Thermodynamic slowing down

The spontaneous mixing of the two polymers will transpire at a rate which reflects the degree of miscibility of the system. As X approaches the critical value for phase separation, "thermodynamic slowing down" of the interdiffusion will occur [12]. The rate of increase of the scattering contrast reflects the proximity of the system to criticality, as well as the strong composition dependence of the glass transition temperature of the blend. Extraction of a value for either the self diffusion constants [13,14] or the interaction parameter is not feasible from the presently available data. 

Secondly, we can note the direction of the effect if the interaction is unfavourable and the polymers are tending towards demixing, with a positive value of X, the diffusion coefficient is reduced - this effect is known as thermodynamic slowing down. Conversely, if the polymers find it energetically favourable to mix, with a negative value of x, the diffusion coefficient is increased by the interaction by a factor which, because of the presence of a factor of N, may be quite significant. 

Figure 4.21. Mutual diffusion coefficients as functions of the concentration for blends of deuterated polystyrene N = 9.8 X 10 ) and normal polystyrene N = 8.7 X 10 ). The diffusion temperatures were 166 °C (o), 174 °C (A), 190 °C (O) and 205 °C ( ). The solid lines are the predictions of equation (4.4.11). The decrease in diffusion coefficient for volume fractions aroimd a half is a direct result of the unfavourable thermodynamies of mixing - thermodynamic slowing down . After Green and Doyle (1987).

We present here a forward recoil spectrometry (FRES) study of thermodynamic slowing down" of mutual diffusion in isotopic polymer mixtures and of the diffusion of homopolymers into symmetric diblock copolymer structures. The measurements of "thermodynamic slowing down" were performed on binary mixtures of normal and deuterated polystyrene (PS). Both the Flory interaction parameter, the upper critical... 

IV. "THERMODYNAMIC SLOWING DOWN" OF MUTUAL DIFFUSION IN ISOTOPIC POLYMER MIXTURES... 

D critical composition 4>c where... 

In the above equations Np and Nh are the number of monomer segments that comprise the deuterated and undeuterated polymer chains, respectively. As X approaches Xs> equivalently, as T approaches the UCST, the system experiences large fluctuations in composition. The extent of the "thermodynamic slowing down" should therefore be enhanced. In cases where X > Xs the mixture is unstable and undergoes phase separation. "Thermodynamic slowing down" effects should not, however, be observable when X = 0-... 

D(4>) is plotted as a function of the average blend composition, avet in Fig. 9 at temperatures of 166, 174, 190 and 205 C. The data at each temperature exhibits a pronounced minimum or "thermodynamic slowing down"... 

The agreement between both sets of experimental data is excellent. The thermodynamic slowing down effects are difficult to observe far from the stability limit as shown in Fig. 11. The stability limit of this PS/d-PS mixture of chains of No = Nh = 2.3x10 was calculated to be Xs(0-5) = 8.7x10 using equation 14. The solid line was computed using x = 1.9x10 ... 

In this paper, we summarize measurements of the temperature- and composition-dependence of the mutual diffusion of deuterated polystyrene (d-PS) chains and protonated poly(xylenyl ether) (PXE) chains which have appeared in more detail elsewhere. By measuring D and D as a function of temperature, one can extract the temperature dependence of X(T ). Because the PS PXE system exhibits a lower critical solution temperature, a large thermodynamic speeding up of diffusion will be observed at low temperatures (X<0) while a thermodynamic slowing down will occur at higher temperatures (x>0). Using these values for we... 

In spite of considerable development of thermodynamics and molecular theory, most of the methods used today are empirical and their operation requires knowledge of experimental values. However, the rate of accumulation of experimental data seems to be slowing down even though the need for precise values is on the rise. It is then necessary to rely on methods said to be predictive and which are only estimates. 

The mean chemical shifts of A- unsubstituted pyrazoles have been used to determine the tautomeric equilibrium constant, but the method often leads to erroneous conclusions (76AHC(Sl)l) unless the equilibrium has been slowed down sufficiently to observe the signals of individual tautomers (Section 4.04.1.5.1). When acetone is used as solvent it is necessary to bear in mind the possibility (depending on the acidity of the pyrazole and the temperature) of observing the signals of the 1 1 adduct (55) whose formation is thermodynamically favoured by lowering the solution temperature (79MI40407). A similar phenomenon is observed when SO2 is used as solvent. 

Shown in Fig. 4a is the temperature dependence of the relaxation time obtained from the isothermal electrical resistivity measurement for Ni Pt performed by Dahmani et al [31. A prominent feature is the appearance of slowing down phenomenon near transition temperature. As is shown in Fig. 4b [32], our PPM calculation is able to reproduce similar phenomenon, although the present study is attempted to LIq ordered phase for which the transition temperature, T]., is 1.89. One can confirm that the relaxation time, r, increases as approaching to l/T). 0.52. This has been explained as the insufficiency of the thermodynamic driving force near the transition temperature in the following manner. 

What could be the reason for this remarkable slowing down of aggregate association Why are mesoglobules not as sticky as anticipated, given the thermodynamically poor conditions to which they are subjected ... 

It is often useful to carry out voltammetric measurements at low temperatures in order to evaluate both the stability of an electrogenerated species (the decrease in temperature will slow down the kinetics of any decomposition processes of the species formed in the electrode process) and the variation in formal electrode potential of a redox couple as a function of temperature. The latter point regards thermodynamic considerations of the redox processes, which will be discussed in Chapter 13, Section 3. 

Biologically mediated redox reactions tend to occur as a series of sequential subreactions, each of which is catalyzed by a specific enzyme and is potentially reversible. But despite favorable thermodynamics, kinetic constraints can slow down or prevent attainment of equilibrium. Since the subreactions generally proceed at unequal rates, the net effect is to make the overall redox reaction function as a imidirectional process that does not reach equilibrium. Since no net energy is produced imder conditions of equilibrium, organisms at equilibrium are by definition dead. Thus, redox disequilibrium is an opportunity to obtain energy as a reaction proceeds toward, but ideally for the sake of the organism does not reach, equilibrium. 

Garrahan and Chandler [230] have recently attempted to rationalize the string-like motion in supercooled liquids based on a completely different concept of dynamic facilitation, derived from the study of magnetic spin models originally developed by Fredrickson and Anderson [231]. Although these spin models seem to exhibit dynamic heterogeneity of some kind and slow relaxation processes, the slowing down of the dynamics in these models is entirely decoupled from the spin model s thermodynamics [116, 230]. In view... 

Eichhom and his co-workers have thoroughly studied the kinetics of the formation and hydrolysis of polydentate Schiff bases in the presence of various cations (9, 10, 25). The reactions are complicated by a factor not found in the absence of metal ions, i.e, the formation of metal chelate complexes stabilizes the Schiff bases thermodynamically but this factor is determined by, and varies with, the central metal ion involved. In the case of bis(2-thiophenyl)-ethylenediamine, both copper (II) and nickel(II) catalyze the hydrolytic decomposition via complex formation. The nickel (I I) is the more effective catalyst from the viewpoint of the actual rate constants. However, it requires an activation energy cf 12.5 kcal., while the corresponding reaction in the copper(II) case requires only 11.3 kcal. The values for the entropies of activation were found to be —30.0 e.u. for the nickel(II) system and — 34.7 e.u. for the copper(II) system. Studies of the rate of formation of the Schiff bases and their metal complexes (25) showed that prior coordination of one of the reactants slowed down the rate of formation of the Schiff base when the other reactant was added. Although copper (more than nickel) favored the production of the Schiff bases from the viewpoint of the thermodynamics of the overall reaction, the formation reactions were slower with copper than with nickel. The rate of hydrolysis of Schiff bases with or/Zw-aminophenols is so fast that the corresponding metal complexes cannot be isolated from solutions containing water (4). 

In addition to the above effects, the intermolecular interaction may affect polymer dynamics through the thermodynamic force. This force makes chains align parallel with each other, and retards the chain rotational diffusion. This slowing down in the isotropic solution is referred to as the pretransition effect. The thermodynamic force also governs the unique rheological behavior of liquid-crystalline solutions as will be explained in Sect. 9. For rodlike polymer solutions, Doi [100] treated the thermodynamic force effects by adding a self-consistent mean field or a molecular field Vscf (a) to the external field potential h in Eq. (40b). Using the second virial approximation (cf. Sect. 2), he formulated Vscf(a), as follows [4] ... 

The dissolution reaction is Pt - Pt2+ + 2e and the value of its reversible thermodynamic potential is 1.2 V on the normal hydrogen scale. The evolution of O2 in acid solution at a current density of, say, 100 mA cm, needs an overpotential on platinum of nearly 1.0 V, i.e., the electrode potential would be >2.0 V. It follows feat at these very anodic potentials platinum would tend to dissolve, although its dissolution would be slowed down by fee fact feat it forms an oxide film at fee potentials concerned. Nevertheless, fee facts stated show feat fee alleged stability of Pt may be more limited than is often thought. This is an important practical conclusion because dissolved Pt from an anode may deposit on fee cathode of fee cell, and instead of having fee surface one started wife as fee cathode, it becomes in fact what is on its surface, platinum. 

If one of conditions (47) is satisfied, the reaction of decomposition becomes thermodynamically possible, though it may be slowed down due to kinetic reasons. 

The basic problem of direct fluorination involves both kinetics and thermodynamics. The rate of the reaction must be slowed down so that the energy liberated from the reaction may be absorbed or carried away. The most significant and crucial innovations in the evolution of the direct fluorination process recently developed by Lagow and Margrave (6) have been kinetic considerations. Their technique has been named the La-Mar direct fluorination process (7). Most of the kinetic considerations involve fluorine dilution schemes and probability considerations. 

There is a severe practical problem in looking for correlations between the rate constants for folding of small proteins and their structural or thermodynamic properties—specific structural features can dominate the rate of folding. For example, we know from the protein engineering studies on barnase and CI2 that specific mutations can slow down the rate of folding by several orders of... 

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