2. Solubility and Molecular Weights

2. Solubility and Molecular Weights

Polymer Solubility 1

TitlesSolubility

◦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 chromatographySolution thermodynamics and

molecular weights


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?


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 Solubility 6.6

n

n

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 blendDGmix (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):

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 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.Polymer Solubility 6.10

The solubility parametersParameters Affecting the

Solubility:GM = HM - T SM


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.

HM Based on Solubility Parameters

Thus the heat of mixing of two substances

dependens on (1 - 2)2


Solubility parameters for common solvents


Solubility parameters for common polymers


Determining The Solubility Parameter δ


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 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.

Intrinsic ViscosityAlternatively, 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.


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


MixMixMix STHG

Entropy Of Mixing ΔS: Statistical thermodynamicsBoltzman Equation:



210

210 !.!/!

NNN

NNN

= number of possible arrangements that the molecule may assume


Sterling Approx.

Volume fraction of solvent and polymer

Mixing Enthalpy ΔH



1


212121 vkTN

H

vRTn

H

vNRTv

H MixMixMix


21vkTNHMix

Chemical Potential and Energy of Mixing


2,,1

011

nPT

Mix

n

G

2222

011 )11()1ln()( vxvvRT

)(1

2122

1212

w

wvv

12

21

M

Mx

Solvent Polymer to of Ratio VolumeMolar

FractionWeight

Fraction Volume

x

w

v

1011 ln aRT

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2. Solubility and Molecular Weights