Surface entropy factor

Tempkin [29] and Jackson [30] characterized the roughness of a crystal surface with a surface entropy factor, a, defined as... 

Bourne JR and Davey ly. The Role of Solvent-Solute Interactions in Determining Crystal Growth Mechanisms from Solution 1. The Surface Entropy Factor. J Cryst Growth 1976 36 278-286. 

The surface entropy factor, a, can be considered a relative measure of the degree of smoothness of a crystal face on the atomic level. In Section 3.9.3 it is shown how a correlates the effect of solvents on both growth rate and growth mechanism. 

The structure of a growing crystal surface at its interface with the growth medium, e.g. a supersaturated solution, has an important bearing on the particular mode of crystal growth adopted. This property has been characterized by a quantity variously designated as a surface roughness or surface entropy factor, or more frequently nowadays simply as the alpha factor (Jack-son, 1958 Tempkin, 1964 Bennema and van der Eerden, 1977) which may be defined by... 

In the limit of an infinite micellar radius, i.e. a charged planar surface, the salt dependence of Ge is solely due to the entropy factor. A difficult question when applying Eq. (6.13) to the salt dependence of the CMC is if Debye-Hiickel correction factors should be included in the monomer activity. When Ge is obtained from a solution of the Poisson-Boltzmann equation in which the correlations between the mobile ions are neglected, it might be that the use of Debye-Hiickel activity factors give an unbalanced treatment. If the correlations between the mobile ions are not considered in the ionic atmosphere of the micelle they should not be included for the free ions in solution. 

Analysis of the potential energy surfaces (PESs) of the interacting magnesium atoms and clusters shows that all processes of magnesium association are activationless. Then, the proportion between clusters of different composition would seem to be determined only by the lifetime of particles in the mobile layer and by the deposition rate from the gas phase. At first glance, there are no reasons for the predominant accumulation of more stable particles. The situation is different if the entropy factor is taken into account. 

In this reaction kinetics analysis the following assumptions were employed The surface entropies of oxygenated species were hnked together, assuming that these species exhibit similar mobility on the surface. Accordingly, the surface entropies of oxygenated species were described in terms of a factor that multiplied the local surface entropies of these species, where the local entropy,. S ioc, for a species is dehned as the vibrational and rotational entropy associated with the species in the gas phase. 

Garrard, S.M., Longenecker, K. L., Lewis, M. E., Sheffield, P.J., Derewenda, Z. S., Expression, purification, and crystallization of the RGS-like domain from the Rho nucleotide exchange factor, PDZ-RhoGEE, using the surface entropy reduction approach. Protein Expr. Purif. 2001, 21, 412-416. 

The energy required to create the cavity (entropy factors and loss of solvent-solvent van der Waals interactions), and the stabilization due to van der Waals interactions between the solute and solvent (which may contain also a small repulsive component), is usually assumed to be proportional to the surface area. The corresponding energy terms... 

The catalytic work on the zeolites has been carried out using the pulse microreactor technique (4) on the following reactions cracking of cumene, isomerization of 1-butene to 2-butene, polymerization of ethylene, equilibration of hydrogen-deuterium gas, and the ortho-para hydrogen conversion. These reactions were studied as a function of replacement of sodium by ammonium ion and subsequent heat treatment of the material (3). Furthermore, in some cases a surface titration of the catalytic sites was used to determine not only the number of sites but also the activity per site. Measurements at different temperatures permitted the determination of the absolute rate at each temperature with subsequent calculation of the activation energy and the entropy factor. For cumene cracking, the number of active sites was found to be equal to the number of sodium ions replaced in the catalyst synthesis by ammonium ions up to about 50% replacement. This proved that the active sites were either Bronsted or Lewis acid sites or both. Physical defects such as strains in the crystals were thus eliminated and the... 

An important result is that the effective desorption energy for the heterogeneous surfaces depends on temperature Nevertheless, let us for a while abandon it and suppose that jjet does not depend on temperature. Another assumption will be that the entropy change is the same for all partial isotherms, independent of EA. Then we take into account Eq. 5.3 for the experimental constant of adsorption and move to the characteristics of desorption from heterogeneous surfaces. It follows that the measurements yield an equilibrium constant, which is to be interpreted as the entropy factor multiplied by the expectation value of the desorption energy factor ... 

It is hard to use thermodynamics to describe states of water molecules in heterogeneous environments such as the surface of Upid bilayers. Clearly, the bound water molecules are stabilized by enthalpy while free molecules are stabilized by entropy factors. One can construct a local free-energy surface that captures some of these... 

Formation of weak boundary layers is confirmed by a study of the molecular mobility of filled epoxy polymers. The availabihty of the solid surface results in a decrease of the molecular mobihty in the boundary layer [21] as a result of limiting the conformation set and adsorption interactions of the polymer molecules with a solid body at the boundary. The nature of the filler surface has little effect on the molecular mobility of the epoxy polymer and on the change of mobility of its side-groups and segments. It has been concluded [21] that the primary role in the change of mobility is played by geometric limitation of the number of possible conformations of macromolecules close to the surface of the particles, i.e., by the entropy factor rather than by energetic interactions of the surfaces. 

The effect of the solid body surface propagates a considerable distance from it that is, the influence of the surface on the chains that are in direct contact with it propagates via other chains into the bulk of the material. The range of action of the surface forces is a consequence of changes in the intermolecular interactions between chains that are directly adjacent to those in contact with the surface. Two factors limit the molecular mobility of chains dose to the boundary adsorption reactions of macromolecules with the surface and decrease of their entropy. Close to the boundary, the macromolecule cannot adopt the same number of conformations as in bulk, so that the surface limits the geometry of the molecule. As a result, the number of states available to the molecule in the surface layer decreases. These limitations on conformation are the primary reason for the decrease of molecular mobility close to the boundary [32]. 

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