Lec-9: Thermodynamics of Polymer Blends ………………….......Eng. Auda Jabbar Ms.C

Thermodynamics of Polymer Blends

Introduction:

· Thermodynamics is derived from two words: ‘Thermo’ which means ‘Heat energy’ and ‘Dynamics’ which means ‘conversion’ or ‘transformation’

Performance of polymer blends depends on the properties of polymeric components, as well as how they are arranged in space. The spatial arrangement is controlled by the thermodynamics and flow-imposed morphology.

Determination of thermodynamic properties such as the phase diagram or the Huggins-Flory binary interaction parameter, χ12, is difficult.

The difficulties originate in high viscosity of macromolecular species, thus slow diffusion toward the equilibrium, heat generation when mixing and dangers of degradation.

For these reasons, there is a tendency to use low molecular homologues or solutions. Furthermore, it is an accepted practice to purify the polymers before measuring their thermodynamic properties. However, the industrial polymers have high molecular weights, and are modified by incorporating low molecular weight additives. Furthermore they are processed under high flow rates and stresses that preclude the possibility of thermodynamic equilibrium. For these and other reasons, a direct application of the laboratory data to industrial systems may not always

be advisable.

Another difficulty originates in the lack of theories able to predict variation of thermodynamic properties for commercially attractive systems with modifiers.

Polymeric Liquid Mixtures:

Polymeric liquid mixtures are conveniently divided into:

1- Solutions (containing a low molecular weight liquid)

2- Blends(containing only macromolecular species)

Polymer Solutions:

►Concentration of polymer solution is given either as:

- volume fraction, φi, or

- wt/vol concentration, c (g/100 mL) ,(for dilute solutions)

►In solutions, the solubility originates mainly from the entropic effects(there is a large number of possible arrangements of macromolecules in space containing small solvent molecules)

►Traditionally, solutions have been used to characterize the polymer:

to measure its molecular weight averages, e.g., number, weight and z- average: Mn, Mw, and Mz, or the size of its macromolecular coil

► The solutions are also used to measure of the thermodynamic interactions between the polymer segments and solvent molecules.

Polymer Blends:

► Concentration is customarily expressed as a mole fraction, xi

►By contrast with solutions, the polymer blends are mostly immiscible

Thermodynamics of Polymer Blends

Blending of polymers is a technological way for providing materials with full set of desired specific properties at the lowest price, e.g. a combination of strength and toughness, strength and solvent resistance, etc.

The most important characteristic of a polymer blend of two (or more) polymers is the phase behavior. Polymer blends (like low molecular weight solvents) can exhibit miscibility or phase separation and various levels of mixing in between the extremes (e.g., partial miscibility).

Whether a particular polymer blend will be homogeneous or phase-separated will depend upon many factors, such as the kinetics of the mixing process , the processing temperature , and the presence of solvent or other additives; however , the primary consideration for determining miscibility of two polymers is a thermodynamic issue that is governed by the Gibbs free-energy equation.

ΔGm = ΔHm – TΔSm…………..…….(9)

where : ΔGm, ΔHm, and ΔSm are the Gibb’s free energy, the enthalpy and entropy of mixing at temperature T, respectively

► If ΔGm is positive over the entire composition range at a given temperature , the two polymers in the blend will separate into phases that are pure in either component , providing that a state of thermodynamic equilibrium has been reached.

► If two polymers are mixed, the most frequent result is a system that exhibits a complete phase separation due to the repulsive interaction between the components (i.e. the chemical incompatibility between the polymers).

►Miscible polymer blend is a polymer blend which is homogeneous down to the molecular level and associated with the negative value of the free energy of mixing.

► The most important factor leading to miscibility in low molecular weight materials is the combinatorial entropy contribution which is very large compared to high molecular weight polymers.

► For complete miscibility , two conditions are necessary:

1- ΔGmmust be negative ;

ΔGm = ΔHm – TΔSm < 0……………………(10)

2-The second derivative of ΔGm with respect to volume fraction of component 2(2) must be grater than zero;

……………………………..…(11)

over the entire composition range.

►If ΔGm< 0, but eq.(11) is not satisfied, the blend will separate at equilibrium into two mixed-composition phases .This means that each phase will contain some of each polymer.

► The value of TΔSm is always positive since there is an increase in the entropy on mixing. Therefore, the sign of ΔGm always depends on the value of the enthalpy of mixing ΔHm. The polymer pairs mix to form a single phase only if the entropic contribution to free energy exceeds the enthalpic contribution, i.e.,

ΔHm < TΔSm …………………….(12)

► For most polymer blends the miscibility increases with increasing the pressure. The effect depends on the magnitude of the heat of mixing ΔHm. For ΔHm < 0 the miscibility is enhanced by compression, whereas for those with ΔHm > 0 it is reduced.

►In general, polymer blends can exhibit a wide range of phase behavior, including upper and lower critical solution temperatures(figure bellow):

Figure : Phase diagram for liquid mixtures with the upper and the lower critical solution temperature, UCST and LCST, respectively.

♦There are three regions of different degree of miscibility:

1.The single-phase miscible region between the two binodals

2.The four fragmented metastable regions between binodals and spinodals

3.The two-phase separated regions of immiscibility, bordered by the spinodals

♦ The diagram also shows two critical solution temperatures, the lower, LCST (at higher temperature), and the upper, UCST (at lower temperature). The phase diagram with two critical points is a rule for mixtures of low molar mass components, whereas the polymer blends usually show either LCST (most) or UCST.

In principle, every miscible blend is bounded by upper (LCST) and lower (UCST) temperature limits. However, in reality the LCST may be higher than the degradation temperature of the blend and UCST may be lower than the Tg and hence can not be determined.

♦The binodals separate miscible (one-phase) and metastable region, the spinodals separate metastable and two-phase region.

The thermodynamic conditions for phase separations are given by:

…........................(13)

……………….(14)

♦ The phase separation takes place when a single-phase system suffers a change of either composition, temperature or pressure that forces it to enter either the metastable or the spinodal region.

♦ When the system enters from single-phase region into the metastable region, the phase separation occurs by the mechanism resembling crystallization – slow nucleation followed by growth of the phase separated domains.

♦ By contrast, when the system is forced to jump from a single-phase into the spinodal region of immiscibility the phases separate spontaneously by a mechanism called spinodal decomposition.

►►Gibbs Phase Rule:

For the discussions of phase diagrams it is important to know how many of the state variables one may change without going through a phase transition.

The total number of variables required to describe a system by Eq 8 is N + 2, where N is number of components and “2” stands, e.g., for V and T.

For a closed system the number of intensive variables (also known as a

degree of freedom), is given by the “Gibbs the phase rule:”