Landel

Figure C2.1.15. Schematic representation of tire typicai compiiance of a poiymer as a function of temperature. (C) VOGEL-FULCHER AND WILLIAMS-LANDEL-FERRY EQUATIONS...

The Arrhenius equation holds for many solutions and for polymer melts well above their glass-transition temperatures. For polymers closer to their T and for concentrated polymer and oligomer solutions, the WiUiams-Landel-Ferry (WLF) equation (24) works better (25,26). With a proper choice of reference temperature T, the ratio of the viscosity to the viscosity at the reference temperature can be expressed as a single universal equation (eq. 8) ... 

S. P. Landels, M. M. Smart,. Bakker, and. Shimosato, "Controlled Release Fertilisers and Nitrification Inhibitors," Chemical Economics Handbook, SRI International, Menlo Park, Calif., 1989. 

S. P. Landels, Proceedings of the Controlled Felease Fertiliser Workshop, TVA National Fertiliser and Environmental Research Center, July 30—31, 1991, pp. 87-101. 

Williams, Landel and Ferry developed an empirical relationship for this type of shift factor. This has the form... 

Fabis F, Jolivet-Fouchet S, Robba M, Landelle H, Rault S (1998) Tetrahedron 54 10789... 

The value of Uj. itself is obtained by using the so-called WLF equation (7.18), first proposed by Williams, Landel, and Ferry in 1955. 

The glass transition temperature can be chosen as the reference temperature, though this was not recommended by Williams, Landel, and Ferry, who preferred to use a temperature slightly above T. In order to determine relaxation times, and hence a, use can be made of dynamic mechanical, stress relaxation, or viscosity measurements. 

When the test temperature is raised, the rate of Brownian motion increases by a certain factor, denoted Ox. and it would therefore be necessary to raise the frequency of oscillation by the same factor flx to obtain the same physical response, as shown in Figure 1.6. The dependence of Uj upon the temperature difference T—Tg follows a characteristic equation, given by Williams, Landel, and Ferry (WLF) [11] ... 

M.L. Williams, R.E. Landel, and J.D. Ferry, The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming Uquids, J. Am. Chem. Soc., 77, 3701-3707, 1955. 

Nielsen LE, Landel RF (1994) Mechanical properties of polymers and composites. Marcel Dekker, New York... 

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