Viscosity determination from

Shear rate when molten polymer flows Melt viscosity of polymer blend Viscosity determined from MFI values Melt strength of polymer Time... 

The apparent viscosity determined from eqns 7.13 and 7.17 is at most 15% greater than the apparent viscosity determined using the Rabinowitsch method (eqns 7.13 and 7.19). For practical purposes, this error (although a systematic error) is considered to be acceptable. This is a reasonable procedure in quality control when polymers are to be compared, and no absolute quantities are required. 

Table 5 shows the given (determined by LALLS) and intrinsic viscosities determined from an online viscometer (Viscotek Model 110) and the measured determined by different calibration techniques for six samples. The deviations [(measured -given )/(given )] x 100 between... 

In Figiures 9.7 and 9.8, the data were generated using an in-house developed rheometer [89], while in Figure 9.9, the data were obtained using a melt spinning apparatus [86]. It should be noted that tt e melt spinning apparatus does not provide steady extensionai flow conditions and hence Ae extensionai viscosities determined from such an instru-... 

W-band EPR was also recently used to help obtain accurate values for the rigid-limit g matrix and nitrogen hyperfine tensor for a spin probe (abbreviated HTAB) in a multi-frequency study of the adsorption and aggregation of the surfactants cetylpyridinium chloride and and cetylpyridinium salicylate on silica surfaces.Polarities and local viscosities (determined from the dynamics of the spin probe) were then deduced. 

Coefficients a and b can also be determined from the kinematic viscosities at 100 and 210°F. 

Both the intrinsic viscosity and GPC behavior of random coils are related to the radius of gyration as the appropriate size parameter. We shall see how the radius of gyration can be determined from solution viscosity data for these... 

Hven fractionated polymer samples are generally polydisperse, which means that the molecular weight determined from intrinsic viscosity experiments is an average value. The average obtained is the viscosity average as defined by Eqs. (1.20) and (2.40) as seen by the following argument ... 

Of the models Hsted in Table 1, the Newtonian is the simplest. It fits water, solvents, and many polymer solutions over a wide strain rate range. The plastic or Bingham body model predicts constant plastic viscosity above a yield stress. This model works for a number of dispersions, including some pigment pastes. Yield stress, Tq, and plastic (Bingham) viscosity, = (t — Tq )/7, may be determined from the intercept and the slope beyond the intercept, respectively, of a shear stress vs shear rate plot. 

Capillary Viscometers. Capillary flow measurement is a popular method for measuring viscosity (21,145,146) it is also the oldest. A Hquid drains or is forced through a fine-bore tube, and the viscosity is determined from the measured flow, appHed pressure, and tube dimensions. The basic equation is the Hagen-Poiseuike expression (eq. 17), where Tj is the viscosity, r the radius of the capillary, /S.p the pressure drop through the capillary, IV the volume of hquid that flows in time /, and U the length of the capillary. 

Absolute viscosities are difficult to measure with capillary viscometers, but viscosities relative to some standard fluid of known viscosity, such as water, are readily determined. The viscometer is caHbrated with the reference fluid, and viscosities of other fluids relative to the reference sample are determined from their flow times. 

Piston Cylinder (Extrusion). Pressure-driven piston cylinder capillary viscometers, ie, extmsion rheometers (Fig. 25), are used primarily to measure the melt viscosity of polymers and other viscous materials (21,47,49,50). A reservoir is connected to a capillary tube, and molten polymer or another material is extmded through the capillary by means of a piston to which a constant force is appHed. Viscosity can be determined from the volumetric flow rate and the pressure drop along the capillary. The basic method and test conditions for a number of thermoplastics are described in ASTM D1238. Melt viscoelasticity can influence the results (160). 

Polymer melts are frequendy non-Newtonian. In this case the earlier expression given for the shear rate at the capillary wall does not hold. A correction factor (3n + 1)/4n, called the Rabinowitsch correction, must be appHed in such a way that equation 21 appHes, where 7 is the tme shear rate at the wall and nis 2l power law factor (eq. 22) determined from the slope of a log—log plot of the tme shear stress at the wad, T, vs 7. For a Newtonian hquid, n = 1. A tme apparent viscosity, Tj, can be calculated from equation 23. 

A constant is often determined from measurements with a Newtonian oil, particularly when the caUbrations are suppHed by the manufacturer. This constant is vaUd only for Newtonian specimens if used with non-Newtonian fluids, it gives a viscosity based on an inaccurate shear rate. However, for relative measurements this value can be useful. Employment of an instmment constant can save a great deal of time and effort and increase accuracy because end and edge effects, sHppage, turbulent interferences, etc, are included. 

Therefore, the viscosity can be determined from the torque and angular velocity. However, the viscosity is usually calculated from the shear rate and shear stress, which can be obtained from the Margules equation. The shear rate is given by equation 27, where r is any given radius. 

Viscosity can also be determined from the rising rate of an air bubble through a Hquid. This simple technique is widely used for routine viscosity measurements of Newtonian fluids. A bubble tube viscometer consists of a glass tube of a certain size to which Hquid is added until a small air space remains at the top. The tube is then capped. When it is inverted, the air bubble rises through the Hquid. The rise time in seconds may be taken as a measure of viscosity, or an approximate viscosity in mm /s may be calculated from it. In an older method that is commonly used, the rate of rise is matched to that of a member of a series of standards, eg, with that of the Gardner-Holdt bubble tubes. Unfortunately, this technique employs a nonlinear scale of letter designations and may be difficult to interpret. 

Another type of experiment involves a fluid filament being drawn upward against gravity from a reservoir of the fluid (101,213,214), a phenomenon often called the tubeless siphon. The maximum height of the siphon is a measure of the spinnabiUty and extensional viscosity of the fluid. Mote quantitative measures of stress, strain, and strain rate can be determined from the pressure difference and filament diameter. A more recent filament stretching device ia which the specimen is held between two disks that move apart allows measurements ia low viscosity Hquids (215). AH of these methods are limited to spinnable fluids under small total strains and strain rates. High strain rates tend to break the column or filament. 

Cure Characteristics. Methods of natural rubber production and raw material properties vary from factory to factory and area to area. Consequentiy, the cure characteristics of natural mbber can vary, even within a particular grade. Factors such as maturation, method and pH of coagulation, preservatives, dry mbber content and viscosity-stabilizing agents, eg, hydroxylamine-neutral sulfate, influence the cure characteristics of natural mbber. Therefore the consistency of cure for different grades of mbber is determined from compounds mixed to the ACSl formulation (27). The ACSl formulation is as follows natural mbber, 100 stearic acid, 0.5 zinc oxide, 6.0 sulfur, 3.5 and 2-mercaptobenzothiazole (MBT), 0.5. 

The number-average molecular weight of dimethylsiloxane can also be determined from the intrinsic viscosity [Tj, dL/g] (extrapolated to zero viscosity) ia toluene or methyl ethyl ketone according to the foUowiag equatioa (339,340) ... 

For normal velocity distribution in straight circular pipes at locations preceded by runs of at least 50 diameters without pipe fittings or other obstructions, the graph in Fig. 10-7 shows the ratio of mean velocity V to velocity at the center plotted against the Reynolds number, where D = inside pipe diameter, p = flmd density, and [L = fluid viscosity, all in consistent units. Mean velocity is readily determined from this graph and a pitot reading at the center of the pipe if the quantity Du p/ I is less than 2000 or greater than 5000. The method is unreliable at intermediate values of the Reynolds number. 

In the equation referred to above, it is assumed that there is 100 percent transmission of the shear rate in the shear stress. However, with the slurry viscosity determined essentially by the properties of the slurry, at high concentrations of slurries there is a shppage factor. Internal motion of particles in the fluids over and around each other can reduce the effective transmission of viscosity efficiencies from 100 percent to as low as 30 percent. 

Since pc 1/2, we observe that Me 2Mg, as commonly observed. Mg is determined from the onset of the rubbery plateau by dynamic mechanical spectroscopy and Me is determined at the onset of the highly entangled zero-shear viscosity law, T) M. This provides a new interpretation of the critical entanglement molecular weight Mg, as the molecular weight at which entanglement percolation occurs while the dynamics changes from Rouse to reptation. It also represents the... 

From the y(jc) functions and the two melt temperatures used, and by using the viscosity curves from rheological examinations (Fig. 11), viscosity distributions T](jc) of the two pure components were easily determined, as shown in Figs. 15a and 15b. Subsequently, the viscosity ratio functions 6(jc) were also calculated (Fig. 16). All four curves fall slightly from the core to the outside. 

Figure 10-155. Shell-side friction factor, f , for pressure drop calculation is determined from plot vs. Reynolds Number, z = viscosity at average flowing temperature, centipoise. (Used by permission Brown Fintube Co., A Koch Engineering Company, Houston, Texas.)...

The hydrodynamic radius reflects the effect of coil size on polymer transport properties and can be determined from the sedimentation or diffusion coefficients at infinite dilution from the relation Rh = kBT/6itri5D (D = translational diffusion coefficient extrapolated to zero concentration, kB = Boltzmann constant, T = absolute temperature and r s = solvent viscosity). 

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