University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Nanopore Sensors Using Silicon and Carbon Nanotube Channels
Topics:
Silicon nanopores (Graduate Student: Rui Qiao)
Carbon nanotubes (Graduate Student: Sony Joseph)
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Silicon Nanopores
Objective: Develop nanopore sensors using bio-mimetics (fabrication of 1 nm channels is now possible)
Tasks Understand fluid flow through nanodiameter silicon
channels – pressure as well as electrically mediated fluid flow
Understand ion concentrations and their interaction with fluid flow
Attach binding sites to channel walls and investigate fluid flow, ion concentrations etc.
Develop nanopore sensors by attaching various binding sites (control charge on the surface of the wall) and mimic biological principles
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Silicon Nanopores: Accomplishments last 6 Months
Predicted ion concentrations using channels widths ranging from 1-10 nm
Predicted fluid flow (specifically velocity profiles) for simple LJ fluids, water and water under electric field
Developed enhanced continuum theories Developed multiscale methods to efficiently capture near-wall
non-continuum behavior
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Electroosmotic Flow: Mathematical Theory
02
0u
Epu E2
0u
E1
p1
uuu E2
Poisson-Boltzmann equation
Laplace equation
Stokes model
Navier-Stokes model
E
/czi
ii2 )
RT
Fzexp(
ze
Tkc i
2i
22D
Bi
i
2i
2i,0
BD zec
Tk
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
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 <111> direction, and only the outmost layer is charged
Force calculation Lennard-Jones interaction, electrostatic interaction and external electrical field
66
1212
LJ r
c
r
cU
ij
jiElec r
4
1U
ii qEF
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
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:
• 4.87nm4.43nm3.487nm
Wall charge density
• 0.12C/m2
Number of molecules:
• 2246 water molecules
• 32 Cl- ions
• 1288 Si atoms
E
Si <111> surface (4 layers)
x
yz
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Simulation Results
Water density profile across the channel
Channel width: 3.487nmSurface charge density: +0.12C/m2 (i.e.,0.1e/wall atom)External field: 0.55V/nm
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Ion Distribution: moderate surface charge density
Channel width: 3.487nmSurface charge density: +0.12C/m2 (0.1e/wall atom, uniform charge distribution)System: water molecules (2246) and Cl- ions(32)
Cl- concentration profile across the channel (=+0.12C/m2)
Correlation between Cl- concentration and water density
profile across the channel
0
5
10
15
20
25
30
0 0.5 1 1.5 2 2.5 3
position (nm)
Cl c
oncentr
atio
n (
mol/l
)
0
30
60
90
120
150
180
Wate
r concentr
atio
n (
mol/l
)
Cl
Water
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Ion Distribution: Electrolyte (positively charged wall)
Channel width: 3.487nmSurface charge density: +0.12C/m2 (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)
Con
cent
rati
on (
mol
/l)
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: 3.487nmSurface charge density: -0.12C/m2 (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)
Con
cent
rati
on (
mol
/l)
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Modified Poisson-Boltzmann Equation
Poisson-Boltzmann equation
/czi
i,0i2 Poisson Equation
At equilibrium, chemical potential of an ion must be uniform in the entire channel: i i B i B 0 ,iz e k T log c k T log c
Boltzmann distribution )RT
zFexp(cc i,0i
(Only electrostatic interaction is considered)
To account for wall efects, we introduce an excess chemical potential ex:
i i B i ex ,i B 0 ,iz e k T log c k T log c
)RT
exp()RT
zFexp(cc ex
i,0i
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
W = 2.22nm = 0.12C/m2 Extract ex
Apply ex
to a
wider c
hann
el
W = 3.49nm =
0.12C/m2
Water density profile
Modified Poisson-Boltzmann Equation: ResultsC
once
ntra
tion
(m
ol/l
)
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
EOflow: Counter Ion only (W=3.487nm)
Channel width: 3.487nmFluid: water (2286) and Cl- ions (32)Wall charge density: +0.12C/m2
External electrical field: 0.55V/nmDebye length: 1.10nm (c0 0.15M)
Velocity profile across the channel
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Channel width: 3.487nmFluid: water (2186), Na+ (62) and Cl- (30) ionsWall charge density: -0.12C/m2
External electrical field: 0.55V/nmDebye length: 0.31nm (c0 1.1M)
Velocity profile across the channel
EOflow: Electrolyte (W=3.487nm)
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Multiscale Approach
MD Region
MD Region
Continuum Region
Alternative Approach Do MD on a fine scale Embed MD data into coarse scale continuum simulation
W2
W
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
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
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Nanopore Sensors Using Carbon Nanotubes
Sony Joseph
Karl HessN. R. Aluru
Thanks to: Jay Mashl & Eric Jakobsson with help on Gromacs
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Figure from Mashl/Jakobsson
Ion Channel Based Nanopore Sensors
Single molecule detection Power of protein engineering Current flow changed by binding Frequency reveals concentration Amplitude reveals identity Durable only in lab setting
Biomimetics: Functionality of ion channels into nanopores (CNTs)
Ideal for IC based chips
Fundamental issues: Transport of water, electrolytes and analytes through CNT
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Nature 414, 188 - 190 (2001) Our Simulations
Occupancy of Water in SWCNT
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
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
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
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
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
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
University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS
Summary Silicon and CNT based nanopore sensors can be designed with
fundamental understanding of nanofluidics, ion channel and other principles
Continuum theories are questionable for channel diameters smaller than 4 fluid diameters
Enhanced continuum theories and multiscale methods will be critical for design of nanopore sensors and other devices