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Molecular Mechanics and Molecular DynamicsAnalysis of Drexler-Merkle Gears and Neon Pump

by
T. Cagin1*, A. Jaramillo-Botero2, G. Gao1, and W. A. Goddard, III1
1California Institute of Technology, MSC, BI, Pasadena, CA, U.S.
2Pontificia Universidad Javeriana, Cali, Colombia (Visiting Associate, MSC).
tahir@wag.caltech.edu, ajaramil@wag.caltech.edu,
gao@wag.caltech.edu, wag@wag.caltech.edu

This is a paper of a talk given at the Fifth Foresight Conference on Molecular Nanotechnology.
It has been submitted for publication in the special Conference issue of Nanotechnology.


Abstract

Over the past two years at the Materials and Process Simulation Center, we have been developing simulation approaches for studying the molecular nanomachine designs pioneered by Drexler and Merkle. These nanomachine designs, such as planetary gears and neon pump are described with atomistic details and involves up to 10000 atoms.

With the Dreiding and Universal Force Fields, we have optimized the structures of the two Planetary Gear design and Neon Pump. At the Fourth Foresight conference, we reported rotational impulse dynamics studies of the first and second generation designs of Planetary Gears undergoing very high frequency rotational motions. We will explore stability of these designs in the lower frequency regimes which require long time simulations. We will report the molecular mechanics and molecular dynamics simulations performed on these model systems. We explore the following modes in these studies:

   1.Impulse mode
   2.Constant angular velocity -Perpetual rotation -
   3.Constant torque -Acceleration from rest-

Introduction

In order to lay a foundation for creating a technology for manufacturing at the nanoscale level, Eric Drexler, Ralph Merkle, and collaborators1-3 have been analyzing designs for mechanical systems at the nanoscale (1 to 100 nm) that could in principle be manufactured.  We discuss herein some of the design optimization, and dynamics simulations, performed on these devices along with their corresponding results and analysis.

Nanoscale Machines

At the nanoscale one can no longer think of the material as a continuum whose properties change continuously as it is cut and shaped. Rather one has to consider that it is formed from discrete atoms. Thus at the nanoscale one has a supermolecule rather than a finely divided solid. This requires one to analyze how the elements of normal macromaterials design change as the scale is reduced from mm to micron to nanometers. The differences are dramatic. For a macrosystem a long alkane molecule or a flake of MoS2 might serve as a lubricant, but for a system built on the scale of nm, such molecules may act as dirt that would clog and disable the nanosystem. Similarly the scaling of vibrations, electrical forces, thermal expansion, magnetic interactions, and surface tension with size can lead to phenomena very different at the scale of atoms than at the macroscale.  Indeed in Nanosystems2, Drexler considered many aspects of how the scaling of familiar macroscopic concepts changes as one goes to the nanoscale.

In order to make progress here it is necessary to consider specific nanoscale supermolecular systems which could in principle be manufactured.  Without worrying about the practical aspects of synthesizing the system, can one make supermolecular assemblies that would function as useful nanoscale machines? Can one design synthetic procedures that could in principle manufacture these machines?  Again it is not essential to have a practical cost-effective design. It is sufficient to demonstrate the existence theorem, that sequences of steps involving real atoms with the properties of real molecules can indeed lead to processes that would manufacture nanoscale machines with useful functionality.  If the goal is achievable, then we can focus on ways to achieve the design in a practical fashion.

"Our ability to model molecular machines (systems and devices) - of specific kinds, designed in part for ease of modeling - has far outrun our ability to make them.  Design calculations and computational experiments enable the theoretical study of these devices, independent of the technologies needed to implement them." 2

Planetary Gear

 
Figure 1.  1st generation Planetary Gear (lateral and top views)

Number of atoms: 3557
Molecular Weight: 51009.8439813
Molecular Volume: 33458.272

Along these lines Merkle and Drexler3 have designed a nanoscale planetary gear with eight moving parts (see Fig. 1) using molecular mechanics force fields such as DREIDING4 to ensure that the bond lengths, bond angles, van der Waals distances, and strain energies are reasonable.  Based on their design we carried out and reported at the 1995 Nanotechnology conferences a molecular dynamics simulation to test the properties of this gear 5. Using somewhat extreme conditions (rapid accelerations and high frequency rotations), we found significant instabilities in this design. In response Merkle and Drexler 6improved their designs (see Fig. 2) to achieve much more stable motions.
 
 

Figure 2. 2nd generation Planetary Gear (lateral and top views)

Number of atoms: 4235
Exact Molecular Weight: 72491.9465915
Molecular Volume: 47585.964
 

Observed Results

We find that this new design is more stable; however, it also has too much slip.  That is the actual distances between the atoms for the specific set of atoms in this supermolecular system leads to spacings between the gear teeth and the opposing gear faces that are easily stripped. The problem is that a careful balance must be achieved between: It is possible to balance these in the static system, but the dynamical motions lead to fluctuations (vibrations) that allow slippage.  This is not a calamity and does not mean that nanotechnology will not work. It means that we have a lot of hard work to do in designing prototype systems and testing them.

The problem here is the discreteness of the atoms. A macroscopic system is treated as a continuum. To make a gear one can design the shape of the gear teeth and the shape of the opposing teeth of the face to have exactly the same spacing as the gears turn. It is then only necessary to design the casting or injection molding system with appropriate tolerances to achieve good performance. The discreteness of the atoms plays no role when these tolerances are 0.0001 inch = 2.54 10-3 urn.

Neon Pump

 
 
Figure 3a.  Complete Neon Pump. 
 
Figure 3b. Helical rotor.
Figure 3. Neon Pump design
 

Number of atoms: 6165
Molecular Weight: 88190.8126747
Molecular Volume: 63984.232

More recently Drexler and Merkle3 have designed a nanomachine (Fig. 3) which in one mode could serve as a pump for Ne and in another could serve to convert Ne pressure to rotary power. We investigate this system using accurate force fields and molecular dynamics simulations to test and refine the concepts.

Static analysis

The initial tests performed on the Neon Pump involve a 0 K simulation, using the Universal Force Fields (UFF) 7, and partial charges obtained from Gasteiger method, to establish the effect of rotor-casing, rotor-casing-Ne interactions.  The following test where performed;
   In a sense, we can consider these simulations as being two rigid body (rotor-casing) and multiple body (rotor-casing-Ne atoms).
 

Figure 4. Energy curve during 360o rotation shows helix interactions and slight rotor deformation after minimization of structure (no Ne) (gif file 5.6K)
 
Figure 5. Force levels during the rotation shows magnitude of forces required to set the system in motion through an externally applied force directly on rotor or by indirect forces induced by high pressure (no Ne) (gif file 7.7K) 
 
Gif movie set up by: MCOO
Figure 6. Actual Trajectory of Neon atoms (blue: 28) during pumping action
 Figure 7. Results of 3.4 revolution with 28 Ne atoms in pump chamber: a) total energy (gif file 8.8K), b) maximum forces (gif file 8.4K), c) RMS forces (gif file 8.8K)
 

Simulation shows a total of 245 rotation steps (5o each), for a total of 3.4 revolutions.  Results clearly show higher energy due to Ne-Ne/Ne-rotor/Ne-casing interactions during their travel through the helix.  The number of Ne inside the helix chamber reduces as the rotations step axis increases.  Energy becomes negative since only Ne atoms are considered.

The ground rules here are that a realistic FF be used and that all pieces be treated at the atomic level (but some might
be semi-rigid). This will use the FF developed for nanosynthesis.  Also we want to consider the effect of energy release in the chemical steps on the thermal fluctuations in these systems (which may cause displacements and vibrations).

Molecular Dynamics Simulations using Rotational Impulse Dynamics

The MD simulation initiated by a rotational impulse to the input unit. In the course of simulation this angular momentum is slowly transferred to the output unit.

Over 12.0 picoseconds simulation, the input unit completes one full cycle and the output unit completes almost a half cycle and the rail completes a quarter cycle. Over the run the initial angular kinetic energy partially dissipates through conversion into thermal energy via atomic collisions.

We imagine that the eventual design would have the functionality of a planetary gear but might have an appearance completely different than the macroscopic systems. Thus because a gear tooth in the xy plane cannot be atomically smooth in the z direction, we may develop a Vee design so that the Vee shape of the gear tooth in the z direction nestles within a Vee notch in the race to keep stability in the z direction as the teeth contact in the xy plane. This design would make no sense for a macroscopic gear system since the gear could never be placed inside the race. However for a molecular system one could imagine that the gear is constructed and that the race is constructed all except for a last joining unit. The parts could be assembled and then the final connections on the face made to complete the design.

The preliminary tests performed on the Neon pump demonstrate an appropriate functional behavior.  The structural deformations of the rotor can cause instabilities at low and high rotational frecuencies.  The forced translations show that at very low perpendicular forces due to pump action total energy rises significantly and again the structure deforms.

Control of Power Input for NanoGears and Pumps

For all three devices we study, the driver unit is a rotary component. In order to mimic operational conditions, we designed various power input profiles to drive the devices. Under such conditions these devices are not represented by thermodynamic equilibrium, but rather they are driven systems represented as in steady state thermodynamic systems.

The modes of input power profiles we used are:

1.Impulse mode: A rotational angular velocity is applied to the input unit at t=0.

2.Constant angular velocity: The input unit is maintained at a constant rate of rotation about the chosen axis. Unless a heat sink is supplied (Nose-Hoover thermostat or Gaussian isokinetic thermostat, or Langevin Bath) the model system heats up, and it is driven away from the steady thermodynamic state.

3.Time dependent angular velocity: The input unit is driven by a time dependent angular velocity. The functional forms for time dependence should be bounded functions, especially periodic functions, sine, saw tooth, etc. This mode of operation must also be maintained at steady state by an heat bath

4.Constant torque - Acceleration from rest.This is especially important to simulate the early stages of the operation. Where a constant angular acceleration rate starts system from rest.

5. Time dependent angular acceleration mode. This mode is similar to that of time dependent angular velocity profile imposed on the input unit. Especially periodic functions for input torque has the system to remain within stability limits.

We have implemented these driving modes into Cerius2 program environment8 using the Software Developers Kit9 version 3.0. The module utilizes graphics, communication, user interface and data model subsystems of Cerius2. In this implementation, user may choose any one of the energy and force evaluators. It can either be the Cerius2 Open Force Field module or an independent energy and force evaluator (user developed). In our computations we used the Cerius2 OFF module. This development is an attempt to supply a nanomachine specific simulation module10 which could be used by various nanotechnologist, Figure 8.

Figure 8. Cerius2 Graphical User Interface to nanomachine simulator.
a. Impulse Setup (jpg 15K)
b. Dynamics (jpg 25K)
c. Run Simulation Panel (jpg 40K)

Dynamics Simulation of Gears and Neon Pump are performed at various input conditions: Constant angular velocity and constant angular acceleration for both gear designs and neon pump. We have also utilized sinusoidal driving conditions:

W(t)=Wo sin (wt)

W can either be angular velocity or angular acceleration, w is the frequency of the power source. We especially investigated the temperature profile as a function of time. To see if the sytem is driven too far from equilibrium we turned off the temperature control (Under these conditions a power source exists, but no sink mechanism is turned on.) The time variation of the kinetic temperature of various systems and driving conditions are given in the following figures.


  Figure 9. Kinetic Temperature vs different driving conditions.
9a) Kinetic Temperature of Generation 1 Planetary Gear driven by constant initial angular velocity. Initial 2000 iterations kinetic energy maintained at a constant value.
9b) Kinetic Temperature of Generation 2 Planetary Gear driven by constant angular velocity. Initial 2000 iterations kinetic energy maintained at a constant value.
9c) Kinetic Temperature of Generation 2 Planetary Gear driven by a sine wave angular velocity. Initial 2000 iterations kinetic energy maintained at a constant value.
9d) Cold Start with a sinusoidal driving torque applied.

Concluding Remarks

Of course, we know that nanoscale machines are possible. Nature has figured out methods of synthesizing quite remarkable nanoscale machines that function reliably, are synthesized cheaply and reliably (often self correcting) from readily available materials and energy sources, and are environmentally benign (biodegradable).  Indeed modern science is finding ways to manipulate these systems to manufacture modified molecules and systems with predesigned properties and functionalities. However, the complex chemistry and biology involved in such systems limits the applications and flexibility to modify these systems for dramatically different applications. Thus it is important to determine the feasibility of designing and making nanoscale machines with new functionality and characteristics.

References

  1. K.E, Drexler, Engines of Creation, 1986
  2. K. E. Drexler, Nanosystems: Molecular Machinery, Manufacturing, and Computation, 1992
  3. K. E. Drexler and R. Merkle, First generation planetary gear
  4. B. D. Olafson, and W. A.Goddard III, J. Phys. Chem. 94, 8897 (1990), DREIDING: A Generic Force Field for Molecular Simulations, S. L. Mayo,
  5. G. Gao, T. Cagin, W. A. Goddard III, "MD Simulation of the Drexler-Merkle Nanoscale Planetary Gear". to be  published. Presented by WAG at the 1995 Nanotechnology Conference sponsored by the Foresight Institute, Oct. 1995.
  6. K. E. Drexler and R. Merkle, Second generation planetary gear. Presented at the 1995 Nanotechnology Conference sponsored by the Foresight Institute, Oct. 1995.
  7. A.K. Rappe, C.J. Casewit, K.S. Colwell, W.A. Goddard-III, W.M.Skiff.  J. Am. Chem. Soc, 1992, 114,10024-10035
  8. Cerius2 Program, Molecular Simulations Incorporated, San Diego, CA.
  9. Software Developers Kit, Version 3.0, Molecular Simulations Incorporated, 1997.
  10. Tahir Cagin, NanoSim: A Nanomachine Simulation Program, 1997. This is a nanosystem simulation program interfaced to Cerius2 program environment using Software Developers Kit.

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