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
Lec-9: Thermodynamics of Polymer Blends ………………….......Eng. Auda Jabbar Ms.C
► 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 phaseseparated 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.
Lec-9: Thermodynamics of Polymer Blends ………………….......Eng. Auda Jabbar Ms.C
► 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)
Lec-9: Thermodynamics of Polymer Blends ………………….......Eng. Auda Jabbar Ms.C
► 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):
Lec-9: Thermodynamics of Polymer Blends ………………….......Eng. Auda Jabbar Ms.C
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:
Lec-9: Thermodynamics of Polymer Blends ………………….......Eng. Auda Jabbar Ms.C
…........................(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.
Lec-9: Thermodynamics of Polymer Blends ………………….......Eng. Auda Jabbar Ms.C
♦ 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.
Lec-9: Thermodynamics of Polymer Blends ………………….......Eng. Auda Jabbar Ms.C
►►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:”
Lec-9: Thermodynamics of Polymer Blends ………………….......Eng. Auda Jabbar Ms.C