Flex energy

We can demonstrate the utility of the Gibbs-DiMarzio theory by applying it to the calculation of the Tg of a random copolymer. Let us assume that the flex energy of a random copolymer composed of A and B monomer units is given by... 

Here 3 is a dimensionless parameter equal to -e/kTg where is the flex energy and k is Boltzmann s constant. In accordance with the assumption that Vq decreases monotonically with decreasing equations (1) and (2) can be solved iteratively by maintaining nP and r constant while simultaneously varying Vq until a unique 3 derived... 

A quite different approach is adopted in the statistical mechanical theory expounded by Gibbs and DiMarzio. They considered that the rotating unit could exist in two stable conformations (which might correspond to the trans and gauche conformers discussed earher), separated by a standard state energy difference, AE°, called the flex energy. Using the techniques of statistical thermodynamics, they calculated the partition of the units between these two forms. In theory, the... 

If this result is applied to PMMA we find that the difference in flex energies, Ae, between the syndiotactic and isotactic isomers of any polyalkyl methacrylate configurational pair is 191R or about 380 cals/mole, and, it is predicted the T difference for any member of the series should be 112°. Tflis is based on the assumption, it must be emphasized, that the configurational effect is an intramolecular effect. 

AQ pT 2, and finally is evaluated by setting the entropy in equation 28 equal to zero. It is difficult to correlate the flex energy e with rotational conformational energies from other sources (80), but good agreement has been found in several cases (7). 

It has been common practice to blend plasticisers with certain polymers since the early days of the plastics industry when Alexander Parkes introduced Parkesine. When they were first used their function was primarily to act as spacers between the polymer molecules. Less energy was therefore required for molecular bond rotation and polymers became capable of flow at temperatures below their decomposition temperature. It was subsequently found that plasticisers could serve two additional purposes, to lower the melt viscosity and to change physical properties of the product such as to increase softness and flexibility and decrease the cold flex temperature (a measure of the temperature below which the polymer compound loses its flexibility). 

The overall energy from the filtered broadband plotted against measurement location provides an approximation of the mode shape of the installed machine. Figure 44.31 illustrates a vertical broadband plot taken from a Spencer blower. Note that the motor appears to be flexing in the vertical direction. Extremely high amplitudes are present in the motor s outboard bearing and the amplitudes decrease at subsequent measurement points across the machine. 

Horizontal Figure 44.38 illustrates horizontal mechanical looseness, which is also common to machine-trains. In this example, the machine s support legs flex in the horizontal plane. Unlike the vertical looseness illustrated in Figure 44.37, gravity is uniform at each leg and there is no increased impact energy as the leg s direction is reversed. 

While most stationary machine components move during normal operation, they are not always resonant. Some degree of flexing or movement is common in most stationary machine-trains and structural members. The amount of movement depends on the spring constant or stiffness of the member. However, when an energy source coincides and couples with the natural frequency of a structure, excessive and extremely destructive vibration amplitudes result. 

Ludington, D. and Johnson, E. L. (2003). Dairy Farm Energy Audit Summary Flex Tech Services. New York State Energy Research and Development Authority, Albany, NY. http //www. nyserda.org/publications/dairyfarmenergysummary.pdf. (accessed 24.10.10). 

Later on12, Koshland proposed the induced fit model of the active site action that considers that during the formation of the enzyme-substrate complex, the enzyme can change its conformation so as to wrap the substrate like it happens when a hand (substrate) fits in a globe (enzyme). This flexing puts the active site and bonds in the substrate under strain, which weakens the bonds and helps to lower the activation energy for the catalyzed reaction. 

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