1. Polymer dissolution Fractionation Gas permeation

2. Key learning outcomes
Polymer dissolution and solubility, what effects/enhances/prevents…
Good, poor and theta solvents
Solvent mixtures
Polymer fractionation (separation)
Gas and vapor permeation/permeability
What factors influence it, mechanism
How it is measured

3. Dissolution
Polymer dissolution is slow a process and occurs in two stages:
Polymer swelling
The dissolution step itself
If the polymer-solvent interactions are stronger than the polymer-polymer 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

4. 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

5. 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

6. Polymers in solution The molecule forms a globule in a poor solvent
The molecule forms an extended coil in a good solvent

7. Effect of intermolecular interactions

8. 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

9. 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

10. Hydrogen bonds

13. 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

14. Mixtures of two solvents
Polymers are soluble in solvent mixtures, but not in either solvent alone
Polymer
Solvent 1
Solvent 2
Polystyrene
Acetone
Nonane
Methylacetate
Phenol
Polyvinyli acetate
Water
Ethanol
CCl4
Polymethyl methacrylate
Propanol
Polyvinylchloride
Carbonsulfide
Nitromethane
Trichloroethylene
Polycholoroprene
Hexane

15. 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
In some cases the increase in temperature causes the polymer to precipitate from the solution

16. 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 Θ-temperature. 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.

17. Polymer dissolution
In a Θ-solvent, the polymer maintains its average end-to-end distance
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

18. Polymer solutions

19. 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

20. 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

21. Degree of solvation Examples: Polymer Solvent  polyisobutene
cyklohexane
0,5
benzene
0,3
cellulose nitrate (12,2% N)
n-butylacetate 1
propylacetate 3
ethylacetate 5
methylacetate 11
polyvinylalcohol
water 95
polystyrene
methylethylketone
0,7

22. 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:

23. 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

24. Solubility parameters

25. 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:
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

26. Predicting solubility
The Hildebrand equation relates the energy of mixing to the energies of vaporization of the pure components
Vm = volume of the mixture
v1 = volume fraction of solvent
v2 = volume fraction of polymer
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

27. Solubility parameters
Parameters are usually marked:
d1 = solubility parameter of solvent
d2 = solubility parameter of polymer

28. Solubility
In order to have a not-too-high DH value, the term 𝛿 1 − 𝛿 must be relatively small. If 𝛿 1 − 𝛿 = 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 A, B are the solubility parameters of the solvent and polymer, representing the cohesive energy densities

29. Solubility

30. Solubility

31. 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

32. Classification of solubility parameters with regard to hydrogen bonding
Ability to form hydrogen bonds in solution is low, moderate or high:
Solvent
 (J/cm3)½
Low hydrogen bonding
n-hexane 30
CCl4 36
benzene 38
chloroform 39
nitromethane 53
Solvent
 (J/cm3)½
Moderate hydrogen bonding
diethylether 31
ethylacetate 38
tetrahydrofuran 40
acetone 42
ethylene carbonate 61
dimethylformamide 51

33. Classification of solubility parameters with regard to hydrogen bonding
Solvent
 (J/cm3)½
High hydrogen bonding
2-ethylhexanol 40
n-butanol 48
isopropanol
ethanol 55
water 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

34. Polymer fractionation

35. Macromolecules
Classification can be done according to three main properties:
Molecular weight
Chemical composition
Molecular configuration and structure
Fractionation by solubility
Fractionation by chromatography
Fractionation by sedimentation
Fractionation by diffusion

36. 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)

37. Continuous polymer fractionation
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
Miscibility gap: a region for a mixture of components where the mixture exists as two or more phases
The polymer solution and theta solvent/EA aren’t miscible

38. Fractionation column (packed with glass beads)
Sol: colloidal suspension of very small particles (shorter polymer chains)
Theta solvent with shorter polymer chains
solution of the polymer (dissolved)
Theta solvent
Gel: Three-dimensional polymer network suspended in liquid
Feed solution with longer chains (the shorter ones were removed and transferred into the theta solvent – forming the sol phase)

39. Continuous polymer fractionation
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
Polymer species of lower molecular weight are preferentially removed (easier to solvate)
Upon pumping the polymer solution and theta solvent in a proper ratio, two phases are eventually formed (sol and gel), which can be separated via:
Gravity (provided the densities are sufficiently different)
Temperature:
cooling, T2<T1 ; in the case of phase separation on heating, T2>T1

40. 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

41. 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

42. AUC
Synthetic and native polymers which are soluble in water or any organic solvent, dispersions of nanoparticles
Sample mass: < 100 mg
Molar mass range: g/mol
Particle size range: nm

43. 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

44. Principle of GPC:
Polystyrene gel
Polymer molecules

45. Gas/vapor permeability

46. Importance: high or low
Application
Penetrant
Design goal
Packaging
Gas, moisture
High barrier
Additives
Plasticizers, dyes
Gas separation
Gases
Selectivity
Analytical chemistry
Ions
High selectivity
Monomer removal
Unreacted monomer
Low barrier
Polymer electrolytes
Ionic conductivity
Drug implants
Pharmaceuticals
Controlled release
Biosensors
Biomolecules

47. 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

48. 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

49. 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:
the size and physical state of the small molecule
the morphology of the polymer
the compatibility or solubility limit of the solute within the polymer matrix
the volatility of the solute
the surface- or interfacial energies of the monolayer films

50. 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

51. Gas permeability through a polymer film 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

52. 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

53. Diffusion; Fick’s law
Adsorption and desorption are much faster than diffusion, so the rate of gas permeation is determined by diffusion
Rate of diffusion/diffusion flux (J) depends on diffusion coefficient (D) and change in concentration (c) according to Fick’s law:
x is position (thickness)
At low concentrations i.e. diffusion coefficient is not dependent on concentration:
l = thickness of the film

54. Diffusion: Henry’s law
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:
Combining the two equations we get the flux through a flat membrane:
Flux: flow rate per unit area
DS is nominated permeability P

55. Permeation P0 = experimentally determined coefficient
Permeability is dependent on temperature according to the following equation:
Rate of gas permeation, G:
P0 = experimentally determined coefficient
Ep = Activation energy for gas permeation

57. Permeability
Gas permeation through a multilayer film can be estimated as follows:
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

58. Barrier properties: multilayer films
The barrier property of a multilayer film is obtained by the cumulative resistances of the different layers and outermost surfaces r1 and r2:
graphically:

59. Permeability: film thickness
Oxygen transfer (left) and water vapour transfer (right) depend on the thickness of the film:

60. 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
Unit for vapour permeability

61. Effect of temperature

62. 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:
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

63. Rate versus temperature
Permeation rates typically change 5-7% per oC

64. Determination of gas permeability coefficients

65. 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 = 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

66. Standard measurement: ISO 2556:1974
Determination of the gas transmission rate of films and thin sheets under atmospheric pressure - Manometric method
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

67. Determination of gas permeation coefficients

68. 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

69. Measurement of water vapour transmission rate in highly-permeable films
Schematic representation of the wet cup test.
© This slide is made available for non-commercial use only. Please note that permission may be required for re-use of images in which the copyright is owned by a third party.
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 , 2001

70. 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

71. 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)

72. Permeability: examples

73. Next week: Imaging of polymer morphology: AFM, SEM, TEM
Stability and degradation