Modeling of Additives

Industrial crystallization processes rarely involve pure materials, but are rather used as purification process to achieve purified material and are often conducted from melt or solution. The presence of any other molecules but the crystalline material (substrate) frequently causes significant changes in the crystalline morphology [42—45]. Components denoted as additives or impurities predominantly occur in small amounts, whereas a solvent is represented by a large number of molecules in a mixed system. Here, the modeling procedure conducted for morphology prediction in the presence of additives is described. 

Berkovitch-Yellin [46] introduces a simple approach for the morphology prediction in the presence of additives. Herein, the additive molecule is build into the unit cell to replace each of the host molecules stepwise. The structure of the polar surfaces is analyzed and the mappings of the corresponding electrostatic potentials are employed to determine the solvent effect. The method supphes accurate results and considers the solvent and the additive effect, respectively. Nonetheless, it is lacking the implementation of the concentration of solute, solvent, and potential additives in the solution. 

Bennema et al. [47] introduce a modeling concept for the prediction of crystal morphology grown in the presence of additives, which is based on the knowledge of the internal crystal structure. The method employs the theory of the roughening temperature [48]. Preliminary investigations on the solid-liquid interface revealed an intensive structuring of molecules in the interfacial fluid phase and none in the bulk fluid phase [49]. 

By means of the approach presented by Liu and Bennema [50,51], the habitcontrolling factors and the relative growth rate are related via the crystal growth mechanism. The PBC theory as well as the interfacial structure analysis forms the 

Investigations of Docherty and coworkers [24,25] aimed to model the effect of tailor-made additives. Disruptive and blocking additives disturb the local symmetry of the crystal. In terms of the presented approach, the molecules in the central crystal unit cell are stepwise replaced by an additive molecule, and the surrounding unit cells consist of host molecules (build-in). The obtained slice and attachment energies in presence of the additive are averaged. The attachment energy in 

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As in our previous notations, the species superscript 0 is for the matrix component and the species superscript 1 denotes the fluid component. The fluid-matrix interaction is chosen between a fluid particle and a monomer belonging to a chain by using the model of additive hard spheres. The fluid-matrix and fluid-fluid interactions are... 

The equilibrium modelling of additives in bilayers is already a challenging task. For example, in MD simulations it is difficult to consider very low loading... 

Brandsch, J. Mercea, P. Piringer, O. Modeling of Additive Diffusion Coefficients in Polymers. New Developments in the Chemistry of Packaging Materials ACS Symposium Series, ACS, Washington, D.C. 1999. 

Limm, W., and Hollifield, H.C., 1996, Modeling of additive diffusion in polyolefins. Food Additives and Contaminants 13, No. 8, 949-967. 

AB cos A A = odor intensity of component A, B = odor intensity of component B, Mixture = odor intensity of the mixture, cosA= cosine of the angle separating these vectors). Laffort and Dravnieks suggested another ("U") model of additivity which seems more tractable (5). 

Albeit the problem structure for branching pipehnes is generally similar to a pipehne structure with multiple depots located along one main pipeline, it comphcates the mathematical formulation by forcing to track batches along the pipeline branches which equals the modelling of additional pipelines. In the follow-up paper (MirHas-... 

Arriola, D.J. (1989) Modeling of Addition Polymerization Systems. PhD Thesis, University of Wisconsin-Madison, USA. 

Paciorek et al. [23] studied the crosslinking of amines on several fluoro-compoimd models. The model of addition of butylamine onto 1,5,5-tri-hydro-4-iodoperfluorooctane and 4-hydroperfluoroheptene-3, in diethylether at room temperature, is the only one known. It proceeds according to the following scheme ... 

Only one model of addition of amines on partially fluorinated molecules was studied. Indeed, the study of addition of equimolar quantities of monoamines (butylamine, dibutylamine and triethylamine) onto 4,4-dihydro-3-iodoper-fiuoroheptane as a model molecule, in diethylether at room temperatme [22] afforded 80, 94 and 81% of the amine hydroiodides, respectively. But, by determining the time required for a given reaction mixture to reach a pH value of 6, it is concluded that the reaction with butylamine is faster than that using dibutylamine. This latter system is faster than that involving triethylamine. 

J. Brandsch, P. Mercea, O. Piringer. Modeling of additive diffusion coefficients in polyolefins. Food Packaging Testing Methods and Applications, S.J. Risch editor, pp. 27-36, ACS Symposium Series Washington DC, 753 (2000). 

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