Rupture, required energy

Steurer and Hess (17) have already calculated that the kinetic energy from the impact of balls (in a colloid ball mill used by Staudingcr - Vol. II, p. 276) on cellulose fibres should be sufficient to rupture covalent bonds in cellulose such as C-C, C-0. Breaking such bonds requires energy of the order 80 -90 kcal. This statement was substantiated by Swedish authors [18] who found experimentally that the covalent bonds in cellulose, as above, can be ruptured by mechanical action (in an agate ball mill). It has been known since 1895/96. thanks to the work of Bruley (Vol. II, p, 276), that pulping nitrocellulose reduces the viscosity of its solutions, but only now the experimental facts can be explained in terms of breaking the covalent bonds. This was done by T. Urbanski... 

Here the reaction process is one of spontaneous transformation, which requires sufficient energy to be present in the ether molecule to permit the rupture of a carbon-carbon bond. This energy is obviously internal to the molecule and cannot be represented as a translational-energy term. The pertinent question to ask is how a molecule acquires the required energy for the transformation to occur, and the answer lies in a consideration of the energy exchange from external (kinetic) to internal (rotational and vibrational) modes in polyatomic molecules. 

Brittle and tough high polymers like polystyrene and PMMA have high strength and very low extensibility and whereas plastics like polyethylene and plasticised PVC have relatively high extensibility and require much more energy to produce rupture, this energy is represented by the area under the stress-strain curve. 

The following eonsiders a situation that involves all vapor relief. The size of a vapor phase rupture disk required is determined hy assuming that all of the heat energy is absorbed by the vaporization of the liquid. At the set temperature, the heat release rate q is... 

It is estimated that each year approximately 150 million tonnes of nitrogen are fixed biologically compared to 120 million tonnes fixed industrially by the Haber process (p. 421). In both cases N2 is converted to NH3, requiring the rupture of the N=N triple bond which has the highest dissociation energy (945.41 kJmol )... 

Forming the activated complex shown in Figure 11.8 requires the absorption of relatively little energy, because it requires only the weakening of reactant bonds rather than their rupture. 

Feed ratio of OC2H5 TEOS groups to OH chain ends. b Volume fraction of polymer present at swelling equilibrium in benzene at room temperature. c Elongation at initial upturn in modulus. d Ultimate strength as represented by the nominal stress at rupture. Energy required for rupture... 

The activation energy found for the decomposition of an individual oxalate ion in a KBr matrix (270 15 kJ mole-1) [292,294] is regarded as the energy requirement for C—C bond rupture. The generally lower values of E observed for many oxalates ( 165—175 kJ mole-1) are attributed to the facilitation of reaction at the reactant—product interface. 

When describing the effect of an external force, we must first define the force itself. A lay person s definition of a force is the amount of effort to get the desired effect. As scientists, we need a more precise definition of force. With a precise definition we can understand and quantify the effect of an applied force on a polymeric material. The mathematical definition of force is the work (which is a form of energy) required to move an object over some distance. Another way to define a force is in terms of the acceleration it creates when applied to some object of a mass m. In our everyday experiences, the first explanation is a simple idea to relate to. When we push a stalled car we exert a force on it. We could easily quantify the force from the weight of the car, the slope of the hill it is sitting on, and how far we must push it. Once we begin to talk about forces in polymer systems, the ideas become a bit more complicated. For example, the force required to open a bag of candy is defined by the work required to deform the bag until it ruptures by overcoming the intermolecular forces which hold the plastic together. 

When pipe or vessel ruptures are investigated, it is important to know the pressures required to create the damage and ultimately to determine the magnitude and source of energy. 

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