Entropic ’’tension

As expected, the length of the tube grows linearly with the polymer molecular weight (the number N of reptons in a cluster). Notice that the entropic tension and the average cluster size increase with the coordination number 2. 

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). 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

Lindahl, E. and Edholm, O. (2000). Spatial and energetic-entropic decomposition of surface tension in lipid bilayers from molecular dynamics simulations, J. Chem. Phys., 113, 3882-3893. 

In the case where the macromolecular backbone is flexible, the axial tension may affect the molecular conformation. Flexibility of the main chain can be realized by bond rotational isomerism and minimizes the entropic penalty caused by the stretching of the main chain. As depicted in Fig. 21 on the right ... 

As can be seen, the magnitude of the entropic contribution can be directly evaluated by measuring the temperature dependence of the interfacial tension. A detailed discussion on the further use of these equations can be found elsewhere (Baszkin and Norde, 2000). 

Hydrophobic binding. The hydrophobic effect can have both enthalpic and entropic components, although the classical hydrophobic effect is entropic in origin (Section 1.9.1). Studies on the associations between planar aromatic molecules show an approximately linear relationship between the interaction energy and their mutual contact surface area with slope 64 dyn cm-1, very close to the macroscopic surface tension of water (72 dyn cm-1). Hence, in the absence of specific host or guest interactions with the solvent the hydrophobic effect can be calculated solely from the energy required to create a free surface of 1 A2 which amounts to 7.2 X 10 12 J or 0.43 kjA 2 mol. ... 

One way to improve the Adam-Gibbs model is to include details of the structure of the interface between the various aperiodic minima [39]. Near the Kauzmann temperature, the interface broadens, and correct scaling laws are obtained by wetting the droplet surface [39]. In this case, the surface tension of the entropic droplet is a function of its radius and can be obtained by renormalization group arguments. Analysis reveals that the activation barrier to configuration rearrangement is [39]... 

The resulting physical picture of a rubber-like system as a close-packed collection of mers is radically different from the two-phase image introduced by James and Guth [10]. The latter represents mbber as a network of chains, which act as entropic springs in tension, embedded in a bath of simple liquid. The bath gives rise to an isotropic pressure, whereas the network is responsible for the deviatoric stress. More recent physical pictures consider as well the distribution of network junctions in the liquid and the action of these junctions as constraints on the free motion of a generic chain of the network. The current description is on the mer or atomic level and treats the full stress tensor, both the mean and deviatoric portions, in terms of atomic interactions. 

Fig. 8 Monomer chemical potential in a droplet comprising monomer and hydrophobe as a function of the monomer volume fraction (top) and droplet radius (bottom). The global potential (as given by Ugelstad s equation) is given, as well as the entropic term due to mixing and the Laplace term due to surface tension. Parameters m Y=l Vm,h=0 y=25 mN/m Vjn=l-1 10 m mol T=298.15 K (p =0,96 r =100 nm...

In Fig. 9c, the effects of different surface tension values on the equilibrium are examined. By decreasing the interfacial tension, the Laplace term becomes less significant than the contribution given by the entropy of mixing, and therefore ripening is decreased and stability is enhanced. Theoretically, in a system with zero surface tension at the oil/water interface, the total monomer chemical potential is given solely by the entropic terms, and it is always stable. 

Using [2.2.9] the surface tension of a pure liquid can be split into its entropic and energetic contribution. For a pure liquid, where the Gibbs dividing plane is determined by setting n°= 0, introducing U° =U°/A and S° =S°/A as the interfacial excess energy and entropy p>er unit area, respectively, we have... 

Fowkes own expression does not contciin the entropic contribution but has a term accounting for the surface pressure of the SG interface (we do not need that because our y is the surface tension of the solid in the presence of vajx)ur). 

Figure 5 shows the temperature dependence of the surface tension. The differences between calculated values and the experimental ones do not exceed ca. 1 mN m-1. An adjustable parameter is not used by assuming that the k does not vary with the temperature and is fixed at 0.5, a theoretical value for both PS and PVME. This indicates that the simulated equation-of-state parameters for the component polymers are reasonable. It has been known that the LCST behaviors are originated from the specific interactions between components and/or the finite compressibility of mixture and that the phase separation is entropically... 

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