1. Polymer-Polymer Miscibility
When two hydrocarbons such as dodecane and 2,4,6,8,10-pentamethyldodecane are combined, we (not surprisingly) generate a homogeneous solution:
It is therefore interesting that polymeric analogues of these compounds, poly(ethylene) and poly(propylene) do not mix, but when combined produce a dispersion of one material in the other.
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2. Polymer-Solvent Miscibility
Phase diagrams for four samples of polystyrene mixed with cyclohexane plotted against the volume fraction of polystyrene. The molecular weight of each fraction is given.
The dashed lines show the predictions of the Flory-Huggins theory for two of the fractions. f2
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3. Industrial Relevance of Polymer Solubility
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4. Thermodynamics of Mixing
Whether the mixing of two compounds generates a homogeneous solution or a blend depends on the Gibbs energy change of mixing.
A-B solution
mA moles mB moles
material A material B or
immiscible blend
DGmix (Joules/gram) is defined by:
DGmix = DHmix -T DSmix
where DHmix = HAB - (xAHA + xBHB)
DSmix = SAB - (xASA + xBSB)
and xA, xB are the mole fractions of each material.
DGmix < 0
DGmix > 0
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5. Thermodynamics of Mixing: Small Molecules
Ethanol(1) / n-heptane(2) at 50ºC
Ethanol(1) / chloroform(2) at 50ºC
Ethanol(1) / water(2) at 50ºC
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6. Entropy of Mixing
Consider the two-dimensional lattice representation of a solvent (open circles) and its polymeric solute (solid circles):
small polymeric
molecule solute
solute
Mixing of small molecules results in a greater number of possible molecular arrangements than the mixing of a polymeric solute with a solvent.
While DSmix is always negative (promoting solubility), its magnitude is less for polymeric systems than for solutions of small molecules
When dealing with polymer solubility, the enthalpic contribution DHmix to the Gibbs energy of mixing is critical.
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7. Entropy of Mixing : Flory-Huggins Theory
The total configurational entropy of mixing (J/K) created in forming a solution from n1 moles of solvent and n2 moles of solute (polymer) is:
where fi is the component volume fraction in the mixture:
and
xi represents the number of segments in the species
for a usual monomeric solvent, xi = 1
xi for a polymer corresponds roughly (but not exactly) to the repeat unit
On the previous slide, f1, f2 and n1 are equivalent in the two lattice representations, but n2 = 20 for the monomeric solute, while n2 = 1 for the polymeric solute.
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8. Enthalpy of Mixing DHmix can be a positive or negative quantity
If A-A and B-B interactions are stronger than A-B interactions, then DHmix > 0 (unmixed state is lower in energy)
If A-B interactions are stronger than pure component interactions, then DHmix < 0 (solution state is lower in energy)
An ideal solution is defined as one in which the interactions between all components are equivalent. As a result,
DHmix = HAB - (wAHA + wBHB) = 0 for an ideal mixture
In general, most polymer-solvent interactions produce DHmix > 0, the exceptional cases being those in which significant hydrogen bonding between components is possible.
Predicting solubility in polymer systems often amounts to considering the magnitude of DHmix > 0.
If the enthalpy of mixing is greater than TDSmix, then we know that the lower Gibbs energy condition is the unmixed state.
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9. Enthalpy of Mixing : Flory-Huggins Theory
The enthalpy of mixing accounts for changes in adjacent-neighbour interactions in the solution (lattice), specifically the replacement of [1,1] and [2,2] interactions with [1,2] interactions upon mixing:
where f2 = volume fraction of polymer,
n1 = moles of solvent,
x1 = segments per solvent molecule (usually 1),
c = Flory-Huggins interaction parameter (dimensionless).
The Flory-Huggins parameter characterizes the interaction energy per solvent molecule.
independent of concentration
inversely related to temperature
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10. Gibbs Energy of Mixing: Flory-Huggins Theory
Combining expressions for the enthalpy and entropy of mixing generates the free energy of mixing:
The two contributions to the Gibbs energy are configurational entropy as well as an interaction entropy and enthalpy (characterized by c).
Note that for complete miscibility over all concentrations, c for the solute-solvent pair at the T of interest must be less than 0.5.
If c > 0.5, then DGmix > 0 and phase separation occurs
If c < 0.5, then DGmix < 0 over the whole composition range.
The temperature at which c = 0.5 is the theta temperature.
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11. Factors Influencing Polymer-Solvent Miscibility
Based on the Flory-Huggins treatment of polymer solubility, we can explain the influence of the following variables on miscibility:
1. Temperature: The sign of DGmix is determined by the Flory-
Huggins interaction parameter, c.
As temperature rises, c decreases thereby improving solubility.
Upper solution critical temperature (UCST) behaviour is explained by Flory-Huggins theory, but LCST is not.
2. Molecular Weight: Increasing molecular weight reduces the
configurational entropy of mixing, thereby
reducing solubility.
3. Crystallinity: A semi-crystalline polymer has a more positive
DHmix = HAB - xAHA - xBHB due to the heat of
fusion that is lost upon mixing.
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12. DHmix and the Solubility Parameter
The most popular predictor of polymer solubility is the solubility parameter, i. Originally developed to guide solvent selection in the paint and coatings industry, it is widely used in spite of its limitations.
For regular solutions in which intermolecular attractions are minimal, DHmix can be estimated through:
where DU1,2 = internal energy change of mixing per unit volume,
i = volume fraction of component i in the proposed mixture,
i = solubility parameter of component i: (cal/cm3)1/2
Note that this formula always predicts DHmix > 0, which holds only for regular solutions.
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13. Solubility Parameter
The aforementioned solubility parameter is defined as:
d = (DEv / n)1/2
where DEv = molar change of internal energy on vapourization
n = molar volume of the material
As defined, d reflects the cohesive energy density of a material, or the energy of vapourization per unit volume.
While a precise prediction of solubility requires an exact knowledge of the Gibbs energy of mixing, solubility parameters are frequently used as a rough estimator.
In general, a polymer will dissolve in a given solvent if the absolute value of the difference in d between the materials is less than 1 (cal/cm3)1/2.
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14. Determining the Solubility Parameter
The conditions of greatest polymer solubility exist when the solubility parameters of polymer and solvent match.
If the polymer is crosslinked, it cannot dissolve but only swell as solvent penetrates the material.
The solubility parameter
of a polymer is therefore
determined by exposing
it to different solvents,
and observing the  at
which swelling is
maximized.
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15. Solubility Parameters of Select Materials
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16. Solubility Parameters of Select Materials
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17. Flory-Huggins and Solubility Parameters
Given that the enthalpy of mixing has been treated by Hildebrand’s solubility parameter approach and Flory-Huggins interaction parameter, it is not surprising that the resulting parameters are related.
Solubility parameters allow a mixture property to be derived from pure component values
F-H interaction parameters are component dependent, requiring the user to find more specific data
Equating the heat of mixing expressions of the two treatments provides the following relationship:
where c1 = interaction parameter
Vp = volume of 1 mole of polymer segments
i = solubility parameter of polymer i
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18. Partial Miscibility of Polymers in Solvents
Idealized representation of three generalized possibilities for the dependence of the Gibbs free energy of mixing, DGm, of a binary mixture on composition (volume fraction of polymer, f2) at constant P and T.
I. Total immiscibility;
II. Partial miscibility;
III. Total miscibility.
Curve II represents the intermediate case of partial miscibility whereby the mixture will separate into two phases whose compositions () are marked by the volume-fraction coordinates, f2A and f2B, corresponding to points of common tangent to the free-energy curve.
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19. Partial Miscibility of Polymers in Solvents
Phase diagrams for the polystyrene-acetone system showing both UCSTs and LCSTs.
Molecular weights of the polystyrene fractions are indicated.
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20. Polymer Solubility: Summary
Encyclopedia of Polymer Science, Vol 15, pg 401 says it best...
A polymer is often soluble in a low molecular weight liquid if:
the two components are similar chemically or are so constituted that specific attractive interactions such as hydrogen bonding take place between them;
the molecular weight of the polymer is low;
the bulk polymer is not crystalline;
the temperature is elevated (except in systems with LCST).
The method of solubility parameters can be useful for identifying potential solvents for a polymer.
Some polymers that are not soluble in pure liquids can be dissolved in a multi-component solvent mixture.
Binary polymer-polymer mixtures are usually immiscible except when they possess a complementary dissimilarity that leads to negative heats of mixing.
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21. Polymer Alloys and Blends
The entropy contribution to the Gibbs energy of mixing for polymer systems is small, making the likelihood of attaining a polymer alloy (miscible) versus a blend (immiscible) relatively low.
Some degree of exothermic interaction between the polymer components (DHmix) is necessary to obtain a polymer alloy.
Hydrogen bonding, dipole and/or acid-base interactions between polymer different segments must be greater in magnitude than their pure component strengths.
Nevertheless, polymer pair miscibility is not necessarily uncommon.
Examples of alloying polymers include
poly(styrene)/poly(phenylene oxide),
poly(vinylchloride)/poly(-caprolactone)
poly(methylmethacrylate)/poly(styrene-co-acrylonitrile)
See J. Macromol. Sci.- Rev. Macromol. Chem., C18(1), (1980) for further information.
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22. Dilute Solution Viscosity
The “strength” of a solvent for a given polymer not only effects solubility, but the conformation of chains in solution.
A polymer dissolved in a “poor” solvent tends to aggregate while a “good” solvent interacts with the polymer chain to create an expanded conformation.
Increasing temperature has a similar effect to solvent strength.
The viscosity of a polymer
solution is therefore dependent
on solvent strength.
Consider Einstein’s equation:
h=hs(1+2.5f)
where h is the viscosity
hs is the solvent viscosity
and f is the volume fraction of
dispersed spheres.
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23. Dilute Solution Viscosity
Shown below is the intrinsic viscosity of
A: Poly(isobutylene) and
B: Poly(styrene)
as a function of solubility parameter.
When d for the solvent matches
that of the polymer, the chain
conformation is most expanded,
resulting in a maximum viscosity.
This is another method of
determining the solubility
parameter of a given polymer.
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24. Concentrated Solutions - Plasticizers
Important commercial products are solutions where the polymer is the principal component.
Poly(vinyl chloride) is a rigid material (pipes, house siding), but is transformed into a leathery material upon addition of a few percent of dioctylphthate, a common plasticizer.
Plasticizers are small molecules that dissolve within a polymeric matrix to greatly alter the material’s viscosity.
Should they be “good” solvents in a thermodynamic sense or relatively “poor” solvents?
On what basis would you choose a plasticizing agent?
What process would you use to mix the agent with the polymer?
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