By Allen J. Bard, Israel Rubinstein
For greater than 3 many years the Electroanalytical Chemistry sequence has brought the main in-depth and important learn concerning matters in electrochemistry. Volume 22 maintains this gold-standard with useful stories of contemporary functions, in addition to cutting edge contributions from across the world revered specialists—highlighting the emergence of latest applied sciences and tendencies within the box. past volumes within the sequence have been “highly prompt” through the magazine of the yankee Chemical Society and regarded “essential” by means of the magazine of stable country Electrochemistry, and this quantity maintains with a suite of cutting-edge advances and experiences of the top quality.
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Extra info for Electroanalytical Chemistry: A Series of Advances, Vol. 22
The boundary condition is controlled by the extent to which the liquid ‘‘feels’’ a spatial corrugation in the surface energy of the solid. This depends on a number of interfacial parameters, including the strength of the liquid-liquid and liquid-solid interactions, the commensurability of the substrate and the liquid densities, characteristic sizes, and also the roughness of the interface. In order to quantify the slippage eﬀect, the slip length, Electrochemical Quartz Crystal Microbalance 21 k, is usually introduced [65,67,68].
The corresponding contribution has the form of the Sauerbrey equation. This eﬀect does not exist for smooth interfaces. The second term in Eq. (42) and Eq. (44) describes a viscous contribution to the QCM response. Its contribution to Df has the form of the QCM response at a smooth liquid/solid interface, but includes an additional factor R that is a roughness factor of the surface. The latter is a consequence of the fact that for l/d >> 1 the liquid ‘‘sees’’ the interface as being locally ﬂat, but with R time its apparent surface area.
4)] with the Newtonian equation of motion for the surface ﬁlm: Dm f x2 uf ðxÞ ¼ lq d uðz; wÞ dz at z ¼ d ð10Þ where uf (x) is the displacement of the ﬁlm. Here the shear stress, Àlqdu(z,x)/dz, plays the rule of the external force acting on the ﬁlm. Here and everywhere below we use in Eq. (4) lq instead of c66, neglecting small values xgq and e226 =e22 . Solving Eqs. (4) and (10) under the standard boundary condition, namely that (1) at the unrestricted surface, z = 0, the shear stress equals zero and (2) at the surface z = d the quartz surface displacement is equal to the surface ﬁlm displacement, one obtains the Sauerbrey equation.