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AN INTERACTIVE NANOMANIPULATION VISUALIZATION BASED ON MOLECULARDYNAMICS SIMULATION AND VIRTUAL REALITY

Chun-Ta Chen1, Shin-Yong Chen2, Chien-Hsiang Liao3 and Shi-Chang Zeng11Department of Mechatronic Technology, National Taiwan Normal University, Taipei City, Taiwan

2Department of Automation and Control Engineering, Far East University, Tainan City, Taiwan3Department of Electrical and Computer Engineering, National Chiao Tung University, Hsinchu City, Taiwan

E-mail: [email protected]; [email protected]; [email protected]; [email protected]

ICETI 2012-Q1045_SCINo. 13-CSME-86, E.I.C. Accession 3544

ABSTRACTIn this paper, an interactive virtual environment for nanomanipulation is developed. The technique fornanomanipulation visualization is based on molecular dynamics simulation and virtual reality. Using thedeveloped interactive virtual environment for the intuitive nanomanipulation visualization, the operator cancharacterize and control the behavior of nanoparticles in the virtual SPM through physical simulation and3D visualization.

Keywords: nanomanipulation; virtual reality; molecular dynamics; scanning probe microscopy.

VISUALISATION DE NANOMANIPULATION INTERACTIVE BASÉE SUR LA SIMULATIONDYNAMIQUE MOLÉCULAIRE ET LA RÉALITÉ VIRTUELLE

RÉSUMÉDans cet article, un environnement virtuel interactif pour la nanomanipulation est développé. La techniquepour la visualisation de la nanomanipulation est basée sur la simulation moléculaire dynamique et la réalitévirtuelle. En utilisant l’environnement virtuel interactif développé pour la visualisation intuitive de nanoma-nipulation, l’opérateur peut caractériser et contrôler le comportement de nanoparticules dans le SPM virtuelpar simulation physique et visualisation en 3D.

Mots-clés : nanomanipulation ; réalité virtuelle ; dynamique moléculaire ; microscope-sonde à balayage.

991Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 3, 2013

1. INTRODUCTION

Recent advances in nanotechnology have raised the possibility that samples can be accessed and manipulatedon the nanometer and atomic scale. Thus, some fundamental physics phenomena of the samples or molecularbiology on the nanometer scale, e.g., friction, lubrication, and tribology, can be gained with new insights.

In order to have access to the molecular samples, the required apparatuses are developed to allow aninteraction with the nanosamples. There are several kinds of scanning probe microscope (SPMs), e.g., theSTM (scanning tunneling microscope) and AFM (atomic force microscope) are best known for their abilityto visualize surfaces of materials with the highest spatial resolution or to manipulate a single atom andnanoscale samples.

Jung et al. [1] used a nanoengineering approach based on STM to position molecules on surfaces. Themolecules range from small alkanethiols to larger biosystems such as proteins or DNA. Beton et al. [2]positioned the individual C60 molecules on an Si(111)–(7×7) surface by the tip of a STM. For the AFMapparatus for the molecule manipulation on the non-conductive samples, Junno et al. [3] reported the appli-cation of AFM to manipulate and position nanometer-sized particles with nanometer precision. Requichaet al. [4] described the first step towards the construction of NEMS by assembling nanometer-scale objectsusing an SPM as a robot. More recently, Rieder’s group has shown that it is possible to determine whetheratoms can be pushed or pulled on a surface by examining the signals acquired by the scanning tunnelingmicroscope during the atomic manipulation [5].

Nevertheless, these instruments for nanoscale manipulations are generally expensive, and sometimes along-term training is required. In addition, researchers often prefer a check by a visual presentation suchthat problems may be found before going to implementation with STMs or AFMs.

Thanks to the advent of the hardware and software of the computer science, VR environments providethe visualization on new experiment possibilities with numerical simulations, and also allow a detailedinvestigation to a complex system. Therefore, VR technology has attracted the attention of many researchersin the fields of robotics [6–8], automation [9], molecular dynamics [10], and so on.

In this paper, an interactive virtual environment for the single-tip SPM-based nanomanipulation is de-veloped. Based on the molecular dynamics (MD) simulation and VR technology, the goal is not only toallow the visualization on steering the virtual SPM, but also to give the dynamics simulation and interactivemanipulation of graphical atoms.

2. PROBE-BASED NANOMANIPULATION

2.1. Modes of OperationProbe-based manipulation is very useful as an apparatus prototyping technique. Especially, advances in SPMhave made manipulating matter on the nanoscale a reality so that an atom can be placed at the designatedpositions and nanostructures can be built atom-by-atom.

Single-tip SPM is mainly comprised of a noble metal sharpened to an atomic sized tip, which is mountedon a piezoelectrically driven linear platform. The single-tip SPM may be operated in the two distinct modes:contact mode and non-contact mode. When a sample is manipulated in contact mode that is generally usedin most AFM procedures, the tip is continuously touching the sample such that significant normal and lateralforces may be exerted on the sample [11].

In the non-contact mode, the tip is never in contact with the specimen. As such, one can use the pushingor pulling depending on the repulsive forces or the attractive forces between the tip and the manipulatednanoparticles to move the nanoparticles [12] as shown in Fig. 1. Consequently, the SPM can now be al-lowed to carry out engineering operations on single atom and molecules, thereby providing an alternativefabrication technique.

992 Transactions of the Canadian Society for Mechanical Engineering, Vol. 37, No. 3, 2013

Fig. 1. (a) Pulling and (b) pushing a nanoparticle in a non-contact mode.

2.2. Forces in ProbeWhen two nanoparticles are in close proximity, such an action presents various kinds of forces, such as theVan der Waals, electrostatic forces and hydration forces. These kinds of forces depend on the characteristicsof the nanoparticle pairs, and the located environment.

As a probe moves toward a fixed manipulated nanoparticle from a large distance, in which no force exerts,until the tip almost touches the nanoparticle, attraction forces are first generated prior to touching, and thenthe repulsion forces appear at almost touching.

In this paper, the focus is to use the SPM-based nanomanipulation by the non-contact mode to virtu-ally manipulate a graphical nanoscaled particle on a single-crystal substrate. Therefore, the motion of themanipulated nanoparticles should be analyzed from the tip-sample interaction in accordance with the MDdevelopment.

3. NANOMANIPULATION MODELING

3.1. Molecular DynamicsMD is based on a potential function to derive the intermolecular or interatomic forces, and then the equationsof motion for the associated nanoparticles can be developed using the Newton law such that the correspond-ing trajectories of the manipulated nanoparticles can be determined via numerical calculations. Furthermore,it is assumed that the gravity can be neglected compared to the intermolecular force, the dynamic equationsof the ith nanoparticle can be expressed as

Fi = mid2ri

dt2 =−N

∑j=1j 6=i

dU(ri j)

dri j

ri j

ri j, (1)

in which Fi is the force exerting at the ith nanoparticle, mi is the mass, ri is the position vector, N is thetotal nanoparticle number in the considered system, and U(ri j) is the potential being the function of theseparation of the nanoparticle i and j, i.e., ri j = ri j = ri− r j.

When there is a Van der Waals force between two nanoparticles with a separation r, then the generalizedinteraction between nanoparticles can be given by the Mie pair potential [13], and for the special case beingthe Lennard–Jones potential, the potential function [14] is

U(r) = kε [(σ/r)n− (σ/r)m], (2)


Table 1. Non-dimensional scaling quantities for MD equations.Parameter Non-dimensionalPosition vector r∗ = r/σ

Force F∗ = Fσ/ε

Velocity v∗ = v(m/ε)1/2

Time t∗ = t[ε/(mσ2)]1/2

Kinetic energy E∗ = E/ε

Potential energy U∗ =U/ε

in which k = (n/(n−m))(n/m)m/(n−m), and ε and σ are the respective bonding energy and the balancedistance that should be determined by an experiment. For some used atoms, these values can be referredto as in [15]. Moreover, the constants m and n are related to the attractive force and the repulsive force,respectively.

In general, the attractive contribution from the Van der Waals interaction potential varies with the inverse-sixth power of the distance, i.e. m=6. The repulsive Van der Waals potential gives the contribution on therepulsive item with n=12 [16].

Substituting the potential expression, Eq. (2), into Eq. (1), the governing equations for the ith nanoparticlecan be expressed as

mid2ri

dt2 = kε

N

∑j=1j 6=i

[(nσnr−n−2

i j −mσmr−m−2

i j )ri j]. (3)

To determine the trajectory of a manipulated nanoparticle, an efficient numerical integral is required forthe large number of molecules/atoms. In this paper, the Verlet’s algorithm [17] is employed to solve for themolecular dynamics equations. For the time step ∆t, the position vector of the ith nanoparticle at time t +∆tcan be approximated as

ri(t +∆t) = 2ri(t)− ri(t−∆t)+d2ri(t)

dt2 ∆t2. (4)

It is noted that the higher order terms in Eq. (4) are neglected. When Eq. (3) for the acceleration issubstituted into Eq. (4), the position vector of the ith nanoparticle at time t +∆t is given in a discrete formas

ri(t +∆t) = 2ri(t)− ri(t−∆t)+ kε

N

∑j=1j 6=i

[(nσnr−n−2

i j −mσmr−m−2

i j )ri j]∆t2/mi. (5)

Thus, the velocity at time t can be expressed as

vi(t) = [ri(t +∆t)− ri(t)]/∆t. (6)

3.2. Non-Dimensional ScalingIn the MD simulation, many physical and geometrical parameters are involved. Moreover, these involvedparameters are very small such that the numerical integral may result in very large errors for the obtainedresults. Therefore, it is better to solve for the MD problems with the fewer involved parameters. In addition,it will be efficient with fewer parameters in solving MD. In this regard, a non-dimensional scaling is em-ployed to simplify the developed MD equations, Eqs. (5) and (6), for the numerical analyses. The requirednon-dimensional scaling quantities for the MD parameters are shown in Table 1.


Substituting the defined non-dimensional scaling physical parameters into Eqs. (5) and (6), the non-dimensional governing MD equations can be expressed as

r∗i (t∗+∆t∗) = 2r∗i (t

∗)− r∗i (t∗−∆t∗)+ k

N

∑j=1j 6=i

[(n(r∗i j)−n−2−m(r∗i j)

−m−2)r∗ij](∆t∗)2, (7)

v∗i (t∗) = [r∗i (t

∗+∆t∗)− r∗i (t∗)]/∆t∗, (8)

in which the non-dimensional exerting force at the manipulated nanoparticle is

F∗ = kN

∑j=1j 6=i

[(n(r∗i j)−n−2−m(r∗i j)

−m−2)r∗i j](∆t∗)2. (9)

It is seen that the transformed non-dimensional MD equations only relate to the non-dimensional positionvectors of the ith nanoparticle, the corresponding separation between the nanoparticle i and j and the non-dimensional time.

In the simulation, the non-dimensional scaling for all the physical parameters is first taken according toTable 1, and then substituted into Eqs. (7) and (8) to solve for the non-dimensional position of the manip-ulated nanoparticle at the next step and the current non-dimensional velocity. Moreover, the correspondingnon-dimensional exerting force at the manipulated nanoparticle can be obtained from Eq. (9). Subsequently,these non-dimensional quantities will be transformed back to the real physical data for displaying.

4. VIRTUAL NANOMANIPULATION ENVIRONMENT

4.1. Software ArchitectureVR is a high-end human-computer interface so that a user can be allowed to interact with the simulatedenvironment in real time and through sensorial channels. Moreover, the increased interaction lets the userfeel immersed in the real world. Therefore, VR-based man-machine is feasible for the real-time explorationof the nanomanipulation.

The VR interface should combine real-world user and physical model presence with a computationalmodel and data. The user manipulates the model, and the model can be tracked and displayed on the com-puter screen. In this way, the software architecture in the designed virtual nanomanipulation platform iscomposed of the following modules: (1) an interactive virtual environment module (IVEM) for manipulat-ing a nanoparticle; (2) device interface module (DIM) for controlling a virtual single-tip nanomanipulator;(3) molecular dynamics calculation module (MDCM) to determine the trajectory of a manipulated nanopar-ticle.

Models of the environment and the nanoparticles of the IVEM are constructed using the Turespace andPro/E software, and then remitted to the EON Studio for the VR presentation. The generated visualizationprogram is for displaying, animating and analyzing the nanomanipulation system using 3D graphics. Thevirtual single-tip nanomanipulator in the VR is controlled by a mouse via the DIM. The displayed single-tipnanomanipulator in the interactive virtual environment can be moved by clicking and dragging the single-tip SPM graphic. Moreover, the positions of the tip can be recorded and stored for the molecular dynamicscalculation. The required MD calculation is carried out in the MDCM based on the developed MD equations.Therefore, the obtained numerical data for the trajectory of manipulated nanoparticles are sent to IVEM torender the virtual environment such that the visualization in 3D virtual world for the nanomanipulation iscompleted. It is noted that the developed DIM can be modified to accommodate other manipulating devicessuch as haptic force feedback devices, and real SPMs. The architecture of our developed interactive virtualenvironment and building technique for the nanomanipulation is shown in Fig. 2.


Fig. 2. Architecture of interactive virtual environment and making technology for nanomanipulation.

4.2. Design of a Virtual NanomanipulationThe designed interactive virtual environment for the visualization of the probe-based nanomanipulationis shown in Fig. 3. For the man-computer interface, the window (III) displays the operated probe and themanipulated nanoparticle. For now, the probe is supposed to be composed of ten atoms, and the manipulatedatom is located on the single-crystal substrate.

While operating this virtual probe, the exerting forces at the probe and at the manipulated nanoparti-cle are presented respectively as (I) and (II) by the time history. The icons shown by (IV) are related tothe pre-processing and post-processing including specifying the initial relative positions of the tip and thenanoparticles, starting/ending the implementation as well as saving the results for plotting.

In the proposed virtual nanomanipulation platform, the virtual tip can be moved by directly clicking thebuilt tip graphic in the window (III), or clicking the arrow icons in (V). In addition, the real-time positionsof the tip and the manipulated atom can be separately displayed in (VI) and (VII).

5. EVALUATION

5.1. Physical ParametersFor an evaluation of the designed interactive virtual nanomanipulation, it is supposed that a Xe located onthe Cu substrate will be moved in a non-contact mode, i.e. the pulling and pushing methods. The tip is a Wprobe. The corresponding physical parameters of the associated atoms are shown in Table 2. Moreover, thebonding energy and the balance distance of the Xe atom are respectively 3.2044× 10−20 J and 3.89Å foruse in the MD equations.


Fig. 3. Interactive virtual environment for nanomanipulaton.

Table 2. Physical parameters of associated atoms.Cu W Xe

Mass (kg) ×10−25 1.0556 3.05 2.15Radius(Å) 1.28 1.41 1.24

5.2. Simulations and ImplementationIn the first trial, the pushing mode is used to move the sample Xe atom in the X-direction. The initialpositions of the probe and the sample atom can be set on the interactive virtual nanomapulation platform as0rtip = [0.2 2 8]T (Å), 0rs = [2 2 2.48]T (Å), thus, the W-made tip is operated by clicking the +X icon on(V) of the platform.

During the virtual operation process, the distance from the probe to the sample atom Xe, i.e. rts = |rts|=|rtip− rs|, the magnitude and the components of the position vector of the sample atom Xe are shown inFig. 4. Also, the corresponding force exerting at the sample atom Xe is presented in Fig. 5. It can be seenthat an attracted force is generated so that the sample atom moves toward the probe, then at t = 0.017 sec, theexerting force is transited to the repulsive force to push the manipulated nanoparticle. Also, the manipulatedsample atom Xe has a motion in the Y -direction due to the exerting from the Cu substrate.

The second trial is based on the pulling mode, in which the initial probe position is 0rtip = [2 2 8]T

(Å) and position of the sample atom is located at 0rs = [0.2 2 2.48]T (Å). Similar to the pushing mode,the probe is dragged to move in the positive X-direction, the distance between the sample atom Xe and theprobe as well as the position of the Xe is shown in Fig. 6. Moreover, the corresponding force exerting at the


Fig. 4. Distance between Xe and probe and position of Xe in pushing mode.

Fig. 5. Exerting force at the sample atom in pushing mode.

Fig. 6. Distance between Xe and probe and position of Xe in pulling mode.

sample atom Xe is plotted in Fig. 7. The results show that an attractive force is first generated, and then theexerting force becomes the repulsive force at t = 0.024 sec.

In comparison of the manipulation results for the pushing mode and pulling mode, the maximum deviation


Fig. 7. Exerting force at the sample atom in pulling mode.

in the y axis for the pushing mode is ∆rsy = 11 (Å), being larger than the maximum y-component deviationby the pushing mode, i.e. ∆rsy = 5 (Å). Moreover, the simulatied results can be validated as compared to[18].

6. CONCLUSIONS

In this paper, an interactive virtual environment for nanomanipulation has been developed. The objectiveis to interface MD and nanomanipulation computations with real-time truly VR simulations such that thevisualization of the manipulated nanoparticle can be rendered through the computer screen. Furthermore,the simulation results are investigated and discussed by the non-contact pushing mode and pulling mode.

The ability to interact with computer-generated objects in the same manner that one would interact withreal objects allows for the nanoeducation, nanomanipulation training, repair or modification simulation usingthe single-tip nanomanipulation on structures built by other means. In the next step, the interface to a realSPM will be integrated to present the visualization of the physical nanomanipulation.

ACKNOWLEDGEMENT

This work was supported by the National Science Council of the ROC under grant No. NSC 100-2221-E-003-030.

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