Expansion/contraction

Ring Expansion/Contraction via Sigrnatropic Rearrangements - Cope Rearrangement... 

Table 10-56 gives values for the modulus of elasticity for nonmetals however, no specific stress-limiting criteria or methods of stress analysis are presented. Stress-strain behavior of most nonmetals differs considerably from that of metals and is less well-defined for mathematic analysis. The piping system should be designed and laid out so that flexural stresses resulting from displacement due to expansion, contraction, and other movement are minimized. This concept requires special attention to supports, terminals, and other restraints. 

Actual system heat loss (or gain) will normally exceed calculated values because of projertions, axial and longitudinal seams, expansion-contraction openings, moisture, workers skill, and physical abuse. 

The selection of a sampling site and the number of sampling points required are based on attempts to get representative samples. To accomplish this, the samphng site should be at least eight stack or duel diameters downstream and two diameters upstream from any flow disturbance, such as a bend, expansion, contraction, valve, fitting, or visible flame. 

From point of any of type of disturbance (bend, expansion, contraction, etc.)... 

Number of velocity heads for fittings, expansions, contractions, and bends... 

To minimize the stresses induced by differential thermal expansion/contraction one must (1) employ fastening techniques that allow relative movement between the component parts of the composite structure, (2) minimize the difference in coefficient of linear thermal expansion between the materials... 

Some manufacturers of this type of boiler claim that water treatment of any kind is not necessary and that no chemicals are required, especially with smaller units below, say, 240 kWh (800 lb/hr). Instead they rely on the on-off expansion-contraction cycles within the vessel to drop scale from the heating elements, or on a daily manual flush of the boiler vessel together with frequent replacement of elements and periodic acid cleaning. (Some improved design models thankfully have an automatic flush system that is actuated upon boiler shutdown.)... 

S. Talabani and G. Hareland. Expansion-contraction cycles for cement optimized as a function of additives. In Proceedings Volume, pages 277-284. SPE Prod Oper Symp (Oklahoma City, OK, 4/2-474), 1995. 

On the carbons, nitrogens and oxygens expansions up to octapole level were introduced, whereas the expansions were limited to quadrupole level for the hydrogen atoms. All atoms were given a k expansion/contraction parameter for the spherical monopole term, and all atoms except the hydrogens were given k parameters to expand or contract the non-spherical poles. The k and k values on 0(1) and 0(3), on N(l) and N(3), on C(l) and C(3) and on 0(21) and 0(22) were constrained to be equal. 

One of the more recently exploited forms of thermal analysis is the group of techniques known as thermomechanical analysis (TMA). These techniques are based on the measurement of mechanical properties such as expansion, contraction, extension or penetration of materials as a function of temperature. TMA curves obtained in this way are characteristic of the sample. The technique has obvious practical value in the study and assessment of the mechanical properties of materials. Measurements over the temperature range - 100°C to 1000°C may be made. Figure 11.19 shows a study of a polymeric material based upon linear expansion measurements. 

Laminate expansion/contraction characteristics were determined with a DuPont Model 942 TMA. In this test the movement of an 0.38 cm diameter, hemispherical-tipped quartz probe resting on the specimen was monitored as the specimen was heated from room temperature through its softening range. 

Are provisions made for expansion, contraction, jarring, vibration, and settling ... 

More recently, the same principle was applied by the same authors to cyclic alkanes for catalytic ring expansion, contraction and metathesis-polymerization (Scheme 13.24) [44]. By using the tandem dehydrogenation-olefin metathesis system shown in Scheme 13.23, it was possible to achieve a metathesis-cyclooligomerization of COA and cyclodecane (CDA). This afforded cycloalkanes with different carbon numbers, predominantly multiples of the substrate carbon number the major products were dimers, with successively smaller proportions of higher cyclo-oligomers and polymers. 

Dilatometric methods. This can be a sensitive method and relies on the different phases taking part in the phase transformation having different coefficients of thermal expansion. The expansion/contraction of a sample is then measured by a dilatometer. Cahn et al. (1987) used dilatometry to examine the order-disorder transformation in a number of alloys in the Ni-Al-Fe system. Figure 4.9 shows an expansion vs temperature plot for a (Ni79.9Al2o.i)o.s7Feo.i3 alloy where a transition from an ordered LI2 compound (7 ) to a two-phase mixture of 7 and a Ni-rich f c.c. Al phase (7) occurs. The method was then used to determine the 7 /(7 + 7O phase boundary as a function of Fe content, at a constant Ni/Al ratio, and the results are shown in Fig. 4.10. The technique has been used on numerous other occasions,... 

External plasticizers are not permanent. Plasticizer molecules associate with one another eventually creating preferred migration routes to the material s surface where the plasticizer is rubbed or washed away. The preferential association of plasticizers also leaves some sites less flexible and creates variations in the material s stress-strain and expansion-contraction behaviors. 

Kricheldorf HR, Lee S-R, Schittenhehn N (1998) Macrocyclic polymerization of (thio) lactones - stepwise ring expansion contraction. Macromol Chem Phys 199 273-282... 

To preserve the shell structure of the spherical component of the valence density, the radial function of the bonded atom may be described by the isolated atom radial dependence, modified by the k expansion-contraction parameter. 

The nature of the charge density parameters to be added to those of the structure refinement follows from the charge density formalisms discussed in chapter 3. For the atom-centered multipole formalism as defined in Eq. (3.35), they are the valence shell populations, PLval, and the populations PUmp of the multipolar density functions on each of the atoms, and the k expansion-contraction parameters for... 

---