Modeling and simulation of the dynamics, contact mechanics and control of the nanomanipulation of elliptical porous alumina nanoparticles based on atomic force microscopy

Highlights

• Dynamic, and contact mechanics relations of manipulation will be examined.

• The actuators used in AFM were modeled to control the manipulation process.

• The mechanical properties of alumina nanoparticles were obtained using experimental tests.

• Simulation was carried out to validate the system performance for elliptical porous alumina nanoparticles.

Abstract

Nowadays, AFM-based robots are widely utilized for transporting different nanoparticles. Using this devise as a tool for nanomanipulation, it is possible to specify the exact location of a nanoparticle in micro/nano-scale. In the fields of dynamics, contact mechanics and control of nanomanipulation for atomic force microscopy, accurate investigation and analysis of the motion of nanoparticles and the robustness of the control algorithm are among the most important goals that arise. In fact, one tries to achieve these two goals by applying the appropriate dynamics and control to the system. Moreover, the controlled displacement of nanoparticles and accurate and proper dynamic modeling can greatly help manipulation. Therefore, in the present study, static, dynamic, and contact mechanics models for the nanomanipulation of elliptical porous alumina nanoparticles were developed. Also, sliding and rolling modes were considered for this type of nanoparticles. The dynamic results showed that, for elliptical porous nanoparticles, increasing the porosity coefficient first leads to sliding and increases the difference between the forces required for sliding and rolling. However, for simple elliptical nanoparticles, the particle first rolls and then slides on the surface. In addition, by using contact mechanics equations, the penetration depth between the nanoparticle and the substrate and that between the nanoparticle and the tip were calculated to be approximately 6.2 nm and 1.4 nm, respectively. Subsequently, a sliding mode controller was modeled in order to control the deviation of the probe from the vertical and the displacement in the direction of motion. The results showed that convergence was achieved in less than 0.1s for all porosity coefficients considered.

Introduction

Nowadays, given the significance of nanotechnology, the equipment used in this branch of science is attracting much attention. Among this equipment, atomic force microscopy (AFM) has numerous applications in various fields, such as particle imaging and surface topology, identifying the unknown characteristics of particles using contact mechanics resulting from nanoindentation and nanoscratch tests, and transporting and controlling the movement of particles via the rules governing manipulation in order to obtain a certain path (Korayem and Khaksar, 2020). AFM is one of the most common nano-robots used and has many applications. One of the most significant applications of this device is nanomanipulation. All the different factors must be taken into account in this process. An important factor affecting this process is the porosity of materials commonly used in industry and its effect on the processes involving dynamics, contact mechanics, and control (Khaksar and Jahanshahi, 2019). The manipulation applications of AFM can be categorized as follows: 1. Micro/nano assembly of electronic and optical parts (Junno et al., 1998) 2. Identifying material properties using active pushing (Tafazzoli, 2005) 3. Creating specific patterns for industrial and ornamental purposes (Tafazzoli, 2005) 4. Fabricating carbon nanotubes (CNTs) and creating various patterns based on them (Hertel et al., 1998) 5. Chemical bonding of components (Requicha et al., 2001) 6. Producing electrodes used in biosensors (Iost et al., 2011).

Controlled pushing for nanoparticles is also employed for nanotribological purposes. Therefore, the accurate and proper dynamic modeling of nanoparticles is the main tool for manipulation processes. Alumina or aluminum oxide is an amorphous ceramic that is widely used in various industries including the medical industry for producing dental implants and their composites. This means that alumina is cheaper than other nanomaterials such as carbon nanotubes and can be used in nanocomposite production (Guo et al., 2006). In addition, alumina is a porous material and has acceptable surface and mechanical properties. Therefore, because of the practical reasons mentioned above, studying the dynamics and control of the nanomanipulation of this material is of particular importance. As a result, researchers have used AFM to examine the dynamics (Gigli et al., 2018; Tian et al., 2010; Qin et al., 2013), contact mechanics (Müser, 2014; Fok et al., 2005; Korayem et al., 2019) and control (Yu et al., 2019; Liaw et al., 2008; Yang et al., 2018) of the nanomanipulation of nanoparticles with different geometries.

Korayem and Khaksar (2019) investigated the effect of impact in the manipulation process based on AFM. They developed the Hertz, JKR, and Jamari impact models for cubic and elliptical nanoparticles. Panahi et al. (2019) studied the manipulation of elliptical nanoparticles, taking into account roughness. In this study, manipulation was investigated in two phases, namely from when the probe and the particle come into contact until when the motion starts (phase one) and from when the motion starts until when the particle reaches the target point (phase 2). A comparison between the obtained results and available experimental works revealed good agreement between the two. Sagar Chowdhury et al. (2013) organized a planning and control method to automate the indirect manipulation of cells using silica beads in gripper formats. Songyu Hu and Dong Sun (Hu and Sun, 2011) used a robot-tweezer manipulation system to overcome the issues of the automatic movement of biological cells, where the optical tweezers act as special robots. Tao Ju et al. (2011) presented a path-planning method for cell movement, where the cell is trapped by an optical tweezer and is moved in a controlled way toward the target position. Yanhua Wu et al. (2009) focused on key methods which make use of tweezers, i.e. path-planning and image processing methods for implementing single-beam optical traps for the automatic manipulation of biological cells. Zhan Gao and Anatole Lecuyer (Gao and Lécuyer, 2009) described a virtual reality device for the path-planning and manipulation of nanoparticles. This device is able to model the interactions between the tip of the AFM and the carbon nanotubes on the substrate and to create the safe and optimal manipulation path. Yangming Zhang et al. (2017), investigated the modeling, controller design and experimental evaluation for very high-precision control from a piezoelectric servo base parallel to the x-y direction. Wei Wei and Guo Lei (Wei and Guo, 2016), considered the irregular movement of a sample microcantilever tip in an AFM. Qi Ningning et al. (Qi et al., 2016), designed a model of a horizontal AFM system based on the modified Prandtl-Ishlinskii (P-I) hysteresis model based on 2-DOF (feedforward and feed-backward) control. This will further improve the tracking performance of the AFM system in the horizontal direction. Songsong Lu et al. (2016) presented a method combining a robust controller and an optimal notch filter for the purpose of high precision periodic path-planning for a nanomanipulation system. Korayem et al. (2012) designed a sliding mode controller (SMC) as a robust chattering free controller to push nanoparticles on a path. The simulation results showed that the mentioned robust controllers are not only for output disturbances. Rather, the chattering free sliding mode control law is able to successfully accomplish the task of pushing the nanoparticles.

According to the investigations carried out, AFM is an important tool for surface imaging, and the authors of this paper gained an interest in discovering the movements of nanoparticles during AFM-based nanomanipulation due to the high capability of this nano-robot in transporting particles and fabricating nano-scale structures (Mofidian et al., 2020; Sadeghzadeh and Khatibi, 2017). Due to the impossibility of simultaneously performing and observing the manipulation, the dynamic simulation of the particle movement on a nanometric scale for this process has become a topic of interest for this investigation. Since the nanoparticles may not simultaneously move and be observed during manipulation, the only solution is to determine the forces exerted on the cantilever probe. Consequently, the exact calculation of these forces is of utmost importance to a successful and accurate manipulation. Dynamic analysis is inevitable in the design, construction, and maintenance of structures. When these structures are of nano-scale sizes or smaller, proper dynamic analysis can contribute to the design improvement, pre-determined applications, or even the fabrication steps (Korayem et al., 2016). The fundamental issue in accurate AFM-based positioning of nanoparticles is the computation of the critical force and the time of motion. The critical force and the time are the most significant parameters in the accurate location of nanoparticles. In addition, given that the surface of the material intended for the control process has anomalies itself, considering various porosities during the modeling process leads to a more realistic interpretation of the issue. Since ceramics are a widely used material in the industry due to their high porosity and alumina is a major ceramic, mechanical properties and manipulation analysis of these materials is especially important.

As seen previously, most of the works in the field of nanomanipulation are based on AFM. Furthermore, these works consider only the motion of the probe of the AFM, the kinematics and dynamics of manipulation in simplified form, and only simple particles. Since the particles in nature are not simple, manipulation can be greatly affected. Therefore, it is very important to identify the factors that cause porosity and to investigate its effect on the manipulation process. Also, since in the present study, elliptical porous nanoparticles with different porosity coefficients have been considered, an appropriate control method along with the identification and modeling of different terms in the dynamic model of particle manipulation using AFM is of utmost significance.

In the present study, the kinematic, dynamic, and contact mechanics relations of manipulation will be examined first. Then, the actuators used in AFM were assessed and modeled in order to control the manipulation process. Using experimental tests, the mechanical properties of alumina nanoparticles were obtained for use in the simulation. Finally, simulation was carried out to validate the system performance, to evaluate the effect of changes in important parameters, and to examine the dynamics, contact mechanics and control modeling of the manipulation process for elliptical porous alumina nanoparticles.