Spinodal Decomposition In Polymer Blends Research Articles

Phase-field simulation of thermally induced spinodal decomposition in polymer blends

A phase-field simulation of thermally induced phase separation with various initial average concentrations under different quench depths is systematically carried out in this paper. The resultant morphology of the phase-separated materials is determined by the quench temperature and the average concentration. A detailed understanding of the effects of quench depth during the phase separation process of spinodal decomposition (SD) is presented. The coarsening mechanism with various average concentrations is investigated. In addition, hydrodynamic effects play an important role in phase separation in liquid immiscible alloys. Therefore, a systematic comparison between systems with and without hydrodynamic effects under different conditions is also considered. The model developed and the results obtained could shed light on using SD in immiscible polymer systems to obtain desired nanostructures for advanced applications.

Percolation-to-droplets transition during spinodal decomposition in polymer blends, morphology analysis.

Phase separation kinetics of the off-critical mixture of polystyrene and poly(methylphenylsiloxane) is studied by the time-resolved light scattering and optical microscopy. The results from the light scattering experiments are correlated with the images obtained by the optical microscopic observation in order to find characteristic features of the scattering intensity during the percolation-to-droplets morphology transition. At the beginning of the spinodal decomposition process only a bicontinuous network is present in the system and the light scattering intensity has only one peak. The network coarsens and at the same time small droplets appear in the system resulting in a growth of the scattering intensity at very small wave vectors. When the large network starts to break up into disjoint elongated domains a second peak in the scattering intensity appears. Finally, both peaks merge into a single peak at zero wave vector, indicating a complete transformation of elongated domains into spherical droplets of variable sizes. The comparison of the direct microscopic observations with the light scattering spectra shows that the process of breaking up of the bicontinuous network starts when the growth of the first peak, corresponding to the bicontinuous pattern, becomes very slow (essentially pinned down).

Crystallization of polycarbonate induced by spinodal decomposition in polymer blends

Abstract We found that amorphous polycarbonate (PC) can be crystallized in several minutes by blending poly(ethylene oxide) (PEO). When the blends were annealed in the two-phase region below the upper critical solution temperature, highly interconnected two-phase structure characteristic of the spinodal decomposition was developed and then the crystallization occurred in the PC-rich phase during the spinodal decomposition. As the molecular weight of PEO decreased, the crystallization rate decreased and the crystallizable temperature became narrower in spite of the acceleration of the polymeric segmental motion. These results suggest that the crystallization of the PC is not induced by the acceleration of the polymeric segmental motion, but by the up-hill diffusion of the liquid–liquid phase separation via spinodal decomposition. Owing to the competitive progress of the crystallization and the spinodal decomposition, the melting peak of the PC crystallites shifted to lower temperature with increasing annealing temperature.

Polydisperse Au nanoclusters on silicon: fractal aggregates via spinodal decomposition?

Deposition of polydisperse Au nanoclusters onto Si via condensation from toluene produces aggregates that may be structurally characterised in terms of their fractal dimension ( D f). Atomic force microscopy reveals a transition (as a function of position on the sample surface) from a percolating, gel-like cluster network to isolated, low D f aggregates, highlighting the key role that local cluster concentration plays in determining the morphology of nanocluster arrays. Although the fractal dimension values measured are consistent with nucleation processes, the cluster layer morphologies bear a striking resemblance to the patterns observed following spinodal decomposition of polymer blends and binary fluid mixtures.

Asymmetric landscapes of early spinodal decomposition

We address the effect of an asymmetric concentration-dependent mobility on the early stages of spinodal decomposition in polymer blends and solutions, and characterise it quantitatively. This is particularly important when one of the components has a slower dynamics than the other, e.g., because it is closer to its glass transition, or is weakly cross-linked. Composition mode coupling is proposed as the underlying physical mechanism, and then investigated by means of numerical simulations of the Cahn-Hilliard equation in one (1d) and two (2d) dimensions. In general, this coupling broadens the peak in the structure factor: in 1d an asymmetric concentration profile is obtained, with sharpened interfaces, whereas in 2d the formation is favoured of sharp peaks of the phase rich in the more mobile component. It is shown how the changing morphology of this phase-separating system can be described with the aid of Minkowski functionals.

Bulk Spinodal Decomposition Studied by Atomic Force Microscopy and Light Scattering

We report the first observation of bulk spinodal decomposition in polymer blends using atomic force microscopy (AFM). The fracture of a phase-separated thick film of tetramethyl bisphenol A polycarbonate (TMPC) and polystyrene (PS) is shown to induce a surface roughness that is resolvable by AFM. The resulting topography reproduces the spinodal morphology and is analyzed quantitatively. We investigate simultaneously the surfaces and bulk of the TMPC/PS films, a blend known to exhibit surface-directed spinodal decomposition. The structure factors obtained from a 2D-FFT of “bulk” AFM images and from time-resolved light scattering (LS) do not coincidethis is discussed in terms of the 2D (AFM) and 3D (LS) analysis involved. We finally compute general expressions relating 2D and 3D structure factors for a number of structures relevant to phase separation phenomena.

Viscoelastic Effects on the Early Stages of Phase Separation in Polymer Blends

We modify the Cahn-Hilliard theory of concentration fluctuation dynamics to account for the short-time networklike nature of high molecular weight polymers. We propose an additional term in the free energy, due to elastic energy arising from the finite lifetime of entanglements. If we assume a single-exponential decay time for the entanglements, the equation of motion is governed by two exponential modes. For quenches into the two-phase region, the faster mode always decays with time, and the slower mode grows. The theory successfully accounts for data from spinodal decomposition of polymer blends containing at least one component of very high molecular weight.

On spinodal decomposition of binary polymer blends under shear flows

A continuum model describing the spinodal decomposition of polymer blends under externally applied shear has been developed. Numerical simulations were conducted for two-dimensional Couette flow. The morphology of the resulting polymer blend was established by competition between diffusion, forced convection and the internally driven flows which arise from concentration gradients. Diffusion and the internal flows tended to give compact and particulate morphologies. Externally imposed shear tended to give elongated structures, but a dynamic equilibrium was sometimes established. If flow was stopped, the elongated structures were comparatively stable when subjected only to diffusion (Ostwald ripening) but were unstable when subjected to the internally driven flows. These results represent a first attempt at understanding the structures of polymer blends prepared in melt processing equipment.

On “Pinning” Domain Growth in Two-Phase Polymer Liquids

What has been reported as “pinning” or severely reduced growth rates of phase-separated domains in off-critical polymer blends is shown to be the normal effect of crossover between two kinetic regimes associated with morphology of the liquid−liquid system. The bicontinuous liquid microstructure formed by spinodal decomposition grows rapidly by hydrodynamic coarsening where size ξ ∼ Lt until the percolated system dissociates into droplets. The droplets then grow by classical coarsening with radius increasing as r̄ 3 ∼ Kt, where K may be calculated for Ostwald ripening and/or coalescence with no impediments to mobility at any size scale. Apparent pinning persists for the induction period Δt ≈ r̄ 3/K required for the slower particle growth to be observed, and the characteristic r̄ ∝ t1/3 behavior is not recovered for approximately 10Δt. Numerical simulations of spinodal decomposition in polymer blends, which to date omit hydrodynamics, are unable to capture the change in growth mechanism and rate on switching from percolated to droplet morphology.

Early states of spinodal decomposition in polymer blends studied with SANS

Time-resolved SANS experiments were performed on two polymer blends after a temperature step. The results are discussed in terms of the Cahn—Hilliard—Cook theory. A non-local Onsager coefficient and non-exponential relaxation were observed.

Effect of a Block Copolymer on the Kinetics of Spinodal Decomposition of Polymer Blends. 2. Scaled Structure Factor

Effects of adding a small amount of a block copolymer to polymer blends composed of the same constituent polymers as the block copolymer on the kinetics of later-stage spinodal decomposition (SD) were investigated by a time-resolved light scattering at three different temperatures in a deep quench condition. Changes in the scaled structure factors F(x)= q m (t;T,O) 3 I(x,t;T,O) with x= q/q m (t;T,O) as a function of the composition of the block copolymer O were analyzed at various temperatures T, where q m (t;T,O) appears. Itwas found that the scaled structure factor obtained for each blend was almost identical, independent of the amount of the block copolymer

Effect of a block copolymer on the kinetics of spinodal decomposition of polymer blends. 1. Nonuniversality in scaled characteristic quantities versus reduced time

Effects of adding a small amount of a block copolymer to polymer blends composed of the same constituent polymers as the block copolymer on the kinetics of early-to-late-stage spinodal decomposition (SD) were investigated by a time-resolved light scattering (LS) at three different temperatures in a deep quench condition. The early-stage SD for the blends with and without the block copolymer was well described by the linearized theory of SD over the small q range covered by the LS method. At each temperature, the coarsening process of the structure self-assembled via SD, as observed by the time changes of the peak scattering intensity I m (t) and the scattering vector q m (t), was slowed with increasing block copolymer content

Monte Carlo simulation of polymeric materials: Recent progress

AbstractMonte Carlo simulations are presented, dealing with phase diagrams of block copolymer melts and polymer blends, including the unmixing kinetics of the latter systems. The theoretical background is briefly reviewed: Ginzburg‐type criteria reveal that in mixtures of long flexible polymers a “crossover” occurs from mean‐field behavior (as described by Flory‐Huggins theory) to nonclassical Ising‐type behavior, and spinodal curves can be unusually sharp. This crossover is demonstrated by large scale simulations of the bond fluctuation model, and it is also shown that for symmetric mixtures the critical temperature scales with chain length as Tc α N. The prefactor in this relation is distinctly smaller than predicted by Flory‐Huggins, but the Curro‐Schweizer integral equation theory prediction Tc α √N is clearly ruled out. Tests of the Cahn theory on the initial stages of spinodal decomposition of polymer blends will also be reported.To conclude, the mesophase formation in block copolymers is discussed, and it is shown that the simulations agree very well with experiment. The pronounced chain stretching that already occurs in the disordered phase is compelling evidence against the validity of simple random phase approximation concepts for these systems. This shows how Monte Carlo simulations can assist in better understanding large classes of polymeric materials.

Nonlinear kinetics of spinodal decomposition, and dissolution of inhomogeneities formed by spinodal decomposition in polymer blends

AbstractNonlinear kinetics of both spinodal decomposition at early stages, and the dissolution of homogeneities formed during spinodal decomposition, is studied. Variation of the scattering intensity during a complete cycle consisting of a step temperature change from T1 in the one‐phase region to T2 in the two‐phase region, a period of spinodal decomposition followed by a temperature drop from T2 back to T1, and the subsequent relaxation to the original equilibrium state, is investigated at various wavenumbers. Step temperature changes within one‐phase region are also investigated.

Fractal behavior of spinodal decomposition in polymer blends

Fractal behaviour of ramified domains in the late stage of spinodal phase separation in a binary polymer blend of poly(vinyl acetate) with poly(methyl methacrylate) was investigated by optical microscopic method. In the late stage of the spinodal decomposition, the fractal dimension D is about 1.64. It implies that some anomalous properties of irregular structure probably may be explained by fractal concepts.

Computer vision methods for the study of spinodal decomposition in polymer blends

AbstractWe demonstrate the use of computer vision techniques and optical microscopy to follow the kinetics and microstructure during spinodal decomposition of a polymer blend. Among other features, the mean of the population of the local maxima of the gradients in each image is computed; this global feature is shown to co‐develop with the phase separation of the blend. An algorithm is presented which employs the gradient magnitude technique to analyze optical images of spinodally decomposing polymer blends. This algorithm has been used to extract the Cahn‐Hilliard spinodal growth rates for a binary blend of polystyrene with poly(vinyl methyl ether). We show that the spinodal temperature can be found from the temperature dependence of this growth rate. We also show how additional shape features such as compactness might be used to study, the same binary blend.

Phase separation in a thermotropic copolyester via spinodal decomposition

Novel experimental evidence is presented for the phase heterogeneity of a thermotropic copolyester containing 50 % of p-hydroxybenzdic acid (HB). Characteristic phase morphologies accompanying spinodal decomposition in polymer blends can be detected. Fractionation and a NMR-analysis demonstrate that the copolyester contains two constituents which differ in their HB-contents.

Structure evolution during spinodal decomposition of polymer blends

Structure evolution during spinodal decomposition of polymer blends

Dynamics of fluctuations and spinodal decomposition in polymer blends. II

We reconsider the initial growth process of the unstable concentration fluctuations when a polymer blend of A and B chains (NA = NB) is rapidly quenched into the unstable region. We correct an earlier result and now predict (i) that the unstable wavelength 2π/? is on the order of R0 (ideal chain radius) for the case of strong segregation, and (ii) the corresponding growth rate is proportional to the melt reptation diffusion constant. These results are consistant with the phase separation kinetics observed in polystyrene–poly(vinyl methyl ether) blends by Nishi, Wang, and Kwei.

Dynamics of fluctuations and spinodal decomposition in polymer blends

We discuss here some qualitative features of the concentration fluctuations in binary polymer melts A+B, A and B being long, flexible chains, with a Flory interaction parameter χ which can be positive (favoring segregation), or negative. In the one phase domain, the fluctuations of long wavelength (2π/q) are expected to relax by a reptation process. At shorter wavelengths (qR0≳1, where R0 is the size of one chain) equilibration takes place by local adjustment of each chain inside a fixed ’’tube’’: the predicted relaxation rates τq−1 are proportional to q6 for χ?0. (For a negative χ, opposing segregation, one expects τq−1∼q4). In the two phase domain, where the trend towards segregation is strong (χN≫1, N being the number of monomers per chain), one should observe a very anomalous type of spinodal decomposition: in the early stages, the growing fluctuations have a wavelength comparable to the thickness of the interfacial region, and small compared with R0: the growth is realized through local adjustment. During the later stages (Ostwald ripening) the size R(t) of the growing droplets should change from a t1/5 behavior (when R≲R0) to a t1/3 behavior (in the classical limit R≳R0).