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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
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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 • Determination of number average MW • Weight average MW • Light scattering • Intrinsic viscosity • Mark-Houwink relationship
Title (contd.) • Gel permeation chromatography • Solution thermodynamics and molecular weights
How 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<Tg) T is important . Why? What does swelling mean?
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.
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 mA grams mB grams polymer A material B + immiscible blend DGmix (Joules/gram) is defined by: DGmix = DHmix -T DSmix where DHmix = HAB - (wAHA + wBHB) DSmix = SAB - (wASA + wBSB) and wA, wB are the weight fractions of each material. DGmix < 0 DGmix > 0
Entropy of Mixing Consider the two-dimensional lattice representation of a solvent (open circles) and its 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 positive (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.
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.
The solubility parameters • Parameters Affecting the Solubility: GM = HM - T SM VMrepresents the total volume of the mixture, Erepresents the energy of vaporization to a gas at zero pressure (i.e., at infinite separation of the molecules), and Vis the molar volume of the components, for both species 1 and 2. The quantity vrepresents the volume fraction of component 1 or 2 in the mixture.
HM Based on Solubility Parameters • Thus the heat of mixing of two substances dependens on (1 - 2)2
Theoretical Calculations G = group molar attraction constant
Group molar attraction constants Unit G= (cal-cm3)1/2/mol
—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.
The 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 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 mostexpanded in the best solvent, the intrinsic viscosity will be highest for the best match in solubility parameter. 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.
Entropy Of Mixing ΔS: Statistical thermodynamics • Boltzman Equation:
= number of possible arrangements that the molecule may assume
Sterling Approx. Volume fraction of solvent and polymer
