Cross Effects

However, a potential may give rise to more than one type of flux. There are cross-effects A temperature difference can also result in diffusion, called thermal diffusion, and a concentration difference can result in a heat current. The general relation between fluxes 7, and the driving potentials A) is of the form of linear relations... 

One also obtains analogous findings with trace-crossing effects for the electropolymerization of thiophene and pyrrole. This cannot be explained by a simple linear reaction sequence, as presented in Scheme I, because it indicates competing homogeneous and heterogeneous electron transfer processes. Measurements carried out in a diluted solution of JV-phenylcarbazole provide a more accurate insight into the reaction mechanism (Fig. 2). 

Finally, we have discussed the effect of incomplete Cj oxidation product formation for fuel cell applications and the implications of these processes for reaction modeling. While for standard DMFC applications, formaldehyde and formic acid formation will be negligible, they may become important for low temperature applications and for microstructured cells with high space velocities. For reaction modeling, we have particularly stressed the need for an improved kinetic data base, including kinetic data under defined reaction and transport conditions and kinetic measurements on the oxidation of Ci mixtures with defined amounts of formaldehyde and formic acid, for a better understanding of cross effects between the different reactants at an operating fuel cell anode. 

However, it must be stressed that pharmaceutical expenditure is just another input in health production policies, and its complementariness or substitutability with other inputs, and cross-effects in general, make it necessary to take an overall approach to ary rationalization process. In pharmaceutical policy in particular, it is impossible to ignore the deficits caused by distribution costs, the absence of real competition in the dispensing market and the perverse effects of the present system of remuneration for pharmacists. 

Fig. 3 Multisweep cyclic voltammogram (6 scans) trace-crossing effect during potentiodynamic polymerization of N-benzyl-3,4-dimethoxy-pyrrole in acetonitrile, 0.1 M TBAPFe, +1% H2O, = 200 mV s T = 298 K.

Uphill diffusion of some components is reported in silicate melts (e.g., Sato, 1975 Watson, 1982a Zhang et al., 1989 Lesher, 1994 Van Der Laan et al., 1994). Recall that uphill diffusion in binary systems is rare and occurs only when the two-component phase undergoes spinodal decomposition. In multicomponent systems, uphiU diffusion often occurs even when the phase is stable, and may be explained by cross-effects of diffusion by other components. 

Studies on the cross-effects of herbivore and pathogen infestation on direct defenses have yielded results that can be quite different for different systems (Karban and Kuc, 1999 Stout and Bostock, 1999 Rostas et al., 2003). The cucumber pi ant has been studied in detail with several pathogens and herbivores (Apriyanto and Potter, 1990 Ajlan and Potter, 1991 Moran, 1998). In most cases, infection with one pathogen caused a systemic resistance to other pathogens but had no... 

How does pathogen infestation affect odor emissions and does it interfere with emissions induced by insect herbivores So far, only one study has specifically looked at this cross-effect (Cardoza et al, 2002). It showed that insect feeding (beet armyworm, S. exigua) and fungus infection (white mold, Sclerotium rolfsii) resulted in distinctly different odor blends in peanut plants, whereas plants that were simultaneously infested by these two antagonists released a mix of both blends. 

Rost s, M., Simon, M. and Hilker, M. (2003). Ecological cross-effects of induced plant responses towards herbivores and phytopathogenic fungi. Basic and Applied Ecology 4 43-62. 

Equations (4.16) and (4.17) are examples of the so-called cross effects whereby a force Ac can induce fluxes j) despite that X = 0. Another example of a cross effect is thermotransport in which temperature gradients (fluxes of heat) induce fluxes of atomic species, j,. An application of this concept is the steady state demixing of a (closed solid) solution system, which has been exposed to a temperature gradient (heat flux). This is the Ludwig-Soret effect originally observed with fluid systems. 

However, before going into this problem, let us briefly extend the treatment on steady state demixing given in Section 8.2 and depicted in Figure 8-2 by including cross effects. We denote the transport coefficients by Ljj and replace the fluxes ji = Lj-Vrh by jj = Lii-Vt]j+YljLij-V>jj(iJ = A,B) in the steady state condition (Eqn. (8.8)). In contrast to Eqn. (8.10), the result is [H. Schmalzried, W. Laqua (1981) M. Martin (1991)]... 

Let us now turn to cross effects proper between electronic and ionic fluxes. Considering the general nature of cross effects in crystals, our analysis will be performed in some depth. It gives us the tools for a correct application of SE transport theory (see Section 4.2.2) and explains to some extent the physical meaning of the cross coefficients. Let us illustrate the problem using a semiconducting binary compound such as a transition-metal oxide. In A, 0 crystals with the B1 structure, oxygen... 

Equations (8.48)-(8.50) define three independent transport coefficients for the two building units (A,h), namely L, and Lhh, in terms of the 21 independent transport coefficients of the SE set. They are sufficient to describe the transport in A O. The cross coefficient LAh expresses the coupling between the ionic and electronic fluxes. If ATh ) = 0, the electronic flux is due only to the cross effect and given by... 

If AT(A2+) = 0, then the cation flux is due only to the cross effect given by... 

In this section, we consider the influence of inhomogeneous stress on matter transport. Tb illustrate the problem, let us formulate a simple transport equation diffusion of an interstitial component i in an otherwise immobile solid (e.g., H in Pd). Furthermore, we neglect cross effects. For an electrically neutral species i (i.e., H) we then have... 

In Eqs. 2.20 and 2.22, the diagonal terms, Laa, are called direct coefficients they couple each flux to its conjugate driving force. The off-diagonal terms are called coupling coefficients and are responsible for the coupling effects (also called cross effects) identified above. 

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