Ion transport, dynamics

The model introduced in Section 5.3 is linear, which has proven capable of capturing the material and device dynamics reasonably well. In the remainder of this chapter we discuss several refinements of the model to incorporate nonlinear electrochemical and mechanical effects in conjugated polymer actuators. In this section we examine the modeling of a key electrochemical nonlinearity in these materials, namely, the effect of the redox level on the ion transport dynamics. The redox level refers to the extent to which the conjugated polymer is reduced or oxidized, and is determined by the amount of ions incorporated into the polymer matrix. The effect of redox level on conductivity and Young s modulus has been documented [Boxall and Osteryoung (2004) Christophersen et al. (2006) De Rossi et al. 

In Section 5.3, the transport of ions in the polymer is solely determined by the diffusion dynamics. Considering further electric field-induced ion migration, we extend the ion transport dynamics (5.1) to [Fang et al. (2008b)]... 

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

More detailed theoretical approaches which have merit are the configurational entropy model of Gibbs et al. [65, 66] and dynamic bond percolation (DBP) theory [67], a microscopic model specifically adapted by Ratner and co-workers to describe long-range ion transport in polymer electrolytes. 

In connection with the content of this section, dynamic features of ion transports through polyvinyl chloride membranes [27,28], ion-exchange resin membranes [29,30], or BLMs [31-36] have been discussed in the light of VCTTMs. For wide and pertinent applications of the VCTTM, however, further investigations have been required on the experimental and theoretical methods to analyze VCTTM quantitatively. 

The favourable properties which mark out vesicles as protocell models were confirmed by computer simulation (Pohorill and Wilson, 1995). These researchers studied the molecular dynamics of simple membrane/water boundary layers the bilayer surface fluctuated in time and space. The model membrane consisted of glycerine-1-monooleate defects were present which allowed ion transport to occur, whereby negative ions passed through the bilayer more easily than positive ions. The membrane-water boundary layer should be particularly suited to reactions which are accelerated by heterogeneous catalysis. Thus, the authors believe that these vesicles fulfil almost all the conditions required for the first protocells on earth ... 

The high temperature XRPD technique can be used to investigate the dynamics of solid-state ion exchange of zeolites. Data suggest that the rate of Cd2+ ion transport in the zeolite Y micropores controls the rate of the solid-state ion exchange. 

Numerical solution of Chazelviel s equations is hampered by the enormous variation in characteristic lengths, from the cell size (about one cm) to the charge region (100 pm in the binary solution experiments with cell potentials of several volts), to the double layer (100 mn). Bazant treated the full dynamic problem, rather than a static concentration profile, and found a wave solution for transport in the bulk solution [42], The ion-transport equations are taken together with Poisson s equation. The result is a singular perturbative problem with the small parameter A. 

These materials are introduced in Chapter 5 and only brief mention of them is necessary here. It is important to appreciate that polymer electrolytes, which consist of salts, e.g. Nal, dissolved in solid cation coordinating polymers, e.g. (CH2CH20) , conduct by quite a different mechanism from crystalline or glass electrolytes. Ion transport in polymers relies on the dynamics of the framework (i.e. the polymer chains) in contrast to hopping within a rigid framework. Intense efforts are being made to make use of these materials as electrolytes in all solid state lithium batteries for both microelectronic medical and vehicle traction applications. 

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 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. 

In an early study, Mauritz et al. investigated anion—cation interactions within Nation sulfonate membranes versus degree of hydration using FTIR/ ATR and solid state NMR (SSNMR) spectroscopies. An understanding of the dynamic ionic—hydrate molecular structures within and between the sulfonate clusters is essential for a fundamental understanding of the action of these membranes in ion transport. This information can be directly related to the equilibrium water swelling that, in turn, influences molecular migration. 

Gurtovenko, A.A., Vattulainen, I. Pore formation coupled to ion transport through lipid membranes as induced by transmembrane ionic charge imbalance atomistic molecular dynamics study. J. Am. Chem. Soc. 2005, 127, 17570-1. 

Perhaps the most outstanding advantage of the use of radioisotopes is the opportunity offered to trace dynamic mechanisms. Such biological phenomena as ion transport across cell membranes, turnover, intermediary metabolism, or translocation in plants could, before the advent of radiotracer methods, be approached only indirectly. 

Subject areas for the Series include solutions of electrolytes, liquid mixtures, chemical equilibria in solution, acid-base equilibria, vapour-liquid equilibria, liquid-liquid equilibria, solid-liquid equilibria, equilibria in analytical chemistry, dissolution of gases in liquids, dissolution and precipitation, solubility in cryogenic solvents, molten salt systems, solubility measurement techniques, solid solutions, reactions within the solid phase, ion transport reactions away from the interface (i.e. in homogeneous, bulk systems), liquid crystalline systems, solutions of macrocyclic compounds (including macrocyclic electrolytes), polymer systems, molecular dynamic simulations, structural chemistry of liquids and solutions, predictive techniques for properties of solutions, complex and multi-component solutions applications, of solution chemistry to materials and metallurgy (oxide solutions, alloys, mattes etc.), medical aspects of solubility, and environmental issues involving solution phenomena and homogeneous component phenomena. 

Characterize the structure and dynamics of active sites in enzymes and the correlated motions of secondary and tertiary structures. Measure half-lifetimes of individual steps of electron- and ion-transport during catalytic cycles. Synthesize ligands for metal centers and functionalize inorganic pores to attain enzyme-like activity and selectivity with inorganic-like robustness. 

In living cells the potential dynamically changes as different ion transporters and channels controlled by various mechanisms open and close. Approaches to and examples of modeling cellular electrophysiology are covered in greater depth in Chapter 7. 

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