Expansion mechanism

Lines or equipment which can be left full of liquid under non-flow conditions and which can be heated while completely blocked-in must have some means of relieving pressure built up by thermal expansion of the contained liquid. Solar radiation, as well as other heat sources, must be considered. Lines or equipment which are hotter than ambient when blocked in and which cannot otherwise be heated above the blocked-in temperature do not need protection against liquid thermal expansion. The following are common examples of some thermal expansion mechanisms. 

Plasticization has been explained by a variety of theories in an attempt to explain how the plasticizer reduces the rigidity of the final part. All theories rely on the premise that the plasticizer reduces the strength of the intermolecular forces between the polymer chains. The theories fall into two broad categories interference mechanisms and expansion mechanisms. The interference mechanisms state that plasticizer molecules interact only weakly with the polymer chains after separating the chains from one another, thereby reducing the overall cohesion of the material. The expansion mechanisms state that the reduced rigidity arises from an increase in the free volume of the system as the system expands to incorporate bulky,... 

The unexpected variety found in cationic polymerizations is well illustrated by recent findings concerning the polymerization of dioxolan by perchloric acid. Gresham91 had been unable to find end-groups in polydioxolans made under anhydrous conditions and concluded that they were cyclic. His result has been confirmed by studies made with anhydrous perchloric acid as catalyst [92]. Since it is extremely unlikely that complete absence of chain ends can be achieved by a cyclization of long chains, and from other evidence, we concluded that the polymerization takes place without formation of chain ends, i.e. by a ring expansion mechanism ... 

The propagation for cyclic formals also involves a solvated oxonium ion and a highly polar monomer [10, 12]. Since under optimum conditions the polymers are essentially free from any kind of end-group (except very small amounts of -OH) Plesch and Westermann [36, 37] concluded that they must be formed by a ring-expansion mechanism, involving a 4-centred transition state ... 

Since the carboxonium ion has been eliminated as a possible propagating species, one is left with two alternatives which we may call the Keele and the Mainz theories. Plesch and Westermann [6, 8] have suggested that the cyclic formals polymerise by a ring-expansion mechanism, in which no free end is ever formed. This is illustrated in Reaction (B), where Y = H if the initiator is a protonic acid, and Y = Et if the initiator is a... 

The ring expansion mechanism is of course only a special case of the well-known mechanism by which dioxolan reacts with non-cyclic formals e.g., (I) and CH2-(OMe)2 give (MeOCH2OCH2-)2 in this way. It also accounts in a simple manner for the cleanness of the monomer-polymer equilibrium and for the high yields of cyclic dimer (without any detectable linear fragments) which are obtainable from 1,3-dioxane and 1,3-dioxepan [8]. 

It follows that when the water content of the reaction mixtures is less than ca. 10 4 M the propagation is principally by secondary oxonium ions, and that it must therefore go by the ring-expansion mechanism of Plesch and Westermann. 

Since most types of experimental inadequacy or incompetence produce more ethanol in the hydrolysate than could be derived from fert.-oxonium ions, one must conclude from this evidence that the propagating species is a secondary oxonium ion. It follows necessarily that the ring-expansion mechanism is the best representation of the propagation reaction, that tert.-oxonium ions do not play an essential role in the polymerisation of DCA by perchloric acid, and that therefore this part of the old controversy appears now to be settled. 

The present author holds the view that since the number of end-groups is always much smaller than the number of polymer molecules, a ring-expansion mechanism, analogous to reaction (4), is the most plausible. This matter will be discussed in Section 5. 

Thus, when one looks sufficiently critically at the ideas currently under discussion one finds that there appears to be no good reason for discarding the conventional tert.-oxonium ion as the propagating species, and that the only clearly identifiable problem is whether propagation through these conventional tert.-oxonium ions goes by the Jaacks mechanism or by the ring-expansion mechanism. This is a difficult matter to resolve experimentally because the direct discrimination between the microcyclic ions (II), (VIII), and (IX) on the one hand and the macrocyclic ion (V) on the other, requires subtle and sensitive techniques. 

As far as the polymerisations of DCA other than DXL by non-protonic initiators are concerned, Kops and Spanggaard [11] favour the ring expansion mechanism for the dimerisation and polymerisation of the cis- and tnms-7,9-dioxabicyclo[4.3.0] nonanes by phosphorus pentafluoride or triethyloxonium hexachloroantimonate, although they have not obtained any definitive evidence for it. 

All this evidence taken together indicates very strongly that the two types of monomers polymerise by different mechanisms. Whilst this conclusion does not necessarily support the ring-expansion mechanism for the DCA, it makes the propagation via the microcyclic tert.-oxonium ion (XIV) appear very unlikely. 

The volume increase is in turn due to the thermal expansion mechanism referred to above. It can be quantified by equation 13.2,... 

It is indubitable that in mechanically undisturbed wind flow the expansion mechanism is always the same, merely the boundary conditions at ground level are more obvious for the tested emission heights. The dilution factor after 60m is about 2-104 at a wind speed of 2, 5m/s. 

The thermal conductivity, thermal expansion, mechanical properties at low strain rates and dynamic mechanical properties of a collection of crosslinked closed cell PE foams manufactured by a high pressure nitrogen solution process were studied as a function of the cell size. The... 

The expansion mechanism associated with the formation of ettringite in cement is not clear and several hypotheses have been advanced [77]. A... 

The authors propose that the dimers are formed by a ring-expansion mechanism comparable to the polymerization mechanism for cyclic acetals proposed by Plesch... 

Cohen (C55) reviewed theories of the expansion mechanism. Probably a majority of workers (e.g. Refs I9,I10,O16,O24,BI33) have attributed expansion to forces exerted by the growth of the ettringite crystals. Of other theories, the most significant is that proposed by Mehta (MlOO). who attributed it to imbibition of water by the gelatinous layer of colloidal ettringite. On this hypothesis, expansion does not occur with the larger crystals formed at low CaO concentrations because these do not form... 

Figure 1.17. Successive stages of the breakaway of a liquid drop from the orifice of a stalagmometer. Details of the process depend on the dynamics of the surface expansion, mechanical vibrations and oscillations. The little additional drop in the last sketch is called a satellite. Sometimes there are more of these.

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