Forced oscillation measurements

Cohen, R.E., Tschoegl,N.W, Dynamic mechanical properties of block copolymer blends—a study of the effects of terminal chains in elastomeric materials. I. Torsion pendulum measurements. Intern. J, Polymeric Mater. 2, 49-69 (1972) II. Forced oscillation measurements. Ibid 2, 205-223 (1973) III. A mechanical model for entanglement slippage. Ibid (in press). 

Creep tests can be performed with steady rotating viscometers. Conventional forced-oscillation measurements can also be performed with ordinary shear geometries such as plate-plate or plate-cone systems in rotating rheometers. 

The most widely used technique is the sinusoidal oscillatory or forced oscillation measurements. Oscillatory measurements consist of subject-... 

This chapter is concerned with just one of this class of thickeners, namely a hydrophobically modified (hydroxyethyl)cellulose (HMHEC), Hercules WSP D-47. Gelman and Barth (i) reported on the viscosity of such HMHECs. This sample contained up to four hexadecyl chains grafted to the cellulose backbone. The preparative route was that described by Landoll (2). The dilute solution properties were characterized by capillary viscom-etry, whereas the more concentrated solutions were characterized by continuous-shear viscometry, forced oscillation measurements, and shear-wave propagation. In addition, the adsorption onto polymer latex particles was investigated. 

With a new software program it is possible to measure the Texture Constant" of pectins. This Texture Constant K is calculated by the ratio of the maximum force during the time interval of the measurement and the measured area below the force-time curve. The resulting constants K correlate well with the dynamic Weissenberg number of oscillating measurements carried through with the same pectin gels. 

There are several possible approaches to the measurement of dynamic properties using forced oscillation of the test piece and the methods can be classified in various ways. The first distinction is between forced vibration at or near resonance and forced vibration away from resonance, with measurements at frequencies away from resonance being by far the most common. 

Prior to the experiments, the polymer sample is fixed between two clamps and the sample dimensions are measured carefully. One of the two clamps is fixed, while the other can be moved up and down. To this clamp, a sinusoidal deformation with an amplitude e and a frequency to is applied and the corresponding force is measured, which can be transferred into the stress a a with the sample dimensions. From these two quantities the complex modulus of elasticity E is measured in dependence of sample temperature T and oscillation frequency to. 

A harmonic oscillator can only change its vibrational quantum number by one when it absorbs a photon (Av = 1) therefore, the only frequencies which can be absorbed are near the classical vibrational frequency co = -JkJJi. The absorption will also change the rotational quantum number (Ay = 1). In practice, this means that the infrared spectrum of a small molecule has rotational structure, which permits bond length measurement as well as force constant measurement (Figure 8.6). 

This formalism has been employed [ 118] to address the chemicurrent measured in experiments of the adsorption of hydrogen atoms on copper surfaces [119]. Satisfactory agreement with the experiment has been obtained. However, only one single trajectory of a hydrogen atom impinging on the top site has entered the forced oscillator description so that the effect of corrugation has been entirely neglected. 

Notice thaty(0 oscillates around the zero line as shown in the figure. Also, since at the beginning of the curve the force oscillations can be very large relative to the absolute magnitude of either the measured or fitted force, the division of the absolute residual F(t) - F (t) by F (i) can yield absurdly big numbers. Consequently this initial part of the normalized data, in our experience up to a displacement of about... 

The problem appearing in the calculation of G and G from free oscillations under torsion lies in that (7 is measured at a complex frequency and not at a real value co as is usual in forced oscillations (11). Consequently,... 

Forced oscillations in torsion are used in the most versatile and accurate technique for measuring the viscoelastic functions, in the frequency domain, of melts and concentration solutions (12). In this case, the second-order differential equation governing the motion is given by... 

Cantilevers in AFM function as force transducers converting unknown force to measurable deflection. The value of the unknown force can then be expressed by Hookean mechanics following spring constant calibrations. In addition to static point loads, cantilevers can also be vibrated, e.g., by an oscillation piezo to which the fixed end of the beam is attached (or by other approaches). Excitation frequency, oscillation amplitude, and phase relationships are variables that govern dynamic tapping (intermittent contact) imaging. This problem will be discussed in the next section. 

Figure 8.16. Measured force between two mica surfaces immersed in 10 M KCl solution. The force oscillates with a periodicity of 2.5 to 3.0 A, about equal to the diameter of a water molecule. The numbers count how many molecular layers of water are expected to be between the surfaces at each oscillation. (Adapted from j. N. Israelachvili. 1985. Measurements of hydration forces between macroscopic surfaces. Chemica Scripta 25 7-14. Used with permission.)...

FIG. 15 Force normalized by radius as a function of surface separation between mica surfaces precoated with PCMA. The forces were measured across an aqueous 10 4 M KBr solution containing 0.1 cmc SDS. The forces measured during the first ( ) and the second ( ) approach are illustrated. The vertical lines illustrate the position of the oscillating branches of the force curve and the arrows inward jumps. (Adopted from Ref. 71.)... 

The forces measured at higher surfactant concentration, up to 2 cmc (1.7 X 10 2 M), also display oscillations with a periodicity of 40 A. One example of such a force curve, measured at an SDS concentration of 1 cmc, is illustrated in Figure 17. We note that the periodicity of the oscillations remains unchanged when the SDS concentration is increased, but the number of oscillations and their magnitude differs. This is more clearly shown in Figure... 

Two unknowns require two measurements. For a free oscillator these measurements are the resonant frequency and the damping. For a forced oscillator the favored combination is the amplitude ratio and phase angle over a range of applied frequencies. This combination is not available for the evaluation of coatings because of the requirement that one surface be free. The two measurements described in the example below are damping and phase angle. 

Rotational Rheometry. Two instruments were used for these measurements. An Instron model 3250 rheometer was used for measuring rotational viscometry and forced oscillation as a function of frequency with strains in the region of 0.5. A Bohlin VOR rheometer was used for dynamic measurements at smaller strains (i.e., 0.1). 

Forced-Oscillation Experiments. The dynamic moduli were measured as a function of frequency. At high strains (ca. 0.6), the Instron rheometer was used, whereas at lower strains (typically 0.16), the Bohlin VOR rheometer was used because of its greater sensitivity. Figure 6 shows the results obtained for the storage (G ) and loss (G") moduli for a 0.5-g dL" ... 

Lorino AM, Lofaso R Abi-Nader F, Drogou I, Dahan E, Zerah F, et al. Nasal air-fiow resistance measurement forced oscillation technique versus posterior rhino-manometry. Eur Respir J 1998 11 720-725. 

Another group of procedures subjects the sample to continuous forced oscillations. The resulting stresses and deformations can be measured independently of each other with the most commonly used instrument of this group, the rheovibron. Since the rheovibron applies a tensile stress, the moduli obtained are tensile moduli and not shear moduli, as is the case with the torsion pendulum. 

The most important measurements for characterizing emulsions are forced oscillation rheometry studies. The presence of significant elasticity clearly defines whether or not a stable emulsion has been formed. The viscosity by itself can be an indicator of the stability of die emulsion, although it is not necessarily conclusive, unless one is fully certain of the viscosity of the starting oil. Color is an indicator, but may not be definitive. This laboratory s experience is that all table emulsions were reddish. Some mesostable emulsions were also reddish and unstable emulsions were always the color of the starting oil. Water content is not an indicator of stability and is error prone because of the excess of water that may be present. It should be noted, however, that stable emulsions have water contents greater than 70% and that unstable emulsions or... 

Emulsion properties and stability can be measured by rheological studies and dielectric spectroscopy. Rheological studies include forced oscillation experi ments. The formation of stable emulsions is marked by a sharp increase in the elastic modulus. Water con tent is not a good indicator of emulsion characteristics other than that low water contents (<50%) indicate that an emulsion has not been formed and that the product is entrained water-in-oil. Interfacial measure ments are useful for measuring the film strength of... 

Thus G and G are obtained by measuring /o. 00, and 8. The difficult quantity to determine is 8. The best method is to convert 0 into a voltage using a rotational transducer. The phase difference 8 between this voltage and the torque current can then be obtained by one of a number of precise electrical methods. This forced-oscillation technique is used most efficiently at frequencies somewhat remote from the resonant frequency of the system. 

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