Dynamics of Phase Separation

The flow behavior of the polymer blends is quite complex, influenced by the equilibrium thermodynamic, dynamics of phase separation, morphology, and flow geometry [2]. The flow properties of a two phase blend of incompatible polymers are determined by the properties of the component, that is the continuous phase while adding a low-viscosity component to a high-viscosity component melt. As long as the latter forms a continuous phase, the viscosity of the blend remains high. As soon as the phase inversion [2] occurs, the viscosity of the blend falls sharply, even with a relatively low content of low-viscosity component. Therefore, the S-shaped concentration dependence of the viscosity of blend of incompatible polymers is an indication of phase inversion. The temperature dependence of the viscosity of blends is determined by the viscous flow of the dispersion medium, which is affected by the presence of a second component. 

Similar arguments explaining the phase separation were employed by Chou et al. [44]. The dynamics of phase separation was observed using an optical microscope during the course of polyurethane-unsaturated polyester IPN formation at different temperature. Chou et al. suggested that an interconnected phase formed through the spinodal decomposition mechanism developed quickly and was followed by the coalescence of the periodic phase to form a droplet/matrix type of morphology. The secondary phase separation occurred within both the droplet and the matrix phases. Chou et al. did not explain, however, why secondary phase separation occurred. 

Equation (53) describes the dynamics of phase separation in the presence of a spatially periodic forcing following a quench from the stable one-phase region (e < 0) to a reference temperature in the two-phase region (e > 0). In the following only the case of a symmetric quench with / dry = 0 as initial condition at t = 0 will be considered. 

The second is to examine the dynamics of phase separation and phase dissolution which can be pursued by scattering techniques. This topic involves the fundamental problem of self-organization in polymer systems under non-equilibrium conditions. 

Thermal fluctuations can contribute dominantly to the scattering intensity right after the isothermal phase separation starts [70,76], Therefore, conditions 1) and 3) must be fulfilled to ensure that the effect of thermal noise is negligible. The dynamics of phase separation can be adequately described by the mean-field model if condition 2) is satisfied. Condition 2) is a direct consequence of the Landau Ginzburg criterion [75]. Thus, one may establish prerequisites for Eqs. (27) and (33) are the conditions 1) and 3), while Eq. (34) requires conditions 2) and 3). For example, Eq. (27) and as a consequence Eq. (33) cannot be confirmed experimentally not even for small values of q if the quench depth e is too small [70]. Moreover, owing to the effect of thermal fluctuations, Eq. (33) fails at q as qc even if the Landau Ginzburg criterion is fulfilled [70,77]. Thus, in the former case condition 2) is violated whereas in the latter example conditions 1) and 3) are not satisfied. 

P. Kablinski, W.-J. Ma, A, Maritan, J. Koplik and J. R. Banavar, Molecular Dynamics of Phase Separation in Narrow Channels, Phys. Rev. E 41 (1993) R2265-R2268. 

When a binary mixture is quenched in the unstable coexistence region, by thermal treatment or pressure changes or simply by mixing the two macromolecules, fluctuations in density grow with time, and finally result in a complete phase separation. The dynamics of phase separation are generally divided into early, intermediate and late stages. The different stages can be described by means of the temporal evolution of the scattered intensity function.20-22... 

As Eq 2.73 indicates, the light scattering intensity, I(q, t) is proportional to S (q, t). For this reason the plot of I(q, t) vs. q (at constant decomposition time and temperature) already provides evidence of the dynamics of phase separation in polymer blends. 

The mechanism of phase separation is analyzed from the R vs. q dependence. The dynamics of phase separation within the SD domain starts with balance between the thermodynamics and material flux. The mean field theory of phase separation leads to the following simple form of the virtual structure function, S(q) [Cahn and Hilliard, 1958] ... 

Phase Field Approach to Thermodynamics and Dynamics of Phase Separation and Crystallization of Polypropylene Isomers and Ethylene-Propylene-Diene Terpolymer Blends... 

M. Doroshenko, et al., Monitoring the dynamics of phase separation in a polymer blend by confocal imaging and fluorescence correlation spectroscopy, Macromol. Rapid Commun. 33 (18) (2012) 1568—1573. 

Coarsening Dynamics of Phase Separation During the Late Stages... 

El-Mabrouk, K. and Bousmina, M. (2005) Effect of hydrodynamics on dynamics of phase separation in polystyrene/poly (vinyl methyl ether) blend. Polymer,... 

Jyotishkumar, P., Ozdilek, C., Moldenaers, P., Sinturel, C., Janke, A., Pionteck, P., and Thomas, S. (2010) Dynamics of phase separation in poly(acrylonitrile-hutadiene-... 

Here, is the volume fraction of A block in diblock copolymer. To study the dynamics of phase separation, the polymeric external potential dynamics (EPD) method can be employed, which was proposed by Maurits and Fraaije [23] in dynamic density functional theory (DDFT) method (bead-string model). In EPD, the monomer concentration is a conserved quantity, and the polymer dynamics is inherently of Rouse type. The external dynamical equation in terms of the potential field m,- is expressed as... 

The same conclusion emerges when one considers the dynamics of phase separation in experiments where one quenches a polymer blend into the two-phase region underneath the misdbility gap (Fig. 7.1). The initially inhomogeneous state is unstable and fluctuations grow with time t after the quench their characteristic wavelength Am(/) (which shows up by a peak in the scattering function S q, t) at a wavenumber q = qm t) = 2n/Xm(t)) again is typically of the order of " 10 A. 

Influence of Nanoparticles on the Dynamics of Phase Separation in Polymer Blends... 

Let us now return to the case of a ternary mixture (nanopartide/homopolymer A/ homopolymer B) and consider its thermodynamic phase behavior. From dynamic simulations, we have already determined that nanopartides can change at least the dynamics of phase separation if the polymers are immisdble. Can the particles modify the phase boundaries itself ... 

Laradji and Here [72] have simulated the dynamics of phase separation in binary blends in the presence of nanorods the simulations predicted that rods would dramatically slow down, and possibly stop, the phase separation, leading to the stabilization of a single-phase morphology. Still, it is not clear whether this morphology is a simple homogeneous structure or, more likely, a complicated phase like a microemulsion. Similarly, there have been some experimental studies [50] suggesting that nanoplatelets could lead to microemulsion-like behavior, when platelets occupy interfaces between A-rich and B-rich domains and stabilize them. At present, to our knowledge, there is no satisfactory theory to describe this behavior, and more research is needed. 

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