# Mechanism-Independent Manipulation of Single-Wall Carbon Nanotubes with Atomic Force Microscopy Tip

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Manipulating Scheme

#### 2.2. DE Algorithm

#### 2.2.1. Initialization

_{1}is the length of CNT after pushing, and L is the length before pushing.

#### 2.2.2. Mutation

#### 2.2.3. Crossover

#### 2.2.4. Selection

#### 2.3. AFM Experiments

## 3. Results and Discussion

#### 3.1. Parameters Space Optimization

#### 3.2. Intrinsic Parameters of DE Optimization

#### 3.2.1. F Value Optimization

#### 3.2.2. Cr Value Optimization

#### 3.3. Pushing Parameter Combination

_{m}was measured, as shown in Figure 6. The measured values all approached the target pushing distance Δx with a 10% error.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the manipulation system. The diagram depicts the tip pushing carbon nanotubes (CNTs) technique loop used for manipulating parameter optimization based on the differential evolution (DE) algorithm and three pushing parameters. Pushing distance Δx, the interval between the adjacent pushing path Δy, and pushing step n were fed into the manipulating system. The length ratio of CNT before and after pushing operation was the objective function used to suggest new parameters in the next iteration. The optimization process continues until reaching the desired state.

**Figure 3.**Carbon nanotube (CNT) bending test by atomic force microscopy (AFM) pushing operation with a single path. The bar chart describes the free length Δl under pushing distance Δx used in our study. The inlet image is the AFM image illustrated the free length and the interval between adjacent pushing path Δy.

**Figure 4.**Differential evolution based on the length ratio in feedback control for pushing CNT operation with (

**a**) F = 0.3, (

**b**) F = 0.4, and (

**c**) F = 0.5. The peak length ratio value in each step iteration of every set is listed in (

**d**). In each iteration, four groups of combinations were studied.

**Figure 5.**Differential evolution based on the length ratio in feedback control for pushing CNT operation with (

**a**) Cr = 0.3, (

**b**) Cr = 0.4, (

**c**) Cr = 0.5, (

**d**) Cr = 0.6, and (

**e**) Cr = 0.7. The peak length ratio value in each step iteration of every set experiments is listed in (

**f**). In each iteration, four groups of combinations were studied.

**Figure 6.**AFM images of CNT before and after pushing operation with different parameter combinations. The arrows in the left column of the AFM images denote the multipoint method and pushing direction. (

**a**), (

**c**), (

**e**) and (

**g**) are the AFM images before manipulating operation, (

**b**), (

**d**), (

**f**) and (

**h**) are the AFM images after manipulation with parameter combinations respectively. The vectors in the left column are the parameter combinations used in the manipulation, and R is the length ratio, Δx

_{m}is the distance between the position of CNTs before and after manipulating.

**Figure 7.**Pushing parameter region with higher length ratio value. The lines were obtained by connecting the same R-value combination points.

**Table 1.**Parameter combinations used in manipulating operation having R-value above 0.90 for all experimental data. (Δx, Δy, n) denotes the parameter values in the parameter combination.

R | 0.90 | 0.92 | 0.93 | 0.95 | |
---|---|---|---|---|---|

No. | |||||

1 | (100, 200, 2) | (50, 200, 1) | (200, 50, 1) | (30, 50, 1) | |

2 | (200, 200, 1) | (100, 200, 1) | - | (30, 100, 1) | |

3 | (300, 100, 1) | (200, 100, 1) | - | (50, 50, 1) | |

4 | (400, 50, 1) | - | - | (50, 100, 1) | |

5 | (100,100,2) | - | - | (100, 100, 1) | |

6 | - | - | - | (100, 50, 1) |

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**MDPI and ACS Style**

Ju, D.; Zhang, Y.; Li, R.; Liu, S.; Li, L.; Chen, H.
Mechanism-Independent Manipulation of Single-Wall Carbon Nanotubes with Atomic Force Microscopy Tip. *Nanomaterials* **2020**, *10*, 1494.
https://doi.org/10.3390/nano10081494

**AMA Style**

Ju D, Zhang Y, Li R, Liu S, Li L, Chen H.
Mechanism-Independent Manipulation of Single-Wall Carbon Nanotubes with Atomic Force Microscopy Tip. *Nanomaterials*. 2020; 10(8):1494.
https://doi.org/10.3390/nano10081494

**Chicago/Turabian Style**

Ju, Dianming, Ying Zhang, Rui Li, Shuang Liu, Longhai Li, and Haitao Chen.
2020. "Mechanism-Independent Manipulation of Single-Wall Carbon Nanotubes with Atomic Force Microscopy Tip" *Nanomaterials* 10, no. 8: 1494.
https://doi.org/10.3390/nano10081494