Alternative models

Several models that depart partially or totally from DLVO have been proposed. One such model is the Spitzer dissociative electrical double layer theory (Spitzer 1984, 2003 and references therein). It essentially uses the linearized PB equation (which is consistent with Maxwellian electromagnetism) along with a coion exclusion boundary, which prevents ions of the same charge as the surface becomes too close in practice, this avoids negative concentrations, which will be predicted by the linear PB theory. It also includes a double layer association parameter a, which gives the fractions of counterions that are associated to the surface forming the Stern layer (Spitzer 1992). This theory, however, has not been further developed. 

Another line of thought has been developed by Ninham and coworkers (Ninham and Yaminsky 1997 Ninham 1999 Bostrom, Williams, and Ninham 2001 Bostrom, Deniz et al. 2006 Bostrom, Tavares et al. 2006 Ninham 2006 Parsons and Ninham 2010), consisting essentially of the introduction of ion-specific interactions through ion dispersion energies. It considers ionic dispersion and image potentials, giving 

From this short summary, it should be evident that the whole subject of what may be termed post DLVO theories remains controversial, and publications supporting these two different approaches continue to be published (Lian and Ma 2007 Liu, Moreno, and Neretnieks 2009 Ise 2010 Lee and Ng 2010). As discussed in Section 6.6.1 for many problems in soil science, however, the DLVO theory provides adequate predictions. 

In this chapter, the interaction in colloidal particle systems, based on the principles developed in Chapters 3 through 5, has been studied. The DLVO theory, the mainstream formalism yet employed to rationalize colloidal behavior, has been developed. The shortcomings of DLVO as well as proposed improvements or different 

Adamczyk, Z., and T. G. M. Van De Ven. 1984. Kinetics of particle accumulation at collector surfaces. I. Approximate analytical solutions. Journal of Colloid and Interface Science 97, no. 1 68-90. doi 10.1016/0021-9797(84)90276-5. 

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Null (1970) discusses some alternate models for the excess Gibbs energy which appear to be well suited for systems whose activity coefficients show extrema. 

An alternative model has been proposed in which the chiral mobile-phase additive is thought to modify the conventional, achiral stationary phase in situ thus, dynamically generating a chiral stationary phase. In this case, the enantioseparation is governed by the differences in the association between the enantiomers and the chiral selector in the stationary phase. 

At the in vivo assay level, the classic ip-ip (iateraperitoneal) in vivo model has been replaced as a selection criteria for advancement of new dmg candidates to clinical trial. More stringent alternative models iaclude subcutaneous or subrenal capsule implantation of tumor followed by iatravenous dmg dosiag (7) and the human tumor xenograft models ia aude mice (8). 

Proc., 65(3), 45 (1986)] is preferred. To use this and alternate models, dimensional characteristics of structured packing must be defined. Figure 14-51 shows nomenclature and definitions of key dimensions. Not shown, but also important, is the angle the corrugations make with the horizontal (usu y 45 or 60°). Then the Rocha et al. predictive equation is ... 

Once the model parameters have been estimated, analysts should perform a sensitivity analysis to establish the uniqueness of the parameters and the model. Figure 30-9 presents a procedure for performing this sensitivity analysis. If the model will ultimately be used for exploration of other operating conditions, analysts should use the results of the sensitivity analysis to estabhsh the error in extrapolation that will result from database/model interactions, database uncertainties, plant fluctuations, and alternative models. These sensitivity analyses and subsequent extrapolations will assist analysts in determining whether the results of the unit test will lead to results suitable for the intended purpose. 

The procedure given in Fig. 30-15 leaves much to analysts. Criteria for selecting the number ana location of measurements for a particular piece of equipment or unit have not been established in the literature. Therefore, there is heavy reliance on examining alternative models at the bottom of the procedure. The creativity of analysts to develop alternative explanations for performance or hypotheses explaining why the present model might be wrong is a particularly important skill. 

The merits and demerits of the many computer-simulation approaches to grain growth are critically analysed in a book chapter by Humphreys and Hatherly (1995), and the reader is referred to this to gain an appreciation of how alternative modelling strategies can be compared and evaluated. A still more recent and very clear critical comparison of the various modelling approaches is by Miodownik (2001). 

As indicated, an implicit assumption of the JKR theory is that there are no interactions outside the contact radius. More specifically, the energy arguments used in the development of the JKR theory do not allow specific locations of the adhesion forces to be determined except that they must be associated with the contact line where the two surfaces of the particle and substrate become joined. Adhesion-induced stresses act at the surface and not a result of action-at-a-distance interatomic forces. This results in a stress singularity at the circumference of the contact radius [41]. The validity of this assumption was first questioned by Derjaguin et al. [42], who proposed an alternative model of adhesion (commonly referred to as the DMT theory ). Needless to say, the predictions of the JKR and DMT models are vastly different, as discussed by Tabor [41]. 

The scaling dependence of the diffusion coefficient on N and Cobs Iso poses a number of questions. While the original scaling predictions, based on reptation dynamics [26,38], oc N, have been verified by some measurements [91,98], significant discrepancies have been reported too [95,96]. Attempts to interpret existing data in terms of alternative models, e.g., by the so-called hydrodynamic scaling model [96], fail to describe observations [100,101]. 

Next, Ah and Ad are written in terms of partition functions (see Section 5.2), which are in principle calculable from quantum mechanical results together with experimental vibrational frequencies. The application of this approach to mechanistic problems involves postulating alternative models of the transition state, estimating the appropriate molecular properties of the hypothetical transition state species, and calculating the corresponding k lko values for comparison with experiment.""- " "P... 

One of these alternate models, postulated by Gunter Wachtershanser, involves an archaic version of the TCA cycle running in the reverse (reductive) direction. Reversal of the TCA cycle results in assimilation of CO9 and fixation of carbon as shown. For each turn of the reversed cycle, two carbons are fixed in the formation of isocitrate and two more are fixed in the reductive transformation of acetyl-CoA to oxaloacetate. Thus, for every succinate that enters the reversed cycle, two succinates are returned, making the cycle highly antocatalytic. Because TCA cycle intermediates are involved in many biosynthetic pathways (see Section 20.13), a reversed TCA cycle would be a bountiful and broad source of metabolic substrates. 

Horst mechanism of PVC stabilization. In fact, based on his observations Naqvi [134] has proposed an alternative model for the degradation and stabilization of PVC based on polar interactions within the polymer matrix, which will be discussed in the following section (Section VI). 

Naqvi [134] has proposed an alternative model to the Frye and Horst mechanism for the degradation and stabilization of PVC. At room temperature, PVC is well below its glass transition temperature (about 81°C). The low thermal stability of the polymer may be due to the presence of undesirable concentrations of like-poles in the more or less frozen matrix with strong dipoles. Such concentrations, randomly distributed in the polymer matrix, may be considered to constitute weak or high energy spots in the polymer, the possible sites of initiation of thermal dehydrochlorination. 

Every alternating atom in the PDMS chain is the electronegative oxygen, which makes it a polar polymer. The authors observed that at low loadings of PDMS, PVC is destabilized. This is to be expected according to the alternative model for degradation and stabilization of PVC put forward by Naqvi. But for compositions with 50% or more PDMS, both polymers are stabilized. No possible explanation can be given for this reversal in thermal stability at this time. 

We will not go any further into the interesting speculations Minsky offers in his 1982 paper [minsky82]. The point of these speculations was not to propose a serious alternative model of fundamental physics, per se, but to stimulate thinking along the. lines of What if physics were, fundamentally, discrete How would we describe the processes we now think we iinderstaiul with our continuous models Two questions that we will repeatedly come back to in this concluding chapter. 

This discrepancy between experiment and theory (and many others) can be explained in terms of an alternative model of covalent bonding, the molecular orbital (MO) approach. Molecular orbital theory treats bonds in terms of orbitals characteristic of the molecule as a whole. To apply this approach, we carry out three basic operations. 

In his original paper,2 Cram disclosed an alternative model that rationalizes the preferred stereochemical course of nucleophilic additions to chiral carbonyl compounds containing an a heteroatom that is capable of forming a complex with the organometallic reagent. This model, known as the Cram cyclic or Cram chelate model, has been extensively studied by Cram9 and by others,410... 

Starting from ( )-enolates, the corresponding argument predicts that transition state 10a is lower in energy than the alternative model which suffers from mutual steric hindrance of the substituent R1 and the methyl group in a gauche orientation thus, stereoconvergence results. 

Two versions of an alternate model were also introduced, where the mesophase layer was assumed as possessing variable mechanical and physical properties, accomodating a smooth transition of the properties of the inclusions with those of the matrix, by assuring in a very short distance the progressive, from the inclusion-matrix boundaries outwards, change of the characteristic quantities of the one phase, in order to match those of the other phase. 

Though these are alternative models, they are both particular cases of the non-adiabatic impact theory of angular momentum relaxation in gases. Thus, we prefer to call them models of weak and strong collisions , as is usually done in analogous problems [13, 33],... 

At higher pressures only Raman spectroscopy data are available. Because the rotational structure is smoothed, either quantum theory or classical theory may be used. At a mixture pressure above 10 atm the spectra of CO and N2 obtained in [230] were well described classically (Fig. 5.11). For the lowest densities (10-15 amagat) the band contours have a characteristic asymmetric shape. The asymmetry disappears at higher pressures when the contour is sufficiently narrowed. The decrease of width with 1/tj measured in [230] by NMR is closer to the strong collision model in the case of CO and to the weak collision model in the case of N2. This conclusion was confirmed in [215] by presenting the results in universal coordinates of Fig. 5.12. It is also seen that both systems are still far away from the fast modulation (perturbation theory) limit where the upper and lower borders established by alternative models merge into a universal curve independent of collision strength. 

In the following, a detailed exposition of Bartell s (1961a) theory of steric isotope effects will be given (Section II, A), and an alternative model will be developed, based on somewhat different assumptions about the timing in the transition state, which leads to predictions at variance with the experimental results (Section II, B). In both of these sub-sections, special reference will be made to the work of Melander and Carter (1964). Finally, a selective non-comprehensive review of other experimental work in this field will be presented (Section III). 

Steps 1 through 9 constitute a model for heterogeneous catalysis in a fixed-bed reactor. There are many variations, particularly for Steps 4 through 6. For example, the Eley-Rideal mechanism described in Problem 10.4 envisions an adsorbed molecule reacting directly with a molecule in the gas phase. Other models contemplate a mixture of surface sites that can have different catalytic activity. For example, the platinum and the alumina used for hydrocarbon reforming may catalyze different reactions. Alternative models lead to rate expressions that differ in the details, but the functional forms for the rate expressions are usually similar. 

Numerous QSAR tools have been developed [152, 154] and used in modeling physicochemical data. These vary from simple linear to more complex nonlinear models, as well as classification models. A popular approach more recently became the construction of consensus or ensemble models ( combinatorial QSAR ) combining the predictions of several individual approaches [155]. Or, alternatively, models can be built by rurming the same approach, such as a neural network of a decision tree, many times and combining the output into a single prediction. 

Girault and Schiffrin [4] proposed an alternative model, which questioned the concept of the ion-free inner layer at the ITIES. They suggested that the interfacial region is not molecularly sharp, but consist of a mixed solvent region with a continuous change in the solvent properties [Fig. 1(b)]. Interfacial solvent mixing should lead to the mixed solvation of ions at the ITIES, which influences the surface excess of water [4]. Existence of the mixed solvent layer has been supported by theoretical calculations for the lattice-gas model of the liquid-liquid interface [23], which suggest that the thickness of this layer depends on the miscibility of the two solvents [23]. However, for solvents of experimental interest, the interfacial thickness approaches the sum of solvent radii, which is comparable with the inner-layer thickness in the MVN model. 

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