Since single nanopores were firstly proposed as a potential rapid and low-cost tool for DNA sequencing in 1990s (PNAS, 1996, 93, 13770), extensive studies on both biological and synthetic nanopores and nanochannels have been reported. Nanochannel based stochastic sensing at single molecular level has been widely reported through the detection of transient ionic current changes induced by geometry blockage due to analytes translocation. Novel properties, including ion current rectification (ICR), memristive and memcapacitive behaviors were reported. These fundamental properties of nanochannels arise from the nanoscale dimensions and enables applications not only in single molecule sensing, but also in drug delivery, electrochemical energy conversion, concentration enrichment and separation, nanoprecipitation, nanoelectronics etc. Electrostatic interactions at nanometer-scale between the fixed surface charges and mobile charges in solution play major roles in those applications due to high surface to volume ratio. However, the knowledge of surface charge density (SCD) at nanometer scale is inaccessible within nanoconfinement and often extrapolated from bulk planar values. The determination of SCD at nanometer scale is urgently needed for the interpretation of aforementioned phenomena. This dissertation mainly focuses on the determination of SCD confined at a nanoscale device with known geometry via combined electroanalytical measurements and theoretical simulation. The measured currents through charged nanodevices are different for potentials with the same amplitude but opposite polarities, which deviates away from linear Ohm's behavior, known as ICR. Through theoretical simulation of experiments by solving Poisson and Nernst-Planck equations, the SCD within nanoconfinement is directly quantified for the first time. An exponential gradient SCD is introduced on the interior surface of a conical nanopre based on the gradient distribution of applied electric field. The physical origin is proposed based on the facilitated deprotonation of surface functional groups by the applied electric field. The two parameters that describe the non-uniform SCD distribution: maximum SCD and distribution length are determined by fitting high- and low-conductivity current respectively. The model is validated and applied successfully for quantification and prediction of mass transport behavior in different electrolyte solutions. Furthermore, because the surface charge distribution, the transport behaviors are intrinsicaly heterogeneous at nanometer scale, the concept is extended to noninvasively determine the surface modification efficacy of individual nanopore devices. Preliminary results of single molecule sensing based on streptavidin-iminobiotin are included. The pH dependent binding affinity of streptavidin-iminobiotin binding is confirmed by different current change signals ("steps" and "spikes") observed at different pHs. Qualitative concentration and potential dependence have been established. The chemically modified nanopores are demonstrated to be reusable through regenerating binding surface.

This thesis considers two areas of research in non-equilibrium soft matter at the mesoscale. In the first part we introduce active colloids in the context of active matter and focus on the particular case of phoretic colloids. The general theory of phoresis is presented along with an expression for the phoretic velocity of a colloid and its rotational diffusion in two and three dimensions. We introduce a model for thermally active colloids that absorb light and emit heat and propel through thermophoresis. Using this model we develop the equations of motion for their collective dynamics and consider excluded volume through a lattice gas formalism. Solutions to the thermoattractive collective dynamics are studied in one dimension analytically and numerically. A few numerical results are presented for the collective dynamics in two dimensions. We simulate an unconfined system of thermally active colloids under directed illumination with simple projection based geometric optics. This system self-organises into a comet-like swarm and exhibits a wide range of non- equilibrium phenomena. In the second part we review the background of polymer translocation, including key experiments, theoretical progress and simulation studies. We present, discuss and use a common model to investigate the potential of patterned nanopores for stochastic sensing and identification of polynucleotides and other heteropolymers. Three pore patterns are characterised in terms of the response of a homopolymer with varying attractive affinity. This is extended to simple periodic block co-polymer heterostructures and a model device is proposed and demonstrated with two stochastic sensing algorithms. We find that mul- tiple sequential measurements of the translocation time is sufficient for identification with high accuracy. Motivated by fluctuating biological channels and the prospect of frequency based selectivity we investigate the response of a homopolymer through a pore that has a time dependent geometry. We show that a time dependent mobility can capture many features of the frequency response.