Entropically

The entropically driven disorder-order transition in hard-sphere fluids was originally discovered in computer simulations [58, 59]. The development of colloidal suspensions behaving as hard spheres (i.e., having negligible Hamaker constants, see Section VI-3) provided the means to experimentally verify the transition. Experimental data on the nucleation of hard-sphere colloidal crystals [60] allows one to extract the hard-sphere solid-liquid interfacial tension, 7 = 0.55 0.02k T/o, where a is the hard-sphere diameter [61]. This value agrees well with that found from density functional theory, 7 = 0.6 0.02k r/a 2 [21] (Section IX-2A). 

The well defined contact geometry and the ionic structure of the mica surface favours observation of structural and solvation forces. Besides a monotonic entropic repulsion one may observe superimposed periodic force modulations. It is commonly believed that these modulations are due to a metastable layering at surface separations below some 3-10 molecular diameters. These diflftise layers are very difficult to observe with other teclmiques [92]. The periodicity of these oscillatory forces is regularly found to correspond to the characteristic molecular diameter. Figure Bl.20.7 shows a typical measurement of solvation forces in the case of ethanol between mica. 

Lee J 1993 New Monte Carlo algorithm—entropic sampling Phys. Rev.L 71 211-14... 

Hard-sphere models lack a characteristic energy scale and, hence, only entropic packing effects can be investigated. A more realistic modelling has to take hard-core-like repulsion at small distances and an attractive interaction at intennediate distances into account. In non-polar liquids the attraction is of the van der Waals type and decays with the sixth power of the interparticle distance r. It can be modelled in the fonn of a Leimard-Jones potential Fj j(r) between segments... 

Page, M. L., Jencks, W. P. Entropic contributions to rate accelerations in enzymic and intramolecular interactions and the chelate effect. Proc. Natl. Acad. Sci. USA 68 (1971) 1678-1683... 

The thermodynamic properties that we have considered so far, such as the internal energy, the pressure and the heat capacity are collectively known as the mechanical properties and can be routinely obtained from a Monte Carlo or molecular dynamics simulation. Other thermodynamic properties are difficult to determine accurately without resorting to special techniques. These are the so-called entropic or thermal properties the free energy, the chemical potential and the entropy itself. The difference between the mechanical emd thermal properties is that the mechanical properties are related to the derivative of the partition function whereas the thermal properties are directly related to the partition function itself. To illustrate the difference between these two classes of properties, let us consider the internal energy, U, and the Fielmholtz free energy, A. These are related to the partition function by ... 

Water-soluble globular proteins usually have an interior composed almost entirely of non polar, hydrophobic amino acids such as phenylalanine, tryptophan, valine and leucine witl polar and charged amino acids such as lysine and arginine located on the surface of thi molecule. This packing of hydrophobic residues is a consequence of the hydrophobic effeci which is the most important factor that contributes to protein stability. The molecula basis for the hydrophobic effect continues to be the subject of some debate but is general considered to be entropic in origin. Moreover, it is the entropy change of the solvent that i... 

In the case of the retro Diels-Alder reaction, the nature of the activated complex plays a key role. In the activation process of this transformation, the reaction centre undergoes changes, mainly in the electron distributions, that cause a lowering of the chemical potential of the surrounding water molecules. Most likely, the latter is a consequence of an increased interaction between the reaction centre and the water molecules. Since the enforced hydrophobic effect is entropic in origin, this implies that the orientational constraints of the water molecules in the hydrophobic hydration shell are relieved in the activation process. Hence, it almost seems as if in the activated complex, the hydrocarbon part of the reaction centre is involved in hydrogen bonding interactions. Note that the... 

Monte Carlo simulations are an efficient way of predicting liquid structure, including the preferred orientation of liquid molecules near a surface. This is an efficient method because it is not necessary to compute energy derivatives, thus reducing the time required for each iteration. The statistical nature of these simulations ensures that both enthalpic and entropic effects are included. 

By following the standard procedures of statistical mechanics, one arrives at an equation which can be converted into the BET equation (2.12) by the simple substitution 9i/9i , ki = c. Thus parameter c acquires a significance different from that in the BET theory in essence it now involves entropic terms as well as energetic terms. 

Examples of the hydroquinone inclusion compounds (91,93) are those formed with HCl, H2S, SO2, CH OH, HCOOH, CH CN (but not with C2H 0H, CH COOH or any other nitrile), benzene, thiophene, CH, noble gases, and other substances that can fit and remain inside the 0.4 nm cavities of the host crystals. That is, clathration of hydroquinone is essentially physical in nature, not chemical. A less than stoichiometric ratio of the guest may result, indicating that not all void spaces are occupied during formation of the framework. Hydroquinone clathrates are very stable at atmospheric pressure and room temperature. Thermodynamic studies suggest them to be entropic in nature (88). 

AH) and entropic (AT) parts, is affected by concentration, temperature T, and pressure P, or volume H. To have miscibility (2—4), AG must be negative and satisfy the additional following requirement which ensures stability against... 

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