2. Solubility and Molecular Weights Polymer Solubility1

Titles Solubility ◦ Solubility parameters ◦ Experimental determination Thermodynamics of Mixing ◦ Types of Solutions ◦ Dilute solutions ◦ Flory-Huggins parameter Polymer Solubility2

Titles (contd.) Molecular Weights ◦ Average Molecular weights ◦ Number average molecular weights ◦ Determination of number average MW ◦ Weight average MW ◦ Light scattering Intrinsic viscosity ◦ Mark-Houwink relationship Polymer Solubility3

Title (contd.) Gel permeation chromatography Solution thermodynamics and molecular weights Polymer Solubility4

How Does a Polymer Dissolve? There are two distinguishable modes of solvent diffusion into a polymer. 1.Fickian diffusion, (T>Tg) 2.non-Fickian phenomenon known as case II swelling, (T<Tg) T is important. Why? What does swelling mean? Polymer Solubility5

Solubility is different in Polymers compared to small Molecules: An example 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. Polymer Solubility6.6

Industrial Relevance of Polymer Solubility Polymer Solubility6.7

Mixing Or Not? 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 grams m B grams polymer A material B + immiscible blend  G mix (Joules/gram) is defined by:  G mix =  H mix -T  S mix where  H mix = H AB - (w A H A + w B H B )  S mix = S AB - (w A S A + w B S B ) and w A, w B are the weight fractions of each material.  G mix < 0  G mix > 0 Polymer Solubility6.8

Entropy of Mixing Consider the two-dimensional lattice representation of a solvent (open circles) and its 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 positive (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. Polymer Solubility6.9

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. Polymer Solubility6.10

The solubility parameters Parameters Affecting the Solubility:  G M =  H M - T  S M Polymer Solubility11 V M represents the total volume of the mixture,  E represents the energy of vaporization to a gas at zero pressure (i.e., at infinite separation of the molecules), 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 in the mixture.

 H M Based on Solubility Parameters Thus the heat of mixing of two substances dependens on (  1 -  2 ) 2 Polymer Solubility12

Solubility parameters for common solvents Polymer Solubility13

Solubility parameters for common polymers Polymer Solubility14

Determining The Solubility Parameter δ Polymer Solubility15

Theoretical Calculations Polymer Solubility16 G = group molar attraction constant

Group molar attraction constants Polymer Solubility17 Unit G= (cal-cm 3 ) 1/2 /mol

Polymer 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 Crosslinking 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. Polymer Solubility6.19

Polymer Solubility20 The swelling coefficient, Q, is defined by, where m is the weight of the swollen sample, m 0 is the dry weight, and  s is the density of the swelling agent.

The effect of IPN Polymer Solubility21 Here, the swelling behavior of a cross-linked polyurethane and a crosslinked polystyrene are shown, together with the 50/50 interpenetrating polymer network made from these two polymers. Both the homopolymers and the interpenetrating polymer network exhibit single peaks, albeit that the IPN peak is somewhat broader and appears in-between its two homopolymers.

Intrinsic Viscosity Alternatively, the solubility parameter may be determined by measuring the intrinsic viscosity Since 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 mixing Polymer Solubility23

Entropy Of Mixing ΔS : Statistical thermodynamics Boltzman Equation: Polymer Solubility24

Polymer Solubility25  = number of possible arrangements that the molecule may assume

Polymer Solubility26 Sterling Approx. Volume fraction of solvent and polymer

Mixing Enthalpy ΔH Polymer Solubility27

Polymer Solubility28 1

Polymer Solubility29

Polymer Solubility30

Dilute Solutions Polymer Solubility31 Heat of mixing (Flory- Huggins parameters): Free-energy of mixing Partial Molar Free Energy of Mixing:

Chemical Potential and Energy of Mixing Polymer Solubility32