Description of electrolyte transport

Description of electrolyte transport using the MSA for simple electrolytes, polyelectrolytes and micelles 

Description of the concentration dependence of the transport coefficients of electrolytes is one of the oldest open problem in physical chemistry. Since the early papers ofOnsager et al in 1926 [1] and in 1932 [2], where limiting laws for the conductance were given, and later extended to the self diffusion for single ions [3] and ionic mixtures [4], progress has been difficult. 

In 1957 Onsager et al. [4] made an attempt to extend the validity of the conductivity limiting law to higher concentrations, using the Debye-Hiickel equilibrium pair distribution functions [6]. At the same level, concentration dependence for self-diffusion was obtained [7, 8]. 

Ebeling et al [9, 10] used the restricted primitive model (equal size ions in a dielectric continuum) to describe the variation of conductance with concentration. They used MSA distribution functions to compute the relaxation contribution. 

We present here the basis of the development and the main results. 

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The electrolyte concentration is very important when it comes to discussing mechanisms of ion transport. Molar conductivity-concentration data show conductivity behaviour characteristic of ion association, even at very low salt concentrations (0.01 mol dm ). Vibrational spectra show that by increasing the salt concentration, there is a change in the environment of the ions due to coulomb interactions. In fact, many polymer electrolyte systems are studied at concentrations greatly in excess of 1.0 mol dm (corresponding to ether oxygen to cation ratios of less than 20 1) and charge transport in such systems may have more in common with that of molten salt hydrates or coulomb fluids. However, it is unlikely that any of the models discussed here will offer a unique description of ion transport in a dynamic polymer electrolyte host. Models which have been used or developed to describe ion transport in polymer electrolytes are outlined below. 

The model system for biological membranes is the so-called artificial lipid membrane made of two monolayers of lipid between two (aqueous) electrolyte solutions. The thickness of such a membrane can vary over a wide range and this introduces some ambiguity in deciding what kind of model should be the basis for the mathematical description of ion transport and other properties. Two extreme concepts can be distinguished. 

The initial emphasis on evaluation and modeling of losses in the membrane electrolyte was required because this unique component of the PEFC is quite different from the electrolytes employed in other, low-temperature, fuel cell systems. One very important element which determines the performance of the PEFC is the water-content dependence of the protonic conductivity in the ionomeric membrane. The water profile established across and along [106]) the membrane at steady state is thus an important performance-determining element. The water profile in the membrane is determined, in turn, by the eombined effects of several flux elements presented schematically in Fig. 27. Under some conditions (typically, Pcath > Pan), an additional flux component due to hydraulic permeability has to be considered (see Eq. (16)). A mathematical description of water transport in the membrane requires knowledge of the detailed dependencies on water content of (1) the electroosmotic drag coefficient (water transport coupled to proton transport) and (2) the water diffusion coefficient. Experimental evaluation of these parameters is described in detail in Section 5.3.2. 

The water distribution within a polymer electrolyte fuel cell (PEFC) has been modeled at various levels of sophistication by several groups. Verbrugge and coworkers [83-85] have carried out extensive modeling of transport properties in immersed perfluorosulfonate ionomers based on dilute-solution theory. Fales et al. [109] reported an isothermal water map based on hydraulic permeability and electro-osmotic drag data. Though the model was relatively simple, some broad conclusions concerning membrane humidification conditions were reached. Fuller and Newman [104] applied concentrated-solution theory and employed limited earlier literature data on transport properties to produce a general description of water transport in fuel cell membranes. The last contribution emphasizes water distribution within the membrane. Boundary values were set rather arbitrarily. 

Transportation of Li in the electrolyte through the SEI may occur via several different mechanisms. One possible mechanism is that Li after desolvation directly passes through pores since SEI is porous the other possibility is that Li after desolvation exchanges with Li in the SEI. Recently, Harris et al. provided a more detailed description of ion transport mechanisms in SEI film by using isotope-labeled electrolyte approach [71]. They immersed three copper electrodes which were preformed SEI in LiC104 EC/DEC electrolyte into 1 M LiBp4 EC/DEC electrolyte for 30 s, 3 min, and 15 min. After immersion, the electrodes were rinsed with DMC solvent and then transferred under Ar to a time-of-flight secondary ion mass spectrometer (TOF-MS) the results are shown in Fig. 5.24. 

The description of the transport properties of electrolyte solutions requires some basic information on the hydrodynamic interactions between the solute particles. 

The authors are aware of the fact that, although this book demonstrates the significant progress that has been made in this held in the past decade, there is still a need for additional experimental and theoretical work in many parts of the transport-property surface. In the individual chapters, an attempt is made to specify the relevant needs in each density domain. It should be noted that this volume is restricted to a discussion of nonelectrolytes. In spite of their technological importance, ionic systems, including ionized gases and plasmas, molten metals and aqueous electrolyte solutions are not included because of the different nature of the interaction forces. A complete description of the transport properties of these fluids and fluid mixtures would occupy another volume. 

We now turn to transport properties of electrolytes. As mentioned above this problem is much more complicated than the equilibrium one because the solvent plays a crucial role in the description of dissipative phenomena. As a matter of fact, no general solution exists to this problem, because the statistical description of the liquid state is still at a very primitive stage. 

The first half of this chapter concentrates on the mechanisms of ion conduction. A basic model of ion transport is presented which contains the essential features necessary to describe conduction in the different classes of solid electrolyte. The model is based on the isolated hopping of the mobile ions in addition, brief mention is made of the influence of ion interactions between both the mobile ions and the immobile ions of the solid lattice (ion hopping) and between different mobile ions. The latter leads to either ion ordering or the formation of a more dynamic structure, the ion atmosphere. It is likely that in solid electrolytes, such ion interactions and cooperative ion movements are important and must be taken into account if a quantitative description of ionic conductivity is to be attempted. In this chapter, the emphasis is on presenting the basic elements of ion transport and comparing ionic conductivity in different classes of solid electrolyte which possess different gross structural features. Refinements of the basic model presented here are then described in Chapter 3. 

The thermodynamics of insertion electrodes is discussed in detail in Chapter 7. In the present chapter attention is focused mainly on the general kinetic aspects of electrode reactions and on the techniques by which the transport of species within electrodes may be determined. The electrodes are treated in a general fashion as exhibiting mixed ionic and electronic transport, and attention is concentrated on the description of the coupled transport of these species. In this context it is useful to consider that an electronically conducting lead provides the electrons at the electrodes and compensates the charges of the ions transferred by the electrolyte. 

A further important step forward was the work of Nemst [73, 74] and Planck [81, 82] on transport in electrolyte solutions. Here the concept of the diffusion potential was defined diffusion potential arises when the mobihties of the electrically-charged components of the electrolyte are different and is important both for description of conditions within membranes as well as for quantitative determination of the liquid-junction potential. 

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... 

S0l., So2 and SHlo refer to the respective source terms owing to the ORR, e is the electrolyte phase potential, cGl is the oxygen concentration and cHlo is the water vapor concentration, Ke is the proton conductivity duly modified w.r.t. to the actual electrolyte volume fraction, Dsa is the oxygen diffusivity and is the vapor diffusivity. The details about the DNS model for pore-scale description of species and charge transport in the CL microstructure along with its capability of discerning the compositional influence on the CL performance as well as local overpotential and reaction current distributions are furnished in our work.25 27,67... 

These four equations form the basis for a description of the mass transport in electrolytic solutions. To solve these equations, we must calculate the bulk solution velocity from a knowledge of the fluid mechanics. 

Low salt rejection RO membranes (e.g., R < 0.5 for NaCl) are sometimes classified as nanoporous and allow retention of sugars and large molecules while permeating small electrolytes. In this case, a hindered transport description of the process would be appropriate with the water and nonrejected electrolytes being treated as a single fluid and the rejected sugar considered the solute. 

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