Viscosity concentration dependent

Figure 14.8 shows the shear viscosity-concentration dependencies for EDA... 

Here M is the mass of a mole of colloids, representing their molecular weight, and a is their radius. Now let us turn our attention to a polymer coil. The viscosity-concentration dependence of dilute polymers can be... 

Utracki LA (1991) On the viscosity-concentration dependence of immisdble polymer blends. JRheol 35 1615-1637... 

L. A. Utracki, On the Viscosity-concentration Dependence of Immiscible Polymer Blends, J. Rheol., 35, 1615-1637 (1991). 

A possible and most likely explanation for the low value of viscosity for the mixtures based on Equation 4.7 is the very different viscosity dependence on concentration for the peetin and LB gum solutions, and not a true antagonism. To work with these gum solutions at equal concentration and to detect some possible synergism or antagonism between them, we must take into account the viscosity-concentration dependence of dilute gum solutions over the range of concentrations of each gum in the mixture. 

It should be noted that the Doi and Ohta theory predicts oifly an enhancement of viscosity, the so called emulsion-hke behavior that results in positive deviation from the log-additivity rule, PDB. However, the theory does not have a mechanism that may generate an opposite behavior that may result in a negative deviation from the log-additivity rule, NDB. The latter deviation has been reported for the viscosity vs. concentration dependencies of PET/PA-66 blends [Utracki et ah, 1982]. The NDB deviation was introduced into the viscosity-concentration dependence of immiscible polymer blends in the form of interlayer slip caused by steady-state shearing at large strains that modify the morphology [Utracki, 1991]. 

From the discussion of phase inversion in Sect. 7.1.2, the emulsion model predicts that immiscible blends should show positive deviation, PDB, from the log-additivity rule In r] = X In T]i. However, while PDB has been found in about 60 % of such blends, the remaining four types (see Fig. 7.32) must also be accounted for. This means that at least one other mechanism must be considered when modeling the viscosity-concentration dependence of polymer blends. This second mechanism should lead to the opposite effect, which is to the negative deviation fi om the log-additivity rule, NDB. 

Fig. 18.17 The five types of the viscosity/concentration dependence in polymer blend (Utracki 1991)...

Another approach to miscibility effect on flow is through analysis of the constant stress viscosity-concentration dependence. For solutions of small molecules, the log-additivity rule is most often found ... 

The viscosity of dispersions with various PAni contents was determined using a Couette viscosimeter. The results are shown in Fig. 19.6 (see Section II.C). The viscosity-concentration dependence obeys Relationship (3),... 

By describing the concentration dependence of an observable property as a power series, Eq. (9.9) plays a comparable role for viscosity as Eq. (8.83) does for osmotic pressure. 

Polymer solution viscosity is dependent on the concentration of the solvent, the molecular weight of the polymer, the polymer composition, the solvent composition, and the temperature. More extensive information on the properties of polymer solutions may be found ia refereaces 9 and 54—56. 

The flow behavior of the polymer blends is quite complex, influenced by the equilibrium thermodynamic, dynamics of phase separation, morphology, and flow geometry [2]. The flow properties of a two phase blend of incompatible polymers are determined by the properties of the component, that is the continuous phase while adding a low-viscosity component to a high-viscosity component melt. As long as the latter forms a continuous phase, the viscosity of the blend remains high. As soon as the phase inversion [2] occurs, the viscosity of the blend falls sharply, even with a relatively low content of low-viscosity component. Therefore, the S-shaped concentration dependence of the viscosity of blend of incompatible polymers is an indication of phase inversion. The temperature dependence of the viscosity of blends is determined by the viscous flow of the dispersion medium, which is affected by the presence of a second component. 

The majority of investigators consider it permissible and convenient to use, when calculating the boundary layer thickness, the relationships describing the concentration dependence of viscosity in the high and medium concentration range (basically Mooney s equation) [67 — 71]. 

A comparison of values of yield stress for filled polymers of the same nature but of different molecular weights is of fundamental interest. An example of experimental results very clearly answering the question about the role of molecular weight is given in Fig. 9, where the concentration dependences of yield stress are presented for two filled poly(isobutilene)s with the viscosity differing by more than 103 times. As is seen, a difference between molecular weights and, as a result, a vast difference in the viscosity of a polymer, do not affect the values of yield stress. 

In coordinates r sp — cpr we can expect a generalized concentration dependence of the viscosity in the form ... 

The function T)sp(cpr) of power type is not always convenient for presenting concentration dependence of the viscosity due to very many arbitrary coefficients cn. The exponential Mooney formula deserves much more attention in this connection ... 

At least, in absolute majority of cases, where the concentration dependence of viscosity is discussed, the case at hand is a shear flow. At the same time, it is by no means obvious (to be more exact the reverse is valid) that the values of the viscosity of dispersions determined during shear, will correlate with the values of the viscosity measured at other types of stressed state, for example at extension. Then a concept on the viscosity of suspensions (except ultimately diluted) loses its unambiguousness, and correspondingly the coefficients cn cease to be characteristics of the system, because they become dependent on the type of flow. 

Fig. 13. Pattern of variation of concentration dependence of suspension viscosity when the ratio between the length and diameter of aniso-diametricity of filler s particles increases. The arrow indicates the direction of growth of 1/d of filler s particles. The slop of the initial part of line A (for spherical particles) is 2.5...

The simplest indicator of conformation comes not from but the sedimentation concentration dependence coefficient, ks. Wales and Van Holde [106] were the first to show that the ratio of fcs to the intrinsic viscosity, [/ ] was a measure of particle conformation. It was shown empirically by Creeth and Knight [107] that this has a value of 1.6 for compact spheres and non-draining coils, and adopted lower values for more extended structures. Rowe [36,37] subsequently provided a derivation for rigid particles, a derivation later supported by Lavrenko and coworkers [10]. The Rowe theory assumed there were no free-draining effects and also that the solvent had suf-... 

The value of critical concentration depends strongly on the pectin being used. Figure 2 gives the viscosity curves of two different pectins at the same concentration of 2.5 % w/w. The different production parameters, that have been used for these pectins, have strongly influenced their flow behaviour. The enzymatic reduction of the molecular weight down to... 

During drying an outward flow of Pt can exist, leading to loss of dispersion. The resulting system will depend on many factors, including impregnation time and pH value, viscosity, concentration of the impregnating solution, and the presence of other ions or solute in the solution. 

The viscosity level in the range of the Newtonian viscosity r 0 of the flow curve can be determined on the basis of molecular models. For this, just a single point measurement in the zero-shear viscosity range is necessary, when applying the Mark-Houwink relationship. This zero-shear viscosity, q0, depends on the concentration and molar mass of the dissolved polymer for a given solvent, pressure, temperature, molar mass distribution Mw/Mn, i.e. 

The measurement of viscosity is important for many food products as the flow properties of the material relate directly to how the product will perform or be perceived by the consumer. Measurements of fluid viscosity were based on a correlation between relaxation times and fluid viscosity. The dependence of relaxation times on fluid viscosity was predicted and demonstrated in the late 1940 s [29]. This type of correlation has been found to hold for a large number of simple fluid foods including molten hard candies, concentrated coffee and concentrated milk. Shown in Figure 4.7.6 are the relaxation times measured at 10 MHz for solutions of rehydrated instant coffee compared with measured Newtonian viscosities of the solution. The correlations and the measurement provide an accurate estimate of viscosity at a specific shear rate. 

Fig. 66. Concentration dependence of r H(c)/r s result of seperate fits o results of viscosity measurements on PDMS solutions (Mw = 7400). The result of the simultaneous fit considering the linear term in r H(c) = r 0(l + [r ]c + kH[r ]2c2) is given by the solid line the inclusion of a quadratic term leads to the dashed line. The point-dashed line indicates the macroscopic viscosity for M = 60000 g/mol. (Reprinted with permission from [40]. Copyright 1984 American Chemical Society, Washington)...

Fig. 2 a Concentration dependences of reduced viscosity values at 20 and 50 °C for aqueous solutions of PAAm and b partially hydrophobized PAAm prepared accordingly to Scheme 3 (the data from [23])... 

Figure 2. Concentration dependence of aqueous solutions of PATE on the apparent viscosity.

V, is the molar volume of polymer or solvent, as appropriate, and the concentration is in mass per unit volume. It can be seen from Equation (2.42) that the interaction term changes with the square of the polymer concentration but more importantly for our discussion is the implications of the value of x- When x = 0.5 we are left with the van t Hoff expression which describes the osmotic pressure of an ideal polymer solution. A sol vent/temperature condition that yields this result is known as the 0-condition. For example, the 0-temperature for poly(styrene) in cyclohexane is 311.5 K. At this temperature, the poly(styrene) molecule is at its closest to a random coil configuration because its conformation is unperturbed by specific solvent effects. If x is greater than 0.5 we have a poor solvent for our polymer and the coil will collapse. At x values less than 0.5 we have the polymer in a good solvent and the conformation will be expanded in order to pack as many solvent molecules around each chain segment as possible. A 0-condition is often used when determining the molecular weight of a polymer by measurement of the concentration dependence of viscosity, for example, but solution polymers are invariably used in better than 0-conditions. 

There are numerous equations in the literature describing the concentration dependence of the viscosity of dispersions. Some are from curve fitting whilst others are based on a model of the flow. A common theme is to start with a dilute dispersion, for which we may define the viscosity from the hydrodynamic analysis, and then to consider what occurs when more particles are added to replace some of the continuous phase. The best analysis of this situation is due to Dougherty and Krieger18 and the analysis presented here, due to Ball and Richmond,19 is particularly transparent and emphasises the problem of excluded volume. The starting point is the differentiation of Equation (3.42) to give the initial rate of change of viscosity with concentration ... 

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