Phase transition temperatures dimers

With regards to the repulsive case, the model adsorption isotherm reproduces the MC data fairly well for w/keT. The discrepancy in the case w/kal links to the order-disorder phase transitions that dimers develop on a square lattice at w/kBTe w3, 6c =l/2 and w/kaTc 5, 0c =2/3 (see ref. [5]). These transitions can not be reproduced by the approximation (mean field) used in eq. (8). As it is clear from Figure 2, the simulated isotherm for w/keT=4 display a plateau (characteristic of an ordered phase) at 6=>l/2 since w/kBTc <4. However, only a knee around 0=2/3 is visible at this temperature because w/ksTc 4. A deeper discussion of the referred phase transitions can be found in ref. [5]. 

To investigate the effect of adding monomeric and dimeric CD on the change of phase transition temperature of the polymers P18 and P19, we performed turbidity measurements at the same polymer concentration as above in the presence of a defined amount of Me-P-CD and CD dimer, respectively (Fig. 25 a,b) [61,62], As reported previously [56-59], we found that addition of Me-p-CD led to cloud points of polymers P18 and P19 of 32°C, which correlates to the LCST of pure poly(NIPAAM). This increase of the cloud points relative to the cloud points of pure P18 and P19 results from the inclusion of the hydrophobic adamantyl units by Me-P-CD. 

Figure 21. Relative content of cyclic dimers (x), open associates (A), and monomers (O) in different phase states of the 7AOBA ( , ) are the data for dilution of the 7AOBA in CCI4. The vertical dashed lines correspond to the phase transition temperatures. (From Ref. 57.)...

Similar experiments performed at higher CTAB concentrations near the phase transition from isotropic solution to lyotropic liquid crystals show that the phase transition temperature is affected by the presence of rheologically active compounds (155,161). Figure 13 demonstrates that the phase transition temperature increases when small amounts of 9-anthracene carboxylic acid are solubilized. Irradiation at X = 366 nm, i.e. photodimerization, removes the effect, and reirradiation at X = 254 nm (splitting of the dimers) causes a reincrease of the phase transition temperature. 

There are few examples of liquid crystalline primary amides of carboxylic acids (e.g. 25 [246], further [247]). The unusually high transition temperatures of these compounds (two ring Schiff bases usually have a phase transition temperature below 100 C) are due to the formation of dimers. 

In the C4H8O2 case the metal-insulator phase transition seems to originate from structural modihcations as a function of temperature. Dimerization would explain such a transition because of the induced opening of the gap. 

An exception to the rule that lowering the Iciiiperaiure cutises transitions to phases with increased order sometimes occurs for polar compounds w hich form the smectic l. phase (a layered structure formed by molecular dimers). Decreasing the temperature cutises u transition front nematic to smectic. 1,.,. but a further lowering of the temperature produces J transition back to the nematic phase tcalled the reentrant nematic phase). Electric or magnetic fields also may induce mesomorphic phase transitions. 

Peierls showed 74 [41,42] that an instability in a one-dimensional chain, with one electron per site, driven by electron-phonon interactions, can lead to a subtle structural distortion and to a first-order Peierls phase transition, at and below a finite temperature TP (the Peierls temperature) [42], For instance, at and below Tp either a dimerization into two sets of unequal interparticle distances d and d" (such that d + d" = 2d) or some other structural distortion must occur. The electronic energy of the metallic chain may also be lowered by the formation of a charge-density wave (CDW) of amplitude p(x) ... 

The temperature dependences of optical properties of organic conductors beyond the phase-transition region have not been investigated sufficiently so far. The quantitative temperature studies of the e-mv coupling are very difficult and possible only for some selected low-dimensional salts. It was shown [94,95] that an analysis of T dependence of the IR spectra of the salts composed of isolated dimers (TCNQ)2- makes it possible to pinpoint the main mechanisms responsible for thermal evolution of the IR spectra and changes in the absorption coefficients. Among other things it was... 

Recently, the spectral study of DMTM(TCNQ)2 phase transition was performed [60]. The salt is a quarter-filled organic semiconductor containing segregated chains of TCNQ dimers and DMTM counterions. This material undergoes an inverted Peierls transition, which has tentatively been explained in terms of a crystal-field distortion. It was shown that the experimental values of unperturbed phonon frequencies and e-mv coupling constants are nearly independent of temperature. The dimer model fails to reproduce the phonon intensities and line shapes and underestimates the coupling constants, whereas the CDW model produces better results... 

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