Extensional viscosity of polymer melts

Measurements of rheological quantities on the tensile deformation of polymer melts used to be extremely difficult and required the development of special techniques. 

The usual shear measurements on polymer melts are performed as steady-state experiments in which a stationary state of shear deformation is maintained. A steady-state experiment on tensile deformation, however, means an imitation of a melt spinning process. This type of experiment has several disadvantages  

In a number of publications in this field an incorrect interpretation of the experimental results may have been presented. Therefore, in a number of investigations on tensile deformation, non-steady-state techniques have been used. In these experiments, a cylindrical beam of the material is gradually extended from its original length L0 at t = 0 to a length L at time t. From the definition of the rate of deformation e, a constant value 

In these experiments, the tensile force is measured as a function of time, so that at a constant rate of deformation e it is possible to calculate the true tensile stress and the extensional viscosity r/c rc/s at an arbitrary time t. The elastic properties of the deformation can be determined by measuring the elastic strain e. 

For correlating extensional viscosity data, it is obvious to attempt the same method as was used for non-steady state shear viscosity. Thus, the ratio r)Jrjeo is presumed to be determined by two dimensionless groups i0 and f/i0. As e is constant (i.e. qe), the ratio of these groups is equal to the tensile deformation e. Therefore, t/t0 will likewise be a function of t/xa and . 

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Extensional Viscosity. AH three types of extensional viscosity can be measured (101,103) uniaxial, biaxial, and pure shear. Only a few commercial instmments are available, however, and most measurements are made with improvised equipment. Extensional viscosity of polymer melts can be estimated from converging flow (entrance pressure) or from a melt strength drawdown test (208). 

This effect may be responsible for the popular belief that the extensional viscosity of polymer melts increases with increasing rate of deformation. Obviously, this statement is too simplistic, as one more parameter is needed to describe the relationship between extensional viscosity and rate of deformation. The situation is even more complicated. It is certain that the correlation of Fig. 15.22 has no universal validity, but depends on the nature of the polymer. Therefore, at this moment it is not possible to predict the extensional viscosity behaviour of an arbitrary polymer. 

Fig. 7.11 Illustration of three typical cases of extensional viscosity of polymer melt changing with extensional stress...

The molecular theory of extensional viscosity of polymer melts is again based oti the standard tube model. It considers the linear viscoelastic factors such as reptation, tube length fluctuations, and thermal constraint release, as well as the nonlinear viscoelastic factors such as segment orientations, elastic contractimi along the tube, and convective constraint release (Marrucci and lannirubertok 2004). Thus, it predicts the extensional stress-strain curve of monodispersed linear polymers, as illustrated in Fig. 7.12. At the first stage, the extensional viscosity of polymer melts exhibits the Newtonian-fluid behavior, following Trouton s ratio... 

A large number of techniques have been proposed for the measurement of the extensional viscosity of polymer melts. Only a few of these have been described here details of others may be found in the literature cited. These techniques have achieved a certain degree of maturity, and commercial instruments are available. There is, nonetheless, considerable scope for further improvements, especially in extending existing techniques to low-viscosity melts. 

Cogswell, F.N. (1972) Measuring extensional viscosities of polymer melts, Trans. Soc. Rheol, 16,383-403. 

Figure 14 The effect of branching on the extensional viscosity of polymer melts.

Two techniques for measuring uniaxial extensional viscosity of polymer melts are shown in Figure 3.24. In the first technique (Ballman method) poiymer melt is either glued or clamped at both ends, and then one end is moved in such a manner as to generate either a uniform extension rate, e, or a constant tensile stress. In the Meissner method, both ends of the melt are pulled at a constant velocity either to achieve a uniform extension rate or to provide a constant stress. 

In recent times, the introduction of more sophisticated rheological methods and especially the ability to determine independently the shear and extensional viscosity of polymer melts, the design and correlation between molecular structure and rheology has been more accessible to industrial practitioners. Processes such as extrusion blow molding involve those types of deformations such as shear and extension, which can be determined using capillary rheometry and extensional viscosity measurements, which can be related to the formation and blowing of the parison. 

Barnes, H. A. Roberts, G. P. A simple empirical model describing the steady-state shear and extensional viscosities of polymer melts, J. Non-Newtonial Huid Mech., 44, pp. 113-126 (1992). 

A method for measuring the uniaxial extensional viscosity of polymer soHds and melts uses a tensile tester in a Hquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extmder may be part of the apparatus and may be combined with a device for clamping the extmded material (220). However, most of the mote recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is appHed, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

Various instruments are available to measure the viscosity of polymer melts and solutions, and more generally their rheological behavior, which include capillary and rotational viscometers. The former can be used to measure parameters such as shear viscosity, melt fracture, and extensional viscosity, which are important for many polymer processes. The latter type of device can be used in either steady or oscillatory mode, thus providing a measure of the viscosity as well as viscoelasticity (G", G, and tan 5) as a function of frequency and temperature. 

Unlike shear viscosity, extensional viscosity has no meaning unless the type of deformation is specified. The three types of extensional viscosity identified and measured are uniaxial or simple, biaxial, and pure shear. Uniaxial viscosity is the only one used to characterize fluids. It has been employed mainly in the study of polymer melts, but also for other fluids. For a Newtonian fluid, the uniaxial extensional viscosity is three times the shear viscosity ... 

The principal quantities determining the rheological behaviour of polymer melts are the viscosity and normal stress coefficients in shear and extensional... 

For concentrated polymer solutions, the behaviour in extensional deformation shows a great correspondence to that of polymer melts. At low rates of deformation the extensional viscosity has the theoretical value of three times the shear viscosity. At higher rates of deformation, the experimental results show different types of behaviour. In some cases, the extensional viscosity decreases with increasing rate of extension in the same way as the shear viscosity decreases with increasing shear rate. In other cases, however, a slight increase of the extensional viscosity with increasing rate of extension was observed. 

Figure 20.10. Effect of polymer chain branching on shear and extensional viscosities of (a) branched LDPE (low-density polyethylene) melts, and (b) dough.

In this section, only measurements of shear viscosity have been addressed. However, some other devices are available that can assist in the characterization of the rheology of polymer melts under different types of deformation, other than shear. For instance, extensional viscosities can... 

Poly(bulylene succinate) (PBS) is another biodegradable polymer which is not commonly blended with polyolefins. However, Yang et al. [94] investigated the eflect of PBS content, extrusion rate, and extensional strain rate on the melt strength and extensional viscosity of LDPE/PBS blends using a melt-spinning technique, and developed extensional master curves. Based on both the extensional master curve and a neural network method, they compared the predicted extensional viscosities with the experimental data of the LDPE/PBS blends. 

Figure 19 The shear and extensional viscosities of three polymer melts.

As we see, these procedures are quite difficult, and thus it is not surprising that few commercial instruments are available to measure extensional viscosity. The present choice is quite small, being limited to Rheometric Scientific s RME extensional viscometer for polymer melts. Anyone interested in measuring extensional viscosity of other systems will have to resort to home-made instruments. 

Then, secondly, in the production of man-made fibres, polymer melts are extruded through many-holed spinnerets, and the hardening threads are quickly woimd up imto drums, i.e. they are stretched. If the extensional viscosity of the still-molten stretched portion of the threads is an increasing function of extension rate, the tendency for the thread to neck and break is inhibited, see the right-hand side of... 

Unlike shear viscosity, extensional viscosity has no meaning unless the type of deformation is specified. The three types of extensional viscosity identified aind measured are uniaxial or simple, biaxial, and pure shear. Uniaxial viscosity is the only one used to characterize fluids. It has been employed mainly in the study of polymer melts, but also for other fluids. For a Newtonian fluid, the uniaxial extensional viscosity is three times the shear viscosity ( fe)uni = 3/ . This is confirmed at very low shear rates in Figure 13, which provides a typical example of the extensional viscosity behavior of a polymer (129). The two other extensional viscosities are used to study elastomers in the form of films or sheets. Uniaxial and biaxial extensions are important in industry (118,125-128,130,132), the former for the spinning of textile fibers and roller spattering of paints, and the latter for blow molding, vacuum forming, film blowing, and foam processes. 

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