Model systems for immiscible blends

Most polymer blends are immiscible. Their flow is complex not only due to the presence of several phases having different rheological properties (as it will be demonstrated later, even in blends of two polymers the third phase, the interphase, must be taken into account), but also due to strain sensitivity of blend morphology. Such complexity of flow behavior can be best put in perspective by comparing it to flow of better understood systems, suspensions, emulsions, and block copolymers. 

Flow of suspensions of solid particles in Newtonian liquids is relatively well understood, and these systems provide good model for flow of polymer blends, where the viscosity of dispersed polymer is much higher than that of the matrix polymer. 

Flow of emulsions provides the best model for polymer blends, where the viscosity of both polymers is comparable. The microrheology of emulsions provides the best, predictive approach to morphological changes that take place during flow of polymer blends. The effect of emulsifiers on the drop size and its stability in emulsions has direct equivalence in the compatibilization effects in polymer blends. 

Finally, the rheological behavior of block copolymers serves as a model for well compatibilized blends, with perfect adhesion between the phases. The copolymers provide important insight into the effects of the chemical nature of the two components, and the origin of the yield phenomena. 

There are two reasons for discussing the solid-inliquid dispersions in the chapter dedicated to flow of polymer blends [Utracki, 1995]. Historically, the first systematically studied multiphase systems 

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Since the flow of PAB is complex, it is useful to revert to simple models, for example, for miscible blends to solutions or mixtures of polymer fractions, for immiscible blends to emulsions or suspensions, and for compatibilized blends to block copolymers (Table 2.1). It is also advisable to study flow behavior of multiphase systems at constant stress (not at constant deformation rate) [2, 3]. 

For predicting the phase inversion and co-continuous regime in immiscible blend systems, various empirical and semi-empirical models exist [5], A model, valid for high viscosity ratios and elevated shear rates, was established by Utracki [46] ... 

The properties of block copolymers, on the other hand, cannot be calculated without additional information concerning the block sizes, and whether or not the different blocks aggregate into domains. The results of calculations using the methods developed in this book can be inserted as input parameters into models for the thermoelastic and transport properties of multiphase polymeric systems such as blends and block copolymers of immiscible polymers, semicrystalline polymers, and polymers containing various types of fillers. A review of the morphologies and properties of multiphase materials, and of some composite models which we have found to be useful in such applications, will be postponed to Chapter 19 and Chapter 20, where the most likely future directions for research on such materials will also be pointed out. 

Due to the phase-separated structure of immiscible polymer blends including phase boundaries in the corresponding dielectric spectra, MaxweU/Wagner polarization process can be observed especially at low frequencies. As discussed in Sect. 12.2.3.3, the theoretical equations are complex and hard to solve. For certain model systems like inclusion in poly(carbonate filled) with poly(ethylene oxide) (Hayward et al. 1992), it could be shown that for low concentrations the most important quantities are the volume fraction, the geometry of the dispersed phase... 

Because of the complex flow behavior ofviscoelastic polymer blends its interpretation becomes easier when compared with the simpler, model systems discussed in Sections 2.1.1 and 2.1.2. For the dominant immiscible blends the emulsions of one liquid dispersed in another provide the best model. While compatibilizers are used for stabilization of blends, in emulsion a diversity of surfactants has been employed. As in blends, a progressive increase of concentration of the emulsion minor phase invariably leads to the co-continuity of phases and phase inversion. However, while emulsion phase inversion is controlled mainly by the emulsifier, in blends the inversion mainly depends on the viscosity ratio, A = th/th (Figure 2.3) [4]. 

Rheology is a part of continuum mechanics that assumes continuity, homogeneity and isotropy. In multiphase systems, there is a discontinuity of material properties across the interface, a concentration gradient, and inter-dependence between the flow field and morphology. The flow behavior of blends is complex, caused by viscoelasticity of the phases, the viscosity ratio, A (that varies over a wide range), as well as diverse and variable morphology. To understand the flow behavior of polymer blends, it is beneficial to refer to simpler models — for miscible blends to solutions and mixtures of fractions, while for immiscible systems to emulsions, block copolymers, and suspensions [1,24]. 

Other models are based upon the immiscibility of polymer blends described above, and they model the system as Newtonian drops of the dispersed polymer with concentration (pi in a Newtonian medium of the second polymer with concentration (p2 = — (pi. There exists some concentration, cpu = cp2i — 1, at which phase inversion takes place that is, at snfficiently high concentration, the droplet phase suddenly becomes continuous, and the second phase forms droplets. The phase inversion concentration has been shown to correlate with the viscosity ratio, A. = r i/r 2, and the intrinsic viscosity for at least a dozen polymer alloys and blends ... 

K. W. Foreman and K. F. Freed (1998) Lattice cluster theory of multicomponent polymer systems Chain semiflexibility and speciflc interactions. Advances in Chemical Physics 103, pp. 335-390 K. F. Freed and J. Dudowicz (1998) Lattice cluster theory for pedestrians The incompressible limit and the miscibility of polyolefin blends. Macromolecules 31, pp. 6681-6690 E. Helfand and Y. Tagami (1972) Theory of interface between immiscible polymers. 2. J. Chem. Phys. 56, p. 3592 E. Helfand (1975) Theory of inhomogeneous polymers - fundamentals of Gaussian random-walk model. J. Chem. Phys. 62, pp. 999-1005... 

It is usually difficult to isolate and characterize a copolymer from a melt-processed polymer blend. Model studies of copolymer formation between immiscible polymers have been performed either in solution (where there is unlimited interfacial volume for reaction) or using hot-pressed films of the polymers (where the interfacial volume for reaction is strictly controlled at a fixed phase interface). Model smdies using low molecular weight analogs of the reactive polymers are useful but their applicability to high molecular weight reacting systems is limited. 

The combination of experimental evidence and computational modeling show conclusively that stable, homogeneously blended (bulk-immiscible) mixed-polymer composites can be formed in a single microparticle of variable size. To our knowledge, this represents a new method for suppressing phase-separation in polymer-blend systems without compatibilizers that allows formation of polymer composite micro- and nanoparticles with tunable properties such as dielectric constant. Conditions of rapid solvent evaporation (e.g. small (<10 pm) droplets or high vapor pressure solvents) and low polymer mobility must be satisfied in order to form homogeneous particles. While this work was obviously focused on polymeric systems, it should be pointed out that the... 

Cho et al. (2000) studied the segregation dynamics of block copolymers to the interface of an immiscible polymer blend and compared experimental results to the predictions of various theories for a poly(styrene-b-dimethylsiloxane) [P(S-b-DMS) M = 13,000] symmetric diblock copolymer system added to a molten blend of the corresponding immiscible homopolymers. They used the pendant drop technique at intermediate times and compared their results to the predictions of diffusion-limited segregation models proposed by Budkowski, Losch, and Klein (BLK) and by Semenov that have been modified to treat interfacial tension data. The apparent block copolymer diffusion coefficients obtained from the two analyses fall in the range of 10 -10 cm /s, in agreement with the estimated self-diffusion coefficient of the PDMS homopolymer matrix. 

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