Free volume rheology

It was also noted by Farrington and co-workers that the chemical nature of the end-groups may have a substantial effect on the viscosity of bulk dendrimers, even under iso-free volume conditions [49]. This seems consistent with the establishment of interdendrimer interactions and supramolecular organization at rest in the bulk state. However, as in most other areas of dendrimer rheology, more data are desirable before definite conclusions can be drawn. 

An important difference between the PS-gas systems (Kwag et al., 1999) and the PDMS-C02 system (Gerhardt et al., 1997) is that the viscosity measurements of the PS-gas systems are conducted at temperatures within 75 °C of T of PS, whereas the PDMS-C02 measurements were performed nearly 200 °C above Tg of PDMS. The difference between these two thermal regimes leads to several differences in the observed rheological behavior. The viscosity reductions relative to the pure polymer are much greater for PS-gas systems than for PDMS-C02 systems at similar dissolved gas compositions, and the dependence of ac on temperature is much more pronounced for the PS-gas systems. These trends are consistent with the observations of Gerhardt et al. (1997, 1998) that the effect of dissolved gas on polymer melt viscosity occurs primarily through a free-volume mechanism. 

A modified version of the free-volume theory is used to calculate the viscoelastic scaling factor or the Newtonian viscosity reduction where the fractional free volumes of pure polymer and polymer-SCF mixtures are determined from thermodynamic data and equation-of-state models. The significance of the combined EOS and free-volume theory is that the viscoelastic scaling factor can be predicted accurately without requiring any mixture rheological data. 

Bulk creep and recovery in systems with viscosity dependent upon free volume. Trans. Soc. Rheology 5, 285—296 (1961b). 

In some more recent theories, it was suggested that the free volume of the system could really be taken into account in describing the rheological properties of suspensions. This direction, however, is not sufficiently developed. 

These equations can be related to one another by assuming the free volume is proportional to the coefficient of thermal expansion, a, near T0 [i.e., Vf a(T- 7J,)]. (There is also the WLF equation, which we will get into later in Chapter 13, Mechanical and Rheological Properties.)... 

K8. Koppelmann, j. The dependence of relaxation times on free volume in high polymers. Proc. of the 4" Int. Congr. on Rheology. Vol. 3, S. 361—377, New York John Wiley Sons 1965. 

Keywords oligoethylsiloxane, compositions, rheology, free volume theory... 

Rheological properties of the oligoethylsiloxane-based compositions with additives are of vital importance for the selection of maintenance conditions of various items, but they have not been studied yet. No data on such composition-fluidity relationships (unconfined fluctuating free volume and viscous flow activation energy values) are available. 

The macroscopic free-volume is an important parameter closely related to the rheological behavior of an amorphous material. It is generally accepted that the glass transition is regarded as an iso-free-volume state, and the free-volume fraction (fg) at the Tg is around 0.025 for many monomers and polymers. The WLF method has been widely used for determining the macroscopic fg value. On the other hand, the microscopic analysis of the free-volume has also been uti-... 

Two types of rheological phenomena can be used for the detection of blend s miscibility (1) influence of polydispersity on the rheological functions, and (2) the inherent nature of the two-phase flow. The first type draws conclusions about miscibility from, e.g., coordinates of the relaxation spectmm maximum cross-point coordinates (G, CO ) [Zeichner and Patel, 1981] free volume gradient of viscosity a = d(lnT]) / df the initial slope of the stress growth function S = d(lnr +g)/dlnt the power-law exponent n = d(lnOj2)/dlny = S, etc. The second type involves evaluation of the extrudate swell parameter, B = D/D, strain (or form) recovery, apparent yield stress, etc. 

There is a mounting evidence that PDB is not a rule for miscible polymer blends. Depending on the system and method of preparation, polymer blends can show either a positive deviation, negative deviation, or additivity. Note that miscibility in polymeric systems requires strong specific interactions, which in turn affect the free volume, thus the rheological behavior. It has been demonstrated that Newtonian viscosity can be described by the relation [Utracki, 1983 1985 1986] ... 

Rheological Properties. Incorporation of ions into a polymer invariably causes an increase in the melt viscosity of the polymer. This is mainly due to the strong association between the ionic segments (which lead to the so called bluster formation in some cases ) which can best be described as time - dependent crosslinks. Such crosslinks are regarded as extra entanglements or as decreasing the segmental mobility which can be described by free volume considerations. 

Bartos, J., Kristiak, J., Sausa, O., and Zrubova, J., Experimental free volume aspects of the polymer rheology as obtained by positron annihilation lifetime spectroscopy, Macromol. Symp.,15%, 111-123 (2000). 

Several investigators in the field of rheology have suggested that free volume is a good unifying parameter to describe changes in the timescale of material response in polymers. Free volume is the portion of the specific volume of the material that is unoccupied by the molecules. Researchers have applied the concept of free volume to develop a non-linear viscoelastic constitutive relationship [2] as well as for modeling coupled diffusion in viscoelastic materials [1]. 

The second dependence in Eq. (2.32) is valid when all fractions are either entangled or not. In consequence, the relaxation spectrum of a miscible polymer blend is a linear combination of the component relaxation spectra and their weight fractions, W(. A strong deviation from linearity in plots of log Hq versus Mw/Afn and log Wmax versus log r]o indicates immiscibility [87, 88]. The principle that in miscible blends polydispersity can be calculated and used to test for system miscibility was extended to other rheological functions sensitive to polydispersity, namely, the power-law exponent (n), the cross-point coordinates (G, o) ), the free volume gradient of viscosity, the initial slope of stress growth function, and so on [3]. 

Utracki, L.A. (1989) Polymer Alloys and Blends, Hanser Publishers, Munich. SteDer, R. and Zuchowska, D. (1990) Free volume theory for rheological properties of polymer blends. J. pl. Pdlym. Sci., 41 (7-8), 1595-1607. 

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