Modeling the Conductivity and Diffusion Permeability of a Track-Etched Membrane Taking into Account a Loose Layer.

The microheterogeneous model makes it possible to describe the main transport properties of ion-exchange membranes using a single set of input parameters. This paper describes an adaptation of the microheterogeneous model for describing the electrical conductivity and diffusion permeability of a track-etched membrane (TEM). Usually, the transport parameters of TEMs are evaluated assuming that ion transfer occurs through the solution filling the membrane pores, which are cylindrical and oriented normally to the membrane surface. The version of the microheterogeneous model developed in this paper takes into account the presence of a loose layer, which forms as an intermediate layer between the pore solution and the membrane bulk material during track etching. It is assumed that this layer can be considered as a "gel phase" in the framework of the microheterogeneous model due to the fixed hydroxyl and carboxyl groups, which imparts ion exchange properties to the loose layer. The qualitative and quantitative agreement between the calculated and experimental concentration dependencies of the conductivity and diffusion permeability is discussed. The role of the model input parameters is described in relation to the structural features of the membrane. In particular, the inclination of the pores relative to the surface and their narrowing in the middle part of the membrane can be important for their properties.

Accurate characterization of single track-etched, conical nanopores.

Single track-etched conical nanopores in polymer foils have attracted considerable attention in recent years due to their potential applications in biosensing, nanofluidics, information processing, and other fields. The performance of a nanopore critically depends on the size and shape of its narrowest, nanometer-sized region. In this paper, we reconstructed the profiles of both doubly-conical and conical pores, using an algorithm based on conductometric measurements performed in the course of etching, coupled with SEM data. We showed that pore constriction deviates from the conical shape, and the deviation depends on the energy loss of the particle that produced the track. Funnel-like profiles of tracks of four ions with different atomic numbers were derived from experimental data. The simulations, using a Poisson-Nernst-Planck model, demonstrated that the ion current rectification properties of the funnel-shaped asymmetrical pores significantly differ from those of conical ones if the tip radius of the pore is smaller than 10 nm. Upon subjecting to further etching, the pores gradually approach the "ideal" conical geometry, and the ion transport properties of these two pore configurations become almost indistinguishable.

Asymmetric ion track nanopores for sensor technology. Reconstruction of pore profile from conductometric measurements.

We reconstruct the profile of asymmetric ion track nanopores from an algorithm developed for conductometric measurements of symmetric nanopores. The validity of the reconstruction is supported by FESEM observations. Our analysis reveals that asymmetric pores fabricated by one-sided etching are funnel-like and not conical. The analysis provides the constriction diameter and the pore profile as a function of etching time. The reconstruction of the pore profile defines the starting conditions of asymmetric nanopores at breakthrough. The deviation from the conical shape is most pronounced at the pore tip. This critical zone dominates transport properties relevant to ion conductance, selectivity, current rectification, resistive pulse sensing and biosensors. The classical cone approximation used until now underestimates the tip diameter by a factor of two. As transport processes in nanopores depend in a highly nonlinear way on the constriction diameter the presented reconstruction must be taken into account when studying ionic and molecular transport processes in asymmetric pores.

Effect of nanopore geometry on ion current rectification.

We present the results of systematic studies of ion current rectification performed on artificial asymmetric nanopores with different geometries and dimensions. The nanopores are fabricated by the ion track etching method using surfactant-doped alkaline solutions. By varying the alkali concentration in the etchant and the etching time, control over the pore profile and dimensions is achieved. The pore geometry is characterized in detail using field-emission scanning electron microscopy. The dependence of the ion current rectification ratio on the pore length, tip diameter, and the degree of pore taper is analysed. The experimental data are compared to the calculations based on the Poisson-Nernst-Planck equations. A strong effect of the tip geometry on the diode-like behaviour is confirmed.

Ultrasound attenuation in cylindrical micro-pores: nondestructive porometry of ion-track membranes.

The propagation of ultrasonic waves in the cylindrical micro-pores (pore diam. 1 microm) of ion-track membranes (ITMs) is studied. This membrane fabrication technique provides unique possibilities to obtain cylindrical micro-pores with a very high degree of accuracy in pore shape, size, and orientation. Several ITMs were specially produced having the same pore diameter, orientation, and geometry, but different thickness. Porosity, pore diameter, and shape were determined using scanning electron microscopy, and then the coefficient of ultrasound transmission was measured using air coupling and spectral analysis. These experimental conditions permit us to eliminate the influence of the boundary conditions and to achieve a strong decoupling between the fluid filling the pores and the solid constituent of the membrane. Hence, the velocity and the attenuation coefficient for ultrasound propagation in the pores can be measured. These parameters are compared with the predictions made by conventional theories for sound propagation in porous media and in cylindrical channels. The conclusions of this work provide a better understanding of wave propagation in micro-pores and establish the basis of an ultrasonic porometry technique for ITMs.

Pore structure and function of synthetic nanopores with fixed charges: tip shape and rectification properties.

We present a complete theoretical study of the relationship between the structure (tip shape and dimensions) and function (selectivity and rectification) of asymmetric nanopores on the basis of previous experimental studies. The theoretical model uses a continuum approach based on the Nernst-Planck equations. According to our results, the nanopore transport properties, such as current-voltage (I-V) characteristics, conductance, rectification ratio, and selectivity, are dictated mainly by the shape of the pore tip (we have distinguished bullet-like, conical, trumpet-like, and hybrid shapes) and the concentration of pore surface charges. As a consequence, the nanopore performance in practical applications will depend not only on the base and tip openings but also on the pore shape. In particular, we show that the pore opening dimensions estimated from the pore conductance can be very different, depending on the pore shape assumed. The results obtained can also be of practical relevance for the design of nanopores, nanopipettes, and nanoelectrodes, where the electrical interactions between the charges attached to the nanostructure and the mobile charges confined in the reduced volume of the inside solution dictate the device performance in practical applications. Because single tracks are the elementary building blocks for nanoporous membranes, the understanding and control of their individual properties should also be crucial in protein separation, water desalination, and bio-molecule detection using arrays of identical nanopores.