Diffusion spinodal decomposition

Dynamic Phenomena Inter diffusion, Spinodal Decomposition... 

Binder K 1983 Collective diffusion, nucleation, and spinodal decomposition in polymer mixtures J. Chem. Phys. 79 6387... 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

Phases may also become unstable with regard to compositional fluctuations, and the effect of compositional fluctuations on the stability of a solution is considered in Section 5.2. This is a theme of considerable practical interest that is closely connected to spinodal decomposition, a diffusion-free decomposition not hindered by activation energy. 

Let us now consider a system composed of a polymer and a solvent. For compositions in between the inflection points, solvent molecules will diffuse into the solvent-rich phase, and the polymer molecules diffuse in the polymer-rich phase. Thus diffusion occurs against a concentration gradient. Therefore, this type of phase separation is known as up-hill diffusion. The up-hill diffusion leads to a spontaneous decomposition and it is therefore also named spinodal decomposition. The formation of two phases via spinodal decomposition occurs immediately upon reaching the spinodal decomposition region and does not require any activation energy. 

Uphill diffusion in binary systems and spinodal decomposition... 

From the above analysis, it can be seen that D in Pick s first law J = -DVC (Equation 3-6) may be either positive or negative (accounting for uphill diffusion), and it can vary from positive to negative along a spinodal decomposition diffusion profile. If, on the other hand. Pick s law is modified as J = -(T>/y)Va (Equation 3-61), then V is always positive in a binary system. 

Uphill diffusion in a binary system is rare and occurs only when the phase undergoes spinodal decomposition. In multicomponent systems, uphill diffusion occurs often, even when the phase is stable. The cause for uphill diffusion in multicomponent systems is different from that in binary systems and will be discussed later. 

The initial stage of spinodal decomposition can be expressed as follows by the diffusion equation ... 

The discussion up to this point has been concerned essentially with metal alloys in which the atoms are necessarily electrically neutral. In ionic systems, an electric diffusion potential builds up during the spinodal decomposition process. The local gradient of this potential provides an additional driving force, which acts upon the diffusing species and this has to be taken into account in the derivation of the equivalents of Eqns. (12.28) and (12.30). The formal treatment of this situation has not yet been carried out satisfactorily [A.V. Virkar, M. R. Plichta (1983)]. We can expect that the spinodal process is governed by the slower cation, for example, in a ternary AX-BX crystal. The electrical part of the driving force is generally nonlinear so that linearized kinetic equations cannot immediately be applied. 

Figure 18.7 Interfaces resulting from two types of continuous transformation, (a) Initial structure consisting of randomly mixed alloy, (b) After spinodal decomposition. Regions of B-rich and B-lean phases separated by diffuse interfaces formed as a result of long-range diffusion, (c) After an ordering transformation. Equivalent ordering variants (domains) separated by two antiphase boundaries (APBs). The APBs result from A and B atomic rearrangement onto different sublattices in each domain.

In concentrated Al-Zn alloys, the kinetics of precipitation of the equilibrium 0 phase from a are too rapid to allow the study of spinodal decomposition. An Al-22 at. % Zn alloy, however, has decomposition temperatures low enough to permit spinodal decomposition to be studied. For Al-22 at. % Zn, the chemical spinodal temperature is 536 K and the coherent spinodal temperature is 510 K. The early stages of decomposition are described by the diffusion equation... 

Neutral NIPA gel is the most extensively studied among known gels from the standpoint of phase transition, and thus, various physical properties around the transition have been reported. These include the shear and bulk modulus [20, 24], the diffusion constant of the network [25], spinodal decomposition [26], specific heat [21], critical properties of gels in mixed solvents [8] and the effect of uniaxial [27] and hydrostatic [28] pressures on the transition, and so... 

The local composition changes during spinodal decomposition and precipitation by nucleation and growth are compared in Figure 11.24. It is interesting to note that spinodal decomposition requires uphill diffusion. The boundary between... 

Keywords Cahn-Hilliard model Diffusion Nonlinear dynamics Pattern selection Polymer blends Soret effect Spinodal decomposition Thermal diffusion... 

Sj = Dj/D and D = (MkBTc b )/v are the Soret and the diffusion coefficient, respectively. In the absence of thermal diffusion, (49) reduces to the well known Cahn-Hilliard equation, which belongs to the universality class described by model B [3], In fact, (49) gives a universal description of a system in the vicinity of a critical point leading to spinodal decomposition. 

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