Facile Fabrication of Electrically Conductive Low-Density Polyethylene

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Facile Fabrication of Electrically Conductive Low density polyethylene/ Carbon Fiber Tubes for Novel Smart Materials via Multi-axial Orientation Yijun Li, Min Nie, and Qi Wang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b17131 • Publication Date (Web): 13 Dec 2017 Downloaded from http://pubs.acs.org on December 15, 2017

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ACS Applied Materials & Interfaces

Facile Fabrication of Electrically Conductive Low density polyethylene/Carbon Fiber Tubes for Novel Smart Materials via Multi-axial Orientation Yijun Li†, Min Nie*†, Qi Wang† †: State Key Laboratory of Polymer Materials Engineering, Polymer Research Institute of Sichuan University, Chengdu 610065, China Email: [email protected] Fax:

+86-28-85402465

Tel:

+86-28-85405133

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Abstract: Electromechanical sensors are indispensable components in functional devices and robotics application. However, the fabrication of the sensors still maintain a challenging issue that high percolation threshold and easy failure of conductive network are derived from uniaxial orientation of conductive fillers in practical melt processing. Herein, we reported a facile fabrication method to prepare multi-axial low density polyethylene (LDPE) /carbon fibers (CFs) tube with bidirectional controllable electrical conductivity and sensitive strain-responsive performance via rotation extrusion technology. The multi-dimensional helical flow is confirmed in the reverse rotation extrusion and the CFs readily responds to the flow field leading to a multiaxial orientation in the LDPE matrix. On contrast to uniaxial LDPE/CF composites which performs a “head to head” conjunction, multi-axial orientated CF networks exhibit a unique multi-layer structure where the CFs with distinct orientation direction intersect in the interface, endowing LDPE/CF composites with low percolation threshold (15wt%) to those of the uniaxial ones (~35wt%). The angles between two axes play a vital role in determining the density of the conductive networks in the interface, which is predominant in tuning the bending-responsive behaviors with a gauge factor range from 12.5 to 56.3 and corresponding linear respond region from ~15% to ~1%. Such superior performance of conductive LDPE/CF tube confirms that the design of multi-axial orientation paves a novel way to facile fabrication of advanced cost-effective CF-based smart materials, shedding light on promising applications such as smart materials, and intelligent engineering monitoring. Keywords: Conductive polymer composites; Smart materials; Rotation Extrusion; Strain Sensors; Carbon fibers

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Introduction With increasing demand for functional devices and robotics application, smart materials are becoming a predominant frontier owing to promising usage in personalized health monitoring, motion detection and human-machine communication. Therefore, simple, low cost and scalable fabrication strategies for smart materials have always attracted not only academic but also industrial attentions1-7. Generally, functional devices can detect the variation of resistance, capacitance, and other electrical parameters and thus respond to the external stimulus such as deformation8, voltage9, radio wave10, humidity11, pH12, and pressure13, et al. Conductive polymer composites (CPCs), with the merits of high flexibility, low weight and good processability, are considered as ideal candidates for smart materials14. The orientation of the conductive filler always exists in the practical processing of CPCs. The preferred orientation transforms the filler connection to “head to head” joints, and resultantly increases percolation threshold in both in-plane and through-plane direction15-17. Nevertheless, excellent smart materials require as low as possible percolation threshold, which is derived from two aspects. On the one hand, conductive fillers are usually far more expensive than polymer matrix, which leads to low economic affordability with high filler loadings18-19. On the other hand, inferior mechanical properties can occur with severe interfacial deterioration. Comparing with most polymers, conductive fillers exhibit inherent low interfacial adhesion with each other. As a result, when exerted stress is applied, conductive fillers readily detach and slip, leading to rapid failure of the materials20. 3



To date, manipulation of the dispersion of the conductive fillers to increase conductive pathway density in the matrix is the most common approach to reduce conductive percolation threshold21-24. To serve this purpose, selective distribution of the conductive fillers in the interface of two incompatible polymer blend25-26 and in the polymer latex27-28 are considered as most common methods to obtain stable conductive network. However, some intrinsic drawbacks still stand in the way of low cost scalable fabrication, such as complicated manufacturing procedure, too many influencing factors (interfacial energies between fillers and polymers, blending time, shear rate, etc.) and so on. Apart from increasing the content of conductive fillers in the interfaces, some novel processing technologies allow subtle regulation of geometrical patterns and dimension of the conductive network, showing light to another approach to facile fabrication of CPCs29-30. In these cases, the probability of the contact between neighboring conductive fillers significantly increase or the insulated polymer gaps decrease enough to permit electrons to pass through via enhanced tunneling effect. Ke31 incorporated a hybrid conductive networks by using carbon nanotubes (CNTs) and carbon black (CB) in the poly(vinylidene fluoride) (PVDF) nanocomposites to increase conductive filler connectivity, and successfully increase the sensing linear region during stretching from ~2% to ~6%. Park32 adopted a foaming strategy to enhance the inter-connectivity of fiber through biaxial orientation around the growing bubbles in the injection molding, and an increase of the conductivity up to 4 orders of magnitude was achieved. By the charming work of Jiang33-34, a flow-induced 4


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assembly of 1D conductive network in polymer films exhibits fantastic anisotropic conductivity, in which the electrical resistivity in parallel direction is almost eight orders of magnitude lower than that in the vertical direction. Obviously, it is extremely effective and beneficial to increase the randomness during processing, which can not only maintain the conductivity but also endow CPCs with enhanced stability during deformation. Very recently, we reported a biaxial reinforced polybutene-1(PB-1)/polystyrene (PS) tube with adoption of helical flow generated by rotation extrusion equipment35. Multi-axial orientation that the PS microfibers display reverse orientation in the inner and outer walls is detected, offering us a rational deduction that the multi-axial orientation may promote the probability for the anisotropic fillers to intersect and increase the effective density of the conductive networks. Carbon fibers (CFs) exhibit obvious advantages over other carbonaceous fillers, such as low cost, convenient for even dispersion and anisotropic structure for easy respond to flow, making it ideal tracing elements to monitor the multi-dimensional flow generated by rotation extrusion. Moreover, connections of CFs can easily detach with each other under external stress36-37. As a result, the conductive network readily changes, making it highly sensitive to deformation. It is predictable that materials with multi-axial orientated CFs can drastically decrease the percolation threshold, and promote the stability under deformation. Accordingly, two issues have to be addressed: (1) what is the multi-dimensional flow generated via rotation extrusion? (2) How does CFs respond to the helical flow? In this study, we firstly analysis the helical flow 5



pattern and filler respond by computer simulation and characterization of CF alignment in reverse rotation extrusion. Then we studied the correlation between the filler orientation patterns to the electrical conductivity and sensing capabilities as a function of rotation rate. This study can not only provide sufficient information to reveal the underlying relationship between filler orientation and percolation threshold, but also permit the development of guidelines for the design of a new generation of smart materials. 2. Experimental section 2.1. Materials The raw materials used in this study are commercially available LDPE and short-cut CF. LDPE (2426H) was purchased from Lanzhou petrochemical Co., China with a melt flow of 1.9 g/10min (190oC/2.16kg). The CF (T700) are kindly supplied by Sinofibers Technology Developing Co., Ltd. China with a density of 1.76 g/cm3, diameter of 7 µm and electric conductivity of about 1 S/cm. 2.2. Sample preparation The master batch of the granulated LDPE/CF composite with a CF weight ratio of 50wt% was firstly prepared by a single screw HAAKE rheometer with a rotation rate of 30rpm at 180oC. The granules of the pre-mixed LDPE/CF composites were then manually mixed with the pure LDPE to dilute the expected content of CFs, namely 5wt%, 10wt%, 15wt%, 20wt%, 25wt% 30wt%, 40wt% and 50wt%, and then fed into the self-designed rotation extrusion equipment (Figure 1(a)), where the die and mandrel can rotate independently. The multi-dimensional flow is generated by 6


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controlling the rotation direction and rate of the mandrel and die. In this study, reverse rotation of the mandrel and die was conducted, that is, the die rotated in the clockwise direction while the die did in anticlockwise direction. The rotation rates were 10 r/min, 20 r/min, 30 r/min and 40 r/min for both mandrel and die. The conventional LDPE/CF with uniaxial orientation was also prepared while the mandrel and die remained stationary. All tubes were prepared in approximate size with an outer and inner diameter of 3mm and 2mm, respectively. 2.3. Characterization 2.3.1. Morphological characterization Scanning electron microscope (SEM) was applied to investigate the morphology of the conductive tubes. The samples of the cross and longitude sections were directly cut from the tubes and etched in a permanganic etchant for 4hours to expose the CF encapsulated by LDPE38. 2.3.2 Electric measurements All the samples for electric measurements were cleaned by ethanol prior to tests. The measurements were done in both axial and radial directions i.e. the direction parallel and perpendicular to the orientation direction. In order to measure the volume conductivity, two kinds of machines were utilized. The volume electrical conductivities higher than 10-6 S/m were measured using a Keithley 4200 apparatus; while Keithley 6517B high-resistance meter was suitable for volume electrical conductivity below 10-6 S/m. For ensuring good contact of the sample surface with the

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electrodes, copper wires were stuck to the sample surface with conductive silver glue. The detailed elaboration of the samples was shown in Fig. 1. 2.3.3. Length distribution of the CFs The testing samples were directly cut from the LDPE/CF tubes and observed by a Leica DM2500P polarized optical microscope (POM) connected with a hot stage (Linkam THMS600) and a pixel camera. The samples were firstly heated to 180oC to melt the LDPE phase and then the lengths of the CFs were recorded by the Linkage software provided by Linkam Scientific Instruments. Over 200 CFs were recorded to calculate the mean length and distribution for each sample. 2.3.4. Sensing properties The bending deformation was conducted on a universal testing machine (RGL-10, Shenzhen Reger Instrument Co., Ltd.) with a 20mm support span. LDPE/CF tubes were connected to a Keithley 4200 apparatus with the help of the copper wire and silver glue. The deformation speed was set as 2mm/min and the resistance was recorded once the bending began.

Figure 1 The illustration of (a) the rotation extrusion rheometer, (b) the electrical measurement in axial and radial directions. 8


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3. Results and discussion 3.1. Flow pattern and morphological analysis

Figure 2 (a) The simulation results of the flow pattern in reverse rotation extrusion with a rotation rate of 10r/min and (b) the corresponding velocity distribution along the thickness direction (ND). In rotating extrusion, the hoop flow is applied to the polymer melt by the rotation of the mandrel and die, and the speed can be adjusted by the rotation speed of the mandrel and die. As well-accepted, computer simulation is a powerful tool for visualization of complicated polymeric flow during processing39-41 and ANSYS Polyflow ver. 15.0, which is the mostly widely used commercially available finite element coded software, was employed in this study (simulation parameters are available in supporting information). In the simulation, the polymer melts were considered to be incompressible and steady with no slip along the wall. Through the joint solution of Bird-Carreau constitutive equation42 and Navier-Stokes moving equation43 which best described the low shear rate behavior of the viscosity, the visualize graphics of the polymer fluid in the rotated die can be obtained as shown in Fig. 2a. More details of the above numerical method and the solution technique is 9



referred as Polyflow manual44. Within Couette hoop flow, a velocity gradient with reverse directions is about to form perpendicular to the thick direction (ND) and substantially offset each other in the core. During rotation extrusion, with superposition of the hoop flow by mandrel and die rotations and axial flow by extrusion, polymer melts go ahead in the concentric spiral flow with different speed. It should be addressed that there is an angle between the moving directions of the spiral flow in different layers, and thus numerous intersections maybe generated at the interface due to the formation of turbulence.

Figure 3 The alignments of CFs in inner walls of the LDPE tubes with rotation rate of (a) 0 rpm, (b)20rpm, (c)40/min and the outer walls (a’~c’), correspondingly. The white arrow indicates the extrusion direction(ED). Figure 3 shows the SEM photos of the outer and inner surfaces of the LDPE/CF tubes. Similar to previous studies on anisotropic fillers35, 45-46, CFs deviate off the axial direction when the hoop stress is exerted on the polymer melt during rotation 10


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extrusion, and the deviating angles of CFs increase with the elevated rotation rate. In accordance with the simulation results, the deviating direction of CFs in the inner and outer walls is completely opposite given the enantiomorphic helix generated by reverse rotating pattern. The cross and longitude sections of the LDPE/CF tube were observed to show the distributions of the CFs inside the tubes, and the results are shown in Fig. 4. In conventional extruded tubes, CFs uniformly aligned along the extrusion direction (ED) and isolated with each other from inner surface to the outer surface. However, CFs in rotation extrusion performed a distinct distribution in the skin and core regions. At the skin region, in spite of the deflection in the ED, CFs displayed a relatively parallel and isolated morphology like the conventional ones, while the distribution of the CFs was relatively random at the core, where a multi-axial and overlapped CF network was constructed.

Figure 4 The alignment of CFs in convention (a)~(d) and rotation extruded (e)~(h) LDPE/CF tubes in both cross and longitude section. 11



Herein, an unavoidable problem occurs that how the deviation influences the intersection of CFs. In order to answer this question, a simple mathematical model is constructed by Mat lab computer program to simulate the probability of intersection. During simulation, N randomly distributed lines with fixed length L are planted in a unit-size square, with half in y-axis and another in a deviation angle. The two alignment directions represent the different orientation of the CFs in the adjacent flow layers as evidenced in Fig. 2(a). According to work by Winey47, the line length in simulation is set to be 0.2 for best describing the conductive filler with aspect ratio(L/D) of ~20. The intersection probability is calculated through dividing the number of intersecting lines by the total number. Moreover, an experimental statistic from SEM photos is also conducted for validation purpose. Figure 5 displays the results in two limited conditions at 10o and 40o and clearly demonstrated that it is more likely for CFs to intersect with each other in large deviation angle. In our case, high rotation rate offers more opportunities for CFs intersections, so as to construct conductive network in the processing procedure. The results can also explain the parallel and isolated morphology in the skin region of the rotation extruded tubes. As previously demonstrated, the velocity difference is rather small in adjacent helical flow in the skin, while mutations in the velocity direction occur at the core layer. Accordingly, the multi-dimensional flow in reverse rotation extrusion is confirmed by the multi-axial orientation of the CFs

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Figure 5 The effect of the rotation rate on the probability of the intersection of CFs. The results are obtained from both computer simulation (N=150, L=0.2) and experimental statistic from SEM photos (CFwt%=20). Aiming to comprehensive understanding, a schematic illustration of the multi-axial orientation of the CFs is displayed in Fig.6. On the basis of the orientation direction, the network generated by reverse rotation extrusion can be divided into 3 layers, i.e. the inner wall layer, the core layer and outer wall layer. It is also vital to notice that high probability to intersect and overlap can be easily achieved at the interface between adjacent layers, while the connectivity in the individual layer is much more difficult due to uniaxial alignment.

Figure 6 The schematic illustration of the multi-axial orientated networks of the CFs generated by reverse rotation extrusion. 13



3.2. Electric conductivity of the LDPE/CF tubes Figure 7(a)-(d) depict the percolation curves of the LDPE/CF tubes in both axial direction and radial direction. The conventional extruded tubes show a lower axial electrical conductivity (1.2×10-3S/cm), and higher percolation threshold (~35wt%) than that in rotation extruded tubs (15wt%). As demonstrated by many publications48-49, the preferable alignment decreases the likelihood of CF being connected with each other. The plateau observed at high content of CFs is due to the constriction resistance at the contact spots. However, the plateau is reached at different rotation rate for each sample as shown in Fig. 7(b): tubes with 10wt%CFs reaches at 30rpm, 20wt% and above at 10rpm, indicating that high rotation rate will facilitate the formation of conductive networks. Fig. 7(c) and (d) display the radial conductivity as a function of CF content and rotation rate, respectively. It should be mentioned that the percolation threshold in radial direction significantly linked with both CF content and rotation rate. Moreover, the axial conductivities were about one order of magnitude higher than those in the radial direction. Therefore, it can be deduced that intrinsically different conductive networks form in axial and radial directions. As the morphological analysis suggests, the conductive networks readily form at the interface, leading to an axially orientated concentric architecture. On the other hand, high hoop speed is exerted to the polymer melt during extrusion, resulting in uniform and isolated alignment. Only if the rotation rate is high enough for CFs to deviate in each layer, can the interfaces be connected. Apparently, CFs in axial

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direction has more extensive and steady connection points than those in the radial direction.

Figure 7 Electric conductivity of the LDPE/CF conductive tube in axial and radial direction as a function of CF content (a and c), and rotation rate (b and d), respectively. It is interesting to see that the anisotropic conductivity of the LDPE/CF tubes can be tuned via controlling the CF content and rotation rate. As displayed in Fig. 8, two different tubes can be obtained i.e. biaxially conductive or uniaxially conductive tubes. Compared with traditional isotropic CPCs, CPCs featuring with anisotropic electric conductivity exhibit much more potential in the current developing electronic industry50-52. Generally, the formation of anisotropic conductivity involves the formation of preferred filler orientation or ordered 1D assembly. As we discussed earlier, the multi-axial orientation of the CFs endows the tubes with uniform orientation in each layer, and thus the conductivity in the trough-plane direction 15



drastically decreases. The key point in tuning the conductive anisotropy is based on the filler content. With low CF content, the connectivity in radial direction is far more difficult than that in axial direction due to relatively large mean gap distance between adjacent CFs, and hence the tubes only exhibit uniaxial conductivity. On the other hand, the mean gap distance decreases drastically at high CF content, leading to easy contact in both directions. It is also notable that there is a tunable region existing in the intermediate range of CF content, in which a mutation from uniaxial to biaxial conductivity occurs as the rotation rate elevated.

Figure 8 The electric conductivity of various LDPE/CF tubes in axial (AC) and radial directions (RC). It is also important to figure out the role of tunneling effect in the conductive mechanism which usually exhibits pronounced impact on the conductivity of the anisotropic CPCs 53. For further investigation, the current-voltage (I-V) characteristics were detected by estimating the linear regression (Ohm’s law) expressed as: 16


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IA∙V

(4)

where A is the electrical conductance. The values of A and R-squared value (R2) are summarized in Table 1. As evidenced, the values of A are again equivalent to the increasing content of the CFs and the rotation rate. The R-squared value indicates the proximity of the I–V behavior to Ohm’s law. When the R-squared value is greater than 0.99, the I–V curves are a linear relationship which be assumed to follow Ohm’s law behavior. According to Fig. 9 and Table 1, all tubes satisfy well with the Ohm’s law, demonstrating the direct contact is the dominant reason for the tube conductivity.

Figure 9 Current-voltage characteristic of reverse rotation extrusion tubes with CF content of (a) 15wt% (b) 20wt% (c)25wt% (d)30wt%. The measured current in tubes with 10rpm at 15wt% has been mollified by 20 to enable its visualization in the plot. Table 1 The parameters related to the I–V characteristics linear regression shown in Fig. 8. Content of CF

Rotation Rate

A

R2

15wt%

10

0.067±0.017

0.9990

17



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20

0.33±0.010

0.9942

30

0.70±0.035

0.9847

40

3.6±0.033

0.9995

10

0.64±0.006

0.9995

20

3.0±0.089

0.9956

30

4.4±0.066

0.9989

40

5.1±0.032

0.9998

10

2.1±0.015

0.9997

20

3.2±0.12

0.9809

30

5.7±0.075

0.9992

40

14.6±0.090

0.9998

10

6.4±0.069

0.9994

20

19.7±0.73

0.9931

30

19.3±0.66

0.9942

40

14.6±0.25

0.9986

20wt%

25wt%

30wt%

As we demonstrated earlier, the radial conductivity is derived from the increasing randomness in the individual layer, so the following tests concerning anisotropic conductivity are all conducted in the axial direction. For quantitative analysis, the orientation factor (F) of the CFs in the axial direction is calculated according to the following equation introduced by Park32: F=

1 ∑ cos2 α cos 2 β n

(1)

18


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where n is the total number of the measured fibers. α and β are the fiber deflection angles in and out of the plane, respectively. In this study, α was directly determined by the SEM photos of the tube surface while β is fixed to 0o on account of the advective assumptions. The conductivity in the axial direction is plotted as a function of orientation factors, as shown in Fig. 10. According to the orientation percolation theory that the electrical conductivity follows the power law dependence in orientation, an orientation percolation (Fc) can also be detected47. These orientation factors decrease drastically when elevated rotation rate was introduced to the extrusion. Comparing the Fc values of the tubes with different rotation rates from

Table 2, it is interesting to see that the Fc varies little in all samples. Balburg54 and Stuart55 had conducted a series stimulating studies about the effect of orientation on the percolation threshold of the anisotropic conductive fillers, and drawn an accordant conclusion that the increasing isotropy led to better conductivity and lower percolation in high aspect ratio conductive filler system. We would like to attribute the derivation of this invalidity to the specific multi-layer and multi-axial morphology, which is distinct essentially from the isotropic morphology as the aforementioned model assumed. Instead of increasing the randomness in a single plane, CFs with multi-axial orientations are more likely to join together in the interface. The advective assumption is unambiguously inappropriate in the rotation extrusion, because the increasing rotation rate indeed generates turbulent leading to disorder in each layer. The content of the CFs also contributed to the promotion of the conductivity, when the conductive pathways formed. Because high amount of the CFs effectively 19



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decreased the mean gap width of the insulated polymer, the numbers of the fiber-to-fiber contacts will significantly increase, once the fibers begin to offset.

Figure 10 The electric conductivity of the LDPE/CF conductive tube in ED as a function of CF orientation function.

Table 2 the orientation factors and the orientation percolation threshold obtained in various LDPE/CF tubes.

10r/min

20r/min

30r/min

40r/min

Fc

15wt%

0.95

0.86

0.78

0.54

0.95

20wt%

0.95

0.87

0.78

0.54

0.99

25wt%

0.95

0.86

0.79

0.55

0.99

30wt%

0.94

0.85

0.79

0.55

0.95

Apart from the orientation threshold which focuses on conductivity in single plane, the content percolation theory predicts the dependence of the conductivity on filler concentration by taking all planes into consideration:

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σ =σ 0(φ − φ c)t

(2)

where the σ is the composite volume conductivity, σ0 is the conductivity of the filler and ϕ, ϕ c and t are the fraction of the fillers, percolation threshold and critical exponent, respectively. It is notable that t is related to the dimensionality of the conductive networks where t≈2 and t ≈1.3 are for three-dimensional (3D) and two-dimensional (2D) conductive networks, respectively. According to Table 3, the tubes with high rotation rate present lower ϕc than the low rate ones. By increasing the randomness inside the tubes, the percolation threshold reduces due to increased likelihood of connection. However, the values of t exhibit abnormal trend comparing to ϕc. The conductive networks are typical 3D in tubes with 10rpm, and suddenly decrease to 2D when the rotation rate increases to 20rpm. As well demonstrated, two factors play a determining role in t values, i.e. the isotropy and the filler aspect ratio. It is easy to comprehend that high rotation rate inevitably causes turbulent flow leading to increasing isotropy and is verified by the increasing t values from 20rpm to 30rpm standing for the transformation of the 2D network to 3D one. Therefore, the only possible derivation of the mutation at 10rpm should be attributed to the changes in fiber aspect ratio. The length distribution and morphology of the CFs are all shown in Fig. 11. Despite the deviation angle at 10r / min CF is small, the aspect ratio maintains well. The matrix exists more than 400µm long CFs, which can penetrate each layer, favoring the formation of 3D network structure. Nevertheless, as the rotation rate increases to 20rpm, a large amount of CFs will be further broken down into pieces with a length of 21



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less than 150µm. On account of the insufficient degree of deviation, CFs in adjacent layers are inaccessible and thus only 2D network is formed. With the increasing rotation rate, the 3D network will be re-formed due to the elevated deviation angles.

Table 3 The parameters related to the percolation threshold shown in ED. Lnσ0

t

ϕc

R2

F10

2.64

1.78

0.0744

0.9991

F20

2.22

1.29

0.0602

0.9878

F30

2.60

1.49

0.0537

0.9901

F40

3.02

1.51

0.0540

0.9933

22


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Figure 11 The length distribution and morphology of the CFs in reverse rotational extrusion with rotation rate of (a)10r/min, (b)20r/min, (c)30r/min and (d)40r/min, and (e) the schematic illustration of the effect of long CF.

3.3. Sensor characterization The electrical conductivity and electromechanical behaviors depend strongly on the conductive network topology as well as its evolution against the external stress. Besides, fillers dimensionality and structure are also deemed to have a crucial influence on the conductive network structure and final electrical performances. CF/polymer composites have an inherent advantage in designing practical sensors owing to variable resistance derived from easy breakage and dislocation of the CF joints56-59. As previously explained, uniaxial orientated CFs performs a “head to head” connection which easily disconnects under stress. Easy failure of the conductive network not only narrows down the linear application range but also leads to excessive resistance changes making it difficult to accurately characterize changes in strain. In this study, aiming to verify the potential application of strain sensors, bending deformation is utilized which providing variations in length and cross-sectional area as well as the distance of adjacent CFs. As show in Fig.12, the relative change in resistance (∆R/R0) is unambiguously linked to descending distance during bending. In the small strain region (less than 2mm), the ∆R/R0 increase linearly, while following an exponential change once the descending distance exceeds the critical value. The physical phenomenon behind the electromechanical difference between the conventional and rotation extruded tubes can be interpreted by the 23



interaction between LDPE matrix and CFs. CFs can be regarded as rigid elements during deformation compared with elastic LDPE matrix. During bending, the tubes are under stretching stress in the axial direction causing plastic deformation of the LDPE matrix and in the meantime, the CFs detach out of plane with the motion of the attached LDPE molecules60. Instead of creating gaps and cavities in uniaxial tubes, multi-axial orientation increases the contact density of CFs endowing the conductive network with greater deformation tolerance. The numbers of disconnected CFs gradually increases by dislocation which remains intact during stretching, until the destruction of the CF networks where tunneling resistance increases exponentially as the gaps between adjacent conductive fillers widen on stretching61. Interestingly, the linearity and sensitivity can be tuned by adjusting the rotation rate to the need for individual applications. The linear variation interval increases from 2mm to more than 6mm with increasing rotation rate, as a result of the optimum formation of connection points in high deviation angles. The gauge factors (GF) are ∆/

also obtained which is defined as follows, GF=

, where ε represents the applied

strain. Since the tubes with 10rpm display the minimum linear range, the maximum distance under investigation was set to 2mm, which corresponds to a strain of 1.98% at the lower surface. When the rotation rates increase from 10rpm to 40rpm, the GFs are calculated to be 56.3, 42.5, 28.8 and 12.5, and the corresponding linearity range from 1% to 15%. It is easy to comprehend that the sparse conductive network forms due to fewer intersection points in low rotation rate, and resultantly easily trigger the transformation of conductive mechanism from filler contact to tunneling effect during 24


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bending. With increasing rotation rate, the density of the intersection points of the CFs will drastically increase. Since the piezoresistivity of our strain sensor are not derived from the fracture or the crack propagation, the dislocations of the intersection points generated by the deformation of the LDPE matrix gradually increase and bear much higher strain, causing the resistance of the strain sensor to linearly increase. In comparison with other melt-processed sensors, our tubular sensors exhibit 2 advantages: tunable GF and linearity and easy and scalable fabrication. As described in Fig. 12(c), the carbonaceous sensors fabricated by melt processing often exhibit low GF and narrow linearity, which severely affect the effectiveness and applicability of the sensors. By simply controlling the orientation of the CFs, a series of tunable CF-based sensors can be archived. It is of great commercial significance to achieve an easy and cost-effective fabrication of sensors applicable to distinct situations, for instance sensors with relatively high GF for monitoring the fracture and failure of materials and low GF suitable for measuring large strains with simple external electronics. Moreover, it is notable that this technology is based on melt extrusion. Without complicated processing parameters and procedure, a scalable and efficient fabrication can be achieved.

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Figure 12 (a) The resistance-descending distance relationship for the LDPE/CF tubes with 20wt% where most LDPE/CF sensors display good linearity according to the inserted displacement-time curve. (b) The schematic illustration of the deformation of the conductive networks. (b1) and (b3) are the conductive network in conventional tubes before and after stretching, and (b2) and (b4) are for rotational tubes. (c) Comparison of the GF-linearity relationship with other carbonaceous fillers such as carbon nanotube (CNT)57, carbon paper (CP)62, carbon black (CB)57 and single carbon fiber (S-CF)63. Rotation extruded LDPE/CF tubes are marked as CF-X where X stands for the rotation rate. (d) The digital photo of the LDPE/CF tube.

4. Conclusion The role of multi-axial orientation generated by rotation extrusion on electrical conductivity and sensitive strain-responsive performance in low density polyethylene 26


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(LDPE)/carbon fibers (CFs) tubes is highlighted in this study. Due to the formation of 3-layers structure, a conductive network is constructed in the interface of the CF layers, decreasing the percolation threshold from ~35wt% in uni-axial tubes to 15wt% in rotation extruded ones. By increasing the rotation rate, the conductive networks transform from 3D to 2D due to the breakage of the CFs and in the meantime endow the tubes with bidirectional conductivity. The conductive theory analysis shows that the contact of the conductive filler is the main reason for the formation of the conductive network, and the multi-axial orientation leads to wide linear region and high sensitivity in the LDPE/CF tubes with gauge factors range of 12.5 to 56.3 as a function of rotation rate. The multiaxial orientated LDPE/CF tubes display huge potential in sensing devices in a wide range of application.

Acknowledgements This work is financiered by the National Natural Science Foundation of China (51127003 and 51721091), State Key Laboratory of Polymer Materials Engineering (Grant No. sklpme2016-3-05), the Program of Innovative Research Team for Young Scientists of Sichuan Province (2016TD0010) and the Program of Introducing Talents of Discipline to Universities (B13040). We are also very grateful to Dr. Shibing Bai and Mr. Lin Pi for their help with simulation and discussion on multi-axial orientation.

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Facile Fabrication of Electrically Conductive Low-Density Polyethylene

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