Free energy attractive

If (00 is low enough to allow for the classical limit, the attraction free energy becomes... 

The magnitude of the depletion attraction free energy, is proportional to the osmotic pressure of the polymer solution, which in turn is determined by

molecular weight M. The range of depletion attraction is proportional to the thickness of the depletion zone. A, which is roughly equal to the radius of gyration, Rq, of the free polymer. A simple expression for Gdep is [7],... 

When a solution of 1 or 2% tristearate in triglyceride oil, made at about 70°C, is cooled to room temperature, small tristearate crystals form, and these tend to aggregate rapidly. Assuming the crystals to be spheres of about 0.1 pm diameter, what would be the attractive free energy between them Is this sufficient to cause aggregation It is also observed that the addition of a little glycerol monolaurate to the system tends to cause disaggregation. How could that be explained ... 

Note Particles can aggregate because of the attractive free energy acting between them. However, aggregation will decrease the translational mixing entropy of the particles, and that would counteract aggregation. It can be derived that the average free... 

Equilibrium measurements with V and different naphthalene derivatives in aqueous solution showed attractive free energies of up to 7 kcal/mol (Chart III) (35), if both lipophilic and electrostatic contributions are present. Comparison of all available association constants (35, 40), however, clearly shows that the lipophilic part is always dominating [other than in the immo-... 

For the attractive part j]] we need the specifics of the system, as discussed in the next sections. For all three systems we consider first the pair potential W H), where H is the interparticle distance H is zero for particles in contact We shall use only the relative particle separation h = HI a, where a is the particle radius. In all cases W(h) = for h<0. The pair potential is characterized by the strength e = — W(0) and by the relative range q = KT ja, where is the range of the attraction. From an appropriate expression for W h) as a function of e and q the attractive free energy can be derived, and from f=fo+fii as a function of T], e and q all thermodynamic properties (including the phase behavior) follow from standard thermodynamics. For example, the chemical potential i of the spherical particles and the pressure p of the system are given by ... 

As is clear from the three hydrophilic items shown at the bottom of Table 8.1, (and also from the other items shown in that table), iJy its very nature, the strong attractive free energy of the hydrophobic effect is always present in all interactions taking place in water. What makes a compound or particle hydrophilic (i.e., repulsive in water), is its ability to achieve a Lewis acid-base repulsion that is significantly larger than the underlying hydrophobic attraction. (It should be remembered that usually a fairly small, but non-negligible Lifshitz-van der Waals attraction must also be surmounted, cf. Tables 8.1 and 8.2. 

Figure B3.3.10. Contour plots of the free energy landscape associated with crystal niicleation for spherical particles with short-range attractions. The axes represent the number of atoms identifiable as belonging to a high-density cluster, and as being in a crystalline environment, respectively, (a) State point significantly below the metastable critical temperature. The niicleation pathway involves simple growth of a crystalline nucleus, (b) State point at the metastable critical temperature. The niicleation pathway is significantly curved, and the initial nucleus is liqiiidlike rather than crystalline. Thanks are due to D Frenkel and P R ten Wolde for this figure. For fiirther details see [189].

In case of the rigid lock-and-key type receptor forming five hydrogen bonds plus two extended electrostatic attractions (Fig. 3a), one mismatched hydrogen bond will result in only a small reduction in overall binding free energy 4.18-8.36 kJ mol (1-2 kcal mol ) out of... 

Modem understanding of the hydrophobic effect attributes it primarily to a decrease in the number of hydrogen bonds that can be achieved by the water molecules when they are near a nonpolar surface. This view is confirmed by computer simulations of nonpolar solutes in water [15]. To a first approximation, the magnimde of the free energy associated with the nonpolar contribution can thus be considered to be proportional to the number of solvent molecules in the first solvation shell. This idea leads to a convenient and attractive approximation that is used extensively in biophysical applications [9,16-18]. It consists in assuming that the nonpolar free energy contribution is directly related to the SASA [9],... 

A statistical mechanical fonnulation of implicit solvent representations provides a robust theoretical framework for understanding the influence of solvation biomolecular systems. A decomposition of the free energy in tenns of nonpolar and electrostatic contributions, AVF = AVF " + AVF ° , is central to many approximate treatments. An attractive and widely used treatment consists in representing the nonpolar contribution AVF " by a SASA surface tension term with Eq. (15) and the electrostatic contribution by using the... 

When a gas comes in contact with a solid surface, under suitable conditions of temperature and pressure, the concentration of the gas (the adsorbate) is always found to be greater near the surface (the adsorbent) than in the bulk of the gas phase. This process is known as adsorption. In all solids, the surface atoms are influenced by unbalanced attractive forces normal to the surface plane adsorption of gas molecules at the interface partially restores the balance of forces. Adsorption is spontaneous and is accompanied by a decrease in the free energy of the system. In the gas phase the adsorbate has three degrees of freedom in the adsorbed phase it has only two. This decrease in entropy means that the adsorption process is always exothermic. Adsorption may be either physical or chemical in nature. In the former, the process is dominated by molecular interaction forces, e.g., van der Waals and dispersion forces. The formation of the physically adsorbed layer is analogous to the condensation of a vapor into a liquid in fret, the heat of adsorption for this process is similar to that of liquefoction. 

In the case of an associating fluid with the repulsive-attractive reference system potential, the attractive van der Waals forces between molecules may also be considered in a perturbational manner [114]. The Helmholtz free energy can be written as a sum of three terms... 

The excess free energy is divided into terms representing the contributions due to repulsive and attractive nonassociative forces acting between molecules, as well as into a contribution arising from association [38,39]... 

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