Amorphous polymers elastic moduli

On comparison of the yield strengths and elastic moduli of amorphous polymers well below their glass transition temperature it is observed that the differences between polymers are quite small. Yield strengths are of the order of 8000 Ibf/in (55 MPa) and tension modulus values are of the order of 500 000 Ibf/in (3450 MPa). In the molecular weight range in which these materials are used differences in molecular weight have little effect. 

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... 

From these definitions one may corroborate the intention of HTS in chemistry and materials science. The total speed-up factor of this part of the R D (Research and Development) process, as stated earlier, is between 5 and 50, but contrary to most of the pharma applications true (semi-) quantitative answers will result. As a result, this approach is essentially applicable in any segment of R D. On the other hand, this approach requires methods of experimentation that have almost the same if not the same accuracy as in the traditional one-experiment-at-the time approach. This is key as (i) in process optimisation accuracy is key and (ii) in research, also in academic research, accuracy is important as some polymer properties do not span a wide range of values (e.g., the elastic modulus of amorphous polymers) or may depend critically on molecular weight distribution or molecular order. 

Softening as a result of micro-Brownian motion occurs in amorphous and crystalline polymers, even if they are crosslinked. However, there are characteristic differences in the temperature-dependence of mechanical properties like hardness, elastic modulus, or mechanic strength when different classes of polymers change into the molten state. In amorphous, non-crosslinked polymers, raise of temperature to values above results in a decrease of viscosity until the material starts to flow. Parallel to this softening the elastic modulus and the strength decrease (see Fig. 1.9). 

In reality, the morphology of a polycrystalline thermoplastic consists of spherulites which holds for common PP, PE, PA 6, PA 6,6 and PEEK crystalHzed under common conditions. Some semicrystalhne polymers as weU as the above mentioned moderately filled ones may exhibit lameUar crystahine morphology without any spherulitic order. As a result of random orientation of individual crystallites in spheruhtes and the manner of their connectivity, the elastic modulus of about 10 GPa has been extrapolated for a hypothetical ideal polycrystalline PE containing no amorphous phase from the dependence of the elastic modulus of PE on the degree of crystallinity. The presence of an amorphous phase which reduces the content of the crystalline phase results in a further reduction of the overaU elastic modulus of the semicrystalhne polymers compared to ideal mono crystals. 

Table 5.2 lists polymers and their tendency toward crystallinity. Yield stress and strength, and hardness increase with an increase in crystallinity as does elastic modulus and stiffness. Physical factors that increase crystallinity, such as slower cooling and annealing, also tend to increase the stiffness, hardness, and modulus of a polymeric material. Thus polymers with at least some degree of crystallinity are denser, stiffer, and stronger than amorphous polymers. However, the amorphous region contributes to the toughness and flexibility of polymers. 

In the following, we calculate K and H for the model of polymer film in which part of the amorphous phase is connected in series with the crystalline phase and part in parallel (Fig. 10). The amorphous phase is characterized by a complex elastic modulus,... 

It is known that in the glassy state below the glass transition temperature the physical properties of epoxy resin as well as other amorphous polymers are generally little dependent on temperature and structure 1,28). Also, the modulus of elasticity (E) does only weakly depend on the crosslinking density. 

The curve of the tensile modulus versus temperature for the amorphous polymer shows five regions of elastic behaviour (Fig. 13.4) ... 

The considerable increase of elastic modulus with low amoimt of ultrafine amorphous silica Si02 (< 0.1 pm) shows the nanoparticles to be well dispersed. It cannot be explained by classical models (Kemer, Nielsen) we have to take into account that a part of the polymer matrix is occluded in the aggregates. It can also be explained by adsorption of the polymer on the surface of the silica. Silica-PP adhesion is high, and so the molecular mobility is reduced this effect is all the more important as the surface area is high (> 150 m /g). This effect has been observed on elastomeric materials, where polymer adsorption on silica control the modulus [23]. 

The interest in multicomponent materials, in the past, has led to many attempts to relate their mechanical behaviour to that of the constituent phases (Hull, 1981). Several theoretical developments have concentrated on the study of the elastic moduli of two-component systems (Arridge, 1975 Peterlin, 1973). Specifically, the application of composite theories to relationships between elastic modulus and microstructure applies for semicrystalline polymers exhibiting distinct crystalline and amorphous phases (Andrews, 1974). Furthermore, as discussed in Chapter 4, the elastic modulus has been shown to be correlated to microhardness for lamellar PE. In addition, H has been shown to be a property that describes a semicrystalline polymer as a composite material consisting of stiff (crystals) and soft, compliant elements. Application of this concept to lamellar PE involves, however, certain difficulties. This material has a microstructure that requires specific methods of analysis involving the calculation of the volume fraction of crystallized material, crystal shape and dimensions, etc. (Balta Calleja et al, 1981). 

The time-temperature equivalence principle makes it possible to predict the viscoelastic properties of an amorphous polymer at one temperature from measurements made at other temperatures. The major effect of a temperature increase is to increase the rates of the various modes of retarded conformational elastic response, that is, to reduce the retarding viscosity values in the spring-dashpot model. This appears as a shift of the creep function along the log t scale to shorter times. A secondary effect of increasing temperature is to increase the elastic moduli slightly because an equilibrium conformational modulus tends to be proportional to the absolute temperature (13). 

The heterogeneity of the crystalline polymer solid is accentuated still more in the case of mechanical properties by the enormous mechanical anisotropy of the crystals and the large difference in the elastic moduli of the crystalline and amorphous components. With polyethylene, the elastic modulus of the crystals is 3452 or 2403 X 1010 dynes/cm2 in the chain direction (E ) and 4 X 1010 dynes/cm2 in the lateral direction (E ) (2, 3). The elastic modulus of the amorphous component (Ea) of polyethylene is 109-1010 dynes/cm2 (4). This is significantly less than Eu and Ebut at least 10 times the elastic modulus of a rubber that has about five monomers in the chain segments between the crosslinks. This is quite surprising since room temperature is far above the glass transition temperature of polyethylene (Tg is either —20°C or — 120°C), and therefore one would expect a fully developed rubbery... 

Hyflon AD amorphous fluoropolymer is used in optical devices, pellicles in semiconductor manufacture, as a dielectric and as a separation membrane. Small amounts of TDD have been used as a modifier in ethylene-chlorotrifluoroethylene polymers to increase stress crack resistance. Minute amounts of TDD are used also as a modifier in polytetrafluoroethylene to improve elastic modulus, reduce creep and permeability and increase transparency. It has been suggested that the much higher reactivity of TDD and other fluorinated dioxoles relative to other modifiers gives a more uniform distribution of the modifier in the polymer chain that results in a greater increase in the desired properties at lower concentration of modifier in the polymer. 

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