Summary: Last week
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Viscous material and elastic material; viscoelastic
Flow curve
Newtonian and non-Newtonian fluid
Pseudoplastic
WLF equation
Time-temperature superposition
Mechanical models of viscoelastic behaviour
Typical stress-strain curves for polymers in solid state
Polymer dissolution
Fractionation
Gas permeation
Polymer dissolution
Dissolution
• Polymer dissolution is slow a process and occurs in two stages:
1. Polymer swelling
2. The dissolution step itself
• If the polymer-solvent interactions are stronger than the polymerpolymer attraction forces, the chain segments start to absorb
solvent molecules, increasing the volume of the polymer matrix, and
loosening out from their coiled shape
• Segments are solvated instead of aggregated
• Sometimes solvents can not dissolve polymer but cause swelling
• Partly-crystalline polymers often only dissolve at elevated
temperatures, at temperature near the melting temperature of
crystallites
Schematic representation of the dissolution
process for polymer molecules
Polymer molecules in solid state,
just after having been added to a
solvent
First step: a swollen gel in
solvent
Second step: solvated
polymer molecules dispersed
in solution
http://pslc.ws/macrog
Polymer-solvent interactions
• Chain conformation is also affected by solvent, the intermolecular
interactions between polymer chains and solvent molecules have
an associated energy of interaction which can be positive or
negative
• For a good solvent, interactions between polymer segments and
solvent molecules are energetically favorable, and will cause
polymer coils to expand
• For a poor solvent, polymer-polymer self-interactions are
preferred, and the polymer coils will contract
• The quality of the solvent depends on both the chemical
composition of the polymer and solvent molecules and the solution
temperature
Polymers in solution
The molecule forms a
globule in a poor solvent
The molecule forms an
extended coil in a good solvent
Effect of intermolecular
interactions
Effect of intermolecular interactions
• During dissolution, the intermolecular interactions between the
solvent molecules and polymer molecules are disrupted and new
bonds associate the solvent molecules with polymers
• In order for the polymer to dissolve in the solvent, the forces of
intermolecular interactions of the polymer chains must be about as
big as the intermolecular forces in the solvent. If either type of force
is much stronger than the other the dissolution is not possible:
• A polymer
• B solvent
• AB polymer-solvent
– forces AA and AB must be approximately the same as BB
Intermolecular specific interactions
• Specific interactions between neutral molecules:
– dipole-dipole
– dispersion
– inductions
– hydrogen bonding
• Systems containing ions, Coulomb forces
• Ion-dipole interactions between ions and polar molecules
Hydrogen bonds
http://www.chem.ufl.edu/~itl/4411/lectures/lec_g.html
http://www.chem.ufl.edu/~itl/4411/lectures/lec_g.html
Solvent systems (co-solvent)
• Dissolution of polymers using solvent mixtures is more complicated
• Sometimes polymer can be dissolved in a mixture where neither
solvent alone can dissolve the polymer
– Acetone does not dissolve, but swells PS since acetone
molecules associate with one another due to dipole interactions
– On the other hand PS is not dissolved in nonane (C9H20) since
the dispersion forces between PS molecules are stronger than
between nonane and PS
– A mixture of acetone and nonane can be used to dissolve PS at
room temperature since nonane molecules break up the
acetone aggregates
– Non-associated acetone molecules can dissolve PS with dipole
interactions
Mixtures of two solvents
• Polymers are soluble in solvent mixtures, but not in either solvent
alone
Polymer
Polystyrene
Polystyrene
Polystyrene
Polyvinyli acetate
Polyvinyli acetate
Polymethyl methacrylate
Polyvinylchloride
Polyvinylchloride
Polycholoroprene
Solvent 1
Acetone
Methylacetate
Phenol
Water
Ethanol
Propanol
Acetone
Nitromethane
Acetone
Solvent 2
Nonane
Nonane
Acetone
Ethanol
CCl4
Water
Carbonsulfide
Trichloroethylene
Hexane
Co-polymers & the effect of temperature
• The intermolecular interactions are less effective in co-polymers
due to more random structure than in homopolymers, thus they are
often dissolved easier
• Polymers are often dissolved easier at elevated temperatures
– Higher temperature reduces intermolecular interactions and
promotes diffusion which both enhance dissolution
– It is also known that in some cases the increase in temperature
causes the polymer to precipitate from the solution
The Concept of Θ-temperature and Θ-solvent
• At high temperatures, only repulsion forces matter. The polymer coil
swells with respect to its ideal dimensions; this phenomenon is
called the excluded volume effect. In this case, the expansion factor
of the coil, α, is larger than unity
• At low temperatures, attraction forces dominate. The polymer coil
shrinks and forms a condensed globule (the coil-globule transition).
In this case the expansion factor of the coil, α, is smaller than unity
• There should be some intermediate value of T, when the effects of
repulsion and attraction compensate each other and the coil adopts
its ideal-chain (unperturbed) size. This temperature is called the Θtemperature. The expansion factor of the coil, α, is unity
• When the coil adopts its ideal-chain (unperturbed) size in solution,
the solvent is a Θ-solvent.
Polymer dissolution
• Macromolecule in poor, ideal (Θ-), and good solvent.
The molecule forms a
globule in a poor
solvent
Globule to extended coil transition
Ideal solvent (-solvent)
Extended coil in a good solvent
T > Θ, α >1
Polymer solutions
Polymer solubility
• Not all polymers can be dissolved
• The dissolution of polymers depends on their physical properties,
but also on the chemical structure:
• Polarity, molecular weight, branching, crystallinity
• Degree of crosslinking
• The general principle that states like dissolves like is also
appropriate in the case of polymers
• Polar macromolecules such as poly(acrylic acid), poly(acrylamide)
and poly(vinyl alcohol) are soluble in water
• Nonpolar polymers or polymer showing a low polarity such as PS,
PMMA and PVC are soluble in non-polar solvents
• Cross-linked polymers do not dissolve, but usually swell in the
presence of solvent
Degree of solvation
• Solvation is the interaction of a solute with the solvent, which leads
to stabilization of the solute species in the solution
• Degree of solvation (b) is the number of solvent molecules that
attach to a polymer chain
• Degree of solvation varies greatly:
– The smaller it is less the interaction between the solvent
molecules and the polymer
– As the degree of solvation increases the polymer and solvent
molecules aggregate which causes the viscosity to increase
• For technical applications, the best solvent is often one allowing a
high concentration without great increase in solution viscosity
Degree of solvation
• Examples:
Polymer
polyisobutene
polyisobutene
cellulose nitrate (12,2% N)
cellulose nitrate (12,2% N)
cellulose nitrate (12,2% N)
cellulose nitrate (12,2% N)
polyvinylalcohol
polystyrene
polystyrene
Solvent
cyklohexane
benzene
n-butylacetate
propylacetate
ethylacetate
methylacetate
water
benzene
methylethylketone
b
0,5
0,3
1
3
5
11
95
3
0,7
Estimation of interactions
• Interaction between the polymer and solvent can be described with
some other parameters in addition to the degree of solvation
• An Increase in intrinsic viscosity and increase in exponent a in the
Mark-Houwink equation shows increased interaction between
polymer and solvent:
  
a
Km M v
Polymer association in solution
• Polymers can form aggregates in solution the same way as solvent
molecules. The tendency of polymer molecules to associate
depends on the following parameters:
– Polar groups or groups prone to hydrogen bonding in the
molecule (for example C=O, -C-N, and S=O or OH, -COOH, NH2)
– Steric location of these groups (shielded or not)
– Stereospecific structure of the polymer
– Nature of the solvent
– Increase in temperature lowers association
– Increase in concentration increases association in solution
Solubility parameters
Thermodynamic considerations for polymer
solubility
• When a pure polymer is mixed with a pure solvent at a given
temperature and pressure, the free energy of mixing (DG) will be
given by:
DG  DH  TDS
• Dissolution will only take place if DG sign is negative
• Change in entropy (DS) is usually positive, since in solution, the
molecules display a more chaotic arrangement than in the solid
state and the absolute temperature must also be positive
• Enthalpy of mixing (DH) may be either positive or negative
Predicting solubility
• The Hildebrand equation relates the energy of mixing to the
energies of vaporization of the pure components
 DE 
1

DH  Vm 
 V1 
Vm = volume of the mixture
v1 = volume fraction of solvent
v2 = volume fraction of polymer
½
 DE 2 


 V2 
½ 2

 v1v 2

DE1 = energy of vaporization for solvent per mole
DE2 = energy of vaporization for polymer per mole
V1 = molar volume of solvent
V2 = molar volume of polymer
DE1/V1 = cohesive energy density of solvent
DE2/V2 = cohesive energy density of polymer
Solubility parameters
• Parameters are usually marked:
 DE1 


 V1 
½
 d1
 DE 2 


 V2 
½
 d2
 DH  Vmv1v2 d1  d 2 
d1
d2
= solubility parameter of solvent
= solubility parameter of polymer
2
Solubility
DG  DH  TDS
DH  Vm v1v2 d1  d 2 
2
• In order to have a not-too-high DH value, the term 𝛿1 − 𝛿2 2 must
be relatively small. If 𝛿1 − 𝛿2 2 = 0, dissolution depends only on the
entropy of mixing
• Miscibility can be estimated by using solubility parameters, which
are tabulated for many different polymers and solvents
• For most (non-polar) solvents, the enthalpic contribution to the
parameter can be written where dA, dB are the solubility parameters
of the solvent and polymer, representing the cohesive energy
densities
Solubility
Solubility
Effect of hydrogen bonding on solubility
parameters
• If polymer or solvent is polar or has a strong tendency to hydrogen
bond, the interaction parameter alone is not sufficient for estimating
the suitability of the solvent
• Solvents are divided in three groups according to their tendency for
hydrogen bonding - low, moderate and high:
– High hydrogen bonding:
• Organic acids, alcohols, amines and amides
– Moderate hydrogen bonding:
• Ethers, esters and ketones
– Low hydrogen bonding:
• Carbohydrates and chlorinated carbohydrates
Classification of solubility parameters with
regard to hydrogen bonding
• Ability to form hydrogen bonds in solution is low, moderate or high:
Solvent
Low hydrogen bonding
n-hexane
CCl4
benzene
chloroform
nitromethane
d
(J/cm3)½
30
36
38
39
53
Solvent
Moderate hydrogen bonding
diethylether
ethylacetate
tetrahydrofuran
acetone
ethylene carbonate
dimethylformamide
d
(J/cm3)½
31
38
40
42
61
51
Classification of solubility parameters with
regard to hydrogen bonding
Solvent
High hydrogen bonding
2-ethylhexanol
n-butanol
isopropanol
ethanol
water
d
(J/cm3)½
40
48
48
55
98
Solubility parameters have been determined for a number of solvents and
polymers; Polymer Handbook (Ed. J. Brandrup ja E.H. Immergut) lists the
values of ~800 substances
Polymer fractionation
Macromolecules
• Classification can be done according to three main properties:
– Molecular weight
– Chemical composition
– Molecular configuration and structure
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•
Fractionation by solubility
Fractionation by chromatography
Fractionation by sedimentation
Fractionation by diffusion
Most common methods to separate polymer
fractions are:
– Precipitation from solution by adding solvent that does not
dissolve polymer; the largest molecules precipitate first
– Solvent evaporation
– Precipitation by cooling/freezing; the largest molecules
precipitate first (not applicable for all polymers)
– Solvent extraction/leaching: using solvent/s with limited
dissolving power. The smallest molecules dissolve first and are
removed
– Elution
– Chromatography
– Fractionation with two immiscible solvents
– Ultracentrifuge
– Dialysis
– GPC (SEC)
Continuous polymer fractionation
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A homogeneous solution of the polymer is used as feed (FD)
and the pure theta solvent as extracting agent (EA)
The flow rates of these two liquids are chosen in such a
manner that the total composition of the mixture within the
apparatus corresponds to a point inside the miscibility gap
The two phases formed in the column coexist throughout the
process, and the polymer originally contained in the feed
spreads into the phase originating from the extracting agent
During this process the polymer species of lower molecular
weight are preferentially removed from the feed
Upon pumping the polymer solution and solvent in a proper
ratio, two phases are formed and - if their densities differ
sufficiently - transported through the column by gravity so that
they can be collected as gel (GL) and as sol (SL) at the
opposite ends of the apparatus
For systems which phase separate on cooling, T2<T1 ; in the
case of phase separation on heating, T2>T1
http://wolf.chemie.uni-mainz.de
column packed with glass
beads
Dialysis
• Dialysis is a simple process in which small solutes diffuse from a
high concentration solution to a low concentration solution across a
semi-permeable membrane until equilibrium is reached
• A porous membrane selectively allows smaller solutes to pass while
retaining larger species
http://www.spectrumlabs.com
Analytical ultracentrifugation (AUC)
• Can be used for the characterization of polymers, biopolymers,
polyelectrolytes, nanoparticles, dispersions, and other colloidal
systems
• Can be used to determine:
– the molar mass, the particle size, the particle density and
interaction parameters like virial coefficients and association
constants
– determination of the molar mass distribution, the particle size
distribution and the particle density distribution is also possible
• The density gradient method allows fractionating heterogeneous
samples according to their chemical nature
Analytical ultracentrifugation of polymers and nanoparticles by W. Mächtle and L.Börger, 2006
AUC
• Synthetic and native polymers which are soluble in water or any
organic solvent, dispersions of nanoparticles
• Sample mass: < 100 mg
• Molar mass range: 103 - 1014 g/mol
• Particle size range: 1 - 500 nm
Gel permeation cromatography (GPC )
Most widely used method for routine determination of molecular
weight and molecular weight distribution is GPC, separating samples
of polydisperse polymers into fractions of narrower molecular weight
distribution
www.waters.com
GPC measurement
• Columns are packed with small, highly porous beads. Pore
diameters of the beads range from 10 to 107 Å, which approximate
the dimensions of polymer molecules in solution
• During GPC operation, pure pre-filtered solvent is continuously
pumped through the columns at a constant flow rate. Then a small
amount of dilute polymer solution is injected into the solvent stream
and carried to through the columns
• Polymer molecules diffuse from this mobile phase into the
stationary phase in the pores. The smallest polymer molecules
penetrate deeply into the pores whereas the largest molecules pass
through the columns first
GPC
• The concentration of polymer molecules in each eluting fraction is
monitored by a detector, such as IR
• The elution volumes are calibrated with know Mn standards (PS
standards most common)
• Only apparent molecular weights are determined unless molecular
weight standards exist of the same composition and topology as the
samples, LALLS or viscometry is used, or the Mark–Houwink
parameters of standards and sample are known
Principle of GPC:
Polystyrene
Polystyreenigeeli gel
Polymeerimolekyyli
Polymer molecules
GPC
• GPC-SEC is the most widely used technique for the analysis of
polymers
• Can be used for samples soluble in organic and aqueous eluents
and molecular weights from approximately 100 to several million
• If aqueous eluents are used, porous beads or gels can be dextran,
agar, gelatin, polyvinylpyrrolidone, and polyacrylamide in place of
PS gel
Gas/vapor permeability
Importance
Application
Penetrant
Design goal
Packaging
Gas, moisture
High barrier
Additives
Plasticizers, dyes
High barrier
Gas separation
Gases
Selectivity
Analytical chemistry
Ions
High selectivity
Monomer removal
Unreacted monomer
Low barrier
Polymer electrolytes
Ions
Ionic conductivity
Drug implants
Pharmaceuticals
Controlled release
Biosensors
Biomolecules
High selectivity
Gas and vapor permeability
• Permeability of plastics and rubbers is a very important property in
many products, such packaging materials, containers, pipes, tyres,
insulation and coating
• In packaging with polymer materials, water vapour, oxygen, carbon
dioxide, flavour and aroma compounds, additives, and low
molecular weight residual moieties may transfer from either the
internal or external environment through the polymer package wall
• Thin films or coatings may have small holes or pores that let
gas/vapour pass through almost directly
• Non-porous polymer membranes also permeate gases
• Gas will permeate between polymer molecules and diffuse through
the membrane
Mechanisms of transport
• Permeability:
– The amount of a gas/vapour passing through a polymer
membrane of a unit thickness, per unit area, per second, and at
a unit pressure difference
• Modes of transport that can occur are:
– Size exclusion in porous membranes
– Solution-diffusion in non-porous or dense membranes
• Permeability of polymers by penetrant can be explained on the
basis of their solubility and diffusivity, and the structure of the
polymer matrix
Permeation in polymers
• The diffusion of small molecules into polymers is a function of both
the polymer and the molecule diffusing
• Factors which influence diffusion include:
a) the size and physical state of the small molecule
b) the morphology of the polymer
c) the compatibility or solubility limit of the solute within the
polymer matrix
d) the volatility of the solute
e) the surface- or interfacial energies of the monolayer films
Different parameters affecting the permeability
• Enhancing permeation:
– Physical form
• liquids permeate slightly better than saturated vapour
– Plasticizers enhance permeation
• Slowing down/hindering permeation:
– The higher the density of the polymer
– Higher crystallinity since the dissolution and diffusion of gas
occurs in the amorphous regions
– Higher orientation
– Fillers
– Crosslinking
• The size of the polymer molecule has very little effect unless the
macromolecules are relatively small
Gas permeability through a polymer is affected
by:
• Properties of the membrane
– polymer properties
– thickness
– surface area
• Properties of the gas/vapor
• Pressure drop on different sides of the membrane
– Driving force for transport
• Temperature
• Time
Gas permeation
• At higher pressure, the molecules adsorb on the polymer surface. In
the second stage, gas diffuses to the lower pressure; in the third
stage the gas molecules desorb from the surface:
1. Adsorption onto polymer surface
2. Diffusion through bulk polymer
3. Desorption into external phase
Diffusion
• Adsorption and desorption are much faster than diffusion, so the
rate of gas permeation is determined by diffusion
• Rate of diffusion depends on diffusion coefficient (D) and change in
concentration according to Fick’s law:
dc
J  D
dx
• At low concentrations i.e. diffusion coefficient is not dependent on
concentration:
l = thickness of the film
Dc
J  D
l
Diffusion
• The dissolution of gas is based on Henry’s law of solubility, where
the concentration of the gas in the membrane is directly proportional
to the applied gas pressure
• Difference in gas concentration c on the different sides of the
membrane is dependent on the difference in pressure and solubility
coefficient S:
Dc  SDp
• Combining the two equations we get the flux through a flat
membrane:
Dp
Dp
J  DS
P
l
l
DS is nominated permeability P
Permeation
• Permeability is dependent on temperature according to the
following equation:
P  P0 e
 Ep 


 RT 
P0 = experimentally determined coefficient
Ep = Activation energy for gas permeation
• Rate of gas permeation, G:
P
G
l
Permeability
• Gas permeation through a multilayer film can be estimated as
follows:
l1
l2
ln
1
l
 


G P P1 P2
Pn
P = gas permeability through the multilayer laminate
l = total thickness of the laminate
l1 – ln = thicknesses of the layers
P1 – Pn = gas permeabilities for different layers
Barrier property
• The barrier property of a multilayer film is obtained by the
cumulative resistances of the different layers and outermost
surfaces r1 and r2:
n
li
1
 r1  r2  
G
i 1 Pi
graphically:
Permeability
• Oxygen transfer (left) and water vapour transfer (right) depend on
the thickness of the film:
Units for permeability
• For some polymer membranes, the relative humidity has more
effect on the rate of permeation than the pressure difference
• For example PA is very sensitive to humidity
• Several different units are used for gas transmission
• The SI unit for diffusion coefficients is m2/s
• When gas solubility coefficient is expressed in m3/ (m3 Pa) and
vapour kg/ (m3 Pa) the following units are obtained:
Unit for gas permeability
m2  m3
m2
m4


3
s  m  Pa s  Pa s  N
Unit for vapour permeability
m2  kg
kg
m  kg


3
s N
s  m  Pa s  m  Pa
Effect of temperature
Effect of temperature on permeability
• Increasing in temperature enhances gas flow through polymer
• The different coefficients depend on the temperature according to
the following equations:
P  P0 e
 E p / RT 
S  S0 e 
 H S RT 
D  D0 e 
 E D RT 
E p  E D  HS
Ep = activation energy for gas permeation (kJ/mol)
ED = activation energy for diffusion (kJ/mol)
HS = molar enthalpy of solvation (kJ/mol)
P0, D0 and S0 = coefficients
T = absolute temperature
Rate versus temperature
• Permeation rates typically change 5-7% per oC
Determination of gas permeability
coefficients
Determination of gas permeability coefficients
• Gas permeation coefficients are determined by measuring the flow
through the membrane for a fixed time whilst there is a pressure
difference across the membrane
• Equation for calculation:
Q
PtA p1  p2 
l
Q = gas flux through membrane
P = gas permeability coefficients
t = time
A = surface area of the membrane
p1 and p2 = gas pressure on different sides of the membrane
1 = thickness of the membrane
Standard measurements
• Plastics - Determination of the gas transmission rate of films and
thin sheets under atmospheric pressure - Manometric method ISO
2556:1974
– The plastic test specimen separates two chambers; one
contains the test gas at atmospheric pressure, the other of
known initial volume has the air pumped out until the pressure is
practically zero
– The quantity of gas which passes through the specimen from
one chamber to the other is determined as a function of time by
measuring the increase in pressure occurring in the second
chamber by means of a manometer
Determination of gas permeation coefficients
http://www.idspackaging.com
Standard measurements water vapour
transmission rate (WVTR)
• Rigid cellular plastics - Determination of water vapour transmission
properties ISO 1663:2007
• Specifies a method of determining the water vapour transmission
rate, water vapour permeance, water vapour permeability and water
vapour diffusion resistance index for rigid cellular plastics
• Permeability – the ability of a permeate to penetrate a solid
• Permeance – the degree to which a material allows flow of matter
through it
Measurement of water vapour transmission rate
in highly-permeable films
• In this method, the test film covers a Petri dish filled with distilled
water
• The mass of water lost from the dish is monitored as a function of
time, and the WVTR is calculated from the steady-state region
Journal of Applied Polymer Science
Volume 81, Issue 7, pages 1624-1633, 2001
Oxygen transmission rate (OTR)
• OTR is the steady-state rate at which oxygen gas permeates
through a film at specified conditions of temperature and relative
humidity
• Values are expressed in cc/100 in2/24 hr in US standard units and
cc/m2/24 hr in metric units
• Standard test conditions are 23°C (73°F) and 0% RH
Oxygen transmission coefficient of various
polymers
1) 25deg C
(Kobunshi to Mizu)
2) 30deg C (Polymer
handbook)
3) 23deg C (Polymer
handbook)
4) 20deg C (Nippon
Gohsei
measurement)
Unnumbered: 25deg C (Polymer handbook)
Permeability: examples
Next week:
• Imaging of polymer morphology: AFM, SEM, TEM
• Stability and degradation