Affinity electrochemical

Although multistep affinity assays with redox-labeled targets have been described (Wang et al. [117]), most of the assays use enzyme-labeled species in conventional indirect formats (competitive, non-competitive). Direct EILAs based on multistep electrochemical affinity assays have also been developed with excellent results. In all these cases the MIP is used to extract the analyte from the sample and, after elution, the analyte is carried on to the electrochemical flow-through cell for being detected. 

For charged particles (ions), the electrostatic energy of the transfer is incorporated by using the electrochemical potential defined in Eq. (35) of Chapter 10. The electrochemical affinity is... 

Yoon s group has made significant contributions in the development of dendrimer-based electrochemical affinity biosensors [172-179] and highlights of their research work have been appraised recently [77],... 

The stoichiometric number, v, of a given reaction step is defined as the number of times that step must occur for one turnover of the whole reaction. The overall stoichiometric number of a reaction is specifically the number of times the rds has to occur. This is an important quantity with respect to mechanism elucidation and was originally defined by Horiuti for the hydrogen reaction.45,46 According to the stoichiometric number concept of Horiuti, V for each reaction step will multiply the Gibbs energy change (or as it is also called, its electrochemical affinity) for that step, Agi, and the affinity, AG, for the overall reaction is... 

Two papers on the theory of SBSCs have appeared. The magnitude of the voltage attainable across metal-semiconductor interfaces in thermodynamic disequilibrium has been formulated in terms of electrochemical affinities, using the method of irreversible thermodynamics.70 The role of the interfacial layer, which may act to increase the open-circuit voltage and the fill factor, has also been discussed.71... 

In line with Eq. (3.36), the electrochemical affinity of chemically reacting ions is defined by... 

Thus the electrochemical affinity is equal to the ordinary chemical affinity... 

In the previous section, we used electrode potential without any strict definition. However, it should be defined in advance, in order to better understand it. Originally, the electrode potential was closely related to Gibbs free energy change of a reaction at the interface (electrode). It is also related to chemical affinity. In this electrochemical case, we might say that the electrode reaction should be related to electrochemical affinity. So what is electrochemical affinity To answer this question and others would lead to a complete understanding of what electrode potential is and what it really means. We would like to introduce the concept of inner potential for the explanation. 

The potential difference is closely related to the difference of the electrochemical potential based on the electrochemical affinity. If we could measure A(p directly, we could organize the table of electromotive forces based on the Galvani potential difference. However, A

reference electrode to measure the half cell potential at an electrode. When a certain electrcxle is coupled with a reference electrode, then the electromotive force can be measured. Since we usually use some reference electrodes as standards, the electromotive force is defined as the equilibrium potential of the reaction. The table was made in such a way and the hydrogen reference electrode was used to measure and calculate potentials for the half cell reactions. 

We shall call A the electrochemical affinity of the cell. It is the sum of the chemical affinity A and of the electric affinity zFU. At equilibrium we have... 

The electrochemical affinity defined in (25) is related to the overtensions and the ohmic drop RI as follows ... 

The total electrochemical affinity of the cell can be regarded as the sum of an anodic electrochemical affinity A = zFr, a cathodic electrochemical affinity Joule effect... 

The connection between overtensions and electrochemical affinities, which so far has received little attention by electrochemists, is of fundamental importance and affords a most useful channel for the introduction of thermodynamic considerations into electrode kinetics. 

Let us add at this point that the electrochemical affinity A of the cell reaction and the electrochemical tension E may be written under forms similar to (49) and (50) ... 

From (37) we see that the electrochemical affinity A of a cell consists of three contributions due to the anodic and cathodic overtensions and to the ohmic drop. If one of the overtensions is zero, as is the case for the reference electrode of the tensiometric cell, and if an RI correction is made, we can write for a single electrode... 

The ion X, coming from the bulk of phase II, first traverses the diffusion layer dc and there is a corresponding electrochemical affinity ... 

Let us consider the mechanism of the electrode process as a sequence of elementary reactions all of which, in a steady state, occur at the same velocity, equal to the overall velocity, when stoichiometry is properly taken into account. Let us designate by j the rate-determining step and let us assume that it occurs yj times during one occurrence of the overall process. The number yj is the stoichiometric number of step j. Let us consider the system as being in a state close to electrochemical equilibrium for which it can safely be assumed that the electrochemical affinities of all other... 

Let us first consider the case where step j concentrates the total electrochemical affinity of the process, making A, ...Aj iy Aj+i,... practically equal to zero. For instance, j could be a charge or discharge step with all approach steps practically at their respective equilibria (see the discussion in section II.2). We then have yjAj = A [see (99)], and from (109) we obtain... 

Let us now consider the case in which step j does not involve the total electrochemical affinity of the overall process but only the constant fraction d of A ... 

It is of course possible that other steps besides that of discharge could involve appreciable fractions of the total electrochemical affinity and greater fractions than those of the approach steps which we have just considered. Dehydration of a hydrated ion, gradual penetration of through the transfer layer, entry of the deposited X into the metal lattice, etc. are such possibilities. These situations may still correspond to Tafel formulas, but with and different from 0 and x, respectively. 

If the electrochemical affinities of steps other than III can be taken as equal to zero, we have... 

We neglect the mass transfer electrochemical affinity p.fi — fin. We thus have, as in (139),... 

If the approach process e (a)e (a ) were to have a zero electrochemical affinity, we would haveiv - = 0 and according to (201),... 

Corrections depending on the features of the electrochemical double layer will be applicable to the factor exp(—af z/RT) (once this factor has been introduced a priori) when the approach process H (c)H (h) is not at electrochemical equilibrium, when the process of extraction of the electron also involves a nonzero electrochemical affinity, when a nonequilibrium adsorption process precedes discharge, etc. 

Van Rysselberghe, Electrochemical Affinity—Studies in Electrochemical Thermodynamics and Kinetics, Hermann, Paris, 1955 Lange and Gohr, Thermodyna-mische Elektrochemie, Hiithig Verlag, Heidelberg, 1962. 

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