Reduced modulus

Figure 43 shows the hardness and reduced modulus of Fe-N/Ti-N multilayers versus the thickness of the Fe-N layer. It is found that the hardness of the multilayers decreases with the thickness of the Fe-N layer, but increases with the applied normal force. Under higher normal force, the hardness does not change much if the thickness of the Fe-N layer is thicker than 20 nm. The reduced modulus of the multilayers with different Fe-N layer thickness is always within the range of 170-190 GPa. There is no obvious relationship between the reduced modulus and the thickness of the Fe-N layer. 

Regiodefects are less readily incorporated into crystallites than defect-free chain sequences. In semicrystalline polymers, increasing levels of misinsertion result in reduced crystallinity. This can affect numerous physical properties, resulting in reduced modulus, lower heat distortion temperature, and decreased tensile strength. 

Stereodefects reduce the overall regularity of an isotactic polymer chain and hinder its ability to crystallize. As the concentration of defects increases, the degree of crystallinity falls, resulting in reduced density, reduced melting temperatures, lower heat distortion temperatures, reduced modulus, and reduced yield stress. 

In this contribution, we report equilibrium modulus and sol fraction measurements on diepoxidet-monoepoxide-diamine networks and polyoxypropylene triol-diisocyanate networks and a comparison with calculated values. A practically zero (epoxides) or low (polyurethanes) Mooney-Rivlin constant C and a low and accounted for wastage of bonds in elastically inactive cycles are the advantages of the systems. Plots of reduced modulus against the gel fraction have been used, because they have been found to minimize the effect of EIC, incompleteness of the reaction, or possible errors in analytical characteristics (16-20). A full account of the work on epoxy and polyurethane networks including the statistical derivation of various structural parameters will be published separately elsewhere. 

Therefore in this Rouse regime of unentangled semidilute solutions where hydrodynamic interaction is screened, both the reduced viscosity and reduced modulus decrease with increase in polymer concentration in salt free solutions... 

Plasticization is the process in which the plasticizer molecules neutralize the secondary valence bonds, known as van der Waal s force between the polymer molecules. It increases the mobility of the polymer chains and reduces the crystallinity. These phenomena become evident in reduced modulus or stiffness, increased elongation and flexibility, and lowering of the brittle or softening temperature of the plasticized product. The effect of plasticizers on polymers is the subject of the first chapter by E. H. Immergut and H. F. Mark. 

Since the reduced modulus G refers to the unswollen, unstrained, isotropic network, the question arises, first, whether it should be the same for a given network, regardless of the swelling solvent. It was found that for PDMS networks as well as for polystyrene networks the value of G is not the same for a given gel whatever the swelling solvent may be14,22. This result, which implies that the swelling solvent influ-... 

Let us compare the behavior of networks exhibiting different crosslink functionalities. Qualitatively it is known that an increase of/results in a small decrease of the swelling ratio Q — at constant molecular weight of the elastic chains34 -, and in a rather sharp increase of the reduced modulus G 22 ... 

Of the two groups, the reactive diluents are generally preferred for structural adhesives applications because they do not degrade end properties as much as the unreactive diluents do. Note that diluents, either reactive or unreactive, do not necessarily result in an increase in elongation of the cured epoxy. They may only reduce modulus and hardness. Their enhancement regarding flexibility will depend on the component s functionality and molecular nature. 

Fig. 13.56 is chosen as an example showing the curves of polyisobutylene. These curves were corrected (reduced) for density and temperature. An arbitrary temperature T0 (K) (25 °C) was selected as the reference temperature. The reduced modulus values were calculated by... 

Fig. 13. Dependence of the reduced modulus G, (mol/cm ) and of the trapped entanglement contribution A (mol/cm ) on r for the cured DGEBA-PGE-DDM systems q measurements in the...

Figure 5.19 (a) The reduced modulus G /vksT, and (b) the relaxation time t, as functions of concentration of the polymer described in the caption to Fig. 5-18. The solid and dashed lines are...

Reduced modulus of elasticity 5648 for NF Lactose-315 (compression pressure 5.49-54.90 MPa) ... 

Fig. 9 Loss angle as a function of the reduced modulus (ratio of complex modulus and plateau modulus) for polystyrene samples. (From RQfP )...

Fig. 4 The equilibrium swollen normalized gel volume V q of ionic PNIPAAm hydrogels as function of the numberof charges per network chain (see (3)) (a) Reduced modulus Gr of ionic PNIPAAm hydrogels as function of the normalized gel volume (b) The mole fractions x,- of AMPS Na are indicated in the figure. Reprinted from Gundogan et al. (2002) with permission of American Chemical Society...

The reduced modulus Gr is defined as the ratio of the elastic modulus of the gel at a given degree of swelling Qv = l/v 2 to that one of the same gel after its preparation. Gr is given for a network of Gaussian chains by (Flory 1953)... 

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