Single pseudo

Some force fields use the so-called united atom approach where (for example) a methyl group is treated as a single pseudo-atom. They arose historically in order to save computer resource when dealing with large systems such as amino-acid chains. 

Pairwise symmetry of cross peaks to a single pseudo-diagonal applies only to the direct correlation peaks in OQ- and 2Q-HoMQC spectra. All other peaks, and those in correlations of higher number of quanta, occupy systematic and predictable positions, of course, but their relative location can not be expressed in terms of mirror image symmetry of some kind. 

However, if the atoms are not related by symmetry, the normal rules break down. The homoionic N-N bond in the hydrazinium ion is an electron pair bond, but one in which N1 contributes 1.25 and N2 0.75 electrons. How can we apply the bond valence model in such cases where no solution to the network equations is possible One approach is to isolate the non-bipartite portion of the graph into a complex pseudo-atom. Thus in the hydrazinium ion the homoionic bond and its two terminating N atoms are treated as a single pseudo-anion which forms six bonds with a valence sum equal to the formal charge of —4. 

The alternative version (obtained by using the Clausius-Clapeyron thermodynamic relationship, which only holds if the mixture behaves as a single pseudo-component) is ... 

The kinetics of the hydrolysis of acetic anhydride in dilute hydrochloric acid, Scheme 1.9, may be described by a single pseudo-first-order rate constant, k, and the investigation by calorimetry combined with IR spectroscopy, as we shall see in Chapter 8, provides a clear distinction between the heat change due to mixing of the acetic anhydride into the aqueous solution and that due to the subsequent hydrolysis. This model of the reaction is sufficient for devising a safe and efficient large-scale process. We know from other evidence, of course, that the reaction at the molecular level is not a single-step process - it involves tetrahedral intermediates - but this does not detract from the validity or usefulness of the model for technical purposes. 

The analysis of a multiphase flow system is complex, in part because of the difficulties in assessing the dynamic responses of each phase and the interactions between the phases. In some special cases, the gas-solid mixture can be treated as a single pseudo-homogeneous phase in which general thermodynamic properties of a gas-solid mixture can be defined. This treatment provides an estimate for the bulk behavior of the gas-solid flow. The following treatment is based on the work of Rudinger (1980). 

In writing these equations all products of devolatilization are lumped into a single pseudo-component, V. Equations (7) through... 

It is worth noting that some cyclic molecules play an important role in the mechanism. Another interesting feature results from the use of lumped compounds. The lumping of different species into a single pseudocompound causes a reduction in the complexity of the reacting system. For example, the 4 isomers of the branched C6 paraffins are lumped into a single pseudo-compound the 12 alkylbenzenes from C9 to C2o are described by three pseudo-compounds, C9, C1S and C20, etc. 

To estimate the isomerization rate coefficients, eqn 5.8 is applied to the time required for close approach to the straight-line behavior of the first-order curves. Judging this time to be about 25 minutes for a 90% approach to the steady-state isomer distribution, eqn 5.8 yields k 0.1 min-1. With this value and an isomerization equilibrium constant Kn = 20 at 150°C calculated from thermochemical data [5,6] (with 2-cis and 2-trans pentene lumped into a single pseudo-component), eqns 5.40 give as rough estimates... 

Application of the general formula for simple pathways allows any simple network to be reduced to one with only single, pseudo-first order steps between adjacent nodes or end members and adjacent nodes. 

The study of the first portion, olefin to aldehyde and paraffin, can be conducted under normal reaction conditions. For the mathematical evaluation, aldehyde and all products arising from it—alcohol, aldol, and heavy alcohol—are lumped into one single pseudo-species (counting aldol and heavy alcohol each as two aldehyde molecules). This is possible because, in the network, the aldehyde marks a point of no return Once a molecule has been converted to aldehyde, it can only remain aldehyde or react on to alcohol, aldol, or heavy alcohol, but not revert back to olefin or paraffin. 

Several steps in a cycle may be fast enough for quasi-equilibrium. If two or more such steps are successive, all the cycle members involved can be lumped into a single pseudo-component. 

With lumping of X, X2, and X3 into a single pseudo-species XL (shown in box), the reduced cycle now has only two members cat and X. The Briggs-Haldane equation 8.21 applies, without restriction to initial rate and with index X replaced by L ... 

Naphtha feed is treated as a single pseudo species. Naphthas, used as pyrolysis feedstocks, are mainly composed of paraffins and naphthenes, with lesser amounts of aromatics. Olefin content is usually very small. Consistent with observed pyrolytic behavior of paraffins and naphthenes (15,16,26,27,28), feed decomposition is assumed to follow first-order kinetics. Equation 3 of the reactor model can be simplified as follows. 

The volatile combustion usually refers to oxidation of CH4, C2H6,... C9H20, C2H4, C3H6, etc. in high temperature. The process can be described by different models. For some applications, a single pseudo reaction step may be sufficient. For each composition in volatile matter, this is expressed by the general equation for reaction,... 

This book does not discuss the details of alkali-oil chemistry related to saponification. It assnmes a highly oil-solnble single pseudo-acid component (HA) in oil. The alkali-oil chemistry is described by partitioning of this pseudoacid component between the oleic and aqneons phases and snbseqnent hydrolysis in the presence of alkali to prodnce a solnble anionic snrfactant A (its component is conventionally denoted by RCOO ), as shown in Fignre 10.3. 

Pseudo-homogeneous models. Fluid and solid phases are considered as a single pseudo-phase and the balances are imposed for only one phase. Heat and mass transport coefficients inside the bed are calculated by expressions which account for the simultaneous presence of two phases. 

By pseudo-homogeneous models, fixed bed reactors are described without considering the existence of two different phases at least, but imposing balance equations for one single pseudo-phase and calculating chemical-physical properties and transport coefficients by applying empirical expressions. 

An orthogonal set of approximations involves the structural representation of the polymer. As an example. Fig. 1 shows four different ways in which the structure of polyisoprene might be represented in an MD or BD simulation. The top structure (a) is an atomic representation of the polyisoprene repeat unit. The second structure (b) results from coUapsing all the hydrogens onto their parent carbons (the united atom approximation). The third structure (c) further collapses the three carbon centers in the fairly rigid double bond unit into a single pseudo-atom. Any of these three structures might be used in a simulation of local polymer dynamics. The fourth structure (d) shows a bead-... 

Quasi-continuum models Of these, the quasi-continuum model is the most common. Here, the solid-fluid system is considered as a single pseudo-homogeneous phase with properties of its own. These properties, for example, diffusivity, thermal conductivity, and heat transfer coefficient, are not true thermodynamic properties but are termed as effective properties that depend on the properties of the gas and solid components of the pseudo-phase. Unlike in simple homogeneous systems, these properties are anisotropic, that is, they have different values in the radial and axial directions. KuUcami and Doraiswamy (1980) have compiled all the equations for predicting these effective properties. Both radial and axial gradients can be accounted for in this model, as well as the fact that the system is really heterogeneous and hence involves transport effects both within the particles and between the particles and the flowing fluid. 

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