Transcript 2. Solubility and Molecular Weights

2. Solubility and Molecular Weights
Polymer Solubility
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Titles

Solubility
◦ Solubility parameters
◦ Experimental determination

Thermodynamics of Mixing
◦ Types of Solutions
◦ Dilute solutions
◦ Flory-Huggins parameter
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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
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Title (contd.)
Gel permeation chromatography
 Solution thermodynamics and molecular
weights

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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?
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Solubility is different in Polymers
compared to small Molecules:
An example
When
two hydrocarbons such as dodecane and 2,4,6,8,10pentamethyldodecane 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.
n
n
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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
polymer A
mB grams
material B
DGmix < 0
+
DGmix > 0
DGmix (Joules/gram) is defined by:
DGmix = DHmix -T DSmix
where
immiscible blend
DHmix = HAB - (wAHA + wBHB)
DSmix = SAB - (wASA + wBSB)
and wA, wB are the weight fractions of each material.
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Entropy of Mixing
Consider the two-dimensional lattice representation of a solvent
(open circles) and its solute (solid circles):
small
molecule
solute
polymeric
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.
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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.
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The solubility parameters

Parameters Affecting the Solubility:
DGM = DHM - T DSM
VM represents the total
volume of the mixture, DE
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.
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DHM Based on Solubility Parameters
Thus
the heat of mixing
of two substances
dependens on
2
(1 - 2)
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Solubility parameters for common
solvents
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Solubility parameters for common
polymers
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Determining The
Solubility Parameter δ
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Theoretical Calculations
G = group molar attraction constant
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Group molar attraction constants
Unit G= (cal-cm3)1/2/mol
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—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:
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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.
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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.
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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.
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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.
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.
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Thermodynamics of mixing
DGMix  DH Mix  TDSMix
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Entropy Of Mixing ΔS: Statistical
thermodynamics

Boltzman Equation:
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 = number of possible arrangements that the molecule may assume
  N 0! / N1! N 2!.
N 0  N1  N 2
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Sterling Approx.
Volume fraction of
solvent and polymer
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Mixing Enthalpy ΔH
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1
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DH Mix
DH Mix
DH Mix



NRTv1v2 RTn1v2 kTN1v2
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DH Mix  kTN1v2
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Chemical Potential and Energy of
Mixing
1    RT ln a1
0
1

 DGMix 

1    
 n1 T , P ,n2
0
1
2
1
( 1   )  RT ln(1  v2 )  v2 (1  )  v2
x
0
1
w2 1
v2  1  v1 
 2  w2 ( 1   2 )
x

1M 2
2 M1
v  Volume Fraction
w  Weight Fraction
x  Molar Volume Ratio of Polymer toSolvent
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