Entropic force

The forces such as electrical double layer, forces between emulsion droplets, hydrodynamic inertial forces, entropic (Diffusional) forces and the dispersion forces which act on the droplets or between the droplets separated at tens or hundreds of nanometers. Sedimentation and flocculation processes involve the forces such as the centrifugal force, applied electrostatic force and gravitational force. Before discussing the emulsion stability in terms of these forces, we would like to explain the thermodynamics of emulsion stabilization. 

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. 

Pigment dispersions are stabilized by charge repulsion and entropic, ie, steric or osmotic, repulsion. Although both types of stabilization force may be present in most cases, for pigment dispersions in solvent-bome coatings entropic repulsion is usually the most important mechanism for stabilization. 

R. Dickman, P. Attard, V. Simonian. Entropic forces in binary hard sphere mixtures. J Chem Phys 707 205-213, 1997. 

What are the essential features of surfactant systems An important ingredient is obviously the repulsion between water and nonpolar molecules or molecule parts, the hydrophobic force. This interaction is however highly nontrivial, and its analysis is still an active field of research [4,22,23]. Qualitatively, it is usually attributed to the strong orientational and positional correlations between nonpolar molecules in solution and the surrounding water molecules. The origin of the interaction is therefore entropic free water forms a network of hydrogen bonds. In the neighborhood... 

Let us enter the world of liquid crystals built by the purely entropic forces present in hard body systems. The phase diagram of hard spherocylinders (HSC) shows a rich variety of liquid crystalline phases [71,72]. It includes the isotropic, nematic, smectic A, plastic, and solid phases [73]. In a plastic crystal the particle centers lie on lattice sites, but the orientations of the... 

Miscibility or compatibility provided by the compatibilizer or TLCP itself can affect the dimensional stability of in situ composites. The feature of ultra-high modulus and low viscosity melt of a nematic liquid crystalline polymer is suitable to induce greater dimensional stability in the composites. For drawn amorphous polymers, if the formed articles are exposed to sufficiently high temperatures, the extended chains are retracted by the entropic driving force of the stretched backbone, similar to the contraction of the stretched rubber network [61,62]. The presence of filler in the extruded articles significantly reduces the total extent of recoil. This can be attributed to the orientation of the fibers in the direction of drawing, which may act as a constraint for a certain amount of polymeric material surrounding them. 

It is worth recalling that any of the molecular force laws given by Eqs. (13-16) are derived within the framework of the freely-jointed model which considers the polymer chain as completely limp except for the spring force which resists stretching thus f(r) is purely entropic in nature and comes from the flexibility of the joints which permits the existence of a large number of conformations. With rodlike polymers, the statistical number of conformations is reduced to one and f(r) actually vanishes when the chain is in a fully extended state. 

The behavior of a bead-spring chain immersed in a flowing solvent could be envisioned as the following under the influence of hydrodynamic drag forces (fH), each bead tends to move differently and to distort the equilibrium distance. It is pulled back, however, by the entropic need of the molecule to retain its coiled shape, represented by the restoring forces (fs) and materialized by the spring in the model. The random bombardment of the solvent molecules on the polymer beads is taken into account by time smoothed Brownian forces (fB). Finally inertial forces (f1) are introduced into the forces balance equation by the bead mass (m) times the acceleration ( ) of one bead relative to the others ... 

The entropic force fs, given as the negative of the gradient of the spring potential energy, is represented by one of the various kinds of springs used in molecular models (Fig. 3). 

The value should be that of single polymer chain elasticity caused by entropic contribution. At first glance, the force data fluctuated a great deal. However, this fluctuation was due to the thermal noise imposed on the cantilever. A simple estimation told us that the root-mean-square (RMS) noise in the force signal (AF-lS-b pN) for an extension length from 300 to 350 nm was almost comparable with the thermal noise, AF= -21.6 pN. 

Althongh van der Waals forces are present in every system, they dominate the disjoining pressnre in only a few simple cases, such as interactions of nonpolar and inert atoms and molecnles. It is common for surfaces to be charged, particularly when exposed to water or a liquid with a high dielectric constant, due to the dissociation of surface ionic groups or adsorption of ions from solution, hi these cases, repulsive double-layer forces originating from electrostatic and entropic interactions may dominate the disjoining pressure. These forces decay exponentially [5,6] ... 

Macromolecules exchange internal surface hydrogen bonds for hydrogen bonds to water. Entropic forces dictate that macromolecules expose polar regions to an aqueous interface and bury nonpolar regions. 

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