Hypothetical polymers

Table 1.4 Some Classified Molecular Weight Data for a Hypothetical Polymer Used in Example 1.5...

The temperature-time superposition principle is illustrated in Figure 8 by a hypothetical polymer with a TK value of 0°C for the case of stress relaxation. First, experimental stress relaxation curves are obtained at a series of temperatures over as great a time period as is convenient, say from 1 min to 10 min (1 week) in (he example in Figure 8. In making the master curve from the experimental data, the stress relaxation modulus ,(0 must first be multiplied by a small temperature correction factor/(r). Above Tg this correction factor is where Ttrt is the chosen reference... 

The presented explanation for the existence of the fracture envelope will be used in formulating a fracture criterion for polymer fibres. Let us suppose a hypothetical polymer fibre with chains having a single orientation angle in the unloaded state. The shape of the fracture envelope is now calculated by taking into account the shear deformation of the chains only. For this case the work per unit volume up to fracture is given by... 

Figure 2.1 Exploded views showing the nonporous membrane size-exclusion phenomenon in the uptake and loss of organic compounds. Middle illustration shows the movement of contaminant molecules through transient pores in the membrane and retention (membrane exclusion) of much larger lipid molecules. Upper illustration shows similarly scaled space-filled molecular models of some organic contaminants and triolein, along with the hypothetical polymer pore (transient) size. Reprinted with permission from the American Petroleum Institute (Huckinset al., 2002).

Figure 7 A similar diagram to that of Figure 6, except that the heteroatomic molecule BSNSH6, and the hypothetical polymer (BNH2) is used.

Example 1.3 illustrates these relationships for a hypothetical polymer. 

Fig. 5. Schematic of the heat capacity on cooling and heating at largely different rates in the glass transition region. Top Curves Cooling at 5.0 K/min, heating at 0.25 K/min. Bottom Curves Cooling at 5.0 K/min, heating at 150 K/min. (Hypothetical polymer, time dependence as in polystyrene)...

McMaster simulated binodal and spinodal curves for hypothetical polymer pairs with various values of the Equation-of-state parameters We have also simulated many hypothetical spinodal curves using the equations presented in the previous section and some of these are presented in Figs. 25 and 26. Various other workers have also calculated theoretical curves. An assessment of the effect of changes in the various properties is presented below. 

Figure 14.17 Dependence of properties on molecular weight (hypothetical polymers) [11].

FIGURE 20.1 A representation of a hypothetical polymer sample composed of equal weights of 1,000 and 10,000 molecular weight (M,) material. 

Figure 1.28. A phase diagram for a (hypothetical) polymer-solvent or pol5mier-polymer system showing both lower (LCST) and upper (UCST) critical solution temperatures. The boundary may be determined by locating the cloud point as a function of temperature for a fixed composition as the system moves from being a single-phase system to being a two-phase system and vice versa.

When only one species of monomer is used to build a macromolecule, the product is a homopolymer, normally referred to simply as a polymer. The word homopolymer often is used more broadly to describe polymers whose structure can be represented by repetition of a single type of repeating unit which may contain one or more species of monomer unit. Thus, a hypothetical polymer is also a homopolymer, e.g., poly(ethylene... 

Figure 6.12. Schematic illustration of the repeat unit of a hypothetical polymer, illustrating the application of the rules for determining the value of the structural parameter x8. There are four methylene units, pointed out by solid arrows, which are in the side group but not in the ring. There are also two tertiary carbon atoms, pointed out by dashed arrows, in the side group. Consequently, x8 = (-4+2) = -2 for this polymer.

Figure 3. TGA thermogram for a hypothetical polymer. (Reproduced with permission from Ref. 17. Copyright 1971 National Academy of Sciences.)...

The band structure of the hypothetical polymer [cis-(R)CNSN], indicates that it should be a conducting material like (SN), but such polymers have not been prepared. Conducting polymers with p-phenylene groups in the backbone are obtained by extending the metathetical reactions described in the previous section ... 

To illustrate the difference between the two most important jnolecular-weight averages, consider a hypothetical polymer containing 10 molecules of molecular weight 1,000 and 1 molecule of molecular weight 10,000. The number-average molecular weight would be... 

A numerical example serves to highlight the differences in the various averages. Consider a hypothetical polymer sample composed of chains of four distinct molar masses, 100,000,200,000, 500,000, and 1,000,000 g mol" in the ratio 1 5 3 1, than... 

It is not unreasonable therefore that the modes of deformation observed with this wide range of polymers should be so diverse. Let us now attempt to understand how the yield anisotropy of a hypothetical polymer might develop as the degree of orientation is increase starting with the isotropic polymer. 

With a hypothetical polymer, it is convenient to represent the biodegradation process by the following generalized sequence [1]. 

Dilatometric diagram of a hypothetic polymer, obtainable in crystalline and amorphous state. 

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