Layer compression

P. Richetti, P. Kekicheff, P. Barois. Measurement of the layer compressibility modulus of a lamellar mesophase with a surface forces apparatus. J Phys II 5 1129-1154, 1995. 

Double-jet crystal growth method, 19 179 Double-layer compression, 11 631 Double-layer forces, flocculation and,... 

Bilayer compression force (kN) First-layer compression force (kN) Tablet cylindrical height (mm) Tablet hardness (N) Tablet friability (% 500 Drops)... 

By adding the function u(x) to the phase factor in (4) one can describe departures from the planar (lamellar, one-dimensional) layer arrangement, which is characteristic for the 2D structures. The first term in (3) is the smectic layer compressibility energy. It is zero when layers are of the equilibrium thickness. If cx(T) > 0, the second term in (3) requires the director to be along the smectic layer normal (the smectic-A phase). If c (T) < 0, this term would prefer the director to lie in the smectic plane. So the last term in (3) is needed to stabilize a finite tilt of the director with respect to the smectic layer normal. In addition this term gives the energy penalty for the spatial variation of the smectic layer normal. 

Fig. 9 Critical values as functions of the flow alignment parameter X for various viscosities (a, b) and compressibilities (c, d). In the upper row we plot this dependence for a set of (isotropic) viscosities ranging from v, = 1 (thick solid line,) down to V = 10 3 (thick dashed line,). The lower row illustrates the behavior for varying layer compressibility Bo with Bo 3 f°r the thick solid curve and Bo = 100 for the thick dashed curve. In all plots the thin solid lines give the behavior for some intermediate values. For an interpretation of this behavior see the text...

Electrical double layer compression. Addition of small amounts of electrolyte to dispersed colloidal particles causes them to coagulate. In coagulation, the particles are closely clustered together and hard to disperse again. The addition of an electrolyte... 

The destabilization of colloids through the addition of counterions should be done in conjunction with the application of the complete coagulation process. Four methods are used to bring about this process double-layer compression, charge neutralization, entrapment in a precipitate, and intraparticle bridging. 

Double-layer compression—A mode of destabilizing a colloid produced by thinning out the electric double layer. 

In thermotropic (solvent-free) smectic-A phases, two types of distortion are permitted, namely, splaying of the director (which corresponds to bending of the layers) and layer compression. Note The material itself is assumed to remain incompressible only the layers compress.) For weak distortions, the free energy cost of these is given by (de Gennes and Frost 1993)... 

Here u is the position of a layer plane and z is the position coordinate locally parallel to the director n, where n is parallel to the average molecular axis, which is assumed to remain normal to the layer plane, du/dz = e is the compressional (or dilational) strain. Thus, layer bending and layer compression are characterized by a splay (or layer-bend) modulus K and a compression modulus B. Other kinds of distortion present in nematics, such as bend or twisting of the director n, are not compatible with layers that remain nearly parallel, and hence are forbidden. Equation (10-36) is not invariant to rotations of frame, and its validity is limited to weak distortions a rotationally invariant expression has been given by -Grinstein and Pelcovits (1981).---------------------------------------------------------... 

For small-molecule thermotropic smectic-A phases, typical values of two elastic constants are K 10 dyn and B 10 dyn/cm (Ostwald and Allain 1985). For lyotropic smectics, such as those made from surfactants in oil or water solvents, the layer compression modulus B can be much lower (see Chapter 12). From B and K, a length scale A. = ( 1 /B) 1 nm is defined it is called the permeation depth and its magnitude... 

When the layers of a lamellar block copolymer are distorted, the free energy density is augmented by a distortional term that can, like the smectic-A phase, be described as the sum of layer compression/dilation and layer-bending energies ... 

L /polymer extensibility smectic-layer compressive modulus E E, Finger strain tensor B , Cauchy strain tensor yriso/r, capillary number characteristic ratio, defined by R )q — Ccotib translational diffusivity-------------------------... 

At low concentrations of dissolved organic matter (DOM) (<0.01 mg of C/L) and at low ionic strength (10-3 M), the hematite particles are positively charged at this pH and are stabilized electrostatically by interacting diffuse layers with characteristic (Debye) lengths of 10 nm. As the ionic strength is increased to 10 1 M at these low DOM concentrations, the diffuse layers are compressed to 1 nm, and attractive van der Waals forces promote attachment in classical Derjaguin-Landau-Verwey-Overbeek (DLVO) destabilization by what has been termed double-layer compression. 

Figures 3b, 4 and 5a show that this is the only mechanism by which BTA" ions are adsorbed on the silica surface. The slope of the cation-exchange curve is almost equal to unity (Fig.4a) since the effectiveness of adsorption reaches about 0.8 /imol-m . Contrary to the surfactant, the polar head is not able to reverse the surface charge from negative to positive (Fig.4b). The electrophoretic mobility scarcely depends on the amount adsorbed, except for the terminal part of the adsorption interval where its negative value decreases a little. As the pH curve shows the same tendency (Fig.3b), the final rise in the neutralization efficiency of the polar head can be ascribed to effect of the double layer compression induced by the increasing ionic strength in the bulk phase.

Current research is investigating two approaches to achieve inertial confinement fusion. In the direct approach a short wavelength, high intensity laser pulse is focused directly on the pellet containing the fusion fuel. The outer layers of the pellet are violently vaporized and heated to a high temperature. This process is termed ablation. The expansion of the hot outer layer compresses the inner core of the pellet causing it to implode. Energy from the hot outer layers and the laser continue to heat the inner core until it reaches fusion temperatures. 

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