Polymer fluids theory

Sohweizer K S and Curro J G 1997 Integral equation theories of the struoture, thermodynamios and phase transitions of polymer fluids Adv. Chem. Phys. 98 1... 

Hydrodynamic interaction is a long-range interaction mediated by the solvent medium and constitutes a cornerstone in any theory of polymer fluids. Although the mathematical formulation needs somewhat elaborate methods, the idea of hydrodynamic interaction is easy to understand suppose that a force is somehow exerted on a Newtonian solvent at the origin. This force sets the surrounding solvent in motion away from the origin, a velocity field is created which decreases as ... 

Lustig, SR Camthers, JM Peppas, NA, Continuum Thermodynamics and Transport Theory for Polymer-Fluid Mixtures, Chemical Engineering Science 12, 3037, 1992. 

The fundamental processes and mechanisms that control single-screw extrusion are presented in Chapters 5 through 8. These processes include solids conveying, melting, polymer fluid flow, and mixing. The analyses presented in these chapters focus on easily utilized functions needed to assess the operation of the single-screw extruder. The derivation of these relationships will be presented in detail in the appendices for those who desire to explore the theory of extrusion in more detail. 

Gibbs and DiMarzio [47] (GD) first developed a systematic statistical mechanical theory of glass formation in polymer fluids, based on experimental observations and on lattice model calculations by Meyer, Flory, Huggins, and... 

Another class of thermodynamic barrier theories focuses on the large increases in the elastic constants that accompany glass formation. (These theoretical approaches seem especially appropriate to polymer fluids below the crossover temperature Fj.) In particular, the barrier height governing particle displacement in the shoving model [57] is taken to be on the order of the elastic energy GqoVo required to displace a particle on a scale comparable to the interparticle distance,... 

According to Eq.(8.52), negative values of G at low frequencies occur if Nt becomes proportional to a power of shear rate less than one, a condition which should be attainable at moderate shear rates in concentrated solutions of polymers with narrow molecular weight distribution. Thus, any molecular theory which predicts rj and N1 as functions of shear rate, and which is also consistent with the BKZ and simple fluid theories should automatically yield superimposed moduli which satisfy Eqs.(8.49)-(8.52) without special assumptions about entanglement mechanisms. 

The reptation theory of viscoelasticity developed by Doi Edvards has paractically predetermined the appearance of Curtiss-Bird s reptation theory55). The latter is constructed on the basis of general kinetic theory of polymer fluids in phase space. According to the Curtiss-Bird theory, the longitudinal viscosity may increase only by a factor of two compared to the initial value. Note that a more significant increase in longitudinal viscosity was observed in experiments. 

Prokunin AN (1978) Nonlinear elastic effects in extension of polymer fluids. Experiment and Theory. Preprint. Inst. Appl Mech Acad Sci USSR, Moscow, No 104... 

In the previous sections, theories were reviewed where the optical properties of polymer liquids were cast in terms of the microscopic properties of the constituent chains. The dynamics of polymer chains subject to external fields that orient and distort these complex liquids are considered in this section for a variety of systems ranging from dilute solutions to melts. Detailed descriptions of theories for the dynamics and structure of polymer fluids subject to flow are found in a number of books, including those by Bird et al. [62], Doi and Edwards [63], and Larson [64],... 

The contribution "Application of Meso-Scale Field-based Models to Predict Stability of Particle Dispersions in Polymer Melts" by Prasanna Jog, Valeriy Ginzburg, Rakesh Srivastava, Jeffrey Weinhold, Shekhar Jain, and Walter Chapman examines and compares Self Consistent Field Theory and interfacial Statistical Associating Fluid Theory for use in predicting the thermodynamic phase behavior of dispersions in polymer melts. Such dispersions are of quite some technological importance in the... 

R.J.Gordon, W.R.Schowalter, Anisotropic fluid theory a different approach to the dumbbell theory of dilute polymer solutions, Trans Soc. Rheol. 15(1972), 79-97. 

In spite of the experimental results mentioned above, there is at present no accepted theory for macroscopic slip with polymer fluids. Analytical modelling results have indeed already been published [9-10, 17-20]. Generally, the laws assume a linear relation between stress at the wall and slip velocity [9], which can then be extended by a non-linear relation to high stress values [10, 17-20]. These often have the advantage of being simple to use, but nevertheless have serious drawbacks. 

This theory takes into account the micro-rotational effects due to rotation of molecules. This becomes important with polymers or polymeric suspensions. The physical model assigns a substructure to each continuum particle. Each material volume element contains microvolume elements which can translate, rotate, and deform independently of the motion of the microvolime. In the simplest case, these fluids are characterised by 22 viscosity coefficients and the problem is formulated in terms of a system of 19 equations with 19 unknowns. The equations for a 2-D case were solved numerically and compared to experimental results. It is concluded that the model based on the micropolar fluid theory gives a better fit than the Navier - Stokes equations. However, it seems that the difference is small. 

Lustig SR, Camthers JM, and Peppas NA. Continuum thermodynamics and transport theory for polymer-fluid mixtures. Chem. Eng. Sci. 1992 47(12) 3037-3057. 

The liquid may be a good or poor solvent for the polymer. For this type of system a theoretical relation can be obtained for K by applying the Flory equation of state theory ( -i) or lattice fluid theory (7-10) of solutions. An important prerequisite for the application of these theories is for the polymer to behave as an equlibrium liquid. This condition is generally valid for a lightly crosslinked, amorphous polymer above its Tg or for the amorphous component of a semi-crystalline polymer above its Tg. 

Equations of state offer a number of advantages over activity coefficient models for example, they can be applied to both low and high pressures, for properties other than phase equilibria, and the density is not required as an input parameter. However, often they are more difficult to develop for complex fluids and mixtures than are activity coefficient models. Very many equations of state have been proposed for polymers Section 16.7 discusses the reason. Recent reviews have been presented. " " We will not attempt to cover all the various approaches, but essentially discuss in detail only two of them, which seem promising for polymer solutions and blends the cubic equations of state and the SAFT (Statistical Associating Fluid Theory) method. 

Very many noncubic equations of state have been proposed for polymers. Most of them are rather complicated and a few of them, such as several of the models discussed previously, are based on the GC concept, like the GC-Flory and the GCLF equation of state. Several of these equations of state are reviewed elsewhere, and we will restrict here our presentation to one equation of state that is very promising for polymer systems and has already found widespread acceptance. This is the Statistical Associating Fluid Theory (SAFT). 

Orbey, H., Bokis, C.P., and Chen, C.-C., Equation of state modeling of phase equilibrium in the low-density polyethylene process the Sanchez-Lacombe, Statistical Associating Fluid Theory, and the polymer-SRK equation of state, Ind. Eng. Chem. Res., 37, 4481, 1998. 

For the calculations, different EoS have been used the lattice fluid (LF) model developed by Sanchez and Lacombet , as well as two recently developed equations of state - the statistical-associating-fluid theory (SAFT)f l and the perturbed-hard-spheres-chain (PHSC) theoryt ° . Such models have been considered due to their solid physical background and to their ability to represent the equilibrium properties of pure substances and fluid mixfures. As will be shown, fhey are also able to describe, if not to predict completely, the solubility isotherms of gases and vapors in polymeric phases, by using their original equilibrium version for rubbery mixtures, and their respective extensions to non-equilibrium phases (NELF, NE-SAFT, NE-PHSC) for glassy polymers. 

JI1 Jiang, S., An, L., Jiang, B., and Wolf, B. A., Pressure effects on the thermodynamics of fra 5-decahydronaphthalene/polystyrene polymer solutions apphcation of the Sanchez-Lacombe lattice fluid theory (experimeirtal data by S. Jiang), Macromol. Chem. Phys., 204, 692, 2003. 

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