Summary: Last week Viscous material and elastic material; viscoelastic Flow curve Newtonian and non-Newtonian fluid Pseudoplastic WLF equation Time-temperature.

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Presentation on theme: "Summary: Last week Viscous material and elastic material; viscoelastic Flow curve Newtonian and non-Newtonian fluid Pseudoplastic WLF equation Time-temperature."— Presentation transcript:

1 Summary: Last week 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

2 Polymer dissolution Fractionation Gas permeation

3 Polymer dissolution

4 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 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

5 Schematic representation of the dissolution process for polymer molecules First step: a swollen gel in solvent Polymer molecules in solid state, just after having been added to a solvent Second step: solvated polymer molecules dispersed in solution http://pslc.ws/macrog

6 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

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

8 Effect of intermolecular interactions

9 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

10 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

11 Hydrogen bonds

12 http://www.chem.ufl.edu/~itl/4411/lectures/lec_g.html

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14 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 (C 9 H 20 ) 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

15 Mixtures of two solvents Polymers are soluble in solvent mixtures, but not in either solvent alone PolymerSolvent 1Solvent 2 PolystyreneAcetoneNonane PolystyreneMethylacetateNonane PolystyrenePhenolAcetone Polyvinyli acetateWaterEthanol Polyvinyli acetateEthanolCCl 4 Polymethyl methacrylatePropanolWater PolyvinylchlorideAcetoneCarbonsulfide PolyvinylchlorideNitromethaneTrichloroethylene PolycholoropreneAcetoneHexane

16 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

17 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.

18 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

19 Polymer solutions

20 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

21 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 (  ) 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

22 Degree of solvation Examples: PolymerSolvent  polyisobutenecyklohexane0,5 polyisobutenebenzene0,3 cellulose nitrate (12,2% N)n-butylacetate1 cellulose nitrate (12,2% N)propylacetate3 cellulose nitrate (12,2% N)ethylacetate5 cellulose nitrate (12,2% N)methylacetate11 polyvinylalcoholwater95 polystyrenebenzene3 polystyrenemethylethylketone0,7

23 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:

24 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, - NH 2 ) –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

25 Solubility parameters

26 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 (  G) will be given by: Dissolution will only take place if  G sign is negative Change in entropy (  S) 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 (  H) may be either positive or negative

27 Predicting solubility The Hildebrand equation relates the energy of mixing to the energies of vaporization of the pure components  E 1 = energy of vaporization for solvent per mole  E 2 = energy of vaporization for polymer per mole V 1 = molar volume of solvent V 2 = molar volume of polymer  E 1 /V 1 = cohesive energy density of solvent  E 2 /V 2 = cohesive energy density of polymer V m = volume of the mixture v 1 = volume fraction of solvent v 2 = volume fraction of polymer

28 Solubility parameters Parameters are usually marked:  1 = solubility parameter of solvent  2 = solubility parameter of polymer

29 Solubility

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32 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

33 Classification of solubility parameters with regard to hydrogen bonding Ability to form hydrogen bonds in solution is low, moderate or high: Solvent  (J/cm 3 ) ½ Moderate hydrogen bonding diethylether31 ethylacetate38 tetrahydrofuran40 acetone42 ethylene carbonate61 dimethylformamide51 Solvent  (J/cm 3 ) ½ Low hydrogen bonding n-hexane30 CCl 4 36 benzene38 chloroform39 nitromethane53

34 Classification of solubility parameters with regard to hydrogen bonding 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 Solvent  (J/cm 3 ) ½ High hydrogen bonding 2-ethylhexanol40 n-butanol48 isopropanol48 ethanol55 water98

35 Polymer fractionation

36 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

37 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)

38 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 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, T 2 T 1 http://wolf.chemie.uni-mainz.de column packed with glass beads

39 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

40 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

41 AUC Synthetic and native polymers which are soluble in water or any organic solvent, dispersions of nanoparticles Sample mass: < 100 mg Molar mass range: 10 3 - 10 14 g/mol Particle size range: 1 - 500 nm

42 Gel permeation cromatography (GPC ) www.waters.com 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

43 GPC measurement Columns are packed with small, highly porous beads. Pore diameters of the beads range from 10 to 10 7 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

44 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 M n 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

45 Principle of GPC: Polystyrene gel Polymer molecules

46 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

47 Gas/vapor permeability

48 Importance ApplicationPenetrantDesign goal PackagingGas, moistureHigh barrier AdditivesPlasticizers, dyesHigh barrier Gas separationGasesSelectivity Analytical chemistryIonsHigh selectivity Monomer removalUnreacted monomerLow barrier Polymer electrolytesIonsIonic conductivity Drug implantsPharmaceuticalsControlled release BiosensorsBiomoleculesHigh selectivity

49 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

50 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

51 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

52 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 Different parameters affecting the permeability

53 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

54 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

55 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: At low concentrations i.e. diffusion coefficient is not dependent on concentration: l = thickness of the film

56 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: Combining the two equations we get the flux through a flat membrane: DS is nominated permeability P

57 Permeation Permeability is dependent on temperature according to the following equation: Rate of gas permeation, G: P 0 = experimentally determined coefficient E p = Activation energy for gas permeation

58 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 l 1 – l n = thicknesses of the layers P 1 – P n = gas permeabilities for different layers

59 Barrier property The barrier property of a multilayer film is obtained by the cumulative resistances of the different layers and outermost surfaces r 1 and r 2 : graphically:

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

61 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 m 2 /s When gas solubility coefficient is expressed in m 3 / (m 3 Pa) and vapour kg/ (m 3 Pa) the following units are obtained: Unit for gas permeabilityUnit for vapour permeability

62 Effect of temperature

63 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: E p = activation energy for gas permeation (kJ/mol) E D = activation energy for diffusion (kJ/mol) H S = molar enthalpy of solvation (kJ/mol) P 0, D 0 and S 0 = coefficients T = absolute temperature

64 Rate versus temperature Permeation rates typically change 5-7% per o C

65 Determination of gas permeability coefficients

66 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 p 1 and p 2 = gas pressure on different sides of the membrane 1 = thickness of the membrane

67 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

68 Determination of gas permeation coefficients http://www.idspackaging.com

69 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

70 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 Volume 81, Issue 7,

71 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 in 2 /24 hr in US standard units and cc/m 2 /24 hr in metric units Standard test conditions are 23°C (73°F) and 0% RH

72 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)

73 Permeability: examples

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


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