Surface storage modulus

In the general case the phase of oscillations of the surface tension and the phase of periodical alterations of the surface area do not coincide. Then it is convenient to use complex numbers in order to describe the oscillations, and to consider two components of the surface elasticity, the surface storage modulus z, and the surface loss modulus ct... 

Researchers [37] also compared the storage modulus of a 40 phr carbon black-filled compound and a 10 phr SWNT-NR nanocomposite. The different properties between carbon black- and SWNTs-filled NR nanocomposites can be explained in terms of two different filler morphology, particularly surface area, aspect ratio, and stmcture. It can be observed from Figure 28.22 that... 

Lu et al. [7] extended the mass-spring model of the interface to include a dashpot, modeling the interface as viscoelastic, as shown in Fig. 3. The continuous boundary conditions for displacement and shear stress were replaced by the equations of motion of contacting molecules. The interaction forces between the contacting molecules are modeled as a viscoelastic fluid, which results in a complex shear modulus for the interface, G = G + mG", where G is the storage modulus and G" is the loss modulus. G is a continuum molecular interaction between liquid and surface particles, representing the force between particles for a unit shear displacement. The authors also determined a relationship for the slip parameter Eq. (18) in terms of bulk and molecular parameters [7, 43] ... 

The dynamic response of polydimethylsiloxane (PDMS) reinforced with fused silica with and without surface treatment has been discussed in terms of interactions between the filler and polymer [54]. Since bound rubber measurements showed that PDMS chains were strongly attached to the silica surface, agglomeration due to direct contact between silica aggregates was considered an unlikely explanation for the marked increase in storage modulus seen with increasing filler content at low strains. Instead three types of flller-polymer-flller association were proposed which would cause agglomeration, as depicted in Fig. 15. 

The surface rheological properties of the /3-lg/Tween 20 system at the macroscopic a/w interface were examined by a third method, namely surface dilation [40]. Sample data obtained are presented in Figure 24. The surface dilational modulus, (E) of a liquid is the ratio between the small change in surface tension (Ay) and the small change in surface area (AlnA). The surface dilational modulus is a complex quantity. The real part of the modulus is the storage modulus, e (often referred to as the surface dilational elasticity, Ed). The imaginary part is the loss modulus, e , which is related to the product of the surface dilational viscosity and the radial frequency ( jdu). 

Experiments with the /3-lg/Tween 20 system were performed at a macroscopic a/w interface at a /3-lg concentration of 0.2 mg/ml [40]. The data obtained relate to the properties of the interface 20 minutes after formation. Up to R = 1, the storage modulus (dilational elasticity) was large and relatively constant, whereas the loss modulus (dilational viscosity) increased with increasing R. As R was increased to higher values there was a marked decrease in the storage modulus (dilational elasticity) and a gradual increase in the loss modulus (dilational viscosity). In summary, the data show the presence of a transition in surface dilational behavior in this system at a solution composition of approximately R = 1. At this point, there is a transformation in the adsorbed layer properties from elastic to viscous. 

Fig. 1 a,b. Strain amplitude dependence of the complex dynamic modulus E E l i E" in the uniaxial compression mode for natural rubber samples filled with 50 phr carbon black of different grades a storage modulus E b loss modulus E". The N numbers denote various commercial blacks, EB denotes non-commercial experimental blacks. The different blacks vary in specific surface and structure. The strain sweeps were performed with a dynamical testing device EPLEXOR at temperature T = 25 °C, frequency f = 1 Hz, and static pre-deformation of -10 %. The x-axis is the double strain amplitude 2eo... 

Martin and Ricco state that each cross-link formed in the HR-100 film has two effects that can perturb the APM propagation velocity an increase in the elastic storage modulus (G ) and a decrease in the surface mass density (ps) through the liberation of two N2 molecules. Both of these effects should result in an increase in APM velocity, consistent with the positive velocity shift observed during cross-linking. In addition, cross-linking typically decreases the loss modulus (G"), a result of restricting dissipative processes [193]. This is consis-... 

Figure 6.40 Storage modulus ver-sus frequency for suspension of fumed silica (Aerosil R972 surface area = 108 m /g aggregate size 200 nm) at a concentration of = 0.085 in PDMS Mw = 118,000). The modulus for the unfilled PDMS is also shown, as is the modulus for the suspension treated in two differ-ent ways (MSI, MS2) to remove the active silanol groups from the silica particle surface. (From Aranguren et al. 1992, with permission from the Journal of Rheology.)...

Carbon black interacts strongly with polymer (HDPE) to produce a large increase in storage modulus in a manner similar to the surface treated glass beads. The storage modulus is less sensitive to frequency. The storage modulus increase is explained by the effect of modifier on crosslinking. 

The nanodispersion of Si and O throughout the polyimide polymer matrix leads to the formation of a protective silica layer on the polyimide surface when the material reacts with AO [15]. Our data indicates that upon AO exposure, the organic material in the polymer surface erodes, while the atomic oxygen reacts with the nanodispersed POSS to form a silica layer. Therefore, when POSS is copolymerized to form POSS-PI, it imparts remarkable AO resistance, and does so with minor effects in the storage modulus, glass transition temperature, and coefficient of thermal expansion [15]. 

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