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CHEE 890J.S. Parent1 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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CHEE 890J.S. Parent2 Polymer-Solvent Miscibility 22 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.

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CHEE 890J.S. Parent3 Industrial Relevance of Polymer Solubility

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CHEE 890J.S. Parent4 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 m A moles m B moles material A material B + or immiscible blend G mix (Joules/gram) is defined by: G mix = H mix -T S mix where H mix = H AB - (x A H A + x B H B ) S mix = S AB - (x A S A + x B S B ) and x A, x B are the mole fractions of each material. G mix < 0 G mix > 0

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CHEE 890J.S. Parent5 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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CHEE 890J.S. Parent6 Entropy of Mixing Consider the two-dimensional lattice representation of a solvent (open circles) and its polymeric solute (solid circles): smallpolymeric moleculesolute 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 S mix 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 H mix to the Gibbs energy of mixing is critical.

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CHEE 890J.S. Parent7 Entropy of Mixing : Flory-Huggins Theory The total configurational entropy of mixing (J/K) created in forming a solution from n 1 moles of solvent and n 2 moles of solute (polymer) is: where i is the component volume fraction in the mixture: and x i represents the number of segments in the species for a usual monomeric solvent, x i = 1 x i for a polymer corresponds roughly (but not exactly) to the repeat unit On the previous slide, 1, 2 and n 1 are equivalent in the two lattice representations, but n 2 = 20 for the monomeric solute, while n 2 = 1 for the polymeric solute.

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CHEE 890J.S. Parent8 Enthalpy of Mixing H mix can be a positive or negative quantity If A-A and B-B interactions are stronger than A-B interactions, then H mix > 0 (unmixed state is lower in energy) If A-B interactions are stronger than pure component interactions, then H mix < 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, H mix = H AB - (w A H A + w B H B ) = 0 for an ideal mixture In general, most polymer-solvent interactions produce H mix > 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 H mix > 0. If the enthalpy of mixing is greater than T S mix, then we know that the lower Gibbs energy condition is the unmixed state.

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CHEE 890J.S. Parent9 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 2 = volume fraction of polymer, n 1 = moles of solvent, x 1 = segments per solvent molecule (usually 1), = 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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CHEE 890J.S. Parent10 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 ). Note that for complete miscibility over all concentrations, for the solute-solvent pair at the T of interest must be less than 0.5. If > 0.5, then G mix > 0 and phase separation occurs If < 0.5, then G mix < 0 over the whole composition range. The temperature at which = 0.5 is the theta temperature.

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CHEE 890J.S. Parent11 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 G mix is determined by the Flory- Huggins interaction parameter, . As temperature rises, 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 H mix = H AB - x A H A - x B H B due to the heat of fusion that is lost upon mixing.

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CHEE 890J.S. Parent12 H mix 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, H mix can be estimated through: where U 1,2 = 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/cm 3 ) 1/2 Note that this formula always predicts H mix > 0, which holds only for regular solutions.

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CHEE 890J.S. Parent13 Solubility Parameter The aforementioned solubility parameter is defined as: = ( E v / ) 1/2 where E v = molar change of internal energy on vapourization = molar volume of the material As defined, 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 between the materials is less than 1 (cal/cm 3 ) 1/2.

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CHEE 890J.S. Parent14 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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CHEE 890J.S. Parent15 Solubility Parameters of Select Materials

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CHEE 890J.S. Parent16 Solubility Parameters of Select Materials

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CHEE 890J.S. Parent17 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 1 = interaction parameter V p = volume of 1 mole of polymer segments i = solubility parameter of polymer i

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CHEE 890J.S. Parent18 Partial Miscibility of Polymers in Solvents Idealized representation of three generalized possibilities for the dependence of the Gibbs free energy of mixing, G m, of a binary mixture on composition (volume fraction of polymer, 2 ) 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, 2 A and 2 B, corresponding to points of common tangent to the free-energy curve.

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CHEE 890J.S. Parent19 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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CHEE 890J.S. Parent20 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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CHEE 890J.S. Parent21 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 ( H mix ) 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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CHEE 890J.S. Parent22 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: s (1+2.5 ) where is the viscosity s is the solvent viscosity and is the volume fraction of dispersed spheres.

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CHEE 890J.S. Parent23 Dilute Solution Viscosity Shown below is the intrinsic viscosity of A: Poly(isobutylene) and B: Poly(styrene) as a function of solubility parameter. When 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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CHEE 890J.S. Parent24 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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