Polymers elastic modulus

Polymer Elastic modulus (MN/m2) Tensile Strength (MN/m2) Elongation of Break %... 

Type of Polymer Elastic Modulus Yield Stress Ultimate Strength Elongation at Break... 

Fig. 24 Equilibrium cantilever deflection as a function of solution pH. The solid line is experimental results and a sensitivity of 5 x 10 pH for a 10 nm bending deflection resolution can be obtained. The dotted line is obtained with the cantilever and polymer modeled as a composite beam with no slip at the boundary. Small deflections with respect to the length are assumed. Polymer elastic modulus of 85 MPa is used to fit the model to experiments. The inset shows a three-dimensional plot of the deflection of the cantilever/polymer at pH 7.0, obtained from the model. Reproduced with permission from [85]...

Figure 4.2 Dependence of the polymer elastic modulus in the adhesive layer on the distance to the substrate. The modulus is determined by the dynamic (1) and static (2) methods.

As it has been shown above (see the Eqs. (15.7) and (15.15)), the nanocluster relative fraction increasing results to polymers elasticity modulus enhancement similarly to nanofiller contents enhancement in artificial nanocomposites. Therefore, the necessity of quantitative description and subsequent comparison of reinforcement degree for the two indicated above nanocomposites classes appears. The authors of Ref. [58, 59] fulfilled the comparative analysis of reinforcement degree by nanoclusters and by layered silicate (organoclay) for polyarylate and nanocomposite epoxy poly-mer/Na" —montmorillonite [60], accordingly. 

As a factor related to chain motion, one may also consider polymer elastic modulus. As indicated in Properties of Polymers (39), at one time it was hoped that mechanical studies of polymers could be entirely replaced by electrical measurements. There are indeed close similarities between the general shapes and temperature-dependences of the mechanical and dielectric loss curves, but the quantitative connection between these phenomena is not as simple as was origindly believed. Electrical measurements constitute a useful addition to, but not a substitute for, mechanical studies. However, the elastic modulus and the dielectric constant are related to similar physic behavior. These parameters are response functions obtained by stimulating a material and measuring the subsequent relaxation phenomena. Therefore, similar to the dielectric constant, the elastic modulus depends not only on chain motion but also on free space in the polymer matrix. In fact, relaxation phenomenon of... 

Polymer Elastic modulus [MPa] Tensile strength [MPa] Elongation at break [%]... 

The importance of polymer composites arises largely from the fact that such low density materials can have unusually high elastic modulus and tensile strength. Polymers have extensive applications in various fields of industry and agriculture. They are used as constructional materials or protective coatings. Exploitation of polymers is of special importance for products that may be exposed to the radiation or temperature, since the use of polymers make it possible to decrease the consumption of expensive (and, sometimes, deficient) metals and alloys, and to extent the lifetime of the whole product. 

Secondly, the ultimate properties of polymers are of continuous interest. Ultimate properties are the properties of ideal, defect free, structures. So far, for polymer crystals the ultimate elastic modulus and the ultimate tensile strength have not been calculated at an appropriate level. In particular, convergence as a function of basis set size has not been demonstrated, and most calculations have been applied to a single isolated chain rather than a three-dimensional polymer crystal. Using the Car-Parrinello method, we have been able to achieve basis set convergence for the elastic modulus of a three-dimensional infinite polyethylene crystal. These results will also be fliscussed. 

Content of Ot-Olefin. An increase in the a-olefin content of a copolymer results in a decrease of both crystallinity and density, accompanied by a significant reduction of the polymer mechanical modulus (stiffness). Eor example, the modulus values of ethylene—1-butene copolymers with a nonuniform compositional distribution decrease as shown in Table 2 (6). A similar dependence exists for ethylene—1-octene copolymers with uniform branching distribution (7), even though all such materials are, in general, much more elastic (see Table 2). An increase in the a-olefin content in the copolymers also results in a decrease of their tensile strength but a small increase in the elongation at break (8). These two dependencies, however, are not as pronounced as that for the resin modulus. 

The Rheometric Scientific RDA II dynamic analy2er is designed for characteri2ation of polymer melts and soHds in the form of rectangular bars. It makes computer-controUed measurements of dynamic shear viscosity, elastic modulus, loss modulus, tan 5, and linear thermal expansion coefficient over a temperature range of ambient to 600°C (—150°C optional) at frequencies 10 -500 rad/s. It is particularly useful for the characteri2ation of materials that experience considerable changes in properties because of thermal transitions or chemical reactions. 

Langley, N.R. and Polmanteer, K.E., Relation of elastic modulus to crosslink and entanglement concentrations in rubber networks. J. Polym. Sci. Polym. Phys. Ed., 12(6), 1023-1034 (1974). 

To understand the global mechanical and statistical properties of polymeric systems as well as studying the conformational relaxation of melts and amorphous systems, it is important to go beyond the atomistic level. One of the central questions of the physics of polymer melts and networks throughout the last 20 years or so dealt with the role of chain topology for melt dynamics and the elastic modulus of polymer networks. The fact that the different polymer strands cannot cut through each other in the... 

The mechanical properties can be studied by stretching a polymer specimen at constant rate and monitoring the stress produced. The Young (elastic) modulus is determined from the initial linear portion of the stress-strain curve, and other mechanical parameters of interest include the yield and break stresses and the corresponding strain (draw ratio) values. Some of these parameters will be reported in the following paragraphs, referred to as results on thermotropic polybibenzoates with different spacers. The stress-strain plots were obtained at various drawing temperatures and rates. 

The parameters which characterize the thermodynamic equilibrium of the gel, viz. the swelling degree, swelling pressure, as well as other characteristics of the gel like the elastic modulus, can be substantially changed due to changes in external conditions, i.e., temperature, composition of the solution, pressure and some other factors. The changes in the state of the gel which are visually observed as volume changes can be both continuous and discontinuous [96], In principle, the latter is a transition between the phases of different concentration of the network polymer one of which corresponds to the swollen gel and the other to the collapsed one. 

Nielsen proposed a formula [216] for estimating the elasticity modulus of a filled polymer ... 

Fig. 6. Variation of elasticity modulus (E) under tension and yield strain (es) of the polymer matrix (I, I ) and polyethylene-based composites polymerization filled with kaolin (2,20 in function of polymer MM [320], Kaolin content 30% by mass. The specimens were pressed 0.3-0.4mm thick blates stretching rate e = 0.67 min-1...

The peculiarities of dynamic properties of filled polymers were described above in connection with the discussion of the method of determining a yield stress according to frequency dependence of elastic modulus (Fig. 5). Measurements of dynamic properties of highly filled polymer melts hardly have a great independent importance at present, first of all due to a strong amplitude dependence of the modulus, which was observed by everybody who carried out such measurements [3, 5]. 

Considering a fiber or thread of nylon-66, which is an unoriented glassy polymer, its modulus of elasticity is about 2,000 MPa (300,000 psi). Above the Tg its elastic modulus drops even lower, because small stresses will readily straighten the kinked molecular chains. However, once it is extended and has its molecules oriented in the direction of the stress, larger stresses are required to produce added strain. The elastic modulus increases. 

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