University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Nanopore...

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)


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


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


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


Limitations of Continuum Theory


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


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

qq

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


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


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


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


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)


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)


Modified 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


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

)


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


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)


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


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


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


Nanopore Sensors Using Carbon Nanotubes

Sony Joseph

Karl HessN. R. Aluru

Thanks to: Jay Mashl & Eric Jakobsson with help on Gromacs


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


Nature 414, 188 - 190 (2001) Our Simulations

Occupancy of Water in SWCNT


(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


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


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


Occupancy much higher in the presence of electric field even without partial charges

CNT + Artificial Membrane: E = 0.15, No Charge


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


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


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

University of Illinois at Urbana-Champaign Beckman Institute Computational MEMS/NEMS Nanopore...

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