General Experimental Observations

However, water dramatically enhances Diels-Alder rates because the hydrophobic effect brings the two reactants together (for a further discussion see the Going Deeper highlight on page 923). Since four sp- centers are being converted to sp centers, inverse kinetic isotope effects are the norm. Lastly, because two reactants combine to create a product that is smaller in volume than the separate reactants, high pressure will facilitate cycloadditions. 

Another common strategy to facilitate the reaction is to incorporate the diene into a ring, thereby favoring the s-cis geometry required for reaction. The s-cis geometry is required in the cycloaddition for the dienophile to reach both ends of the diene (see margin). 

When the crystallization is conducted over the complete accessible temperature range, i.e. from below the melting temperature to above the glass temperature, a more complex temperature dependence evolves. A typical example is given in Fig. 9.6 for natural rubber.(19) Here the time taken for half of the crystallization to develop is plotted as a function of the crystallization temperature. Many other homopolymers behave in a similar manner. This type of temperature dependence is not restricted to long chain polymers. It is also observed during the crystallization 

Studies of the rates of spherulite formation and growth in thin films have provided important information about the crystallization kinetics of polymers. In the vicinity of the melting temperature, the rate at which spherulites are formed depends very strongly on the crystallization temperature and increases very rapidly 

As the crystallization temperature is lowered the growth rate increases until a maximum is observed. With a further decrease in the temperature, the rate of growth diminishes. The temperature variation of the spherulitic growth rate is thus qualitatively similar to the temperature coefficient of the overall rate of 

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The stage was now set for the 1913 papers published independently by Fajans (1913b) and by Soddy (1913a). The paper by Fajans was published a couple of weeks prior to that by Soddy. Soddy has stated that he had not seen the Fajans paper at the time when he wrote his paper. Both papers try to generalize experimental observations on the chemical identities of decay products in the three natural radioactive decay series. 

The inverse proportionality of Acp with Tg constitutes a general experimental observation for thermosetting polymers, and leads to X < 1, which is a necessary condition to obtain an upward curvature in the Tg vs x function defined by Eq. (4.10). Low values of X are typical of large (Tgoo-Tg0) values. 

The polymerization is kinetically controlled up to the vitrification time, for every cure temperature. Moreover, as in this range of temperatures, gelation arrives before vitrification, the passage through the gel point does not have any influence on the reaction rate this is a general experimental observation for stepwise polymerizations. After vitrification, a significant decrease in the reaction rate occurs, leading to the observed departure of experimental curves from the master curve. 

For any specified drying condition, the calculated water contents arc lower and the porosities higher than those of pure Portland cement pastes, and this appears to be true in varying degrees of composite cements in general. Experimental observations support this conclusion. Non-evapor-able water contents of 2-year-old pastes of w/s ratio 0.5 typically decrease with slag content from around 23% for pure Portland cements to 10 13" for cements with 90% of slag (C42). For the paste to which Table 9.4 refers, the observed non-evaporable water content was 17.7% (H49). Porosities and their relations to physical properties are discussed in Section 9.7. 

In conclusion, both the Graessley and Bueche theories confirm the general experimental observation that the reduced solution viscosity, ti/Doj function of X. Therefore, solution rheological behavior can be described by two material parameters, the zero shear viscosity and polymer response time. In turn, these parameters are functions of macromolecular structure and solvent properties. 

The general experimental observations are that the neutral complexes of Ti -CgRg, and Ti -CgHg are highly fluxional, but those of Ti -CgRg,... 

Three different areas can be defined on this diagram. In area I, the cyclopropanone is more stable than the zwitterion. Theoretically—and this is generally experimentally observed—one should only obtain rearrangement products. However this area corresponds to open-chain a-haloketones, and it is not possible to exclude cyclopropanone formation by a direct intramolecular S 2 reaction, or to rule out substitution processes involving Sy 2 mechanisms. 

Conversely, the problem of the infinite summation can be overcome by rewriting Eq. 10.44 in a time-dependent formulation. The basic idea is to switch from the frequency domain to the time domain by exploiting the properties of the Fourier transform of the delta function. After some mathematical manipulation, the general experimental observable can be rewritten as the Fourier transform of a time-dependent function, the transition dipole moment autocorrelation function. 

Thin films introduce one-dimensional (ID) spatial confinement of polymers and concomitantly affect their crystallization behavior. When the polymer is confined in a ID reduced environment, the formation of crystal nuclei will be drastically affected (especially at higher temperatures). Also, the preferential orientation of polymer crystals will also be influenced by confinement, a phenomenon that has been studied [18, 282-298]. In general, experimental observations regarding the effects of film thickness can be classified into several categories ... 

Since internal energy and entropy come from the two fundamental postulates of thermodynamics—that energy is conserved (First law) and that entropy of the universe always increases (Second law)—we call them fundamental properties. These properties cannot be measured directly. In fact, it could be said that these are not real things (at least in the measurable sense) but rather constmcts of our mind to generalize experimental observations. 

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