Entropy increase with temperature molecular

Eq. (13.37) shows that the modulus of a rubber increases with temperature this is in contrast with the behaviour of polymers that are not cross-linked. The reason of this behaviour is that rubber elasticity is an entropy elasticity in contrast with the energy elasticity in "normal" solids the modulus increases with temperature because of the increased thermal or Brownian motion, which causes the stretched molecular segments to tug at their "anchor points" and try to assume a more probable coiled-up shape. 

Vf is a measure of the space available for the polymer to undergo rotation and translation, and when the polymer is in the liquid and rubber-like states the amount of free volume will increase with temperature as the molecular motion increases. If the viscous polymer is cooled this free volume will contract and eventually reach a critical value where there is insufficient free space to allow large scale segmental motion to take place. Tg is the temperature at which this critical value is reached. A third view of the Tg is that it represents an isoentropic (same entropy) state. 

Here we have the formation of the activated complex from five molecules of nitric acid, previously free, with a high negative entropy change. The concentration of molecular aggregates needed might increase with a fall in temperature in agreement with the characteristics of the reaction already described. It should be noticed that nitration in nitromethane shows the more common type of temperature-dependence (fig. 3.1). 

The high specific heat of water is connected with these changes. By the thermodynamic equation, AS = qn T (when S is the entropy and qn the amount of heat added reversibly at temperature, T), the high specific heat implies that, when water is heated over a given range of temperature, the increase in its entropy is greater than it would be for a normal liquid. The anomalous entropy increase is due to the unusual increase of molecular disorder. 

Standard molar entropies make it possible to compare the entropies of different substances under the same conditions of temperature and pressure. It s apparent from Table 17.1, for example, that the entropies of gaseous substances tend to be larger than those of liquids, which, in turn, tend to be larger than those of solids. Table 17.1 also shows that S° values increase with increasing molecular complexity. Compare, for example, CH3OH, which has S° = 127 J/(K mol), to CH3CH2OH, which has S° = 161 J/(K mol). 

One expects a significant amount of both the native and denatured protein structure in the vicinity of these two temperatures. The disruption of the native state on heating is usually called heat denaturation, since it proceeds with heat absorption and, consequently, with an increase in the molecular enthalpy and entropy. The disruption of the native structure on cooling, which we can call by analogy cold denaturation, should then proceed with a release of heat and, hence, with a decrease in enthalpy and entropy, because both of these functions have reversed their signs before reaching temperature 7 en. ... 

So far the micro-mechanical origin of the Mullins effect is not totally understood [26, 36, 61]. Beside the action of the entropy elastic polymer network that is quite well understood on a molecular-statistical basis [24, 62], the impact of filler particles on stress-strain properties is of high importance. On the one hand the addition of hard filler particles leads to a stiffening of the rubber matrix that can be described by a hydrodynamic strain amplification factor [22, 63-65]. On the other, the constraints introduced into the system by filler-polymer bonds result in a decreased network entropy. Accordingly, the free energy that equals the negative entropy times the temperature increases linear with the effective number of network junctions [64-67]. A further effect is obtained from the formation of filler clusters or a... 

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