Volume collapse

Things appear to have taken a strange turn We started out discussing the free volume and have ended up with an equation which contains no volume at all More specifically, we set out to examine the rate at which the free volume collapses at Tg. A final development of Eq. (4.63) will produce the desired result. 

Hydrocarbons without bulky side groups are held together by London forces, the weakest of intermolecular attractions. This means that the free volume tends to be large for these compounds, so a relatively large amount of cooUng is necessary before the free volume collapses. Thus Tg is low for these compounds. 

A number of electron-transfer reactions of biological interest have been studied using high-pressure techniques (4, 5). These include the oxidation of L-ascorbic acid by [Fe(CN)6]3- (148), [Fe(CN)5N02]3 - (149), and Fe(phen)2(CN)2] (150). The first two reactions are characterized by volumes of activation of -16 and 10 cm3 mol-1, respectively, which indicate that solvent rearrangement as a result of an increase in electrostriction must account for the volume collapse on going to... 

These arguments were apparently in contradiction with electrochemical results reported by Cruanes et al. (158), according to which the reduction of cytochrome c is accompanied by a volume collapse of 24 cm3 mol-1. This value is so large that it almost represents all of the reaction volume found for the investigated reactions discussed above. A reinvestigation of the electrochemistry of cytochrome c as a function of pressure, using cyclic and differential pulse voltammetric techniques (155), revealed a reaction volume of -14.0 0.5 cm3 mol-1 for the reaction... 

The Mott-like transition, a central concept for the description of the actinide metal series, causes the sudden increase of the atomic volumes, encountered when between Pu and Am (Fig. 3). All other properties indicate the onset of a 5f localized behaviour at Am (see Part V) the 5 f pressure, which had contained to smaller values the equilibrium interactinide distance, suddenly gives in, with the withdrawal of the 5f s within the atomic core. The occurrence of such a transition within a series characterized by an unsaturated shell, is a unique phenomenon of the actinide series. In lanthanides, it does not occur except perhaps under pressure in cerium metal the approaching of cerium atoms induces suddenly the itineracy of 4f orbitals and a sudden volume collapse - see Chap. C. Neither it occurs in d-transition metal series, where the atomic volumes have an almost parabolic behaviour when plotted vs. Z (see Fig. 3 and Chap. C). The current... 

When the itinerant state is formed, a volume collapse AV/V is always encountered, as predicted by the theory of the preceding sections. In one of the lanthanides, cerium, this volume collapse is particularly accentuated for its isostructural transition from the y to the a form, possibly associated with a change in metallic valence from three to four (both oxidation numbers are stable in cerium chemistry) (see Fig. 1 of Chap. A),... 

A small negative volume of activation of-5 1 cm3 mol-1 was measured for the decomposition reaction of - " supporting the suggested mechanism. Most likely the C-C bond formation process, associated with a volume collapse, is the dominant factor in determining the sign of A V in this reaction. (The accompanying stretching of the Cu-C bonds will be associated with a volume increase that will partially offset this volume collapse (108))... 

Several other studies have also been made in an attempt to account theoretically for the phase transition in terms different from those of the Flory-Huggins theory. Otake et al. [55] thus proposed a theoretical model that takes hydrophobic interaction into account in explaining the thermally induced discontinuous volume collapse of hydrogels. In addition, Prausnitz et al. [56] proposed a lattice model, an improvement of which was made to explain the swelling curves of gels consisting of /V,/V -methylenebis(acrylamide) (MBA)-crosslinked copolymers of AAm with [(methacrylamide)propyl]trimethyl-ammonium chloride (MAPTAC) [57],... 

As shown in Fig. 25, the aged glass typically has a lesser volume in the glassy state compared to the as-quenched state. It is obvious from the data that the longer the aging time, the larger is the amount of volume lost due to sub-Tg annealing. This observation also fits well into the free-volume collapse model discussed earlier. 

With an air-quench, the density of the fully-crosslinked epoxy drops from 1.230 to 1.215 gem-3. With sub-Tg annealing, an increase of 0.82% in the resin was observed during the 140 °C aging. This direct piece of evidence agrees perfectly with the free volume collapse model in which the resin densifies. Figure 29 summarizes these observations. 

The asymmetry is easily explained by consideration of the effect of free volume on T. Equilibration at a low temperature produces a low free volume after an increase in temperature, the process of volume dilation is therefore sluggish until the free volume has expanded, and the rate of dilation then accelerates autocatalytically. The reverse occurs after a downward jump in temperature the rate of volume shrinkage slows as the free volume collapses. Similar phenomena occur when the pressure, rather than the temperature, is increased or decreased (Ferry 1980). 

After considering and rejecting other interpretations it was suggested that the mechanism was one in which formation of the transition state involved a coherent, partial C-C bond formation that will be associated with a volume collapse and a stretching of the Cu-C bonds. It was further suggested that the latter process will partially offset the volume collapse, but the C-C bond formation dominates in volume terms, consistent with a modest negative volume of activation. 

Tanaka and his coworkers have used Flory s formula with several modifications to understand a discrete phase transition in ionic gels. First, the term Vo IV in Eq. 3 was replaced by the term

volume fraction of the network on condition that the constituent polymer chains have random-walk configurations [5]. Flory assumed that the dry gel (in other words, the network formed by cross-linking of the unswollen polymer at volume V0) satisfies the condition of no polymer interactions i.e., covalently cross-linked PAAm gels in an acetone-water mixture therefore he claimed that the elastic term is generally not a function simply of V0/V (=[Pg.594]

We have discussed the role of hydrogen bonding and hydrophobic interaction in the volume collapse of NIPA-AAc gels. However, one may claim that the gel system examined would be a special kind of polyelectrolyte gel. Thus we have tired further to examine the effects of both intermolecular forces on the gel transition with another polyelectrolyte gel. 

Urea, being a water structure breaker, would weaken the hydrophobic interaction between solute molecules as reported in several previous studies (see Ref. 76). It is thus necessary for us to examine the effects of urea on the hydrophobic interaction in the present gel system. However, this is a considerably difficult problem which, to our knowledge, has not yet been dealt with by any researchers in the field of polyelectrolyte gels. The main reason is the lack of information about whether hydrophobic interaction plays a role in the volume collapse of usual polyelectrolyte gels with a lot of hydrophilic ionizable groups, such as the LPEI gels in question. As a novel approach in order to overcome this difficulty, we examined the swelling curves of the LPEI gel as a function of the concentration of anionic surfactants in the presence and absence of urea. 

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