Shear measurements, dynamic oscillatory

In this section three topics are discussed (1) the molecular weight dependence of the rheological properties (2) the interrelation between steady shear and dynamic oscillatory shear measurements and (3) the effect of branching. The importance of the second topic rests on the fact that dynamic oscillatory properties are easier to measure and can be obtained at higher equivalent shear rates than are possible for the steady shear flow properties obtained by means of rotary rheometers. 

Brown, W Schillen, K Hvidt, S, Triblock Copolymers in Aqueous Solution Studied by Static and Dynamic Light Scattering and Oscillatory Shear Measurements. Influence of Relative Block Sizes, Journal of Physical Chemistry 96, 038, 1992. 

Dynamic oscillatory shear measurements of polymeric materials are generally performed by applying a time dependent strain of y(t) = y0sin(cot) and the resultant shear stress is a(t) = y0[G sin(a)t) + G"cos(cot)], with G and G" being the storage and loss modulus, respectively. 

Fig. 2.5. Steady-state and dynamic oscillatory flow measurements on a 2 wt. per cent solution of polystyrene S 111 in Aroclor 1248 according to Philippoff (57). ( ) steady shear viscosity (a) dynamic viscosity tj, ( ) cot 1% from flow birefringence, (A) cot <5 from dynamic measurements, all at 25° C. (o) cot 8 from dynamic measurements at 5° C. Steady-state flow properties as functions of shear rate q, dynamic properties as functions of angular frequency m. Shift factor aT which is equal to unity for 25° C, is explained in the text, cot 2 % and cot 8 are expressed in terms of shear (see eqs. 2.11 and 2.22)...

In dynamic oscillatory measurements, however, higher order relaxation times (i.e. shorter times), which do not noticeably contribute to the zero shear viscosity, can become of importance when the frequency is increased. For this purpose, Ferry and co-operators 123, 14) proposed the following, rather crude approximation of the relaxation times [cf. eq. (3.50)] ... 

Thurston and Schrag (187) have proposed to use the measurement of dynamic birefringence of solutions in oscillatory shear, in order to determine the influences of the above mentioned three parameters on the dynamic oscillatory behaviour at intermediate and high frequencies. 

To obtain measurements during oscillatory shear, the drive motor causes the fixture to oscillate from high to low shear rates deforming the sample. The transducer detects the periodic stress which is generated by the deformation. The magnitude of the stress is converted into dynamic shear moduli. 

The evolution of the dynamic viscosity rp (co, x) or of the dynamic shear complex modulus G (co.x) as a function of conversion, x, can be followed by dynamic mechanical measurements using oscillatory shear deformation between two parallel plates at constant angular frequency, co = 2irf (f = frequency in Hz). In addition, the frequency sweep at certain time intervals during a slow reaction (x constant) allows determination of the frequency dependence of elastic quantities at the particular conversion. During such experiments, storage G (co), and loss G"(co) shear moduli and their ratio, the loss factor tan8(co), are obtained ... 

Both strain- and stress-controlled rotational rheometers are widely employed to study the flow properties of non-Newtonian fluids. Different measuring geometries can be used, but coaxial cylinder, cone-plate and plate-plate are the most common choices. Using rotational rheometers, two experimental modes are mostly used to study the behavior of semi-dilute pectin solutions steady shear measurements and dynamic measurements. In the former, samples are sheared at a constant direction of shear, whereas in the latter, an oscillatory shear is used. 

Steady shear flow measnrements, however, can measure only viscosity and the first normal stress difference, and it is difficult to derive information abont fluid structure from such measurements. Instead, dynamic oscillatory rheological measurements are nsed to characterize both enhanced oil recovery polymer solutions and polymer crosslinker gel systems (Prud Homme et al., 1983 Knoll and Pmd Homme, 1987). Dynamic oscillatory measurements differ from steady shear viscosity measnrements in that a sinusoidal movement is imposed on the fluid system rather than a continnons, nnidirectional movement. In other words, the following displacement is imposed ... 

Dynamic shear rheology involves measuring the resistance to dynamic oscillatory flows. Dynamic moduli such as the storage (or solid-like) modulus (G ), the loss (or fluid-like) modulus (G"), the loss tangent (tan 8 = G"IG ) and the complex viscosity ( / ) can all be used to characterize deformation resistance to dynamic oscillation of a sinusoidally imposed deformation with a characteristic frequency of oscillation (o). 

FIGURE 5.9 Illustration of dynamic (oscillatory) measurement of rheological properties. In (a) the applied shear strain (y) is shown as a function of time t oscillation frequency. In (b d) the resulting shear stress a is given for an elastic, a viscous, and a viscoelastic response. 5 is the phase or loss angle. See text. 

These differences are shown in the following examples where measurements of the dynamic moduli, G and G" are used to monitor the structure of gel networks. Measurements are performed by imposing an oscillatory shear field on the material and measuring the oscillatory stress response. The stress is decomposed into a component in phase with the displacement (which defines the storage modulus G ) and a component 90 out of phase (which defines the loss modulus G"). The value of G indicates the elastic and network structure in the system (15, 17, 18) and can be interpreted by using polymer kinetic theories. 

Wasan and his research group focused on the field of interfacial rheology during the past three decades [15]. They developed novel instruments, such as oscillatory deep-channel interfacial viscometer [20,21,28] and biconical bob oscillatory interfacial rheometer [29] for interfacial shear measurement and the maximum bubble-pressure method [15,29,30] and the controlled drop tensiometer [1,31] for interfacial dilatational measurement, to resolve complex interfacial flow behavior in dynamic stress conditions [1,15,27,32-35]. Their research has clearly demonstrated the importance of interfacial rheology in the coalescence process of emulsions and foams. In connection with the maximum bubble-pressure method, it has been used in the BLM system to access the properties of lipid bilayers formed from a variety of surfactants [17,28,36]. 

Brown, W., Schillen, K. and Almgren, M., 1991. Micelle and gel formation in a poly(ethylene oxide)/poly(propylene oxide)/poly(ethylene oxide) triblock copolymer in water solution. Dynamic and static light scattering and oscillatory shear measurements. Journal of Physical Chemistry, 95, 1850-1858. 

Dynamic mechanical properties are measured to evaluate melt rheology of thermoplastics with and without additives which may modify rheological characteristics of these compositions. " Dynamic oscillatory shear rheometers are used for these purposes. Two geometries of test fixtures are used including parallel plates and cone and plate. Instrument use for these measurements must be capable of measuring forces (stress or strain) and frequency. Temperature must be controlled in a broad range and various modes of temperature sweeps should be available. Sample geometry is not specified but it should be suitable for measurement in particular experimental setup. 

One of the most common transient shear flows used to analyze the rheological characteristics of macromolecular fluids is that of small strain dynamic oscillatory flow. Measurements are usually carried out at strain levels where the stresses are directly proportional to strain. In this experiment, components of stress in phase (G", which is called the loss modulus) with strain rate and those out of phase (G, which is called the storage modulus) are measured as a function of angular frequency (w). G represents... 

However, dynamic measurements, such as the oscillatory tests, are preferred in practice over the steady shear measurements for determining the viscoelastic properties of fluids. This is not only because of the difficulty in determining the first normal stress coefficient accurately, but the determination of a fluid s viscosity by steady shear measurement is only a partial characterization of a viscoelastic fluid s properties. 

Although the dynamic shear rheometer (DSR) can measure dynamic viscosity, its main use is to determine the viscous and elastic behaviour of bituminous binders at medium to high temperatures, particularly to determine the complex shear modulus (G ) and the phase angle (5) of bituminous binders when tested in dynamic (oscillatory) shear, using parallel plate geometry. Details for determining viscosity with DSR can be found in Tredrea (2007). 

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