Modeling in Electrochemistry

Our purpose in this chapter is to review the nature of mathematical modeling in the context of modem electrochemistry and to describe how current and emerging trends in computer applications and system development are intended to assist practitioners. One trend is toward the merger of these two disciplines as computer-aided mathematical modeling. 

As indicated above, there are a large number of modeling packages on the market. Some of those are mentioned below. In the vast majority, differential equations that describe the electrochemical setup are solved using numeric methods. Two of the most common methods are the finite-difference method and the finite-elements method. These are discussed in some detail in this chapter, including example calculations in Section 15.3. We begin with a few general remarks. 

The term modeling refers to a process of determining an appropriate description of reality that approximates its behavior to some specified degree of accuracy. Models are constructed using well-understood primitive components, or building blocks, defined by their inherent functionality and also their interaction mechanism. 

Fundamentals of Electrochemical Deposition, Second Edition. By Milan Paunovic and Mordechay Schlesinger Copyright 2006 John Wiley Sons, Inc. 

A paper airplane and a plasticine car each represent models that might apply, say, in aerospace or automotive research and development. That each approximates the reality of actual aircraft and motor vehicles is intuitively obvious, yet it is immediately clear that neither suffices to explain the theory of their operation or to overcome production problems. Paper and plasticine and even fashion modehng provide types of media that appeal to visual appreciation but fail to provide deep understanding of fundamental issues. To overcome this lack, better media that allow for truer representation and insightful analyses are required. 

Mathematical modeling is used extensively in electrochemistry, and as new applications arise, techniques of modeling evolve as well. A particular area of interest in electrochemistry is electrostatics. Research in electrostatics is concerned with is- 

The first step involves specification of the model properties. Usually one begins with geometric configuration that is, the physical layout of the passive and active elements. This task is facilitated by drawing a facsimile of the system. This process is 

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It is seen from the above that the present book contains a number of different types of material, and it is likely that on first reading, some readers, will want to use some chapters, whereas others may want to use different ones. For this reason the chapters and their various sections have been made independent of each other as far as possible. Certain chapters can be omitted without causing difficulties in reading succeeding chapters. For example, Chapters 3 (on metals and metal surfaces), 7 (on nucleation and growth models), 14 (on in situ characterization of depKJsition processes), and 15 (mathematical modeling in electrochemistry) can be omitted on first reading. Thus, the book can be used in a variety of ways to serve the needs of different readers. 

The application of first principles methods to the study of electrocatalysis in fuel cells has gained significant momentum in recent years. Browse any issue of a journal with theoretical electrochemistry content and you will notice a few theoretical study articles. Theoretical modeling in electrochemistry has certainly reached the stage at which it can begin to complement experimental methods, and provide insight into the atomic scale features that control the chemistry at the aqueous/metal interface [101]. 

M. Schlesinger, Mathematical Modeling in Electrochemistry, in Modem Aspects of Electrochemistry, Vol. 43, M. Schlesinger, Ed., Springer, New York, 2008. 

Mathematical modeling in electrochemistry using finite element and finite difference methods... 

The reader is presented with ten chapters written by 21 experts in the fields of modelling in electrochemistry and its many subfields. The first chapter deals with the subject of modelling in electrochemistry in general. The second and third chapters take up issues dealing with optics as related to applications in nanoelectrochemistry. The fourth, fifth and sixth chapters refer to surface electrochemistry. The last of these introduces the subject of Monte Carlo simulations... 

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