Non-Stoichiometric Models

This ion interaction retention model of IPC emphasized the role played by the electrical double layer in enhancing analyte retention even if retention modeling was only qualitatively attempted. It was soon realized that the analyte transfer through an electrified interface could not be properly described without dealing with electrochemical potentials. An important drawback shared by all stoichiometric models was neglecting the establishment of the stationary phase electrostatic potential. It is important to note that not even the most recent stoichiometric comprehensive models for both classical [17] and neoteric [18] IPRs can give a true description of the retention mechanism because stoichiometric constants are not actually constant in the presence of a stationary phase-bulk eluent electrified interface [19,20], These observations led to the development of non-stoichiometric models of IPC. Since stoichiometric models are not well founded in physical chemistry, in the interest of brevity they will not be described in more depth. 

All non-stoichiometric models adopt the electrical double layer concept and disagree with the stoichiometric hypothesis of an electroneutral stationary phase they emphasize the higher adsorbophilicity of the IPR compared to that of its counter ion a surface excess of IPR ions generates a primary charged layer and a charged interface. Like-sign co-ions are repelled from the surface while IPR counter ions are attracted by the charged surface. 

Conversely, according to the description of the electrical double layer based on the Stern-Gouy-Chapman (S-G-C) version of the theory [24], counter ions cannot get closer to the surface than a certain distance (plane of closest approach of counter ions). Chemically adsorbed ions are located at the inner Helmholtz plane (IHP), while non-chemically adsorbed ions are located in the outer Helmholtz plane (OHP) at a distance x from the surface. The potential difference between this plane and the bulk solution is 1 ohp- In this version of the theory, Pqhp replaces P in all equations. Two regions are discernible in the double layer the compact area between the charged surface and the OHP in which the potential decays linearly and the diffuse layer in which the potential decay is almost exponential due to screening effects. 

FIGURE 3.2 Gouy-Chapman double layer model. 

The first attempts of Bidlingmeyer and co-workers [15,16] to formulate an ion interaction model quantitatively [21-23] did not provide a rigorous description of the system. Stranahan and Deming [22] accounted for electrostatic effects via a simplified activity coefficient in the stationary phase. An interfadal tension decrease with increasing IPR concentration was considered responsible for the appearance of maxima in the plot of retention factor, k versus IPR concentration, but experimental results were at odds with known surfactant chemistry. 

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Fiery1 252-254) studied only the last stage of the reactions, i.e. when the concentration of reactive end groups has been greatly decreased and when the dielectric properties of the medium (ester or polyester) no longer change with conversion. Under these conditions, he showed that the overall reaction order relative to various model esterifications and polyesterifications is 3. As a general rule, it is accepted that the order with respect to acid is two which means that the add behaves both as reactant and as catalyst. However, the only way to determine experimentally reaction orders with respect to add and alcohol would be to carry out kinetic studies on non-stoichiometric systems. 

Note 2 A model network is not necessarily a perfect network. If a non-linear polymerization is used to prepare the network, non-stoichiometric amounts of reactants or incomplete reaction can lead to network containing loose ends. If the crosslinking of existing polymer chains is used to prepare the network, then two loose ends per existing polymer chain result. In the absence of chain entanglements, loose ends can never be elastically active network chains. 

Chapter S examines various models used to describe solution and compmmd phases, including those based on random substitution, the sub-lattice model, stoichiometric and non-stoichiometric compounds and models applicable to ionic liquids and aqueous solutions. Tbermodynamic models are a central issue to CALPHAD, but it should be emphasised that their success depends on the input of suitable coefficients which are usually derived empirically. An important question is, therefore, how far it is possible to eliminate the empirical element of phase diagram calculations by substituting a treatment based on first principles, using only wave-mecbanics and atomic properties. This becomes especially important when there is an absence of experimental data, which is frequently the case for the metastable phases that have also to be considered within the framework of CALPHAD methods. 

This example, which may be the most simple model of non-stoichiometric compounds, is important for understanding the following examples. 

This situation can be expressed in terms of the band model as shown in Fig. 1.24. Stoichiometric NiO is an intrinsic semiconductor, having an energy gap of Eq (=Eq—E ). Non-stoichiometric Nij O, which has metal vacancies or electronic defects, has an acceptor level A between the valence... 

Chapter 2 describes non-stoichiometric compounds derived from extended defects . Research in this field showed significant growth towards the end of the 1960s (although important papers by Professor A. Magneli and Professor A. D, Wadsley were published in the 1950s), initiated by the proposition of the shear structure model by Professor J. S. Anderson and... 

Modeling diffusion-coupled vaporization processes associated with non-stoichiometric carbides requires the use of the chemical diffusion coefficient, D, for the calculation of temporal C concentrations. Clearly D will have a strong concentration dependence. In principle, the concentration dependence should be calculable from measured D (NC,T) and ac(Nc,T) values. However, our attempts and those of Wakelkamp31 to verify the correlation have been unsuccessful for TiC, ZrC, VC, and TaC. The disparity is probably based in the approximations used to derive these equations. For example, Howard and Lidiard32 have shown that the right hand sides of equations 3.10 and 3.11 are approximate and proposed that additional terms are needed. 

Based on the fluorite-type module theory the thermodynamic properties, hysteresis, and reactions between the homologous series can be elucidated and the structures of homologous series experimentally discovered may be modeled. Using these principles a wide range of non-stoichiometric ternary lanthanide higher oxides from RO2 to R2O3 were founded. 

PEC formation in a concentration range of the component solutions below 1-10-3 g/mL resulted in stable dispersions of PEC particles when non-stoichiometric mixing ratios are used. In general, the scattering functions of the PECs could be well fitted by the model of polydisperse systems of homo-... 

Computer Modelling of the Defect Structure of Non-Stoichiometric Binary Transition Metal Oxides. 

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