Nanoscale Tension Sensor Based On Black Phosphorus

When 2D materials are attached to a substrate, the Van der Waals force between 2D materials and the substrate will add strain on the materials. Strain plays an important role in changing the properties of the materials and it also serves as an exploitable tool for engineering the properties of 2D materials.(so-called strain engineering) Here is a good review article on 2D materials strain engineering

Black phosphorus(BP) is a new member of the 2D material family. Its puckered atomic structure makes its properties highly anisotropic. For the aspect of mechanical properties, it is especially stretchy in the armchair direction and is relatively rigid in zigzag direction. The stretching or compressing could change its lattice structure and further change its electronic properties like conductivity. Thus it has the potential to be used as a strain sensor which can detect both magnitude and direction of the strain. To convert this potential into practical use we should first systemically explore the properties change behaver under strain.

Figure1: Atomic structure of black phosphorus, Likai Li et al.Nature Nanotechnology, 9(5):372-377,2014.

Several ways could be used to add strain on 2D materials. We choose the simplest way, in which the 2D material is transferred to a soft substrate and we bend the substrate. Thus a uniaxial strain could be passed to the material. In our experiment the few-layer black phosphorus to the Kapton polyimide film (served as soft substrates in our experiments). As we could bend the polymer film to different extent or in different directions, we could add strain on BP accordingly.

Figure2: The device I constructed to bent the substrate in a controlable way

Method I: ABAQUS simulation

ABAQUS is a professional finite element analysis software that are widely used in industry. It could overkill the problem of simulating the substrate defromation. As I spent sometime learning it, I find there are just too many parameters to set. To get the optimist result, a lot of time would be needed on trails in seeking of optimistic parameters.

Figure3: ABAQUS simulation result

Method II: determine strain directly form the photos

Another method is to calculate the strain through geometry. The simplest model tells us that the strain of a bent beam is given by ε = h/2R, where h is the thickness and R is the radius of the local tangentcircle. I took a lot of photos, and then used to yank out the profile of the substrate through Web Plot Digitizer. Then I wrote a MATLAB program to fit the profile curve and calculate the radus of the tangentcircle.

Figure4: The motion stage

Figure5:Output of MATLAB program. The blue solid line represents the profile of the substrate. Dots near the apex (marked by red +) are analyzed to get the radius at the apex, the tangent line(black dots) and the tangentcircle(red solid line) are simultaneously shown on the diagram.

Method III:Measuring through strain gages Most of the commercial strain gages utilize the fact that the resistance of a colume-shape resistor depends on its resistivity, cross section and length, namely R = ρl / S. Commercial strain gages have copper wires inside to serve as detectors (Fig 5). By definition 1% strain will cause 1% change on the length, besides, there will also be 1% change on the cross section due to the unchanged total volume. So the precentage of resisance change will be twice of the strain when strain is small.(1×(1 + x)/(1 - x) ≈ 1 + 2x, where x«1)

Figure6: Commercial gage

To achieve a high sensibility, the standard setup is to attach 4 strain gages on the substrate, 2 on one side and 2 on the other and using them to form a wheatstone bridge and measure the voltage difference between two midpoints as shown in figure7 .

Vout = [R1/(R1+R2)-R4/(R4+R3))]Vin

Combining with R1 = R3 = R + ΔR, R2 = R4 = R - ΔR, we have

Vout = [ΔR / R]Vin

figure7: configuration of bridge circuit

figure8: photos of the bridge circuit

For detailed information please refer to the attached experimental report.

  • bp_tension_sensor.txt
  • 最后更改: 2016/03/24 11:27
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