Polymer solution properties, model interactions

Prediction of Polymer Solution Properties from a Model of Chain Conformations and Interactions... 

The dynamical properties of polymer molecules in solution have been investigated using MPC dynamics [75-77]. Polymer transport properties are strongly influenced by hydrodynamic interactions. These effects manifest themselves in both the center-of-mass diffusion coefficients and the dynamic structure factors of polymer molecules in solution. For example, if hydrodynamic interactions are neglected, the diffusion coefficient scales with the number of monomers as D Dq /Nb, where Do is the diffusion coefficient of a polymer bead and N), is the number of beads in the polymer. If hydrodynamic interactions are included, the diffusion coefficient adopts a Stokes-Einstein formD kltT/cnr NlJ2, where c is a factor that depends on the polymer chain model. This scaling has been confirmed in MPC simulations of the polymer dynamics [75]. 

The viscosity of a polymer solution is one of its most distinctive properties. The spatial extension of the molecules is great enough so that the solute particles cut across velocity gradients and increase the viscosity in the manner suggested by Figure 4.8. In this regard they are no different from the rigid spheres of the Einstein model. What is different for these molecules is the internal structure of the dispersed units, which are flexible and swollen with solvent. The viscosity of a polymer solution depends, therefore, on the polymer-solvent interactions, as well as on the properties of the polymer itself. 

Universal models of polymer solutions attempt to describe a variety of large-scale properties with a minimum number of phenomenological parameters. Some theories (Flory, 1969) predict these parameters through microscopic models of bond geometry and interactions, and difficult but... 

The Rouse model is the earliest and simplest molecular model that predicts a nontrivial distribution of polymer relaxation times. As described below, real polymeric liquids do in fact show many relaxation modes. However, in most polymer liquids, the relaxation modes observed do not correspond very well to the mode distribution predicted by the Rouse theory. For polymer solutions that are dilute, there are hydrodynamic interactions that affect the viscoelastic properties of the solution and that are unaccounted for in the Rouse theory. These are discussed below in Section 3.6.1.2. In most concentrated solutions or melts, entanglements between long polymer molecules greatly slow polymer relaxation, and, again, this is not accounted for in the Rouse theory. Reptation theories for entangled... 

The failure of the van Laar model to give realistic predictions of the thermodynamic properties of polymer solutions arises from the assumption made in this model that the solvent and solute molecules are identical in size. However, Flory [1] and Huggins [2] proposed, independently, a modified lattice theory which takes into account the large differences in size between solvent and polymer molecules, in addition to Intermolecular interactions. 

The simple Flory-Huggins %-function, combined with the solubility parameter approach may be used for a first rough guess about solvent activities of polymer solutions, if no experimental data are available. Nothing more should be expected. This also holds true for any calculations with the UNIFAC-fv or other group-contribution models. For a quantitative representation of solvent activities of polymer solutions, more sophisticated models have to be applied. The choice of a dedicated model, however, may depend, even today, on the nature of the polymer-solvent system and its physical properties (polar or non-polar, association or donor-acceptor interactions, subcritical or supercritical solvents, etc.), on the ranges of temperature, pressure and concentration one is interested in, on the question whether a special solution, special mixture, special application is to be handled or a more universal application is to be foxmd or a software tool is to be developed, on munerical simplicity or, on the other hand, on numerical stability and physically meaningftd roots of the non-linear equation systems to be solved. Finally, it may depend on the experience of the user (and sometimes it still seems to be a matter of taste). 

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