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WO2021260587A1 - Techniques améliorées pour l'agrandissement et la formation de nanopores - Google Patents

Techniques améliorées pour l'agrandissement et la formation de nanopores Download PDF

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Publication number
WO2021260587A1
WO2021260587A1 PCT/IB2021/055559 IB2021055559W WO2021260587A1 WO 2021260587 A1 WO2021260587 A1 WO 2021260587A1 IB 2021055559 W IB2021055559 W IB 2021055559W WO 2021260587 A1 WO2021260587 A1 WO 2021260587A1
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Prior art keywords
nanopore
membrane
value
electric potential
potential
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English (en)
Inventor
Vincent TABARD-COSSA
Kyle BRIGGS
Matthew Waugh
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University of Ottawa
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University of Ottawa
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01D—SEPARATION
    • B01D67/00—Processes specially adapted for manufacturing semi-permeable membranes for separation processes or apparatus
    • B01D67/0081—After-treatment of organic or inorganic membranes
    • B01D67/009—After-treatment of organic or inorganic membranes with wave-energy, particle-radiation or plasma
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01D—SEPARATION
    • B01D71/00—Semi-permeable membranes for separation processes or apparatus characterised by the material; Manufacturing processes specially adapted therefor
    • B01D71/02—Inorganic material
    • B01D71/0215—Silicon carbide; Silicon nitride; Silicon oxycarbide
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
    • G01N15/08—Investigating permeability, pore-volume, or surface area of porous materials
    • G01N15/088—Investigating volume, surface area, size or distribution of pores; Porosimetry
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01D—SEPARATION
    • B01D2325/00—Details relating to properties of membranes
    • B01D2325/02—Details relating to pores or porosity of the membranes
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
    • B01D—SEPARATION
    • B01D2325/00—Details relating to properties of membranes
    • B01D2325/02—Details relating to pores or porosity of the membranes
    • B01D2325/0282—Dynamic pores-stimuli responsive membranes, e.g. thermoresponsive or pH-responsive
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B82—NANOTECHNOLOGY
    • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
    • B82Y5/00—Nanobiotechnology or nanomedicine, e.g. protein engineering or drug delivery

Definitions

  • the present disclosure relates to mechanisms by which to control the solid- state nanopore enlargement process under electrical stress.
  • Nanopores - nanometer scale holes that can be used to detect and interrogate single biomolecules one at a time - are poised to deliver on decades of promise in diverse fields, ranging from disease diagnostics and DNA sequencing to next- generation methods of archival information storage.
  • the high cost of the equipment needed to fabricate and subsequently control the size of solid-state nanopores was prohibitive, as was the low yield of useful nanopores, preventing this promising technology from making it out of a few well-equipped research labs.
  • a method for enlarging the size of a nanopore formed in a membrane.
  • the method includes: disposing a membrane in a conductive liquid, where the membrane has a nanopore formed therein; selecting a value for an electric potential that induces an electric field in the nanopore cooperatively with setting conductivity of the conductive liquid, such that current through the nanopore is maximized at the chosen potential and the electric field in the nanopore is less than a maximum electric field threshold; and applying the electrical potential across the nanopore at the selected value, thereby enlarging the size of the nanopore.
  • the method may further include increasing the conductivity of the conductive liquid while applying the electrical potential at the selected value across the nanopore.
  • the value of the electric potential is set to induce an electric field that is one third the nominal dielectric strength of the membrane. In another example, the value of the electric potential is set to induce an electric field that is one half the nominal dielectric strength of the membrane.
  • the method for enlarging the nanopore can be combined with techniques for creating the nanopore in the membrane.
  • a membrane without a nanopore is disposed in a conductive liquid.
  • the method includes: applying an electric potential across the membrane, thereby creating a nanopore in the membrane; and enlarging size of the nanopore while the membrane remains in the conductive liquid.
  • Figures 1 A and 1 B are diagrams depicting an example apparatus for fabricating and conditioning nanopores in a membrane.
  • Figure 2 is a flowchart presenting an overview of the method for enlarging the size of a nanopore.
  • Figure 3 is a flowchart showing the method of enlarging the size of a nanopore combined with the controlled breakdown technique for forming the nanopore.
  • Figure 4A is a graph comparing pore growth rates when high and low conductivity electrolyte solutions are alternatively used to enlarge a nanopore.
  • Figures 4B and 4C are graphs comparing pore growth rates when similar conductivity solutions with different total electrolyte concentrations and cations are alternately used to enlarge nanopores.
  • Figure 5 is a graph showing the enlargement time required to reach certain nanopore sizes for two pores in 3.6 M LiCI pH 8 versus nine pores in 4 M KCI pH 8 demonstrating that pores grown in higher conductivity solutions reach the same target pore size faster than those grown in lower conductivity solutions.
  • Figure 6 is a graph showing typical results from a nanopore enlarged under conditions of alternating acidic and alkaline electrolyte with equal conductivities.
  • Figures 7 A and 7 B are plots generated from DNA translocation data of pores enlarged using high conductivity solutions, comparing maximum current blockage caused by a DNA molecule partially obstructing the pore versus dwell time of the molecule in the pore, where an example of a membrane with a single pore is shown in Fig 7A and an example of a different membrane containing two pores in shown in Fig. 7B.
  • Figures 1A and 1 B depict an example apparatus for fabricating one or more nanopores in a membrane.
  • the apparatus is comprised generally of a fluidic cell 22; a pair of electrodes 24 electrically coupled to a voltage source; and a controller 26 interfaced with the current amplifier circuit 25.
  • the voltage source is not shown but can be integrated on the circuit board with the current amplifier circuit 25.
  • the fluidic cell 22 is further defined by two reservoirs 33 fluidly coupled to each other via a passageway 34 as best seen in Figure 1 B.
  • a current amplifier circuit 25 is used to measure the current flow between the two reservoirs 33.
  • the controller 26 may be implemented by a data acquisition circuit 28 coupled to a personal computer 27 or another type of computing device.
  • the fluidic cell 22 and/or the entire system can be disposed in a grounded faraday cage 23 to isolate electric noise.
  • the setup is like that which is commonly used for biomolecular detection in the field of nanopore sensing.
  • Other setups for fabricating a nanopore are also contemplated by this disclosure.
  • a silicon chip 31 is used to support a membrane 30.
  • the silicon chip 31 is sandwiched between two silicone gaskets 32 and then positioned between the two reservoirs 33 of the fluidic cell 22.
  • the fluidic cell 22 is comprised of polytetrafluoroethylene (PTFE) although other materials are contemplated.
  • PTFE polytetrafluoroethylene
  • a small pressure is applied to the two gaskets 32 by the fluidic cell 22 to seal the contact tightly.
  • the two reservoirs 33 are filled with a conductive liquid, and the two electrodes 24 are inserted into the respective reservoirs of the fluidic cell 22.
  • the membrane 30 is comprised of a dielectric material, such as silicon nitride (SiN x ).
  • a dielectric material such as silicon nitride (SiN x ).
  • Membranes are preferably thin, with a thickness on the order of 10 nm, although membranes having different thicknesses are contemplated by this disclosure.
  • atomically thin membranes may be comprised of other materials such as graphene, molybdenum disulfide and the like. It is also contemplated that the membranes may be comprised of multiple layers of materials, including dielectric materials and/or conductive materials.
  • the current amplifier circuit 25 is a simple operational- amplifier circuit to read and control voltage and current. Operational-amplifiers are powered by a ⁇ 20 volt voltage source. In operation, the circuit takes in a command voltage (Vcommand) between ⁇ 10 volts from a computer-controlled data acquisition card, which is amplified to ⁇ 20 volts, and sets the potential across the membrane. Current flow between the two electrodes is measured at one or both electrodes with pA sensitivity. More specifically, current is measured with a transimpedance amplifier topology. The measured current signal (lout), converted to a voltage signal by the current amplifier circuit, is digitized by the data acquisition circuit and fed continuously into the controller.
  • Vcommand command voltage
  • Vcommand command voltage
  • a computer-controlled data acquisition card which is amplified to ⁇ 20 volts
  • Current flow between the two electrodes is measured at one or both electrodes with pA sensitivity. More specifically, current is measured with a transimpedance amplifier topology.
  • the measured current signal (lout)
  • the current is monitored in real time by the controller, for example at a frequency of 10 Hz, though faster sampling rate can be used for faster response time.
  • Other circuit arrangements for applying a potential and measuring a current fall within the scope of this disclosure. Conversely, circuit arrangements that apply a current to the electrodes and measure a potential are also envisioned.
  • nanopore growth is primarily driven by the level of ionic current passing through the nanopore, rather than the strength of the electric field generating the current. Additionally, enlargement has a much weaker pH dependence than does nanopore formation. Results presented below indicate that the probability of forming additional (unwanted) pores during nanopore growth can be decoupled from the rate of growth of the nanopore, allowing for fast pore enlargement to any size without risking further nanopore formation.
  • Figure 2 provides an overview of the method for enlarging the size of an existing nanopore formed in a membrane.
  • the membrane is disposed between two reservoirs containing conductive liquid in a setup, for example as described above in relation to Figures 1A and 1 B.
  • the conductive liquid is an aqueous salt solution.
  • aqueous salt solutions one can envision other types of conductive liquids. For example, one could use ionic liquids or salts dissolved in non-aqueous media, such as organic solvents.
  • conductive liquids include but are not limited to aqueous monovalent salt solutions; aqueous salt solutions of valence of one or more; as well as salts of various valence dissolved in organic solvents such as ethanol, DMSO, isopropanol, chloroform, etc.
  • An electric potential i.e., voltage
  • the magnitude of the electric potential is selected cooperatively with setting conductivity of the conductive liquid, such that the current through the nanopore is maximized at the selected value and the electric field in the nanopore is less than a maximum electric field threshold.
  • the value of the electric potential is preferably set to induce an electric field that is less than (or equal to) one half the nominal dielectric strength of the membrane. In one example, the value of the electric potential is set to induce an electric field that is one third of the nominal dielectric strength of the membrane. In other example, the value of the electric potential is based on the voltage at which the nanopore was formed as is further described below.
  • the conductivity of the conductive liquid is set so that the current through the nanopore is maximized at the selected electric potential.
  • Current through the nanopore to first order, is given by where s is the solution conductivity, determined by the salt concentration and identity, V is the voltage applied, L is the membrane thickness, and d is the pore diameter. Since L and d are changing during the process due to the conditioning, conductivity of the liquid is the remaining controllable variable. Because the objective is to maximize current, this means the method should maximize the conductivity of the liquid. For most salt types, this means using a saturated solution of the given salt for the solvent, and to choose a salt that is maximally conductive from among the available options.
  • the electric potential applied across the nanopore for enlargement remains unchanged (e.g., 3-4 volts) while the size of the nanopore is determined.
  • the higher electric potential applied across the nanopore for enlargement is lowered to determine the size of the nanopore.
  • the electric potential is preferably lowered to a value where the pore is guaranteed to be ohmic (e.g., 200mV). For example, an electric potential on the order of 3-4 volts may be applied during a first period of time and then lowered for a subsequent period of time which allows for measurement.
  • the enlargement and measurement periods can be alternated until the nanopore reaches the desired size. In either case, the magnitude of the current passing through the nanopore is compared at 43 to a predetermined threshold, where the threshold corresponds to the desired size for the nanopore. When the monitored current reaches (or exceeds) the threshold, the applied voltage is terminated at 44.
  • Other conditions for stopping the pore growth such as choosing a maximally acceptable value for the low-frequency noise of the nanopores, are also contemplated by this disclosure.
  • the conditioning speed can be increased by increasing the conductivity of the conductive liquid. That is, the conductivity of the conductive liquid can be increased in situ during the enlargement process. In one embodiment, the conductivity is increased by increasing the temperature of the liquid. This can be accomplished in different ways, including using a resistive heating element placed in the conductive liquid or through the use of a light source (e.g., laser).
  • a light source e.g., laser
  • an array of nanopores may be formed on a membrane. In this case, one or more of the nanopores can be selectively enlarged by directing a laser beam onto the nanopores of interest, thereby enlarging only these selected pores in the array of nanopores.
  • the conductivity of the liquid is dependent on temperature, it is not necessarily monotonical and does not necessarily increase with increased temperature. In some instances, it is envisioned that conductivity may be increased with decreasing temperature. It is also envisioned that at lower temperatures it is possible that the redox reactions that enable current to pass though the membrane will happen more slowly, effectively increasing the dielectric strength of the membrane and allowing higher voltages, and therefore higher ionic currents, to be used during the enlargement process without risking additional nanopores opening.
  • Fabricating nanopores using controlled breakdown is one known technique for creating a nanopore in a membrane.
  • the technique described above for enlarging the size of a nanopore can be combined with the controlled breakdown technique as shown in Figure 3. It is readily understood that the enlarging technique can also be combined with any other methods for creating nanopores as well.
  • a membrane is disposed in a conductive liquid of a setup, for example as described above in relation to Figures 1A and 1 B.
  • An electric potential i.e. , voltage
  • a constant voltage is applied to the membrane.
  • the applied voltage is ramped up over time until the breakdown occurs and the nanopore is formed.
  • the electric potential applied to the membrane preferably has a magnitude that induces an electric field having a value greater than 0.1 volt per nanometer across the membrane.
  • the size of the nanopore is preferably determined at 52. To do so, another voltage is applied across the nanopore, thereby generating a current that flow through the nanopore. The magnitude of the voltage is selected to ensure that the size of the nanopore remains unchanged, is smaller than the voltage used to create the nanopore, and is such that the nanopore has an Ohmic current response to the chosen voltage value. Current flow through the nanopore is measured and then used to determine the size of the nanopore. Nanopore size can be inferred from the following equation, using the same variable definitions as defined above:
  • L is equal to the nominal membrane thickness, but other methods of measuring L are also possible.
  • the size of the nanopore can be enlarged.
  • the membrane remains in the same conductive liquid in which the nanopore was formed.
  • the conductive liquid encompassing the membrane may be different from the conductive liquid in which the nanopore was formed. That is, the conductive solution in the setup is changed.
  • an electric potential is reapplied at 53 across the membrane.
  • the value of the electric potential is selected cooperatively with setting the conductivity of the liquid, such that the current through the nanopore is maximized at the selected value and the electric field in the nanopore is less than a maximum electric field threshold.
  • the value of the electric potential is determined by the voltage at which the breakdown occurred.
  • the value of the electric potential is set at less than one half the voltage at which the breakdown occurred and preferably at one third the voltage at which the breakdown occurred.
  • the value of the electric potential is correlated to the nominal dielectric strength of the membrane, such as one third or one half of the nominal dielectric strength of the membrane.
  • the applied voltage can be lowered to a value where the pore is in ohmic regime for measurement purposes.
  • the magnitude of the current is compared at 55 to a predetermined threshold, where the threshold corresponds to the desired size for the nanopore.
  • the applied voltage is terminated at 56.
  • Other conditions for stopping the pore growth such as choosing a maximally acceptable value for the low-frequency noise of the nanopores, are also contemplated by this disclosure.
  • FIG. 4A An example growth profile of a pore enlarged in two different solutions is shown in Figure 4A.
  • the voltage was pulsed between ⁇ 4.5 V with a 4 seconds hold time in each voltage polarity, with a measurement of the pore size occurring every 5 cycles totaling 40 seconds of electrical stress.
  • the electrolyte was then swapped, and the measurements repeated for a total of ten solution changes.
  • a +200 mV bias was applied for 7 seconds, where the first 5 seconds allowed the capacitive current to decay and the faradaic current to stabilize, followed by a current measurement averaged over the last 2 seconds. This depends on the chip capacitance (exposed area to liquid and dielectric properties) and can be shorter with low cap chips. The same procedure was then repeated using a -200 mV bias.
  • the pore conductance G was calculated and used to determine nanopore diameter d using standard methods: where the effective length of the pore L is assumed to be the membrane thickness and the solution conductivity s is known. Note that pore size is not measured in the low conductivity condition directly since the size model used performs poorly in low salt concentrations.
  • the growth rates of the pores are strongly determined by the conductivity of the solution and therefore the current passing through the pore.
  • the nanopore consistently grew faster in the 3.6 M LiCI solution, at an average rate of about 0.11 nm cycle 1 , whereas growth was near negligible using the 10 mM LiCI, at about 0.02 nm cycle 1 .
  • the pores grown in the 4 M KCI solution consistently reached the specified pore size faster than the pores grown in the 3.6 M LiCI solution, where the conductivity of the 4 M KCI was approximately two times higher than the 3.6 M LiCI. Note however that the growth rate difference exceeds this factor.
  • Increasing the solution conductivity was shown to be a practical method of reducing pore enlargement time and can reduce the time required to make a usable nanopore by an order of magnitude.
  • growth rate shows instead a ⁇ 2-fold increase in growth rate as shown in Figure 6. While the difference in enlargement rate is small, it is statistically significant at the p ⁇ 0.05 level, with pH 10 promoting faster pore growth than pH 4.
  • the ratio of growth rates in pH 10 to pH 4 for adjacent conditioning cycles at ⁇ 3.5 V being 1.8 ⁇ 0.3, and 1.6 ⁇ 0.2 at ⁇ 4 V (error bars given 95% confidence interval). Note that this is opposite to the trend for fabrication times, in which more acidic pH values tend to result in much shorter fabrication times. This pH dependency cannot be explained by a Joule heating mechanism for pore growth, since the level of current passing through the pore in both cases is the same.
  • DNA translocation experiments were conducted on pores enlarged using high conductivity solutions to assess the presence of a single nanopore in the membrane. Following pore enlargement to a target size, nanopores are electrically characterized to obtain more accurate size measurements and information about their ionic current noise profiles. Typically, a 30 seconds current trace is recorded using an applied bias of ⁇ 200 mV, and the corresponding power spectral density (PSD) plots are generated from this data. Pore size is also calculated as in the equation given in [0029] from an l-V curve swept from -200 mV to +200 mV. Pore size measured from conductance works well for a membrane containing a single nanopore, but the method cannot infer the presence of multiple pores.
  • PSD power spectral density
  • the calculated pore size in a membrane containing potentially two or more pores is measured as a single pore with an equivalent conductance to the multiple existing pores.
  • Figure 7 A show a low Mf noise pore of 20 nm diameter immersed in 3.6 M LiCI, at 200 mV, with 2.56 nM 4 kbp dsDNA on the one side of the membrane.
  • two levels of current blockage are observed: one for translocation events where the DNA polymer passes through the pore unfolded, and the other where it passes through partially folded.
  • Figure 7B demonstrates the case of two pores existing in a membrane. This pore was fabricated and enlarged under identical conditions to the single pore previously discussed. Four blockage levels are observed, due to the presence of multiple pores of various sizes, where each pore was represented by one folded and one unfolded blockage level.
  • pores enlarged in high conductivity solutions are not exempt from the possibility of creating multiple pores, but the speed of pore enlargement is instead decoupled from the mechanism by which additional pores are formed, allowing faster growth at lower voltage and consequently reduced probability of multiple pore formation before the desired pore size is reached.
  • a general rule of thumb for preventing the formation of multiple pores is to limit the pore enlargement voltage to no more than half of the fabrication voltage, though it is possible to effectively enlarge a pore with significantly less voltage even than this if a high-conductivity electrolyte is used to mediate the process.
  • Best practice for reliably enlarging a nanopore without risking fabrication of additional pores during the enlargement step is to use a high-conductivity solution combined with a pulsed voltage of approximately one third of the voltage at which the pore was formed during the fabrication step.
  • the primary driver of pore growth is the ionic current which passes the nanopore, but it is not the whole story, indicating that Joule heating alone is not the mechanism for pore growth. While certainly consistent with a current-driven mechanism, it is not consistent with the observed pH dependence. Given the high efficiency of heat dissipation in nanoscale geometries, it is also unlikely that Joule heating through ionic current could raise the temperature of the pore to a level that could cause material damage.
  • nanopores were individually fabricated in 40 mih c 40 mhi, 12 ⁇ 1 nm thick silicon nitride membranes. Each membrane was supported on a 200 mhi thick silicon frame with overall dimensions of 5 mm c 5 mm. All membranes were purchased from Norcada lnc (NBPX5004Z-HR).
  • the membranes Prior to nanopore fabrication, the membranes were piranha cleaned in a 3: 1 solution of H 2 S0 4 :H 2 0 2 at approximately 90° C for one hour. After cleaning, these chips were immediately rinsed free of the acid using ultrapure water and then mounted into sealed, 3D printed flow cells filled with the appropriate filtered and degassed electrolyte solution.
  • first, second, third, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms may be only used to distinguish one element, component, region, layer or section from another region, layer or section. Terms such as “first,” “second,” and other numerical terms when used herein do not imply a sequence or order unless clearly indicated by the context. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the example embodiments.
  • Spatially relative terms such as “inner,” “outer,” “beneath,” “below,” “lower,” “above,” “upper,” and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. Spatially relative terms may be intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the example term “below” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.

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Abstract

Un procédé est présenté pour agrandir la taille d'un nanopore formé dans une membrane. Le procédé comprend : la disposition d'une membrane dans un liquide conducteur, la membrane ayant un nanopore formé à l'intérieur de celle-ci ; sélectionner une valeur pour un potentiel électrique qui induit un champ électrique dans le nanopore en coopération avec la conductivité de réglage du liquide conducteur, de telle sorte que le courant à travers le nanopore est maximisé au potentiel choisi et que le champ électrique dans le nanopore est inférieur à un seuil de champ électrique maximal ; et l'application du potentiel électrique à travers le nanopore à la valeur sélectionnée, ce qui permet d'agrandir la taille du nanopore.
PCT/IB2021/055559 2020-06-23 2021-06-23 Techniques améliorées pour l'agrandissement et la formation de nanopores Ceased WO2021260587A1 (fr)

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Cited By (1)

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CN114965582A (zh) * 2022-01-06 2022-08-30 山东大学 一种多孔膜的孔径和孔密度的测量方法

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WO2013167955A1 (fr) * 2012-05-07 2013-11-14 The University Of Ottawa Fabrication de nanopores à l'aide de champs électriques élevés
WO2016135656A1 (fr) * 2015-02-24 2016-09-01 The University Of Ottawa Fabrication de nanopores de localisation sur une membrane par éclairage laser pendant une dégradation contrôlée

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WO2013167955A1 (fr) * 2012-05-07 2013-11-14 The University Of Ottawa Fabrication de nanopores à l'aide de champs électriques élevés
WO2013167952A1 (fr) * 2012-05-07 2013-11-14 The University Of Ottawa Procédé pour l'ajustement de la taille de nanopores à l'état solide
WO2016135656A1 (fr) * 2015-02-24 2016-09-01 The University Of Ottawa Fabrication de nanopores de localisation sur une membrane par éclairage laser pendant une dégradation contrôlée

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114965582A (zh) * 2022-01-06 2022-08-30 山东大学 一种多孔膜的孔径和孔密度的测量方法

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