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272 CHAPTER 3















                      Fig. 3.25.  (a) A space charge produced by excess electrons
                      or holes often exists inside the semiconductor, (b) The space
                      charge density varies with distance from the semiconductor–
                      electrolyte interface.


            description to give the linearized Poisson–Boltzmann equation illustrates therefore a
            characteristic development of electrochemical thinking.
               It is not surprising that the Poisson–Boltzmann approach has been used frequently
            in computing interactions between charged entities. Mention may be made of the Gouy
            theory (Fig. 3.24) of the interaction between a charged electrode and the ions in a
            solution (see Chapter 6). Other examples are the distribution (Fig. 3.25) of electrons
            or holes  inside  a  semiconductor in the  vicinity  of the  semiconductor–electrolyte
            interface (see Chapter 6) and the distribution (Fig. 3.26) of charges near a polyelec-
            trolyte molecule or a colloidal particle (see Chapter 6).
               However, one must not overstress the triumphs of the Debye–Hückel limiting law
            [Eq. (3.90)]. Models are always simplifications of reality. They never treat all its
            complexities and thus there can never be a perfect fit between experiment and the
            predictions based on a model.



















                      Fig. 3.26.  (a) A colloidal particle is surrounded by an ionic
                      cloud of excess charge density, which (b) varies with dis-
                      tance from the surface of the colloidal particle.
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