Thermodynamics order

TNC.75. G. Dewel, D. Kondepudi, and I. Prigogine, Chemistry far from equilibrium—Thermodynamics, Order and Chaos, New Chemistry, 1997. 

As has been discussed by Hsich [12, 13], any chemical relaxation (reaction) or structural relaxation can be explained from irreversible thermodynamic fluctuation theory in which changes of physical and mechanical properties during the relaxation process can be interpreted and predicted from the mean square fluctuations of thermodynamic ordering parameters. Then the physical or mechanical properties at any given cure time can be written as a relaxation function ... 

Finally, solid films of some polysilylenes exhibit thermochromism and undergo true thermodynamic order-disorder phase transitions at much higher temperatures 18, 19, 47, 48) than in solution (typically, Tq 40-80 °C). In the context of the theory, a larger refractive index of the neat solid compared with that of the dilute solution results in a higher predicted Tq 21). However, we do not believe that the observed high TqS in films can be explained solely by this effect. Previous explanations have been made exclusively in terms of side-chain crystallization 18, 19, 48). Packing effects should be more important in the solid state, but both intramolecular and intermolecular packing effects must be carefully considered. Indeed, the fact... 

The smectic state, apart from exhibiting a rich variety of modifications, is also thermodynamically ordered. Thus, there is a well-defined sequence of phases formed on cooling from the isotropic liquid. For instance, the following transition sequence would be observed for a ferrocene liquid crystal exhibiting enantiotropic smectic C, smectic A and nematic phases ... 

Twenty-one Raman-active modes are expected in A2 a and 48 Raman-active modes in P2 a. The mode at 455 cm is Raman inactive in the high symmetry phase. From the thermal evolution of its scattering intensity (Fig. 7) we find that the low-temperature values extrapolate to zero at 496 K. At higher temperatures, strong scattering intensity persists and decreases linearly with increasing temperature. The extrapolated scattering intensity vanishes at the y- 3 transition point near 825 K. At T < 496 K the quantitative relationship between the intensity and the thermodynamic order parameter Q for the P - a transition is described by... 

These workers also note that carbon nucleophiles are more reactive toward carbon (SN2) than toward hydrogen (E2). A calculation of carbon basicities places carbon on top of the thermodynamic order (C- > N , S >... 

Some people prefer to use the multiple time step approach to handle fast degrees of freedom, while others prefer to use constraints, and there are situations in which both techniques are applicable. Constraints also find an application in the study of rare events, where a system may be studied at the top of a free energy barrier (see later), or for convenience when it is desired to fix a thermodynamic order parameter or ordering direction... 

The nature and number of any mesophases that are formed by a given material, and the temperatures at which they exist must be determined experimentally. This requires recourse to a selection of physical techniques, some of which are described below. However, it is helpful to know that, in most cases, the thermodynamic ordering of the various (fluid) mesophases maintains a fairly constant order that is given in Scheme 1 (although note that out-of-sequence or re-entrant phases are known).It is rather unlikely that a single material will show all of these phases and it is found empirically that certain combinations are more likely than others. ... 

Scheme 1 Normal thermodynamic ordering of liquid-crystal mesophases.

Dewel, Guy, DUip Kondepudi, and Ilya Prigogine. Chemistry Far from Equilibrium Thermodynamics, Order, and Chaos. In The New Chemistry, edited by Nona Hall, 440-446. Cambridge Cambridge University Press (2000). This chapter describes the mathematics of systems far removed fi-om equihbrium and the chemical consequences. 

Second Law of Thermodynamics order that we are dealing really with a maximum. Thus,... 

Another useful tool used in conjunction with identification of liquid crystals by microscopy is a listing of the thermodynamic ordering of mesophases. For calamitic smectic phases this ordering is ... 

Phase transitions can also be classified by their thermodynamic order , which is the order of the derivative of the Gibbs free energy. In the present book we are mainly interested in pressure-induced transformations, which involve a discontinuous change of volume, i.e. first-order phase transitions. In second-order phase transitions the second derivative of the Gibbs free energy with respect to volume, which is proportional to the compressibility, is discontinuous. Experimentally it can be very difficult to distinguish between a second-order phase transition and a weakly first-order one. 

This phenomenon can also lead to an effect known as re-entrant behavior. Thus, there is an accepted thermodynamic ordering of liquid crystal phases, which is shown in 1 for the phases considered so far ... 

The voltage of an electrochemical cell is a thermodynamic order of magnitude it is the difference in potential which is established, with a current of strictly zero, between the two electrodes. The absolute value (i.e. regardless of the sign) is called the electromotive force of the cell (eml) and... 

As will be detailed in the following, there are two important questions about these phase diagrams the existence and location of critical or triple points, and the thermodynamic order of the phase transitions, especially for the liquid-solid equilibrium. Following the pioneering work of Thorny and Duval [37], many investigations of phase transitions occiuring in physisorbed monolayers on solid siufaces have been made, and some broad reviews can be foimd in articles and books [9,10,12,15,65,67,96-99]. 

The field terms may stabilize or destabilize the intrinsic thermodynamic order of a mesophase, and hence increase or decrease the temperature of its transition to a less ordered phase. The shift in the transition temperature is calculated by comparing the electric (magnetic) energy with the transition enthalpy or some other competing thermodynamic quantity (e.g. elastic energy). Below we consider examles. 

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