Interaction parameters, miscibility, blended

This last type of ternary blend has been studied for PCL with two other polymers which are mutually immiscible but each of which is miscible with PCL. This problem can be considered as one in which the miscible component, in this case PCL, partitions itself between the other components according to the interaction parameters and blend composition. Depending on the relative affinities of PCL for the other components, the PCL will not distribute itself equally between them but will favour one component over the other. This situation is seen in blends of PCL with phenoxy and SAN-15 [136]. 

The miscibility of novel olefinic block copolymers (OBCs) with random ethylene-octene (EO) copolymers was studied using blends of two homogeneous random EO copolymers as a model system. The critical comonomer content difference for miscibility between OBC and random EO blend was observed to be lower than that for the blend of two random EO copolymers. The OBC and random EO blend also exhibited a broader partial miscibility window. Interaction parameters for blends of two EO copolymers were extracted from partially miscible blends. 

There are many examples known where a random copolymer Al, comprised of monomers 1 and 2, is miscible with a homopolymer B, comprised of monomer 3, even though neither homopolymer 1 or 2 is miscible with homopolymer 3, as illustrated by Table 2. The binary interaction model offers a relatively simple explanation for the increased likelihood of random copolymers forming miscible blends with other polymers. The overall interaction parameter for such blends can be shown (eg, by simplifying eq. 8) to have the form of equation 9 (133—134). 

Lohse et al. have summarized the results of recent work in this area [21]. The focus of the work is obtaining the interaction parameter x of the Hory-Huggins-Stavermann equation for the free energy of mixing per unit volume for a polymer blend. For two polymers to be miscible, the interaction parameter has to be very small, of the order of 0.01. The interaction density coefficient X = ( y/y)R7 , a more relevant term, is directly measured by SANS using random phase approximation study. It may be related to the square of the Hildebrand solubility parameter (d) difference which is an established criterion for polymer-polymer miscibility ... 

Attractive interactions are also the reason for the self-assembly of PS-fo-PB-fo-PMMA at the interface of poly(styrene-co-acrylonitrile), SAN, and poly(2,6-dimethylphenylene ether), PPE. In this blend, PS and PPE are miscible on one side and PMMA and SAN are miscible on the other one, with negative / parameters. This blend, in which the rubbery domain is located at the interface between SAN/PMMA and PPE/PS, was originally prepared by coprecipitation of all components from a common solution [195]. From a processing point of view, in this system the difficulty was to get the dispersion of PPE in SAN via melt mixing of SAN, PPE and the triblock terpolymer. 

Melting Point Depression. A more quantitative evaluation of the relationships existing between lignin structure and blend miscibility is possible through the Tm depression observed in these materials. For semi-crystalline blend systems, such as these, the polymer-polymer interaction parameter, B , can be determined through the following simplified expression (15) ... 

Since there had not been any measurements of thermal diffusion and Soret coefficients in polymer blends, the first task was the investigation of the Soret effect in the model polymer blend poly(dimethyl siloxane) (PDMS) and poly(ethyl-methyl siloxane) (PEMS). This polymer system has been chosen because of its conveniently located lower miscibility gap with a critical temperature that can easily be adjusted within the experimentally interesting range between room temperature and 100 °C by a suitable choice of the molar masses [81, 82], Furthermore, extensive characterization work has already been done for PDMS/PEMS blends, including the determination of activation energies and Flory-Huggins interaction parameters [7, 8, 83, 84],... 

The first is to develop thermodynamic issues to understand the complex phase behavior of polymer blends. Experimental determination of miscibility regions provides the individual segmental interaction parameters necessary for predictions of various phase equilibria. 

For a fixed strain rate, a comparison of Eq. (74) and experimental data [51, 52] of miscible blends is shown in Fig. 32. Curves 1 and 2 represent, respectively, the PPO/PS blends in compression, and the PPO/PS-pCIS blends in tension.Table 2 lists the three parameters fjf2, CK, and A/f2 used in curves 1 and 2. The unique feature here is the presence of a maximum yield (or strength) for 0 <

nonequilibrium interaction (A < 0). Such phenomenon does not occur in incompatible blends or composite systems. Table 2 also reveals that the frozen-in free volume fractions which are equal to 0.0243 and 0.0211 for polystyrene and for PPO, respectively. These are reasonable values for polymers in the glassy state. In the search for strong blends, we prefer to have —A/f2 > 1, and a larger difference between the yield stresses of blending polymers. 

The utility of the DSC for studying polymer-polymer miscibility has been demonstrated for poly(vinyl chloride)/nitrile rubber polyfvinyl methyl ether)/poly-styrene and poly(2,6-dimethyl 1,4-diphenylene oxide)/poly(styrene-co-chloro-styrene)It has also been particularly useful for measuring the melting point depressions of crystalline polymers in blends Mn order to calculate the interaction parameter as will be discussed later. 

Figure 2 - Calorimetry results for three miscible blends of PIP and PBD (sample designations in this and the ensuing figures are defined in Table II). The uppermost curve has the lowest spinodal interaction parameter value (1.7 x 10 ). Broad glass transitions are observed in both it and the curve for blend IB, for which X = 7.6 X 10-3.

The spontaneous mixing of the two polymers will transpire at a rate which reflects the degree of miscibility of the system. As X approaches the critical value for phase separation, "thermodynamic slowing down" of the interdiffusion will occur [12]. The rate of increase of the scattering contrast reflects the proximity of the system to criticality, as well as the strong composition dependence of the glass transition temperature of the blend. Extraction of a value for either the self diffusion constants [13,14] or the interaction parameter is not feasible from the presently available data. 

The temperature dependence of the total interaction parameter shows that there exists an optimum condition for the composition at a given temperature (Fig. 3). Binary blends of PEO/PS and PEO/PAA are immiscible and miscible, respectively, at room temperature. The shape of curves implies that the homopol-ymer/homopolymer blends will exhibit UCST behaviors. A drastic effect of the sequence distribution on the miscibility can be found in Fig. 4. As the AA content in SAA increases from 5 mol% (Fig. 4a) to 7 mol% (Fig. 4b) to 10mol% (Fig. 4c), the blend becomes more miscible. The blend with random copolymers becomes miscible at a composition between 5 and 7 mol%, which agrees well with the experimental results [15]. At 7 mol%, the blend with block copolymers shows positive x> while the blend with random copolymers has negative y. This is very interesting because the miscibility could be controlled only by the change of copolymer sequence distributions. 

IGC was used to determine the thermodynamic miscibility behavior of several polymer blends polystyrene-poly(n-butyl methacrylate), poly(vinylidene fluoride)-poly(methyl methacrylate), and polystyrene-poly(2,6-dimethyl-1,4-phenylene oxide) blends. Specific retention volumes were measured for a variety of probes in pure and mixed stationary phases of the molten polymers, and Flory-Huggins interaction parameters were calculated. A generally consistent and realistic measure of the polymer-polymer interaction can be obtained with this technique. 

PMMA is typical of many polymer pairs, for which the parameter is positive and of order 0.01, making only low molar mass polymers form miscible blends. PVME/PS, PS/PPO, and PS/TMPC have a strongly negative x parameter over a wide range of temperatures (of order — 0.01) but since >0 and Bblends phase separate on heating. PEO/ PMMA, PP/hhPP and PlB/hhPP, all represent blends with very weak interactions between components (x = 0). 

Since this critical interaction parameter is very small for blends of long chains, most polymer blends have x > Xc and thus are phase separated over some composition range (within the miscibility gap). Only blends with either very weak repulsion (0 < x < Xc), or a net attraction between components of the mixture (x < 0) form homogeneous (single-phase) blends over the whole composition range. 

The Flory interaction parameter in miscible polymer blends is measured using small-angle neutron scattering, usually involving deuterium label-... 

Predicting blend miscibility correctly is, however, often considerably more challenging than one might guess by looking at the equations given above or even their somewhat more refined versions. Flory-Huggins interaction parameters, their more elaborate versions, and alternative methods such as the equation-of-state theories [9] discussed in Section 3.E, all provide correct predictions in many cases, but unfortunately provide incorrect predictions in many other cases. 

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