Spinodal Decomposition In Binary Mixtures Research Articles

Two-dimensional Cahn-Hilliard simulations for coarsening kinetics of spinodal decomposition in binary mixtures.

The evolution of the microstructure due to spinodal decomposition in phase separated mixtures has a strong impact on the final material properties. In the late stage of coarsening, the system is characterized by the growth of a single characteristic length scale L ∼ Ctα. To understand the structure-property relationship, the knowledge of the coarsening exponent α and the coarsening rate constant C is mandatory. Since the existing literature is not entirely consistent, we perform phase field simulations based on the Cahn-Hilliard equation. We restrict ourselves to binary mixtures using a symmetric Flory-Huggins free energy and a constant composition-independent mobility term and show that the coarsening for off-critical mixtures is slower than the expected t1/3-growth. Instead, we find α to be dependent on the mixture composition and associate this with the observed morphologies. Finally, we propose a model to describe the complete coarsening kinetics including the rate constant C.

Multiparticle collision dynamics for fluid interfaces with near-contact interactions.

We present an extension of the multiparticle collision dynamics method for flows with complex interfaces, including supramolecular near-contact interactions mimicking the effect of surfactants. The new method is demonstrated for the case of (i) short range repulsion of droplets in close contact, (ii) arrested phase separation, and (iii) different pattern formation during spinodal decomposition of binary mixtures.

Spinodal Theory: A Common Rupturing Mechanism in Spinodal Dewetting and Surface Directed Phase Separation (Some Technological Aspects: Spatial Correlations and the Significance of Dipole-Quadrupole Interaction in Spinodal Dewetting)

The emerging structures in spinodal dewetting of thin nano films and spinodal decomposition of binary mixtures are found to be similar with certain differences attributed to the nonlinearities inherent in the wetting forces. This paper deals with the technological aspects of the spinodal processes by giving a brief account of the theory and to correlate the two phenomena termed as spinodal dewetting of thin nanofilms and surface-directed phase separation. The MC simulation micrographs at early stage of spinodal dewetting of a (linear) polymer film confined between two hard walls (using FENE potential between the beads on same chain and Morse potential between inter and intra chain beads) show similarities with surface-directed phase separation (using metropolis algorithm) in creation of holes. The spinodal dewetting is also criticized on the basis of global minimization of free energy emerging from dipole-quadrupole interactions. A novel molecular scale-driving mechanism coming from asymmetric interface formation in spinodal processes is also proposed. It can be believed that the modeling done with the films under confinement of two walls works as a classical mathematical ansatz to the dipole-quadrupole interaction coming from quantum origins and giving rise to lateral interactions in the process reflecting a colossal behavior in thin nano films though weak in nature.

Spinodal decomposition of binary mixtures with composition-dependent heat conductivities

Spinodal decomposition of a very viscous binary mixture is simulated, assuming that the fluid is bounded by two walls that are instantaneously quenched below the critical temperature. As usual, the mixture phase separates by forming dendritic structures whose size grows with time. While in conventional spinodal decomposition the morphology of the mixture is isotropic, here we show that, when the two components of the mixture have different heat conductivities, the configuration of the mixture may become anisotropic, depending on whether heat propagates slower or faster than mass. Specifically, for large heat conductivity differences, when the Lewis number is small, dendrites tend to align parallel to the isothermal lines; when it is large, dendrites progressively align perpendicular to the isothermal lines. This behavior can be explained observing that the morphology of the mixture is the result of two competing effects: on one hand, the mixture phase separates as soon as its temperature reaches its critical value and therefore it tends to follow the isothermal lines; on the other hand, the system tend to maximize heat transport, and therefore dendrites tend to span between the two quenched walls, i.e. perpendicular to the isothermal lines. This explanation is confirmed showing that when the imposed temperature difference between the side walls (and therefore the heat flux at equilibrium as well) is increased, dendrites tend to align across the walls more and more.

The Morphology and Dynamics of Substrate Effects on Spinodal Decomposition in Binary Mixtures with Short‐Range Potential

AbstractSummary: The SDSD of binary mixture with short‐range potential is numerically simulated in 3D by cell dynamic system (CDSs), focusing on the phase morphology and dynamics in the parallel cross‐sections. The formation mechanism and growth law of the wetting layer are analyzed taking thermal noise effects into account. The simulated results show that the phase inversion in the parallel cross‐sections can be observed near the substrate interface. Without thermal noise, the growth law of the wetting layer is simply logarithmic. However, when the strength of thermal noise is large enough, the LS growth law can be found for a short‐range surface field. The results demonstrate that thermal noise can increase the extent of phase separation and lead to a transformation between partial and complete wetting for the substrate interface. The evolution of the phase in the parallel cross‐sections obeys the LS growth law and is self‐similar regardless of the effects of thermal noise.Simulated pattern evolution at different values of z at τ = 1 000 with G = 0.magnified imageSimulated pattern evolution at different values of z at τ = 1 000 with G = 0.

Cellular Automata Model of Phase Transition in Binary Mixtures

We investigate the dynamical behavior of spinodal decomposition in binary mixtures using a variation on the Rothman−Keller cellular automaton, in which particles of type A(B) move toward domains of greater concentration of A(B). Domain growth and system morphologies are determined via the pair correlation function, revealing that (i) the characteristic domain size grows as R(t) ≈ t1/3 and (ii) the configurations of the mixtures at different times are self-similar. These results did not change when different game rules were adopted, indicating that self-similarity and the 1/3 scaling law constitute fundamental properties of any diffusion-driven phase separation process. The same model also was applied to describe the mixing process, and, as expected, it was determined that the characteristic time was dependent on the square of a characteristic linear dimension of the system.

The Cahn-Hilliard equation with dynamic boundary conditions

This paper is concerned with the following Cahn-Hilliard equation $ \psi _t = \Delta \mu, $ where $ \mu= -\Delta \psi -\psi +\psi ^3, $ subject on the boundary $\Gamma$ to the following dynamic boundary condition $ \sigma _s \Delta _{||} \psi - \partial _{\nu} \psi + h_s -g_s \psi = \frac{1}{\Gamma _s} \psi _t $ and $ \partial _{\nu} \mu =0, $ and the initial condition $ \psi |_{t=0}= \psi _0. $ This problem was recently proposed by physicists to describe spinodal decomposition of binary mixtures where the effective interaction between the wall (i.e., the boundary $\Gamma$) and two mixture components are short-ranged. The global existence and uniqueness of solutions to this initial boundary value problem with highest-order boundary conditions is proved.

Shock wave stability under the spinodal decomposition of binary mixtures

A diffusion equation for a binary mixture and spinodal decomposition in the case of phase separation are considered. It is shown that, if the binding force between polymer chain links is weak, the diffusion equation for a binary mixture allows for the reduction to the Burgers equation with “viscosity”; that is, the coexistence of rarefaction waves and shock density waves is a possibility. The effect of strong bonds between polymer chain links on the spinodal decomposition dynamics is studied. It is demonstrated that strong bonding may cause a multiflux wave system with alternate stability to arise when the viscosity varies.

Binary fluid demixing: The crossover region

By performing lattice Boltzmann simulations of a binary mixture, we scrutinize the dynamical scaling hypothesis for the spinodal decomposition of binary mixtures for the crossover region, i.e., the region of parameters in the growth curve where neither inertia nor viscous forces dominate the coarsening process. Our results give no evidence for a breakdown of scaling in this region, as might arise if the process were limited by molecular scale physics at the point of fluid pinch-off between domains. A careful data analysis allows us to refine previous estimates on the width of the crossover region which is somewhat narrower than previously reported.

Dewetting: film rupture by nucleation in the spinodal regime.

Unstable thin liquid films on solid substrates dewet by hole nucleation on defects or by a linear surface instability (spinodal dewetting). A system with destabilizing short-range and stabilizing long-range molecular interactions is investigated. We show that, for a subrange within the linearly unstable film thickness range, nucleation determines the final structure, whereas spinodal dewetting is of negligible influence. The results are also applicable to the spinodal decomposition of binary mixtures.

Surface enrichment effect on the morphological transitions induced by directional quenching for binary mixtures

The morphological transitions during directional quenching-induced spinodal decomposition in binary mixtures are investigated by computer simulation. By setting the quenching front between the stable and unstable phases, and shifting the front with a constant velocity, the evolution of the domain morphologies is examined numerically on the basis of the time-dependent Ginzburg–Landau (TDGL) equation. Three different types of morphologies are found for the critical quenching. One is irregular morphology (IM), which is essentially equivalent to that produced by homogeneous quenching. The other two are regular, representing the characteristics of the directional quenching process. One is regular lamellar morphology (RLM) and the other is regular column morphology (RCM). By varying the shifting velocity of the cooling front, two morphological transition velocities, va from IM to RLM, and vi from RLM to RCM, are observed. In contrast to that, for the case of off-critical quenching, a new transition velocity vb from RCM back to RLM can be found if the cooling front is further shifted slower. This characteristic morphological transition is attributed to the surface enrichment effect appearing in the nonequal volume fraction system, which competes with linear instability triggered by initial thermal fluctuation in the early stage of spinodal decomposition. Detailed studies reveal that RLM can be easily formed and thus the region of RCM is reduced when the surface enrichment effect is stronger. On the other hand, RCM will be preferred if the initial thermal fluctuation is stronger. The quantitative relation between lamella width and shifting velocity of the cooling front is also presented.

Spinodal Decomposition of Binary Mixtures in Uniform Shear Flow

The spinodal decomposition of binary mixtures in uniform shear flow is studied in the context of the time-dependent Ginzburg-Landau equation, approximated at one-loop order. We show that the structure factor obeys a generalized dynamical scaling with different growth exponents ${\ensuremath{\alpha}}_{x}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5/4$ and ${\ensuremath{\alpha}}_{y}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/4$ in the flow and in the shear directions, respectively. The excess viscosity $\ensuremath{\Delta}\ensuremath{\eta}$ after reaching a maximum relaxes to zero as ${\ensuremath{\gamma}}^{\ensuremath{-}2}{t}^{\ensuremath{-}3/2}$, $\ensuremath{\gamma}$ being the shear rate. $\ensuremath{\Delta}\ensuremath{\eta}$ and other observables exhibit log-time periodic oscillations which can be interpreted as due to a growth mechanism where stretching and breakup of domains cyclically occur.

Surface effects on spinodal decomposition in binary mixtures: The case with long-ranged surface fields

We present detailed numerical results for phase-separation kinetics of critical binary mixtures in the vicinity of a surface that exerts a long-ranged attractive force on one of the components of the mixture. We consider surface potentials of the form $V(Z)\ensuremath{\sim}{Z}^{\ensuremath{-}n}$, where $Z$ is the distance from the surface and $n=1,2,3$. In particular, we investigate the interplay of the surface wetting layer with the dynamics of domain growth. We find that the wetting layer at the surface exhibits power-law growth with an exponent that depends on $n$, in contrast to the case with a short-ranged surface potential, where the growth is presumably logarithmic. From correlation functions, we identify characteristic length scales in directions parallel and perpendicular to the surface. We observe a regime of accelerated growth in the parallel direction and critically examine some possible explanations for this.

Spinodal decomposition in binary mixtures.

We study the early stage of the phase separation of a binary mixture far from its critical point of demixing. Whenever the mixture of two mutually repulsive species is quenched to a temperature below its critical point of miscibility, the effect of the enthalpic repulsive force prevails upon the entropic tendency to mix, so that the system eventually separates itno two coexisting phases. We have developed a highly nonlinear model, in close analogy with the linear theory of Cahn and Hilliard, where a generalized free energy is defined in terms of two parameters \ensuremath{\psi} and a, the first describing the equilibrium composition of the two phases, ad the second denoting a characteristic length scale that is inversely proportional to the equilibrium surface tension. The linear stability analysis predicts that any perturbation of the initial mixture composition with wave number k smaller than \ensuremath{\surd}2\ensuremath{\psi} /a will grow exponentially in time, with a maximum growth corresponding to ${\mathit{k}}_{\mathrm{max}}$= \ensuremath{\surd}\ensuremath{\psi} /a. A numerical solution of the equation shows that nonlinear effects saturate the exponential growth, and that the concentraiton distribution tends to a steady state, peroidic profile with wavelength \ensuremath{\lambda}=2\ensuremath{\pi}a/ \ensuremath{\surd}\ensuremath{\psi} corresponding to the fastest growing mode of the linear regime. The main result of our theoretical model is that this steady state does not depend on the form of the initial perturbation to the homogeneous composition profile. \textcopyright{} 1996 The American Physical Society.

Surface effects on spinodal decomposition in binary mixtures and the interplay with wetting phenomena.

The phase separation of binary mixtures in a semi-infinite geometry is investigated both by a phenomenological theory and by numerical calculations using a discrete equivalent of the descriptive equations. In the framework of ``model B'' (which describes solid binary mixtures), attention is paid to a proper treatment of the boundary conditions at the free surfaces. We confine ourselves to short-range surface forces and consider parameter values that correspond to both nonwet and wet surfaces in thermal equilibrium. During the initial stages of spinodal decomposition, after a quench from considering an initial condition that corresponds to a completely random concentration distribution, one finds a rather rapid growth of a thin surface enrichment layer of the component that is energetically preferred by the surface. This layer stabilizes a growing concentration wave in the direction normal to the surface, whose oscillations are damped to zero as one goes into the bulk. Studying concentration correlations in the direction parallel to the surface at a distance z from it, one can define a length scale ${\mathit{l}}_{\mathrm{\ensuremath{\parallel}}}$(z,t) describing the coarsening of the growing domains. We find that ${\mathit{l}}_{\mathrm{\ensuremath{\parallel}}}$(z,t)\ensuremath{\approxeq}A(z)+B(z)${\mathit{t}}^{\mathit{a}}$ for large t, with an amplitude B(z) that increases as z\ensuremath{\rightarrow}0 and an exponent a which is close to that for Lifshitz-Slyozov growth, viz., a\ensuremath{\approxeq}1/3. This increase is due to an orientation of the growing elongated domains parallel to the surface near z=0. There is surprisingly little influence of the wetting transition on these phenomena--even for a wet surface the growth of the wetting layer is only logarithmic in time for short-range surface forces, and hence does not significantly affect phenomena on the faster time scales of spinodal decomposition. Experimental findings on the interplay of spinodal decomposition and wetting are critically discussed.

Kinetically stable polymers and the problem of the glass transition in polymers

A previously obtained non-linear equation for the relaxation in the density of a single-component polymeric liquid has been investigated in order to describe the glass-transition in polymers. As in the case of the equation for the spinodal decomposition of binary mixtures, a thermodynamically favourable stationary solution is achieved by passing through a sequence of rearrangements of labile but kinetically stable structures, close to the labile stationary solutions. Relaxation occurs as the alternation of rapid rearrangement of this type with long retardations.

Polymer blends

AbstractSmall angle neutron scattering may be used to provide information on the thermodynamic basis of polymer‐polymer miscibility via the temperature and concentration dependences of the observed interaction parameters. The kinetics of the phase separation process may also be followed and this in turn gives further information about the blend compatibility as well as providing tests of current theories of spinodal decomposition in binary mixtures.

Scattering function and the dynamics of phase separation in polymer mixtures under shear flow

The phenomenological mean-field theory describing concentration fluctuations and spinodal decomposition of binary mixtures of long flexible macromolecules is generalized to mixtures under steady shear flow. This shear flow leads to a partial orientation and stretching of the coils, as well as to an anisotropic deformation of concentration fluctuations. Generalizing the approach of Onuki and Kawasaki, we obtain the collective scattering function describing these concentration fluctuations in the mixture under shear flow. Both the steady-state situation in the one-phase region and the initial stages of spinodal decomposition for concentrations inside of the spinodal curve are considered.

Kinetics of phase separation in the presence of slowly relaxing structural variables

The linearized Cahn–Hilliard theory of spinodal decomposition of binary mixtures is generalized to the case where there is a coupling to a slowly relaxing variable (e.g., phase separation of polymer mixtures near a glass transition, etc.). A very simplified model calculation is presented which shows that even in the very early stages pronounced deviations may occur from the simple exponential growth predicted by the standard linear theory. Also the growth rate of the unstable fluctuations is strongly affected: A regime is identified where the initial growth rate is independent of wave number k and controlled by the relaxation rate of the structural variable, rather than given by the standard ‘‘uphill diffusion’’ with diffusivity linearly decreasing with k2. Possible applications of these ideas to real systems are briefly discussed.

IS LASER-INDUCED NUCLEATION DUE TO A BULK LONG-WAVELENGTH INSTABILITY ?

The speculative suggestion is made that laser-Induced Nucleation of single crystals from amorphous thin films is due to an instability of the system against certain long-wavelength fluctuations, analogous to spinodal decomposition of binary mixtures.