Composites: Part B 72 (2015) 45–52

Contents lists available at ScienceDirect

Composites: Part B

journal homepage: www.elsevier .com/locate /composi tesb

Evolution of nano-junctions in piezoresistive nanostrand composites

http://dx.doi.org/10.1016/j.compositesb.2014.11.0281359-8368/� 2014 Elsevier Ltd. All rights reserved.

Abbreviation: NiN, nickel nanostrand.⇑ Corresponding author. Tel.: +1 (801) 422 4636.

E-mail addresses: r.adam.bilodeau@gmail.com (R. Adam Bilodeau), dfullwood@byu.edu (D.T. Fullwood), john_colton@byu.edu (J.S. Colton), jyeager@lanl.gov(J.D. Yeager), abowden@byu.edu (A.E. Bowden), tylerdpark@gmail.com (T. Park).

1 Tel.: +1 (801) 422 4636.2 Tel.: +1 (801) 422 4361.

R. Adam Bilodeau a,1, David T. Fullwood a,⇑, John S. Colton b,2, John D. Yeager b,2, Anton E. Bowden a,1,Tyler Park b,2

a Department of Mechanical Engineering 435 CTB, Brigham Young University, Provo, UT 84602, United Statesb Department of Physics and Astronomy N283 ESC, Brigham Young University, Provo, UT 84602, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 15 April 2014Received in revised form 7 October 2014Accepted 26 November 2014Available online 15 December 2014

Keywords:A. Polymer-matrix composites (PMCs)A. Nano-structuresB. Electrical propertiesB. Microstructure

When nickel nanostrands (NiNs) are embedded inside of highly flexible silicone, the silicone becomes anextremely piezoresistive sensor capable of measuring a large dynamic range of strains. These sensorsexperience an increase in conductance of several orders of magnitude when strained to 40% elongation.It has been hypothesized that this effect stems from a net change in average junction distance betweenthe conductive particles when the overall material is strained. The quantum tunneling resistance acrossthese gaps is highly sensitive to junction distance, resulting in the immense piezoresistive effect. In thispaper, the average junction distance is monitored using dielectric spectroscopy while the material isstrained. By incorporating new barrier height measurements of the base silicone material from a nano-indentation experiment, this experiment validates previous assumptions that, on average, the junctionsbetween NiNs decrease while the sample is strained, instigating the large piezoresistive effect. The natureof the material’s response to strain is explored and discussed.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

In recent years there has been a push for the development ofmultifunctional composite materials that integrate physical prop-erties such as flexibility and durability with other desirable proper-ties in order to provide new alternatives to traditional materials.Such composites can benefit greatly from what may be genericallytermed the ‘‘nano-effect’’; for example, the unexpected propertiesof nano-scaled fillers that exhibit unusual, and often extreme,properties [1,2]. Nano-fillers are being used in many cases toimprove mechanical properties such as toughness, modulus andstrength with unexpected improvements in many cases [3–5].One particular area of active research relates to the developmentof conductive composites made with nano-fillers [6–10].

Conductive composites have shown particularly interesting mul-tifunctional properties that often enable them to be used in sensingsituations [11–17]. One extreme example involves a silicone/nickel

nanostrand nanocomposite material that exhibits a very largepiezoresistive response to applied strain, arising from nano-effectsbetween the conductive fillers. Related materials showspromise as large strain sensors, undergoing an unusual increase inconductivity as tensile strain is applied [18–22].

Attempts have been made by Johnson et al. to develop a numer-ical model that can both explain and predict the behavior of thismaterial under strain [23,24]. Johnson’s model predicts that quan-tum mechanical effects play a principal part in the change of resis-tivity in the composite material, as opposed to other proposedtheories such as density or alignment changes of conductive filler[25]. It is proposed that the ultra-low density clusters of nickelnano-particles are pushed together as they are embedded intothe polymer matrix. A nano-layer of adsorbed polymer producesa tiny gap, or junction, between the clusters, across which elec-trons can potentially pass via a quantum tunneling mechanism[26]. As the macro-scale material is deformed, small changes inthese nano-junctions produce exponential changes in the tunnel-ing resistance across them, leading to paths of low resistanceacross the sample and the related extreme piezoresistivity.

The Johnson implementation of the quantum tunneling/perco-lation model uses a simple Monte-Carlo simulation of the evolvingnano-junctions between conductive filler particles in the material.This stochastic representation of the nanojunctions is combinedwith a standard percolation model for resistance in conductive

Fig. 1. A high density cluster of NiNs inside the silicone matrix. Several nanostrandshave been highlighted in yellow. The smooth, reflective material on the right side ofthe picture is matrix material with few or no NiNs embedded along the border ofthe material. (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)

46 R. Adam Bilodeau et al. / Composites: Part B 72 (2015) 45–52

networks [24,27]. While the resultant approach shows promisingagreement with general resistance trends, many parameters inthe simulation were approximated using incomplete assumptions,and current models of gap evolution are extremely simplistic[28,29]. Perhaps the most critical information missing from allsuch models is measured data for the junction gap (or junctiondistance) in the composite. In an effort to fill in this missing infor-mation, this paper directly measures the average junction distancebetween the nickel nanostrands (NiNs) in composite gauges under-going various degrees of strain.

A previously developed method to measure average nano-junc-tion distances was adapted to provide the data required to improvethe existing model [30]. The composite material was strainedinside an impedance analyzer, facilitating measurement of thechanging dielectric constant of the material. The dielectric constantwas used to calculate the average junction distance. The results ofthis experiment will be used to continue to develop the multiscalemodel, and this novel experimental method could be applied byother research teams trying to understand the conductive natureof other nanocomposite materials. This method has limitations asit only provides a single number average junction distance, butthe trends observed provide strong evidence for both the simplequantum tunneling effect predictions and the more advanced per-colation model.

Most of the work in the aforementioned theories is based onquantum tunneling equations. The quantum tunneling barrierheight of a material (the resistance that a material naturally hasto certain quantum effects) is critical for the accuracy of these cal-culations. Previous work pioneered a new method to properlymeasure this barrier height involving precision nanoindentationwith a conductive probe [24,27]. This paper utilizes recent refine-ments of the technique as outlined by Koecher et al. [30] to provideimproved and robust barrier height results on the material.

2. Experiment

2.1. Materials

A single sample of catalyzed Sylgard 184, a common commer-cial silicone produced by Dow Corning�, was used for the barrierheight measurement tests (see Section 2.2). Sylgard 184 is a non-conductive, flexible silicone base useful for making highly deform-able sensors. Nickel substrates for this test were purchased fromNational Electronic Alloys�, flattened, sanded and polished with aseries of increasingly fine slurries (including colloidal silica). Aftera final electropolishing step, the substrates were cleaned with ace-tone and ethanol. Immediately prior to film deposition, atmo-spheric plasma etching was used as a final cleaning step. Thesilicone was deposited onto the substrates and cured by bakingat 110 �C for 18 h. Because the area used in nanoindentation isextremely small, it was possible to reuse the same sample formany tests.

Samples of the nanocomposite conductive material used in thejunction distance tests (see Section 2.3) were prepared by mixingconductive particles with Sylgard 184. The conductive fillers werenickel nanostrands—high aspect ratio nanoparticles with a uniquebifurcated structure. They are made by Conductive Composites,LLC through a proprietary chemical vapor deposition (CVD) pro-cess. This process creates a highly porous mass with a volumefraction in air of less than 1%. The porous nanostrand mass is bro-ken apart and mixed into the samples. This experiment used vol-ume fractions in polymer ranging from 7% Ni to 13% Ni. Thecomposite was then cast into a long, wide, thin aluminum moldand, after being warmed to 75 �C to encourage polymerization,was allowed to cure at room temperature for several days. Fig. 1

shows a cluster of NiNs inside of a cured silicone matrix as photo-graphed in a SEM.

2.2. Barrier height measurements

A series of nine tests were performed in order to determine thequantum tunneling barrier height of the Sylgard 184. Measure-ment of the barrier height was performed following the methodof Koecher et al. [30]. Briefly, a Hysitron nanoindenter was oper-ated in the nanoscale electrical contact resistance (nanoECR�)mode, which provides continuous measurement of electrical cur-rent during indentation by using a conductive stage and boron-doped conductive diamond tip with a 5 V bias voltage. As the tipmoves downwards through the silicone towards the Ni substrate,the current suddenly increases from zero when electrons are ableto tunnel through some minimal thickness of the polymer. Thisjump in current is approximately linear with probe position anda linear regression can be used to calculate impedance as a func-tion of distance between the tip and the substrate [30]. The barrierheight (k) is then calculated from the slope (m) of that function asshown in Eq. (1). For more details, the reader is referred to thealready published work.

k ðeVÞ ¼ m1:025

� �2ð1Þ

Note that only the initial linear increase in current is used,because after several nm the indenter has pushed through thepolymer and into the conductive substrate. After this point, varia-tions in the current are a function of indenter geometry and sub-strate deformation. The barrier height calculations are calibratedby a standard indent into gold, wherein the barrier height of airis measured and verified against literature reports.

2.3. Junction distance

The nanocomposite material consists of a network of conductivestrands separated by junctions that possess both a characteristicresistance and capacitance. Previous studies in nanocompositematerials have modeled the nano-junctions between particles ofthe filler material as a parallel resister and capacitor circuit[29,31,32]. The relaxation frequency of this network relates to boththe size and dielectric properties of the junctions. Previous analysishas produced the following equation that correlates the relaxation

R. Adam Bilodeau et al. / Composites: Part B 72 (2015) 45–52 47

frequency of the junctions (xc) with the junction distance inmeters (d):

xc ¼3e2

8phe0

k0

erexpð�k0dÞ ð2Þ

where k0 is a constant used to simplify the equation above and is:

k0 ¼4p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið2mekÞ

ph

ð3Þ

In these equations, e is the charge of an electron, h is Planck’s con-stant, me is the mass of an electron, k is the barrier height, e0 is thepermittivity of free space, and er is the characteristic relative per-mittivity (also known as the dielectric constant) of the silicone [30].

The characteristic frequency (xc) can be measured by chartingthe frequency dependence of the relative permittivity (see Eq. (5)below). Once that is known, Eqs. (2) and (3) can be used to solvefor the junction distance d. An impedance analyzer with a fre-quency range of 5 Hz–13 MHz (HP model 4192A) was used to mea-sure the relative permittivity. To eliminate potential strayadmittance and residual impedance errors, a dielectric test fixture(HP model 16451B) for dielectric constant measurement of solidmaterials was attached. The electrode used in this fixture was a5 mm guarded electrode which eliminates edge capacitance error.

To prevent conductance errors through the sample from affect-ing the results, a non-contacting electrode method was used perthe manufacturer’s specifications. In this method two tests arerun using the analyzer, one with the sample between the parallelplates of the analyzer and the other without the sample betweenthe plates (see Fig. 2). When the sample is between the parallelplates it is modeled as two capacitors in series (sample-filledregion and the air space region). The relative permittivity of thesample for a given frequency can then be calculated using Eq. (4):

Fig. 2. Non-contacting electrode method. MUT stands for Material Under Test and is cthickness of the sample. (Image obtained from user manual [33].).

Fig. 3. Drawing of the tensile stage use

er ¼1

1� ð1� Cs1Cs2Þ tg

ta

ð4Þ

where again er is the relative permittivity and Cs1 is the capacitancewithout the sample inserted, Cs2 is the capacitance with the sampleinserted, tg is the distance between electrodes, and ta is the thick-ness of the sample [30].

The fundamental property of interest for the silicone-basednanocomposites is the piezoresistivity, or the change of resistancethat the material experiences while being strained. In order toproperly predict the electrical resistance between two conductiveparticles, both the resistance of the material and the change inthe size of the junction under strain must be measured. Havingboth of these properties measured, the quantum tunneling modelcan be properly adjusted to represent the effects of strain on thesegauges. To measure both of these properties, an in-situ tensilestage was designed to hold the samples securely in place on thebase plate of the dielectric test fixture (see Fig. 3). The two anchorpoints were designed with a large stiffness to prevent the stagefrom bending while straining samples. The threaded rod can alsobe rotated by degrees, causing translational motion in one anchor.This setup allows the sample to be strained by small, quantifiableamounts, and maintains a constant strain while the dielectric testsare being run. The anchor points were designed to be 1 mm lowerthan the unguarded electrode (Fig. 2) so a slight elastic tensionkeeps the sample flat against the electrode (not shown in Fig. 3),even while the sample experiences Poisson thinning due to strainsof upwards of 40%. This ensures that the sample does not lift off thestage during testing. Lift off needs to be avoided as it could poten-tially alter the current pathway in the test setup, creating threecapacitors in series and rendering Eq. (4) irrelevant.

alled the sample in this paper, tg is the distance between electrodes, and ta is the

d in the experimental procedure.

48 R. Adam Bilodeau et al. / Composites: Part B 72 (2015) 45–52

During testing, samples are anchored to the stage at both ends.Each sample is then gently tightened until it is flat against the bot-tom electrode of the impedance analyzer, without any initialstrain. The top electrode (attached to a micrometer) is slowly low-ered until it makes contact with the sample. Initial measurementsare taken of several geometric and material properties: sampleresistance at 5 Hz and 1 MHz voltage frequencies, sample thicknessand sample length. The top electrode is then raised to a set heightto begin sampling the relative permittivity. The capacitance is sam-pled across a logarithmic scale of frequencies from 500 Hz toupwards of 13 MHz. These measurements are processed to calcu-late the relative permittivity using the method described earlierwith Eq. (4). After taking the capacitance measurements, the sam-ple is then strained by rotating the threaded rod on the stage onehalf turn (corresponding to about 1% strain) and all of the measure-ments are taken again in the same order. This procedure is fol-lowed until either the relative permittivity test resulted in anunchanging dataset or the sample exhibited obvious mechanicalfailure.

Once the relative permittivity for a volume fraction is measuredover a broad range of frequencies, the data is plotted onto a loga-rithmic scale and a characteristic curve becomes evident. A singleterm of the Cole–Cole equation (Eq. (5)) was fit to the sets of thedielectric data [30]. The fit yields values for rdc, the relaxation timesj, the relaxation strength Dej, and the broadness parameter aj. Thecharacteristic frequency xc ¼ 1=sj can then be obtained andinserted into Eq. (2) and the junction distance can be evaluated.

eðxÞ ¼ e1 þX

j

Dej

1þ ðixsjÞajþ rdc

ixe0ð5Þ

3. Results

3.1. Barrier height measurements

Fig. 4 shows data for several indents on the same sample of Syl-gard 184 without any composite mixtures. Current is plotted as afunction of indenter tip displacement. Load-depth data was alsotaken during the measurement, and in all cases the load increasedas the silicone was compressed prior to any observable conductiv-ity. ‘‘Zero’’ conductivity was observed at initial depths as character-ized by random oscillations positive and negative about zerocurrent. The beginning of the conductive region was indicated bythe first point of increasing positive current without subsequentlybeing followed by negative current measurements, as can be seen

Fig. 4. The current through a reference Sylgard 184 sample is plotted vs theindenter tip displacement for multiple indentation tests. Initial jumps in conduc-tivity are approximated as linear. Data points on the x-axis are equivalent to 0, andnot included in curve fits. Tests are offset along the x-axis for clarity.

in the figure. Note that the data has some expected variability fromeither small variations in the local chemistry or structure of the sil-icone or from statistical variations in the indentation test itself.

The average barrier height was measured at 1.08 eV, with astandard deviation of 0.51 eV. The average height is higher thanthe previously reported value by Johnson et al. (0.28 eV) but thenew result is consistent with the expected range for polymers[24,27,30]. The discrepancy is likely a result of significantlyimproved methods and equipment as compared to Johnson’s initialwork, as the lab where both sets of measurements were performedwas recently upgraded. The new value is assumed to be a muchbetter representation of the actual quantum tunneling barrierheight as it is closer to the quantum tunneling barrier heights ofother non-conductive materials tested by Koecher et al. [30]. Thisnew value for the barrier height was then used to calculate theaverage junction distance (using Eq. (1)).

3.2. Determining junction distance

Multiple factors influence the average junction distance in asample, including strain and volume fraction of embedded NiNs.Several samples of differing nickel volume fractions were preparedof the nickel silicone composite material. A series of junction dis-tance measurement tests were performed on each sample. Theresultant measured averages were plotted against the samplestrain. Because the junction distance decreased with strain untilreaching a minimum value, the junction distance vs strain resultwas empirically modeled with an exponentially decaying functionas seen in Fig. 5.

The data was fit to the following function where d is the junc-tion distance, e is the strain of the material and d1 is the averagejunction distance at an infinite amount of strain, the asymptotefor the data.

d ¼ A � exp�es

� �þ d1 ð6Þ

A and s are fitting parameters describing the exponential decay.The parameter d1 was left as a free parameter for the optimizationalgorithm for the 7%, 9% and 11% volume fractions. However, forthe 13% volume fraction sample, this resulted in an unreasonablelarge uncertainty on the value due to the absence of data pointsat high strains (discussed below). Hence the value of d1 for the13% volume fraction material was obtained by extrapolating fromthe parameters calculated in the 7%, 9% and 11% tests. This resultedin a good fit to the data, with reasonable values for the 13% volumefraction asymptote (within the range of uncertainty for a freely fit-ted parameter). Table 1 lists the values for A, s, and d1 for each of

Fig. 5. Measured average junction distances vs strain for the 7% volume fractionmaterial. The red fitted curve is an exponential decay function that has been fit tothe data. (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)

Table 1Results from the curve fits applied to the average junction distance data.

Volume fraction (%) A (nm) s d1 (nm)

7 2.79 6.66 1.329 4.55 5.31 1.27

11 1.14 8.60 1.2413 9.64 15.67 1.22

Fig. 6. The fitted exponential decay functions for the 7%, 9%, 11%, and 13% VF ofNiNs samples. The solid sections are where the curves were fit to measured data,and the dashed extensions are the estimated projections of the curve as the strainincreases to infinity.

R. Adam Bilodeau et al. / Composites: Part B 72 (2015) 45–52 49

the volume fractions and Fig. 6 shows the exponential decay curvesof gap vs strain of all four samples. The solid portions of the lines inFig. 6 indicate the range at which the curve was fit to data points,and the dashed portion of the curves are the projection as thecurves approach d1. The implications of these results are discussedin Section 4.1.

4. Discussion

4.1. Junction distance

One of the limitations encountered while running the tests onthe higher volume fractions was brought about by the limited fre-quency range of the impedance analyzer. The equipment used hada maximum frequency of 13 MHz, which restricted the minimummeasurable decay time (tau) to approximately 2 ns, which corre-sponds to an average junction distance of about 1.3 nm. Since the13% VF had an average junction distance significantly smaller than1.3 nm, it was not possible to properly measure enough of thedecay curve to develop a strong predictive value of the minimumaverage junction distance. This led to the approach described inSection 3.2 for determining the asymptotic gap value. Furthermore,the impedance analyzer could only produce reliable data for fre-quencies greater than 1 kHz, resulting in a maximum measurablejunction distance of approximately 2 nm. Regardless of the limita-tions from the equipment used, there are many important conclu-sions that can be drawn from the data.

It has previously been predicted that an increase in the volumefraction of NiNs in the silicone base would result in smallerjunction distances for the as-made material [24]. Intuition hassuggested that as the volume fraction of NiNs embedded in thecomposite increases, their average separation is smaller. Theexperiment performed has provided strong support for this predic-tion. Although the data in Fig. 6 is capped at about 2 nm, reducingthe accuracy of predictions for 0% strain, the available data and fit-

ted curves suggest that the samples with lower volume fractionshave larger junction distances at 0% strain.

As mentioned in the introduction, previous researchers alsohypothesized that one of the influential factors in the extremepiezoresistivity of the composite material tested in this paper is adecreasing average junction distance with applied strain [23,24].Simply put, this is because as the sample is strained longitudinally,the cross-sectional area decreases due to the Poisson effect. Thus,at the microstructural level, the NiNs are pulled towards each otherin the cross-section plane even as they are being separated in thelongitudinal direction. Since the quantum mechanical tunnelingresistance between particles exhibits an extreme change for a verysmall change in junction distance, it was hypothesized that even aminor decrease in the average junction distance could have signif-icant effects. Fig. 6 confirms previous predictions of decreasingjunction distance. Looking at the plotted data, all four samplesdemonstrate a decrease in the average junction distance forincreased strain, confirming one of the hypotheses presented byJohnson et al. [24].

As mentioned previously (Section 2.3), when a sample wasstrained the electrical resistance across the sample was measuredwith a 5 Hz AC voltage (to prevent any capacitance resistancespikes) while the thickness of the material section was alsorecorded. In order to compensate for the changing thickness ofthe samples, the measured resistance values were converted toresistivity. To get the resistivity (q) of the material, the samplewas modeled as a truncated conical resistor having smaller radiusa (equal to the radius of the smaller plate) and larger radius b(equal to the radius of a circle whose area is the same as the areaof material on the larger plate). By integrating the differential resis-tance of concentric cylindrical slabs in series it is easy to show thatthe overall resistance is R ¼ qt=pab. The resistivity was calculatedusing this relationship based on the experimental values of resis-tance R and sample thickness t gathered during experimentation.

Fig. 7 compares the behavior, under strain, of the material resis-tivity with that of the calculated average junction distance for the7% volume fraction sample. Note that the resistivity begins to leveloff at about 2–3% strain earlier than the average junction distance.This latency suggests that the changing junction distance is notnecessarily the only factor in determining the overall resistanceof the composite material. The difference is subtle, and we felt thatit was important to investigate the validity of this finding in thecontext of quantum tunneling resistivity of a single junction gap.

To further explore this effect, the average junction distance wasused in the quantum tunneling resistivity equation (Eq. (7)) inorder to determine the resistivity across a single gap the same sizeas the measured average [34].

qtðsÞ ¼h2

e2ffiffiffiffiffiffiffiffiffiffi2mkp exp

4pffiffiffiffiffiffiffiffiffiffi2mkp

hd

!ð7Þ

In this equation, h is Planck’s constant, e is the electron charge, m isthe electron mass, k is the tunneling barrier height (J), and d is thedistance between the two conductive particles (m) as previouslydefined. Both resistivity data sets were plotted against each other(displayed on a log–log plot in Fig. 8) to determine the potentialrelationship between them. In this figure, there are clearly at leasttwo regimes where the data has different correlation patterns (seenas the two lines fit to the data). This evidence suggests a complexrelationship between the local resistance between nickel particlesand the global overall resistance. It strongly suggests that the nat-ure of the lattice network of NiNs embedded inside the siliconehas an effect on the global resistance which is more than just a sim-ple weighted average of individual gap resistances (calculated fromtheir resistivity). The junction on the graph separating the tworegions occurred at about 19% strain. The other volume fractions

Fig. 7. A comparison of the measured material resistivity of the sample with the measured average junction distance measured at a common strain percentage for the 7%volume fraction material. The asymptote for the measured resistance appears to begin before the asymptote for the average junction distance.

Fig. 8. The material bulk resistivity plotted against the resistivity of a singlejunction the size of the average, at all strain values of the 7% VF sample. The twodistinct portions of the curve strongly suggest that average junction distance is notthe only factor affecting the measured resistance.

50 R. Adam Bilodeau et al. / Composites: Part B 72 (2015) 45–52

did not have enough data to develop the characteristic resistancecurves and plot in a similar manner.

Previously hypothesized percolation models may potentiallyhelp explain these observations. In the percolation model, theoverall resistance is not only related to the resistance across thenano-junctions, but also to the density of junctions across whichelectricity is flowing. As a critical density of such junctions isapproached, the nature of the global resistance changes sharply.Hence these results may give alternative evidence for such amodel; though, for further details, readers are referred to the pub-lished work [24]. More work is required to incorporate the exper-imental results of this paper into such a model.

The results discussed above give new insights into the behaviorof the small junctions between conductive particles, but they donot explain the behavior. In previous work it was assumed thatconductive particles were coated with an adsorbed layer of poly-mer molecules [24]. This adsorbed layer becomes a minimumthickness of material surrounding any one nickel particle, prevent-ing other nickel particles from coming into closer proximity. Theresults presented above (see Fig. 6) provide some support for thisprediction: the 7%, 9% and 11% (by volume) samples have a non-zero asymptotic junction distance (d1). However, this theoryrequires that polymers be bonded to the particles in the compositematerial [28]; silicone does not bond well to many substances,including nickel, though it does effectively fill voids between par-

ticles. Scanning electron images of torn composites with nickelsheathed carbon fibers reveal potentially clean nickel surfaces thatdo not appear to have a surface layer of silicone bonded to them.The best resolution of these images, however, is only about 1 lm,so the images are not conclusive evidence.

The authors propose an alternative model of the molecularinteractions. This model considers the silicone molecules as inde-pendent, long polymer chains (e.g., ‘‘strands of spaghetti’’) withweak molecular bonds to the nickel substrates. All silicones havea basic silicon-oxygen backbone, with functional groups attachedto the silicon atom. These polymeric chains have functional groupsattached to both ends that allow them to link together to create thesolid-form rubbery silicone. Sylgard 184 is mainly composed ofpolydimethylsiloxane (PDMS), a silicone polymer with simplefunctional groups that have relatively little interaction with eachother and generally do not have cross-linking capabilities [35].Since the polymer can only bond at its end functional groups, thereis no covalent chemical interaction between the densely packednickel crystalline form and the polymer net that grows to encaseit [36]. Without bonds between the nickel and the silicone, thestrands of nickel are simply surrounded in a flexible networkwhich allows limited translational and rotational motion. To con-tinue the culinary metaphor, this is much like a metal fork on aplate of cooked spaghetti (the fork represents a NiN and the spa-ghetti represents silicone). Even though the spaghetti noodles arenot glued to each other or the fork, the fork is still suspended abovethe plate. If the utensil is embedded in the spaghetti, the utensilcan still move and rotate within the surrounding net because thereis nothing bonding the metal to the noodle. When subjected to aforce, the noodles can stretch and even slip around the fork with-out changing the fork’s location relative to the plate. It is the samewith the NiNs in the polymer silicone. The polymers are long, flex-ible chains that can move around the NiNs. The chains that arefound in the gap between two NiNs can fill large gaps whenrelaxed. However, when the material is strained, the chains beginto align, creating negative pressure regions that draw the NiNs clo-ser together (see Fig. 9) [36].

The ‘‘spaghetti model’’ also predicts that there will be a mini-mum junction distance for any given volume fraction of NiNsand silicone. The polymer chains between the NiNs are capableof elongating under strain by unfolding the polymer chains; how-ever, even if all of the polymers are stretched to their maximumtensile limit, there will remain a minimal intertwining of thechains in between the NiNs keeping them apart. This minimumdistance would be influenced by the amount of polymer that was

Fig. 9. The PDMS polymer chains (left) are wound around each other and space theNiNs (not the true shape in the diagram) apart. When the polymer is strained(right), the polymer chains straighten out and align with each other shrinking thegap between NiNs.

R. Adam Bilodeau et al. / Composites: Part B 72 (2015) 45–52 51

initially present between the NiNs in the unstrained sample. Thisprediction is also supported by the data presented in Fig. 6.

The two models have very similar predictive properties, eachwith its strengths and weaknesses. Both accurately predict thatthere will be a minimum junction distance between NiNs that can-not be closed off completely through Poisson contraction. Bothmodels also predict an ‘absolute minimum’ distance betweenstrands. The spaghetti model suggests that this minimum couldbe as small as the distance across a single polymer chain. Theadsorbed layer theory, however, requires typically that there betwo layers of bonded silicone between the NiNs (one layerattached to each nickel particle) at an absolute minimum junctiondistance, this being potentially a much larger minimum distance.The adsorbed layer thickness model does have an advantage in thatit presents a very generic model that can be easily adapted math-ematically to many types of polymer, including ones that mayexperience covalent bonding with the nickel. The spaghetti modelis only applicable to PDMS and other inert, non-cross-linking sili-cones and polymers. It will require further work and information(such as accurate estimates of molecule widths) to attempt todetermine which model is best to use in simulating the behaviorof these high deflection strain gauges.

If similar tests are repeated using an impedance analyzer with ahigher frequency range than the one available for this study it maybe possible to develop more accurate curves that extend to smallerjunction distances. Commercially available impedance analyzerscan have a frequency range of up to 1 GHz, which could theoreti-cally characterize average gaps down to the 1.05 nm range (for Syl-gard 184). This could potentially reveal a ‘‘true minimum’’ (asmallest-possible average junction distance) or it might demon-strate the potential for average junction distances down to a nearly0 nm junction distance. If an average junction distance is found tobe close to, or below, the minimum junction distance required bythe adsorbed layer thickness theory, then it would provide strongevidence against this theory.

5. Conclusion

Dielectric spectroscopy of strained piezoresistive nanocompos-ites was implemented to determine the evolution of junctionsbetween the conductive particulates in the material. Essentialand improved barrier height measurements of the silicone basewere provided using a nanoindenter-based method. The combinedapproach permits a closer analysis and better understanding of theinternal structure of a silicone-nickel material while undergoingstrain. The data confirms that there is a decrease in the averagejunction distance between NiNs in a silicone/NiN composite asthe material is strained in tension (decreases of at least 30% weremeasured in this experiment). All four samples demonstrate adecrease in the average junction distance for increased strain. Fur-

thermore, there is a clear decrease in average junction distancewith an increase in the volume fraction of NiNs in the silicone base,supporting current theories.

The present work encourages the need for a percolation model(or some other model) in addition to the quantum tunnelingmodel, in order to accurately predict the conductivity of the mate-rial. For example, a plot of the measured resistivity vs the quantumtunneling resistivity (Fig. 8) resulted in two distinct regions thatmay relate to onset of (or termination of) percolation. The resultsare also suggestive of a minimum average junction distance pervolume fraction ranging from 1.22 to 1.32 nm after a certainamount of strain, which limits how close the nanoparticles canapproach regardless of additional strain. This behavior is consistentwith two different models of the NiN-silicone interactions—i.e. theadsorbed layer model and the ‘‘spaghetti’’ model described previ-ously. We also anticipate that the described experimental setupcould be used in the future to gain an even greater understandinginto the nature of deformation-dependent changes to junctions inother elastic conductive composites.

Acknowledgements

This work was performed, in part, at the Center for IntegratedNanotechnologies, a U.S. Department of Energy, Office of BasicEnergy Sciences user facility. Los Alamos National Laboratory, anaffirmative action equal opportunity employer, is operated by LosAlamos National Security, LLC, for the National Nuclear SecurityAdministration of the U.S. Department of Energy under contractDE-AC52-06NA25396.

Contract grant sponsor: NSF, contract grant number: CMMI-1235365.

References

[1] He J-H, Wan Y-Q, Xu L. Nano-effects, quantum-like properties in electrospunnanofibers. Chaos, Solitons Fractals 2007;33:26–37.

[2] Ramsden JJ. Nanotechnology: an introduction. Amsterdam: Elsevier; 2011.[3] Jajam KC, Tippur HV. Quasi-static and dynamic fracture behavior of particulate

polymer composites: a study of nano- vs. micro-size filler and loading-rateeffects. Composites Part B 2012;43(8):3467–81.

[4] Liu H-Y, Wang G-T, Mai Y-W, Zeng Y. On fracture toughness of nano-particlemodified epoxy. Composites Part B 2011;42(8):2170–5.

[5] Faleh H, Al-Mahaidi R, Shen L. Fabrication and characterization of nano-particles-enhanced epoxy. Composites Part B 2012;43(8):3076–80.

[6] Lalli JH, Claus RO, Hill AB, Mecham JB, Davis BA, Subramanayan S, et al.Commercial applications of metal rubber. In: Edward VW, editor. SmartStructures and Materials 2005. SPIE; 2005. p. 1–7.

[7] Tang G, Jiang Z-G, Li X, Zhang H-B, Hong S, Yu Z-Z. Electrically conductiverubbery epoxy/diamine-functionalized graphene nanocomposites withimproved mechanical properties. Composites Part B 2014;67:564–70.

[8] Li N, Huang Y, Du F, He X, Lin X, Gao H, et al. Electromagnetic interference(EMI) shielding of single-walled carbon nanotube epoxy composites. Nano Lett2006;6(6):1141–5.

[9] Gardea F, Lagoudas DC. Characterization of electrical and thermal properties ofcarbon nanotube/epoxy composites. Composites Part B 2014;56:611–20.

[10] Saw LN, Mariatti M, Azura AR, Azizan A, Kim JK. Transparent, electricallyconductive, and flexible films made from multiwalled carbon nanotube/epoxycomposites. Composites Part B 2012;43(8):2973–9.

[11] Flandin L, Brechet Y, Cavaille JY. Electrically conductive polymernanocomposites as deformation sensors. Compos Sci Technol2001;61(6):895–901.

[12] Park J-M, Kim D-S, Kim S-J, Kim P-G, Yoon D-J, DeVries KL. Inherent sensingand interfacial evaluation of carbon nanofiber and nanotube/epoxycomposites using electrical resistance measurement and micromechanicaltechnique. Composites Part B 2007;38(7–8):847–61.

[13] Knite M. Polyisoprene-carbon black nanocomposites as tensile strain andpressure sensor materials. Sens Actuators, A 2004;110(1–3):142–9.

[14] Pham GT, Park Y-B, Liang Z, Zhang C, Wang B. Processing and modeling ofconductive thermoplastic/carbon nanotube films for strain sensing.Composites Part B 2008;39:209–16.

[15] Johnson TM, Fullwood DT, Hansen G. Strain monitoring of carbon fibercomposite via embedded nickel nano-particles. Composites Part B2012;43(3):1155–63.

[16] Grammatikos SA, Paipetis AS. On the electrical properties of multi scalereinforced composites for damage accumulation monitoring. Composites PartB 2012;43(6):2687–96.

52 R. Adam Bilodeau et al. / Composites: Part B 72 (2015) 45–52

[17] Le J-L, Du H, Pang SD. Use of 2D Graphene Nanoplatelets (GNP) in cementcomposites for structural health evaluation. Composites Part B2014;67:555–63.

[18] Johnson O, Gardner C, Fullwood D, Adams B, Hansen G, Kalidindi S. Textures ofdispersion of nickel nanostrand composites, and modeling of piezoresistivebehavior. In: Proceedings of MS&T. Pittsburgh, Conference, Conference 2009.

[19] Johnson OK, Gardner CJ, Fullwood DT, Adams BL, Hansen G. Deciphering thestructure of nano-nickel composites. In: Proceedings of SAMPE. Baltimore,Conference, Conference 2009.

[20] Johnson O, Kaschner G, Mason T, Fullwood D, Adams B, Hansen G.Optimization of Nickel nanocomposite for large strain sensing applications.Sens Actuators A 2010.

[21] Johnson OK, Kaschner GC, Mason TA, Fullwood DT, Hyatt T, Adams BL, et al.Extreme piezoresistivity of silicone/nickel nanocomposite for high resolutionlarge strain measurement. TMS 2010. Seattle 2010.

[22] Shui XP, Chung DDL. A new electromechanical effect in discontinuous-filamentelastomer-matrix composites. Smart Mater Struct 1997;6(1):102–5.

[23] Johnson O, Fullwood D. A percolation/quantum tunneling model for theunique behavior of multifunctional silicone/nickel nanostrandnanocomposites. In: Proceedings of SAMPE. Salt Lake City, Conference,Conference 2010.

[24] Johnson O, Gardner C, Mara N, Dattelbaum A, Kaschner G, Mason T, et al.Multi-scale model for the extreme piezoresistivity in silicone/nickelnanostrand/nickel coated carbon fiber nanocomposites. MetTransA2011;42(13):3898–906.

[25] Radhakrishnan S, Chakne S, Shelke PN. High piezoresistivity in conductingpolymer composites. Mater Lett 1994;18(5–6):358–62.

[26] Hu N, Karube Y, Yan C, Masuda Z, Fukunaga H. Tunneling effect in a polymer/carbon nanotube nanocomposite strain sensor. Acta Mater 2008:56.

[27] Johnson OK, Mara N, Kaschner GC, Mason TA, Fullwood DT, Adams BL, et al.Multi-scale model for the extreme piezoresistivity in silicone/nickel‘‘nanostrand’’/nickel coated carbon fiber nanocomposite. In: Proceedings ofTMS 2010. Seattle, Conference, Conference 2010.

[28] Litvinov V, Steeman P. EPDM-carbon black interactions and the reinforcementmechanisms, as studied by low-resolution H-1 NMR. Macromolecules1999;32(25):8476–90.

[29] Meier JG, Mani JW, Klüppel M. Analysis of carbon black networking inelastomers by dielectric spectroscopy. Phys Rev B 2007:75.

[30] Koecher M, Yeager J, Park T, Mara N, Fullwood D, Hansen N, Colton JS.Characterization of Nickel nanostrand nanocomposites through dielectricspectroscopy and nanoindentation. Polym Eng Sci 2013;53(12):2666–73.

[31] Fritzsche J, Lorenz H, Klüppel M. CNT based elastomer-hybrid-nanocompositeswith promising mechanical and electrical properties. Macromol Mater Eng2009;294(9):551–60.

[32] Abuzaid WZ, Sangid MD, Carroll JD, Sehitoglu H, Lambros J. Slip transfer andplastic strain accumulation across grain boundaries in Hastelloy X. J MechPhys Solids 2012;60(6):1201–20.

[33] Packard H. Dielectric Constant measurement of solid materials.[34] Hu N, Karube Y, Yan C, Masuda Z, Fukunaga H. Tunneling effect in a polymer/

carbon nanotube nanocomposite strain sensor. Acta Mater2008;56(13):2929–36.

[35] Chiang P-J, Kuo C-C, Zamay TN, Zamay AS, Jen C-P. Quantitative evaluation ofthe depletion efficiency of nanofractures generated by nanoparticle-assistedjunction gap breakdown for protein concentration. Microelectron Eng2014;115:39–45.

[36] Roland CM. Chapter 3 – structure characterization in the science andtechnology of elastomers. In: Mark JE, Erman B, Roland CM, editors. Thescience and technology of rubber. Boston: Academic Press; 2013. p. 115–66.