Finite-Size Charged Species Diffusion and pH Change in Nanochannels.

Molecular transport through nanofluidic structures exhibits properties that are unique at the nanoscale. The high surface-to-volume ratio of nanometer-sized confined spaces renders particle interactions with the surface of central importance. The electrical double layer (EDL) at the solid-liquid interface of charged surfaces generates an enrichment of counterions and the exclusion of co-ions that lead to a change in their diffusivity. In addition, the diffusive transport is altered by steric and hydrodynamic interactions between fluid molecules and the boundaries. An extensive body of literature investigates molecular transport at the nanoscale. However, most studies account for ionic species as point charges, severely limiting the applicability of the results to "large" nanofluidic systems. Moreover, and even more importantly, the change of pH in the nanoconfined region inside nanochannels has been completely overlooked. Corroborated by experimental data, here we present an all-encompassing analysis of molecular diffusion from the micro- to the ultra-nanoscale. While accounting for finite-size ions, we compute self-consistently the pH inside the channels. Surprisingly, we found that the concentration of ions H+ can change by more than 2 orders of magnitude compared to the bulk, hugely affecting molecular transport. Further, we found that counterions exhibit both enrichment and exclusion, depending on the size of nanochannels. Achieving a greater understanding of the effective transport properties of fluids at the nanoscale will fill the gap in knowledge that still limits development of innovative systems for medicine and industrial applications alike.

Gas Flow at the Ultra-nanoscale: Universal Predictive Model and Validation in Nanochannels of Ångstrom-Level Resolution.

Gas transport across nanoscale pores is determinant in molecular exchange in living organisms as well as in a broad spectrum of technologies. Here, we report an unprecedented theoretical and experimental analysis of gas transport in a consistent set of confining nanochannels ranging in size from the ultra-nanoscale to the sub-microscale. A generally applicable theoretical approach quantitatively predicting confined gas flow in the Knudsen and transition regime was developed. Unlike current theories, specifically designed for very simple channel geometries, our approach can be applied to virtually all geometries, for which the probability distribution of path lengths for particle-interface collisions can be computed, either analytically or by numerical simulations. To generate a much needed benchmark experimental model, we manufactured extremely reproducible membranes with two-dimensional nanochannels. Channel sizes ranged from 2.5 to 250 nm, and angstrom level of size control and interface tolerances were achieved using leading-edge nanofabrication techniques. We then measured gas flow in the Knudsen number range from 0.2 to 20. Excellent agreement between theoretical predictions and experimental data was found, demonstrating the validity and potential of our approach.

Unexpected behaviors in molecular transport through size-controlled nanochannels down to the ultra-nanoscale.

Ionic transport through nanofluidic systems is a problem of fundamental interest in transport physics and has broad relevance in desalination, fuel cells, batteries, filtration, and drug delivery. When the dimension of the fluidic system approaches the size of molecules in solution, fluid properties are not homogeneous and a departure in behavior is observed with respect to continuum-based theories. Here we present a systematic study of the transport of charged and neutral small molecules in an ideal nanofluidic platform with precise channels from the sub-microscale to the ultra-nanoscale (<5 nm). Surprisingly, we find that diffusive transport of nano-confined neutral molecules matches that of charged molecules, as though the former carry an effective charge. Further, approaching the ultra-nanoscale molecular diffusivities suddenly drop by up to an order of magnitude for all molecules, irrespective of their electric charge. New theoretical investigations will be required to shed light onto these intriguing results.

Fragmentation approach to the point-island model with hindered aggregation: Accessing the barrier energy.

We study the effect of hindered aggregation on the island formation process in a one- (1D) and two-dimensional (2D) point-island model for epitaxial growth with arbitrary critical nucleus size i. In our model, the attachment of monomers to preexisting islands is hindered by an additional attachment barrier, characterized by length l_{a}. For l_{a}=0 the islands behave as perfect sinks while for l_{a}→∞ they behave as reflecting boundaries. For intermediate values of l_{a}, the system exhibits a crossover between two different kinds of processes, diffusion-limited aggregation and attachment-limited aggregation. We calculate the growth exponents of the density of islands and monomers for the low coverage and aggregation regimes. The capture-zone (CZ) distributions are also calculated for different values of i and l_{a}. In order to obtain a good spatial description of the nucleation process, we propose a fragmentation model, which is based on an approximate description of nucleation inside of the gaps for 1D and the CZs for 2D. In both cases, the nucleation is described by using two different physically rooted probabilities, which are related with the microscopic parameters of the model (i and l_{a}). We test our analytical model with extensive numerical simulations and previously established results. The proposed model describes excellently the statistical behavior of the system for arbitrary values of l_{a} and i=1, 2, and 3.

Nanoparticles heat through light localization.

Aqueous solutions containing light-absorbing nanoparticles have recently been shown to produce steam at high efficiencies upon solar illumination, even when the temperature of the bulk fluid volume remains far below its boiling point. Here we show that this phenomenon is due to a collective effect mediated by multiple light scattering from the dispersed nanoparticles. Randomly positioned nanoparticles that both scatter and absorb light are able to concentrate light energy into mesoscale volumes near the illuminated surface of the liquid. The resulting light absorption creates intense localized heating and efficient vaporization of the surrounding liquid. Light trapping-induced localized heating provides the mechanism for low-temperature light-induced steam generation and is consistent with classical heat transfer.

Scaling and Exponent Equalities in Island Nucleation: Novel Results and Application to Organic Films.

It is known in thin-film deposition that the density of nucleated clusters N varies with the deposition rate F as a power law, N ∼ Fα. The exponent α is a function of the critical nucleus size i in a way that changes with the aggregation limiting process. We extend here the derivation of the analytical capture-zone distribution function Pß(s) = aß ·sß ·exp(-bßs2) of Pimpinelli and Einstein to generic aggregation-limiting processes. We show that the parameter ß is generally related to the critical nucleus size i and to the exponent α by the equality α·ß = i, in the case of compact islands. This remarkable result allows one to measure i with no a priori knowledge of the actual aggregation mechanism. We apply this equality to measuring the critical nucleus size for pentacene deposition on mica. This system shows a crossover from diffusion-limited to attachment-limited aggregation with increasing deposition rates.

Mean-field approximation for spacing distribution functions in classical systems.

We propose a mean-field method to calculate approximately the spacing distribution functions p((n))(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p((n))(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.

Spacing distribution functions for the one-dimensional point-island model with irreversible attachment.

We study the configurational structure of the point-island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density p(n)(XY)(x,y), which represents the probability density to have nucleation at position x within a gap of size y. Our proposed functional form for p(n)(XY)(x,y) describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system.

Effects of impurities on surface morphology: some examples.

Small amounts of impurities are known to have remarkably great influence on surface morphology. We discuss three examples that arise in our research. First, we consider impurities codeposited during epitaxial growth, paying particular attention to Cu(100). After many layers of growth, the impurities can dramatically alter the surface morphology, changing the wavelength of the meandering instability and producing small square-base pyramids. Second, we consider the decoration of both island and vacancy island edges on Ag(111) with C(60). We use this system as a prototype to model how edge decoration with impurities can have a striking effect on the shape of the island as well as the dynamics of edge fluctuations. Finally, we show that about one per cent of pentacene quinone impurities alters the size of the critical nucleus in submonolayer pentacene deposition. This provides a platform on which to discuss our recent work characterizing the capture-zone distribution associated with the islands in terms of the generalized Wigner distribution, a simple one-parameter expression in which the characteristic exponent is the size of the smallest stable island.

Capture-zone scaling in island nucleation: universal fluctuation behavior.

In island nucleation and growth, the distribution of capture zones (in essence proximity cells) can be described by a simple expression generalizing the Wigner surmise (power-law rise, Gaussian decay) from random matrix theory that accounts for spacing distributions in a host of fluctuation phenomena. Its single adjustable parameter, the power-law exponent, can be simply related to the critical nucleus of growth models and the substrate dimensionality. We compare with extensive published kinetic Monte Carlo data and limited experimental data. A phenomenological theory elucidates the result.

Distinctive fluctuations in a confined geometry.

Spurred by recent theoretical predictions [Phys. Rev. E 69, 035102(R) (2004)10.1103/PhysRevE.69.035102; Surf. Sci. Lett. 598, L355 (2005)10.1016/j.susc.2005.09.023], we find experimentally using STM line scans that the fluctuations of the step bounding a facet exhibit scaling properties distinct from those of isolated steps or steps on vicinal surfaces. The correlation functions go as t0.15 +/- 0.03 decidedly different from the t0.26 +/- 0.02 behavior for fluctuations of isolated steps. From the exponents, we categorize the universality, confirming the prediction that the nonlinear term of the Kardar-Parisi-Zhang equation, long known to play a central role in nonequilibrium phenomena, can also arise from the curvature or potential-asymmetry contribution to the step free energy.

New types of unstable step-flow growth on Si(111)-(7 x 7) during molecular beam epitaxy: scaling and universality.

New types of unstable homoepitaxial growth of vicinal surfaces are studied using ex situ atomic force microscopy. The growth features are two types of step bunching with straight step edges between 700 and 775 degrees C and one type of simultaneous bunching and meandering at 800 degrees C. The results of a quantitative size scaling analysis of the straight steps are discussed from the perspective of universality classes in bunching theory.

Evolution of terrace-width distributions on vicinal surfaces: Fokker-Planck derivation of the generalized Wigner surmise.

We use a Fokker-Planck equation to justify the generalization of the Wigner surmise for the energy-level spacing in quantum systems to the simple expression for the equilibrium terrace-width distribution of steps--with arbitrary-strength repulsions--on a vicinal surface, taking advantage of analogies to one-dimensional models of interacting, spinless fermions. This approach leads to an analytic description of the evolution toward equilibrium of steps from several experimentally relevant initial distributions: step bunches, perfect cleaved crystals, and prequench equilibrated distributions at different temperatures.