Mesoscopic effect

Sufficiently far from equilibrium, which is the only interesting regime for current generation, the Tafel law (129), (130) with effective parameters is used in the simulations. Measurements performed on model electrocatalysts suggest different values for these parameters depending on the particular catalysts used or just their different structure. The mesoscopic effects in electrocatalysis are the hot topic nowadays [127, 187-189] and they are probable candidates for one of the reasons of this variance. The main cause of this variance may be associated with the complicated interplay between adsorption and reaction stages, and a modeler interested in fuel... 

Fabrication of nano-sized metallic clusters on the surfaces and die study of their catalytic properties are a hot topic in electrocatalysis, for both tailoring new catalysts and understanding the interplay between the structure and catalytic activity (including possible mesoscopic effects) in the existing catalysts. From the dreams about the invisible we may thus come back to eardi, and ask ourselves whether the images of these clusters represent the reality. The question is motivated by often-met differences in the shapes of the clusters prescribed by STM and by transmission electron microscopy (TEM), by miraculous double clusters, etc. 

The structural characterization of electrode surfaces on the mesoscopic scale is a prerequisite for the elucidation of mesoscopic effects on electrochemical reactivity. The most straightforward approach to access the mesoscopic scale is the application of scanning probes under in-situ electrochemical conditions. Three different applications of STM have been discussed, namely the structural characterization of model electrodes, the visualization of dynamic processes on the nanometer-scale, and the defined modification of electrode surfaces. 

Keywords Moving contact line, fluid mechanics, viscous fluid, mesoscopic effects... 

Brinkmann, M. and J.-J. Andre (1999). Eleclrodeposited lithium phthalocyanine thin films. Part II Magnetic properties and mesoscopic effects. J. Mater. Chem. 9, 1511-1520. 

Balevicius, V, Gdaniec, Z., Aidas, K. and Tamuliene, J., NMR and quantum chemistry study of mesoscopic effects in ionic liquids, J. Phys. Chem. A114, 5365-5371 (2010). 

The above dimensional analysis is at rather phenomenological and/or macroscopic levels, although it has succeeded in explaining the simulation results. Indeed, in the above analysis, we have neglected mesoscopic effects such as the system inhomogeneity, density fluctuations, and collective vortex motion. Thus, to understand the annihilation dynamics in a mesoscopic level, the statistical-mechanical treatment is needed. Here, as one of such attempts, we review the hydrodynamical approach for the annihilation dynamics due to Ginzberg et al. [7]. 

So far we have assumed a step function behaviour of /x° and, almost exclusively, attributed the mesoscopic effects to changes in the electrical potential (see Fig. 5.107). But this structural invariance cannot be fulfilled down to the smallest dimensions. More subtle changes in the basic atomic structure (ionic and atomic standard potentials) are to be expected. This becomes evident when we build up solids from... 

Continuum models go one step frirtlier and drop the notion of particles altogether. Two classes of models shall be discussed field theoretical models that describe the equilibrium properties in temis of spatially varying fields of mesoscopic quantities (e.g., density or composition of a mixture) and effective interface models that describe the state of the system only in temis of the position of mterfaces. Sometimes these models can be derived from a mesoscopic model (e.g., the Edwards Hamiltonian for polymeric systems) but often the Hamiltonians are based on general symmetry considerations (e.g., Landau-Ginzburg models). These models are well suited to examine the generic universal features of mesoscopic behaviour. 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

These quantum effects, though they do not generally affect significantly the magnitude of the resistivity, introduce new features in the low temperature transport effects [8]. So, in addition to the semiclassical ideal and residual resistivities discussed above, we must take into account the contributions due to quantum localisation and interaction effects. These localisation effects were found to confirm the 2D character of conduction in MWCNT. In the same way, experiments performed at the mesoscopic scale revealed quantum oscillations of the electrical conductance as a function of magnetic field, the so-called universal conductance fluctuations (Sec. 5.2). 

Typical magnetoconductance data for the individual MWCNT are shown in Fig. 4. At low temperature, reproducible aperiodic fluctuations appear in the magnetoconduclance. The positions of the peaks and the valleys with respect to magnetic field are temperature independent. In Fig. 5, we present the temperature dependence of the peak-to-peak amplitude of the conductance fluctuations for three selected peaks (see Fig. 4) as well as the rms amplitude of the fluctuations, rms[AG]. It may be seen that the fiuctuations have constant amplitudes at low temperature, which decrease slowly with increasing temperature following a weak power law at higher temperature. The turnover in the temperature dependence of the conductance fluctuations occurs at a critical temperature Tc = 0.3 K which, in contrast to the values discussed above, is independent of the magnetic field. This behaviour was found to be consistent with a quantum transport effect of universal character, the universal conductance fluctuations (UCF) [25,26]. UCFs were previously observed in mesoscopic weakly disordered... 

So, despite the very small diameter of the MWCNT with respeet to the de Broglie wavelengths of the charge carriers, the cylindrical structure of the honeycomb lattice gives rise to a 2D electron gas for both weak localisation and UCF effects. Indeed, both the amplitude and the temperature dependence of the conductance fluctuations were found to be consistent with the universal conductance fluctuations models for mesoscopic 2D systems applied to the particular cylindrical structure of MWCNTs [10]. 

From this short discussion, it is clear that atomistically detailed molecular dynamics or Monte Carlo simulations can provide a wealth of information on systems on a local molecular atomistic level. They can, in particular, address problems where small changes in chemical composition have a drastic effect. Since chemical detail is avoided in mesoscopic models, these can often capture such effects only indirectly. 

Colloidal suspensions are systems of small mesoscopic solid particles suspended in an atomic liquid [1,2]. We will use the term colloid a little loosely, in the sense of colloidal particle. The particles may be irregularly or regularly shaped (Fig. 1). Among the regular shapes are tiny spherical balls, but also cylindrical rods or flat platelets. As the particles are solid, fluctuations of their form do not occur as they do in micellar systems. Not all particles in a suspension will, in general, have the same form. This is an intrinsic effect of the mesoscopic physics. Of course in an atomic system, say silicon, all atoms are precisely similar. One is often interested in the con-... 

The characteristic times on which catalytic events occur vary more or less in parallel with the different length scales discussed above. The activation and breaking of a chemical bond inside a molecule occurs in the picosecond regime, completion of an entire reaction cycle from complexation between catalyst and reactants through separation from the product may take anywhere between microseconds for the fastest enzymatic reactions to minutes for complicated reactions on surfaces. On the mesoscopic level, diffusion in and outside pores, and through shaped catalyst particles may take between seconds and minutes, and the residence times of molecules inside entire reactors may be from seconds to, effectively, infinity if the reactants end up in unwanted byproducts such as coke, which stay on the catalyst. 

In this sense, similar to other contributions in this volume, we will attempt to bridge the gap from microscopic to mesoscopic and thereafter to the semimacroscopic [45] regime within a simulation scheme. Firstly, we will describe in detail a mapping procedure to go from a microscopic description of a polymer chain to a mesoscopic description which allows a fairly effective simulation procedure on a coarse-grained level [43]. The choice of three modifications of one polymer... 

As has already been emphasized in Fig. 1.1, there is the further problem of connecting the mesoscopic scale, where one considers length scales from the size of effective monomers to the scale of the whole coils, to still much larger scales, to describe structures formed by multichain heterophase systems. Examples of such problems are polymer blends, where droplets of the minority phase exist on the background of the majority matrix, etc. The treatment of... 

Hybrid MPC-MD schemes may be constructed where the mesoscopic dynamics of the bath is coupled to the molecular dynamics of solute species without introducing explicit solute-bath intermolecular forces. In such a hybrid scheme, between multiparticle collision events at times x, solute particles propagate by Newton s equations of motion in the absence of solvent forces. In order to couple solute and bath particles, the solute particles are included in the multiparticle collision step [40]. The above equations describe the dynamics provided the interaction potential is replaced by Vj(rJVs) and interactions between solute and bath particles are neglected. This type of hybrid MD-MPC dynamics also satisfies the conservation laws and preserves phase space volumes. Since bath particles can penetrate solute particles, specific structural solute-bath effects cannot be treated by this rule. However, simulations may be more efficient since the solute-solvent forces do not have to be computed. 

Hybrid MPC-MD schemes are an appropriate way to describe bead-spring polymer motions in solution because they combine a mesoscopic treatment of the polymer chain with a mesoscopic treatment of the solvent in a way that accounts for all hydrodynamic effects. These methods also allow one to treat polymer dynamics in fluid flows. 

Multiparticle collision dynamics describes the interactions in a many-body system in terms of effective collisions that occur at discrete time intervals. Although the dynamics is a simplified representation of real dynamics, it conserves mass, momentum, and energy and preserves phase space volumes. Consequently, it retains many of the basic characteristics of classical Newtonian dynamics. The statistical mechanical basis of multiparticle collision dynamics is well established. Starting with the specification of the dynamics and the collision model, one may verify its dynamical properties, derive macroscopic laws, and, perhaps most importantly, obtain expressions for the transport coefficients. These features distinguish MPC dynamics from a number of other mesoscopic schemes. In order to describe solute motion in solution, MPC dynamics may be combined with molecular dynamics to construct hybrid schemes that can be used to explore a variety of phenomena. The fact that hydrodynamic interactions are properly accounted for in hybrid MPC-MD dynamics makes it a useful tool for the investigation of polymer and colloid dynamics. Since it is a particle-based scheme it incorporates fluctuations so that the reactive and nonreactive dynamics in small systems where such effects are important can be studied. 

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