Electrostatic component additivity approach

Whether the use of 1,3-interactions in place of L-M-L force constants is a valid approach depends on the metal ion being considered. If it is a metal for which the M-L bonding is primarily electrostatic, such as an alkali, alkaline earth or rare earth metal, then 1,3-interactions are definitely preferable. In such cases it may be important to include an electrostatic component in the 1,3-interactions in addition to the usual van der Waals term. If, however, the metal ion is one that has a clear preference for a particular coordination geometry, then inclusion of at least a component of the L-M-L force constants may be indicated (see Chapter 11, Section 11.1). Recently, a model which includes both 1,3-interactions and force constants for the L-M-L angles has been described1 lsl Other approaches are discussed in Chapter 2, Section 2.2.2. 

The simplest approach to minimizing protein-wall interaction is to use a buffer pH at which interactions do not occur. At acidic pH the silanols on the surface of the capillary are protonated, and the net charge of the proteins is positive. At high pH, the wall is negatively charged, and so are the sample components. Both conditions result in electrostatic repulsion. Problems associated with operation at pH extremes include the potential instability of proteins (denaturation, degradation, and precipitation) and the limited pH range in which to achieve resolution. Additionally, operation at extreme pH does not eliminate all nonspecific interactions. 

The DLVO theory [1,2], which describes the interaction in colloidal dispersions, is widely used now when studying behavior of colloidal systems. According to the theory, the pair interaction potential of a couple of macroscopic particles is calculated on the basis of additivity of the repulsive and attractive components. For truly electrostatic systems, a repulsive part is due to the electrostatic interaction of likely charged macroscopic objects. If colloidal particles are immersed into an electrolyte solution, this repulsive, Coulombic interaction is shielded by counterions, which are forming the diffuse layer around particles. A significant interaction occurs only when two double layers are sufficiently overlapping during approach of those particles. 

For the case of a purely electrostatic external potential, P = (F , 0), the complete proof of the relativistic HK-theorem can be repeated using just the zeroth component f (x) of the four current (in the following often denoted by the more familiar n x)), i.e. the structure of the external potential determines the minimum set of basic variables for a DFT approach. As a consequence the ground state and all observables, in this case, can be understood as unique functionals of the density n only. This does, however, not imply that the spatial components of the current vanish, but rather that j(jc) = < o[w]liWI oM) has to be interpreted as a functional of n(x). Thus for standard electronic structure problems one can choose between a four current DFT description and a formulation solely in terms of n x), although one might expect the former approach to be more useful in applications to systems with j x) 0 as soon as approximations are involved. This situation is similar to the nonrelativistic case where for a spin-polarised system not subject to an external magnetic field B both the 0 limit of spin-density functional theory as well as the original pure density functional theory can be used. While the former leads in practice to more accurate results for actual spin-polarised systems (as one additional symmetry of the system is take into account explicitly), both approaches coincide for unpolarized systems. 

An additional advantage of the integrated circuit technology is the ability to integrate the various components, such as the transducer, reactor, valve, pump etc., within the electronic system, forming refined flow-analysis systems on silicon wafers. Several approaches, such as electrostatic, electromagnetic, piezoelectric, thermopneumatic and thermoelectric can be employed for force transduction in the microvalves, these are also applicable to micropumps. Based on these approaches, two versions of micropumps have been developed. These are connected in parallel the first pump (dual pump) is activated with periodic two-phase voltage, while the second pump (the buffer pump) is driven by two piezoelectric actuators. Microsensors of two kinds are described below a thermopile based- and a thermistor based microbiosensor. 

In addition to the ion-electrostatic factor of colloid stability, which we have discussed, there are also other factors leading to the appearance of a positive disjoining pressure, (/ ) > 0, that prevents particles from approaching each other under the action of the attractive (negative) component of the disjoining pressure, rimoi( ) < 0. The most essential factors are as follows (Figure 4.9) ... 

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