Functional group models

Discrete functional group model. The discrete functional group model makes the... 

Electrostatic discrete functional group models. The development of charge on the surface of the humic macromolecule decreases the tendency to dissociate protons from the acid functional groups. To overcome this problem an electrostatic correction factor is introduced into the acid dissociation and complexation constants. This is similar to the approach adopted for the SCMs for inorganic surfaces. 

The model of Tipping et al. (1988) is an example of an electrostatic discrete functional group model. The effects of variable solution ionic strength and pH on the apparent surface acidity constants (polyelectrolyte effects) are accounted for by the incorporation of an electrostatic term exp(—2wzZ) in the equilibrium constants. A brief description of the model is given below. 

In modeling the polycondensation kinetics, there is also a question of how we define the reaction rate constants. In the above reaction represented by a functional-group modeling framework, the forward rate constant k is the reaction rate constant for reaction of a methyl ester group with a hydroxyl group, not the reaction rate constant for DMT and ethylene glycol molecules. For example, the above reaction can be represented as follows ... 

Example 5 (Modehng melt-phase PET production in a batch reactor using the functional-group modeling approach) Using the reaction rates in Equations 7.23-7.25, the following dynamic component material balance equations can be derived ... 

Reaction scheme using molecular-species modeling approach Scheme using functional-group modeling approach... 

Table 7.3 Dynamic model of a batch nylon 6,6 evaporator, accounting for cyclic oligomer and HMD loss using the functional-group modeling approach...

The functional-group model (in Table 7.3) has nine differential equations, whereas the molecular-species model has an infinite number. The final equation at the bottom of both tables accounts for changes in the volume V of the reacting mixture, due to evaporation of water and HMD. The differential equations in the tables can be solved numerically using standard ordinary differential equation (ODE) solvers. 

The easiest method for obtaining the number-average chain length for the evaporator contents, using either of the two models, is to divide the total number of molecules that have been consumed by polymerization or remain unreacted in the vessel by the final number of molecules in the vessel. For example, using the functional-group modeling approach, first solve the differential equations to obtain concentrations for aU of the spedes at the time of interest and then compute ... 

The example above demonstrates that it is often more convenient to use the functional-group modehng approach rather than detailed molecular-species-modehng. The full molecular-species-modeling approach is required in complicated situations that are not well handled by the simpler functional-group modeling approach [12,17]. 

Three modeling approaches can be applied to the esterification reaction kinetics the molecular species model, the functional group model, and the overall reaction model. These are schematically illustrated in Scheme 4.5. 

Esterification and polycondensation kinetics of PPSu synthesis can be well described on the basis of rather simple simulation models, taking into account the reaction kinetics and the functional group modeling approach. The latter is a very beneficial technique which includes aspects of the reaction mechanism although with the minimum computational effort. 

Lindeman-Adams [54] and Grant-Paul [55,56] models. In both, the effects of various a, p, y, and 5 substituents on the chemical shielding of a particular carbon are summed. The Lindeman-Adams scheme focuses on saturated hydrocarbons and is therefore most applicable to polyolefins. The Grant-Paul rules apply to saturated carbons, but include corrections for other functional groups. Models which approximate chemical shifts for substituted aromatic [16] and olefinic [57] carbons have also been developed. An example of the use of these calculational schemes is given in Sec. III.B.l. 

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