## Super sensitive, not so silly, putty

Many composites blend stiff materials, such as glass or carbon fibers, into a softer elastic polymer matrix to generate a material with better overall mechanical toughness. Boland *et al.* added graphene to a lightly cross-linked silicone polymer (also known as Silly Putty). The resulting composite has unusual mechanical properties, allowing the manufacture of strain sensors that can detect respiration and the footsteps of spiders.

*Science*, this issue p. 1257

## Abstract

Despite its widespread use in nanocomposites, the effect of embedding graphene in highly viscoelastic polymer matrices is not well understood. We added graphene to a lightly cross-linked polysilicone, often encountered as Silly Putty, changing its electromechanical properties substantially. The resulting nanocomposites display unusual electromechanical behavior, such as postdeformation temporal relaxation of electrical resistance and nonmonotonic changes in resistivity with strain. These phenomena are associated with the mobility of the nanosheets in the low-viscosity polymer matrix. By considering both the connectivity and mobility of the nanosheets, we developed a quantitative model that completely describes the electromechanical properties. These nanocomposites are sensitive electromechanical sensors with gauge factors >500 that can measure pulse, blood pressure, and even the impact associated with the footsteps of a small spider.

There is widespread interest in graphene because of its exceptional physical properties (*1*). An important application area involves the addition of graphene to polymers, usually to enhance electrical, mechanical, or barrier properties (*2*). One important property of polymers is viscoelasticity; their mechanical properties demonstrate a combination of viscous and elastic properties, resulting in interesting time-dependent phenomena (*3*). Although the rheology of graphene-polymer nanocomposites has been investigated (*4*), the effects of viscoelastic matrices—in particular, the implications of very low matrix viscosities—have not been explored.

We studied the effect of adding graphene to a lightly cross-linked silicone polymer [commonly found as the novelty material Silly Putty (Crayola, Easton, PA)] that is a highly viscoelastic material under ambient conditions (*5*). Addition of graphene to the polymer renders it conductive and increases its stiffness. However, it retains its viscoelastic characteristics, and because of the low matrix viscosity, the nanosheets are mobile and respond to deformation in a time-dependent manner. In particular, they form mobile networks that break and reform during mechanical deformation. This has led to the development of a high-performance sensing material, “G-putty,” that can monitor deformation, pressure, and impact at a level of sensitivity that is so precise that it allows even the footsteps of small spiders to be monitored.

We prepared graphene by means of liquid-phase-exfoliation of graphite in *N*-methyl-pyrrolidone (*6*), producing nanosheets with lengths of ~200 to 800 nm (Fig. 1, A and B). The nanosheets were then transferred (*7*) to chloroform and mixed with homemade “silly putty”: silicone oil (Fig. 1B, inset) cross-linked with boric acid (supplementary text and figs. S1 to S5) (*8*). Whereas the pristine putty was adhesive, malleable, and somewhat liquid-like, addition of graphene gave a stiffer, more solid-like material (Fig. 1C and figs. S6 to S8, S16, and S25). Scanning electron microscopy (SEM) imaging showed the G-putty to contain large quantities of nanosheets arranged in a dense, uniform, and isotropic network (Fig. 1D and fig. S7). The electrical conductivity of the G-putty increased strongly with graphene content, reaching ~0.1 S/m at ~15 volume % (Fig. 1E). According to percolation theory, the nanocomposite conductivity scales with filler volume fraction as
(1)where and *n*_{e} are the percolation threshold and exponent, respectively (*9*). This equation fits the data well, giving = 1.75 volume % and *n*_{e} = 11.9. Although the percolation threshold is roughly as expected (*10*), the exponent is large, which is consistent with a broad distribution of intersheet junction resistances (*11*). Detailed analysis of the mechanical properties of G-putty show it to display viscoelastic behavior, which is consistent with the standard linear solid model (figs. S1, S9 to S14, and S22 to S24) (*5*, *8*). All mechanical properties change with graphene content; for example, the stiffness increases as a power law (Fig. 1F and fig. S11).

Most relevant are the rheological properties. Shown in Fig. 2A are typical plots of storage (*G*′) and loss (*G*′′) modulus versus oscillatory strain amplitude, γ_{0} (all rheological data are provided in figs. S15 to S21). Although both *G*′ and *G*′′ increase with graphene content (Fig. 2B and fig. S15), the *G*′ versus behavior can be analyzed via the cluster-cluster-aggregation model that treats the filler network as a fractal object, giving
(2)where *d*_{N} and *d*_{B} are the fractal dimensions of the network and its backbone, respectively (*12*, *13*). As expected, the data follow a power law with exponent of 3.1 ± 0.5.

Although both *G*′ and *G*′′ are invariant with strain for the putty, they both tend to fall with increasing strain amplitude for all nanocomposites. For filled elastomers, this is known as the Payne effect (*14*) and has been explained by Kraus (*12*, *15*) via the strain-dependent breaking and reforming of interparticle connections in the filler network. Then, the number density of connections depends on γ_{0} as*N* = *N*_{0}[1 + (γ_{0}/γ_{c})^{2}* ^{m}*]

^{–1}(3)where

*N*

_{0}is the initial connection density,

*m*is the network structure factor, and γ

_{c}is the yield strain. This leads to the equation(4)where and are the storage moduli in the limit of low and high frequencies, respectively (

*12*). This model fits the data extremely well (Fig. 2A and figs. S17 and S18). Extracting γ

_{c}and plotting versus in Fig. 2C shows a power law with exponent –1.71 ± 0.3. Such behavior is consistent with the prediction of Shih

*et al*. for fractal particulate networks (

*13*)(5)Combining the fits in Fig. 2, B and C, allows us to estimate

*d*

_{B}= 1.4 ± 0.2 and

*d*

_{N}= 1.6 ± 0.2, which is similar to carbon-black composites (

*12*) but somewhat smaller than the values of ~2 found for nanoclay networks (

*16*). In addition, the Krauss fits give structure factors close to

*m*= 0.5, which is typical for filled elastomers (Fig. 2D) (

*12*). These are consistent with the value of

*m*= 0.46 predicted by the Huber-Vilgis model

*m*= (2 +

*d*

_{N}–

*d*

_{B})

^{–1}(6)supporting the validity of this analysis (

*12*).

Of particular interest is the extremely low dynamic viscosity, , of the matrix (Fig. 2E). Although the viscosity increases with as a power law (fig. S21), the zero-shear viscosity of the putty is low compared with solid polymers at ~3000 Pa s, which is consistent with its highly viscoelastic liquid-like nature. Such low viscosity may allow an unusual degree of nanosheet mobility. We can test this by applying a tensile step strain (2%) to the G-putty and monitoring the graphene network relaxation via its electrical resistance (Fig. 2F and fig. S25). The resistance increases sharply on application of the strain before decaying slowly as a power law (Fig. 2F, inset). The resistance decay is very slow compared with the stress relaxation (τ ~ 1 s) (figs. S22 to S24), with the power law indicating that a wide range of decay times are involved (figs. S25 and S26) (*17*). We interpret this behavior as the strain rapidly deforming the network and breaking nanosheet-nanosheet connections, thus increasing the resistance. However, because of the low matrix viscosity, the nanosheets are somewhat mobile and may move by diffusion or in response to the applied field via induced dipoles (figs. S27 to S33). This allows the network to slowly relax, reforming connections and giving a resistance decrease. This network relaxation can be thought of as a self-healing process. Such filler mobility is unprecedented in nanocomposites at room temperature (fig. S27). However, it also represents plasticity, meaning deformations are not fully reversible (fig. S32).

We have characterized the electrical response of the G-putty to tensile and compressive deformation (Fig. 3A). In all cases (figs. S34 to S43), the fractional resistance change, Δ*R*/*R*_{0}, increased linearly at low strain before decreasing rapidly at higher strain, always falling below its initial value. This is considerably different to the normally observed monotonic increase of Δ*R*/*R*_{0} with strain (*18*, *19*). The initial linear increase in Δ*R*/*R*_{0} with ε means that the G-putty can be used as a strain sensor. The sensitivity, *G* (defined at low strain by Δ*R*/*R*_{0} = *G*ε), is plotted versus in Fig. 3B. As , *G* increases significantly (*18*), reaching at 6.8 volume % for tensile measurements. These values surpass those of most strain sensors (nanocomposite sensors usually have *G* < 40) (fig. S58) (*8*, *18*, *19*).

To understand this unusual behavior mechanistically, we plotted resistivity ρ (calculated assuming constant volume) versus strain, observing a resistivity increase at low strain followed by a large decrease (Fig. 3C and fig. S44 to S48). Having considered other models, we propose that deformation of the nanosheet network modifies its connectivity and therefore its resistivity (figs. S2 to S5 and supplementary text S4) (*8*). We write the number density of internanosheet connections as the sum of a term analogous to Eq. 3 {*N*_{1} = *N*_{0}[1 + (ε/ε_{c})^{2}* ^{m}*]

^{–1}} and a term representing the reformation of connections due to diffusive or field-driven mobility of the nanosheets (

*N*

_{2}=

*k*

_{2}

*t*). Combined with a modified percolation-type relation, (

*n*is a scaling exponent), and using gives(7)where . We found that this expression fits the low-strain data extremely well in all cases (figs. S44 to S50). The fit-values of

_{ε}*m*cluster around 0.5 as expected (Fig. 3D).

Equation 7 leads to an expression for *G*(8)that we can apply, using the fit parameters associated with Eq. 7 (supplementary text S4) (*8*). As shown in Fig. 3B, the calculated and measured values for *G* match very well. We found that both *n*_{ε} and *G* increase as the polymer molecular weight and hence viscosity decrease (fig. S51).

With these properties, G-putty is a high-performance electromechanical sensing material that can sense joint motion, breathing, and heartbeat (Fig. 4, A to C, fig. S52). When mounted on the carotid artery, the G-putty acts as a pressure sensor outputting a waveform representing the aortic pressure, allowing pulse monitoring (Fig. 4C). The unprecedented sensitivity of G-putty allows resolution of the characteristic double peak and dicrotic notch. Through careful calibration, the peak-to-peak amplitude of the waveform can be converted to pulse (blood) pressure, finding the expected value of ~40 mmHg (figs. S53 to S57 and supplementary text S11) (*8*).

We also tested the G-putty as an impact sensor by dropping balls of different mass *m* into a thin putty sheet from different heights *h*. The resultant resistance waveforms show a rapid jump on impact followed by a power law decay (Fig. 4D), which is consistent with Eq. 7 (supplementary text S5) (*8*). The peak change in Δ*R*/*R*_{0} scales with impact energy (*E _{mgh}* =

*mgh*) (Fig. 4E). We can understand this by considering the conversion of kinetic energy to elastic energy of the network and using Eq. 7 to translate the resultant strain into a resistance change (supplementary text S5) (

*8*), finding(9)where

*W*and

*y*

_{0}are the width and thickness of the putty sensor, respectively, and

*E*is the putty stiffness. Fitting the data in Fig. 4E to Eq. 9 gives

*m*= 0.5, as expected, and

*n*

_{ε}/ε

*~ 5 and so*

_{c}*G*~ 7, which is in reasonable agreement with the compression data in Fig. 3B (fig. S49). To highlight the potential of G-putty as an impact sensor, we caught a small spider (mass, ∼20 mg) (Fig. 4F, inset) and induced it to walk over a clingfilm-coated G-putty sensor. The resultant resistance plot is presented in Fig. 4F and shows individual spider footsteps, demonstrating the high sensitivity of this material.

Adding graphene to a highly viscoelastic polymer gives a composite with unprecedented electromechanical properties characterized by mobile nanosheets and nonmonotonic resistance changes as the material is strained. The nanocomposites are extremely sensitive electromechanical sensors that will find applications in a range of devices.

## Supplementary Materials

www.sciencemag.org/content/354/6317/1257/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S58

Table S1

Movie S1

## References and Notes

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**Acknowledgments:**We acknowledge the Science Foundation Ireland–funded AMBER research center (SFI/12/RC/2278). J.N.C. and R.J.Y. acknowledge funding from the European Union Seventh Framework Program under grant agreements 604391 and 696656, Graphene Flagship. G.R. and M.E.M. acknowledge funding from Science Foundation Ireland (G22226/RFP-1/MTR/3135) and support from COST action MP1305. “Graphene Polymer Nanocomposites” was filed at the European Patent Organisation (EP16182749.8) on 4 August 2016; inventors, J.N.C., U.K., and C.B.; assignee, Trinity College Dublin.