Concentration, polymer, model

R. B. Pandey, A. Milchev, K. Binder. Semidilute and concentrated polymer solutions near attractive walls Dynamic Monte Carlo simulation of density and pressure profiles of a coarse-grained model. Macromolecules 50 1194-1204, 1997. 

On the basis of theoretical calculations Chance et al. [203] have interpreted electrochemical measurements using a scheme similar to that of MacDiarmid et al. [181] and Wnek [169] in which the first oxidation peak seen in cyclic voltammetry (at approx. + 0.2 V vs. SCE) represents the oxidation of the leucoemeraldine (1 A)x form of the polymer to produce an increasing number of quinoid repeat units, with the eventual formation of the (1 A-2S")x/2 polyemeraldine form by the end of the first cyclic voltammetric peak. The second peak (attributed by Kobayashi to degradation of the material) is attributed to the conversion of the (1 A-2S")x/2 form to the pernigraniline form (2A)X and the cathodic peaks to the reverse processes. The first process involves only electron transfer, whereas the second also involves the loss of protons and thus might be expected to show pH dependence (whereas the first should not), and this is apparently the case. Thus the second peak would represent the production of the diprotonated (2S )X form at low pH and the (2A)X form at higher pH with these two forms effectively in equilibrium mediated by the H+ concentration. This model is in conflict with the results of Kobayashi et al. [196] who found pH dependence of the position of the first peak. 

Our model predicts destabilization of colloidal dispersions at low polymer concentration and restabilisation in (very) concentrated polymer solutions. This restabilisation is not a kinetic effect, but is governed by equilibrium thermodynamics, the dispersed phase being the situation of lowest free energy at high polymer concentration. Restabilisation is a consequence of the fact that the depletion thickness is, in concentrated polymer solutions, (much) lower than the radius of gyration, leading to a weaker attraction. 

Futerko and Hsing presented a thermodynamic model for water vapor uptake in perfluorosulfonic acid membranes.The following expression was used for the membrane—internal water activity, a, which was borrowed from the standard Flory—Huggins theory of concentrated polymer solutions ... 

Necklace models represent the chain as a connected sequence ctf segments, preserving in some sense the correlation between the spatial relationships among segments and their positions along the chain contour. Simplified versions laid the basis for the kinetic theory of rubber elasticity and were used to evaluate configurational entropy in concentrated polymer solutions. A refined version, the rotational isomeric model, is used to calculate the equilibrium configurational... 

Experimental results presented in this work and in the literature are inconsistent with the assumptions and the physical interpretations implicit in the dual-mode sorption and transport model, and strongly suggest that the sorption and transport in gas-glassy polymer systems should be presented by a concentration-dependent model ... 

The concentration-dependent models attribute the observed pressure dependence of the solubility and diffusion coefficients to the fact that the presence of sorbed gas in a polymer affects the structural and dynamic properties of the polymer, thus affecting the sorption and transport characteristics of the system (3). On the other hand, in the dual-mode model, the pressure-dependent sorption and transport properties arise from a... 

G. G. Fuller and L.G. Leal, Network models of concentrated polymer solutions derived from the Yamamoto network theory, J. Polym. Sci. Phys. Ed., 19,531 (1981). 

Extension of this theory can also be used for treating concentrated polymer solution response. In this case, the motion of, and drag on, a single bead is determined by the mean intermolecular force field. In either the dilute or concentrated solution cases, orientation distribution functions can be obtained that allow for the specification of the stress tensor field involved. For the concentrated spring-bead model, Bird et al. (46) point out that because of the proximity of the surrounding molecules (i.e., spring-beads), it is easier for the model molecule to move in the direction of the polymer chain backbone rather than perpendicular to it. In other words, the polymer finds itself executing a sort of a snake-like motion, called reptation (47), as shown in Fig. 3.8(b). 

The development of the polymer chain in a tube model by M. Doi and S.F. Edwards [51] allowed them to describe on the molecular level a set of hydrodynamic and viscoelastic properties of concentrated polymer solutions and melts. 

Since spectroscopic investigations of such a structure in real polymer chains present difficulties owing to the low concentration of the unit in the polymer (even for low molecular weight polymers), model compounds have been used widely in polymerization studies. 

Fig. 16.9 shows the low frequency slopes of 2 and 1, respectively, as expected for viscoelastic liquids and the high frequency slopes Vi and 2/3 for Rouse s and Zimm s models, respectively. Experimentally it appears that in general Zimm s model is in agreement with very dilute polymer solutions, and Rouse s model at moderately concentrated polymer solutions to polymer melts. An example is presented in Fig. 16.10. The solution of the high molecular weight polystyrene (III) behaves Rouse-like (free-draining), whereas the low molecular weight polystyrene with approximately the same concentration behaves Zimm-like (non-draining). The higher concentrated solution of this polymer illustrates a transition from Zimm-like to Rouse-like behaviour (non-draining nor free-draining, hence with intermediate hydrodynamic interaction).

This section on concentrated suspensions discusses the rheological behavior of sj tems which are colloidally stable and colloidally unstable suspensions. For stable sj tems, the rheology of sterically stabilized and electrostatically stabilized systems wiU be considered. For sterically stabilized suspensions, a hard sphere (or hard particle) model has been successfid. Concentrated suspensions in some cases behave rheologically like concentrated polymer solutions. For this reason, a discussion of the viscosity of concentrated polymer solutions is discussed next before a discussion of concentrated ceramic suspensions. 

They have been developed based on either molecular structure or continuum mechanics where the molecular structure is not considered explicitly and the response of a material is independent of the coordinate system (principle of material indifference). In the former, the polymer molecules are represented by mechanical models and a probability distribution of the molecules, and relationships between macroscopic quantities of interest are derived. Three models have found extensive use in rheology the bead-spring model for dilute polymer solutions, and the transient net work and the reptation models for concentrated polymer solutions and polymer melts. 

The transient net work model is an adaptation of the network theory of rubber elasticity. In concentrated polymer solutions and polymer melts, the network junctions are temporary and not permanent as in chemically crosslinked rubber, so that existing junctions can be destroyed to form new junctions. It can predict many of the linear viscoelastic phenomena and to predict shear-thinning behavior, the rates of creation and loss of segments can be considered to be functions of shear rate. 

Thermodynamic Model for Phase Equilibrium between Polymer Solution and 6/W MlcroemulslonsT figures 6 and / show that when phase separation first occurs, most of the water is in the microemulsion. With an increase in salinity, however, much of the water shifts to the polymer solution. Thus, a concentrated polymer solution becomes dilute on increasing salinity. The objective of this model is to determine the partitioning of water between the microemulsion and the polymer-containing excess brine solution which are in equilibrium. For the sake of simplicity, it is assumed that there is no polymer in the microemulsion phase, and also no microemulsion drops in the polymer solution. The model is illustrated in Figure 12. The model also assumes that the value of the interaction parameter (x) or the volume of the polymer does not change with salinity. 

The zero-shear viscoelastic properties of concentrated polymer solutions or polymer melts are typically defined by two parameters the zero-shear viscosity (f]o) and the zero-shear recovery compliance (/ ). The former is a measure of the dissipation of energy, while the latter is a measure of energy storage. For model polymers, the infiuence of branching is best established for the zero-shear viscosity. When the branch length is short or the concentration of polymer is low (i.e., for solution rheology), it is found that the zero-shear viscosity of the branched polymer is lower than that of the linear. This has been attributed to the smaller mean-square radius of the branched chains and has led to the following relation... 

It is a difficult problem to fit the results in highly concentrated polymer solutions to the existing theories of polymer solutions. However, deGennes mesh model and scaling concepts [16] might provide a qualitative explanation to these phenomena. 

The deficiencies of the Flory-Huggins theory result from the limitations both of the model and of the assumptions employed in its derivation. Thus, the use of a single type of lattice for pure solvent, pure polymer and their mixtures is clearly unrealistic since it requires that there is no volume change upon mixing. The method used in the model to calculate the total number of possible conformations of a polymer molecule in the lattice is also unrealistic since it does not exclude self-intersections of the chain. Moreover, the use of a mean-field approximation to facilitate this calculation, whereby it is assumed that the segments of the previously added polymer molecules are distributed uniformly in the lattice, is satisfactory only when the volume fraction (f>2 of polymer is high, as in relatively concentrated polymer solutions. 

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