Thermodynamic of polymer blends

Assoc.Prof.Dr. Jatyuphorn Wootthikanokkhan

Division of Materials Technology, School of Energy, Environment and Materials, KMUTT, Thailand

Classification of polymer blends (Polymer Alloy Compendium; A Technical note from JICA shortcourse

in High Performance Polymer Technology)

Terms related to polymer blend miscibility (Ref. form Utracki, in Polymer Blend Handbook, 2002, p. 135, ch. 2, Kluwer Academic Publisher.)

Term Definition

Miscible polymer blend Polymer blend, homogeneous down to the molecular level, in which the domain size is comparable to macromolecular dimension.

Immiscible blend Polymer blends whose change in free energy of mixing is greater than zero.

Polymer Alloy Immiscible, compatibilized polymer blend with the modified interface and morphology

Interphase Third phase in binary polymer alloys, endangered by inter-diffusion or compatibilization. Its thickness ~ 2 to 60 nm, depends on polymer mescibility and compatibilization

Compatibilization Process of modification of the inter-phase in immiscible polymer blends, resulting in reduction of the interfacial energy, development and stabilization of the desired morphology, leading to the creation of a polymer alloys with enhanced performance

Dr.J.Wootthikanokkhan, KMUTT

Factors controlling polymer-polymer miscibility

Interaction between the two polymers Solubility parameter Polar interaction and H-bonding

Blend composition

Temperature

Dr.J.Wootthikanokkhan, KMUTT

Effects of blend composition and the resulting phase diagrams

Upper critical solution temperature (UCST) Lower critical solution temperature

(LCST)

Dr.J.Wootthikanokkhan, KMUTT

Examples of blends exhibiting UCST and LCST

UCST; PS/PI, PS/PBu, PS/SBR, PS/PCL

LCST; PVC/PMA,SAN/PMA, EVA/CPE,PC/PCL, PVF2/PVA UCST behavior is common in mixtures of low molecular weight materials

and polymer solution [L.I. Nass et al., Encyclopedia of PVC, 1986]

LCST behavior is a characteristic of negative heat of mixing and negative excess entropy.

Criterions for polymer-polymer miscibility

Thermodynamically, polymer blend will be miscible if two criterions are satisfied, i.e.,

1. The change free energy of mixing should be negative (∆Gmix < 0).

2. The second derivative of the free energy with respect to the volume fraction of a component in the blend should be positive

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Thermodynamic of polymer blend; The first criteria

(k= Boltzmann’s constant = 1.38 ×10-23 J/K)

Representation of two-dimentional Flory-Huggins lattice containing solvent molecules (O) and a low molecular weight solute (•)

n = number of lattice sites (or number of molecules in a case of polymer blend x1 = mole fraction of the solvent

Lattice model for a polymer chain in solution. Symbol represent solvent molecules (o) and polymer chain segment (•)

The subscript 1 indicates solvent, and 2 polymer

Enthalpy change upon mixing

V = molar volume (mL/mol)

Notably, it was claimed that, for the blend system without any specific interactions, miscibility can be expected if δ1 - δ2 < 0.2 (J/mL)1/2. [Utracki, Polymer Blends Handbook, 2002, p.162]

Prediction of a solubility parameter (of liquid)

V = Volume of the mixture

Since polymers are solid and the enthalpy of vaporization cannot be measured. The solubility parameters are determined by; 1. Experimental

1.1 Swelling experiment 1.2 Viscosity measurement

2. Calculation (using group molar attraction constant)

If the polymer is cross-linked, the solubility parameter may be determined by swelling experiments

The swelling coefficient (Q) reaches a maximum when the solubility parameter of the solvent nearly match that of the polymer, for several cross-linked systems: polyurethane (), polystyrene (), and a polyurethane-polystyrene IPN (•)

m = weight of the swollen sample mo = the dry weight

ρs = density of the swelling agent

Determination of the solubility parameter by measuring the intrinsic viscosity

Determination of the solubility parameter, using the intrinsic viscosity method, for polyisobutylene (A) and polystyrene (B). The intrinsic viscosity will be highest for the best match in solubility parameter

Solubility parameters of some common solvents and polymers

Determination of solubility parameter by using group molar attraction constant (F and/or G)

Formula weight of repeating unit

Density of the polymer

Group molar attraction constants at 25 ºC (according to Small; derived from measurement of heat of evaporation)

Unit = (cal/cc)1/2

Determination of solubility parameter

• Example; polystyrene • F.W. = ? • Density = ? • G = ? • Solubility parameter = ?

• Notably, PS and PMMA are immiscible. (How much different of their solubility parameter values ?)

Some drawbacks of the solubility parameter approach

• Omission of the specific interaction effect. (it was assumed that the molecular interactions was non-specific, without hydrogen bonding, ion-ion, ion-dipole interactions that provide negative contribution to the free energy of mixing).

• Effects of structure (isomeric) and orientation on the miscibility were not taken into account.

• Poor reproducibility of the measured values (selection of different commercial resin or using different set of solvents may significantly change the value of measured δ

Experimentally determined and calculated solubility parameters for several polymers (from U. Eisele in “Introduction to polymer science”, Springer-Verlag, 1990)

Second criteria

Thermodynamic of polymer-polymer miscibility

• A negative free energy change is a necessary but not a sufficient condition for homogeneity between two polymers.

• The shape of ∆G, as a function of concentration of one of its constituents at a temperature T, describes homogeneity or heterogeneity of a mixture more appropriately.

• The relation between ∆GM and Φ2 for a completely homogeneous mixture is schematically shown in Figure below which is concave with no inflection points.

Free energy of mixing for binary mixtures as a function of their composition; (A) Immiscibility, (B) Total miscibility, (C) Partial miscibility

∆G > 0 and so this blend is absolutely immiscible, regardless of the composition

∆G < 0 but the second derivative is partly greater than zero. Therefore, this blend is considered partially miscible. (depending on the blend ratio)

∆G < 0 and the second derivative is also less than zero. Therefore, this blend system is totally miscible over the entire range of blend ratio.

A

B

C

Thermodynamic of polymer-polymer miscibility

• The ∆GM against Φ2 curve for a two-phase system has two inflection

points where

•As the temperature decreased for UCST, the two minima moving away from each other.

•As the temperature increase for LCST, the two minima moving away from each other.

Thermodynamic of polymer-polymer miscibility

• The locus of these inflection points in a

temperature versus Φ2 plot (the phase diagram) is the spinodal curve which defines the thermodynamic limits of stability.

• Within this region the second derivative of free energy with respect to composition is negative so that the system is unstable with respect to fluctuations in composition and or temperature change.

• The curve connecting the minima together is the binodal curve which is the equilibrium curve between homogeneous and heterogeneous.

(a) Free energy of mixing as a function of the relative composition of a binary mixture; T1 > T2> T3> T4. (b) LCST phase diagram

meta-stable region

These two regions have different phase separation mechanisms

(a) Free energy of mixing as a function of the relative composition of a binary mixture; T1 > T2> T3> T4. (b) UCST phase diagram

Phase diagram

• The binodal and spinodal curves are only important for theoretical purposes when modelling polymer-polymer miscibility phenomena.

• On the other hand, the cloud point curve, which lies between the binodal and spinodal curves, is often measured experimentally.

• The cloud point curve which is associated with phase separation on heating is referred to as the LCST phase diagram.

• On the other hand, if the heterogeneous mixture become more homogeneous upon raising temperature, the cloud point curve is convex upward and is referred to as UCST.

• In either case the second derivative of free energy change on mixing with respect to the volume fraction of component two in the blend is positive in the homogeneous and in the meta-stable region and become negative in the heterogeneous region.

Weaknesses of the Flory-Huggins theory

• It was assumed that the Flory-Huggins interaction parameter which arises from mixing of n1 moles of polymer (or solvent) with n2 moles of polymer is independent of concentration, pressure, and molecular weight.

• Experimental evidence, however, has shown that these are oversimplified assumptions and the interaction parameter is dependent on the above parameters.

Effect of molecular weight on miscibility

[ref; Polymer science and technology, J.R. Fried, Prentice Hall, 1995]

Effect of pressure on miscibility [Ref; Multi-component polymer systems, edited by I.S.Miles & S. Rostami, 1992, Longman scientific & technical]

The effect of pressure on the interaction parameter was neglected in this calculation. However, both theory and experimental results confirm that pressure induces immiscibility in these mixtures.

Effect of pressure on miscibility [Ref; Multi-component polymer systems, edited by I.S.Miles & S. Rostami, 1992, Longman scientific & technical]

On the other hand, the miscibility in systems with a LCST behavior increased as the pressure increased.

Weaknesses of the Flory-Huggins theory

• Extended Flory-Huggins theory has been developed to predict the miscibility

of polymer blends, taking into account the effect of molecular weight. (see figures on next slides)

• This model, however, still has some weakness, i.e. it fail to predict the experimental results accurately. This is because the theory assume no volume change on mixing (which affect both enthalpic and entropic contributions to the free energy).

• Later, an equation of state theory [Flory, J.Am.Chem.Soc., 89 (1967) 6814] has been developed. It is superior to the original lattice model. The theory, however, ignores the orientation that two polymer chains adapt in respect to one another in forming a specific interaction.

The simulated binodal and spinodal curves for blends of CPE (51 % Cl) and PMMA of different molecular weight. (A) PMMA = 26.4 × 104 g/mol, (B) PMMA = 1.44 × 104

g/mol. [Ref; Multicomponent polymer systems, edited by I.S.Miles & S. Rostami, 1992, Longman scientific & technical]

Note that the experimental cloud point data (from light scattering technique) for two molecular weights of PMMA are also shown