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Polymer-Polymer Miscibility

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:

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Polymer-Polymer Miscibility

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  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. J.S. Parent

  2. f2 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. J.S. Parent

  3. Industrial Relevance of Polymer Solubility J.S. Parent

  4. DGmix < 0 DGmix > 0 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. J.S. Parent

  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 J.S. Parent

  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. J.S. Parent

  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. J.S. Parent

  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. J.S. Parent

  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 J.S. Parent

  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. J.S. Parent

  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. J.S. Parent

  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. J.S. Parent

  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. J.S. Parent

  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. J.S. Parent

  15. Solubility Parameters of Select Materials J.S. Parent

  16. Solubility Parameters of Select Materials J.S. Parent

  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 J.S. Parent

  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. J.S. Parent

  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. J.S. Parent

  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. J.S. Parent

  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), 109-168 (1980) for further information. J.S. Parent

  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. J.S. Parent

  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. J.S. Parent

  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? J.S. Parent

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