Critical binary

By definition assessed databases are focused, usually on material types. The recent A1-, Ni- and Ti-databases (Saunders 1996a-c) and, to a large degree, the Fe-databases produced by KTH in Stockholm are good examples. They contain up to 15 elements and have been designed for use within the composition space associated with the different material types. All, or most, of the critical binary and... 

Let us examine the critical dynamics near the bulk spinodal point in isotropic gels, where K + in = A(T — Ts) is very small, Ts being the so-called spinodal temperature [4,51,83-85]. Here, the linear theory indicates that the conventional diffusion constant D = (K + / )/ is proportional to T — Ts. Tanaka proposed that the density fluctuations should be collectively convected by the fluid velocity field as in near-critical binary mixtures and are governed by the renormalized diffusion constant (Kawasaki s formula) [84],... 

Previous experimental and theoretical studies have found what appears to be clear evidence for cluster formation, or local density enhancement, in near critical solutions (7t12t42-45). These include experimental optical absorption, fluorescence and partial molar volume measurements as well as theoretical simulation studies. These offer compelling evidence for local solvent density enhancement in near critical binary SCF systems. Theoretical models suggest that local density enhancement should be strongly dependent on the relative size and attractive force interactions strengths of the solute and solvent species as well as on bulk density and temperature (7,44). 

In ref. ( °) the applications of the analogous dependences (eq. (1) and (2)) for the pressure evolution of the glass temperature and the melting temperature in supercooled liquids were shown. It is noteworthy that both alcohols and water are important technological agents, also used as additives to the CO2 basic critical system. For the discussed case of binary mixtures of limited miscibility the critical behavior is the inherent feature of the system containing water and alcohol or nitrobenzene or nitrotoluene and alkanes, even under atmospheric pressure. When critical binary mixtures are considered as the base for the SCF technologies, no additional component is needed. 

Analysis of the slow forward relaxation (12) reveals [63] that the associated Kerr constant follows a power law, i.e., B is proportional to the distance in temperature from Tc as (1 — Tc/Ty", with

static electrical birefringence is in accord with the droplet model [66,67] of critical binary mixtures. The central idea of the droplet model is that the electric field distorts (orients or vectorially amplifies) the spontaneous critical concentration fluctuations. The resulting anisotropic fluctuations then play the role of nonspherical particles in ordinary electrical birefringence. The magnitude of the concentration fluctuations rapidly increases as T,. is approached. 

Optohydrodynamics Fluid Actuation by Light, Fig. 2 Variation of the interface bending for increasing beam power P (a) upward and (b) downward continuous Ar" laser beam (wavelength in vacuum io = 514 nm) of beam waist coo- The theoretical profiles (solid lines) are calculated from Eq. 7. Experiments are performed in a phase-separated near-critical binary liquid mixture in order to drastically reduce the interfacial tension when approaching in temperature the critical temperature Tc-... 

Onuki, A. (1986) Shear flow problems in critical binary mixtures. Physica A... 

Huang, J.S., Goldburg, W.I., and Bjerkaas, A.W. (1974) Study of phase separation in a critical binary liquid mixture spinodal decomposition, Phys. Rev. Lett. 32,921. 

Critical binary interaction parameters Nxab and Na and Ncp. understanding and know how to calculate xab, Na, and JVcp... 

The introduction of a relevant expression for the critical determinant in the mean-field lattice gas model for binary systems is discussed here. It leads to an alternative and thermodynamic consistent method of adjusting two-particle interaction functions to experimental critical binary 1iquid-vapour densities. The present approach might lead to new developments in the determination of MFLG parameters for the mixture in small-molecule mixtures and in polymer solutions and polymer mixtures (blends). These relevant critical conditions appear because of the extra constraint, which is the equation of state, put on the hole model, and are... 

Boots has applied the theory of multiple scattering to critical binary mixtures and concludes that it is essentially repeated single scattering so that the general structure of scattering formulae is unaltered. Cohen has considered in detail the theoretical relationships between thermodynamic parameters for polymer solutions and the intensities of Rayleigh and Brillouin scattering peaks. 

Povodyreveta/. (1997) have developedasix-term Landau expansion crossover scaling model to describe the thermodynamic properties of near-critical binary mixtures, based on the same model for pure fluids and the isomorphism principle of the critical phenomena. The model describes densities and concentrations at vapor-liquid equflibrium and isochoric heat capacities in the one-phase region. The description shows crossover from asymptotic Ising-hke critical behavior to classical (mean-field) behavior. This model was applied to aqueous solutions of sodium chloride. 

Kiselev, S. B. Kulikov, V D. (1994) Crossover behaviour of the transport coefficients of critical binary mixtures. Int. J. Thermophys., 15,283-308. 

II.3. Critical binary mixture (Dp= 2.5) In contact with a solid wall, a binary mixture has a concentration Cs at the wall different from the bulk concentration C. If the mixture is near critical, this modification is not restricted to the interface, but extends over a length... 

Mean field theory predicts that the critical lines of blend like and diblock like behavior meet at the isotropic critical lifshitz point and the lifshitz line (LL) which is defined when Q becomes zero. The isotropic critical Lifshitz point represents a new imiversahty class [54-56]. Under special conditions even a tricritical Lifshitz point is predicted [55]. In this article we will discuss in some detail SANS experiments on a mixture of a critical binary (A/B) polymer blend with different concentrations of a symmetric (A-B) diblock copolymer of roughly five times larger molar volume. Under such conditions an isotropic critical Lifshitz point is predicted [55]. 

Figure 15 Schematic representation of hierarchical structures developed in critical binary mixtures of A and B molecules (A/B) in a phase-separation process of the late stage SD. Note that the two components here have the dynamic symmetry (i.e., nearly equal mobilities) and equal volume fraction, (a) to (c) refers to (1) global, (2) interface, and (3) interphase structure and (4) local structure, respectively, where r, Am, Rm, h, int, fr, and Rg refer to the length scale of observation, the characteristic length of the phase-separating domain structures, the scattering mean radius of curvature, the thickness of the diffuse boundary (interphase), the thermal correlation length within the interphase, the thermal correlation length within the phase-separated domains, and the radius of gyration of polymers, respectively. From Hashimoto, T. J. Polym. Sci., Part B Polym. Phys. 2004, 42, 3207-3262.= ...

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