Molecular basis relaxation

Figure 3.16 Some experimental dynamic components, (a) Storage and loss compliance of crystalline polytetrafluoroethylene measured at different frequencies. [Data from E. R. Fitzgerald, J. Chem. Phys. 27 1 180 (1957).] (b) Storage modulus and loss tangent of poly(methyl acrylate) and poly(methyl methacrylate) measured at different temperatures. (Reprinted with permission from J. Heijboer in D. J. Meier (Ed.), Molecular Basis of Transitions and Relaxations, Gordon and Breach, New York, 1978.)...

Clearly, both the pivot and the slithering snake algorithms are incapable of reproducing true chain dynamics at molecular basis, covering the time range of typical chain relaxation times. Therefore, in the following we focus on two alternative methods, broadly used at present to this end. 

Schaefer, J., High Resolution c nmr Studies of Solid Polymers, "Molecular Basis of Transition Relaxation",... 

In Eq. (4.13) NT is the total number of internal degrees of freedom per unit volume which relax by simple diffusion (NT — 3vN for dilute solutions), and t, is the relaxation time of the ith normal mode (/ = 1,2,3NT) for small disturbances. Equation (4.13), together with a stipulation that all relaxation times have the same temperature coefficient, provides, in fact, the molecular basis of time-temperature superposition in linear viscoelasticity. It also reduces to the expression for the equilibrium shear modulus in the kinetic theory of rubber elasticity when tj = oo for some of the modes. 

Heijboer, J. Molecular basis of transitions and relaxations, Meier, D. J. (ed.). Midland macromol. monographs, Vol. 4,15178... 

Trombitas, K., Wu, Y., and McNabb, M. (2003). Molecular basis of passive stress relaxation in human soleus fibers Assessment of role of immunoglobulin domain unfolding. Biophys. J. 85, 3142-3153. 

Thus, specific interactions directly determine the spectroscopic features due to hydrogen bonding of the water molecules, while unspecific interactions arise in all or many polar liquids and are not directly related to the H-bonds. Now it became clear that the basis of four different processes (terms) used in Ref. [17] and mentioned above could rationally be explained on a molecular basis. One may say that specific interactions are more or less cooperative in their nature. They reveal some features of a solid state, while unspecific interactions could be understood in terms of a liquid state of matter, if we consider chaotic gas-like motions of a single polar molecule, namely, rotational motions of a dipole in a dense surroundings of other molecules. The modem aspect of the spectroscopic studies leads us to a conclusion that both gas-like and solid-state-like effects are the characteristic features of water. In this section we will first distinguish between the following two mechanisms of dielectric relaxation ... 

In this section we are going to examine such viscoelastic properties in some detail and we will start by examining in turn three important mechanical methods of measurement creep, stress relaxation, and dynamic mechanical analysis. This will lead us to interesting things like time-temperature equivalence and a discussion of the molecular basis of what we have referred to as relaxation behavior. 

The WLF equation applies to amorphous polymers in the temperature range of Tg to about Tg + lOO C. In this equation J is the reference temperature, these days taken to be the T, while and C2 are constants, initially thought to be universal (with Cx = 17.44 and C2 = 51.6), but now known to vary somewhat from polymer to polymer. These experimental observations bring up a number of interesting questions. What is the molecular basis of the time-temperature superposition principle What is the significance of the log scale and what does the superposition principle tell us about the temperature dependence of relaxation behavior And what about the temperature dependence of a7 at temperatures well below 2 ... 

Family of plant proteins essential for acid-induced cell wall loosening. See Cosgrove, D.J., Relaxation in a high-stress enviromnent the molecular basis of extensible cell walls and cell enlargement, Plant Cell 9, 1031-1041, 1997. 

R. Simha, in Molecular Basis of Transitions and Relaxations, edited by D. J. Meier, Gordon and Breach Science Publishers, London (1978), 203-223. 

The earliest treatment of dielectric relaxation, on a molecular basis, is that of Debye,12 He treated it as a diffusional process, assuming that spherical molecules were rotating in a continuous medium. Applying the Stokes law., he found... 

I ier, D.J., Ed. "Molecular Basis of Transitions and Relaxations" Gordon and Breach Science... 

D. J. Meier (ed.). Molecular basis of relaxations and transitions of polymers (Midland Macromolecular Monographs, Vol. 4), Gordon and Breach, New York, 1978. 

For further study of DMA see, for example Ferry JD (1980) Viscoelastic Properties in Polymers, 3 edition. J. Wiley, New York Ward IM (1983) Mechanical Properties of Solid Polymers, 2 edn. Wdey, New York Meier DJ (1978) Molecular Basis of Transitions and Relaxations. Gordon and Breach, New York McCrum NG, Read BE, Williams G (1967) Anelastic and Dielectric Effects in Polymeric Solids. Wiley, New York Aklonis JJ, MacKnightWJ(1967) Introduction to Polymer Viscoelasticity. Wiley, New York Matsuoka S (1992) Relaxation Phenomena in Polymers. Hanser Publ, Munich. 

Takayanagi M (1978) Midland macromolecular monographs. In Meier DJ (ed) Molecular basis of transition and relaxations, vol 4. Gordon and Breach, London, p 117 Tammann G, Hesse W (1926) The dependence of viscosity upon the temperature of supercooled liquids. Z Anorg Allg Chem 156 245-257... 

It is generally assumed that the description of polymer properties requires a continuous distribution of relaxation times. Numerous forms of the distribution function have been assumed, often for mathematical simplicity or on the basis of physical intuition. It has been found that a fractional power law distribution of relaxation times of the form t leads to hysteresis absorption with aX = m7il2 (Np), when m < 1 (3). The disadvantage of this model is that attempts to justify this distribution of relaxation times on a molecular basis quantitatively have not been successful. Mathematically, almost any experimental result can be expressed in terms of a distribution of relaxation times, but there may not be any physical significance to the distribution. 

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