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Andrew
Corker
^{ab},
Henry C.-H.
Ng
^{b},
Robert J.
Poole
^{b} and
Esther
García-Tuñón
*^{ab}
^{a}Materials Innovation Factory, University of Liverpool, UK. E-mail: Esther.GTunon@liverpool.ac.uk
^{b}Department of Mechanical, Materials and Aerospace Engineering, School of Engineering, University of Liverpool, UK

Received
21st September 2018
, Accepted 12th December 2018

First published on 22nd January 2019

Additive manufacturing (AM) techniques and so-called 2D materials have undergone an explosive growth in the past decade. The former opens multiple possibilities in the manufacturing of multifunctional complex structures, and the latter on a wide range of applications from energy to water purification. Extrusion-based 3D printing, also known as Direct Ink Writing (DIW), robocasting, and often simply 3D printing, provides a unique approach to introduce advanced and high-added-value materials with limited availability into lab-scale manufacturing. On the other hand, 2D colloids of graphene oxide (GO) exhibit a fascinating rheology and can aid the processing of different materials to develop ‘printable’ formulations. This work provides an in-depth rheological study of GO suspensions with a wide range of behaviours from Newtonian-like to viscoelastic ‘printable’ soft solids. The combination of extensional and shear rheology reveals the network formation process as GO concentration increases from <0.1 vol% to 3 vol%. Our results also demonstrate that the quantification of ‘printability’ can be based on three rheology parameters: the stiffness of the network via the storage modulus (G′), the solid-to-liquid transition or flow stress (σ_{f}), and the flow transition index, which relates the flow and yield stresses (FTI = σ_{f}/σ_{y}).

The definition of printability in extrusion-based printing is somewhat vague, and means different things to researchers working towards different applications. For example, the requirements for DIW of glass and bio-printing are different to the needs in complex structures with high level of detail. In 3D-bioprinting inks must have relatively low yield stresses and storage moduli (G′) in order to keep the cells alive;^{12,14} this is also the case for glass formulations, where the stiffness of the inks is key for the successful post-processing stages, in order to avoid opacity and cracking.^{14,20} On the other hand, many other applications in complex hierarchical structures require ‘stiff’ pastes that enable high printing resolutions to be achieved. Despite the differences between these applications, it is generally recognised that printable formulations must be a shear thinning, yield-stress soft material exhibiting solid-like behaviour. The storage modulus (G′) values must be high to retain the shape, to support its own weight and the layers on top and to span across supports. The ‘yield’ stress must also be high enough to retain printing resolution as the filament is deposited, but within certain limits to facilitate an easy flow initiation during the printing process. However, quantification of these general criteria is so far unclear, partly due to the diversity of the rheological methodologies used in the field and a lack of common protocols, and partly due to the wide range of ‘soft-materials’ with complex viscoelastic fingerprints currently used. The rheological parameters are paste specific, i.e. they depend on the intrinsic properties of the materials in the formulation, density, specific surface, etc. and the formulation approach, as a consequence colloidal systems, gels and liquid crystals of 2D materials will respond differently during the printing process. A wide range of colloidal and hydrogel-based formulations can be easily found in the literature, some of them pH or temperature sensitive, solvent and water based. We have developed formulations based on 2D colloids of graphene oxide (GO) in the absence of additives.^{1,4,14} In between macro-molecular assemblies, colloids, gels and liquid crystals, GO suspensions in water are a unique class of soft materials with a fascinating rheological behaviour that does not completely fit in any of the aforementioned classes. Similarly to colloidal systems when concentration increases GO flakes form elastic networks that can be 3D printed and also aid the printing of powders with different chemistries, sizes and shapes.^{14} Unlike particle systems, which often follow the Krieger–Dougherty model (i.e. exponential increase with volume fraction),^{1,4,21} the elasticity of GO networks rapidly increases with concentration following a power law behaviour. According to data compiled from the literature this is common to a variety of GO flakes with different functional groups and lateral dimensions.^{14,22}

Here we provide an in-depth rheology study combining oscillatory, shear and extensional tests that will contribute to the establishment of protocols to define and predict ‘printability’. The work focuses on GO 2D colloids and provides new insights on their behaviour (including a better understanding of network formation, structure breakdown and recovery) that are relevant to many other materials in the ‘flatland’, for example ‘2D polymers’^{23} and other layered materials^{24,25} and crucial to understand their potential role in wet processing and manufacturing. Varying the flake concentration leads to a wide range of behaviours from Newtonian-like to highly elastic, providing a library of formulations with different printing behaviours. The different rheological tests performed on the GO suspensions provide a comprehensive approach to identify the key rheological parameters involved in the printing process and how they relate to each other. Monitoring structure evolution during the transition from LAOS to SAOS (‘recovery’ tests) enables the quantification of the aggregation kinetics and shows how it scales with the stiffness of the network.

Raman spectroscopy was performed on the GO stock solution using a Renishaw inVia confocal Raman Microscope equipped with a 532 nm laser (power 100%, with an 50× objective, and exposure time of 10 s). The surface tension of GO suspensions with different concentrations was measured using the pendant drop method in a Kruss Drop Shape Analyzer DSA100. The relationship between surface tension and gravity determines the shape of the pendant drop. The surface tension is calculated from the shape (using the Kruss software) of a drop of sample suspended in air from a needle (of 2 mm diameter for the 0.1 and 0.2 vol% GO and of 0.5 mm diameter for 0.3 vol% and above). This technique fails when the materials exhibit a yield stress.

Additional amplitude sweeps (strain between 0.01% and 150% at 0.5 Hz) were carried out to determine the linear viscoelastic region (LVR) and quantify the inner structure and break down process. The yield stress, σ_{y}, and yield strain, γ_{y}, values are determined at the limit of the LVR; @rest G′ values were determined as the average within the LVR; and the strain and stress at the flow point, σ_{f} and γ_{f} respectively, were determined at the crossover point (G′ = G′′). We define the flow transition index, FTI = σ_{f}/σ_{y} as a dimensionless parameter to characterise the breaking behaviour of the inner structure, which illustrates the brittle behaviour of the soft material as FTI approaches to 1.^{26,27} Recovery tests consisted of two stages to monitor the transition from LAOS (Large Amplitude, time sweep at 150% strain held for 200 s) to SAOS (Small Amplitude, time sweep at 0.5% strain held for times between 200 s and 60 min) at fixed frequency of 0.5 Hz. This test aims to quantify the recovery behaviour of the formulation upon deposition during the printing process.

Fig. 1 Schematic representation of a GO flake and characterisation results. (a) Scheme illustrating the 2D and amphiphilic nature of GO due to the configuration of different functional groups on the basal plane (carboxylic acids –COOH, hydroxyls –OH, epoxy rings –O–, and un-oxidised islands) and edges (–COOH & –OH) on GO flakes. (b) Image of a GO flake taken with an optical microscope; (c) Raman spectrum showing the characteristic vibrational peaks for GO (D, G and 2D).^{27,29} |

The time evolution of liquid bridges formed from GO suspensions with concentrations from 0.05 vol% to 0.30 vol% (Fig. 3) shows a transition from Newtonian-like (0.05 vol%) to shear thinning behaviour (0.2 and 0.3 vol%). At 0.05 vol% the filament becomes an approximately uniaxial straight-walled column immediately prior to breakup (Fig. 3). When effects of gravity and inertia can be ignored, the diameter of a Newtonian fluid undergoing capillary thinning evolves according to the similarity solution of Papageorgiou [eqn (1)];^{33} where D_{mid} is the filament diameter at mid-height, σ the surface tension and t_{c} the filament breakup time.

(1) |

From the time evolution of the filament diameter at height corresponding to breakup (tracked backwards in time, Fig. 4), we observe that the 0.05 vol% GO solution is linear when near filament breakup, confirming Newtonian-like response to axial elongation [eqn (1)]. At concentrations above 0.05 vol% GO “necking” takes place and a conical taper forms near the breakpoint prior to filament breakup (Fig. 3). For 0.2 and 0.3 vol% concentrations, the time evolution of the filament diameter seems to follow a power law [eqn (2)];^{34,35} where Φ(n) is a numerical constant, K is the consistency factor and n is the power law exponent.

(2) |

Fig. 4 CaBER results: time evolution of filament diameter at height corresponding to breakup (where t = 0 is the breakup time). Each symbol represents a different concentration and each plotted profile is the average of 5 independent measurements per concentration. Data at low concentrations seem to fit to the viscous regime (eqn (1)). At 0.1 vol% there is a transition with a behaviour that do not fit well either with the viscous regime (eqn (1)) or the power law (eqn (2)). Concentrations of 0.3 and 0.4 vol% fit well to power law (eqn (2)) with n values of 0.585 and 0.535 respectively. |

However, at a concentration of 0.1 vol% GO, the time evolution of the filament diameter is not well described by a power law (Fig. 4) and perhaps a better fit to the data is a linear fit for t > −0.0015 s, which suggests Newtonian-like response very near to filament breakup at this concentration. This is highly likely related to the migration of GO flakes from the ‘neck’, as they are not forming a continuous network in the suspension. Using the front factor^{14,30,33,36,37} and assuming that the surface tension is equal to that of water (σ = 72 mN m^{−1} at 20 °C) the slope of the linear fits to the data in Fig. 4a and b yields viscosity values of μ_{s} ≈ 33 mPa s and μ_{s} ≈ 63 mPa s for GO suspensions with concentrations 0.05 vol% and 0.10 vol%, respectively. At concentrations of 0.2 and 0.3 vol% GO; power law exponents obtained from the data in Fig. 4c and d are n = 0.585 and n = 0.535, respectively.

Whilst the observed trends are consistent, the analyses reveal a significant amount of scatter between repeated runs for a given concentration. This can be explained due to the contribution of different aspects: the 2D nature of GO flakes (large lateral surface but thickness in the nm range) that can roll up, bend and twist forming nano-scrolls; the large lateral size distribution (lateral size varying from ∼10 to 230 μm); as well as potential concentration fluctuations due to the observed flake migration within the filaments close to breakup. Despite these uncertainties, extensional tests provide new insights into the behaviour of 2D colloids at very low concentrations and contribute to better understand structural evolution and network formation. The extensional results reveal that the behaviour of GO colloids are also highly concentration dependent at very low concentrations, with Newtonian-like response at a concentration of 0.05 vol% and the emergence of shear-thinning-like behaviour at concentrations as low as 0.20 vol%. At higher concentrations yield stress effects complicate the analysis of CaBER data still further.^{35,38} In fact, samples of GO with concentration higher than 0.3 vol% could not be consistently loaded into the CaBER device using a pipette as the samples would not form straight walled cylinders under their own surface tension prior to initiation of breakup. This leads to inconsistent results due to differences in the initial sample volumes. Further work is required to develop more consistent protocols when using CaBER to materials exhibiting significant yield stress behaviour such as GO at printable concentrations.

Fig. 6 Shear rheology of GO suspensions: (a) effect of flake concentration on zero-shear viscosity and flow index (calculated from viscosity curves in Fig. 5). Zero shear viscosity (determined as the average in the plateau at low shear) increases with GO vol% following a power with an exponent of ∼2.5. At 3 vol% there is a remarkable change of trend that has not been considered for the fit. The flow index, n, is calculated fitting the data within the shear-thinning region (between 0.1 < < 100 s^{−1}) in the viscosity curve to a power law (calculating n − 1 as the slope in the log–log plot (Fig. 5a)). The index gets closer to 0 as the concentration increases. (b) Shear viscosity curves compared with the results of the extended Cox-Merz rule applied to dynamic data from frequency sweeps. The data show that this rule can be applied to concentrations between 0.3 and 1.2 vol% over this shear rate range, but not for higher concentrations. |

Fitting these zero-shear-viscosity values vs. GO content to a power-law confirms that μ_{0} does indeed increase with concentrations up to 2.8 vol% following a power law with an exponent of ∼2.5 (Fig. 6a). This exponent is in good agreement with the trend observed for storage modulus, G′, and yield stress, σ_{y}, that follow a power law with an exponent between 2.5 and 2.9 according to the literature^{14,26,30,36,37} and to the new oscillatory results in this work. From the viscosity curves (Fig. 5a) we find that a 0.1 vol% GO suspension has a slightly shear-thinning behaviour with shear zero viscosity of 9.62 ± 0.05 Pa s and power law exponent n of 0.302 ± 0.014 (Fig. 6a, obtained from the fit of the shear thinning region and calculating n − 1 from the log–log plot in Fig. 5a). According to extensional tests this concentration falls within the transition region from Newtonian-like to non-Newtonian. As the GO concentration increases from 0.1 vol% to 2 vol% the exponent n decreases down to 0.012 ± 0.006, and n approaches to essentially zero at 2.5, 2.8 and 3 vol% GO (Fig. 6a), demonstrating the evolution towards an intensely shear-thinning ‘stiff’ material and more yield-stress-fluid-like behaviour.

We found that at ‘printable’ concentrations (2.5, 2.8 and 3 vol%) the stress becomes essentially independent of the shear rate. Plotting the evolution of shear stress with shear rate (Fig. 5b) it is possible to identify the transition from a power law behaviour (τ ∼ K^{n}) to a regime where the stress is constant (τ ∼ K ∼ τ_{y}). At concentrations of 3 vol% GO, there is a sharp change in the observed trend; μ_{0} increases up to values in the order of 250 kPa and does not follow the same power-law exponent (Fig. 6a). At this concentration, transient effects take place at shear rates above 1 s^{−1} (Fig. 5a) likely due to the high stiffness and brittle response of the sample, and as a consequence, the data in this shear rate region have not been considered in our analysis.

Overall, we find that shear tests complement the results obtained with extensional and surface tension experiments to qualitatively understand network formation and the transition to non-Newtonian behaviour at low concentrations. The flow ramps can also be used to quantify the zero-shear viscosity and power-law exponent at intermediate concentrations between 0.4 vol% and 2 vol%. As we reach the printability window (between 2 and 3 vol% GO) shear tests become more uncertain for quantitative purposes, however these tests provide useful insights to identify the ‘printability’ threshold, i.e. the transition from a power-law behaviour to a regime where n ∼ 0 and the shear stress is therefore independent of the shear rate. Transient effects at low shear (Fig. 5a) may slightly underestimate the zero-shear viscosity. Steady state flow sweeps would be more appropriate to avoid these transient effects, however, further studies at low shear rates are beyond the scope of this work.

From the second step in the sequence, it is possible to determine if the oscillatory data for formulations of 2D GO colloids can be used to approximate the flow behaviour or vice versa. Applying the extended Cox–Merz rule (Rutgers–Delaware, eqn (3))^{14,38} to dynamic data (frequency sweeps, step 2, fixed strain 0.5% (Fig. 7b)) suggest that this empirical rule can be reasonably applied to intermediate concentrations, above 0.3 vol% and below 2 vol% (Fig. 6b).

[η′(γ_{0}ω) = μ()]_{=γ0ω} | (3) |

The transformations (eqn (3)) match reasonably well with the steady state shear results (Fig. 6b) for concentrations within this range. As the concentration increases up to 2 vol% and beyond, as we approach the printable region, the overestimation of the viscosity using dynamic data becomes clear (Fig. 6b). From these results, it seems that the extended Cox–Merz rule can be applied to suspensions of GO colloids at intermediate concentrations.

The concentration of GO flakes has an important effect on the structural recovery after the amplitude sweep (Fig. 7c). At concentrations below 1.2 vol% GO, the networks do not completely recover after breakdown. The percentage of recovery at 0.3 vol% is below ∼50%, at 0.4 vol% around ∼75% and increases up to ∼90% for 0.8 vol% GO, which suggest a Maxwell fluid (viscoelastic liquid) behaviour undergoing permanent deformation.^{14,26} Beyond these concentrations the recovery of the storage modulus, G′, is almost complete within the experimental uncertainty (Fig. 7c), indicating the transition to a Kelvin–Voigt fluid (viscoelastic solid). From these results, we consider that the threshold for network formation or ‘gel’ point takes place between 0.8 and 1.2 vol% GO.

Overall, this 5-step oscillatory sequence provides a qualitative assessment of formulation stability, structural evolution and recovery; it also enables to identify possible non-linear events taking place.^{14,39} However, they still have some limitations to quantitatively determine break-down and recovery parameters during step 4 (amplitude sweep) and step 5 (recovery time sweep). The amplitude sweep does not show the linear viscoelastic (LVR) for any of the concentrations, which suggests that the fixed strain, γ_{0} at 0.5% (selected based on previous work)^{14} is just at the limit or at the start of the ‘yielding’ region. In addition, some of the formulations do not exhibit a ‘flow’ point (crossover G′ = G′′) below 50% (γ_{max} in step 4). Since some of the networks have not been completely broken down, the recovery calculated from step 5 (Fig. 7b) is not fully accurate because each suspension will be recovering from a different initial condition.

We designed two additional experiments to provide a more reliable quantification of the break-down and rebuild stages: a second amplitude sweep under a wider range of strains (0.01 to 150%), and a ‘recovery’ test (transition from LAOS (150%) to SAOS (0.5%)). By representing the viscoelastic properties (G′ & G′′) versus the oscillation stress in the amplitude sweep (Fig. 8a), the evolution of the yielding region as concentration increases is clear. It is possible to quantify the trend of different rheological parameters: the ‘at rest’ structure (as the average of G′ within the LVR, Fig. 8b); γ_{y} and σ_{y} (at the limit of the LVR, Fig. 8a and c); γ_{f} and σ_{f} (at the cross-over point (G′ = G′′), Fig. 8c); and the FTI values (defined in experimental, Fig. 8c). The ‘at rest’ stiffness of the network (G_{LVR}′) follows a power-law relationship (exponent of ∼3) with GO concentrations up to 2.8 vol%, but at 3 vol% there is a remarkable change of trend with G_{LVR}′ values of ∼250 kPa. The flow stress, σ_{f}, also increases with a power exponent of ∼2 in the same range, and a similar jump is observed at 3 vol% with σ_{f} ∼ 5.3 kPa. The evolution of the yield stress, σ_{y}, changes exponentially with the concentration, which leads to FTI values getting closer to ∼10 within the ‘printing region’ (2 < vol% ≤ 3). The FTI evolution seems to be one of the key parameters related with ‘printability’. Below 0.8 vol% the viscoelastic network is very weak with σ_{y} and σ_{f} below ∼1 Pa and ∼20 Pa respectively (Fig. 8c), and the FTI values do not follow a clear trend. Above the 0.8 vol% threshold, FTI values steadily drop from 100 to 10 at 3 vol% (Fig. 8c), which nicely illustrates the transition from a weak network to a stiff and “brittle” soft material. This parameter is indicative of the ability of the structure to yield, break-down and similarly to rebuild during the printing process.

The transition from LAOS to SAOS in the ‘recovery’ tests enables us to monitor the reformation of the network (Fig. 9 and 10), which is a key aspect to enable the printing of complex structures without compromising resolution. Applying a strain of 150% (LAOS) for at least 3 min ensures that all the samples are liquid-like before monitoring the transition to 0.5% strain (SAOS).

Fig. 9 Oscillatory rheology of GO suspensions: recovery behaviour during LAOS-to-SAOS transition. Samples are subjected to a large amplitude (150% strain) time sweep to ensure that they are in the liquid-like regime, followed by a small amplitude (0.5% strain) time sweep. Both fixed at a frequency of 0.5 Hz in a TA ARES G2. The transition region (highlighted in grey) can be divided into three stages each with a different gradient (Fig. 10). |

Fig. 10 Oscillatory rheology of GO suspensions: (a) ‘Recovery’ curve for the 2 vol% GO suspensions illustrating the different recovery stages (I, II, III) highlighted in the graph and that have been considered to calculate the three (dG′/dt) gradients in (b). The curve shows that the main recovery takes place in stage I. The three gradients (b) exhibit a power relationship with 1/G_{end}′ (G′ varies with a power of GO concentration (Fig. 8)). (c) The mutation numbers for stages I, II, III calculated using [eqn (4)] (in the inset) are ∼ constant for the three stages and do not vary with concentration. These parameters demonstrate the proportionality between the ‘rebuilt’ kinetics (dG′/dt) and the stiffness of the network (G′) for GO suspensions. |

GO suspensions with low concentrations show permanent deformation, behaving as a viscoelastic liquid (i.e. Maxwell model); at 0.8 vol% GO and above there is no permanent deformation, these GO networks behave as a viscoelastic solid (i.e. a Kelvin–Voigt model). The change of G′ and G′′ over time during the SAOS test suggests that all the samples recover their stiffness in a similar fashion: a ‘quick’ and steep initial recovery G′ (stage I), followed by a slower increase of viscoelastic properties (stage II) that then leads to a plateau region (stage III) (Fig. 9). A characteristic gradient (dG′/dt, Fig. 10a) for each stage of the ‘rebuild’ can be calculated from the G′ vs. time curves (Fig. 9). Each of the gradients increases with the power of the GO concentration (vol%), or alternatively with the inverse of the storage modulus, G_{end}′ (Fig. 10b) which also increases with GO concentration following a power law (exponent of ∼3, Fig. 8b). The magnitude and timescale of the structural recovery in stage I is key to facilitate ‘printability’. We define a ‘mutation number’ for each stage to quantify both (stiffness and reformation time).^{39} The ‘mutation number’, λ(s) (eqn (4)), scales the magnitude of these gradients with the stiffness (G_{end}′) of the network.

(4) |

Due to the relationship between the kinetics of the recovery (dG′/dt) with the stiffness of the networks (G_{end}′), the mutation numbers for the three stages, λ_{1}, λ_{2} and λ_{3} (with values of ∼10 s, ∼200 s and ∼1000 s respectively), do not depend on GO concentration (i.e. with 1/G_{end}′, Fig. 10c). This is also true for a different gel formulation used for comparative purposes (Fig. 10c). According to our results, the main rheological parameter that quantifies the ‘rebuilt’ is G′. This means that given a formulation, it is possible to determine its ‘printability’ just from an amplitude sweep, using a quantitative criterion based on the G_{LVR}′ value, the flow stress and the FTI. We can then use these parameters to build a ‘printability’ map for our GO formulations and define a quantitative window (Fig. 11): ‘stiffness’ (G_{LVR}′) at rest is at least of the order of ∼10 kPa and FTI approaches values of ∼20 or below, which correspond to at least σ_{f} of 500 Pa and a G_{LVR}′/σ_{f} ratio of 20. Perhaps somewhat surprisingly, these findings confirm that current paste-specific ‘printability’ criteria that rely only on simple G′ and ‘yield stress’ determination^{2,5,6,9,11,40–42} (the latter defined as flow stress, σ_{f}, here) are a valid approach.

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