Shear modulation

DMS 110/120 Bending/Shear Module C io-"-io" 10 -10 " Seiko Instmments, Horsham, Pa. 

Fig. 5. Schematic diagram of AFM setup for shear modulation measurement.

Uq = shear module, quartz Uf = shear module, film... 

The shear modules Go or the Young modules E0 does not depend on time and temperature. Contrary to this defination these modules are often used to describe the whole viscoelastic behaviour including the relaxation processes (Only in these cases the dependence on temperature is sensible). 

We subject a sample of solid polymer material to a sudden deformation process y0, with an elastical stress o0 = Gy0 (G shear modules). The original strain gives rise to an increase of the molecular valency angles and the intermolecular distances. From these molecular deformations an elastic molecular potential A0 arises which in turn causes molecular displacements. These prevail in the direction of the original strain, decreasing the elastic potential A in that neighborhood. We can calculate... 

Figure 19 shows dynamic shear modules (G ) and loss tangent (tan 8) as a functions of temperature for carboxymethylated wood binding various metal ions [49]. The content of carboxymethyl groups in treated wood is about 1.07 mmol/g for each specimen. Dynamic viscoelastic measurements were carried out under vacuum. There are three dispersions in the range below 1(X)°C the P dispersion near 50°C for the carboxymethylcellulose main chain motion in the modified wood, the 7 diversion near 0°C for local mode of wood components related to water, and the 8 dispersion near - 60°C for the side chain... 

Because high fluxes and the abdity to process streams containing suspended solids and fibers are often wanted in the pulp and paper industry, high-shear modules have been developed. Currently existing high-shear modules, excluding tubular modules, are modified plate and frame constructions. Both a cross-rotational module from Metso Paper and a vibration enhanced module (VSEP) from New Logic Inc. have been industrially used or tested in pulp and paper industry applications [48-51]. 

M-Real, Fine paper mill, Kirkniemi, Finland Alho et al. [127] reported a flux of 120 L/(m h) in the filtration of coating color at another M-Real paper miU (Kirkniemi fine paper mill). High-shear modules can recover coating color from wastewater to a higher dry sohds content than traditional modules. For example, a sohds content of 60% has been reached by the CR and the VSEP filters [36,51]. 

Important progress has occurred in our understanding of the processes that control the dependence of the shear modules on tempera-ure and on the frequency of the seismic waves. At temperatures close to the melting point, the shear modulus depends strongly on frequency... 

Figure 4.7 Shear modules, G vs. temperature, measured for a time scale of approximately 1 s, polyfvinyl chloride) plasticized with diethylhexyl succinate. I, 100% monomer, II, 91% III, 79% IV, 70.5% V 60.7% VI, 51.8% VII, 40.8%. (From Schneider, K. and Wolf K., KoHoid Z., 127, 65, 1952.)...

Here 0 is an angle of shear in the plane xy, jj, is the shear module, determined in Refs. [77, 72] for the diluted and concentrated polymeric solutions and melts. 

Due to the inherent symmetry of as-produced textile fabrics, woven composite plates are orthotropic. Their stiffness can be represented by engineering constants Young s modules shear modules Gy and Poisson coefficients py, ij= 1,...,3. If the reinforcement is deformed during production of the composite, or if the preform is net shaped, or for some knitted performs, then the assumption of orthotropy does not necessarily apply and the full stiffness matrix has to be introduced. 

Ge, S., Pu, Y., Zhang, W., Rafailovich, M., Sokolov, J., Buenviaje, C., Buckmaster, R. and Ovemey, R.M., Shear modulation force microscopy study of near surface glass transition temperatures. Phys. Rev. Lett., 85(11), 2340-2343 (2000). 

Theoretical analyses predicted the propagation of low-frequency shear waves in both semidilute polymer solutions [49] and dilute colloidal crystals [50]. Different experimental techniques were applied for their detection and for the determination of the shear modules of colloidal samples [51-54]. The dispersion equation of the transverse waves for the low-frequency regime (wavelengths much larger than the interparticle distance) [55]... 

I>L and are the angular positions of the fibre cross-section at cross-sections L and L -i-1, respectively E and G are Young s and shear module of fibre material, respectively I ly, and /q are moments of inertia of the fibre cross-section with respect to the principal axes and the central axis, respectively b and q are curvature components of the fibre axis in the principal directions of the fibre cross-section w is the fibre torsion s is the curvilinear coordinate along the fibre axis is the tensile force applied to the fibre I is the fibre length F is the area of the fibre cross-section and N is the number of neighbouring VLs to the VL(f, r). 

In the previous sections, some elastic constants were mentioned, namely, E, G, v, 2 and K. The constants E and G, the Young s and the shear modules, respectively, relate to stress-strain relations represented as ... 

The results published for the shift of the glass transition temperature range for freestanding PS films between -70K (thickness 20nm) as measured by ellipsometry ° and OK (thickness 20 nm) as measured by atomic force microscopy (AFM)-based shear modulation spectroscopy or ellipsome-try and The situation is similarly puzzling for... 

Figure 6. Interfacially confined hexadecane measured by SFM shear modulation spectroscopy. The shear response is measured simultaneously with the normal force deflection of the cantilever as function of the cantilever-siicon sample distance. The difference in the bending onset of the two curves defines the interfacially confined boundary layer thickness.

In this paper, we will address the complex issue of the mechanical determination of Tg at surfaces of thick bulk-like, as well as interfacially confined ultrathin polymer films. First, we will show that the pressure exerted by the tip does not affect the glass transition. Then, we will introduce a novel contact mechanical technique to determine the Tg of thin films, shear modulation SPM. Finally we will present Tg results on films where interfacial interactions, remaining stress and conformational changes, formed during film preparation, alter the bulk Tg. 

Figure 1. Schematics of the stationary shear modulation SPM. An externally applied lateral displacement, Ax od causes a shear response, Axs, within the tip sample junction which is counteracted by the cantilever motion, Axi. Here, Axmod = Axs Axl.

With this, we document the complexity of the tip-san le penetration while scanning. Therefore, taking the onset of die penetration as a material property, i.e. the value of Tg, can be very misleading for friction measurements as experimentally confirmed. This is in contrast to shear modulation measurements where the contact location is fixed in space. 

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