Relationship between swelling ratio

Equations (5.51), (5.52) and (5.53) can be cumbersome if they are to be used regularly so the relationships between swelling ratio and recoverable strain are often presented graphically as shown in Fig. 5.11. 

The relationship between swell ratio and foam properties was initially established for LDPE crosslinked by DCP alone. Figure 15.7 shows that an increase in swell ratio is accompanied by a decrease in foam density and an increase in mean cell size. The higher swell ratios are associated with a more loosely crosslinked network (i.e. lower crosslink density) that has a greater ability to expand and hence lowers the foam density. 

FIG. 15.38 Relationship between swelling ratio and recoverable shear strain for long capillary and slit dies. After Powell (1974). 

Table 15.12 gives a survey of the more important rheological equations. Figs. 15.36 and 15.37 (already discussed) show the relationship between swelling ratio and recoverable strain. It is far beyond the scope of this book to go into detail of this subject. The interested reader is referred to, e.g. Collyer (1993), Collyer and Clegg (1998) and Denys (2003). 

Figure 11. Relationship Between Swelling Ratio and % Soluble Extractables for Polyethylene/Peroxlde Mixtures Cured Under Various Temperature Conditions and a Constant Reaction Time of 3 Minutes.

Fig. 9.13. Poly( -caproamide)s with various cross-link densities Relationship between swelling ratios Q in m-cresol and tensile stresses in the dry state at three extensions A. Prom Schaefgen and Flory [114]...

Finally, it has to be mentioned that die swell is also dependent on the kind of convergence of the flow. Fig. 15.38 shows the relationships between swelling and recoverable shear strain as derived by Cogswell (1970) for long capillaries and slit dies BER represents the swelling ratio in capillaries Bsh and Bst that in slit dies in the thickness direction and transverse direction, respectively. Fig. 15.39 shows the analogous relationships for very... 

It has been shown in Chapter XI that the force of retraction in a stretched network structure depends also on the degree of cross-linking. It is possible therefore to eliminate the structure parameter ve/Vo) by combining the elasticity and the swelling equations, and thus to arrive at a relationship between the equilibrium swelling ratio and the force of retraction at an extension a (not to be confused with the swelling factor as). In this manner we obtain from Eq. (XI-44) and Eq. (39)... 

Fig. 135.—The relationship between the equilibrium retractive force T(x (in lbs./in.2) at 241 °C for various multilinked poly (e-caproamides) at the extensions (a) indicated, and their equilibrium swelling ratios in m-cresol at 30°C. O, tetralinked polymers octa-linked polymers. The lines have been calculated according to Eq. (41), with appropriate revision for the octafunctional case (broken lines), an arbitrary value being assigned to the parameter Xi for each elongation. (Schaefgen and Flory.33)...

Figure 5 shows the temperature dependence of the IPNs with various ratios of [EO]/[APy], kept in unit molar ratio [14]. The IPNs swell in lower temperature ranges and shrink in high temperature ranges. The curves show inflection points at around 35 °C. Figure 6 [14] shows the relationship between the swelling ratio at 10 °C and the [EO]/[APy] ratio within the IPNs. Swelling ratio increases as the [EO]/[APy] ratio nears 1 1. The IPN with an equimolar... 

Figure 13.5 The relationship between the linewidth parameter H% and swelling ratio for swollen NR [100]. The measurements were made in deuterochloroform at 23 °C [100]...

Another important parameter is the swelling ratio. A sample is placed in a solvent and the variation of its height is monitored as a function of time through a contact probe. A relationship between sample and solvent allows for the evaluation of the cross-link density and the chain length between cross-links. The technique is named swell ratio testing (SRT) in the American ASTM F2214-02, or hot set test (OST) in the German DIN 57472 Standard. " ... 

The infiltration of water into clay-like materials causes changes in the pore structure of the material. Water molecules place in the solid matrix and become immobile. In consequence the effective porosity and the intrinsic permeability decrease. If the volume expansion of the material is restrained, swelling pressure is observed which increases linearly with the degree of water saturation, Studer et al. (1984), and BSrgesson (1984). The correlation between swelling pressure p, and void ratio e can be expressed best with the following empirical relationship, Bdrgesson et al. (1995) ... 

White and Roman [94] measured the effects of L/D and drawdown on die swell of polypropylene. Figure 3.13 shows the die swell as a function of L/D for Hercules Profax 6523 and four other melts at 180°C. The d/D ratios were measured on frozen extrudates. Figure 3.14 shows the die swell as a function of take-up velocity. The relationship between die swell and die entrance angle for a polypropylene was determined by Huang and White [95]. Figure 3.15 presents their data. 

Parrott et al. [153] found an exact relationship between the rate of water replacement by methanol and the ratio of pores greater than 50 nm. With lowering of this ratio to the level of about 0.4, the diffusion becomes extremely low (Fig. 5.71) the authors attribute this to the filling of pore chaimels by some amount of hydration products. However, Feldman [138] remarks that there are some questions as the water replacement by methanol is concerned. The reactivity of methanol towards Ca(OH)2 and C-S-H, resulting in the formation of calcium methoxide or a methylated complex compounds was reported by some authors [138,156]. These reactions occur very quickly and a substantial amount of products appears, modifying the paste microstracture. The swelling of paste, observed by Feldman [138] was about 0.1 % after 14 days when the paste absorbed 85 % methanol as water replacement. This effect can be attributed to the intrasion of methanol between the layers in C-S-H structure and the calcium methoxide formatioa At extended distance between C-S-H layers the specific surface of paste markedly increases, as it has been proved by Winslow and Diamond [ 13 5]. In turn, the water replacement by propan-2-ol, re-... 

Fig. 3.28, at each shear rate the swell ratio decreases with increasing temperature [32]. However, as shown in Fig. 3.32, the same data superpose rather well when they are plotted instead as a function of the shear stress. That result turns out to be quite general and, of course, quite useful for extrapolation purposes. It is a natural consequence of the temperature invariance of the relationship between a and N and the idea, embodied by Eq. (3.34), that Dq/D for long capillaries depends only on a ratio of stress components in the capillary. 

---