Polymer negatively deviating

The solution analogue of the compressibility factor of a gas is the reduced osmotic pressure (I7/C2). This quantity is shown sch aticaOy in Fig. 3.3 for polymer molecules under different solvency conditions. In a poor solvent for the polymer, negative deviations from ideality are apparent. This can be envisag as arising because the polymer molecules are in dynamic association under such solvency conditions. Since osmotic pressure is a coUigative... 

These equations suggest that a plot of M vs conversion should be linear. A positive deviation from the line predicted by eq. 16 indicates incomplete usage of transfer agent (T) while a negative deviation indicates that other sources of polymer chains are significant (e.g. the initiator). 

The activities of the polymer and monomer of the hypothetical solutions given in Figure 9.6(a) are shown in Figure 9.6(b). While r = 1 corresponds to Raoult law behaviour, strong negative deviations are observed for r = 10, 100 and 1000. 

PAL has been used to study both miscible and immiscible polymer blends [41, 61, 67-70], PAL results have shown both positive and negative deviations from additivity of free volume with blend composition. In the case of multi phase systems, PAL data analysis is complicated by the fact that Ps may diffuse between the different blend phases. 

Improvement in cost, processability, and performance of polymers can also be achieved through blending two or more polymers. The blends may be homogeneous, heterogeneous, or a bit of both. Properties of miscible polymer blends may be intermediate between those of the individual components (i.e., additive behavior), as is typically the case for Tg. In other cases, blend properties may exhibit either positive or negative deviation from additivity. 

The negative deviations of the experimental initial slopes from the theoretical dependences I or II for polymer molecules with low equilibrium rigidity can be understood qualitatively by taking into account the finite character of d, the diameter of a real polymer chain, which was not included in the theories discussed in Chap. 3. 

FIGURE 16.1 Polymer solutions exhibit negative deviations from Raoult s law demonstration for the system n-hexane/polydimethylsiloxane at various polymer molecular weights. (From Dohm, R. and Pfohl, O., Fluid Phase Equilibria, 15, 194—197, 2002. With permission.)... 

This relationship is shown in Figure 13 where Polymer 1 has a permeability 1000 times higher than that of Polymer 2. Published data have small negative deviations from this theoretical relationship. Part of the deviation can be explained by densification of the blend relative to the starting components. Random copolymers, which are forced (by covalent bonds) to imitate combinations of two materials, have permeabilities that are similar to miscible blends. However, the deviations from equation 18 tend to be positive. A series of styrene—methacrylonitrile copolymers were studied (11) and slight positive deviations were found. Figure 14 shows the oxygen permeabilities of a series of vinylidene chloride— -butyl acrylate copolymers [9011-09-0]. 

Relation (3.11) was obtained empirically by Raoult and is called Raoult s law. Hence in ideal solutions Raoult s law holds over the entire range of compositions, this being represented by a straight line in the v or pressure composition curve (Fig. 3.1). In reality, most solutions do not obey Eqs. (3.9) and (3.11). Such solutions are called nonideal, or real. Polymer solutions characteristically display sharp negative deviations from ideality, as can be seen in Fig. 3.1. 

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] ... 

It should be noted that the Doi and Ohta theory predicts oifly an enhancement of viscosity, the so called emulsion-hke behavior that results in positive deviation from the log-additivity rule, PDB. However, the theory does not have a mechanism that may generate an opposite behavior that may result in a negative deviation from the log-additivity rule, NDB. The latter deviation has been reported for the viscosity vs. concentration dependencies of PET/PA-66 blends [Utracki et ah, 1982]. The NDB deviation was introduced into the viscosity-concentration dependence of immiscible polymer blends in the form of interlayer slip caused by steady-state shearing at large strains that modify the morphology [Utracki, 1991]. 

Blending is increasingly carried out to improve processability. In general, low viscosity is considered beneficial to processing. When immiscible polymers are blended, the blend viscosity rarely follows the additivity rule. A negative deviation... 

In the case of both the mechanical properties studied (tensile strength and elongation), on comparison of the properties of the component polymers and the blends, the non-irradiated blends showed negative deviation from the linear additivity of the properties. However, on irradiation, this negative deviation was changed into positive deviation. Some of the mechanical... 

There are four types of the polymer blends (i) Additive blends whose melt viscosity follows Equation 18.3, (ii) Blends with a positive deviation of from Equation 18.3. These include blends with strong interphase interactions, (iii) Blends with a negative deviation from the logarithmic additivity, which is typical of incompatible components with weak interphase interactions, (iv) Blends that show both positive and negative deviations of py from the additive values (such a relationship is typical of materials in which structural changes take place during flowing). 

It is scarcely surprising in light of these positive and negative deviations from ideality, that it is possible to adjust the solvency so that the polymer molecules obey the ideal van t Hoff equation of state, i.e. the second virial coefficient is zero. This is the 0-point. Under these solvency conditions, the macromolecules, which may, for example, be several millions in molecular weight, behave like ideal minimolecules. e. molecules comparable in size and interactions to the molecules of solvent). Of course, obedience to ideal behaviour is evident only up to a concentration of several per cent. Beyond this, the higher virial coefficients involving the higher order many-body interactions manifest themselves and deviations from the ideal van t Hoff limit appear. 

The segmental attraction hypothesis It was pointed out in Section 3.2.7 that in dispersion media that are poorer solvents than -solvents for the polymer, the macromolecular segments experience a mutual attraction. This attraction is responsible for the negative deviations from ideal behaviour displayed by polymer chains in worse than d-solvents (see Fig. 3.3). If the solvency for the polymer is made suitably worse than that of a 0-solvent, phase separation ensues (Flory, 1953). 

Dingihan, G., and Ruckenstein, E., Positive and negative deviations from additivity in drag reduction of binary dilute polymer solutions, A/OjE/., 20, 1222-1224 (1974). 

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