mixtures of polymers

Course M6 – Lecture 321/1/2004 (JAE)

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Dr James Elliott

Mixtures of polymers

Polymers in solution and polymer blends

Course M6 – Lecture 3

21/1/2004

3.1 Introduction

Polymer mixtures are an important part of many industrial processing applications:

– Polymer synthesis– Fibre spinning– Membrane formation

We will also spend some time interpreting the binary phase diagram predicted by Flory-Huggins theory, and looking at demixing processes

– Nucleation and growth– Spinodal decomposition

Finally, we will review the use of solubility parameters, and see how to calculate χ parameters


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3.2.1 FH free energy for polymer blend

Last lecture, we introduced the FH free energy for a polymer/solvent mixtureFor a blend of two polymers, this now looks like :

or, writing Φ1 = Φ, Φ2 = 1 – Φ, and M1 = M2 = M :

2122

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1

1

B

mix χlnln ΦΦ+ΦΦ

+ΦΦ

=MMTk

F

)1(χ)1ln()1(lnB

mix Φ−Φ+Φ−Φ−

+ΦΦ

=MMTk

F

per site

per site

3.2.2 FH free energy for polymer blend

As χ (or equivalently 1/T) is varied, the shape of the free energy curve changes

At χ = 0.5/M, there is a critical point where coexistence of two separate phases is favoured

Concentrations of the phases determined by the double tangent construction


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3.3.1 FH free energy and phase diagrams

The resulting phase diagram can be calculated, and also includes information about kinetics of demixing

Mχ

3.3.2 FH free energy and phase diagrams

Note that for coexistence χ ≥ 0.5/M, so the slightest degree of unfavourable interactions between the two polymers will cause phase separationPolymers are generally immiscibleThis is because the entropy of mixing is greatly reduced compared to mixing of simple solutions as polymers are 1D objects not point-like particlesImmiscibility of polymers has implications for industrial processes such as joining, as polymer-polymer interfaces tend to be very weak


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3.4 Aside on polymer interfaces

5.0K iNaw ≈TkTNkE ii BBχ =≈

w

w = 10-30 ÅχKaw ≈⇒

3.5.1 Nucleation vs. spinodal decomposition

Fundamentally different kinetic mechanisms of demixng

Nucleation and growth

Spinodal decomposition


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3.5.2 Nucleation vs. spinodal decomposition

Very characteristic microstructures can be observed in polymer blends which have separated by the two means

Nucleation and growth Spinodal decomposition

3.6 Coarsening during spinodal decomposition

Linearised approximation breaks down leading to increasing length scale of phase separation


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3.7 Corrections to FH theory

Of course, FH is only a mean-field approximation

In practice, there are a number of complicating factors

The interaction parameter is concentration dependent

Effects of molecular weight polydispersity

Effects of compressibility and thermal expansions

2χ Φ+Φ+= cba

3.8 Upper critical solution temperature (UCST)

If the enthalpic interactions are disfavourable, the mixture will exhibit an upper critical solution temperature

Immiscible at lower T due todisfavourable enthalpicinteractions

Miscible at higher T due to reduced enthalpic interactions


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3.9 Dependence of UCST on molecular weight

Polystyrene and polybutylene blends as a function of PS molecular weight

M(PB) = 2350

• M(PS) = 2250

• M(PS) = 3500

• M(PS) = 5200

3.10 Lower critical solution temperature (LCST)

Returning to the phase diagram, non-FH dependence of χ on temperature leads to critical solution temperatures

Polystyrene and poly(vinyl methylene) exhibit a lower critical solution temperature

Miscible at lower T due to favourable enthalpic interactions.

Immiscible at higher T due to free volume differences

Two phase

One phase


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3.11 UCST and LCST phase diagram types

3.12.1 Solubility parameter approach

Miscibility can be estimated by using solubility parameters, which are tabulated for many different polymers and solventsFor most (non-polar) solvents, the enthalpic contribution to the χ parameter can be written

where δA, δB are the solubility parameters of the solvent and polymer, representing the cohesive energy densities.

( )2BAm

H δδχ −=RTV

( ) 21

mvapδ VH∆=


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3.12.2 Solubility parameter approach

The total χ parameter is then

For polar solvents, need to add correction for the electrostatic couplings between solvent and polymerFrom tables of δ (or measurements) can then estimate χand predict phase diagramCan also deduce χ from molecular simulations

( ) 34.0δδχ 2BA

m +−=RTV

3.13 Solubility of polymers in solvents


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3.14 Solubility params of solvents & polymers

3.15 Determining the χ parameter

Direct measurement of heat of mixing

Measurement of the partial vapour pressure

Scattering

χ is concentration dependent (χS constant)

( ) 22221

011 χ)/11(ln/µµ Φ+Φ−+Φ=− NRT

( ){ } ( ){ } χ2Φ Φ)(S 1222D22

1221D11

1C −+=

−−− qRSNqRSNq


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3.16.1 Calculation of χ from simulation

The following slides demonstrate a molecular simulation of the mixing behaviour between a polymer and a solvent, in this case polystyrene and cyclohexane.The simulation is used to calculate the parameters of the Flory-Huggins model, i.e. the interactions energies and the coordination number.Polystyrene is represented by one monomer unit.

3.16.2 Simulation of the interaction energy

Many different constellations of the two molecules are generated (avoiding close contacts between cyclohexaneand the styrene head and tail) and the interaction energy of each pair is calculated.


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3.16.3 Simulation of the interaction energy

A typical energy distribution obtained from the simulation

The simulation is carried out at a range of temperatures, and the resulting energy curve is fitted by a second order polynomial. This results in a temperature dependent Flory-Huggins interaction parameter.

3.16.4 Simulation of the coordination number

Many clusters are generated to determine how many solvent molecules that can be packed around a monomer


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3.16.5 Simulation of the coordination number

The average coordination number for each of a number of clusters generated by the simulation.

3.16.6 Phase diagram prediction

The Flory-Huggins free energy and resulting phase-diagram as determined from the simulation.For this system, there is an upper critical solution temperature which agrees well with experiment.


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Lecture 3 summary

In this lecture, we discussed the mixing of polymersWe started by reviewing Flory-Huggins theory and its predictions for the phase diagram of polymer mixtures, in particular the transition to coexistenceIn general, polymers are immiscible unless there are strongly favourable enthalpic interactions The temperature dependence of the χ parameter gives rise to a wide variety of phase diagrams including those with upper and lower critical solution temperaturesWe briefly discussed the two kinetic mechanisms of demixing: nucleation and spinodal decompositionFinally, we looked at measuring and calculating χ

mixtures of polymers

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