Viscosity description

The discrepancy indicated requires the application of principally differing approaches to the polymer nanocomposites melt viscosity description. Such an approach can be fractal analysis, within the ffamewoik of which, the authors used the following relationship for fractal liquid viscosity (h) estimation ... 

The indicated above importance of polymer melts viscosity causes the appearance of a considerable number of theoretical treatments, describing this property on the basis of either representations, mainly fiom the point of view of free volume [3], In the present chapter polymer melts viscosity is treated within the framework of fractal analysis [5]. This is due to the fact, that the macromolecular coil in polymer solutions and melts is a fiactal [6] that creates prerequisites for the polymer melt viscosity prediction quite at the synthesis stage. The authors of Ref [7] demonstrated the possibility of polymer melts viscosity description and prediction within the fiamework of fiactal analysis on the example of two polymers of different classes—aromatic poly-ethersulfonoformals (APESF) and high-density polyethylene (HOPE). MFI values were determined on the automatic capillary viscometer IIRT-A at temperatures and loads, listed in Table 1. The fiactal dimension of a macromo-... 

Apart from chemical composition, an important variable in the description of emulsions is the volume fraction, outer phase. For spherical droplets, of radius a, the volume fraction is given by the number density, n, times the spherical volume, 0 = Ava nl2>. It is easy to show that the maximum packing fraction of spheres is 0 = 0.74 (see Problem XIV-2). Many physical properties of emulsions can be characterized by their volume fraction. The viscosity of a dilute suspension of rigid spheres is an example where the Einstein limiting law is [2]... 

As it has appeared in recent years that many hmdamental aspects of elementary chemical reactions in solution can be understood on the basis of the dependence of reaction rate coefficients on solvent density [2, 3, 4 and 5], increasing attention is paid to reaction kinetics in the gas-to-liquid transition range and supercritical fluids under varying pressure. In this way, the essential differences between the regime of binary collisions in the low-pressure gas phase and tliat of a dense enviromnent with typical many-body interactions become apparent. An extremely useful approach in this respect is the investigation of rate coefficients, reaction yields and concentration-time profiles of some typical model reactions over as wide a pressure range as possible, which pemiits the continuous and well controlled variation of the physical properties of the solvent. Among these the most important are density, polarity and viscosity in a contimiiim description or collision frequency. 

Polymers owe much of their attractiveness to their ease of processing. In many important teclmiques, such as injection moulding, fibre spinning and film fonnation, polymers are processed in the melt, so that their flow behaviour is of paramount importance. Because of the viscoelastic properties of polymers, their flow behaviour is much more complex than that of Newtonian liquids for which the viscosity is the only essential parameter. In polymer melts, the recoverable shear compliance, which relates to the elastic forces, is used in addition to the viscosity in the description of flow [48]. 

A frequently used example of Oldroyd-type constitutive equations is the Oldroyd-B model. The Oldroyd-B model can be thought of as a description of the constitutive behaviour of a fluid made by the dissolution of a (UCM) fluid in a Newtonian solvent . Here, the parameter A, called the retardation time is de.fined as A = A (r s/(ri + s), where 7]s is the viscosity of the solvent. Hence the extra stress tensor in the Oldroyd-B model is made up of Maxwell and solvent contributions. The Oldroyd-B constitutive equation is written as... 

By analogy with Eq. (3.1), we seek a description for the relationship between stress and strain. The former is the shearing force per unit area, which we symbolize as as in Chap. 2. For shear strain we use the symbol y it is the rate of change of 7 that is involved in the definition of viscosity in Eq. (2.2). As in the analysis of tensile deformation, we write the strain AL/L, but this time AL is in the direction of the force, while L is at right angles to it. These quantities are shown in Fig. 3.6. It is convenient to describe the sample deformation in terms of the angle 6, also shown in Fig. 3.6. For distortion which is independent of time we continue to consider only the equilibrium behavior-stress and strain are proportional with proportionality constant G ... 

Flow Past Deformable Bodies. The flow of fluids past deformable surfaces is often important, eg, contact of Hquids with gas bubbles or with drops of another Hquid. Proper description of the flow must allow for both the deformation of these bodies from their shapes in the absence of flow and for the internal circulations that may be set up within the drops or bubbles in response to the external flow. DeformabiUty is related to the interfacial tension and density difference between the phases internal circulation is related to the drop viscosity. A proper description of the flow involves not only the Reynolds number, dFp/p., but also other dimensionless groups, eg, the viscosity ratio, 1 /p En tvos number (En ), Api5 /o and the Morton number (Mo),giJ.iAp/plG (6). 

There are two problems in the manufacture of PS removal of the heat of polymeriza tion (ca 700 kj /kg (300 Btu/lb)) of styrene polymerized and the simultaneous handling of a partially converted polymer symp with a viscosity of ca 10 mPa(=cP). The latter problem strongly aggravates the former. A wide variety of solutions to these problems have been reported for the four mechanisms described earlier, ie, free radical, anionic, cationic, and Ziegler, several processes can be used. Table 6 summarizes the processes which have been used to implement each mechanism for Hquid-phase systems. Free-radical polymerization of styrenic systems, primarily in solution, is of principal commercial interest. Details of suspension processes, which are declining in importance, are available (208,209), as are descriptions of emulsion processes (210) and summaries of the historical development of styrene polymerization processes (208,211,212). 

Solution Process. With the exception of fibrous triacetate, practically all cellulose acetate is manufactured by a solution process using sulfuric acid catalyst with acetic anhydride in an acetic acid solvent. An excellent description of this process is given (85). In the process (Fig. 8), cellulose (ca 400 kg) is treated with ca 1200 kg acetic anhydride in 1600 kg acetic acid solvent and 28—40 kg sulfuric acid (7—10% based on cellulose) as catalyst. During the exothermic reaction, the temperature is controlled at 40—45°C to minimize cellulose degradation. After the reaction solution becomes clear and fiber-free and the desired viscosity has been achieved, sufficient aqueous acetic acid (60—70% acid) is added to destroy the excess anhydride and provide 10—15% free water for hydrolysis. At this point, the sulfuric acid catalyst may be partially neutralized with calcium, magnesium, or sodium salts for better control of product molecular weight. 

Following the general trend of looldng for a molecular description of the properties of matter, self-diffusion in liquids has become a key quantity for interpretation and modeling of transport in liquids [5]. Self-diffusion coefficients can be combined with other data, such as viscosities, electrical conductivities, densities, etc., in order to evaluate and improve solvodynamic models such as the Stokes-Einstein type [6-9]. From temperature-dependent measurements, activation energies can be calculated by the Arrhenius or the Vogel-Tamman-Fulcher equation (VTF), in order to evaluate models that treat the diffusion process similarly to diffusion in the solid state with jump or hole models [1, 2, 7]. 

Though the accuracy of description of flow curves of real polymer melts, attained by means of Eq. (10), is not always sufficient, but doubtless the equation of such a structure based on the idea of relaxation mechanism of non-Newtonian polymer flow, correctly reflects the main peculiarities of viscous properties. Therefore while discussing the effect a filler has on the viscosity properties of polymer melts, besides the dependences Y(filler modifies the characteristic time of relaxation. According to [19], a possible form of the X versus

[Pg.86]

However, dendrimeric and hyperbranched polyesters are more soluble than the linear ones (respectively 1.05, 0.70, and 0.02 g/mL in acetone). The solution behavior has been investigated, and in the case of aromatic hyperbranched polyesters,84 a very low a-value of the Mark-Houvink-Sakurada equation 0/ = KMa) and low intrinsic viscosity were observed. Frechet presented a description of the intrinsic viscosity as a function of the molar mass85 for different architectures The hyperbranched macromolecules show a nonlinear variation for low molecular weight and a bell-shaped curve is observed in the case of dendrimers (Fig. 5.18). 

Antonietti M., Briel A., Fosrster S. Quantitative Description of the Intrinsic Viscosity of Branched. Polyelectrolytes. Macromolecules 1997, 30, 2700-2704. 

A description is given of a comparative study of the glycolysis of PETP waste soft drinks bottles by various mixtures of EG and DEG with subsequent polyesterification of the glycolysed products by maleic anhydride in order to obtain unsaturated polyesters suitable for the production of varnishes. The processing characteristics such as viscosity, exotherm temperatures of curing, compatibility of resins with monomers was investigated with respect to the type and amount of reactive monomers. The mechanical properties of varnishes produced were analysed. 13 refs. 

It was also found that the viscosity also increased in the same manner as in 2- There have been many theoretical descriptions for polymer-solvent friction.As an extreme case, a single... 

Perrin model and the Johansson and Elvingston model fall above the experimental data. Also shown in this figure is the prediction from the Stokes-Einstein-Smoluchowski expression, whereby the Stokes-Einstein expression is modified with the inclusion of the Ein-stein-Smoluchowski expression for the effect of solute on viscosity. Penke et al. [290] found that the Mackie-Meares equation fit the water diffusion data however, upon consideration of water interactions with the polymer gel, through measurements of longitudinal relaxation, adsorption interactions incorporated within the volume averaging theory also well described the experimental results. The volume averaging theory had the advantage that it could describe the effect of Bis on the relaxation within the same framework as the description of the diffusion coefficient. 

During the production of the chapter, a current review of the RFOT theory has appeared in print [V. Lubchenko and P. G. Wolynes, Annu. Rev. Phys. Chem. 58, 235 (2007)]. In addition, microscopic descriptions of the onset of activationless reconfigurations [J. D. Stevenson, J. Schmalian, and P. G Wolynes, Nat. Phys. 2, 268 (2006)] and prefactors for viscosity and ionic conductivity of deeply supercooled melts [V. Lubchenko, J. Chem. Phys. 126, 174503 (2007)] are now available. 

Ikegami Imai (1962) made a study of precipitation and hydration using turbidity, conductance, refractive index and viscosity measurements. The following account is based on their description. 

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