Abstract. We consider a critical binary mixture made of two incompatible polymers A and B, confined between two parallel plates 1 and 2, which are at a finite distance L from each other. We assume that the latter adsorb strongly both polymers at a temperature above the consolute point c T . The strong fluctuations of composition generate a Casimir force between the two plates. Our aim is precisely the computation of such a force as a function of the separation L. Use is made of the standard 4 ψ -theory, where ψ is the composition fluctuation or order parameter. We show that the presence of surfaces can be taken into account by imposing two boundary conditions, which depend on two couples of parameters: ( ) h play the role of magnetic fields. We prove that these parameters depend explicitly on the surface chemical potentials changes 1 µ and 2 µ , and the energies A δ and B δ necessary to adsorb one A-monomer and one B-monomer on the surfaces. For simplification, we choose two special boundary conditions: symmetric and asymmetric plates, depending on whether the plates have the same or opposite preferences for polymers A and B. We also show that the surface coupling constants i c 's are negative. Thus, the system we consider belongs to the same universality class as the traditional extraordinary transition. We demonstrate that, in the strong adsorption limit, both i c 's and i h 's become infinite, so that the resulting Casimir force becomes universal. For both symmetric and asymmetric plates, we find that the (attractive and repulsive) Casimir forces (per unit area) decrease with the distance L according to a negative, and we compute exactly the corresponding universal amplitudes.Finally, the obtained Casimir force for critical polymer blends is compared to that resulting from vacuum fluctuations of a magnetic field confined to the same geometry. In both cases, the forces decay with separation L according to the same law.
We consider here a low-density assembly of colloidal particles immersed in a critical polymer mixture of two chemically incompatible polymers. We assume that, close to the critical point of the free mixture, the colloids prefer to be surrounded by one polymer (critical adsorption). As result, one is assisted to a reversible colloidal aggregation in the nonpreferred phase, due the existence of a long-range attractive Casimir force between particles. This aggregation is a phase transition driving the colloidal system from dilute to dense phases, as the usual gas-liquid transition. We are interested in a quantitative investigation of the phase diagram of the immersed colloids. We suppose that the positions of particles are disordered, and the disorder is quenched and follows a Gaussian distribution. To apprehend the problem, use is made of the standard phi(4) theory, where the field phi represents the composition fluctuation (order parameter), combined with the standard cumulant method. First, we derive the expression of the effective free energy of colloids and show that this is of Flory-Huggins type. Second, we find that the interaction parameter u between colloids is simply a linear combination of the isotherm compressibility and specific heat of the free mixture. Third, with the help of the derived effective free energy, we determine the complete shape of the phase diagram (binodal and spinodal) in the (Psi,u) plane, with Psi as the volume fraction of immersed colloids. The continuous "gas-liquid" transition occurs at some critical point K of coordinates (Psi(c) = 0.5,u(c) = 2). Finally, we emphasize that the present work is a natural extension of that, relative to simple liquid mixtures incorporating colloids.
In this study, we focused on the presentation of clay minerals, their conditions of formation and their different categories. We also reported the importance of purification in removing impurities and the responses induced by heat treatment of these minerals. Techniques used to detect clay minerals are also exposed. On the other hand, the mineralogical, physicochemical and thermal properties have a direct impact on the field of use of these minerals. These properties differ from one mineral to another, depending on the structure and chemical composition. Moreover, the remarkable properties of smectites make these minerals the most preferred for the industry and also in the environmental field. Due to their brilliant firing properties, illites are suitable for the construction industry. Moreover, the purification by acids (acetic acid and HCl) allows the removal of most associated minerals, and thus a secure access to the clays' characteristics and a very strong sensitization even to the small variation. Finally, the ethylene glycol (EG) swelling test only affects the basal distance of smectites, increasing this distance to 17 Å, but heating to 500°C destroys kaolinite, and closes the basal distance of smectites and vermiculites to 10 Å. Illites and chlorites show no response to these two treatments (EG, heating to 500°C).
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