2. Solubility and Molecular Weights

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2. Solubility and Molecular Weights. Titles. Solubility Solubility parameters Experimental determination Thermodynamics of Mixing Types of Solutions Dilute solutions Flory-Huggins parameter. Titles (contd.). Molecular Weights Average Molecular weights Number average molecular weights - PowerPoint PPT Presentation

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2. Solubility and Molecular Weights

2. Solubility and Molecular WeightsPolymer Solubility1TitlesSolubilitySolubility parametersExperimental determinationThermodynamics of MixingTypes of SolutionsDilute solutionsFlory-Huggins parameterPolymer Solubility2Titles (contd.)Molecular WeightsAverage Molecular weightsNumber average molecular weightsDetermination of number average MWWeight average MWLight scatteringIntrinsic viscosityMark-Houwink relationship

Polymer Solubility3Title (contd.)Gel permeation chromatographySolution thermodynamics and molecular weightsPolymer Solubility4How Does a Polymer Dissolve?There are two distinguishable modes of solvent diffusion into a polymer.Fickian diffusion, (T>Tg)non-Fickian phenomenon known as case II swelling, (T 0Polymer Solubility6.88Entropy of MixingConsider the two-dimensional lattice representation of a solvent (open circles) and its solute (solid circles):

smallpolymericmoleculesolutesolute

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 positive (promoting solubility), its magnitude is less for polymeric systems than for solutions of small moleculesWhen dealing with polymer solubility, the enthalpic contribution DHmix to the Gibbs energy of mixing is critical.

Polymer Solubility6.99Enthalpy of MixingDHmix can be a positive or negative quantityIf 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.

Polymer Solubility6.1010The solubility parametersParameters Affecting the Solubility:GM = HM - T SM

Polymer Solubility11

VM represents the total volume of the mixture, E represents the energyof vaporization to a gas at zero pressure (i.e., at infinite separation of themolecules), and V is the molar volume of the components, for both species 1 and 2. The quantity v represents the volume fraction of component 1 or 2 inthe mixture.A negative value of DGM indicates that the solution process will occur spontaneously.11HM Based on Solubility ParametersThus the heat of mixing of two substances dependens on (1 - 2)2 Polymer Solubility12These relationships are meaningful only for positive heats of mixing; thatis, when the heat of mixing term opposes solution. Since (d1 - d2)2 cannot benegative, equations (3.2) and (3.3) break down for negative heats of mixing.12Solubility parameters for common solventsPolymer Solubility13

Solubility parameters for common polymersPolymer Solubility14

Determining The Solubility Parameter Polymer Solubility15Theoretical CalculationsPolymer Solubility16

G = group molar attraction constant

Group molar attraction constants have been calculated by Small (11) andHoy (12). Table 3.3 (11) presents a wide range of values of G for chemical groups16Group molar attraction constantsPolymer Solubility17

Unit G= (cal-cm3)1/2/mol1 (cal/cm3)1/2 = 2.046 x 103 (J/m3)1/217Polymer Solubility18

CH2 , G = 133, -CH- , G=28, phenyl group, G = 735.The density of polystyrene is 1.05 g/cm3, and the mer molecular weight is 104 g/mol. Then:

Solubility Parameter and CrosslinkingThe 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.Polymer Solubility6.19

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Polymer Solubility20The swelling coefficient, Q, is defined by,where m is the weight of the swollen sample, m0 is the dry weight, and s is the density of the swelling agent.The effect of IPN

Polymer Solubility21Here, the swelling behavior of a cross-linked polyurethane and a crosslinkedpolystyrene are shown, together with the 50/50 interpenetratingpolymer network made from these two polymers. Both the homopolymers andthe interpenetrating polymer network exhibit single peaks, albeit that the IPN peak is somewhat broader and appears in-between its two homopolymers.Figure 3.1 The swelling coefficient, Q, reaches a maximum when the solubility parameter ofthe solvent nearly matches that of the polymer, for several cross-linked systems: polyurethane(), polystyrene (), and a polyurethanepolystyrene interpenetrating polymer networks () (9).Solvents having solubility parameters near 2 104 (J/m3)1/2 will swell the IPN best.21Intrinsic ViscosityAlternatively, the solubility parameter may be determined by measuring the intrinsic viscositySince the chain conformation is most expanded in the best solvent, the intrinsic viscosity will be highest for the best match in solubility parameter.Polymer Solubility22

Determination of the solubility parameter, using the intrinsic viscosity method ,for polyisobutene (A) and polystyrene (B). The intrinsic viscosity, [], is a measure of the individual chain size.Thermodynamics of mixingPolymer Solubility23

Entropy Of Mixing S: Statistical thermodynamicsBoltzman Equation:Polymer Solubility24

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= number of possible arrangements that the molecule may assume

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Sterling Approx.

Volume fraction of solvent and polymerMixing Enthalpy HPolymer Solubility27

Polymer Solubility28

1Polymer Solubility29

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Dilute SolutionsPolymer Solubility31Heat of mixing (Flory-Huggins parameters):

Free-energy of mixing

Partial Molar Free Energy of Mixing:

Chemical Potential and Energy of MixingPolymer Solubility32

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