Expansion upon heating

The L-taloseptanoside 456 was formed in 74% yield by ring expansion upon heating the dimesyl compound 451 in methanol containing barium carbonate. Participation by the ring sulfur atom and formation of intermediate episulfonium ions 452 and 454, as shown in Scheme 106, has been suggested. The pyranoside 455 was also isolated as minor product (13%). 

This is illustrated by the TMA thermogram of San le H37T15D2, cured 2X at 12 m/min, which is shown in Figure 5. Instead of a monotonic increase in thermal expansion upon heating, the as-cured sample shown in Figure 5(a) exhibits a net decrease in thickness beginning at 27°C and continuing until 90°C. Above 90°C the rate of thermal expansion... 

If a weight is suspended from a rubber band, and the band is then heated (taking care not to burn it), the rubber band will contract appreciably. All materials other than polymers will undergo thermal expansion upon heating (assuming that no phase transformation has occurred over the temperature range). 

By comparing Figure 2.10a to Figure 2.10b, we can estimate the difference in c and Cpfor the different phases of matter. If species A is in the fiquid or solid phase, its volume expansion upon heating should be relatively small that is, the molar volumes of hquids and solids do not change much with temperature. Hence, the piston depicted... 

Thermal Properties. Refractories, like most other soHds, expand upon heating, but much less than most metals. The degree of expansion depends on the chemical composition. A diagram of the thermal expansion of the most common refractories is shown in Figure 1. 

Expansion and contraction of siUca gel monoliths show hysteresis upon heating and cooling. As long as the sample was cycled below approximately 500°C, there was no hysteresis and the monolith was thermally stable (6,23). 

Dioxenes react, as expected, to produce thermally unstable dihalocyclo-propanes in high yield [51, 89]. Upon heating, the bicyclic system rearranges to yield the dichloromethyl-1,4-dioxene, whereas the tricyclic system, derived from the benzo-l,4-dioxene undergoes ring expansion to produce the benzo-1,5-dioxepin (Scheme 7.11). 

All three quantities (V, H and S) show an upward jump at upon heating (apart from pathological liquids such as water as regards V). At Tg there is, however, no jump, so AV = 0, Mi = 0 and A5 = 0, but a bend, or a jump in their first derivatives. For V, H and S this means, respectively, jumps in the coefficient of expansion a, in the specific heat c and in the compressibility k. 

One of the rare examples of an intramolecular ring expansion leading to a 1,3-oxathiane is depicted in Equation (97). The sulfurane precursor 235 thus upon heating rearranged to 1,3-oxathiane 236 <1996JA697>. 

This equation neglects the effects of expansion upon both the heat and the entropy, but the errors largely cancel when combined in Eq. (7). 

Fluorinated dihalocarbenes have been used as central synthons in the synthesis of fluorinated aromatics from cyclopentadienes.62 The reaction proceeds via a fluorinated fused bicyclic cyclopropane, which upon heating undergoes a ring opening to achieve the ring expansion of the second cycle. 

FIGURE 6.23 (See color insert following page 530.) IR images of an intumescent coating on steel plate upon heating at t = 0 s (a) and at the maximum of expansion (b). 

The dicyclopropyl ketimine 198 prepared from the 0,N-cyclopropanone hemiacetal 194 (vide supra, Sect. 4.9, Eq. (62)), heated in xylene with ammonium chloride for 4 hr underwent ring expansion exclusively to the enamine 399 followed by isomerization to the cyclopropyl pyrroline 400. Although further ring expansion was not observed on prolonged heating, 400 was converted to the hydrobromide 401 with anhydrous HBr 2091 which upon heating to 140 °C for 10 min experienced a second cyclopropyl imine rearrangement to provide the pyrrolizidone 403 in 51 % yield, most probably via the HBr adduct 401 by cyclization to the pyrroline 402 followed by acid-induced hydrolysis, Eq. (95) 129). 

Isothermal expansion of an ideal gas Let us consider that a cylinder fitted with a frictionless piston contains a gas and is heated to the system shown in Figure 1.3. Normally, the temperature of the system increases upon heating, but one wants to maintain a constant temperature for the system during this isothermal process. The piston exerts an external pressure on the system, and the gas expands. Since no temperature change takes place, the change in the internal energy is equal to zero (AE = 0) because the internal energy is only a function of temperature. Then, Equation (1.14) becomes ... 

As an amorphous polymer, lignin undergoes chain segment motion upon heating. This motion, a glass transition, is characteristic of all amorphous polymers, and is indicated by an endothermic shift in the DTA or DSC curves. This glass transition is accompanied by abrupt changes in free volume, heat capacity, and thermal expansion coefficient. 

Sol-gel methods are used to prepare a heterogeneous, nanometer composite of calcium zirconium phosphate and strontium zirconium phosphate, Cao.sSro.sZrsOn. In this composite, individual domains both expand and contract upon heating, leading to a material with virtually zero thermal expansion over the range 0-500 °C. 

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