Constant-volume transition

Kato, T., Phase transition behaviors of a main chain liquid crystal and elucidation of constant-volume transition entropy [in Japanese], Master s thesis, Tokyo Institute of Technology, 2002. 

The present examples have provided a useful test for the validity of the hypothetical process adopted conventionally for the estimation of the constant-volume transition entropy. Although the estimation of the yu value using the relation y = a/ rmder ordinary pressure (method 1) is simple, the process should not be excluded because of its simplicity unless a more prevailing form of y(V) is known. 

Estimation of Constant-Volume Transition Entropies at the NI and CN Interphase... 

As comparison of Tables 2 and 4 indicates, the changes in volume and entropy at the NI transition obtained for the mainchain dimer and trimer liquid crystals are much larger than those reported for conventional monomer liquid crystals [112]. In Tables 2 and 3, the constant-volume transition entropies (AStr)v are expressed in terms of joules per mole per kelvin. The conformational entropy changes estimated on the basis of the NMR quadrupolar splitting data observed in the LC state are as follows = 13.3... 

For MBBE-6, the ytr values are also available from method 2 (Sect. 3.2.1). As mentioned in the preceding section, the difference between methods 1 and 2 is quite small except for kcn(N). An increment of 25% in ycN(N) gives rise to a decrease in ( AScn)v by approximately 20% from those listed in colunm 7 of Table 3. As shown in Tables 2 and 3, the experimental values of the latent entropy (AStr)p (column 6) are quite divergent depending on the method PVT or DIA) employed in the measurement. This is also a source of the uncertainties in the final estimates of the constant-volume transition entropy (AStr)v (column 7). 

Constant-volume transition entropy RIS/ H NMR analysis Segmented LC... 

Comparison with the Constant-Volume Transition Entropy. 117... 

Just as one may wish to specify the temperature in a molecular dynamics simulation, so may be desired to maintain the system at a constant pressure. This enables the behavior of the system to be explored as a function of the pressure, enabling one to study phenomer such as the onset of pressure-induced phase transitions. Many experimental measuremen are made under conditions of constant temperature and pressure, and so simulations in tl isothermal-isobaric ensemble are most directly relevant to experimental data. Certai structural rearrangements may be achieved more easily in an isobaric simulation than i a simulation at constant volume. Constant pressure conditions may also be importai when the number of particles in the system changes (as in some of the test particle methoc for calculating free energies and chemical potentials see Section 8.9). 

The standard entropy difference between the reactant(s) of a reaction and the activated complex of the transition state, at the same temperature and pressure. Entropy of activation is symbolized by either A5 or and is equal to (A// - AG )IT where A// is the enthalpy of activation, AG is the Gibbs free energy of activation, and T is the absolute temperature (provided that all rate constants other than first-order are expressed in temperature-independent concentration units such as molarity). Technically, this quantity is the entropy of activation at constant pressure, and from this value, the entropy of activation at constant volume can be deduced. See Transition-State Theory (Thermodynamics) Gibbs Free Energy of Activation Enthalpy of Activation Volume of Activation Entropy and Enthalpy of Activation (Enzymatic)... 

The transition at 19° C involves an expansion of 0.0058 cm3/g (Clark and Muus). Sincethe transition temperatureincreaseswith pressure by about 0.013° C per atmosphere (Beecroft and Swenson), the latent heat is about 3.2 cal/g. These values are for the crystal and would be reduced in proportion to the crystalline content. The transition at 30° C is only about one-tenth as large. The over-all increase in entropy at these transitions is about 0.0108 cal deg-1g-1. The portion due to the increase in volume is (a// ) A V, where a is the volumetric coefficient of thermal expansion and / is the compressibility. Since the compressibility of the crystal is not known, this quantity is somewhat uncertain. Using the average of the values of a (Quinn, Roberts, and Work) and p (Weir, 1951) for the whole polymer above and below the transitions, it appears that (a/P)A V is about 0.0041 cal deg 1g 1. The entropy of the transition corrected to constant volume is, therefore, about 0.0067 cal deg g-1. 

At high temperature, TTF TCNQ is metallic, with a(T) oc T-2 3 since TTF TCNQ has a fairly high coefficient of thermal expansion, a more meaningful quantity to consider is the conductivity at constant volume phonon scattering processes are dominant. A CDW starts at about 160K on the TCNQ stacks at 54 K, CDW s on different TCNQ chains couple at 49 K a CDW starts on the TTF stacks, and by 38 K a full Peierls transition is seen. At TP the TTF molecules slip by only about 0.034 A along their long molecular axis. 

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