CN106570297A - Ion rectification research method of tapered nanopore with pH-adjustable electrolyte layer - Google Patents

Abstract

The invention discloses an ion rectification research method of a tapered nanopore with a pH-adjustable electrolyte layer. On the basis of a structural characteristic of the tapered nanopore, the simulated size and boundary condition of the nanopore are set; initial conditions of the laminar flow, sparse material transferring, and static electric field in the nanopore are set; and the surface-ion-penetrable electrolyte layer thickness of the nanopore is set and the electric charge density in the electrolyte layer changes with the pH change. The improved stokes-brinkman equation and multi-ion PNP equation for ion transporting are used. Four kinds of ions in a solution is studied comprehensively, wherein four kinds of ions include two kinds of ions separated from background salt and H+ and OH- that decide pH values. Rectification characteristics of the tapered nanopore with the pH-adjustable electrolyte layer under different pHs and with different solution concentration values can be simulated.

Description

A kind of taper nanometer ionic porogen rectification research method with the adjustable dielectric substrates of pH

Technical field

Present invention design nanometer ionic porogen transmission, ion rectification analog simulation research method, belong to microfluidic art.

Background technology

Particular types ion can be selectively passed through by biological ion passage in organism to be inspired, people are to exploitation Synthesis device based on nano-pore is come the transmission of active control ion, fluid and biomone and for various bio-sensing applications The interest rapid growth of the little biomolecule of detection.Significantly improving for 1-5 nanofabrication techniques is also made based on the technology of nano-pore Research and application become possible to.The characteristic length scales of 6-7 nano-pores generally can be compared with Debye-Huckel screening radius, in this length In degree, electrostatic reciprocation becomes substantially and can the notable transport phenomena obtained in nano-pore.Research discovery, the ion in nano-pore Transmission is under certain conditions surface charge control, unrelated with overall ion concentration.This characteristic of 8-10 nano-pores causes Several interesting transport phenomenas, for example, ion selectivity, ion concentration polarization and gas current rectification.Especially at last In kind of situation, nano-pore shows a kind of I-E characteristic of asymmetrical similar diode, and this characteristic is to receive fluid to patrol Collect the basis of device structure.

What Wei et al. was observed for 1997 in a taper quartz nanopippettes.Nanopippettes ion current Size depend on adopted electric field direction, present a kind of preferential current direction.When aperture is suitable with Debye length, Gas current rectification can occur in taper nano-pore.Non-uniform holes along taper nano-pore can cause different degrees of electricity double Layer is overlapped.As a result, geometry it is asymmetric can cause it is uneven along hole axle ion distribution, this results in taper nano-pore from Electron current rectification.

Biological ion passage can adjust their the electric charge attributes based on localized chemical environment, and this localized chemical environment Can be activated by external stimulation.For example, it is stipulated that the biological ion passage of pH value is adjustable comprising pH generally in nano-pore The active control transmitted to ion of physical chemistry group.The pH used for reference in biological ion passage is adjusted, and people have carried out in a large number Research making synthesis nano-pore that there is in chemistry bionic intelligence nano-pore.Polyeletrolyte brush is considered as to pass through Powered macromolecular chain is transplanted to the surface of solids so as to change a kind of current techique of molecular interface.The charging shape of polyelectrolyte layers State depends on local ph and salinity, and this causes the adjustable ion transmission of the formation pH in synthesis nano-pore to be possibly realized.Cause This, can provide a kind of flexible using the functionalization of the synthesis nano-pore of polyeletrolyte brush for the rectification characteristic for controlling nano-pore Means.

The content of the invention

The present invention provides a kind of taper nanometer ionic porogen rectification research method with the adjustable dielectric substrates of pH, and analogue simulation is taken off Show the adjustable ion rectification characteristics of pH in taper nano-pore.

The present invention is as follows using technical scheme：

Step 1：An axial length is adopted for L_NTaper nanometer pore model, this nano-pore is embedded into one along bag Include nanometer hole wall in the film with homogeneous polymerization electrolyte brush layer that interior whole film face extremities are transplanted, as shown in Figure 1. It is assumed that polyelectrolyte layers are transparent ion, even structure and have unified thickness R_s.The film of functionalization Two big same liquid liquid storage pools are separated, a kind of incompressible electrolysis for including four kinds of ions have been loaded with liquid storage pool Matter solution.The transport of all kinds ion between two liquid storage pools will dome radius be R by_T, base radius are R_BCone Shape nano-pore.Two axial lengths are L_R, radius is R_RLiquid storage pool it is all sufficiently large so that every where away from film The concentration for planting ion all maintains the overall ion concentration for being it.One external electrical pressure reduction is applied in and is located remotely from the two of nano-pore Between two electrodes in individual liquid liquid storage pool.Gas current is result in through the ion transport of nano-pore.Due to taper nanometer The axially symmetric property in hole, adopts the cylindrical-coordinate system (r, z) with the center of nano-pore as origin.Employ by improved Stokes-Brinkman equations and PNP equations composition continuity model come simulate hydrodynamics, electrostatics and ion fortune It is defeated.

(1) improved Stokes-Brinkman equations

Wherein, p, η and u are respectively Fluid pressure, fluid viscosity and fluid velocity vectors.Be it is mobile from The space charge density of son, wherein, F, N, z_iAnd c_iIt is respectively Faraday constant, ionic species sum, the chemical combination of i-th kind of ion Valency and concentration.φ is potential.H=0 and 1 is respectively the region for representing region and the inside outside polyelectrolyte layers.γ is The fluid dynamic coefficient of friction of polyelectrolyte layers.The left side Section 3 of equation 1 is represented in electric field and electrolyte solution The electrostatic force that interaction between net charge density causes, it can cause EOF.Because EOF Reynolds number in nano-pore Very little, the Inertia in equation 1 can safely be ignored.

(2) PNP equations

In above formula, ε_fIt is the absolute dielectric constant of fluid；ρ_PEIt is the space charge density of polyelectrolyte layers；N_iAnd D_i It is respectively the flux density and diffusivity of i-th kind of ion.R and T are respectively the absolute temperature of universal gas constant and fluid.Note Meaning, ion flux density N_iFirst, second, and third represent respectively convection current, diffusion and electron transfer flux.

Step 2：The functionalization of the nano-pore with the adjustable zwitterionic polyeletrolyte brush of pH value has been implemented Regulation pH value obtains the feasibility of gas current rectification in so as to confirm taper nano-pore.Hypothesis is finally transplanted to a nanometer hole wall Polyelectrolyte layers not only carried acidic components but also carried basic functional group, AH and BH⁺, experience following dissociation reaction：

Make K_A=[A^-][H⁺]/[AH] and K_B=[B] [H⁺]/[BH⁺] it is two equilibrium constants for dissociating reaction, wherein [X] Refer to the molarity of X in polyelectrolyte layers.The total concentration of acidic components and basic functional group is respectively N_A=[A^-]+ [AH] and N_B=[B]+[BH⁺], based on this, the charge density of polyelectrolyte layers can be derived as in equation (3)：

Step 3：Close coupling governing equation (1)-(4) are solved using following boundary condition.

(1) electricity contacted with bottom on liquid storage pool end and nano-pore top is respectively φ (anode)=V and φ is (cloudy Pole)=0.Corresponding ion concentration reaches their population value, it is, c_i=C_i0.It is appointed as not having at the two ends of liquid storage pool The standard flow of external voltage gradient, that is, p=0.

(2) zero surface charge is adopted on the border of two liquid storage pools away from nano-pore, that is,Zero standard Quasi- ionic flux, that is, nN_i=0 and sliding velocity boundary condition.Herein n represents the unit normal vector on surface.

(3) the whole film surface comprising nanometer hole wall is uncharged, can not penetrate ion and without sliding, point Do not obeyAnd u=0.

(4) all it is continuous at the interface of potential, electric field, ion concentration and flow field between polyelectrolyte layers and liquid 's.

(5) axis along nano-pore is appointed as axial symmetry boundary condition.

Step 4：Resulting gas current is by along the male or female positioned at liquid storage pool end in nano-pore The net current integration on surface is obtained：

Description of the drawings

Fig. 1 is subject in the taper nano-pore with the adjustable polyeletrolyte layer function of pH value of external electrical field effect Ion transports schematic diagram.

Fig. 2 is to work as C_KClAt pH=10 (solid line) during=10mM, electric current when pH=6 (dotted line) and pH=3 (chain-dotted line)- Voltage curve

Fig. 3 is to work as C_KClElectricity during=100mM, in pH=10 (solid line), pH=6 (dotted line) and pH=3 (chain-dotted line) Stream-voltage curve

Fig. 4 is to work as C_KClElectricity during=200mM, in pH=10 (solid line), pH=6 (dotted line) and pH=3 (chain-dotted line) Stream-voltage curve

Fig. 5 is to work as pH=3, C_KClWhen=100mM, V=-1V, along the average cross-section ion concentration of taper nanometer axially bored line (dotted line is H+, and solid line is K+, and dash line is Cl-, and chain-dotted line is OH-).

Fig. 6 is to work as pH=3, C_KClWhen=100mM, V=0V, along the average cross-section ion concentration of taper nanometer axially bored line (dotted line is H+, and solid line is K+, and dash line is Cl-, and chain-dotted line is OH-).

Fig. 7 is to work as pH=3, C_KClWhen=100mM, V=1V, along the average cross-section ion concentration of taper nanometer axially bored line (dotted line is H+, and solid line is K+, and dash line is Cl-, and chain-dotted line is OH-).

Fig. 8 is to work as pH=6, C_KClWhen=100mM, V=-1V, along the average cross-section ion concentration of taper nanometer axially bored line (dotted line is H+, and solid line is K+, and dash line is Cl-, and chain-dotted line is OH-).

Fig. 9 is to work as pH=6, C_KClWhen=100mM, V=0V, along the average cross-section ion concentration of taper nanometer axially bored line (dotted line is H+, and solid line is K+, and dash line is Cl-, and chain-dotted line is OH-).

Figure 10 is to work as pH=6, C_KClWhen=100mM, V=1V, along the average cross-section ion concentration of taper nanometer axially bored line (dotted line is H+, and solid line is K+, and dash line is Cl-, and chain-dotted line is OH-).

Figure 11 is to work as pH=10, C_KClWhen=100mM, V=-1V, the average cross-section ion along taper nanometer axially bored line is dense Degree (dotted line is H+, and solid line is K+, and dash line is Cl-, and chain-dotted line is OH-).

Figure 12 is to work as pH=6, C_KClWhen=100mM, V=0V, along the average cross-section ion concentration of taper nanometer axially bored line (dotted line is H+, and solid line is K+, and dash line is Cl-, and chain-dotted line is OH-).

Figure 13 is to work as pH=10, C_KClWhen=100mM, V=-1V, the average cross-section ion along taper nanometer axially bored line is dense Degree (dotted line is H+, and solid line is K+, and dash line is Cl-, and chain-dotted line is OH-).

Figure 14 is current rectification ratio with pH change curves.Solid line, dotted line and chain-dotted line represent respectively C_KCl=10mM, 100mM And 200mM.

Figure 15 is the volume average charge density of external voltage polyelectrolyte layer when being 0 with pH change curves.Solid line, dotted line C is represented respectively with chain-dotted line_KCl=10mM, 100mM and 200mM.

Specific embodiment

With reference to example, the invention will be further described, but not limited to this.

A kind of taper nanometer ionic porogen rectification research method with the adjustable dielectric substrates of pH of the present invention is received based on taper Metre hole, sets nanoporous size, background concentration of salt solution, setting multiple physical field boundary condition and primary condition is determined, using layer Stream, the transmission of dilute material and Electrostatic Field Model, the multiple physical field coupling model of foundation.Using finite element solving.

Embodiment：

(1) background salt is that total concentration is C_KClKCl, and background solution pH (=- log [H⁺]₀) it is by KOH and HCI Adjustment, [H⁺]₀It is H⁺Overall molal volume concentration.So, four for considering in our current research kind leading ion is H⁺、K⁺、Cl⁺ And OH^-.Make C₁₀、C₂₀、C₃₀And C₄₀It is respectively the total concentration of these ions.Due to net electroneutral it is assumed that following condition is suitable for： If pH >=7, C₁₀=10^-pH+3,C₂₀=C_KCl-10^-pH+3+10^-(14-pH)+3,C₃₀=C_KClAnd C₄₀=10^-(14-pH)+3；If pH is ＜ 7,C₁₀=10^(-pH+3),C₂₀=C_KCl,C₃₀=C_KCl+10^(-pH+3)-10^-(14-pH)+3And C₄₀=10^-(14-pH)+3。

(2) liquid storage pool size in taper nano-pore two ends is all L_R=R_R=200nm.The axial length of taper nano-pore, also The thickness for being film is L_N=500nm.The radius of nano-pore top and nano-pore bottom is respectively R_T=10nm and R_B=65nm. The thickness of the final polyelectrolyte layers along the transplanting of whole film is R_s=5nm.It is contemplated that a typical amino acid polymerization Dielectric substrate, N_A=N_B=300mM, pK_A=-logK_A=2.2 (α-carboxyl) and pK_B=-logK_B=9 (alpha-amidos).⁶³λ=(η/ γ)^1/2It is the pliability (or Brinkman shielding lengths) of polyelectrolyte layers, λ=1nm here.H⁺、K⁺、Cl^-And OH^-Ion Diffusivity be respectively D₁=9.31 × 10^-9、D₂=1.96 × 10^-9、D₃=2.03 × 10^-9And D₄=5.30 × 10^-9m²s^-1. Other physical parameters used in emulation are ε_f=7.08 × 10^-10Fm^-1, R=8.31J (K^-1mol^-1), F=96490Cmol^-1, η =1 × 10^-3Pas and T=300K.Across film adopt scope for -1V to 1V electrical potential difference to produce nano-pore in ion-conductance Stream.

(3) Fig. 2-4 shows that the nano-pore of functionalization is separately fixed at C in overall salinity_KCl=10mM, 100mM, Current -voltage curve during different pH value under 200mM.Positive-ion current is defined as when positive potential is applied in anode, direction The electric current of bottom is flowed to from nano-pore top.In by comparing Fig. 2 during pH=10 (solid line) apply formed objects electrical potential difference but The size of opposite polarity gas current, it has been found that the electrolyte solution in taper nano-pore shows as the characteristic of diode Rather than the characteristic of ohmic resistor, here it is gas current rectifier phenomena.In fig. 2, when pH value is reduced to pH=6 (dotted line) When, the size of gas current also correspondingly reduces.Additionally, rectification characteristic is almost disappeared.In fig. 2, if pH value is further PH=3 (chain-dotted line) is reduced to, compared with the situation of pH=10, the privileged direction of rectification characteristic is overturned.Obviously, pH value management The gas current rectification in taper nano-pore can be considerably adjusted.Such as Fig. 3 (C_KCl=100mM) shown in, when the totality of background salt When concentration increases, the size of nano-pore ion current also increasing, this is because ion concentration and corresponding electrical conductivity Increase.Additionally, the salinity of totality can also affect rectification characteristic.However, shadow of the pH value management to rectification characteristic privileged direction Ring in different C_KClAll it is quite similar under value.

(4) in order to elaborate the impact that pH value manages the gas current rectification in the taper nano-pore to functionalization, figure 5-11 depict C_KClDuring=100mM, along the average cross-section concentration of four kinds of ions of nanometer axially bored line, it is defined as：

c_a,i=∫_sc_ids/∫_sds (8)

Apply as pH=3 and not electrical potential difference (Fig. 6), anion Cl is mainly full of in nano-pore^-.This means polymerization Dielectric substrate is positively charged in pH=3, and this can attract in turn more anion to enter nano-pore.Because Cl^-'s Total concentration compares OH^-Total concentration it is much higher, in nano-pore, anion Cl^-Significantly dominate anion OH^-.Because from Nano-pore top to nano-pore bottom electric double layer degree of overlapping reduces, so from top to bottom, the average cross-section of anion is dense Degree is gradually reduced.In contrast, from top to bottom, the average cross-section concentration of cation gradually increases.Note, on top and The peak value of bottom is caused by the polyelectrolyte layers on the film contacted with liquid storage pool.It is this along the non-of taper nano-pore Uniform ion distribution is closely similar with the ion distribution received in fluid diode.Main difference is non-equal between two kinds of situations The principle of even ion distribution, they be respectively by powered taper nano-pore geometry it is asymmetric and receiving fluid diode Two-part contrary charging scheme cause.In our current research, when using negative electrical potential difference (Fig. 5), with what is increased The slightly close top of peak value, the cation and anion in nano-pore is both increased.Correspondingly, nano-pore internal electrolyte solution Conductance is enhanced.Conversely, when using positive electrical potential difference (Fig. 7), cation and anion all can be reduced from nano-pore, be led Cause the decline of electric conductivity in nano-pore.Using different electrical potential difference zwitterions increase and reduce can be by by taper nano-pore Regard that one is received fluid diode to be understood as.Therefore, the ion under the effect of the negative potential with ion enrichment effect Electric current is bigger than the electric current under the effect of the positive potential with ion dissipation effect, this explains rectification characteristic and with it is first previous It is a little consistent to the research of unmodified nano-pore.When as pH=6 and not applying electrical potential difference (Fig. 9), the concentration of cation is slightly higher In the concentration of anion, this means that nano-pore into electronegative.By verifying nano-pore ion current and total dense Absolute difference between degree, it is clear that it can be concluded that because pH value is more slightly higher than isopotential point, the electricity of polyelectrolyte layers Lotus is very weak.Because the electric charge of polyelectrolyte layers becomes negatively chargedly slight, in positive potential difference (Figure 10) and negative electricity potential difference (Fig. 8) When slight ion aggregation and ion diffusion can occur respectively.

As pH=10, the ion distribution in the nano-pore without electrical potential difference (Figure 12) shows the electric charge of polyelectrolyte layers It is still negative value.Additionally, dramatically increasing for the quantity of electric charge, result in more obvious gas current rectification.It is similar to the situation of pH=6, Positive electrical potential difference and negative electrical potential difference can respectively cause the dissipation (11) of the aggregation (Figure 13) and ion of ion.So, with band just The situation of the polyelectrolyte layers of electric charge is conversely, when polyelectrolyte layers are negatively charged, the privileged direction of gas current is from top Point to bottom in portion.

(6) rectification characteristic can be quantified by the ratio of the gas current under the equal-sized electrical potential difference of opposite polarity, Namely IR=| I (V)/I (- V) |.Figure 14 shows, when the size of the electrical potential difference for being adopted is 1V, IR is a letter of pH value Number.When pH value is in intermediate range near equipotential (namely pH=5.6), according toShow, rectification characteristic is substantially Disappear.In order to the electric charge that the polyelectrolyte layers caused by pH value management are better described is adjusted, Figure 15 is shown without outer Impact of the pH value to the volume average charge density of polyelectrolyte layers during portion's electrical potential difference, it is defined as：

In above formula, Ω_PERepresent the volume of polyelectrolyte layers.It will be apparent that the equipotential of nano-pore is attached in pH=5.6 Closely, herein the net charge of polyelectrolyte layers is zero.Once nano-pore becomes not charged, rectification characteristic is also disappeared.Work as liquid Solution becomes more alkaline, and polyelectrolyte layers can become with more negative electricity (Figure 15).In this case, by IR ＞ 1 can be shown that, the privileged direction of gas current is to point to bottom from top.In C_KCl=100mM and C_KClDuring=200mM, work as pH value When rising to 10 from 6, the value monotonic increase of IR, the size of the quantity of electric charge also monotonic increase.However, in C_KClPH=8.5 at=10mM Near, IR values are maximized, and this shows at medium charge, and gas current rectification is tended to maximize.This is because more electricity Lotus is often limited in more ions in electric double layer, and this correspondingly reduces electron transfer ionic flux.Before us Research it has also been found that obtain the electric charge of the nano-pore of IR maximums, referred to as critical charge, depending on overall salinity.Work as totality Salinity is relatively low, and critical charge is relatively low.For example, as shown in figure 15, in C_KClWhen near=10mM, pH=8.5, Critical charge is probably ρ_{A, PE}=-0.41 × 10⁷Cm^-3.This effect also explains in C_KCl=100mM and C_KCl=200mMmM When the IR values peak point that is not reaching to from pH=6 to pH=10.When liquid solution becomes acid higher, polyelectrolyte layers become Into positively charged, and the quantity of electric charge increases as pH value must decline.Therefore, can be shown that by 0 ＜ IR ＜ 1, gas current it is excellent First direction overturns.However, charge value of the charge value ratio in sour environment in alkaline environment is much lower.So, work as pH value When reducing to 3 from 6, IR value monotone decreasings.The prediction numerically of these impacts to pH value to gas current rectification with reported Germicidal efficacy it is consistent in nature.Can be summarized as, the electric charge of polyelectrolyte layers can be in very large range by pH value control System, even if the polarity of electric charge may be overturned.Therefore, we can adjust taper nano-pore by adjusting the pH value of solution Rectification characteristic.

Claims (5)

1. a kind of taper nanometer ionic porogen rectification research method with the adjustable dielectric substrates of pH, comprises the steps, its feature exists In：

Step (1) analyze physical field governing equation, this analog simulation mainly include improved Stokes-Brinkman equations and PNP equations.

Step (2) determines simulation parameter numerical value, including solution concentration, electric-field intensity, pH value, ion diffusion system according to simulated conditions Number, electrolyte layer grafting density, etc. parameter values.

Step (3) determines each physics field boundary condition of taper nano-pore and initial value, and charge density changes with pH in dielectric substrate And change.

Step (4) carries out multiple physical field coupling Simulation to solution in nano-pore using setting numerical value in step (2) and (3), adopts Direct solution carries out analogue simulation.

Step (5) analyzes nano-pore intermediate ion situation of change according to emulation data analysis nano-pore intermediate ion rectification characteristic.

2. a kind of analogue simulation side of the taper nanometer ionic porogen rectification with the adjustable dielectric substrates of pH as claimed in claim 1 Method, it is characterised in that the improvement Stokes-Brinkman equations adopted in the step (1)

$\▿p+\mathrm{\η}{\▿}^{2}u-{\mathrm{\ρ}}_e\▿\mathrm{\φ}-h\mathrm{\γ}u=0$

$\▿\·u=0$

PNP equations

$-{\mathrm{\ϵ}}_f{\▿}^2\mathrm{\φ}={\mathrm{\ρ}}_e+{\mathrm{h\ρ}}_{PE}$

$\▿\·N_i=\▿\·({\mathrm{uc}}_i-D_i\▿c_i-z_i\frac{D_i}{RT}{\mathrm{Fc}}_i\▿\mathrm{\φ})=0,i=1,...,N$

3. a kind of taper nanometer ionic porogen rectification research method with the adjustable dielectric substrates of pH as claimed in claim 1, its spy Levy and be, the determination of step (2) simulation parameter includes electric-field intensity, solution concentration, dielectric substrate grafting density.

4. as claimed in claim 1 a kind of taper nanometer ionic porogen rectification research method with the adjustable dielectric substrates of pH, its feature It is that charge density changes with pH and changes in step (3) the taper nanoporous surface dielectric substrate, and each physical field side The setting of boundary's condition and initial value.

5. as claimed in claim 1 a kind of taper nanometer ionic porogen rectification research method with the adjustable dielectric substrates of pH, its feature It is that nanometer ionic porogen rectification characteristic under different pH condition is analyzed in the step (4).