Elastic area modulus

This is characterized by an isothermal area expansion (or compressibility) compressibility and expansibility are used interchangeably when referring to the elastic area modulus K, given by the equation... 

To examine this peculiar behavior, we have converted the elastic compressibility modulus, per unit area, Y (Fig. 12a), to the modulus per chain, Y = F/10 F (Fig. 12b). The elastic compressibility modulus per chain is practically constant, 0.6 0.1 pN/chain, at high densities and jumps to another constant value, 4.4 0.7 pN/chain, when the density decreases below the critical value. The ionization degree, a, of the carboxylic acid determined by FTIR spectroscopy gradually decreases with increasing chain density due to the charge regulation mechanism (also plotted in Fig. 12b). This shows that a does not account for the abrupt change in the elastic compressibihty modulus. 

FIG. 12 Plots of elastic compressibility modulus (a) per unit area, Y and (b) that per chain, Y, of 2C18PLGA(48) brushes as a function of chain density F. The ionization degree of the carboxylic acid group, a, is also plotted in part b. 

Figure 20. (a) The (dimensionless) lateral compressibility (dilatational modulus, elastic area expansion modulus) (left ordinate) and the dimensionless area per molecule (right ordinate) as a function of the tail length (t) of the PC lipids in equilibrium bilayer membranes. The conversion to real compressibilities and areas per molecule is discussed in the text, (b) The (dimensionless) surface tension and the (dimensionless) lateral compressibility as a function of the relative expansion for the C PC lipid... 

Until recently there was only limited knowledge on the mechanical properties of animal cells. Micromanipulation has allowed some progress in this area. Figure 11 shows typical force-sampling time data for a hybridoma, with a bursting force of a few micro-Newtons. From such data the intrinsic mechanical properties of cell diameter, membrane tension at bursting and elastic area compressibility modulus can be... 

Fig. 4.4 Yield stress normalized by the elastic shear modulus plotted against a size scale parameter (volume per surface area) illustrating the six orders of magnitude of stress levels and ten orders of magnitude of size related to plastic behavior of single crystal metals [152]...

In what follows, the two fluctuating interfaces will be replaced by many small, independent surfaces of area S, separated by a distance z (see Figure 4). The (metastable) distribution of the distances between the surfaces, in an ensemble subjected to a constant pressure, will be assumed Boltzmannian. It will be also assumed that the fluctuating interfaces have constant total areas and an elastic bending modulus Kq. Let us first consider that the interfaces interact per unit area through a harmonic potential... 

The detection of chemical analytes can be based on changes in one or more of the physical characteristics of a thin film or layer in contact with the device surface. Some of the intrinsic film properties that can be utilized for detection include mass/area, elastic stiffness (modulus), viscoelasticity, viscosity, electrical conductivity, and permittivity. In addition, changes in extrinsic variables such as... 

Film Elasticity The differential change in surface tension of a surface film with relative change in area. Also termed surface elasticity, dilata-tional elasticity, areal elasticity, compressional modulus, surface dilata-tional modulus, or modulus of surface elasticity. For fluid films, the surface tension of one surface is used. The Gibbs film (surface) elasticity is the equilibrium value. If the surface tension is dynamic (time-dependent) in character, then for nonequilibrium values, the term Marangoni film... 

The detection of chemical analytes can be based on changes in one or more of physical characteristics of thin film or layer in contact with the device surface. Some of the intrinsic film properties that can be utilized for detection include mass/area, elastic stiffness (modulus) viscoelasticity, viscosity electrical conductivity, and permittivity. In addition, changes in extrinsic variables such as temperature and pressure also produce a sensor response [31, 32]. SAW sensor works as a mass sensor, when analytes of interest comes in contact of polymer film, which is coated, on SAW device. Desired toxic gas is exposed to the device through the carrier gas such as Na and then gas molecules are desorbed [5, 33, 34]. Device has been tested for determining the characteristics such as (i) frequency shift with different concentration of vapor (ii) transient response for response and recovery times (iii) transient response for reproducibility of the sensor. Since arrangement has been made to compensate the... 

Hoq Mechanical and magnetic measurements Tensile strength, elongation at fiacture, reduction of area, modulus of elasticity, coercive force Fe rich alloys with 0.002 to 0.011 mass% C and up to 5.1 Si mass%... 

Itempera- ture -C ( F) lime, h Ultimate tensile strength Tensile yield strength Elonga- tion, % Reduction of area. Modulus of elasticity ... 

The high elastic modulus, compressive strength, and wear resistance of cemented carbides make them ideal candidates for use in boring bars, long shafts, and plungers, where reduction in deflection, chatter, and vibration are concerns. Metal, ceramic, and carbide powder-compacting dies and punches are generahy made of 6 wt % and 11 wt % Co ahoys, respectively. Another apphcation area for carbides is the synthetic diamond industry where carbides are used for dies and pistons (see Carbon). 

Hertz [27] solved the problem of the contact between two elastic elliptical bodies by modeling each body as an infinite half plane which is loaded over a contact area that is small in comparison to the body itself. The requirement of small areas of contact further allowed Hertz to use a parabola to represent the shape of the profile of the ellipses. In essence. Hertz modeled the interaction of elliptical asperities in contact. Fundamental in his solution is the assumption that, when two elliptical objects are compressed against one another, the shape of the deformed mating surface lies between the shape of the two undeformed surfaces but more closely resembles the shape of the surface with the higher elastic modulus. This means the deformed shape after two spheres are pressed against one another is a spherical shape. 

Indentation has been used for over 100 years to determine hardness of materials [8J. For a given indenter geometry (e.g. spherical or pyramidal), hardness is determined by the ratio of the applied load to the projected area of contact, which was determined optically after indentation. For low loads and contacts with small dimensionality (e.g. when indenting thin films or composites), a new way to determine the contact size was needed. Depth-sensing nanoindentation [2] was developed to eliminate the need to visualize the indents, and resulted in the added capability of measuring properties like elastic modulus and creep. 

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