Reduced mobility coefficient

The central question in a mobility measurement is the relationship between ion swarm velocity and the chanical identity of the ions in the swarm, associated largely with the reduced mobility coefficient Early efforts to relate ion structure or identity to mobility coefficients arose mainly from studies of mono- or diatomic ions in pure gases at subambient pressure and led to models for K (as in Equation 1.7) ... 

Because and hence K are temperature and pressure-dependent, values for K are usually normalized to 273 K and 760 mm Hg and are reported as the reduced mobility coefficient, K, ... 

Fig. 3. The mobility coefficient K describing the movement of an ion swarm in an electric field. The mobility coefficient depends on the cross-section (collision area) ft, the reduced mass /i, and the effective temperature re f of the ion. Collision area ftD will depend on moisture, temperature, drift gas, and molecule.

Assumptions viscosity = 3.5 x 10 N.s/m and solute diffusion coefficient = 2.5 x 10" m /s. (h = reduced plate height, v = reduced mobile phase velocity, flow resistance parameter, and dp = average particle size)... 

According to Equation 10.17, the mobility coefficient varies inversely as the square root of the temperature and reduced mass. This is contradictory to experimental results under conditions used in analytical IMS. 

The validity of the models described can be tested by comparing experimentally measured reduced mobilities of several ions in the linear IMS with the predicted coefficients calculated according to the three models. The main features of interest were the correlations of mass with mobility and temperature with mobility another interesting feature is the effect of the drift gas on mobility coefficients (the last two are discussed in Chapter 11). Six parameters are needed in the modeling a, r, z, polarizability, reduced mass, and temperature. The last three arise from direct physical measurements, while the other parameters (fl, r, z) are optimized by a fitting procedure to minimize the deviation between calculated and measured mobility constants. The values of T and were calculated from a, r, and z, and the dimensionless collision cross section (1 was taken from Table 1 in Reference 9. In practice, a discrete value of a was chosen, and initial values for and z were estimated. The parameters Tq and z were then optimized to obtain a good fit with experimental data points by minimizing the squared sum of deviations between theory and experiment. Special attention... 

In the calculation of diffusion coefficient the Emst-Planck correction for the reduced mobility of ions should be taken into account. 

During the early-stage spinodal decomposition, it suffices that the mobility coefficient, M c), and the thermodynamic factor,/ (c), to be constant at c=Co. In this case, Eqs. (1.4.1) and (1.4.2) reduce to... 

A considerable amount of work has been published on optimizing the experimental conditions for minimum analysis time under various constraints [52]. One complication arises from the definition of reduced mobile-phase velocity. The actual mobile-phase velocity depends largely on the molecular-diffusion coefficient of the analyte. Thus, very small particles can be used for the analysis of high molecular mass compounds, which have low values. The actual flow rate required will remain compatible with pressure constraints despite the resulting high pneumatic or hydraulic resistance. Detailed results obviously depend greatly on the mode of chromatography used. 

All of the studies discussed above have shown that some silane SAMs are efficient in reducing the coefficient of friction, the work of adhesion, and stiction properties however, their wear resistance is not sufficient to provide high durability to the MEMS components [42]. One possible reason for the low wear durability of SAMs is the lack of a mobile portion in the lubricant. Hence, there is no replenishment in these layers as molecules are continuously removed from the contact area during the wear process. Moreover, the worn particles generated as a result of material removal act as a third body and further accelerate the wear of the film. Therefore, we proposed a lubrication concept of overcoating SAMs (bonded) with an ultrathin layer of per-fiuoropolyether (PFPE) (bound + mobile) to improve the wear durability of SAMs and hence that of the Si substrate (fig. 6.1) [43, 44]. The mobile PFPE is expected to lubricate and replenish the worn regions and hence enhance the wear durability. 

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