1. Validity of Molecular Dynamics by Quantum Mechanics
Thomas Prevenslik
QED Radiations
Discovery Bay, Hong Kong
Enter speaker notes here. 1
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

2. Introduction
Molecular Dynamics MD is commonly used to simulate heat transfer at the nanoscale in the belief: Atomistic response using L-J potentials (ab initio) is more accurate than macroscopic finite element FE programs, e.g., ANSYS, COMSOL, etc. In this talk, I show: FE gives equivalent heat transfer to MD, but both are invalid at the nanoscale by quantum mechanics QM And present: Invalid and valid MD solutions by QM 2
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

3. MD and FE Restrictions
MD and FE are restricted by statistical mechanics SM to atoms having thermal heat capacity 3
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

4. MD is therefore valid for bulk PBC simulations
Validity
Historically, MD simulations of the bulk performed under periodic boundary conditions PBC assume atoms have heat capacity
In the macroscopic bulk being simulated, all atoms do indeed have heat capacity
MD is therefore valid for bulk PBC simulations 4
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

5. Problem
Today, MD is not used for bulk simulations, but rather for the atomistic response of discrete nanostructures Problem is MD programs based on SM assume the atom has heat capacity that is the cause of the unphysical results, e.g., Conductivity in Thin films depends on thickness Nanofluids violate mixing rules, etc Why is this so? 5
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

6. Heat Capacity of the Atom
SM, MD and FE (kT > 0)
kT eV QM
(kT = 0)
Nanostructures
For nanostructures, solutions by SM, MD, and FE are invalid by QM 6
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

7. Conservation of Energy
Lack of heat capacity by QM precludes EM energy conservation in discrete nanostructures by an increase in temperature, but how does conservation proceed?
Proposal
Absorbed EM energy is conserved by creating QED induced excitons (holon and electron pairs) at the TIR resonant frequency of the nanostructure.
QED = Quantum Electrodynamics
TIR = Total Internal Reflection
EM = Electromagnetic
Upon recombination, the excitons emit EM radiation that charges the nanostructure or is lost to the surroundings. 7
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

8. TIR Confinement
In 1870, Tyndall showed photons are confined by TIR in the surface of a body if the refractive index of the body is greater than that of the surroundings. Why relevant? NWs have high surface to volume ratio. Absorbed EM energy is concentrated almost totally in the NW surface that coincides with the mode of the TIR photon. Under TIR confinement, QED induces the absorbed EM energy to simultaneously create excitons f = (c/n)/  = 2D E = hf 8
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

9. QED Heat Transfer EM Q abs − Q Excitons = Q cond
Charge EM
radiation
Q abs − Q Excitons = Q cond
QED Excitons = EM radiation + Charge
Conservation by QED Excitons is very rapid
Qabs is conserved before thermalization after which phonons can respond
Q abs = Q Exciton𝑠
No thermal conduction
Q cond  0
Fourier solutions are meaningless
Conductivity remains at bulk
Excitons
Q abs
Phonons
Qcond 9
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

10. MD - Discrete and PBC
Akimov, et al. “Molecular Dynamics of Surface-Moving Thermally Driven Nanocars,”
J. Chem. Theory Comput. 4, 652 (2008).
Sarkar et al., “Molecular dynamics simulation of effective thermal conductivity and study of enhance thermal transport in nanofluids,”
J. Appl. Phys, 102, (2007).
MD for Discrete  kT = 0, But MD assumes kT > 0
Car distorts but does not move
Macroscopic analogy,
FE = MD
Classical Physics does not work
QM differs
No increase in car temperature
Charge is produced by excitons
Cars move by electrostatic interaction
MD for kT > 0 is valid for PBC because atoms in macroscopic nanofluid have kT > 0 10
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

11. T. Prevenslik, “Nanowire Stiffening by Quantum Mechanics ,
MD - NW in Tensile Test L w F
T. Prevenslik, “Nanowire Stiffening by Quantum Mechanics ,
MNHTM , Hong Kong, Dec , 2013
Silver 38 nm NWs x 1,5 micron long were modeled in a smaller size comprising 550 atoms in the FCC configuration with at an atomic spacing of 4.09 Ȧ The NW sides w = 8.18 Ȧ and length L = 87.9 Ȧ. 11
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

12. MD - NW in Tensile Test
To obtain valid MD solutions, the Coulomb force Fij between atoms is modified by the ratio  of thermal energy UkT of the atom to the electrostatic energy UES from the QED induced charge by the excitons.
𝐹 𝑖𝑗 = e 2 4  𝑜 𝑅 𝑖𝑗 2
𝑈 𝑘𝑇 = 3 2 𝑘 𝑇 𝑔𝑟𝑖𝑝
𝑈 𝐸𝑆 = 3 𝑒  𝑜 𝑅 𝑎𝑡𝑜𝑚
= 𝑈 𝑘𝑇 𝑈 𝐸𝑆 = 10  𝑜 𝑘 𝑅 𝑎𝑡𝑜𝑚 𝑇 𝑔𝑟𝑖𝑝 𝑒 2 12
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

13. MD - NW in Uniaxial Tension13
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

14. MD – NW in Triaxial Tension14
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

15. MD- NW Summary
MD solutions valid by QM require the thermal energy of the heating in the tensile test otherwise conserved in classical physics by an increase in temperature to be converted to Coulomb repulsion
For the 8 Ȧ square silver NW, only about 15 % of the thermal kT absorbed by the grips of the tensile test stiffen the NW, the remaining 85% lost to surroundings.
The MD simulation gave the uniaxial Young’s modulus Yo ~ 17 x 106 psi, In the triaxial stress state, Young’s modulus of the NW is Y ~ 31x106 psi. The stiffening enhancement is Y/Yo ~ 1.88.
Strain hardening induces mechanical heating in the NW, but was excluded from the MD simulation.
The 8 Ȧ square NW was simulated for 550 atoms with a PC. Actual NW having diameters of 34 nm require ~ atoms and far larger computation resources. 15
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

16. Conclusions
MD based on SM assuming atoms have kT energy is valid for PBC
MD and FE provide equivalent heat transfer simulations of discrete nanostructures, but both are invalid by QM and give unphysical results
QM negates SM and thermal conduction at the nanoscale
Valid MD of discrete nanostructures requires conservation of absorbed EM energy by the creation of excitons (holon and electron pairs) otherwise conserved in classical physics by increases in temperature. 16
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013

17. Questions & Papers
Enter speaker notes here. 17
ASME 4th Micro/Nanoscale Heat Transfer Conf. (MNHMT-13), Hong Kong, Dec , 2013