Models polymeric solutions

This model then leads us through a thicket of statistical and algebraic detail to the satisfying conclusion that going from small solute molecules to polymeric solutes only requires the replacement of mole fractions with volume fractions within the logarithms. Note that the mole fraction weighting factors are unaffected. 

Viscoelastic properties have been discussed in relation to molar mass, concentration, solvent quality and shear rate. Considering the molecular models presented here, it is possible to describe the flow characteristics of dilute and semi-dilute solutions, as well as in simple shear flow, independent of the molar mass, concentration and thermodynamic quality of the solvent. The derivations can be extended to finite shear, i.e. it is possible to evaluate T) as a function of the shear rate. Furthermore it is now possible to approximate the critical conditions (critical shear rate, critical rate of elongation) at which the onset of mechanical degradation occurs. With these findings it is therefore possible to tune the flow features of a polymeric solution so that it exhibits the desired behaviour under the respective deposit conditions. 

The results of experimental studies aimed at assessing the validity of Eq. (32) have, for the most part, been inconclusive. Although the exact reasons for this are not entirely clear, certain differences between the experimental conditions employed and those upon which the model is based can be readily identified. In most studies the diffusion coefficient for the particular polymeric solution used was not known and was necessarily treated as an adjustable parameter in the theory. A subjective judgment was thus required as to whether the value of the diffusivity which described the data best was a reasonable one. Generally speaking, the resulting values were unrealistically high. 

In this chapter, we focus on iSAFT, a computationally simple, thermodynamically consistent DFT that accurately predicts the structure and thermodynamics of inhomogeneous polymeric solutions and blends (Jain et al., 2007, 2008, 2009 Tripathi and Chapman, 2005a, 2005b). Like molecular simulation, the DFT uses explicit models of molecules, but the DFT is not limited computationally in molecule size or number of components. The DFT shows excellent agreement with molecular simulation for local structure, compressibility effects, and the effects of molecular size. 

In all but the most basic cases of very dilute systems, with microstructural elements such as rigid particles whose properties can be described simply, the development of a theory in a continuum context to describe the dynamical interactions between structure and flow must involve some degree of modeling. For some systems, such as polymeric solutions, we require modeling to describe both polymer-solvent and polymer-polymer interactions, whereas for suspensions or emulsions we may have an exact basis for describing particle-fluid interactions but require modeling via averaging to describe particle-particle interactions. In any case, the successful development of useful theories of microstructured fluids clearly requires experimental input and a comparison between experimental data and model... 

Our discussion here explores active connections between the potential distribution theorem (PDT) and the theory of polymer solutions. In Chapter 4 we have already derived the Flory-Huggins model in broad form, and discussed its basis in a van der Waals model of solution thermodynamics. That derivation highlighted the origins of composition, temperature, and pressure effects on the Flory-Huggins interaction parameter. We recall that this theory is based upon a van der Waals treatment of solutions with the additional assumptions of zero volume of mixing and more technical approximations such as Eq. (4.45), p. 81. Considering a system of a polymer (p) of polymerization index M dissolved in a solvent (s), the Rory-Huggins model is... 

It should be emphasized that many constitutive models have been proposed especially for polymeric solutions and melts, and there is a great deal of current research that is aimed at both new models25 and numerical analysis of fluid motions by use of the existing models 26 The problem is that few have been carefully compared with the behavior of real fluids outside the highly simplistic flows of conventional rheometers, and then mainly under flow conditions in which the perturbations in material structure are weak. Thus there is currently no model that is known to provide quantitatively accurate or even qualitatively reliable descriptions of real complex fluids for a wide spectrum of flows. 

There has been much interest in recent years regarding kinetic modeling of solution FR styrene polymerization. Several kinetic models have been developed for styrene polymerization without added initiators [182-184], using... 

For the model system polymerizations, solutions containing the surfactants, LMA, initiator, and other additives as necessary were prepared in 4-oz narrow-mouth bottles, placed in a Branson B-52 ultrasonic bath for more than 10 min with nitrogen flow into the top of the bottle, capped with Polyseal tops, and tumbled in a water bath overnight at 60 °C. The ultrasonic bath was used both to aid in degassing the sample and to ensure complete equilibrium in the surfactant solutions. 

The osmotic pressure difference can usually be neglected in MF and UF, since the rejected solutes are large and their osmotic pressure small. However, even polymeric solutes can develop a significant osmotic pressure at boundary layer concentrations (Ho and Sirkar (1992)). This naturally implies that the resistance in series model (equation (3.4)) would be more appropriate in MF, while the osmotic pressure model (equation (3.6)) may be more useful in NF and RO. Both models have been applied to UF. 

Elevated temperatures, 70 °C, and enhanced pressures, 5—10 atm, are conventionally used for olefin polymerization. The catalytically active species is formed in situ from a catalyst precursor. The solvent medium changes during the course of reaction. Initially a solvent such as propylene or toluene surrounds the active site, but shortly the active site is encased in a polymeric solution. Seemingly insignificant changes in reaction medium perturb the observed polymeric properties. For these reasons, for modeling studies one must proceed with caution... 

The second approach or microheterogeneous model [1, 19-22] is based upon the principle, that the kinetics of the reaction in its initial stage are not that of a homophase polymerisation in a liquid monomer-polymeric solution, but a heterophase one. The reaction proceeding at the boundary liquid monomer - solid polymer microgranules surface under gel conditions. 

Completely statistical (random) arrangements of the macromolecules without a regular order or orientation, i.e., without constant distances, are known as amorphous states. There is no long-range order whatsoever. The valid model for such states is the statistical coil. This is the dominating secondary structure in synthetic polymers and polymeric solutions. Its determinant parameter is coil density. 

The KSR and Rouse models were subj ected to numerous experimental tests. A reasonably good agreement between the theoretical predictions and experimental data was demonstrated for a variety of dilute polymeric solutions. Further advance in the molecular-kinetic approach to description of relaxation processes in polymeric systems have brought about more sophisticated models. They improve the classical results by taking into account additional factors and/or considering diverse frequency, temperature, and concentration ranges, etc. For the aims of computer simulation of the polymeric liquid dynamics in hydrodynamic problems, either simple approximations of the spectrum, Fi(A), or the model of subchains are usually used. Spriggs law is the most used approximation... 

Ghoniem, S. Rheological behaviour and degradation of polymeric solutions in modelized porous media. Dr. Ing. Thesis, University of Brest (1979)... 

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