Young’s modulus polymer

Consequently, the foam Young s modulus Ef in the [0 01] direction is related to the polymer Young s modulus E, and to the square of the foam relative density, by... 

X -poly (AVGVP)t ) Hydrogel Polymer Young s modulus 7% extension, 37°C Density (mgml ) 2.0 X 10 ... 

Figure 1.6 Idealized modulus-temperature behavior of an amorphous polymer. Young s modulus, stress/strain, Is a measure of stiffness.

Abstract. This paper presents results from quantum molecular dynamics Simula tions applied to catalytic reactions, focusing on ethylene polymerization by metallocene catalysts. The entire reaction path could be monitored, showing the full molecular dynamics of the reaction. Detailed information on, e.g., the importance of the so-called agostic interaction could be obtained. Also presented are results of static simulations of the Car-Parrinello type, applied to orthorhombic crystalline polyethylene. These simulations for the first time led to a first principles value for the ultimate Young s modulus of a synthetic polymer with demonstrated basis set convergence, taking into account the full three-dimensional structure of the crystal. 

Regarding mechanical properties of polymers, the efficiency of the Car-Parrinello approach has enabled us to evaluate the ultimate Young s modulus of orthorhombic polyethylene, and demonstrate basis set convergence for that property. 

Now for some real numbers. Table 3.1 is a ranked list of Young s modulus of materials - we will use it later in solving problems and in selecting materials for particular applications. Diamond is at the top, with a modulus of lOOOGPa soft rubbers and foamed polymers are at the bottom with moduli as low as 0.001 GPa. You can, of course, make special materials with lower moduli - jelly, for instance, has a modulus of about 10 GPa. Practical engineering materials lie in the range 10 to 10 GPa - a... 

Fig. 6.2. How Young s modulus increases witl) increasing density of covalent cross-links in polymers, including rubbers above tbe glass temperature. Below To, be modulus of rubbers increases markedly because tbe Van der Waals bonds take hold. Above Tq they melt, and the modulus drops.

The factor 3 appears because the viscosity is defined for shear deformation - as is the shear modulus G. For tensile deformation we want the viscous equivalent of Young s modulus . The answer is 3ri, for much the same reason that = (8/3)G 3G - see Chapter 3.) Data giving C and Q for polymers are available from suppliers. Then... 

Fig. 23.1. Schematic showing the way in which Young s modulus E for a linear polymer changes with temperature for a fixed loading time.

Fig. 26.4. Young s modulus for wood depends mainly on the relative density p/p,. That along the groin varies os p/p, that across the groin varies roughly os like polymer foams.

Spruce soundboards have a Young s modulus anisotropy of about (11.6 GPa/0.71 GPa) = 16. A replacement material must therefore have a similar anisotropy. This requirement immediately narrows the choice down to composites (isotropic materials like metals or polymers will probably sound awful). 

Figure 8.9. Diagram of the structure of a drawn polymer fibre. The Young s modulus of the crystallised portions is between 50 and 300 GPa, while that of the interspersed amorphous tangles will be only 0.1-5 GPa. Since the strains are additive, the overall modulus is a weighted average of...

Due to the low glass transition and melting temperatures of PDMS polymer, 100% silicone sealant do not substantially stiffen at lower service temperature. Typically, their Young s modulus is maintained within a 25% range over a temperature range of —40 to 80°C. 

Small deformations of the polymers will not cause undue stretching of the randomly coiled chains between crosslinks. Therefore, the established theory of rubber elasticity [8, 23, 24, 25] is applicable if the strands are freely fluctuating. At temperatures well above their glass transition, the molecular strands are usually quite mobile. Under these premises the Young s modulus of the rubberlike polymer in thermal equilibrium is given by ... 

Polymer Dynamic shear modulus (frequency > 1 Hz) S/MPa Quasi-static Young s modulus (frequency 0.01 Hz) E/MPa Ratio 3S/E... 

The PGS obtained by Wang and coworkers was a kind of thermoset elastomer with the Young s modulus of 0.282 0.025 MPa, a tensile strain of at least 267 zE 59.4%, and a tensUe strength was at least 0.5 MPa. The mechanical properties of PGS were well consisted with that of some common soft tissues. Although PGS is a thermoset polymer, its prepolymer can be processed into various shapes by solving it in common organic solvents such as 1,3-dioxolane, tetrahydrofuran, isopropanol, ethanol, and iV,M-dimethylformamide. Porous scaffolds can be fabricated by salt leaching. 

FIGURE 12.17 Young s modulus versus volume fraction of fibers for A, the unaged composites and B, the composites aged at 150°C for 48 h of ethylene-propylene-diene monomer (EPDM) rubber-melamine fiber composites. L indicates test specimens cut in the direction parallel to the milling direction (longitudinal) and T indicates test specimens cut in the direction perpendicular (transverse) to the milling direction. (From Rajeev, R.S., Bhowmick, A.K., De, S.K., Kao, G.I.P., and Bandyopadhyay, S., Polym. Compos., 23, 574, 2002. With permission.)... 

The tensile properties (tensile strength, Young s modulus, and elongation) of unoriented, noncrystalline films were investigated for those polymers that formed clear films by solvent casting. The results collected in Table I allowed several general conclusions. 

Whereas the tensile strength was not a sensitive function of the monomer structure, the tensile modulus (Young s Modulus) was clearly related to the monomer structure. This is expected since the tensile modulus is a measure of the polymer s resistance to deformation and is related to the "stiffness" of a polymeric material. The highest tensile modulus (22,000 kg/cm2,2.2 GPa) was measured for poly(BPA iminocarbonate). Replacement of BPA by Dat-Tyr-Hex reduced the tensile modulus significantly. This observation can possibly be attributed to the presence of the long hexyl ester pendent chain in Dat-Tyr-Hex. Generally, the polyiminocarbonates were somewhat "stiffer" than the corresponding polycarbonates. Thus, the tensile moduli of poly(Dat-Tyr-Hex iminocarbonate) and poly(Dat-Tyr-Hex carbonate) were 16,300 kg/cm2 (1.6 GPa) and 13,900 kg/cm2 (1.3 GPa) respectively. 

Here m is the mode order (m — 1,3,5. .., usually 1 for polyethylenes), c the velocity of light, p the density of the vibrating sequence (density of pure crystal) and E the Young s modulus in the chain direction. The LAM band has been observed in many polymers and has been widely used in structural studies of polyethylenes [94—99,266], as well as other semi-crystalline polymers, such as poly (ethylene oxide) [267], poly(methylene oxide) [268,269] and isotactic poly(propylene) [270,271], The distribution of crystalline thickness can be obtained from the width of the LAM mode, corrected by temperature and frequency factors [272,273] as ... 

Polymer Melting temperature (°C) Young s modulus (GPa) Tensile strength (MPa) Elongation to break (%) Notched izod impact strength (J/m)... 

What is the Young s modulus of the polymer in Problem 1 if Poisson s ratio is 0.35 ... 

---