Diffusivity, mass electrolytes

As repeatedly stressed, the doping processes imply the diffusion of electrolyte counterions to compensate for the electric charge assumed by the polymeric chain and thus polymers are expected to experience changes of mass upon doping. Consequently, by monitoring these changes it is possible to control the nature and the extent of the doping processes. 

As the redox reactions proceed, the availability of the active species at the electrode/electrolyte interface changes. Concentration polarization arises from limited mass transport capabilities, for example, limited diffusion of active species to and from the electrode surface to replace the reacted material to sustain the reaction. Diffusion limitations are relatively slow, and the buildup and decay take >10 s to appear. For limited diffusion the electrolyte solution, the concentration polarization, can be expressed as... 

Transport Processes. The velocity of electrode reactions is controlled by the charge-transfer rate of the electrode process, or by the velocity of the approach of the reactants, to the reaction site. The movement or trausport of reactants to and from the reaction site at the electrode interface is a common feature of all electrode reactions. Transport of reactants and products occurs by diffusion, by migration under a potential field, and by convection. The complete description of transport requires a solution to the transport equations. A full account is given in texts and discussions on hydrodynamic flow. Molecular diffusion in electrolytes is relatively slow. Although the process can be accelerated by stirring, enhanced mass transfer... 

What happens when the dimensions are furthermore reduced Initially, an enhanced diffusive mass transport would be expected. That is true, until the critical dimension is comparable to the thickness of the electrical double layer or the molecular size (a few nanometers) [7,8]. In this case, diffusive mass transport occurs mainly across the electrical double layer where the characteristics (electrical field, ion solvent interaction, viscosity, density, etc.) are different from those of the bulk solution. An important change is that the assumption of electroneutrality and lack of electromigration mass transport is not appropriate, regardless of the electrolyte concentration [9]. Therefore, there are subtle differences between the microelectrodic and nanoelectrodic behaviour. 

Figure 13 shows the potential and concentration distributions for different values of dimensionless potential under conditions when internal pore diffusion (s = 0.1) and local mass transport (y = 10) are a factor. As expected the concentration and relative overpotential decrease further away from the free electrolyte (or membrane) due to the combined effect of diffusion mass transport and the poor penetration of current into the electrode due to ionic conductivity limitations. The major difference in the data is with respect to the variation in reactant concentrations. In the case when an internal mass transport resistance occurs (y = 10) the fall in concentration, at a fixed value of electrode overpotential, is not as great as the case when no internal mass transport resistance occurs. This is due to the resistance causing a reduction in the consumption of reactant locally, and thereby increasing available reactant concentration the effect of which is more significant at higher electrode overpotentials. 

Chapter 1 serves to remind readers of the basic continuity relations for mass, momentum, and energy. Mass transfer fluxes and reference velocity frames are discussed here. Chapter 2 introduces the Maxwell-Stefan relations and, in many ways, is the cornerstone of the theoretical developments in this book. Chapter 2 includes (in Section 2.4) an introductory treatment of diffusion in electrolyte systems. The reader is referred to a dedicated text (e.g., Newman, 1991) for further reading. Chapter 3 introduces the familiar Fick s law for binary mixtures and generalizes it for multicomponent systems. The short section on transformations between fluxes in Section 1.2.1 is needed only to accompany the material in Section 3.2.2. Chapter 2 (The Maxwell-Stefan relations) and Chapter 3 (Fick s laws) can be presented in reverse order if this suits the tastes of the instructor. The material on irreversible thermodynamics in Section 2.3 could be omitted from a short introductory course or postponed until it is required for the treatment of diffusion in electrolyte systems (Section 2.4) and for the development of constitutive relations for simultaneous heat and mass transfer (Section 11.2). The section on irreversible thermodynamics in Chapter 3 should be studied in conjunction with the application of multicomponent diffusion theory in Section 5.6. 

Transport by diffusion. The electrolytic current can be related to the mass flux densities at the electrode surface, J. For an electrochemical reaction, one has... 

We have seen in Chapter 2 that if the Reynolds number is not too high, the resistance to mass transfer to and from an electrode is confined to a hydrodynamic laminar layer adjacent to the surface of the electrode across which ions may be transferred either by diffusion or electrolytic migration. Resistance to mass transfer by diffusion causes concentration gradients to be formed (Fig. 3.6). The concentration profiles, normally curved, have been linearized as explained in Chapter 2. It is assumed that the bulk of the electrolyte is so well stirred that concentration is uniform. Let us use the simple reduction in Eq. (3.65) when considering activation control ... 

The rotating disk electrode is becoming one of the most powerful methods for studying both diffusion in electrolytic solutions and the kinetics of moderately fast electrode reaction because the hydrodynamics and the mass-transfer characteristics are well understood and the current density on the disk electrode is supposed to be uniform. Levich [179] solved the family of equations and provided an empirical relationship between diffusion limiting current (id) and rotation rate ( >) as shown in Eq. (9.42). In particular applications in fuel cells, the empirical relationship which is given by Levich was also used in linear scan voltammetry (LSV) experiment performed on a RDE to study the intrinsic kinetics of the catalyst [151,159,180-190]. However, it is more appropriate to continue the discussion later in detail in the LSV section. 

Water transport in the SOFC electrolyte membrane is primarily by diffusion mass transport... 

Oxygen concentration at the cathode-electrolyte interface is given based on Equation 11.37 for the case with dominant diffusion mass transfer resistance as... 

Similarly to mass diffusion in electrolytes, gas-phase mass diffusion is driven by concentration gradients. If a spray of perfume is released at the front of a classroom, the students... 

Eddy diffusion as a transport mechanism dominates turbulent flow at a planar electrode ia a duct. Close to the electrode, however, transport is by diffusion across a laminar sublayer. Because this sublayer is much thinner than the layer under laminar flow, higher mass-transfer rates under turbulent conditions result. Assuming an essentially constant reactant concentration, the limiting current under turbulent flow is expected to be iadependent of distance ia the direction of electrolyte flow. 

X-ray scattering studies at a renewed pc-Ag/electrolyte interface366,823 provide evidence for assuming that fast relaxation and diffu-sional processes are probable at a renewed Sn + Pb alloy surface. Investigations by secondary-ion mass spectroscopy (SIMS) of the Pb concentration profile in a thin Sn + Pb alloy surface layer show that the concentration penetration depth in the solid phase is on the order of 0.2 pm, which leads to an estimate of a surface diffusion coefficient for Pb atoms in the Sn + Pb alloy surface layer on the order of 10"13 to lCT12 cm2 s i 820 ( p,emicai analysis by electron spectroscopy for chemical analysis (ESCA) and Auger ofjust-renewed Sn + Pb alloy surfaces in a vacuum confirms that enrichment with Pb of the surface layer is probable.810... 

Inside a pit in electrolytic solution, anodic dissolution (the critical dissolution current density, and diffusion of dissolved metal hydrates to the bulk solution outside the pit take place simultaneously, so that the mass transfer is kept in a steady state. According to the theory of mass transport at an electrode surface for anodic dissolution of a metal electrode,32 the total increase of the hydrates inside a pit, AC(0) = AZC,<0),is given by the following equation33,34 ... 

Sontherland, W, A Dynamical Theory of Diffusion for Non-Electrolytes and the Molecnlar Mass of Albnmin, Philosophical Magazine 9, 781, 1905. 

Here, / is the electric field, k is the electrical conductivity or electrolytic conductivity in the Systeme International (SI) unit, X the thermal conductivity, and D the diffusion coefficient. is the electric current per unit area, J, is the heat flow per unit area per unit time, and Ji is the flow of component i in units of mass, or mole, per unit area per unit time. 

Under realistic conditions a balance is secured during current flow because of additional mechanisms of mass transport in the electrolyte diffusion and convection. The initial inbalance between the rates of migration and reaction brings about a change in component concentrations next to the electrode surfaces, and thus gives rise to concentration gradients. As a result, a diffusion flux develops for each component. Moreover, in liquid electrolytes, hydrodynamic flows bringing about convective fluxes Ji j of the dissolved reaction components will almost always arise. 

It was shown in Section 1.8 that in addition to ion migration, diffusion and convection fluxes are a substantial part of mass transport during current flow through electrolyte solutions, securing a mass balance in the system. In the present chapter these processes are discussed in more detail. 

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