Isothermal viscosity behavior

Several researchers have described changes in the isothermal viscosity behavior during the cure of thermosetting resin systems with respect to time by the following expression ... 

The theory of non-isothermal viscoelastic behavior as developed by Hopkins [2] and Haugh [3] may be based on the representation of linear viscoelastic behavior by mechanical models. The linear viscoelastic behavior of polymers in simple shear at constant temperature and prescribed stress history may be expressed in terms of the deformation of a generalized Kelvin model. Spring constants and dashpot viscosity constants of the model have to be appropriately chosen the choice depends on temperature. For the non-isothermal treatment, the elasticity of the springs and the viscosities of the dashpots have to be inserted as functions of temperature. Due to the prescribed temperature history, they become functions of time. 

Fig. 14.15. Behavior of the viscosity of ethane in the vapor j ase along selected isotherms viscosity at the pressure of 1 bar.

A wide variety of physical properties are important in the evaluation of ionic liquids (ILs) for potential use in industrial processes. These include pure component properties such as density, isothermal compressibility, volume expansivity, viscosity, heat capacity, and thermal conductivity. However, a wide variety of mixture properties are also important, the most vital of these being the phase behavior of ionic liquids with other compounds. Knowledge of the phase behavior of ionic liquids with gases, liquids, and solids is necessary to assess the feasibility of their use for reactions, separations, and materials processing. Even from the limited data currently available, it is clear that the cation, the substituents on the cation, and the anion can be chosen to enhance or suppress the solubility of ionic liquids in other compounds and the solubility of other compounds in the ionic liquids. For instance, an increase in allcyl chain length decreases the mutual solubility with water, but some anions ([BFJ , for example) can increase mutual solubility with water (compared to [PFg] , for instance) [1-3]. While many mixture properties and many types of phase behavior are important, we focus here on the solubility of gases in room temperature IFs. 

In the literature there have been repeated reports on an apparent mean-field-like critical behavior of such ternary systems. To our knowledge, this has first been noted by Bulavin and Oleinikova in work performed in the former Soviet Union [162], which only more recently became accessible to a greater community [163], The authors measured and analyzed refractive index data along a near-critical isotherm of the system 3-methylpyridine (3-MP) + water -I- NaCl. The shape of the refractive index isotherm is determined by the exponent <5. Bulavin and Oleinikova found the mean-field value <5 = 3 (cf. Table I). Viscosity data for the same system indicate an Ising-like exponent, but a shrinking of the asymptotic range by added NaCl [164],... 

Recent investigations have shown that the behavior and interactions of surfactants in a polyvinyl acetate latex are quite different and complex compared to that in a polystyrene latex (1, 2). Surfactant adsorption at the fairly polar vinyl acetate latex surface is generally weak (3,4) and at times shows a complex adsorption isotherm (2). Earlier work (5,6) has also shown that anionic surfactants adsorb on polyvinyl acetate, then slowly penetrate into the particle leading to the formation of a poly-electroyte type solubilized polymer-surfactant complex. Such a solubilization process is generally accompanied by an increase in viscosity. The first objective of this work is to better under-stand the effects of type and structure of surfactants on the solubilization phenomena in vinyl acetate and vinyl acetate-butyl acrylate copolymer latexes. 

Although we analyze most polymer processes as isothermal problems, many are non-isothermal even at steady state conditions. The non-isothermal effects during flow are often difficult to analyze, and make analytical solutions cumbersome or, in many cases impossible. The non-isothermal behavior is complicated further when the energy equation and the momentum balance are fully coupled. This occurs when viscous dissipation is sufficiently high to raise the temperature enough to affect the viscosity of the melt. 

White et al. (38,39) presented experimental and theoretical (isothermal linear stability analysis) results that indicate the following first, that polymer melts respond similarly to uniform elongational flow and to melt spinning second, that polymers whose elongational viscosity e) increases with time or strain result in a stable spinline, do not exhibit draw resonance, and undergo cohesive failure at high draw ratios. A prime example of such behavior is LDPE. On the other hand, polymer melts with a decreasing r + (t, e)... 

Thixotropy can be defined as an isothermal, reversible, sol-gel transformation and is a behavior common to many foods. Thixotropy is an effect brought about by mechanical action, and it results in a lowered apparent viscosity. When the body is allowed sufficient time, the apparent viscosity will return to its original value. Such behavior would result in a shear stress-rate-of-shear diagram, as given in Figure 8-19. Increasing shear rate results in increased shear stress up to a maximum after the maximum is reached, decreasing shear rates will result in substantially lower shear stress. 

A generalized kinetic model of cure is developed from the aspect of relaxation phenomena. The model not only can predict modulus and viscosity during the cure cycle under isothermal and non-isothermal cure conditions, but also takes into account filler effects on cure behavior. The increase of carbon black filler loading tends to accelerate the cure reaction and also broadens the relaxation spectrum. The presence of filler reduces the activation energy of viscous flow, but has little effect on the activation energy of the cure reaction. 

A generalized kinetic model of cure has been developed from the aspect of relaxation phenomenon. The model not only can predict isothermal and non-isothermal cure curves using modulus and viscosity data, but also allows us to take into account the effect of filler on cure behavior. The prediction of viscosity and modulus values during the cure cycle allows one to preprogram cure in order to improve the material processing and end-product performance. The important findings of this study... 

Calculations of the relations between the input and output amounts and compositions and the number of extraction stages are based on material balances and equilibrium relations. Knowledge of efficiencies and capacities of the equipment then is applied to find its actual size and configuration. Since extraction processes usually are performed under adiabatic and isothermal conditions, in this respect the design problem is simpler than for thermal separations where enthalpy balances also are involved. On the other hand, the design is complicated by the fact that extraction is feasible only of nonideal liquid mixtures. Consequently, the activity coefficient behaviors of two liquid phases must be taken into account or direct equilibrium data must be available. In countercurrent extraction, critical physical properties such as interfacial tension and viscosities can change dramatically through the extraction system. The variation in physical properties must be evaluated carefully. 

In view of Eq. (6.26) for ideal polymerization kinetics one would normally expect the reaction rate to fall with time, since the monomer and initiator concentrations decrease with conversion. However, the exact opposite behavior is observed in many polymerizations where the rate of polymerization increases with time. A typical example of this phenomenon is shown in Fig. 6.10 for the polymerization of methyl methacrylate in benzene solution at 50°C [49], At monomer concentrations less than about 40 wt% in this case, the rate (slope of conversion vs. time) is approximately as anticipated from the ideal kinetic scheme described in this chapter, that is, the rate decreases gradually as the reaction proceeds and the concentrations of monomer and initiator are depleted. An acceleration is observed, however, at higher monomer concentrations and the curve for the pure monomer shows a dramatic autoacceleration in the polymerization rate. Such behavior is referred to as the gel effect. (The term gel used here is different than the usage in Chapter 5 as it refers only to the sharp increase in viscosity and not to the formation of a cross-linked polymer.) The autoaccelerative gel effect is also known as the Tromsdorff effect or Norrish-Smith effect after pioneering workers in this field. It should be noted that the gel effect is observed under isothermal conditions. It should thus not be confused with the acceleration that would be observed if a polymerization reaction were carried out under nonisotherraal conditions such that the reaction temperature increased with conversion due to exothermicity of the reaction. 

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