followed. Despite the subtle changes of microstructure, GO in all PEG solutions remains nematic LC phases implying the adding PEGs does not disturb the macroscopic LC structure shown in Figure 1a and Figure S1.

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However, these subtle changes of microstructure can influence on the physical properties of GO suspensions significantly. The rheological properties of GO suspensions were measured with oscillatory shear strain and frequency sweep experiments. Figure 2a shows the strain sweep experiment of GO suspension at GO = 0.5wt and cp = 5 wt. First, there is a critical shear strain (*) where storage (G’) and loss (G’’) modulus intersect, which is increased with PEG MW. At the *, the deformation of microstructure of GO LC occurs and more liquid-like property dominates the system (G’’>G’). The * increased from 3% to 4% and 10%, from polymer-free GO suspension to PEG 400 and 10k systems. The *for all PEG MWs are presented in Figure 2b. In addition, we note that PEG can be adsorbed on GO surface and the degree of PEG adsorption increases with MW as confirmed from the TGA result shown in Figure 2c (see Figure S3 and Table S1 for details). The adsorption of polymers on GO surface is considered to increase resistance to flow and requires higher shear strain to be deformed. Thus, increasing polymer MW can be more effective in maintaining the internal structures against shear as polymer protects the structure from the deformation. Second, we note that both G’ and G’’ greatly decrease from pure water to low and high MW PEG addition. To clarify the moduli variation with MW and cp more quantitatively, we performed the frequency sweep experiment at a constant shear strain; the result of GO suspensions at GO = 0.5 wt and cp = 5 wt for varying MW is given in the inset of Figure 2d and other results at other cp are provided in Figure S4. Then, the G’ and G’’ at a given 0.15 Hz are plotted as shown in Figure 2d. In Figure 2d, the G’ continuously decreases with cp, and the higher MW is, the further the modulus decreases. G’ and G’’ decrease from PEG 400 to 1k and 3k while not much quantitative difference is shown at higher MWs. The cp and MW-dependent moduli reduction implies that, unlike the generally accepted concept of polymer physics, the addition of polymers

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reduces the modulus and even higher PEG MW is more effective to reduce the modulus of the material than the lower one, also suggesting the presence of more complex polymer-induced interactions. The reduced G’ or G’’ of GO suspension with PEG implies that the viscosity of GO suspension can be also dropped by adding high MW PEGs, which may resolve the technical issue of GO LC processing; GOs in aqueous solution vitrify near 1 wt of GO concentration commonly acting as an obstacle for GO-based material fabrication while the exact vitrification concentration is dependent on the size and the surface charge of GO.25, 41, 45 To confirm the effect of MW-dependent viscosity reduction, the viscosity of 0.5 wt GO suspensions at different MWs is measured with increasing shear rate. Figure 2e and 2f show the shear viscosity of GO suspension at GO = 0.5 wt for PEG 400 and 10k systems. The GO suspensions in both systems show shear-thinning behavior (~x, where x1 s1).

The exponents of x at high and low shear rates are plotted with cp in Figure S5. The shear

thinning can arise from the collective interactions of GOs based on their highly repulsive nature, noting the shear thinning is a typical sign of non-Newtonian liquid. The addition of entangled polymers in water generally enhances the shear-thinning behavior; however, adding PEGs in aqueous GO suspension ironically reduces the shear thinning and begins to show the property of Newtonian fluid. Thus, the role of polymers in aqueous GO suspension is primarily to reduce the effective volume of repulsive GOs, which ultimately changes the microstructure and reduces the viscosity. Therefore, the bulk properties of GO suspension at low cp (≤10 wt) are determined by the microstructure of GO LC and its non-Newtonian flow property, rather than by the polymer. The same trend was found at GO = 0.8 wt as presented in Figure S6.

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To examine the effect of high and low MW of polymers more quantitatively, the viscosities of GO in aqueous suspension and PEG solutions are compared with the normalized viscosity (r = GO

in PEG soln/GO in water)

with varying cp shown in the insets of Figure 2e and 2f. When r is

greater/smaller than 1, the viscosity of GO in PEG solution increases/decreases compared to the GO in aqueous suspension. While both PEG 400 and 10k systems show the shear rate dependent viscosity reduction (r < 1), adding PEG 10k leads more dramatic reduction, consistent with the result in Figure 2d. The viscosity reduction for other MW is given at Figure S7. Figure 2g shows cp-dependent viscosity reduction for PEG 400 and PEG 10k systems at a constant shear rate (0.1 s-1). While r continuously decreases with cp for PEG 400 system, r is greater than 1 where cp ≤ 0.1 wt and smaller than 1 at higher cp for PEG 10k system. In short, adding smaller than 0.1wt of PEG 10k increases the viscosity of GO suspension whereas the addition of more than 0.1wt of PEG 10k decreases the viscosity of GO suspension significantly. This implies that cp-dependent polymer induced interactions exist, controlling the GO-GO interactions thus changing the bulk property. We further note that increasing viscosity with adding PEG does not guarantee a good stability of LC, but rather aggregated GO decreases GO LC. Taken together, the revealed polymer MW- and cp-dependent microstructures and rheological properties imply that strong polymer mediated interactions exist and govern the GO interactions. To clarify the origin of MW- and cp-dependent viscosity reduction, the total pair interaction energy per unit area is calculated based on the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory and polymer induced depletion attractions.21, 39, 40, 46, 47 The details for the energy calculation are provided in Supporting Information (SI). Figure 3a and 3b show the

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total interaction energy for GO in PEG 400 and 10k solution, respectively. The separated interactions for GO in PEG400 and 10k solution are given in Figure S8. We found that the electrostatic repulsion dominates the GO-GO interactions. While the vitrification, the glass like solidification of materials accompanying the viscosity increase can be caused either by attractive or repulsive interactions between the particles,47 the vitrification with GO exhibiting glassy behavior is found as a result of highly repulsive nature of GO interactions. 41

The addition of both PEG 400 and 10k reduces the repulsive energy, which was the origin of viscosity reduction. In addition, adding PEG 10k reduces it more significantly, which indicates adding PEG 10k is more effective on viscosity reduction than PEG 400. We note that the degree of van der Waals attraction in PEG 400 and 10k is not much different but the depletion attraction can be significantly enhanced with higher MW. Thus, the GO in PEG 10k experiences more reduced repulsion, which lowers the effective volume of GO. In PEG 10k solution, not only the energy barrier is reduced but the range of attraction near the GO surface is much wider than that in PEG 400 system presumably caused by the depletion attraction. The degree of depletion attraction near particle surface increases with cp while the range of attraction is determined from the size of polymer chain, often scaled with the radius of gyration of polymer, Rg.48, 49 The increase of Rg from PEG 400 to PEG 10k system widens the effective range of attraction and changes the total pair interactions of GO greatly.50 One suspects that the slip with polymer near GO can lower the viscosity providing sliphydrodynamic flow. The slip of polymers can occur on the surface of polymer adsorbed GO;

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however, we found that this can be negligible as the viscosity still decreases when the hydration layer for slip was minimized (unpublished data). While the reduced repulsion with increased depletion attraction can cause the reduced effective volume and viscosity, the sufficiently lowered energy barrier simultaneously suggests aggregation of GO as shown in Figure 3b. Indeed, GO was aggregated forming attractive network or gel when PEG was adsorbed little, increasing the viscosity of GO suspension. The aggregation of GO with PEG 400 system was not found in the given range of cp, presumably due to the very narrow range of depletion attraction zone. Here, we clarify that the high viscosity of GO suspension with little polymer is caused by the gelation of attractive GO with depletion whereas the high viscosity of GO suspension without polymer is caused by the glass transition of repulsive GO. However, adding sufficient PEG 10k not only creates depletion attraction but also creates a strong steric barrier on the GO surface preventing the direct contact between GO and thus providing good dispersity. Therefore, GO can be stable without aggregation and remains liquidlike with a sufficient polymer adsorption. To sum up, the role of fundamental interactions are strongly dependent on GO and polymer concentrations. The electrostatic repulsion of GO provides a good dispersion in water, but can also increase the effective volume of GO showing a glassy behavior. While the depletion attractions with sufficient steric repulsions reduces the effective volume of GO reducing the viscosity, depletions with insufficient steric repulsions create the GO agglomerations. Based on the discussed interaction energy estimations, we finally created a schematic viscosity diagram where increment/reduction of viscosity is drawn with varying concentrations of

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GO and PEG 10k as shown in Figure 4a. The viscosity is measured using oscillatory rheometery in the same manner introduced in Figure 2. When the ratio, r is much greater/smaller than 1, the viscosity of GO in PEG solution increases/decreases compared to that of GO in aqueous suspension as marked with red/blue symbols, respectively. The green triangles imply an intermediate viscosity region where the viscosity of GO in PEG solution is similar to that of GO in aqueous suspension as r~100. The viscosity diagram provides an interesting cp-dependent viscosity variation as we predicted. For example, at a fixed GO =1.0 wt, when 0.1 wt of PEG 10k is added, it brings depletion attraction lowering the energy barrier but cannot build a sufficient steric layer. Thus, attractive GO are aggregated and thus the viscosity increases with gelation. Adding more PEG 10k ironically reduce the viscosity as strong steric layer prevents the aggregation. Additionally, we found that there is a threshold concentration (cp,thld) where adding PEG does not vary the viscosity of GO suspension with r 1. Above cp,thld, the viscosity of GO in PEG solution can be lowered by a factor of 101-103. We note that cp,thld increases with GO concentration because cp,thld is considered as the minimum concentration for PEGs to fully adsorb on GO and thus to prevent the direct contact betwen GOs. Surprisingly, the found cp,thld from the viscosity measurement increases in parallel with the critical adsorption curve obtained from the TGA where the mass ratio of GO and PEG 10k is extracted upon a complete adsorption isotherm (Table S1). The reversibility of polymer mediated GO stability was confirmed with dilution experiments. The GO sample labeled as ‘s1’ was aggregated because of insufficient adsorption layer at cp < cp,thld marked in Figure 4a and shown in Figure 4b. Then, the sample was diluted with

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either water or PEG solution and the diluted samples were labeled as ‘s1w’ or ‘s1p’, respectively; the concentrations of GO and PEG were changed with dilution as indicated with the arrows in Figure 4a. While GO in ‘s1w’ remained aggregated as cp is still lower than cp,thld, GO in ‘s1p’ were nicely redispersed forming LC as cp becomes higher than cp,thld as shown in Figure 4b with schemes. The presence or absence of GO aggregation was also confirmed by dynamic light scattering experiments (See Figure S9). The importance of the viscosity diagram is, therefore, to explicitly present a golden ratio between GO and polymer in order to maintain the excellent dispersion and liquid crystallinity of GO solutions, and potentially can be used in many GO-based processing. To demonstrate the effect of adding polymers to GOs in their liquid crystallinity and resulting the microstructure in the application level, we have produced GO fibers from the GO in polymer solutions. The details are found in Methods. Figure 5a, 5b, and 5c show the SEM images of reduced GO fibers spinning from the aqueous suspension, PEG 400 and PEG 10k solutions at cp = 2 wt, respectively. While GOs from pure water are aligned along the spinning direction, defects and voids exist in the cross-sectioned image, and winkles are found on the fiber surface, which can be produced from the volume shrinkage of GO suspensions during the wet-spinning or post-drying process.27 However, GO fibers from both PEG 400 and 10k solutions have less voids with less wrinkles on surface than that from aqueous solution. The degree of GO alignment is qualitatively compared with false-colored images in the right corner of Figure 5. The color indicates the azimuth between GO sheets and the fiber axis at the boundary, which also confirms the GO are aligned better with PEGs. The fibers with PEG have less volume shrinkage than the fibers without PEG during spinning and the remained PEG after drying may prevent the buckling. Although the effect of adding PEG on GO alignment needs to be investigated further considering the dynamic nature of spinning and drying process, the better packing of GO sheets with polymers may partially arise from

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the reduced the effective interspacing between GOs as found in Figure 1d and from the dramatic viscosity reduction, which increase the fiber spinning processibility. Conclusions In summary, we have thoroughly investigated the effect of adding polymers on the liquid crystallinity and rheological property of GO suspensions by varying polymer concentrations and molecular weights. Noting that the vitrification of GO is caused by the repulsive nature of GO, high molecular weight polymer induced depletion effectively decreases the repulsion thus retard the vitrification. While this reduced repulsive nature of GO LC can effectively decrease the system viscosity, GO remains stable with sufficient of polymer adsorption. However, insufficient polymer adsorption at very low cp produces a net attraction for GO, creating aggregated GO attractive network/gels and significantly increases the viscosity of the GO LC. Furthermore, cp,thld have been proposed to provide excellent stability and processability for GO-based applications as polymer can create complex depletion attractions and steric repulsions and thus coordinates GO interactions. Finally, we emphasize that more sophisticated control of GO microstructure and physical properties in advanced GO LC-based applications should begin with an understanding fundamental interactions of GO colloids. Methods Sample Preparation Graphene Oxide (GO) was firstly suspended in water by 1 wt after purification as described elsewhere. The individual GO sheet has a thickness of 1 nm and an average lateral width of 1 m. To study the dispersion of GO in PEG solution, PEG solution was prepared at 50 wt, added to GO suspension and then mixed using a vortex for 10 s. The series of suspension was put in sealed glass vials and kept at room temperature.

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Small-Angle X-ray Scattering (SAXS) SAXS experiments were conducted at the 6D beamline of the Pohang Accelerator Laboratory (PAL) to study the microstructure of GO dispersions. The sample-to-detector distance was 3505 mm and the X-ray energy was 8 keV. The scattered X-rays were analyzed with a CCD area detector (MX-225 HS, Rayonix L.L.C., USA). The 2-D SAXS patterns were averaged by integrating the area within 5° in the stretched direction (see the inset of Figure 1b) and the relative 1-D scattering intensity was plotted as a function of the scattering vector q =(4πsin )/ where  is half of the scattering angle and  is the wavelength. Rheometer Rheological experiments were conducted using kinexus pro+ rheometer with coneand-plate geometry at 20 °C; the cone was 20 mm with an angle of 4° and the gap distance was 143 m. The sample was allowed to rest on the plate for 10 min after loading. Frequency/strain sweep experiments at a constant stain/frequency were performed to measure storage and loss moduli. Shear viscosity shown in Figure 3 was measured in the shear rate range of 0.01 to 100 s-1. SEM image The fiber morphology was imaged using a cold scanning-electron microscope (SEM) (FE-SEM Hitachi, S-4800, 10 keV). Polarized Optical Microscopy (POM) The liquid crystallinity of GO suspensions at each condition was confirmed by POM images. The sample was dropped on a custom-made slide glass, at 0.7 mm thickness, and images were taken at 100x magnification between two crossed polarizers using Olympus BX51M microscope. Thermogravimetric Analysis (TGA) TGA experiment was conducted with Q500 of TA instrument to measure the PEG adsorption onto GO surface. The GO sediments after centrifugation were dried in a vacuum oven to completely evaporate the water and then loaded into a platinum pan. The sample was heated from 30 °C to 700 °C with the heating rate of 10 °C/min in N2 atmosphere.

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Zeta-potential and Dynamic Light Scattering Zetasizer Nano ZS90 (Malvern Instrument) is used to measure the zeta potential () of 0.1 wt GO suspension using a folded capillary cell and to obtain the correlation curves of GO in ‘s1w’ and ‘s1p’. The light source power and wavelength is 4 mW and 633 nm, respectively. Every measurement was performed at a scattered angle of 90° at 25°C. GO fiber spinning GO employed for fiber spinning was supplied from STANDARD GRAPHENE and the lateral size of GO was 30 m. GO LC dopes (2 wt) were injected into the rotating coagulation baths (at 10 rpm) at a rate of 0.4 ml/min. The coagulation baths were ethanol/water (1:3 v/v) solutions of 5 wt CaCl2. After 10 min immersion in coagulation baths, the GO gel fibers were transferred into the mixture of ethanol/water (1:3 v/v) bath to wash away the residual coagulation solution, and the washed GO gel fibers were collected onto a bracket. Dried GO fibers were reduced by immersing them into the hydroiodic acid solution (50 wt) and keeping at 60 °C for 6 h. After cooling to room temperature, the fibers were washed by ethanol and dried at 25 °C under vacuum for 12h. Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (NRF-2018R1A5A1024127, NRF-2016M3A7B4905624). SAXS experiments at PLS-II 6D UNIST-PAL beamline were supported in part by MSIT, POSTECH, and UNIST Central Research Facilities. Author Contributions ‡ S.Y.K initiated and supervised the project. Y.H.S principally performed experiments. S.Y.K. and S.O.K. coordinated the research. T.J.S helped the SAXS measurement. K.E.L carried out the GO synthesis and purification. All authors contributed to manuscript preparation.

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Additional information The Supporting Information is available free of charge via the Internet at http://pubs.acs.org. Calculation details for total interaction energy given in Figure 3; Polarized optical microscopic images of GO suspensions; SAXS 1D scattering intensity I(q) vs. q-vector; TGA results; Additional rheology experiments; Correlation curve for the ‘s1w’ and ‘s1p’ samples in Figure 4;

Corresponding Author * E-mail [email protected] (S. Y. K.); +82 52 217 2558

References

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Figure 1. (a) 2D SAXS patterns of GO LC at various concentration and molecular weight of PEG at a fixed GO concentration (GO = 1.5 wt). (b) The averaged 1D scattered intensity with alignment direction and whole area integration as demonstrated in the inset. (c) Normalized intensity Iq2 vs. q-vector. The inset is I vs. q-vector. (d) The plane-to-plane distance (davg) with polymer molecular weight. The inset is a schematic image of GO in a SAXS capillary cell.

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Figure 2. (a) Strain sweep experiment of 0.5 wt GO suspensions at 1 Hz in water and PEG 400 and 10k systems at cp = 5 wt. Solid and dotted lines represent storage (G’) and loss (G’’) modulus, respectively. (b) The G’ and G’’ crossover strains for varying PEG molecular weight. (c) The number of repeating units (n) of PEG at saturation adsorption on GO, representing the degree of adsorption obtained from TGA. The details are given in Table S1. (d) (inset) Frequency dependent G’ and G’’ of 0.5wt GO suspension with  = 1% at cp = 5 wt%. Results at other cp are given in Figure S4. The G’ and G’’ at 0. 15 Hz found in the inset and Figure S4 are plotted with cp for varying PEG MW. (e) Flow curve of 0.5 wt GO suspension in (e) PEG 400 and (f) PEG 10k solution. The normalized viscosity (r = GO in PEG soln/GO in water) is shown in the insets of (e) and (f). (g) The normalized viscosity at a constant shear rate of 0.13 s-1 is plotted with cp for PEG 400 and 10k solutions.

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Figure 3. Interaction energy per unit area between two GO particles in (a) PEG 400 and (b) PEG 10k solutions at cp = 1, 3, and 5 wt. The non-approachable distance exists due to the surface roughness and adsorbed polymers at sufficient PEG adsorptions.

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Figure 4. Viscosity diagram of GO suspensions with various GO and PEG 10k concentrations. The red circle, green triangle, and blue square indicate high (r >1), intermediate (r ⋍1), and low (r