Carbon Black (CB) is composed of primary particles that fuse into aggregates[31] during production that are visible in transmission electron microscopy (TEM) (Fig. 1A, see Methods section for details). In dispersion or during drying, weaker van der Waals forces connect the aggregates to form agglomerates visible in scanning electron microscopy (SEM) (Fig. 1B)[31]. The overall hierarchical structure of the CB that we used in this work is depicted in Fig. 1C. Raman spectroscopy showed only characteristic carbon peaks at 1341 cm− 1 (D-band) and at 1580 cm− 1 (G-band)[32, 33], indicating the graphitic nature of the CB and the absence of functional groups on its surface (see Figure S1 in the SI). Such carbon surfaces are hydrophobic,[34] suggesting that the powder will weakly interact with polar solvents and form stable suspensions in non-polar liquids. The polarity of the solvent as well as its viscosity will affect CB agglomeration.
We prepared CB suspensions – “Electrofluids” – in PDMS, hexadecane, glycerol, and ethylene glycol. Their electrical conductivities at different CB loadings were determined by measuring the electrical resistance in 4-point-probe configuration (details described in the Method section). The percolation threshold (\({\varphi }_{c}\)) was then determined by fitting to
\(\sigma =A\bullet {(\varphi -{\varphi }_{c})}^{t}\) | (Eq. 2), |
from classical percolation theory,[35] where \(\sigma\) is the electrical conductivity, A is a constant, \(\varphi\) is volume fraction of the filler, and t is a critical exponent.
The percolation thresholds strongly depended on the liquid matrix (Fig. 1D-G). Percolation in PDMS (Sylgard 184) occurred at nearly 5 vol% CB (Fig. 1D). Silicone-CB mixtures have been extensively studied and are commonly used to create conductive solid composites by cross-linking the PDMS matrix.[36] The percolation threshold and the conductivities that we found in suspension are in good agreement with the values reported in the literature for the solid composites.[37]
All other solvents required less CB for percolation. Hexadecane is non-polar like PDMS but has a lower viscosity (ηHexadecane = 3.34 mPa·s versusηPDMS = 4500 mPa·s) and caused a percolation threshold of 1.43 vol% CB, more than 3 times below that for PDMS. A reduced percolation threshold for less viscous liquids has already been reported by Rwei et al.[38] and attributed to a higher mobility of the CB that promotes filler reorganization and the formation of conductive pathways.[38] Similar findings were reported by Bauhofer et al. for carbon nanotubes.[39]
Glycerol is closer in viscosity to PDMS (ηGlycerol = 1480 mPa·s) but caused percolation at 0.41 vol% CB, 10 times below PDMS (Fig. 1F). Glycerol is a small molecule with 3 OH-groups and a high polar moment. The PDMS Si-O backbone is shielded by methyl groups that confer a hydrophobic character. The CB apparently forms agglomerates that fill space with a connected network and reduce the percolation threshold.
Synergic effects of viscosity and polarity lent CB in ethylene glycol (ηEthylene glycol = 16 mPa·s) the lowest percolation threshold of all studied systems (0.17 vol%). Hexadecane has a similar viscosity but is non-polar, increasing the threshold. The strong role of polarity on CB percolation that we find here has not been reported before. In the following, we will test our hypothesis that large agglomerates of CB aggregates form and strongly promote percolation.
We compared the sizes of CB agglomerates in non-polar hexane and polar ethylene glycol using analytical centrifugation (AC) at relatively low CB concentrations of 0.002 wt%. Note that the highly viscous liquids PDMS and glycerol make AC cumbersome and imprecise (see Method section for further details) and were not included. Figure 2A shows the density size distributions. The mean hydrodynamic diameter in hexane was 840 nm, whereas ethylene glycol caused a bimodal distribution with maxima at 1942 and 6478 nm indicating the formation of bigger agglomerates. This result is in good agreement with Subramanian et al. who investigated the effect of lignosulfonates on CB dispersibility in water and found that the most hydrophobic lignosulfonates were the best dispersing agent and decreased the mean particle diameter by reducing agglomeration.[40]
Figure 2B illustrates the model that we propose for CB network formation based on above results. Electrofluids with low CB concentrations in non-polar solvents contain CB aggregates and possibly small agglomerates with diameters of approximately 1 µm. The formation of networks at increasing CB concentrations is dominated by random percolation of CB units that collide.
Polar solvents cause stronger attractions between the CB that induce the formation of larger agglomerates that are several µm in diameter. At very low concentrations, agglomerates cannot span the entire volume. As their concentration increases, they form a percolating network. Compared to non-polar solvents, agglomeration facilitates percolation because larger agglomerates are more efficient in filling up the space. The percolation threshold in non-polar solvents was lower than in polar ones of the same viscosity, too, cf. hexadecane and ethylene glycol in Fig. 1E and G respectively. Their percolation thresholds are smaller than those of more viscous solvents of the same polarities because their reduced viscosity accelerates the formation of agglomerates.
Electrofluids combine electrical conductivity with mechanical adaptability. The electrical percolation study presented above confirms the formation of electrically conductive filler networks and the role of solvent polarity on its formation. These results do not provide insight into the mechanical properties of the formed networks, and mechanical and electrical properties of networks do not necessarily overlap.[41] Therefore, we studied the viscoelastic behavior of the electrofluids and characterized the storage modulus G’ that represents the elastic stored energy and accounts for the stiffness of the material and the loss modulus G’’ that represents the dissipated energy and, therefore, the damping of the material by means of oscillatory rheology. Electrodes were coupled to the rheometer (see Method Section for details) to concurrently measure the electrical resistance of the samples at each strain in-situ. The results for electrofluids containing 5 vol% CB in PDMS and glycerol are shown in Fig. 3A-B (cf. Figure S3 for hexadecane and ethylene glycol).
The loss modulus of the PDMS-based electrofluid exceeded its storage modulus over the entire strain range (Fig. 3A), indicating uniformly viscous behavior.[42] The CB increased the viscosity by up to three orders of magnitude (up to 3500 Pa·s, see flow curves in Figure S4 in the SI) but remained dispersed and did not form agglomerate networks that could sustain solid-like behavior at rest, even above the electrical percolation threshold of 4.92 vol% CB. This is consistent with the formation of the CB network illustrated in Fig. 2B. Figure 3A shows that the electrical resistance (RDC) fluctuated between high values of 108 and 109 Ω when the liquid was strained. The absence of a trend is consistent with a mechanically weak, transient electrical network of CB particles, too.
The storage modulus G’ of the glycerol-based electrofluid in Fig. 3B remained constant at low strains (linear viscoelastic (LVE)-region,) and was much larger than the loss modulus G’’, indicating the formation of a mechanical network that led to a solid-like behavior at rest. The concentration of 5 vol% CB was one order of magnitude above its electric percolation threshold of 0.41 vol% CB. We observed a decrease of G’ and an increase of G’’ at shear strains above 0.148%. The peak in G’’ at 2% strain indicates the breakup of the CB mechanical network; its area has been correlated with the energy dissipated in the process.[42] The subsequent decrease of G’ leads to the flow point, where G’ and G’’ cross indicating the transition from a solid-like to a liquid-like behavior.[42] Amplitude sweeps on electrofluids based on hexadecane and ethylene glycol (Figure S3 in SI) led to similar evolutions of G’ and G’’.
Electrofluids based on glycerol (Fig. 3B), hexadecane (Figure S3A), and ethylene glycol (Figure S3B) with 5 vol% CB were sufficiently far above the electrical percolation threshold to exhibit low electrical resistances at rest and were rheologically similar. The changes of their resistances with strain were in line with the different rheological regions described above. At low strains, resistance remained constant, because the mechanical network absorbed the deformation elastically. At the strain where G’’ increased and plastic deformations ensued, electrical resistances increased, consistent with the breakdown of the filler network. We believe that the plateaus, that the electrical resistance reached at larger strains, are due to transient contacts in a “steady state”, where network connections form and break at identical rates.
The overall stiffness of the material, represented by the G’ value at the LVE-region, is dominated by the filler-filler and filler-matrix interactions. Figure 3C shows that the plateau values of the storage modulus (LVE-region) from amplitude sweeps scaled with CB volume fraction as \({G}^{{\prime }}\sim{\varphi }^{n}\), with n = 5.43 for the non-polar PDMS and n = 3.98 for the polar glycerol.
Glycerol interacts weakly with the non-polar CB that formed a mechanically strong network below 1 vol% CB. The storage modulus increased with CB loading because the network became mechanically stronger. The dispersed CB aggregates in PDMS-based electrofluids (Fig. 2B) interact with the polymer chains and reduce their mobility, reinforcing the mixture even at CB loadings below percolation. This effect is weaker than that of agglomeration in glycerol-based electrofluids, which is reflected in the values of the storage moduli. Similar relations between filler dispersion and the stiffness of solid composites have been reported elsewhere.[43] At CB contents above percolation (5 vol%) in PDMS, a mechanically rigid network formed. The combined contributions of the filler-matrix interactions and the mechanical network formation explain the higher scaling exponent for PDMS than for glycerol.
A low elastic modulus at a high electrical conductivity is beneficial for soft conductors that can be formed by filling electrofluids in an elastic tube, for example. Figure 3D gives the relation between the plateau G’ values and the electrical conductivity (s) of the resting fluid. Both parameters represent the electrofluids at rest. The increase of conductivity with G’ suggests a direct correlation with the stiffness, but the exact relation depends on the polarity of the solvent. The scaling of G’ in glycerol-based electrofluids follows a power law, while that in PDMS only for volume fractions above 7 vol% CB. In consequence, glycerol provided higher conductivities at comparable stiffness. These results highlight the close interplay between the electrical and the mechanical networks and thus, the macroscopic material properties. The non-linear relations enable rational tuning of the rheoelectrical properties of electrofluids.
Consider the use of electrofluids in soft robotics. Some components of soft robots require stable electrical conductivity upon mechanical deformations, others (sensors) must have a high sensitivity to detect small pressures, compressions, strains, bending, etc. We tested the suitability of electrofluids for both cases and loaded different types in silicone tubes that were electrically connected at their ends (see details in the Method section). Figure 4A-B shows a CB-glycerol electrofluid in a silicone tube closing a circuit with an LED. The tube can be stretched without apparent changes in LED light intensity (see Video1 as electronic SI). We quantitatively evaluated the electrical response of encapsulated electrofluids under uniaxial strain. We refer to “piezoresistivity” in the following, extending the term that is well-established in conductive composites analogously for electrofluids. Uniaxial tensile tests were performed on electrofluids with 9 vol% CB in PDMS and in glycerol, and the electrical resistance changes were measured in-situ. The CB concentrations ensured percolation and good electrical conductivity in both solvents. We subjected the sample to cyclical loads resulting in 0–10% strain at a constant strain rate of 10% per second (Fig. 4C). Electrical resistance was recorded during the entire experiment. All details on the setup and program can be found in the Method section and in Figure S6 in the SI.
Figure 4C shows the relative changes in electrical resistances during 1000 cycles. The electrical change for the PDMS-based electrofluid was much higher than that for the glycerol-based one. The effect of the relative concentration of CB respect to the electrical percolation concentration of each system was evaluated by testing a sample with 0.9 vol% CB in glycerol (Figure S5 in the SI) to match the relative difference to the percolation threshold value of the PDMS sample (0.41% and 4.91% respectively). The results revealed that the electrical changes are independent of CB content (see Figure S5). A common parameter that is suitable to evaluate this difference is the gauge factor (GF, see Eq. 1 in the introduction).
The gauge factor of the 9 vol% CB-glycerol was 0.34 ± 0.01, that of 9 vol% CB-PDMS was 2.55 ± 0.2, i.e., more than 7 times larger, indicating a higher sensitivity. This difference is in good agreement with the corresponding rheoelectrical measurement (Fig. 4D), where the increase of electrical resistance beyond the LVE-region was larger for PDMS than for glycerol. Rheoelectrical measurements thus qualitatively predicted the uniaxial tensile test results for electrofluid-based devices and enable a rational fluid design for specific applications.
When a solid conductive composite sample is stretched, its overall resistance tends to increase. This increase can have a geometrical and a piezoresistive component. A material with a Poisson’s ratio of 0.5 (incompressible material, e.g., rubbers and their composites) with a GF = 2 does not exhibit piezoresistivity, i.e., the resistivity of the material remains constant and the change in resistance is purely due to its geometrical deformation. A GF > 2 indicates positive piezoresistivity, i.e., an increase of the material’s resistivity upon strain. Our electrofluids based on CB-PDMS had GF > 2, and their response can be compared to that of liquid metals in tubes, which typically have gauge factors around 2.[24] A GF < 2 indicates negative piezoresistivity; materials with GF = 0 are possible if their negative piezoresistivity matches the geometrical deformation. Such materials are poor sensors but stable conductors. Our glycerol-based electrofluid had changes in resistance of only 3.4% and is suitable to connect a sensor.
The difference between the electrofluids’ GF can be explained when considering their microstructure. Figure 5A depicts the proposed model for each system. Imagine a three-dimensional, open network of strongly attractive CB aggregates, where the glycerol fills the pores. The overall resistance of the CB network is determined by the number and the length of the percolating paths if the resistances of particles and their junctions are uniform and constant. Consider a small uniaxial strain that deforms the network. Particle junctions act as swivels, allowing deformation with scissors kinematics that prevent fracture of the network. Macroscopically, this results in a metamaterial with ΔR = 0, GF = 0, and a negative piezoresistivity that compensates for the geometrical change (cf. Eq. 1). The CB-glycerol electrofluids approximate this metamaterial and exhibit only 3.4% increase in resistance. The CB network resembles “Kirigami” structures at the microscopic scale. It deforms reversibly using kinematics similar to Kirigami conductors and retains most conductivity under strain. The remaining resistance increase indicates limited network damage that recovers when releasing strain (Fig. 5A).
Gauge factor and microstructure of CB-PDMS electrofluids are different because a) a larger fraction of dispersed CB aggregates remains mobile and separated from the percolating network (cf. Figure 2) and b) the attraction between CB surface is reduced by the PDMS chains. The mobile CB aggregates reorganize upon deformation, causing a) an increase in average CB surface-to-surface distances and disruption of CB-CB connections, and b) the formation of new conductive paths that contain more CB units. Both increase the electrical resistance (Fig. 5B).
We exploited the solvent-dependent differences in filler microstructure to design electromechanical components. Figure 5B-D shows elastomer tubes filled with 9 vol% CB in PDMS and 9 vol% CB in glycerol, respectively (see Video2 as electronic SI). We connected them in series and attached them to the finger of a glove. At rest, the electrical signal was constant, and the blue LED was on. Bending the finger increased the resistance of the CB-PDMS electrofluid, triggering the red LED. Bending the wrist deformed the CB-Glycerol electrofluid, but its resistance increase was small, and the red LED remained off. A combination of the two electrofluids thus enabled the design of robotic structures, in which one part serves as a deformation sensor while the other faithfully transmits the signal.