Phase separation in polymer mixtures

The thermodynamic model of polymer binary solutions developed by Flory and presented in Chapter 2 predicts the coexistence of two phases (one rich in polymer and the other poor in polymer) when the temperature is lowered. Equilibrium between the two phases in a binary mixture requires that 

FIGURE 3.3 Plots of the chemical potential difference Ti - ft as a function of polymer volume fraction for different values of %. For x X . this function is monotonically decreasing and the one-phase mixture is stable for all values of V2. For % Xc, this function goes through a minimum and a maximum, and the mixture phase separates. 

FIGURE 3.4 Schematic phase diagram for a binary polymer-solvent mixture showing a UCST. 

Using Equation 3.6, the above criticality conditions yield two equations for the two unknown, V2 c and Xc at the critical point. For large values of x, the results are 

The results of Flory s model are in qualitative agreement with experimental results. As the molecular weight of a polymer increases (i.e., as x increases), the value of the critical volume fraction V2 j moves closer to 0 and the value of Xc approaches 0.5. Since the critical temperature increases as the molecular weight increases, the higher molecular weight samples are less soluble in a given solvent under similar conditions. Note that for the modest value of x = 100, V2 j is approximately 0.1 and Xc is 0.6. 

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Figure 8.3b shows that phase separation in polymer mixtures results in two solution phases which are both dilute with respect to solute. Even the relatively more concentrated phase is only 10-20% by volume in polymer, while the more dilute phase is nearly pure solvent. The important thing to remember from both the theoretical and experimental curves of Fig. 8.3 is that both of the phases which separate contain some polymer. If it is the polymer-rich or precipitated phase that is subjected to further work-up, the method is called fractional precipitation. If the polymer-poor phase is the focus of attention, the method... 

In this section we would like to deal with the kinetics of the liquid-liquid phase separation in polymer mixtures and the reverse phenomenon, the isothermal phase dissolution. Let us consider a blend which exhibits LCST behavior and which is initially in the one-phase region. If the temperature is raised setting the initially homogeneous system into the two-phase region then concentration fluctuations become unstable and phase separation starts. The driving force for this process is provided by the gradient of the chemical potential. The kinetics of phase dissolution, on the other hand, can be studied when phase-separated structures are transferred into the one-phase region below the LCST. 

The experimental evidence for phase separation in polymer mixtures was briefly developed in the previous section. In the present section a thermodynamic explanation for mutual insolubility, or incompatibility, of polymer pairs will be outlined. 

Due to the more pronouncixl dependence of the interaction parameter on both concentration and molecular weight, the phase separation in polymer mixtures is very diverse. 

The method has been used to show that phase separation in poly(phenylene oxide)-toluene occurs by crystallization (see Chapter 12) of the polymer rather than by liquid-liquid phase separation, and to follow the kinetics of the process Kleintjens et al. have used PICS to obtain spinodals for branched polymer solutions. Koningsveld and Kleintjens have used it widely to study phase separation in polymer mixtures. 

Ronca G, Russell TP (1985) Thermodynamics of phase separation in polymer mixtures. 

In considering adhesion of polymer blends to solid, the wetting of the surface is of importance. No data are available. However, the strong interplay between phase separation in polymer mixtures and wetting was discovered. It was found that the wetting plays a drastic role when the minority phase is more wettable to the glass surface. 

In the same maimer, the structures of liquid crystalline phases in the gap between two surfaces can be probed by stud5dng surface forces as first demonstrated by Horn et al. [4]. Since then, the relation between the structural forces in concentrated lyotropic Uquid crystalline systems trapped between two solid supports has been determined and the perturbing effect of the surface has been clearly demonstrated [5]. The surface may induce a surfactant phase at the solid-liquid interface that is different than that found in the bulk. Related phenomena, induced by the preferential interaction between the surface and one of the components in the environment, are capillary condensation [6], capillary evaporation [7] (an important mechanism behind some of the reports concerned with long-range hydrophobic interactions [8]), and surface-induced phase separation in polymer mixtures [9]. 

Figure A2.5.27. The effective coexistence curve exponent P jj = d In v/d In i for a simple mixture N= 1) as a fimction of the temperature parameter i = t / (1 - t) calculated from crossover theory and compared with the corresponding curve from mean-field theory (i.e. from figure A2.5.15). Reproduced from [30], Povodyrev A A, Anisimov M A and Sengers J V 1999 Crossover Flory model for phase separation in polymer solutions Physica A 264 358, figure 3, by pennission of Elsevier Science.

Thermodynamics and kinetics of phase separation of polymer mixtures have benefited greatly from theories of spinodal decomposition and of classical nucleation. In fact, the best documented tests of the theory of spinodal decomposition have been performed on polymer mixtures. 

Kinetics of Phase Separation and Phase Dissolution in Polymer Mixtures. 54... 

Emmerik, P. T. van Smolders, C. A., "Phase Separation in Polymer Solutions. II. Determination of Thermodynamic Parameters of Poly(2,6-dimethyl-1,4-phenylene oxide)Toluene Mixtures," J. Polym. Sci., Part C., 21, 311 (1972). 

Several implications can be drawn directly from Eq. (2-39). First, A // is always positive. Thus, the rule like attracts like, inferred from Eq. (2-30) for molecular mixtures, should also hold at the continuum level. Second, when dispersion forces are dominant, the Hamaker constant is small when ha= b—that is when the dispersed phase (A) has an index of refraction close to that of the medium (B), These rules also apply to molecular mixtures. Nevertheless, small molecules with a significant difference in index of refraction often mix because of the large entropy thereby gained. But particles lose too little entropy on coagulation to resist doing so when there is an attractive van der Waals interaction, and so particle-particle clumping is the norm in suspensions, unless countermeasures are taken to stop it (see Section 7.1). Analogous considerations explain the prevalence of phase separation in polymer blends (see Section 2.3.1.2). 

A. Sariban and K. Binder (1988) Phase-Separation of polymer mixtures in the presence of solvent. Macromolecules 21, pp. 711-726 ibid. (1991) Spinodal decomposition of polymer mixtures - a Monte-Carlo simulation. 24, pp. 578-592 ibid. (1987) Critical properties of the Flory-Huggins lattice model of polymer mixtures. J. Chem. Phys. 86, pp. 5859-5873 ibid. (1988) Interaction effects on linear dimensions of polymer-chains in polymer mixtures. Makromol. Chem. 189, pp. 2357-2365... 

In this paper the discussion was concentrated mainly on the phase separation in polymer solutions due to the change of the composition of the mixture. The basic relations are also valid for phase separations induced by temperature changes, that is thermal gelation and can be applied to glass and metal alloys as well as to polymers. 

Morphology. Phase inversion in polymer mixtures occurs when the volume fraction of the dispersed phase becomes equal to or exceeds 0.5 (14). The driving force is to minimize the interfacial energy of the system. This is not the case here because the volume fraction of the rubber-rich phase at phase inversion is about 0.85. After inversion, the fraction of the continuous rubber-rich phase is only 0.28, and it increases to 0.63 at 12.5% rubber content. Initially, the components are fully soluble and compatible, but as the reactions proceed, the molecular weight of the products increases and phase separation results. The ability to separate and invert is dependent on the viscosity of the medium. The unsaturated polyester forms a gel at conversions as low as 2 to 5%, and both the ability to separate and to invert is impeded. Thus the morphology depends on the two competing effects of phase inversion and... 

FIGURE 6.19 Idealized cases of phase separation in aqueous mixtures of two polymers, concentrations c2 and c 5. (a) Segregative phase separation or incompatibility. (b) Associative phase separation or complex coacervation. The heavy lines denote the binodal (solubility limit), the thin ones are tie lines. The dots indicate critical points. 

In principle, this ratio can also affect the IP concentration profile in a quahta-tive sense. When considering a homogeneous epoxy-amine mixture just brought into contact with the surface of an adherend or a fiUer particle, preferential adsorption of the amine molecules will result in local variations of the amine/epoxy concentration ratio r (to be defined below). Assuming a comparably fast diffusion of the amine molecules, their quick enrichment at the interface will result in a near-interface zone of increased r values and an adjacent zone of amine depletion, i.e., with reduced r values. Similar concentration variations are dealt with in the field of surface-driven phase separation in polymer solutions and mixtures [8]. While the wetting layer is in local equihbrium with the depletion layer, the diffusion from the bulk down the concentration gradient into the latter feeds the growth of the former. 

We present here a study on phase separation of polymer mixtures forced with temporally and spatially periodic irradiation. The main purpose is to elucidate the contribution of the elastic stress associated with the changes in polymer structure generated by chemical reactions. In the temporal modulation experiments, phase separation was induced by periodic irradiation using ultraviolet (uv) light chopped with frequency varying between 1/200 to 100 Hz. 

H02 Holyst, R., Staniszewski, K., Patkowski, A., and Gapinski, J., Hidden minima of the Gibbs free energy revealed in a phase separation in polymer/surfactant/water mixture, J. Phys. Chem. 5,109, 8533, 2005. 

Mesoscopic simulations have been applied to understand phase separation in polymer blends and in polymer/nanofiller mixtures. 

Yao, Y. et al. (2008) Effect of solvent mixture on the nanoscale phase separation in polymer solar cells. Adv. 

The phase separation of polymer mixtures exhibits so great a variety of properties in comparison with LMW mixtures that not all the peculiarities of this phase. separation have hitherto been amenable to a theoretico-calculalioiial justification. 

A version of the corresponding states theory, which is able to predict some new types of the location of the phase separation regions (Figure 3.92) and has proved to be rather fruitful in predicting the incompatibility region (phase separation) of polymer mixtures, has been elaborated by Lacombe and Sanch[Pg.479]

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