Barrierless conditions

The main conceptual advance made in the last few years is the acceptance that electron-transfer process at dye-sensitised systems under barrierless conditions can be purely electronic. A measurement of the nonradiative decay channel due to electron transfer under these conditions gives a direct determination of the electronic coupling. Subsequent to the initial work pointing this out, there have been a number of determinations of extremely fast electron-transfer times at dye-sensitised surfaces. For dye-derivatised TiOi electron-transfer times from 10 fs to 100 fs have been reported by a number of groups (Rehm et al, 1996 Tachibana et al, 1996 Hannappel et al,... 

The forward electron-transfer step can occnr nnder exceptionally fast time scales—faster than nnclear relaxation. The fastest forward electron-transfer times will be realised with dyes that have excited-state surfaces above the CBM (barrierless conditions). For dyes in intimate contact (no intervening solvent or contaminant), the electron coupling can be in the 100 to 1000 cm range (100 fs-10 fs dynamics). 

A barrierless condition also arises when azide is anodically oxidized to nitrogen on a platinum electrode.The probability of this condition is also high when this reaction proceeds on a number of other metals of group VIII, as well as in the case of certain other anodic processes. ... 

V4jcXkBT 4XkBT The maximum rate attainable under barrierless conditions (AG =-X) is then ... 

Fig. 4.13. Variation of r k(0)—the reaction rate k(6) in the barrierless model compared to the spontaneous decay rate 1/t"—versus 6 = r/r". Solid lines [Eq. (4.227)] initial condition po(0, 0) = S(x + c0)) for different values of x0 defining the potential energy W= U(x0)lkBT. Dashed line [Eq. (4.241)] Boltzmann initial distribution.

Thfel slopes different from the usual ones may also result if the r. d. s. proceeds barrierless (i.e., with a = 1) (or quasi-barrierless [201]). Thus, hydrogen evolution with barrierless discharge - step (3) - or barrierless electrochemical desorption - step (4) - as the r. d. s., is expected to occur with a Tafel slope of 60 and 30 mV, respectively [202], This behavior has been reportedly observed with Hg [203], Bi [204], Ag [205], and Au [206]. However, such an experimental observation takes place only under very special conditions and cannot have any relevance to practical electrolysis. 

The high electrophilicity of lb is also demonstrated by the barrierless insertion into H2, T>2, CH4, and CD4 to produce the difluoroolefins 11 and 12, respec-tively. A rapid insertion into H-H and C-H bonds is only expected for highly electrophilic singlet carbenes. [14] Recently Zuev and Sheridan reported that triplet carbenes and open-shell singlet carbenes also insert into H2 in low temperature matrices, but not into D2. [42] Since calculations predict an activation barrier of several kcal/mol for these reactions, a tunneling mechanism was proposed. Singlet closed-shell carbenes were not observed to insert into H2 under similar conditions. This clearly demonstrates the exceptional reactivity of viny-lidene lb, which readily inserts into both H2 and D2. This is backed by calculations at the MP2 or DFT level of theory which predict for the insertion of lb into H-H and C-H bonds very shallow or no activation barriers, while for the parent vinylidene la substantial barriers are expected. [41]... 

The quantum mechanical theory leads to a number of conclusions in respect to the kinetics of electrochemical reactions, in particular to the hydrogen evolution reaction. These conclusions are, to a certain degree, opposite to those of the classical approach. Thus, the consistent incorporation of the electronic energy spectrum in the electrode in the theory leads to the conclusion that barrierless and activationless transitions should be observed under certain conditions. In the theories which consider transitions to only one electronic energy level (the Fermi level), the transition probability should increase, reach a maximum, and then decrease with decrease of the reaction free energy. Experiment shows the existence of the barrierless and activationless processes. 

It is not always, of course, that a barrierless (j3 = 1) or activationless (/3 = 0) process produces slopes corresponding, respectively, to 60 mV and 00. As can be seen, for example, from Eq. (52), under conditions where a preceding equilibrium step is involved, these values of jS may result in slopes corresponding to 0.030 and 0.060 V, respectively. Conversely, it is equally possible that in certain cases, such slopes which are sometimes interpreted as indicative of a slow chemical step, correspond, in fact, to the limiting cases of the electrochemical reaction per 5e, considered above. 

Krishtalik LI (1969) On the conditions favourable to the detection of barrierless electrode processes. J Electroanal Chem 21 421-424... 

Due to very small value of O, for proteins and colloid particles [2], the value of k usually much larger than unity for barrierless transport conditions. In this case, for adsorption time t smaller than (,h = l/( 5gn ) f oo> particle flux and coverage are governed by previously derived dependencies, Eq. (150) and Eq. (170), respectively. 

The occurrence of the linear deposition regimes under barrierless transport conditions in experiments involving colloid particles was often demonstrated [1,76,90,91]. The quantity measured directly in these experiments is the number of particles Np adsorbed over equally sized surface areas A5 (see Fig. 41). Because Ap is a statistical variable which obeys the Poisson fluctuation law for low coverage [173,181,182], the accuracy of determining the average value of Np) is inversely proportional to (where is the total number of particles counted). In the above experiments N, was usually above 1000, which gives the standard deviation of Np) of... 

At ultimate potentials, electrode reactions occurring at the WE in the direction indicated by the subscript are converted to barrierless processes. When the condition E = Eu is introduced into Eqs. (18), the corresponding maximum rates of the electrode reaction in Eq. (1), presented as ultimate current densities, are obtained ... 

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