Current Rectification of a Single Charged Conical nanopore Qi Liu, Peking University Mentor: Prof. Qi Ouyang and Yugangwang
Biological Nanopores Biological ion channels are the principal nanodevices mediating the communication of a cell with other cells via ion transport, and enable the functioning of a living organism. (ion selectivity, Preferential direction of ion flow (current rectification)) Usage in nanotechnology: as biosensors to detect a single biomolecule, such as protein and DNA. Fragile; Fixed size; Complex; Experiments are difficult (patch clamp technique).
Synthetic Nanopores Robust; Flexible in dimension; much more simple to study; experiments are easy to design. Make it possible to Design Biosensors (High speed DNA sequencing). Would it be possible to observe similar transport properties? Recent experiments indicate that the answer is positive. (such as current rectification, ion selectivity). Therefore, we hope to have a full understanding of ion transport properties of these nanopores. A single Conical nanopore on Polyetheylene terephthalate (PET) membrane.
How to make a single conical nanopore on PET membrane. a. Irradiation of the film with swift heavy ions to make a damaged ion track. b. Chemical etching along the damaged ion track
Why Current Rectify? Typical size of the pore: L=12 µm; r b =400nm Adv. Funct. Mater. 2006, 16, 735 746 Experiment study shows: (KCl) r t =3nm a. Surface charge play a vital important role b. R t should not be too large. <20nm
Building a model Under such a dimension, does the classical equations for macro systems still work? As predicted by Richard Feynmann, when objects have dimensions on the nanometer scale, one should be prepared to observe new effects that cannot be explained by classical physics. We do observe new effects that macro pore does not have, but whether there are new physics?! The diameter of the tip is about 10 nm, so we expect the classical equations could still work.
Rachet Model ------a Qualitative model Debye potential It is unconvincing, and the mechanism is not clear. Also, we want a quantitative model.
Our model based on PNP Equations 1. Possion Equation that electrostatic potential should obey: 2. Nernst-Planck equation that governs the ion flux: 3. Steady state continuity constraint: We expect these equations can explain the current rectification effect. Then the rest of our work is to do the calculations.
Difficulties. The combined nonlinear equations are difficult to converge. 1. L(~12000nm) >>r t (~5nm) 2. High surface charged density sharp potential gradient. 3. Combined nonlinear euqaitons Our major work it try to make the numerical solution possible
tactics Finite element method Decompose these equations to two part. 1. Complex equations+ simple boundary conditions 2. Simple equations+ complex boundary conditions Nonlinear term was especially treated.
Details A. Static Boltzman Distribution simplify to one equation+ difficult boundary conditions B. Equations are complex, but the boundary conditions are quite simple. Nonlinearity stem from, multiple, and gradually increase it from 0 to 1
Our results from PNP Eqs. 1. Current Rectification effect. 2. Good agreement with experiment. 3. Slightly adjust parameters would improve the agreement, but this might be meaningless because of the uncertainties in taking parameters, such as surface charge density, the radius of conical nanopore, etc.. 4. PNP equations can essentially be used to study the ion transport properties in a nanopore with such a dimension. r t =3nm, r b =220nm, L=12µm
What results in current rectification --ion enrichment and ion depletion effect Figure: Ion distribution along the axis of the nanopore. Strong ion enrichment and ion depletion effect!!!!! a. Positive voltage bias ion depletion low conductivity b. Negative voltage bias ion enrichment high conductivity
1. When we continually decrease the cone angle, the ion enrichment and ion depletion region shifts from the mid of the pore toward its base end. 2. For cylindrical shape pore, this region reaches its base ends. (observed in experiment) Angle Dependence Cone angle enrichment or depletion region 3. For large angle, the rectification effect will decreases. V=-0.2V, r t =5nm, L =1µm, n 0 =1M
Radial distribution The thick of electric double layer (~ Debye length) is 0.31nm, about tenth of the diameter of the tip. (They do not need to overlap.) The strength of Current rectification effect Vs. cone angle Radial ion distribution. Electric double layer
Surface charge density
Length Dependence It is the cooperation of the small diameter of the tip, and the relatively long cone-shape body of the charged nanopore that contribute to the ion enrichment and depletion effect, resulting in current rectification. I-V curve become almost linear for L<100nm. Remind that r t =3nm, is still much smaller than 100nm. That is why our first months work is so disappointing. Truncate the tip end with a short length, as the tip pore play a much important role in determining the ion transport properties of the conical nanopore.
An intuitive way --compare with complete nanofluidic diode The same kind of ion distribution along the axis. ( K + )
Conclusions PNP equations are applicable to study the properties of these nanopores. There exist strong ion enrichment and depletion effect in the conical charged nanopore. (Surface charge+ long cone shape+ small tip). Changing the cone angle can change the ion enrichment or depletion region and their strength. The diameter of the pore tip that is about 10 times larger than Debye length is small enough to produce current rectification effect.
Of course, the nanopore do not need to be strictly conical shape. Specifically designed nanopore may produce strong current rectification effect, also strong ion selectivity.