Temperature molecular interpretation

The molecular interpretation of this result is as follows above the glass temperature T0 the molecular segments are in vigorous motion and change their positions frequently. Hence, the average nuclear spin interaction is reduced to a minimum. This causes a narrow absorption line. As the kinetic motion of the molecules is decreased by cooling, the frequency of position changes is reduced, and... 

Equation (16-2) allows the calculations of changes in the entropy of a substance, specifically by measuring the heat capacities at different temperatures and the enthalpies of phase changes. If the absolute value of the entropy were known at any one temperature, the measurements of changes in entropy in going from that temperature to another temperature would allow the determination of the absolute value of the entropy at the other temperature. The third law of thermodynamics provides the basis for establishing absolute entropies. The law states that the entropy of any perfect crystal is zero (0) at the temperature of absolute zero (OK or -273.15°C). This is understandable in terms of the molecular interpretation of entropy. In a perfect crystal, every atom is fixed in position, and, at absolute zero, every form of internal energy (such as atomic vibrations) has its lowest possible value. 

It is therefore remarkable that 100 years or so before the laws of thermodynamics were formulated, Daniel Bernoulli developed a billiard ball model of a gas that gave a molecular interpretation to pressure and was later extended to give an understanding of temperature. This is truly a wonderful thing, because all it starts with is the assumption that the atoms or molecules of a gas can be treated as if they behave like perfectly elastic hard spheres—minute and perfect billiard balls. Then Newton s laws of motion are applied and all the gas laws follow, together with a molecular interpretation of temperature and absolute zero. You have no doubt... 

So, a simple approach based on Newton s laws of motion gives us the gas laws, a molecular interpretation of pressure and temperature and a definition of the absolute temperature. This is truly a remarkable achievement and a thing of beauty. 

Aqueous solutions of poly(ethylene oxide), (-CH20CH2-)m (PEO) exhibit unusual phase behavior in the sense that the polymer is soluble in water at room temperature, but phase separates at higher temperatures. Molecular interpretations of this unusual behavior implicate the effect of hydration on the conformational equilibria of the polymer chains based on studies of conforma-honal equilibria of small-molecule analogs of PEO e.g., 1,2 dimethoxyethane (DME), CH3OCH2CH2OCH3. Note that DME conformations are characterized by three consecutive dihedral angles centered on the 0-C, C-C, and C-0 bonds along the chain backbone, which can be found in the trans t, 180°),... 

Sbhnel and Mullin, Garside and recently Barlow and Haymet have discussed the molecular Interpretation of induction times from the standpoint of classical nucleation theory. Crystal nuclei with a critical size must be formed before the new solid phase is visible. According to the model there exists a free energy barrier, AG to the formation of the crystal nuclei. AG is proportional to (InS), where S is the supersaturation ratio. The Gibb s free energy, AG of the supersaturated solution is equal to -RTlnS (R=gas constant T=temperature). The induction time is a function of AG and thus AG according to the following equation... 

Interfacial tensions of fluid-fluid interfaces are well-defined system properties, and measurable by a variety of methods. It may be stated that interfacial tensions are the prime characteristics of phase boundaries. They must have their roots in the molecular interactions and distributions in the interface. No wonder that over almost two centuries attempts have been made to establish such molecular interpretations. At present the situation is such that no generally valid theory is quantitatively available to interpret interfacial tensions of all liquids at all temperatures between the melting point and the critical point. 

The statement that the decreased solubility with Increasing temperature is caused by decreased hydration is a tautology and begs for a molecular interpretation. Not only are PEO-water Interactions Involved, those internally between PEG... 

Figure 12-10 A molecular interpretation of Boyle s Law— the change in pressure of a gas with changes in volume (at constant temperature). The entire apparatus is enclosed in a vacuum. 

Figure 12-12 A molecular interpretation of Charles s Law—the change in volume of a gas with changes in temperature (at constant pressure). At the lower temperature, molecules strike the walls less often and less vigorously. Thus, the volume must be less to maintain the same pressure.

Figure 12-15 A molecular interpretation of deviations from ideal behavior, (a) A sample of gas at a low temperature. Each sphere represents a molecule. Because of their low kinetic energies, attractive forces between molecules can now cause a few molecules to stick together. (b) A sample of gas under high pressure. The molecules are quite close together. The free volume is now a much smaller fraction of the total volume.

The effectiveness of Wilson s model lies in the fact that only two parameters are required to describe the Gibbs energy at a given temperature. Its weakness lies in the fact that there is no clear molecular interpretation of these parameters. Wilson s approach works for a great variety of systems but when the departures from ideality are complex, more detailed models are required. Some extensions of Wilson s work have been discussed by Renon and Prausnitz [8] but they require introduction of more adjustable parameters. 

There are also some ongoing efforts to provide molecular interpretations, and predictive capabilities derived from such interpretations, for the glass transition temperature and other important physical properties of crosslinked polymers. See the work of Chow [137-139] for an example of such efforts which have, so far, shown only very limited success. 

The molecular interpretation of thermodynamic data of temperature and pressure effects on proteins and their reactions is based on the data obtained from small molar mass model compounds in water. Weber and Drickamer [75] have pointed out the role of mechanical effects on the volume of association of molecular complexes by introducing molecular spacers that prevent molecules to get in close contact. As can be seen from Table 2, these mechanical effects can show up considerably in the volume changes, ft is clear that such effects should also influence hydrophobic interactions in proteins. 

According to the kinetic molecular theory, gas pressure is the result of collisions between molecules and the walls of their container. It depends on the frequency of collision per unit area and on how hard the molecules strike the wall. The theory also provides a molecular interpretation of temperature. According to Equation (5.11), the absolute temperature of a gas is a measure of the average kinetic energy of the molecules. In other words, the absolute temperature is an index of the random motion of the molecules—the higher the temperature, the more energetic the molecules. Because it is related to the temperature of the gas sample, random molecular motion is sometimes referred to as thermal motion. 

We now briefly discuss the molecular interpretation of the behavior exhibited by polymers that are held at constant temperature and studied as a function of time in a stress relaxation experiment covering the entire time scale (possibly 14 decades, or more). 

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