Method for predicting piezoresistive performance of carbon nanotube resin-based strain sensor

Abstract

The invention relates to a method for predicting the piezoresistive performance of a carbon nanotube resin-based strain sensor, and the method comprises the following steps: obtaining the total contact resistance of a conductive composite material through N parallel paths composed of carbon nanotubes based on the Simmons tunnel theory; calculating the resistance change rate and the strain; determining the resistance RC of the whole carbon nanotube resin-based composite material; a local coordinate system (x ', y', z ') is established, the coordinate system is obtained by rotating the global coordinate system (x, y, z), and the z' axis is the longitudinal direction of the carbon nanotube. According to the method for predicting the piezoresistive performance of the carbon nanotube resin-based strain sensor, the distribution of the carbon nanotubes in the resin is considered, the change of the distance between particles under the strain action is corrected, the tunnel resistance of the carbon nanotube resin-based composite material and the relation between the resistance change rate and the strain are calculated, and the piezoresistive performance of the sensor is accurately predicted. The precision of the sensor in the design stage is remarkably improved, and the experiment trial-and-error cost is reduced.

Description

Technical Field

[0001] The invention relates to the technical field of electric power equipment, and in particular to a method for predicting the piezoresistive performance of a carbon nanotube resin-based strain sensor. Background Art

[0002] The piezoresistive effect refers to the phenomenon that the resistance of a material changes when it is subjected to external mechanical stress. Carbon nanotube resin-based composite strain sensors are widely used in the sensor field due to their high sensitivity, wide detection range, good stability, easy preparation and processing, strong designability, and wireless detection potential. According to its different application scenarios and needs, the structure, material ratio and other parameters of the sensor need to be precisely designed to obtain the best piezoresistive performance. Although traditional experimental methods can directly measure the piezoresistive properties of materials, they have disadvantages such as long time consumption, high cost, and difficulty in covering the full strain range. Therefore, customized theoretical analysis and prediction of the piezoresistive performance of the sensor are required.

[0003] In recent years, the prediction of piezoresistive performance of carbon nanotube (CNT) strain sensors has mainly focused on theoretical modeling, experimental verification, numerical simulation and other methods. For example, Huang et al. established a numerical simulation model based on an integrated three-dimensional statistical resistor network model, taking into account the tunneling effect between nanofillers, and calculated the piezoresistive behavior of CNT / carbon black (CB) / polyvinylidene fluoride (PVDF) composites, and compared them with previous experimental research results to verify the effectiveness of the model. (“The Numerical and Experimental Investigation of Piezoresistive Performance of Carbon Nanotube / Carbon Black / Polyvinylidene Fluoride Composite”, page 5581, Materials, 2023). Haghgoo et al. predicted the resistivity and piezoresistive sensitivity of CNT polymer piezoresistive sensors based on a three-dimensional Monte Carlo method combined with a percolation model, and compared them with experimental data. Considering the tunneling behavior near the percolation transition, the analysis results are in good agreement with the experimental data. Monte Carlo simulations show that the tunneling resistance of randomly distributed carbon nanotubes depends on the level of agglomeration, and larger agglomerates reduce the piezoresistive sensitivity. (“Simulation of the role of agglomerations in the tunneling conductivity of polymer / carbon nanotube piezoresistive strain sensors,” pp. 110242, Composites Science and Technology, 2023). Arana theoretically and experimentally analyzed the piezoresistive response of strain gauges consisting of a network of carbon nanotubes (CNTs) deposited on a polyimide (Kapton) substrate based on two computational approaches: a continuum finite element model and a multiscale model that includes two-dimensional scales. The study found that the gauge factor increases with increasing number of end rings, decreasing mesh width, and decreasing end ring height, and both modeling approaches are consistent with the observed experimental trends. (“Design and analysis of a carbon nanotube-based strain gauge via multiscale modeling,” pp. 1717-1732, Meccanica, 2023).

[0004] The tunneling effect between carbon nanotubes is the main mechanism of piezoresistivity in carbon nanotube-polymer composites. Existing models have made a lot of assumptions about the behavior of CNT tunneling effect, but its physical basis has not been deeply studied, and it is impossible to accurately predict the piezoresistive performance of sensors. In view of this, we proposed a method to predict the piezoresistive performance of carbon nanotube resin-based strain sensors. Summary of the invention

[0005] The purpose of the present invention is to provide a method for predicting the piezoresistive performance of a carbon nanotube resin-based strain sensor, calculate the relationship between the tunnel resistance and resistance change rate of the carbon nanotube resin-based composite material and the strain, accurately predict the piezoresistive performance of the sensor, and significantly improve the accuracy of the sensor in the design stage.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A method for predicting the piezoresistive performance of a carbon nanotube resin-based strain sensor, the method comprising the following steps:

[0008] S1. Based on Simmons tunneling theory, the conductive composite material consists of N parallel paths composed of carbon nanotubes, and each path consists of M carbon nanotubes. The total contact resistance R of the composite material is obtained. When the carbon nanotube resin-based strain sensor is strained, the number of conductive paths N is calculated;

[0009] S2. Based on the total contact resistance R of the composite material, the relationship between the resistance change rate and the strain is calculated;

[0010] S3. Based on Simmons formula, ignoring the strong reagglomeration tendency of carbon nanotubes, determine the resistance R of the entire carbon nanotube resin matrix composite material C ;

[0011] S4. Establish a local coordinate system (x', y', z'), which is obtained by rotating the global coordinate system (x, y, z), and the z' axis is the longitudinal direction of the carbon nanotube.

[0012] Optionally, the S1 further includes:

[0013] The total resistance is:

[0014] Among them, R m According to Simmons tunnel theory, it can be expressed as:

[0015]

[0016] The conductive network composed of randomly dispersed carbon nanotubes in the matrix is ​​composed of the contact resistance R between adjacent particles. m The intrinsic resistance R of the conductive particles i Together, S2 is the effective cross-sectional area corresponding to the tunneling effect of carbon nanotubes, J is the tunneling current, m is the electron mass, e is the charge, h is the Planck constant, V is the voltage, d is the shortest distance between particles, and E c is the potential barrier between particles.

[0017] Optionally, the number N of conduction paths in S1 is expressed as:

[0018]

[0019] The spacing between carbon nanotubes is from d 0( Initial distance) to d distribution, the spacing d under the action of external force is expressed as:

[0020] d=d0(1+kε)

[0021] Ignoring the intrinsic resistance of the particles and only considering the tunneling effect, the total resistance R of the composite material when strain occurs is expressed as:

[0022]

[0023] Where N0 and N(ε) represent the values ​​of the initial conductive path and the conductive path after deformation, respectively; A, B, C, and D represent the fitting parameters of the carbon nanotube resin-based strain sensor.

[0024] Optionally, the relationship between the resistance change rate and the strain in S2 is expressed as follows:

[0025]

[0026] Substituting the sensitivity coefficient GF into the above formula, we can reorganize it into the following format:

[0027]

[0028] Optionally, the resistance R of the carbon nanotube resin-based composite material in S3 is C for:

[0029]

[0030] The diameter of the carbon nanotube is d c , t is the thickness of the insulating material between the electrodes, E c is the barrier height of the carbon nanotube resin matrix composite material.

[0031] Optionally, the S3 further includes:

[0032] Considering the curvature of carbon nanotubes and the multiple nodes between carbon nanotubes, a coefficient λ is introduced to characterize the curvature of carbon nanotubes. c , defined as the straight-line distance between the starting point and the end point of the carbon nanotube (l eff) and the actual length (l′ CNT ) ratio:

[0033]

[0034] Considering the corrugated carbon nanotubes and carbon nanotube agglomeration effects, a parameter C' is introduced to quantify the content of carbon nanotube agglomerates in the polymer matrix. The resistance of each path is the sum of (1-C')M tunnel resistances corresponding to the number of nodes of a single carbon nanotube. The conductive path is (1-C')M with a length of l eff The straight line segment of

[0035] Establish a Cartesian coordinate system (x, y, z), and each carbon nanotube is represented by a three-dimensional space angle θ and To locate, both angles are between 0 and π. When the potential difference is applied in the y direction, the average length of the projection on the y coordinate axis is expressed as:

[0036]

[0037] Ignoring the length of the carbon nanotube agglomerate, the cubic volume unit (VE) per unit length is expressed as:

[0038] (1-C')Ml y =1

[0039]

[0040] Considering the corrugated carbon nanotubes and carbon nanotube agglomeration effects, the initial test resistance R0 in the undeformed state is expressed as:

[0041]

[0042] Optionally, the projection of the tunnel vector in S4 on the x'-y' plane is expressed as a function of the thickness t0 and the direction angle θ; the initial tunnel vector is written in the global coordinate system (x, y, z) as:

[0043]

[0044] Assuming that the element is subjected to a uniaxial stress σy in the y direction, the elongation of the tunnel vector can be expressed as a function of the strain εy:

[0045]

[0046] The length of the tunnel vector after deformation is:

[0047]

[0048] ψ a =(1+kε y ) 2

[0049] ψ b =(1-νkε y ) 2

[0050]

[0051] The carbon nanotube agglomeration effect and the random orientation of the carbon nanotubes, the overall resistance change rate is calculated as the following average value:

[0052]

[0053] Among them, v represents the Poisson's ratio of the nanocomposite material, and k is actually the linear segment sensitivity coefficient GF.

[0054] The technical effects achieved by the present invention are:

[0055] 1. The piezoresistive performance prediction method of the carbon nanotube resin-based strain sensor takes into account the distribution of carbon nanotubes in the resin, corrects the change in the distance between particles under the action of strain, calculates the relationship between the tunnel resistance and resistance change rate of the carbon nanotube resin-based composite material and the strain, accurately predicts the piezoresistive performance of the sensor, significantly improves the accuracy of the sensor in the design stage, and reduces the cost of experimental trial and error.

[0056] 2. The piezoresistive performance prediction method of the carbon nanotube resin-based strain sensor deeply understands the influence mechanism of different factors on the resistance characteristics of carbon nanotube resin-based composite materials, optimizes the material formula and preparation process, and promotes the customized development of carbon nanotube resin-based composite material strain sensors under different needs through precise analysis of the agglomeration effect and the use of more effective dispersion technology.

[0057] 3. The piezoresistive performance prediction method of the carbon nanotube resin-based strain sensor provides a more sophisticated theoretical support for the design of carbon nanotube resin-based composite strain sensors by comprehensively considering the influence of the corrugated carbon nanotube structure, the carbon nanotube agglomeration effect and the random orientation of carbon nanotubes on the resistance change rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A schematic diagram showing the comparison between the theoretical piezoresistance curve of the present invention and the piezoresistance curve of the experimental result;

[0059] Figure 2 This is a schematic diagram of the conductive path of the conductive composite material of the present invention;

[0060] Figure 3 This is a schematic diagram of a bent carbon nanotube according to the present invention;

[0061] Figure 4 A schematic diagram of a conductive path composed of carbon nanotubes and aggregates of the present invention;

[0062] Figure 5 A schematic diagram of a spherical coordinate system for the orientation of carbon nanotubes of the present invention;

[0063] Figure 6 Schematic diagram of the relative positions of adjacent carbon nanotubes of the present invention, a is a three-dimensional view, b is a cross-sectional view;

[0064] Figure 7 It is a schematic diagram of the local coordinate system in the three-dimensional view and the cross-sectional view of the present invention;

[0065] Figure 8 It is a schematic diagram of the cubic volume unit of the present invention subjected to uniaxial stress on the y-axis. DETAILED DESCRIPTION

[0066] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described in conjunction with the following embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention. As used herein, the terms "parallel" and "perpendicular" are not limited to their strict geometric definitions, but include tolerances for reasonable and inconsistent machining or human errors;

[0067] Combination Figure 1-Figure 8 As shown, the specific features of the method for predicting the piezoresistive performance of the carbon nanotube resin-based strain sensor are described in detail below:

[0068] A method for predicting the piezoresistive performance of a carbon nanotube resin-based strain sensor comprises the following steps:

[0069] Step 1: Based on Simmons tunneling theory, under small strain (<1%), the tunneling effect is the main mechanism of DC conduction of carbon nanotube strain sensors. Figure 2 As shown in the figure, the conductive network composed of randomly dispersed carbon nanotubes in the matrix is ​​composed of the contact resistance R between adjacent particles. m The intrinsic resistance R of the conductive particles i According to Simmons tunneling theory, the particle intrinsic resistance R can be ignored. i , when the conductive composite material consists of N parallel paths composed of carbon nanotubes, and each path consists of M carbon nanotubes, the total contact resistance of the composite material is:

[0070]

[0071] Among them, R m According to Simmons tunnel theory, it can be expressed as:

[0072]

[0073] Among them, S 2is the effective cross-sectional area corresponding to the tunneling effect of carbon nanotubes, J represents the tunneling current, m is the electron mass, e is the charge, h is the Planck constant, V is the voltage, d is the shortest distance between particles, and E c It is the potential barrier between particles (0.5eV~2.5eV for epoxy resin).

[0074] When the carbon nanotube resin-based strain sensor is strained, the number of conductive paths N is expressed as:

[0075]

[0076] Where N0 and N(ε) represent the initial conductive path and the conductive path after deformation, respectively. A, B, C, and D represent the fitting parameters of the carbon nanotube resin-based strain sensor.

[0077] At this time, the distance between carbon nanotubes changes from d 0( Initial distance) to d distribution, the spacing d under the action of external force can be expressed as:

[0078] d=d0(1+kε)

[0079] Ignoring the intrinsic resistance of the particles and only considering the tunneling effect, the total resistance of the composite material when strain occurs can be expressed as R:

[0080]

[0081] Step 2: According to the above resistance relationship, the relationship between resistance change rate and strain can be expressed as follows:

[0082]

[0083] Substituting the sensitivity coefficient GF into the above formula can be reorganized into the following format:

[0084]

[0085] Among them, the fitting parameters of A, B, C, and D for the GT-210 carbon nanotube sensor with a carbon nanotube content of 3.5wt.% are shown in the following table:

[0086] parameter Fitted values A -4.376 B 107.253 C -901.843 D 2455.016

[0087] Step 3: According to Simmons' formula, ignoring the strong reaggregation tendency of carbon nanotubes, the resistance of the entire carbon nanotube resin matrix composite material is determined as follows (applicable to the case where the two electrodes are separated by an electrical insulating material with a thickness of several nanometers):

[0088]

[0089] The diameter of the carbon nanotube is d c , t is the thickness of the insulating material between the electrodes, Ec is the barrier height of the carbon nanotube resin matrix composite material.

[0090] like Figure 3 As shown, considering the curvature of carbon nanotubes and the multiple nodes between carbon nanotubes, a coefficient λ is introduced to characterize the curvature of carbon nanotubes. c , defined as the straight-line distance between the starting point and the end point of the carbon nanotube (l eff ) and the actual length (l′ CNT ) ratio:

[0091]

[0092] Considering the corrugated carbon nanotubes and carbon nanotube agglomeration effects, Figure 4 As shown in the figure, a parameter C' is introduced to quantify the content of carbon nanotube aggregates in the polymer matrix. The resistance of each path is the sum of (1-C')M tunnel resistances corresponding to the number of nodes of a single carbon nanotube. The conductive path is (1-C')M with a length of l eff A straight line segment. Figure 5 As shown, a Cartesian coordinate system (x, y, z) is established, and each carbon nanotube is represented by a three-dimensional space angle θ and To locate, both angles are between 0 and π. When the potential difference is applied in the y direction, the average length of the projection on the y coordinate axis can be expressed as:

[0093]

[0094] Ignoring the length of the carbon nanotube agglomerate, the cubic volume unit (VE) per unit length is expressed as:

[0095] (1-C′)Ml y =1

[0096]

[0097] Considering the corrugated carbon nanotubes and carbon nanotube agglomeration effects, the initial resistance R′0 in the undeformed state can be expressed as:

[0098]

[0099] Step 4: Due to the tunneling effect, the electrical contact between two adjacent carbon nanotubes in the undeformed state always occurs on the side of a cylinder with a radius of t0 that is concentric with the carbon nanotube. Figure 6 As shown, the tunnel vector is defined as the part connecting two adjacent carbon nanotubes, which is located at the point where the tunnel effect occurs.

[0100] Figure 7As shown, a local coordinate system (x', y', z') is established, which is obtained by rotating the global coordinate system (x, y, z), and the z' axis is the longitudinal direction of the carbon nanotube. The projection of the tunnel vector on the x'-y' plane can be expressed as a function of the thickness t0 and the direction angle θ. The initial tunnel vector is written in the global coordinate system (x, y, z) as:

[0101]

[0102] Figure 8 As shown in Figure 1, assuming that the unit is subjected to a uniaxial stress σy in the y direction, the elongation of the tunnel vector can be expressed as a function of the strain εy:

[0103]

[0104] Among them, v represents the Poisson's ratio of the nanocomposite material, and k is actually the linear segment sensitivity coefficient GF. The length of the tunnel vector after deformation is:

[0105]

[0106] ψ a =(1+kε y ) 2

[0107] ψ b =(1-νkε y ) 2

[0108]

[0109] In summary, due to the carbon nanotube agglomeration effect and the random orientation of the carbon nanotubes, the overall resistance change rate can be calculated as the following average value:

[0110]

[0111] The above generally describes the present invention in detail, but it is obvious to a person skilled in the art that some modifications or improvements can be made to the present invention. Therefore, modifications or improvements that do not depart from the spirit of the present invention are within the scope of protection of the present invention.

Claims

1. A method for predicting the piezoresistive performance of a carbon nanotube resin-based strain sensor, characterized in that: The prediction method comprises the following steps: S1. Based on Simmons tunneling theory, the conductive composite material consists of N parallel paths composed of carbon nanotubes, and each path consists of M carbon nanotubes. The total contact resistance R of the composite material is obtained. When the carbon nanotube resin-based strain sensor is strained, the number of conductive paths N is calculated; S2. Based on the total contact resistance R of the composite material, the relationship between the resistance change rate and the strain is calculated; S3. Based on Simmons formula, ignoring the strong reagglomeration tendency of carbon nanotubes, determine the resistance R of the entire carbon nanotube resin matrix composite material C ; S4. Establish a local coordinate system (x', y', z'), which is obtained by rotating the global coordinate system (x, y, z), and the z' axis is the longitudinal direction of the carbon nanotube.

2. The method for predicting piezoresistive performance of a carbon nanotube resin-based strain sensor according to claim 1, characterized in that: Said S1 further comprises: The total resistance is: Among them, R m According to Simmons tunnel theory, it can be expressed as: The conductive network composed of randomly dispersed carbon nanotubes in the matrix is ​​composed of the contact resistance R between adjacent particles. m The intrinsic resistance R of the conductive particles i Together, S 2 is the effective cross-sectional area corresponding to the tunneling effect of carbon nanotubes, J is the tunneling current, m is the electron mass, e is the charge, h is the Planck constant, V is the voltage, d is the shortest distance between particles, and E c is the potential barrier between particles.

3. The method for predicting piezoresistive performance of a carbon nanotube resin-based strain sensor according to claim 2, characterized in that: The number N of conduction paths in S1 is expressed as: The spacing between carbon nanotubes is from d 0( Initial distance) to d distribution, the spacing d under the action of external force is expressed as: d=d0(1+kε) Ignoring the intrinsic resistance of the particles and only considering the tunneling effect, the total resistance R of the composite material when strain occurs is expressed as: Where N0 and N(ε) represent the values ​​of the initial conductive path and the conductive path after deformation, respectively; A, B, C, and D represent the fitting parameters of the carbon nanotube resin-based strain sensor.

4. The method for predicting piezoresistive performance of a carbon nanotube resin-based strain sensor according to claim 1, characterized in that: The relationship between the resistance change rate and strain in S2 is expressed as follows: Substituting the sensitivity coefficient GF into the above formula, we can reorganize it into the following format:

5. The method for predicting piezoresistive performance of a carbon nanotube resin-based strain sensor according to claim 1, characterized in that: The resistance R of the carbon nanotube resin matrix composite material in S3 C for: The diameter of the carbon nanotube is d c , t is the thickness of the insulating material between the electrodes, E c is the barrier height of the carbon nanotube resin matrix composite material.

6. The method for predicting piezoresistive performance of a carbon nanotube resin-based strain sensor according to claim 5, characterized in that: The S3 further comprises: Considering the curvature of carbon nanotubes and the multiple nodes between carbon nanotubes, a coefficient λ is introduced to characterize the curvature of carbon nanotubes. c , defined as the straight-line distance between the starting point and the end point of the carbon nanotube (l eff ) and the actual length (l′ CNT ) ratio: Considering the corrugated carbon nanotubes and carbon nanotube agglomeration effects, a parameter C' is introduced to quantify the content of carbon nanotube agglomerates in the polymer matrix. The resistance of each path is the sum of (1-C')M tunnel resistances corresponding to the number of nodes of a single carbon nanotube. The conductive path is (1-C')M with a length of l eff The straight line segment of Establish a Cartesian coordinate system (x, y, z), and each carbon nanotube is represented by a three-dimensional space angle θ and To locate, both angles are between 0 and π. When the potential difference is applied in the y direction, the average length of the projection on the y coordinate axis is expressed as: Ignoring the length of the carbon nanotube agglomerate, the cubic volume unit (VE) per unit length is expressed as: (1-C′)Ml y =1 Considering the corrugated carbon nanotubes and carbon nanotube agglomeration effects, the initial resistance R′0 in the undeformed state is expressed as:

7. The method for predicting piezoresistive performance of a carbon nanotube resin-based strain sensor according to claim 6, characterized in that: The projection of the tunnel vector in S4 on the x'-y' plane is expressed as a function of the thickness t0 and the direction angle θ; the initial tunnel vector is written in the global coordinate system (x, y, z) as: Assuming that the element is subjected to a uniaxial stress σy in the y direction, the elongation of the tunnel vector can be expressed as a function of the strain εy: The length of the tunnel vector after deformation is: ψ a =(1+kε y ) 2 ψ b =(1-νkε y ) 2 The carbon nanotube agglomeration effect and the random orientation of the carbon nanotubes, the overall resistance change rate is calculated as the following average value: Among them, v represents the Poisson's ratio of the nanocomposite material, and k is actually the linear segment sensitivity coefficient GF.

Images