Page 20 - Analytical Electrochemistry 2d Ed - Jospeh Wang

1-2 FARADAIC PROCESSES 5

FIGURE 1-1 The three modes of mass transport. (Reproduced with permission from
reference 1.)

The ¯ux (J) is a common measure of the rate of mass transport at a ®xed point. It
is de®ned as the number of molecules penetrating a unit area of an imaginary plane
1
in a unit of time, and has the units of mol cm 2 s . The ¯ux to the electrode is
described mathematically by a differential equation, known as the Nernst±Planck
equation, given here for one dimension:

@C x; t† zFDC @f x; t†
J x; t†ˆ D ‡ C x; t†V x; t† 1-3†
@x RT @x

1
where D is the diffusion coef®cient (cm 2 s ), @C x; t†=@x is the concentration
gradient (at distance x and time t), @f x; t†=@x is the potential gradient, z and C are
the charge and concentration, respectively, of the electroactive species, and V x; t† is
the hydrodynamic velocity (in the x direction). In aqueous media, D usually ranges
1
between 10 5 and 10 6 cm 2 s . The current (i) is directly proportional to the ¯ux:

i ˆ nFAJ 1-4†