Miscibility in Polymer Blends and Free Volume

Miscibility in polymer blends is controlled by thermodynamic factors such as the polymer-polymer interaction parameter [8,9], the combinatorial entropy [10,11], polymer-solvent interactions [12,13] and the "free volume effect [14,15] in addition to kinetic factors such as the blending protocol, including the evaporation rate of the solvent and the drying conditions of the samples. If the blends appear to be miscible under the given preparation conditions, as is the ca.se for the blends dcscibcd here, it is important to investigate the reversibility of phase separation since the apparent one-phase state may be only metastable. To obtain reliable information about miscibility in these blends, the miscibility behavior was studied in the presence and absence of solvents under conditions which included a reversibility of pha.se separation. An equilibrium phase boundary was then obtained for the binary blend systems by extrapolating to zero solvent concentration. 

The origin of the critical point can be traced to the temperature effect on miscibility. Patterson [1982] observed that there are three principal contributions to the binary interaction parameter, the dispersive, free volume and specific interactions. As schematically illustrated in Figure 2.16, the temperature affects them differently. Thus, for low molecular weight systems where the dispersion and free volume interactions dominate, the sum of these two has a U-shape, intersecting the critical value of the binary interaction parameter in two places — hence two critical points, UCST and LCST. By contrast, most polymer blends derive their miscibility from the presence of specific interactions, characterized by a large negative value of the interaction parameter that increases with T. The system is also affected by the free volume contribution, as well as relatively unimportant in this case dispersion forces. The sum of the interactions reaches the critical value only at one temperature — LCST. 

There is a mounting evidence that PDB is not a rule for miscible polymer blends. Depending on the system and method of preparation, polymer blends can show either a positive deviation, negative deviation, or additivity. Note that miscibility in polymeric systems requires strong specific interactions, which in turn affect the free volume, thus the rheological behavior. It has been demonstrated that Newtonian viscosity can be described by the relation [Utracki, 1983 1985 1986] ... 

Polymer blends may be characterized in terms of the temperature dependence of the Flury-Huggins interaction parameter (j)- In the case of an upper critical solution temperature (UCST) blend, / decreases with temperature, and the blend remains miscible. For phase separation to occur in a UCST blend, the temperature must be lower than the critical solution temperature. In the case of a lower critical solution temperature (LCST) blend, x increases with temperature, and thus phase separation occurs above the critical solution temperature. The ability of CO2 to mimic heat means that miscibility is enhanced in the case of UCST blends, and for the case of LCST blends the miscibihty is depressed. Ramachandrarao et al. [132] explained this phenomenon by postulating a dilation disparity occurring at higher CO2 concentration as a result of the preferential affinity of CO2 to one of the components of the blend, inducing free-volume and packing disparity. 

Recent developments have been in the area of microthermal analysis using thermal conductivity with thermal diffiisivity signals or AFM to visualize specific areas or domains in the material and perform localized thermal analysis studies (183,184). Relaxational behavior over time and temperature is related to changes in free volume of the material. Positron annihilation lifetime spectroscopy (PALS) measurements of positron lifetimes and intensities are used to estimate both hole sizes and free volume within primarily amorphous phases of polymers. These data are used in measurement of thermal transitions (185,186) structural relaxation including molecular motions (187-189), and effects of additives (190), molecular weight variation (191), and degree of crystallinity (192). It has been used in combination with DSC to analyze the range of miscibility of polymethyl methacrylate poly(ethylene oxide) blends (193). 

Many of the polymer blend systems that were found miscible were also found to exhibit a LCST-type phase separation at elevated temperatures. The % interaction parameters can be expected to increase with increase in temperature. In order to predict this LCST phenomena using the theoretical approach discussed in the above sections, consider a copolymer and homopolymer blend system. The x interaction parameter of a two-component blend comprises two contributions—an exchange interaction and free volume term. Equation (3.27) can be rewritten including the temperature effects as... 

Equations for Tg based on the free-volume concept have been proposed for miscible polymer blends and they are similar to the Kelly-Bueche equation given above for polymer-diluent systems. Likewise, this description in terms of a single Tg over-simplifies the dynamics of the components in the blend and neglects some important elements. An important element for interpreting the relaxation behavior of blends is fluctuations in concentration or composition [102]. Models have been... 

He, H2, O2, Ar, N2, CH4 and CO2 are lower than those calculated from the semi-logarithmic additivity rule, indicating that PMMA is miscible with BCPC over the whole blend composition range. These permeation results can be interpreted in terms of the free volume contraction which has been proposed to describe gas transport behavior in polymer mixtures. Similar observations for the miscible blends of polycarbonate with a copolyester formed from 1,4-cydohexanedimetha-nol and a mixture of terephthalic and isophthaUc adds have been made using CO2 [100]. Negative deviations of both permeability and diffusion coeffidents from simple additivity relations have been observed, and interpreted qualitatively to have resulted from the decrease in volume when the blends were mixed. 

The miscibility of a polymer blend depends on temperature and blend composition, making the investigation of the dynamic behavior of miscible polymer blends very challenging. Associated with the dynamics of miscible polymer blends is the mutual diffusion that, as in determining the self-diffusion coefficient in polymer melts and solutions presented in Chapter 4, can be discussed using molecular theory. Thermodynamic interactions and free-volume effects determine the mutual diffusivity in miscible polymer blends. 

Positron annihilation spectroscopy (PALS) is a technique of free volume determination in polymers that involves the injection of subatomic particles and the measurement of their decay times. This technique can be very sensitive to the degree of miscibihty and free volume behavior of polymer blends. The concept of free volume is important to understand polymer characteristics in the glassy state. For instance, PALS was used to evaluate the free volume sites of thermotropic hquid crystalline polymer blends. These blends presented smaller and fewer free volume sites than expected from a weighted average due to their intrinsic affinity. This is interesting because in contrast to thermoplastic blend results, the degree of blend miscibility alters free volume behavior as a function of blend composition [106]. In addition, the order and the dynamics in the mesophase can be accessed by nuclear magnetic resonance [107]. 

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