Interfacial tension coefficient

According to van Oene (34) the Interfacial tension coefficient depends on the difference between the first normal stress differences, N of the blend components ... 

Of the three popular methods of v-determlnatlon the sessile drop Is the slowest, the pendant drop faster and the spinning drop the most rapid ( S). For commercial resin pairs the first two may require days before the drop reaches Its equilibrium shape. During this time there Is diffusion of the low molar mass fractions toward the interface gradually decreasing the value of the Interfacial tension coefficient (36). These two factors, the normal stress and the time scale, are generally responsible for the poor correlation between the predicted and measured droplet diameters in commercial blends. 

Process of modification of the interfacial properties in immiscible polymer blend, resulting in reduction of the interfacial tension coefficient and stabilization of the desired morphology, thus leading to the creation of a polymer alloy. 

While the reduction of the interfacial tension coefficient, v, is relatively easy by introduction of a macromolecular surfactant , the stabilization of morphology and improvement of the interphasial adhesion in the solid state, may not be so. One may use either a single compatibilizer that can perform all three compatibilization tasks, or a combination of agents, each playing one or two different roles. For example, stabilization of the desired dispersion (accomplished by addition of surfactant to mechanically mixed compound), may be accom-... 

For high molecular weight (M — °o) binary blends, the Helfand and Tagami theory predicts that in binary blends (i) the interfacial thickness, A/ is inversely proportional to the interfacial tension coefficient,v , the product, A/ v being independent of the thermodynamic interaction parameter, X, (ii) the surface free energy is proportional to (iii) the chain-ends of both polymers concentrate at the interface (iv) any low molecular... 

Figure 2.14. Interfacial tension coefficient at 150 C for 46 polymer blends plotted vs. the solubility parameter contributions. R is the correlation coefficient.

Thermodynamics also plays a dominant role in the interphasial phenomena, viz. the interfacial tension coefficient, thickness of the interphase, Al, the rheological properties of the interphase, the adhesion, etc. It is worth recalling that most... 

Similarly, for the symmetrical polymers A and B whose M —> °o, the interfacial thickness, Al , and the interfacial tension coefficient, V , were derived as ... 

Figure 4.2. Temperature dependence of the interfacial tension coefficient for PP/PS (data from Kamal et al., 1994) and for PE/PA, LDPE/PS, and PVDE/EP [Luciani et al, 1996].

The Helfand-Tagami lattice theory predicts that there is reciprocity between the interfacial tension coefficient and the interfacial thickness, and the product, Al , is independent of the thermodynamic binary interaction parameter, Furthermore, the theory led to the conclusions that (i) the surface free energy is proportional to... 

Figure 4.3. Verification of the molecular weight dependence of the interfacial tension coefficient, as predicted by the Helfand-Tagami theory (see Eq 4.6)...

For long copolymer chains (in strongly immiscible, or the wet brush case ), the reduction of the interfacial tension coefficient should follow the relation ... 

Both Eqs 4.16 and 4.17 predict that when adsorption density (Z/a ) is high, the interfacial tension coefficient is low. For the same surface area per chain, longer copolymer chains are predicted to be more efficient. The expressions of Z/a can be obtained, for both wet and dry brushes, as a function of the copolymer chemical potential, ji. The ratio was found to depend on... 

As copolymers are added decreases until (()+ reaches the cmc value, at which the limiting value of the interfacial tension coefficient, is obtained. A question arises whether the copolymer can saturate the interface so that Av = = (kgX/a ) (%/6), and effectively the... 

Two semi-empirical relations between the interfacial tension coefficient and compatibilizer concentration were derived. The first was obtained assuming an analogy between addition of block copolymer to a polymer blend and titration of an emulsion with surfactant [Utracki and Shi, 1992] ... 

A simplified analytical calculations for the case where the interaction parameters obey the assumed relationships, led to the following relation for the reduction of the interfacial tension coefficient in A/B blend upon addition of copolymer XY ... 

The interfacial thickness, Al , and the interfacial tension coefficient, v , are both related to the square root of the thermodynamic binary interaction parameter, — Al directly, whereas inversely, thus their product , Al. v , is to be independent of thermodynamic interactions. The latter conclusion may have limited validity, but the general tendency — the reciprocity between the interfacial tension coefficient and the interphase thickness — is correct. The theory correctiy predicted the magnitude of the interphasial thickness, Al = 1-4 nm. Note that the theory is for A/B binary systems, thus extending these predictions to compatibilized systems, where Al < 65 nm may lead to erroneous expectations. For the latter system the reciprocity between v and Al is not to be expected. 

For the strategies of compatibilization, Helfand s theory provides three important conclusions (1) the chain-ends of both polymers concentrate at the interface, (2) any low molecular weight third component is forced by the thermodynamic forces to the interface, and (3) the interfacial tension coefficient increases with molecular weight up to an asymptotic value. 

Addition of a block copolymer, A-B, to immiscible blend of homopolymers A and B reduces the interfacial tension coefficient similarly as addition of a surfactant affects emulsions. Thus, the idea of the critical micelle concentration, CMC, and the limiting value of the interfacial tension coefficient, can be applied to polymer... 

As seen in Part 4.2, several theoretical approaches have been proposed for the description of the interfacial phenomena. The lattice theories by Helfand, Roe, Noolandi and their collaborators are based on the study of conformation and molecular environment. The derived relations are written in terms of the binary thermodynamic interaction parameter %i2 and the lattice constants. The theories do agree that the interfacial tension coefficient is a function of but the predicted functional dependencies are different Vj %"l2> with exponent n = 1/2 to 3/2, depending on the assumptions. 

These and more recent theories can be considered as guides for the expected dependencies, but they can not be used directly to calculate either the interfacial tension coefficient or the interphase thickness. Since there is a significant disagreement between the theoretical relationships derived... 

In Figure 4.5, the interfacial tension coefficients calculated from Eqs. 4.37 and 4.38 are compared with the experimental values. For the selected pairs of polymers, the latter seems to provide a better correlation with the measured values of V.. ... 

Figure 4.5. Comparison between calculated and measured values of the interfacial tension coefficient from Girifalco Good Eq 4.37, and from the harmonic mean Eq 4.38, incorporating the dispersive and polar contributions.

The interfacial tension coefficient can be calculated from the drop shape using the relation ... 

It seems that Chappelear [1964] was the first who applied this technique to measure the interfacial tension coefficient of polymer blends. Further refinements have been published [Elemans, 1989 Elemans et al., 1990 Elmendorp, 1986]. The method is simple, not requiring special equipment, but the zero-shear viscosity of the investigated polymers at the processing temperature must be known. Typical results obtained this method are shown in Table 4.3. 

Table 4.3. Interfacial tension coefficient as determined using the capillary breakup method p ,uciani et al., 1997]...

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