Modulus Measurements

The isothermal curves of mechanical properties in Chap. 3 are actually master curves constructed on the basis of the principles described here. Note that the manipulations are formally similar to the superpositioning of isotherms for crystallization in Fig. 4.8b, except that the objective here is to connect rather than superimpose the segments. Figure 4.17 shows a set of stress relaxation moduli measured on polystyrene of molecular weight 1.83 X 10 . These moduli were measured over a relatively narrow range of readily accessible times and over the range of temperatures shown in Fig. 4.17. We shall leave as an assignment the construction of a master curve from these data (Problem 10). 

A comparison with the tube diameter derived from plateau moduli measurements on PEB-7 underlines this assertion. The coincidence of tube diameters determined macroscopically by application of the reptation model and direct microscopic results is far better than what could have been expected and strongly underlines the basic validity of the reptation approach. 

The moduli, measured at crosslinking temperature T, which are given in the last two columns of Table IV, are abou two to three fold greater than those computed from phantom theory. Except for the samples with the lowest branching densities, the observed values agree satisfactorily with those for an affine network. 

Elastic moduli measure the resistance to deformation of materials when external forces are applied. Explicitly, moduli M arc the ratio of applied stress cr to the resulting strain e ... 

The broad difference between moduli measured under limited loads, 3.5-8 MPa. 

The absolute values of the reductions in moduli, or increases in Mj, can be Interpreted in terms of small, inelastic loops. The small-strain, static moduli measured are consistent with affine chain behaviour, showing, on the basis of one-membered loops, that between about 10 and 20% of groups react to form inelastic loops by the end of a polymerisation. For the more concentrated systems a significant proportion of this comes from post-gel intramolecular reaction (Pr,e Pr,c) ... 

If the specimen does not have a uniform cross-section along its entire length then any moduli measured on it will be, to some extent, in error. Sometimes it may not be practicable to produce completely uniform specimens. In such cases it may be possible to measure a series of different specimen lengths, so that the shortest is least likely to be non-uniform. However, great care must be taken to avoid any introduction of end-effects by using short specimens. 

Combining the surface dynamic moduli measurements with the morphologies of the LB transferred block copolymer films imaged by atomic force microscopy... 

From the results presented in this Datareview, the quality of the crystals is clearly one of the main problems for the precise determination of the physical properties of the group III nitrides. This is especially true for indium nitride, where no elastic moduli could be measured, due to the lack of single crystals. The differences between the elastic moduli measured with the same technique (Brillouin scattering) in GaN is further proof that the quality and the nature (bulk single crystals or epitaxial layer) of the samples is of primary importance. 

The calculated equilibrium network moduli of elasticity and experimental moduli measured in the rubbery state10,34) of different epoxy-amine networks show quantitative agreement. This means that the real structural nonuniformity of cross-linked epoxy-aromatic amine polymers exists only at the level of statistical deviations of network structure from the ideal one. A comparison of Ecalc and E p is shown in Fig. 4. 

Table 4.3 Results of moduli measurements at 0.48 MHz. on SSBR rubber...

There is a growing tendency to incorporate nanofillers into polymer blends. When the two polymers differ significantly in rigidity, their behavior resembles that of TPE. For example, a blend of PA-6 with PP (PA-6/PP = 70/30) compatibilized with EPR-MA was melt-compounded with 4 phr of MMT-ODA [Chow et al., 2005]. The CPNC had a high degree of clay dispersion and distribution. The dynamic mechanical thermal analyzer (DMTA) data (at 10 Hz) showed a tendency opposite to that observed for TPE The largest enhancement of E was obtained for non-compatibilized CPNC at the lowest temperature of -100°C (by about 25%) the addition of EPR-MA reduced this effect by one-half, up to - -100°C. However, for these systems the tensile moduli measured in steady state and dynamic mode at 23°C were comparable (i.e.. 

Strain produced. Above this so-called proportionality limit, the relationship between stress and strain can be quite different (Section 11.5). For this reason, the modulus of elasticity of polymers is usually measured over a strain of 0.2% and over a time of 100 s. Moduli measured over higher strains or longer times are lower. 

Muratoglu et al. 1995d). This comes close to the tearing moduli measured for some of the toughest pressure-vessel steels and tabulated by Clark et al. (1978). 

The elastic moduli measure the compressibility of a rock i.e. the contraction it undergoes when subjected to a load. This is given by the Young s modulus, a material constant, which describes the stiffness or how easily the material deforms. It is the proportionality constant, E, in Hooke s Law a = Ee, that relates stress and strain and can also be expressed as follows. 

The average elastic moduli measured by the nanoindentation method, where the fiber is under axial compression, is 14.2 and 29.5 GPa for the pitch fiber and the PAN fiber, respectively. These values are much smaller than the values reported under tension, which typically are in the range 200-800 GPa The difTerence in the... 

Figure 12. Comparison of elastic moduli measured by nanoindentation and calculated by FEM...

Shanmugham S, Jeong JW, Alkhateeb A, Aston DE. Pol3rmer nano wire elastic moduli measured with digital pulsed force mode AFM. Langmuir. 2005 21(22) 10214-8. 

In Figure 4, the ratios of the maximum moduli measured for the blends and the neat thermoplastics are plotted versus the LCP content, for the different blends. For the correct interpretation of the data shown in Figure 4, it must be kept in mind that the values of the tensile moduli whose ratios are plotted in the figure are those measured on fibers prepared with the highest windup speeds that could be used for either the blends and the neat polymers. Thus, the ratio of the maximum tensile moduli accounts also for the orientation of the matrix, due to the filament attenuation induced by drawing. 

Ratio of the maximum tensile moduli measured for blend and neat thermoplastic fibers, as a function of the LCP content... 

In experiment, with a 13% racemic solution of PEG in a mixture of methylene cloride and dioxane elastic moduli measures by a light scattering technique, were [243]... 

An atomic force microscope is used to stuviscoelastic state at the temperature of experiment. It is shown that, during the preliminary phase of friction and before the transition to the sliding regime, the contact area remains nearly constant. This allows for a determination of the relaxation and of the complex modulus of the material. A good agreement is found between moduli measured by this method and macroscopically determined ones. The position of the transition is seen to scale with the characteristic size of the contact area but it does not depend on the displacement velocity. Finally, a transient stick-slip regime is observed before the sliding steady state is reached. 

In Fig. 14-13, shear moduli measured at low temperature where the polymer is essentially in the glassy state arc also plotted, and are observed to increase linearly with (/>. In this case, also, agreement is obtained with the theory of van der Poel with a ratio of shear moduli of 8.4 (filler/polymer) and Poisson s ratio of 0.25 and 0.5 respectively for the two phases. Measurements of the bulk modulus Ke for a poly-... 

Fig. 5.15. Storage shear moduli measured for a series of fractions of PS with different molecular weights in the range M = 8.9 10 to M = 5.81 10. The dashed line in the upper right corner indicates the slope corresponding to the power law Eq. (6.81) derived for the Rouse-model of the glass-transition. Data from Onogi et...

The Young s moduli measured at room temperature are lower than the values calculated for the crystal at 1(X)° K,... 

In the case of Dy there is a small minimum near Jn and an abrupt decrease ( 20%) near Tc in EfT) (see fig. 15), which was observed for both cooling and warming processes. A small amount of hysteresis was found in E T) near Tq and in the HAEM state which is characteristic for a first-order transition (Kataev and Sattarov 1989). This behavior essentially differs from that observed for C33(J) measured at ultrasoimd frequencies (see fig. 23). A substantial decrease of Young s moduli measured on poly-and single crystals at the HAEM to FM phase transition was also observed in Tb-Dy, Gd-Dy and Er-Tb alloys (Tishin and Shipilov 1993, Kataev et al. 1989c, Shubin et al. 1985, Kataev and Shubin 1979). 

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