Ion-Current Rectification in Nanofluidic Devices - Nanofluidics: Nanoscience and Nanotechnology - page 173

where the subscript B , R represents the bath and the right hand side. By imposing the
approximation that the electrophoretic mobilities µ K and µ Cl are very close, Equation 8.5 is
simplified to and . On the basis of this
derivation, we can describe the ratios of the current in the channel to that in the bath for
each ion species at the left channel-bath interface, inside the nanochannel and the right
channel-bath interface as following 23,37
(8.6)
Each current ratio listed above can be used to predict whether the ion species in that
position will accumulate or deplete after an electric field is applied.
For example, let us consider the case of a negatively charged nanochannel with
asymmetric bath concentrations. The left bath contains C L = 10 -4 M. The cation/anion ratio
at the left entrance, , is calculated to be ~ 2185, when h = 20 nm and µ s = 4.5 mC/m 2 .
Because the bath concentration on the right side is higher (α is small), we can get the
relation: > ≥ 1. When C H < f /2, both the counter-ion and co-ion currents in both ends of
nanochannel are very similar ( ), while those inside and outside the nanochannel
are very different ( and ). A similar result can be obtained in the
C L bath. In this case, depending on the bias polarity, the accumulation or depletion of both
types of ion take place outside the nanochannel. Because the ion concentration in the
nanochannel is predominately controlled by the surface charge of the channel and does not
change with the bias polarity, the ion conductance is symmetric. On the contrary, when C H
> f/2, as depicted in Figure 8.11(1b), the ion currents in the left and right ends of the
nanochannel are asymmetric ( and ), while at the right entrance, the
ion currents developed inside and outside the nanochannel are very close ( ).
Since the device is forward-biased (i.e. the applied electric field is opposite to the
concentration gradient), as shown in Figure 8.11(1b), more ions are driven into the channel
and less taken out. These uneven fluxes induce accumulation of both K + and Cl - ions
within the nanochannel and depletion of both near the channel entrance in the C L bath.
Opposite results can be obtained at a reverse bias if the electric field is applied
along the concentration gradient. In this situation, as illustrated in Figure 8.11(1c), more
ions are being taken out of the channel than being injected into the channel, resulting in the
depletion of ions in the nanochannel. The results explain why the ion concentration profiles
buckle up at V H = -5 V but sink at V H = 5 V, as shown in Figure 8.9. In addition to the ion
behaviour in the nanochannel, the accumulation and depletion of ions at the regions
adjacent to the channel (i.e. the channel access region), can affect the channel conductance.
The depletion of ions, especially at the channel access in the low-concentration C L bath,
increases the electrical resistance to the ion flux, and therefore generates an access
resistance that is connected in series with the nanochannel. The effect of this access
resistance was observed when C H is increased to 1 M. The resistance reduces the number
of ions to be accumulated or depleted in the nanochannels due to the weakened electric
field inside the nanochannel and hence, reduces the rectifying effect. This analysis can be
applied to a positively charged nanochannel as well. In this case, the relation of the