1. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Nanopore Sensors Using Silicon and Carbon Nanotube Channels Topics: Ê Silicon nanopores (Graduate Student: Rui Qiao) Ë Carbon nanotubes (Graduate Student: Sony Joseph)

2. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Silicon Nanopores èObjective: Develop nanopore sensors using bio-mimetics (fabrication of 1 nm channels is now possible) èTasks 4Understand fluid flow through nanodiameter silicon channels – pressure as well as electrically mediated fluid flow 4Understand ion concentrations and their interaction with fluid flow rAttach binding sites to channel walls and investigate fluid flow, ion concentrations etc. rDevelop nanopore sensors by attaching various binding sites (control charge on the surface of the wall) and mimic biological principles

3. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Silicon Nanopores: Accomplishments last 6 Months èPredicted ion concentrations using channels widths ranging from 1-10 nm èPredicted fluid flow (specifically velocity profiles) for simple LJ fluids, water and water under electric field èDeveloped enhanced continuum theories èDeveloped multiscale methods to efficiently capture near-wall non-continuum behavior

4. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Electroosmotic Flow: Mathematical Theory  Poisson-Boltzmann equation  Laplace equation  Stokes model  Navier-Stokes model

5. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Limitations of Continuum Theory  Poisson-Boltzmann equation  Navier-Stokes model  Ions are assumed to be infinitesimal  Accounts for only ion-ion electrostatic interactions in a mean-field fashion  Ion - fluid (water) interactions neglected  Ion - Wall interactions neglected  Surface charge is assumed to be continuous State variables (e.g., density) do not vary significantly over intermolecular distance Accounts for only fluid-fluid interactions (fluid-Wall interactions neglected) Assumes non-slip boundary conditions Assumes that viscosity depends on local properties (e.g., density) and can be described by a local and linear constitutive relation

6. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS MD Simulation: Details  Models Water: SPC/E model, i.e., water molecule is rigid, hydrogen and oxygen are point charges (O: -0.848e, H: +0.424e) Ions (Na + and Cl - ): modeled as point charge + Lennard-Jones atom Wall: each wall is made of four layers of Silicon atoms oriented in the direction, and only the outmost layer is charged  Force calculation  Lennard-Jones interaction, electrostatic interaction and external electrical field  Updating configuration  Time step ranges from 1.0 to 2.0fs  Temperature of system is regulated to 300K by Berendsen thermostat  Wall atoms are frozen to their original position throughout the simulation  Data analysis Binning method

7. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Simulation system +++++ +++++ +++ +++ + Positively charged Si atom Cl- ion Water molecule Channel system simulated Typical simulation Channel dimensions: 4.87nm  4.43nm  3.487nm Wall charge density 0.12C/m 2 Number of molecules: 2246 water molecules 32 Cl - ions 1288 Si atoms E Si surface (4 layers) x y z

8. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Simulation Results Water density profile across the channel Channel width: 3.487nm Surface charge density:+0.12C/m 2 (i.e.,0.1e/wall atom) External field:0.55V/nm

9. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Ion Distribution: moderate surface charge density Channel width: 3.487nm Surface charge density:+0.12C/m 2 (0.1e/wall atom, uniform charge distribution ) System: water molecules (2246) and Cl - ions(32) Cl - concentration profile across the channel (  =+0.12C/m 2 ) Correlation between Cl - concentration and water density profile across the channel

10. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Ion Distribution: Electrolyte (positively charged wall) Channel width: 3.487nm Surface charge density:+0.12C/m 2 (0.1e/wall atom, uniform charge distribution ) System:water molecules (2186), Na + (30) and Cl - ions (62) Na + and Cl - concentration profile across the channel (positively charged wall) Water concentration profile across the channel (positively charged wall) Concentration (mol/l)

11. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Ion Distribution: Electrolyte (negatively charged wall) Na + and Cl - concentration profile across the channel (negatively charged wall) Channel width: 3.487nm Surface charge density:-0.12C/m 2 (0.1e/wall atom, uniform charge distribution ) System:water molecule (2186), Na + (62) and Cl - ion (30) Water concentration profile across the channel (negatively charged wall) Concentration (mol/l)

12. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Modified Poisson-Boltzmann Equation  Poisson-Boltzmann equation Poisson Equation At equilibrium, chemical potential of an ion must be uniform in the entire channel: Boltzmann distribution (Only electrostatic interaction is considered) To account for wall efects, we introduce an excess chemical potential  ex :

13. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS W = 2.22nm  = 0.12C/m 2 Extract  ex Apply  ex to a wider channel W = 3.49nm  = 0.12C/m 2 Water density profile Modified Poisson-Boltzmann Equation: Results Concentration (mol/l)

14. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS EOflow: Counter Ion only (W=3.487nm) Channel width: 3.487nm Fluid:water (2286) and Cl - ions (32) Wall charge density: +0.12C/m 2 External electrical field:0.55V/nm Debye length:  1.10nm (c 0  0.15M) Velocity profile across the channel 

15. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Channel width: 3.487nm Fluid:water (2186), Na + (62) and Cl - (30) ions Wall charge density: -0.12C/m 2 External electrical field:0.55V/nm Debye length:  0.31nm (c 0  1.1M) Velocity profile across the channel EOflow: Electrolyte (W=3.487nm) 

16. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Multiscale Approach MD Region   Continuum Region  Alternative Approach  Do MD on a fine scale  Embed MD data into coarse scale continuum simulation   

17. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Velocity profile in a 3.487 nm channel Embedding MD Data into Continuum Models Embedding MD velocity (from 2.216nm) near channel wall into simulation of larger channels Velocity profile in a 6.00 nm channel

18. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Remarks Finite size of ion, ion-water and ion-wall interactions are important factors influencing the ion distribution. The classical Poisson- Boltzmann equation is modified to consider such effects. Preliminary results on ion distribution are encouraging MD simulations of Poiseuille flow of Lennard-Jones fluids and water indicate that continuum fluid theory is observed for flow in channels of about 11 diameters of fluid molecules though the density fluctuates significantly over intermolecular distance Significant deviation from continuum behavior occurs when channel width is reduced to about 4 fluid molecule diameters MD simulations of EOflow indicate that continuum flow theory can be used to analyze EOflow in channels as small as 2.216nm provided viscosity variation is considered in continuum theory Deviation of electroosmotic flow behavior from continuum theory is observed in a 0.951nm channel

19. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Nanopore Sensors Using Carbon Nanotubes Sony Joseph Karl Hess N. R. Aluru Thanks to: Jay Mashl & Eric Jakobsson with help on Gromacs

20. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Figure from Mashl/Jakobsson Ion Channel Based Nanopore Sensors rSingle molecule detection rPower of protein engineering rCurrent flow changed by binding rFrequency reveals concentration rAmplitude reveals identity rDurable only in lab setting rBiomimetics: Functionality of ion channels into nanopores (CNTs) rIdeal for IC based chips rFundamental issues: Transport of water, electrolytes and analytes through CNT

21. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Nature 414, 188 - 190 (2001) Our Simulations Occupancy of Water in SWCNT

22. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS (Top) Occupancy of ions in a SWCNT 13.4 A long 21.7 A Dia. Fixed in a 1.85 M KCl (Bottom) Axial field E=0.015 V/nm and partial charges of 0.38e on the rim atoms. In the presence of external electric field and partial charges ions enter much more easily Occupancy of Ions in SWCNT CL- ion K+ ion +0.38e C atom -0.38e C atom Neutral C atom

23. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS  Artificial membrane mimics the lipid bilayer. (eg. Si nanopore)  40 A long, 21.96 A dia (16,16) tube, in a slab 51Ax53Ax39A  Slab is fixed but the tube, ions and water is free to move  Observed Ion diffusion higher than without slab CNT in an Artificial Membrane

24. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS  No external field, 1.5 M KCl  21.696 A dia, 40 A long  Without external electric field, ion occupancy inside the tube is observed to reduce drastically going to almost none in equilibrium. CNT + Artificial Membrane: E = 0, No Charge

25. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS  Occupancy much higher in the presence of electric field even without partial charges CNT + Artificial Membrane: E = 0.15, No Charge

26. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS   Observation: Cl- current much greater than K+ current.  Electrostatic interaction between oppositely charged groups NH3+ and Cl and COO- and K+ makes the ions to remain at the entrance of the tube. Functional Group Attachment: E = -0.15 V/nm

27. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS  K+ occupancy is very low  This is because the interaction energy between COO- and K+ is very high leading to binding. Only a very high electric field can break the potential barrier at the mouth. Functional Group Attachment: E = 0.15 V/nm

28. University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Summary èSilicon and CNT based nanopore sensors can be designed with fundamental understanding of nanofluidics, ion channel and other principles èContinuum theories are questionable for channel diameters smaller than 4 fluid diameters èEnhanced continuum theories and multiscale methods will be critical for design of nanopore sensors and other devices