Equilibria, polymer blend phases

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. 

In fact, even in pure block copolymer (say, diblock copolymer) solutions the self-association behavior of blocks of each type leads to very useful microstructures (see Fig. 1.7), analogous to association colloids formed by short-chain surfactants. The optical, electrical, and mechanical properties of such composites can be significantly different from those of conventional polymer blends (usually simple spherical dispersions). Conventional blends are formed by quenching processes and result in coarse composites in contrast, the above materials result from equilibrium structures and reversible phase transitions and therefore could lead to smart materials capable of responding to suitable external stimuli. 

Surface tension plays a significant role in the deformation of polymers during flow, especially in dispersive mixing of polymer blends. Surface tension, as, between two materials appears as a result of different intermolecular interactions. In a liquid-liquid system, surface tension manifests itself as a force that tends to maintain the surface between the two materials to a minimum. Thus, the equilibrium shape of a droplet inside a matrix, which is at rest, is a sphere. When three phases touch, such as liquid, gas, and solid, we get different contact angles depending on the surface tension between the three phases. 

Finally, a challenging problem is to discuss the influence of hydrodynamic flow fields on the phase behavior of polymer blends. This is of fundamental interest and of technological importance as well since stresses and corresponding deformations are encountered during processing of blends. Extension of studies to blend systems under external flow is necessary for the better understanding of structure formation in polymer blends outside equilibrium. 

Flow imparts both extension and rotation to fluid elements. Thus, polymer molecules will be oriented and stretched under these circumstances and this may result in flow-induced phenomena observed in polymer systems which include phase-changes, crystallization, gelation or fiber formation. More generally, the Gibbs free energy of polymer blends or solutions depends under non-equilibrium conditions not only on temperature, pressure and concentration but also on the conformation of the macromolecules (as an internal variable) and hence, it is sensitive to external forces. 

In Ref. [120] the first time has been reported on flow-induced phase separation in polymer blends. When PS/PVME blends were exposed to shear or extensional flow at lower temperatures, 20 to 30 K below the equilibrium coexistence temperature, phase separation was observed in both flow regimes. As the authors suggest, the stress, rather than the deformation rate, appears to be the most important parameter in flow-induced phase separation. 

A mean field theory has recently been developed to describe polymer blend confined in a thin film (Sect. 3.2.1). This theory includes both surface fields exerted by two external interfaces bounding thin film. A clear picture of this situation is obtained within a Cahn plot, topologically equivalent to the profile s phase portrait d( >/dz vs < >. It predicts two equilibrium morphologies for blends with separated coexisting phases a bilayer structure for antisymmetric surfaces (each attracting different blend component, Fig. 32) and two-dimensional domains for symmetric surfaces (Fig. 31), both observed [94,114,115,117] experimentally. Four finite size effects are predicted by the theory and observed in pioneer experiments [92,121,130,172,220] (see Sect. 3.2.2) focused on (i) surface segregation (ii) the shape of an intrinsic bilayer profile (iii) coexistence conditions (iv) interfacial width. The size effects (i)-(iii) are closely related, while (i) and (ii) are expected to occur for film thickness D smaller than 6-10 times the value of the intrinsic (mean field) interfacial width w. This cross-over D/w ratio is an approximate evaluation, as the exact value depends strongly on the... 

The understanding of the formation of miscible and immiscible polymer blends requires the application of the principles of phase chemistry. A miscible blend may be regarded as a solution of one polymer in the other. The thermodynamic criteria for the miscibility of liquids are well known and may be applied to polymers as a first approximation. The added complexity comes from the long-chain nature of polymers. In addition to the entropic factors there are kinetic factors to be considered. Since in reactive processing the reactions are occurring within a short time, they will very often be a long way from equilibrium. 

One means of this estimation depends on the ability to establish a gradient of magnetization, m r, t) between different types of domains, and subsequently monitor the resultant approach to equilibrium. Examples include crystalline and noncrystalline domains within a homopolymer, and block copolymers where dimensions of separated phases are controlled by block length and polymer blends. The usual diffusion equation describes the behaviour of the magnetization as it approaches equilibrium from an initial nonequilibrium state,... 

Exciplex states only exist at the interface between the two dissimilar polymers in the blend. Reducing the density of these interfaces in the polymer blend is expected to reduce the amount of exciplex observed. For example, annealing mobilizes the polymers and causes the film to move closer to thermodynamic equilibrium, i.e. the two polymers phase separate and the density of heterojunction sites decreases. Indeed, we observe that the amount of exciplex emission is reduced by the annealing treatment [30]. 

The phase diagrams of polymer blends, the pseudo-binary polymer/polymer systems, are much scarcer. Furthermore, owing to the recognized difficulties in determination of the equilibrium properties, the diagrams are either partial, approximate, or built using low molecular weight polymers. Examples are fisted in Table 2.19. In the Table, CST stands for critical solution temperature — L indicates lower CST, U indicates upper CST (see Figure 2.15). 

One of the most serious obstacles in the phase equilibrium studies of polymer blends is the viscosity of the system. At temperahires limited by the degradation the self-diffusion coefficient of macromolecules is of the order of magnitude 10 to 10 m /s [Kausch and Tirrell, 1989]. As a result the phase separation is slow. To accelerate the process a low speed centrifuge, the centrifugal homogenizer (CH), with PICS has been used [Koningsveld et al, 1982]. In short, centrifugation within the immiscibility zone permits determination of binodal and critical points, while the use of PICS mode allows location of the spinodal. 

The semigrand ensemble method can be implemented in different forms for calculation of equilibrium properties, and phase equilibria for inert or reacting mixtures. Recently, it has been applied to simulate phase coexistence for binary polymer blends [85], where advantage was taken of the fact that identity exchanges are employed in lieu of insertions or deletions of full molecules. The semigrand ensemble also provides a convenient framework to treat polydisperse systems (see Section III.F). 

Polymer crystallization has been described in the framework of a phase field free energy pertaining to a crystal order parameter in which = 0 defines the melt and assumes finite values close to unity in the metastable crystal phase, but = 1 at the equilibrium limit (23-25). The crystal phase order parameter (xj/) may be defined as the ratio of the lamellar thickness (f) to the lamellar thickness of a perfect polymer crystal (P), i.e., xlr = l/P, and thus it represents the linear crystallinity, that is, the crystallinity in one dimension. The free energy density of a polymer blend containing one crystalline component may be expressed as... 

In the light of the phase diagram derived earlier for a eonductive polymer blend (Figure 11.124), the energy dissipation meehanism by redispersion ean be understood. It is the energy input driven way baek, of the system from the equilibrium interfacial energy curve at the flocculation point to the fully dispersed, but still phase-separated boundary. 

Phase separation is frequently observed in polymer solutions and it is mainly due to their low entropy of mixing. At a state of equilibrium each species of the mixture is partitioned between two phases, namely, the supernatant (extremely dilute) and precipitated (moderately dilute) phases [78]. Theoretical models and experimental techniques have been developed to predict the solubility behavior of polymer solutions, polymer blends, and other related systems [79, 80]. Simple theories only permit a rather qualitative description of this phenomenon [78]. Refined and improved theoretical and semiempirical models allow a more accurate prediction of the demixing phenomena and related thermodynamic properties [57, 81]. 

Initial works on the phase equilibrium of polymer solutions were concerned with nonpolar solutions using carefully prepared quasi-monodisperse polymer fractions [78]. The theory and practice was later extended to molecularly heterogeneous polymers [84], multicomponent solutions (ternary mixtures) such as polymer/solvent mixture [16, 85] and polymer mixture/solvent [86], and polymer blends [79, 80], among others [87]. Improvements on predicting thermodynamic properties were particularly proposed for polymer solutions of industrial importance, including those having polar and hydrogen-bonded components [16]. 

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