Weeks1-2

Why Study Polymer Science and Processing?

Employment Opportunities:135,000,000 tons of plastics alone are produced annuallyan estimated one in three research dollars in North America isan estimated one in three research dollars in North America is invested in polymer science.

Scientific Interest:Scientific Interest:structure-property relationships of polymers and polymer compoundsh i l difi ti f l f d d li tichemical modification of polymers for advanced applications

polymer blending and compatiblization techniques

Engineering Design Challenges:life-cycle analysesy ypolymer compound developmentdesign/optimization of polymer processing methodologiespolymer synthesis

Introduction CHEE 490 1.1

polymer synthesis

U.S. Polymer Production (billions of pounds)

1993 1992 PLASTICSThermosetting Resins

1993 1992 FIBERSCellulosics

Phenol resins 3.08 2.92 Urea resins 1.74 1.55 Polyesters (unsaturated) 1.26 1.18 Epoxies 0 51 0 46

Rayon 0.28 0.28 Acetate 0.23 0.22

NoncellulosicsEpoxies 0.51 0.46 Melamine resins 0.27 0.23

Thermoplastic Resins

NoncellulosicsPolyester 3.56 3.58 Nylon 2.66 2.56 Olefin 2.14 2.00

Low-density polyethylene 12.04 11.92 PVC and copolymers 10.26 9.99 High-density polyethylene 9.91 9.81 Polystyrene 5 37 5 10

Acrylic 0.43 0.44 Total 9.30 9.07

SYNTHETIC RUBBERPolystyrene 5.37 5.10Polypropylene 8.61 8.42

Total 53.06 51.57

SYNTHETIC RUBBER Styrene-butadiene rubber 1.89 1.92 Polybutadiene 1.03 1.02 Ethylene-propylene rubber 0.58 0.58

Chemical and Engineering News April 11 1994

Nitrile rubber (NBR) 0.14 0.13 Other 1.37 1.42 Total 5.00 5.07


Chemical and Engineering News, April 11, 1994. TOTAL PRODUCTION 67.35 65.71

Polymer Science and Processing Technology

Successful product design requires a knowledge of:the requirements of the final productthe behaviour of polymeric materialsthe behaviour of polymeric materialscommercial polymer processing technologyrelevant cost and market factors.

At the heart of polymer science andtechnology is molecular structure. It gydictates not only final product properties,but polymer synthesis and processingmethods.


methods.

Classification of Polymer Applications

1. Elastomersstatic uses: gaskets, hosesdynamic uses: tires sports equipmentdynamic uses: tires, sports equipment

2. Adhesivesstructural: epoxy resinsstructural: epoxy resinsnon-structural: pressure-sensitive tapes, hot-melt adhesives

3 C ti3. Coatingslacquers, paints

4. Plasticssemi-crystalline: automobile exterioramorphous: packaging films, plexi-glassp p g g p g

5. Fibresnatural/modified: cotton, rayon


natural/modified: cotton, rayonsynthetic: carpeting, apparel

Emphasis of Course Material (Weeks 1-6)

Each of the five applications will be examined from the following perspectives:

Industrial requirements for end-use and processingIndustrial requirements for end use and processing»Basic testing methods

Polymer compound formulationsPolymer compound formulations»essential polymer properties»compound additives

Relevant engineering science»Elastomers: origin of elasticity, crosslinking, reinforcement»Adhesives: surface energy»Coatings: viscosity»Plastics: mechanical properties, polymer composites p p p y p»Fibres: crystallization


Emphasis of Course Material (Weeks 7-12)

Each of the five applications will be examined from the following perspectives:

Industrial polymer processing techniquesIndustrial polymer processing techniques»extrusion» injection molding» fibre spinning» fibre spinning»compression molding»polymer/additive blending

Key processing variables»polymer compound rheology» fluid mechanics

Assessment of processing variablesp g


Design Project

Develop a polymer compound and processing method for a component of your choice.

1. Define engineering and aesthetic qualities.

2 Propose a compounding recipe that will satisfy these2. Propose a compounding recipe that will satisfy theserequirements.

3 R d i t i t h i f3. Recommend appropriate processing techniques formanufacturing the product.

Examples?Contact lens, medical catheter, biodegradable packaging,artificial joint, high-performance tire tread...j g p


Physical Properties of Polymer Compounds

The materials selection component of a part design demands careful consideration of all required properties. Consider the following case studies:following case studies:

electric drill casingautomobile bumperaircraft tireaircraft tire

What properties must a given material provide for each of these components?

As engineers, you must be able to translate qualitative terms (strong, flexible) into engineering terms for which quantitative data is available.

We will survey various physical testing methods that are used industrially, and highlight important behavioural y g g pcharacteristics of polymersThroughout the course we will refer to these testing methods as we examine adhesive, elastomer, plastic, fiber and

Polymer Properties CHEE 490 1.8

as we examine adhesive, elastomer, plastic, fiber and coatings applications.

Polymer Material Selection - Key Questions

When developing a polymer compound for a given application, you may ask yourself the following questions:

What are the maximum and minimum temperatures the compound will experience throughout its lifetime?

» includes manufacturing as well as product use» includes manufacturing as well as product use

To what loads will the material be subjected, and what is the f f l d li ti ?frequency of load application?

»engine mounts, fishing line

Is the part transparent, translucent or opaque? Colouring?

Is flame resistance necessary, and to what environmental yconditions will the product be exposed?

»solvent resistance, oxidative degradation


Static Testing of Polymers and Polymer Compounds

Stress-strain analysis is the most widely used mechanical test. However, it is only a rough guide as to how a material will behave in a given applicationbehave in a given application.

Test specimens are prepared in the form of “dog bones” whose dimensions are known accurately:dimensions are known accurately:

A static test involves deformation of the sample at a steady rate, usually with one end fixed and the other pulled at a constant rate of elongation (tensile testing). The retractive force of the material is recorded as a function of the elongation, and the engineering g g gstress, σ, is calculated as a function of the engineering strain, ε.

Pa:AF

=σL

LΔ=ε


Ao oL


We will soon see that observed polymer properties are strongly dependent on temperature and the applied rate of deformation.

Under some conditions an elastomer can behave like a brittleUnder some conditions, an elastomer can behave like a brittle plastic, and vice-versa.

Three typical behaviours are

A

Three typical behaviours areillustrated here.

A

Often cited sample properties:

B

AA: Ultimate tensile stress (Pa)

and elongation at break (%)B Yield tensile stress Pa

A

B: Yield tensile stress, Pa

Toughness: Area under σ − εcurve


curve.

Compression and Shear vs. Tensile Tests

Stress-strain curves are very dependent on the test method. A modulus determined under compression is generally higher than one derived from a tensile experiment as shown below forone derived from a tensile experiment, as shown below for polystyrene.

Tensile testing is most sensitiveTensile testing is most sensitiveto material flaws and microscopiccracks.

Compression tests tend tobe characteristic of the polymer,while tension tests are morecharacteristic of sample flaws.

Note also that flexural and sheartest modes are commonlyemployed.


employed.


Shown is a representative stress-strain curve for a polymer undergoingpolymer undergoing brittle failure.

An often quoted materialAn often quoted materialproperty is the tensile (or Young’s) modulus, E:

which relates strain to retractive

ε=σ E

stress over the linear region.

E (Pa)Copper 1.2*1011

Polystyrene 3.0*109


Polystyrene 3.0 10Soft Rubber 2.0*106

Mechanical Properties of Representative Polymers

Elastic Yield Ultimate ElongationModulus Strength Strength to Break(GPa) (MPa) (MPa) (%)( ) ( ) ( ) (%)

Poly(propylene) 1.0-1.6 23 24-38 200-600

Poly(styrene) 2 8-3 5 --- 38-55 1-2 5Poly(styrene) 2.8-3.5 --- 38-55 1-2.5

Poly(tetrafluoroethylene) 0.41 10-14 14-28 100-350

Poly(methylmethacrylate) 2 4-2 8 48-62 48-69 2-10Poly(methylmethacrylate) 2.4-2.8 48-62 48-69 2-10

Nylon 3.8 800 25

Poly(ethylene):low-density 0 1-0 3 6 9-14 10-17 400-700Poly(ethylene):low-density 0.1-0.3 6.9-14 10-17 400-700

Note that these values depend on temperature and strain rate.W ill th t b h i i hi hl i fl d b t tWe will see that behaviour is highly influenced by temperature when we examine factors such as degree of crystallinity, glass transitions and melt viscosity.


Temperature Sensitivity of Polymer Properties

Crystallinity and crosslinking of polymer chains influence the modulus of a polymer as shown below.

At room temperature poly(ethylene) is above Tg but belowAt room temperature, poly(ethylene) is above Tg but below Tm, while nylon-6,6 is below both Tg and Tm. What differences in mechanical properties might you expect?


Heat Distortion Temperature

The maximum temperature at which a polymer can be used in rigid material applications is called the softening or heat distortion temperature (HDT)temperature (HDT).

A typical test (plastic sheeting) involves application of a static load, and heating at a rate of 2oC per min. The HDT is defined as the temperature at which the

elongation becomes 2%.

A: Rigid poly(vinyl chloride)50 psi load.

B: Low-density poly(ethylene)B: Low density poly(ethylene)50 psi load.

C: Poly(styrene-co-acrylonitrile)25 psi load25 psi load.

D: Cellulose acetate(Plasticized) 25 psi load.


Transient Testing: Creep Tests

Creep tests can be made under all load conditions, and provide data needed to design products that sustain loads for long periods

A constant stress σ is applied with the strain ε varying withA constant stress, σo, is applied, with the strain, ε, varying with time.

Creep behaviour arises from the viscoelastic properties of polymers and their compounds.

Ab ill t t d th f diff t id li d t i l tAbove are illustrated the response of different idealized materials to step changes in applied stress.

A: Elastic B: Viscous C: Viscoelastic


Transient Testing: Impact Resistance

Impact tests are high-speed fracture teststhat measure the energy required to breaka specimena specimen.

Izod and Charpy (shown to right) impact tests use a weighted pendulum to measuretests use a weighted pendulum to measurethe loss of kinetic energy associated with specimen fracture.

Agreement between different methods can be poor, and results are notmaterial constants, but dependenton sample geometry, notching and size.

Impact strength units vary, but notchedtests are defined in terms of energy perunit length of notch: kJ/m.


unit length of notch: kJ/m.

Transient Testing: Resilience of Cured Elastomers

Resilience tests reflect the ability ofan elastomeric compound to storeand return energy at a givenand return energy at a givenfrequency and temperature.

Change of rebound resilience (h/ho) with temperature T for: 1. cis-poly(isoprene); p y( p )2. poly(isobutylene); 3. poly(chloroprene); 4. poly(methyl methacrylate).


4. poly(methyl methacrylate).

Flow Characteristics – Rheology of Polymer Melts

Polymer melts and solutions are pseudoplastic, meaning that they exhibit shear thinning behavior


Flow Characteristics – Rheology of Polymer Melts

Extensional thickening effects are observed when tracking the extensional viscosity as a function of time. If a sample, initially at its rest state, is subjected to steady simple extension at a rate ε starting at a time=0, the tensile stress growth coefficient defined as:

.

εσ−εσ≡εη+ &&

&),t(),t()t( 2211

E

growth coefficient, defined as:

+ (t,ε

).ε

≡εη&

),t(E

shows the onset of strain

η E+

hardening effects dependon the applied shear rate.


Thermal Expansion

If a part is to be produced within a close dimensional tolerance, careful consideration of thermal expansion/contraction must be made.

Parts are produced in the melt state, and solidify to amorphous or semi-crystalline states.

Changes in density mustChanges in density mustbe taken into account when designing the mold.


Polymer Classification

What distinguishes polymers from other organic compounds is molecular weight and dimension.

Differences in composition, architecture and molecular weightgive rise to differences in mechanical properties (strength, elasticity, toughness) and chemical properties (solubility, aging).

Polymer Classifications CHEE 490 2.1

toughness) and chemical properties (solubility, aging).

Polymer Classification: Thermoplastic/Thermoset

One of the most practical and useful classification of polymer compounds is based on their ability to be refabricated.

Thermoplastic: polymers that can be heat-softened in order toprocess into a desired form.

Polystyrene polyethylenePolystyrene, polyethylenerecyclable food containers

Thermoset: polymers whose individual chains have beenchemically crosslinked by covalent bonds and thereforeresist heat softening, creep and solvent attack.

Phenol-formaldehyde resins, melamine paintspermanent adhesives, coatingsp g


Polymer Classification: Chain Architecture

Linear: A linear polymer chain is one without branches. Its actual conformation may not be “line-like”, but varies with chain stiffness, crystallinity and applied stressescrystallinity and applied stresses.

Branched: Chains with an appreciable number of side-chains are classified as branched These side chains may differ in compositionclassified as branched. These side chains may differ in composition from the polymer backbone.

C li k d A tiCrosslinked: A continuousnetwork of polymer chains isa crosslinked condition. In effect,there is just one polymer chainof infinite molecular weight.

Chain architecture has a dramaticeffect on properties such asviscosity, elasticity and temperature


viscosity, elasticity and temperaturestability.

Polymer Classification: Chemical Microstructure

Homopolymers: polymers derived from a single monomer (can belinear, branched or crosslinked).

poly(ethylene) poly(butadiene)poly(ethylene), poly(butadiene).

Random copolymers: two monomers randomly distributed in chain.AABAAABBABAABBApoly(acrylonitrile-ran-butadiene)

Alternating copolymers: two monomers incorporated sequentiallyABABABABABABABABABABABABABABABABpoly(styrene-alt-maleic anhydride)

Block copolymers: linear arrangement of blocks of high mol weightp y g g gAAAAAAAAAAABBBBBBBBBBBBBBBAAAAAAAApolystyrene-block-polybutadiene-block-polystyrene or poly(styrene-b-butadiene-b-styrene)poly(styrene b butadiene b styrene)

Graft copolymers: differing backbone and side-chain monomerspoly(isobutylene-graft-butadiene)


poly(isobutylene-graft-butadiene)

Polymer Classification: Chemical Class

A popular classification scheme amongst chemists is based on polymer functionality.

P l t OPolyesters: poly(ethylene terephthalate) - Dacron

P l id

C O

O

OHPolyamides:poly(caprolactam) - nylon 6

Urethanes:

N C

OH

Urethanes:carbamate linkages through reaction of diisocyanates and diols. N C

O

O

H

Another (!) classification scheme, again favoured by chemists is based on differences between the polymer and constituent monomer(s)monomer(s).

Condensation polymers: synthesis involves elimination of some small molecule (H2O in the preparation of nylon)Addition polymer: formed without loss of a small molecule i e


Addition polymer: formed without loss of a small molecule i.e. ethylene polymerization to generate poly(ethylene)

Molecular Weight and Composition Distributions

While small molecules are defined uniquely by molecular weight and atomic connectivity, polymers are not. Consider the high-density polyethylene samples whose distribution of moleculardensity polyethylene samples whose distribution of molecular weights are very different.

These materials share theThese materials share thesame chemical composition(-CH2-), but exhibit different

i h t i tiprocessing characteristicsand physical properties.

In addition to molecular weight,chemical structure differs betweenpolymers and even between chains within a given sample. Chemical composition distribution, or the polymer microstructure has an enormous impact on engineering

Distributions CHEE 490 2.7

the polymer microstructure has an enormous impact on engineering properties.

Molecular Weight Averages

Suppose we have a mixture of four different sized ball bearings, and run them across the trough shown below.

What meaningful averages can be calculated?What meaningful averages can be calculated?


Molecular Weight Distribution

The distribution of molecular weights within a polymer is characterized not by a single, unique average, but defined through a number of different waysnumber of different ways.

The number average, Mn,considers the number ofmolecules of each size, Mi, in the sample:

∑ Mn

The weight average M

∑∑=

i

iin n

MnM

The weight average, Mw, considers the mass ofmolecules of each sizewithin the sample:within the sample:

∑∑=

i

iiw w

MwM


∑ i

Molecular Weight Distribution

Given a measure of the continuous molecular weight distribution, molecular weight averages are calculated by integration of the number of chains of each molecular weight N(M):number of chains of each molecular weight N(M):

Number Average:∞

∫0

n

N(M) M dMM

N(M) dM∞

•=∫

∫0

N(M) dM∫

Weight Average:2N(M) M dM

∞

∫0

w

0

MN(M) M dM

∞=

∫


0

Methods of Molecular Weight DeterminationNumber Average Molecular Weight

End-group analysis» determine the number of end-groups in a sample of known mass

C lli ti P tiColligative Properties» most commonly osmotic pressure, but includes boiling point elevation

and freezing point depression

Weight Average Molecular WeightLight scattering

» Use the distribution of scattered light intensity created by a dissolved g y ypolymer sample as an absolute measure of weight-average MW

Viscosity Average Molecular WeightViscometryViscometry

» the viscosity of an infinitely dilute polymer solution relative to the solvent relates to molecular dimension and weight.

Molecular Weight DistributionGel permeation chromatography

» fractionation on the basis of chain aggregate dimension in solution (See 1 f f G C )


slide 1 for an example of GPC output).

Polydispersity

By virtue of its definition, Mw cannot be less than Mn. It is influenced by the high molecular weight fraction of the material to a greater degree than Mngreater degree than Mn.

The ratio of Mw to Mn, defines the polydispersitydefines the polydispersityof a molecular weight distribution.

Low polydispersities (PD=Mw/Mn ≈ 2) generate higher melt viscosity, higher tensile strength and better toughness ingpolyethylene.


Polydispersity

Dependence of melt viscosity on shear rate for two polyethylenes of different molecular weight distribution.


different molecular weight distribution.

Molecular Weight Influence on Physical Properties

In addition to phase transition temperatures, molecular weight distribution alters the physical properties of the bulk state

the properties of an amorphous phase when above Tg arethe properties of an amorphous phase when above Tg are dictated largely by molecular entanglement and weak chain association forces.

MW is therefore expected to affect several amorphous h ti i l diphase properties, including

modulus, viscosity, heat distortion and, as shown to the right, elasticity.

G’ is the storage modulus, whichgis a measure of the energyimparted to the material that isstored elastically.


stored elastically.

Composition Distribution

Inclusion of two or more monomers in a material has a remarkable effect on processing and end-use properties. “Tailored” polymers can be developed through consideration of:can be developed through consideration of:

the character of incorporated monomers and, » polarity of main chain or pendant functionality» potential for crystallizationpotential for crystallization

their sequence distribution within polymer chains.» random chain composition» random chain composition» alternating» block sequencing» graft structure

Note that most polymers are immiscible. While small molecules can be combined to generate single-phase mixtures with unique

ti bl di f l ll lt i di i fproperties, blending of polymers usually results in a dispersion of one material in the other.

Incorporating different monomers in each polymer chain is


often the only means of generating “mixture” behaviour.

Random CopolymersMaterials comprised of a random distribution of different monomers are the most widely employed industrial copolymers.

Compare:Compare:» Polyacrylonitrile, Polybutadiene and Poly(acrylonitrile-co-butadiene)» Polyethylene, isotactic Polypropylene and Poly(ethylene-co-

propylene)propylene)

A wide range of Tm, Tg,degree of crystallinity asdegree of crystallinity aswell as both chemical and physical properties can beadjusted by varying theadjusted by varying the content of each monomer.

Sh h i iShown here is a generic phase diagram for a systemof “semi-crystalline” monomers.


Block CopolymersGiven that very few polymers are miscible, mechanical blending of different materials leads to phase separated mixtures.

Depending on interfacial adhesion and the properties of the continuous phase, the results of blending can be disappointing.Most block copolymer systems exhibit microphase-separated structures with the minor component dispersed in a matrix of the majority phase.Bridging across the phase boundary improves interfacial adhesion and physical properties

TEM of a suspension-prepared ABS. Typically rubber domains in suspension-derived polymer contain substantial amounts of occluded copolymer of styrene and acrylonitrilecopolymer of styrene and acrylonitrile.


Segmented Polyurethanes

Schematic morphology of unstretched semicrystalline polyurethane copolymer (segmented block copolymer)copolymer (segmented block copolymer).

A: hard nylon fibre B: bicomponent nylon-p y

spandexC: mechanical stretch

nylonD: spandex E: extruded latex


Test Your Knowledge

A polymer is fractionated and is found to have the molecular weight distribution shown below. For this continuous distribution, calculate the number- and weight-average molecular weightsthe number and weight average molecular weights.

What is the polydispersity of this sample?


Phase Transitions in Polymer Systems Fried 4.1-4.3

Most products use polymers in their bulk (solid, condensed) state. For these applications, the physical properties detailed in lecture 2 are strongly dependent on phase morphology and as a result onare strongly dependent on phase morphology and, as a result, on temperature.

To clarify key concepts we will handle a few different polymers:To clarify key concepts, we will handle a few different polymers:poly(methylmethacrylate)high density poly(ethylene)l d it l ( th l h )low density poly(ethylene-co-hexene)poly(tetrafluoroethylene)poly(isoprene), cis and trans.

By the end of this lecture topic, you should be able to identify amorphous and crystalline states, relate these to mechanical p yproperties and predict how each material will behave with respect to temperature changes.

Phase Transitions CHEE 490 3.1

Crystalline State

Under appropriate conditions, some polymers can be cooled from a melt condition can generate an imperfect crystal structure.

The basic units of crystalline polymer morphology areThe basic units of crystalline polymer morphology are crystalline lamellae, consisting of folded chains.

Nonadjacent Regular adjacent Irregular adjacentreentry reentry reentry

Crystallization/melting of polymer crystallites is a classical phase transition, identical to that of small molecules.

Below the melting point of the material, a highly organized g p g y gchain conformation is the most stable state for the polymer.The lowest-energy conformation of polymer chains depends on composition - hydrogen bonding, van der Waals


on composition hydrogen bonding, van der Waals interactions.

Crystallinity in Nylon-6,6

Hydrogen bonding between amideHydrogen bonding between amide groups of Nylon-6,6 givesrise to strong interchain

i i i h f dassociations with a preferred orientation. The result is a defined crystal structure, the unit cell of


which is shown here.

Identifying the Crystalline Melting Temperature

A transition in which the first derivatives of the molar Gibbs energy are discontinuous is defined as a first-order phase transitionis defined as a first order phase transition.

The chemical potential of the material changes abruptly at the transition point, Tt.

Heat Capacityp y



Dilatometry studies involve confining the polymer by a well- Li l th lpolymer by a wellcharacterized, inert liquid and recording the change in

Linear polyethylene. Open circles: cooled rapidly from melt to 25°C b f f ithe change in

volume as the temperature is

i d

25°C before fusion.

Solid circles: crystallized at 130°C

varied. for 40 days, then cooled to 25°C prior to fusion.



A Differential Scanning Calorimeter (DSC)controls the energy input to a sample andreference so they remain at the same Tthroughout a programmed temperature rise.

A DSC trace is a plot ofA DSC trace is a plot of energy (ΔH=Hsample-Href) as a function of T.


Factors Influencing Crystallinity

Chain architecture and composition distribution determines whether a polymer exists in a semi-crystalline or completely amorphous statestate.

1. Chain symmetry: symmetrical structures that permit close packing of chains favour crystallinity.p g y y

atactic poly(propylene) versus isotactic (polypropylene)poly(tetrafluoroethylene)?

2. Intermolecular forces: hydrogen bonding and attractive van der Waals forces promote crystallization

atactic poly(vinyl alcohol)atactic-poly(vinyl alcohol)

3. Branching and molecular mass: packing efficiency deteriorates ith i i b hi d th l ti b f f h iwith increasing branching and the relative number of free chain

ends.isotactic(polypropylene)


Factors Influencing Tm

The fundamental equation of thermodynamics for a closed system states: ΔGm = ΔHm - T ΔSmwhere ΔH and ΔS represent the enthalpy and entropy of fusionwhere ΔHm and ΔSm represent the enthalpy and entropy of fusion per repeat unit, respectively.

At the equilibrium temperature, Tm, ΔGm= 0, therefore:

m

mm S

HTΔΔ

=

Polymers in which ΔHm is relatively large (strong intermolecular attraction) and ΔSm relatively small (minimal ordering from melt to crystalline state), the temperature of melting is high.crystalline state), the temperature of melting is high.


Amorphous Bulk State

An amorphous state is one of relative disorder, where chain orientation is not present on a large scale. Physical properties derived from an amorphous phase are strongly dependent onderived from an amorphous phase are strongly dependent on temperature. Consider,

Plexiglass - poly(methyl methacrylate)Natural rubber cis poly(isoprene)Natural rubber - cis-poly(isoprene)

Both exist in an amorphous phase under conditions of common use, but exhibit very different mechanical properties.

If Plexiglass is heated above 105°C, it becomes rubbery. Cool natural rubber below -73 °C and it becomes a brittle, rigid material.

The transition from a glassy to a rubbery state in amorphous materials is called the glass transition temperature, Tg.

Below Tg, there is insufficient thermal energy to allow significant chain mobility or even chain segmental motion. Only cooperative motion of a few atoms of the main chain or side-groups is present,


motion of a few atoms of the main chain or side groups is present, as well as atomic vibrations.

Identifying the Glass Transition Temperature

A transition in which the first derivatives of the molar Gibbs energy areof the molar Gibbs energy are continuous, but the second derivatives are discontinuous is, by definition, a second order phase transitionsecond-order phase transition.

Molar Volume


Identifying the Glass Transition Temperature

Transition from a glass amorphous state to a rubbery amorphous state can be detected by a number of methods.

Dynamic mechanical testingDynamic mechanical testingSpecific volume determinationsDifferential Scanning Calorimetry

Shown here is the specific l T l t fvolume vs. T plot for

poly(vinyl acetate).

Note that the thermalexpansion coefficient changes at Tg, and a g gdiscontinuity is observedat the glass transitionpoint.


point.

Identifying the Glass Transition TemperatureDSC trace of poly(ethylene terephthalate-co-p-oxbenzoate), quenched, reheated, cooled at 0.5°K/min through the glass transition, and reheated for measurement at I0°K/min.

Tg is taken at the temperature at which half the increase in heat capacity has occurred. The width of the transition is indicated by ΔT.


Factors Influencing Tg

Polymers whose structures are flexible, do not provide for strong intermolecular attraction, and do not “pack” well are those with relatively Tg’srelatively Tg s.

Four factors are generally accepted to affect Tg:1 Free volume volume of the material that is not occupied by1. Free volume - volume of the material that is not occupied by

polymer molecules

2 Att ti f h d b di di l i ti2. Attractive forces - hydrogen bonding, dipole association

3. Internal chain mobility - rotational freedom along the chain asinfluenced by side chains.

4. Chain length - shorter chains have greater relative free volume.g g


Molecular Weight Influence on Tg, TmWe discussed factors thatinfluence phase transition temperaturesin polymer systems in Lecture 3.p y yIllustrated here is the specific effectof molecular weight on amorphouspolymers (right) and semi-crystallinepolymers (right) and semi crystallinematerials (below).


Test Your KnowledgeA series of DSC runs is made on an amorphous polymer starting at room temperature but using different heating rates (1 °C/min, 2 °C/min, 5°C/min). Sketch how the observed Tg may vary with heating rate.

Most plastic soda bottles are made from poly(ethylene terephthalate) (PET). One manufacturer is pushing a terpolymer in which some of the ethylene glycol is replaced by a cyclohexanedimethanol for that application. What advantage(s) do you think it might have?


Polymer Phase Transition Temperatures

Phase Transitions II CHEE 490 4.1

Meta-stable, Multi-phase Systems

At 150oC and 1 atm pressure, water exists as .At 80oC and 1 atm pressure, water exists as .At -5oC and 1 atm pressure water exists asAt 5 C and 1 atm pressure, water exists as .

At 100oC and 1 atm pressure, high density polyethylene (Tm=130oC,


At 100 C and 1 atm pressure, high density polyethylene (Tm 130 C, Tg=-100oC) exists as .

Extent of Crystallinity: Density Measurements

Measurements of specific volume (cm3/g) or density (g/cm3) can reflect the degree of crystallinity of a material, if a knowledge of the densities of the amorphous and crystalline phases are known:densities of the amorphous and crystalline phases are known:

a.

c a

ρ−ρφ =

ρ −ρ

where ρ is the density of the sample (as determined by a gradient column or dilatometry), ρa is the density of the amorphous phase,

d t th d it f th t lli h

c a

and ρc represents the density of the crystalline phase.


Extent of Crystallinity: Calorimetry (DSC)Given independent knowledge of the heat of crystallization for a given polymer, one can readily determine the degree of crystallinity (φ) in a sample by DSC: HΔ

where ΔHf sample (J/g) is recorded from the melting endotherm and ΔHf (J/g)

f ,sample.

f

HH

Δφ =

Δ

where ΔHf,sample (J/g) is recorded from the melting endotherm and ΔHf (J/g) is the heat of crystallization for a perfect crystal of the material.


Models of Semi-crystalline Polymer Structure

Many materials crystallize from the melt into organized structures called spherulites, shown below for poly(ethylene oxide):

Crystals grow out radially tocreate aggregates that canreach a few millimetres inreach a few millimetres indiameter.

Note that semi-crystallinepolymers are comprisedof crystalline lamellaeyand amorphous regionsthat “bind” crystallitestogether.


together.

Crystallization Kinetics

Even the most easily crystallized polymers contain amorphous defect regions. The extent of crystallization depends on the rate of crystallization for the material and the time during which a meltcrystallization for the material and the time during which a melt temperature is maintained.

Crystallization occurs below TmCrystallization occurs below Tm, but segmental mobility of chains is required.

Below Tg, the crystallization rate is zero (metastable condition)

Shown is the linear growth rate of poly(ethylene terephthalate) p y( y p )(Tg=69°C, Tm=265°C) as afunction of temperature.


Influence of Crystallization Temperature

The temperature at which a material undergoes crystallization (during injection molding, for example) influences the product and process in several ways:process in several ways:

1. Rate of crystallizationThe growth of the crystalline phase requires a driving force forThe growth of the crystalline phase requires a driving-force for crystal nucleation as well as chain mobility

2 P d t M h l2. Product MorphologyCrystallization at low temperature nucleates a great number of spherulites which grow slowlyHigh temperature crystallization results in rapid growth of relatively few spherulites

3. Ultimate degree of crystallinityThe maximum degree of crystallinity depends on the impingement of spherulites as well as polymer chain mobility


impingement of spherulites as well as polymer chain mobility

Isothermal Crystallization

O O C

OPoly(ether-ether-ketone)Tm = 334oC; Tg = 143oCm g

315°C308°C 312°C

160°C164°C


Simple Crystallization Kinetics: Avrami EquationCrystallization kinetics have been modeled using a framework analogous to raindrops falling in a puddle. These produce expanding circles of waves which intersect and cover the whole surface. The drops may fall sporadically or all at once, but they must strike the puddle surface at random points. The expanding circles of waves, of course, are the growth fronts of the spherulites, and the points of impact are the crystallite nuclei.

Avrami and other have used this conceptual model to develop an empirical equation for crystallization kinetics:

where k is a rate constant (sec-1) and n is a dimensionless parameter that

nkt.X 1 e−= −

( )relates to the type of phase nucleation.

Given that crystallinity is seldom complete, the Avrami equation is commonly modified by the ultimate degree of crystallinity, X∞:

nk tXX 1 e ∞

−

= −


.1 eX∞

Tg/Tm Demo: Glucosepentaacetate

Glucosepentaacetate is not a polymer, but it does exhibit glass transition and crystallization phenomena in a manner that is consistent with polymeric systemsconsistent with polymeric systems.

Melting point = 110°CTg = not well defined but approx 5°C.

At room temperature, the compound is a crystalline solid.Heating to 110°C melts the solid to generate an amorphous phase of liquid-like viscosity.phase of liquid like viscosity.Rapid chilling in ice water creates a glassy, brittle solid.Warming results in a glass to leather transformation Continued working of the sample OContinued working of the samplepromotes further crystallization until a solid powder is observed. O OO

OCH3

O

Why does it crumble where semi-crystalline polymers do not?

O

O

O

OCH3 CH3

CH3CH3


O O

Modulus vs.Temperature: Amorphous PS

Glassy

Leathery

Rubbery

ViscousPolystyrene


Stress applied at x and removed at y

Modulus vs. Temperature: Semi-Crystalline Polymers

Crystallinity and crosslinking of polymer chains influence the modulus of a polymer as shown below.

At room temperature poly(ethylene) is above Tg but belowAt room temperature, poly(ethylene) is above Tg but below Tm, while nylon-6,6 is below both Tg and Tm. What differences in mechanical properties might you expect?


MW Requirements of Industrial Polymers

Elastomersamorphous materials operating above Tg physical props derived from chain entanglement crosslinkingphysical props derived from chain entanglement, crosslinking

Adhesivesrange from elastomeric (pressure sensitive) to semi-g (p )crystalline (hot melt) to glassy (epoxy resins)

Plasticsbroad class of materials whose properties are derived from an amorphous phase and often from a crystalline phase

Fibreshighly crystalline materialsphysical properties derived from degree of crystallinityp y p p g y y

Coatingsmust be applied as a low viscosity medium and “cure” to


yproduce satisfactory properties

Test your knowledgeTwo diols, ethylene glycol (-O-CH2-CH2-O- repeat units) and bisphenol-A (-O-Ph-C(Me)2-Ph-O- repeat units) are commercially available at low cost. Which would you choose for a polyester sample to generate:

transparency?transparency?the highest possible Tg?

This is a plot of the crystal growth t f l (t t th l h l )rate for poly(tetramethylene p-phenylene)

siloxanes of different Mn as a function of crystallization temperature.

Explain why the rate of crystallizationExplain why the rate of crystallization is effectively zero at -10°C and at 130°C, and why a maximum crystallization rate is observed at

i t l 70°Capproximately 70°C.

The melting temperature of this polymer varies with molecular weight, with the g ,Mn=8,700 material having a Tm = 140°C, and the sample with Mn=143,000 having a Tm=155°C. Use your knowledge of the f t th t ff t lti t t t


factors that affect melting temperature to describe the origin of this difference in Tm.

Polymer Solubility

When two hydrocarbons such as dodecane and 2,4,6,8,10-pentamethyldodecane are combined, we (not surprisingly) generate a homogeneous solution:generate a homogeneous solution:

It is therefore interesting that polymeric analogues of these compounds, poly(ethylene) and poly(propylene) do not mix even at hi h t t b t h bi d d di i fhigh temperature, but when combined produce a dispersion of one material in the other.

n

n

Polymer Solubility CHEE 490 5.1

Industrial Relevance of Polymer Solubility

Polymer Solvent Effect ApplicationDiblockcopolymers

Motor Oil Colloidal suspensionsdissolve at high T

Multiviscosity motoroil (10W40)copolymers dissolve at high T,

raising viscosityoil (10W40)

Poly(ethyleneoxide)

Water Reduces turbulent flow Heat exchangesystems lowersoxide) systems, lowerspumping costs

Polyurethanes,cellulose esters

Esters, alcohols,various

Solvent vehicleevaporates leaving film

Varnishes, shellacand adhesivescellulose esters various evaporates, leaving film

for gluesand adhesives

Poly(vinyl chloride) Dibutylphthalate

Plasticizes polymer Lower polymer Tg,making “vinyl”phthalate making vinyl

Polystyrene Poly(phenyleneoxide)

Mutual solution,toughens polystyrene

Impact resistantobjects, appliances

Polystyrene Triglyceride oils Phase separates uponoil polymerization

Oil-based paints,tough, hard coatings


Thermodynamics of Mixing

Whether the mixing of two compounds generates a homogeneous solution or a blend depends on the Gibbs energy change of mixing.

A-B solutionmA grams mB grams polymer A material B ΔG < 0polymer A material B

+

ΔGmix < 0

immiscible blendΔGmix > 0

immiscible blendΔGmix (Joules/gram) is defined by:

ΔGmix = ΔHmix -T ΔSmix

where ΔHmix = HAB - (wAHA + wBHB)ΔSmix = SAB - (wASA + wBSB)


and wA, wB are the weight fractions of each material.

Entropy of Mixing

Consider the two-dimensional lattice representation of a solvent (open circles) and its solute (solid circles):

small polymericmolecule solutemolecule solutesolute

Mixing of small molecules results in a greater number of possible molecular arrangements than the mixing of a polymeric solute with a solvent.

While ΔSmix is always negative (promoting solubility), its mix y g (p g y)magnitude is less for polymeric systems than for solutions of small moleculesWhen dealing with polymer solubility, the enthalpic


When dealing with polymer solubility, the enthalpic contribution ΔHmix to the Gibbs energy of mixing is critical.

Enthalpy of Mixing

ΔHmix can be a positive or negative quantityIf A-A and B-B interactions are stronger than A-B interactions, then ΔH i > 0 (unmixed state is lower in energy)then ΔHmix 0 (unmixed state is lower in energy)If A-B interactions are stronger than pure component interactions, then ΔHmix < 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,

ΔH H ( H + H ) 0 f id l i tΔHmix = HAB - (wAHA + wBHB) = 0 for an ideal mixture

In general, most polymer-solvent interactions produce ΔHmix > 0, the exceptional cases being those in which significant hydrogen bonding between components is possible.

Predicting solubility in polymer systems often amounts to g y p y yconsidering the magnitude of ΔHmix > 0.If the enthalpy of mixing is greater than TΔSmix, then we know that the lower Gibbs energy condition is the unmixed state.


that the lower Gibbs energy condition is the unmixed state.

ΔHmix and the Solubility Parameter

The most popular predictor of polymer solubility is the solubility parameter, δi. Originally developed to guide solvent selection in the paint and coatings industry it is widely used in spite of itspaint and coatings industry, it is widely used in spite of its limitations.

For regular solutions in which intermolecular attractions are minimalFor regular solutions in which intermolecular attractions are minimal, ΔHmix can be estimated through:

32 /l)(UH δδφφΔΔ

where ΔU1,2 = internal energy change of mixing per unit volume,

3221212,12,1 cm/cal)(UH δ−δφφ=Δ≈Δ

φi = volume fraction of component i in the proposed mixture,δi = solubility parameter of component i: (cal/cm3)1/2

Note that this formula always predicts ΔHmix > 0, which holds only for regular solutions.


for regular solutions.

Solubility Parameter

The aforementioned solubility parameter is defined as:

δ = (ΔEv / ν)1/2v

where ΔEv = molar change of internal energy on vapourizationν = molar volume of the material

As defined, δ reflects the cohesive energy density of a material, or the energy of vapourization per unit volume.

While a precise prediction of solubility requires an exact knowledge of the Gibbs energy of mixing, solubility parameters are frequently

d h ti tused as a rough estimator.

In general, a polymer will dissolve in a given solvent if the absolute value of the difference in δ between the materials is less than 1 (cal/cm3)1/2.


Determining the Solubility Parameter

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 swellIf the polymer is crosslinked, it cannot dissolve but only swell as solvent penetrates the material.

The solubility parameter of a polymer is therefore d t i d b idetermined by exposing it to different solvents, and observing the δ at which swelling is maximized.


Solubility Parameters of Select Materials

Material δ (cal/cm3)1/2 Material δ (cal/cm3)1/2

Acetone 9.9 Poly(butadiene) 8.4Benzene 9.2 Poly(ethylene) 7.9Tetrahydrofuran 9.5 Poly(methylmethacrylate) 9.45Carbon tetrachloride 8 6 Poly(tetrafluoroethylene) 6 2Carbon tetrachloride 8.6 Poly(tetrafluoroethylene) 6.2n-Decane 6.6 Poly(isobutylene) 7.85Dibutyl amine 8.1 Poly(styrene) 9.10Mineral spirits 6.9 Cellulose triacetate 13.6Methanol 14.5 Nylon 6,6 13.6Toluene 8.9 Poly(vinyl chloride) 10.5Toluene 8.9 Poly(vinyl chloride) 10.5Water 23.4 Poly(acrylonitrile) 12.4Xylene 8.8


Solubility Parameters of Select Materials


Hansen Solubility Parameter Contribution Model

A more elaborate treatment of the solubility parameter recognizes contributions from fluctuating dipole moments, or dispersion forces, permanent dipole moments and hydrogen-bonding interactionspermanent dipole moments, and hydrogen bonding interactions. Thus, the total cohesion energy for a solvent is:

E = E + E + EEtotal = Edisp + Epolar + EH-bond

With the overall solubility parameter defined as δ2 = ΔE / ν, we get:

δ2 = Edisp / ν + Epolar / ν + EH-bond / νor,

δ2 = δdisp2 + δpolar

2 + δH-bond2

Tabulated values of component parameters for a wide range of p p gsolvents have been generated by fitting of internal energy of vapourization data.

Polymer Solubility 5.12


The Hansen volume of solubility for a polymer is located within a 3-D model by giving the coordinates of the center C

ompo

nent

by giving the coordinates of the center of a solubility sphere (δd, δp, δh) and its radius of interaction (R). Liquids whose parameters lie within the

Pol

ar

pvolume are active solvents.

Dispersion Component

/MPa1/2

Polymer δ δ δ RPolymer δd δ p δ h RCellulose acetate 18.6 12.7 11.0 7.6Chlorinated polypropylene 20.3 6.3 5.4 10.6Isoprene elastomer 16.6 1.4 -0.8 9.6C ll l iCellulose nitrate 15.4 14.7 8.8 11.5Polyamide, thermoplastic 17.4 -1.9 14.9 9.6Poly(isobutylene) 14.5 2.5 4.7 12.7Poly(ethylmethacrylate) 17.6 9.7 4.0 10.6Poly(methyl methacrylate) 18.6 10.5 7.5 8.6Polystyrene 21.3 5.8 4.3 12.7Poly(vinyl acetate) 20.9 11.3 9.6 13.7Poly(vinyl butyral) 18.6 4.4 13.0 10.6


Poly(vinyl butyral) 18.6 4.4 13.0 10.6Poly(vinyl chloride) 18.2 7.5 8.3 3.5

Solvent ∂/MPa ½

∂ ∂ ∂ ∂

1,1 Dichloroethylene 18.8 17.0 6.8 4.5

Ethylene dichloride 20 9 19 0 7 4 4 1

Isophorone 19.9 16.6 8.2 7.4

Di (isobutyl) ketone 16 9 16 0 3 7 4 1∂t ∂d ∂p ∂h

Alkanes

n-Butane 14.1 14.1 0.0 0.0

n-Pentane 14.5 14.5 0.0 0.0

Ethylene dichloride 20.9 19.0 7.4 4.1

Chloroform 19.0 17.8 3.1 5.7

1,1 Dichloroethane 18.5 16.6 8.2 0.4

Trichloroethylene 19.0 18.0 3.1 5.3

Di-(isobutyl) ketone 16.9 16.0 3.7 4.1

Esters

Ethylene carbonate 29.6 19.4 21.7 5.1

Methyl acetate 18.7 15.5 7.2 7.6

n-Hexane 14.9 14.9 0.0 0.0

n-Heptane 15.3 15.3 0.0 0.0

n-Octane 15.5 15.5 0.0 0.0

I 14 3 14 3 0 0 0 0

Carbon tetrachloride 17.8 17.8 0.0 0.6

Chlorobenzene 19.6 19.0 4.3 2.0

o-Dichlorobenzene 20.5 19.2 6.3 3.3

1 1 2 14 7 14 7 1 6 0 0

Ethyl formate 18.7 15.5 7.2 7.6

Propylene 1,2 carbonate 27.3 20.0 18.0 4.1

Ethyl acetate 18.1 15.8 5.3 7.2

Di h l b 17 9 16 6 3 1 6 1Isooctane 14.3 14.3 0.0 0.0

n-Dodecane 16.0 16.0 0.0 0.0

Cyclohexane 16.8 16.8 0.0 0.2

Methylcyclohexane 16.0 16.0 0.0 0.0

1,1,2 Trichlorotrifluoroethane

14.7 14.7 1.6 0.0

Ethers

Tetrahydrofuran 19.4 16.8 5.7 8.0

Diethyl carbonate 17.9 16.6 3.1 6.1

Diethyl sulfate 22.8 15.8 14.7 7.2

n-Butyl acetate 17.4 15.8 3.7 6.3

Isobutyl acetate 16.8 15.1 3.7 6.3

Aromatic Hydrocarbons

Benzene 18.6 18.4 0.0 2.0

Toluene 18.2 18.0 1.4 2.0

1,4 Dioxane 20.5 19.0 1.8 7.4

Diethyl ether 15.8 14.5 2.9 5.1

Dibenzyl ether 19.3 17.4 3.7 7.4

Ketones

2-Ethoxyethyl acetate 20.0 16.0 4.7 10.6

Isoamyl acetate 17.1 15.3 3.1 7.0

Isobutyl isobutyrate 16.5 15.1 2.9 5.9

Napthalene 20.3 19.2 2.0 5.9

Styrene 19.0 18.6 1.0 4.1

o-Xylene 18.0 17.8 1.0 3.1

Ethyl benzene 17.8 17.8 0.6 1.4

Acetone 20.0 15.5 10.4 7.0

Methyl ethyl ketone 19.0 16.0 9.0 5.1

Cyclohexanone 19.6 17.8 6.3 5.1

Nitrogen Compounds

Nitromethane 25.1 15.8 18.8 5.1

Nitroethane 22.7 16.0 15.5 4.5

2-Nitropropane 20.6 16.2 12.1 4.1 y

p- Diethyl benzene 18.0 18.0 0.0 0.6

Halohydrocarbons

Chloro methane 17.0 15.3 6.1 3.9

Diethyl ketone 18.1 15.8 7.6 4.7

Acetophenone 21.8 19.6 8.6 3.7

Methyl isobutyl ketone 17.0 15.3 6.1 4.1

Methyl isoamyl ketone 17 4 16 0 5 7 4 1

p p

Nitrobenzene 22.2 20.0 8.6 4.1

Ethanolamine 31.5 17.2 15.6 21.3

Ethylene diem me 25.3 16.6 8.8 17.0

Methylene chloride 20.3 18.2 6.3 6.1 Methyl isoamyl ketone 17.4 16.0 5.7 4.1

Pyridine 21.8 19.0 8.8 5.9

Morpholine 21.5 18.8 4.9 9.2

Analine 22 6 19 4 5 1 10

Diacetone alcohol 20.8 15.8 8.2 10.8

Ethylene glycol 23 5 16 2 9 2 14 3

Glycerol 36.1 17.4 12.1 29.3

Propylene glycol 30 2 16 8 9 4 23 3Analine 22.6 19.4 5.1 10

N-Methyl-2-pyrrolidone 22.9 18.0 12.3 7.2

Cyclohexylamine 18.9 17.4 3.1 6.6

Quinoline 22.0 19.4 7.0 7.6

Ethylene glycol monoethyl ether

23.5 16.2 9.2 14.3

Diethylene glycol monomethyl ether

22.0 16.2 7.8 12.7

Diethylene glycol h l h

22.3 16.2 9.2 12.3

Propylene glycol 30.2 16.8 9.4 23.3

Diethylene glycol 29.9 16.2 14.7 20.5

Triethylene glycol 27.5 16.0 12.5 18.6

Dipropylene glycol 31.7 16.0 20.3 18.4

Formamide 36.6 17.2 26.2 19.0

N,N-Dimethylformamide

24.8 17.4 13.7 11.3

Sulfur Compounds

monoethyl ether

Ethylene glycol monobutyl ether

20.8 16.0 5.1 12.3

Diethylene glycol monobutyl ether

20.4 16.0 7.0 10.6

Water 47.8 15.6 16.0 42.3

p

Carbon disulfide 20.5 20.5 0.0 0.6

Dimethylsulphoxide 26.7 18.4 16.4 10.2

Ethanethiol 18.6 15.8 6.6 7.2

y

1 -Decanol 20.4 17.6 2.7 10.0

Acids

Formic acid 24.9 14.3 11.9 16.6

Alcohols

Methanol 29.6 15.1 12.3 22.3

Ethanol 26.5 15.8 8.8 19.4

All l l h l 25 7 16 2 10 8 16 8

Acetic acid 21.4 14.5 8.0 13.5

Benzoic acid 21.8 18.2 7.0 9.8

Oleic acid 15.6 14.3 3.1 14.3

St i id 17 6 16 4 3 3 5 5Allyl alcohol 25.7 16.2 10.8 16.8

1-Propanol 24.5 16.0 6.8 17.4

2-Propanol 23.5 15.8 6.1 16.4

1-B utanol 23.1 16.0 5.7 15.8

Stearic acid 17.6 16.4 3.3 5.5

Phenols

Phenol 24.1 18.0 5.9 14.9

Resorcinol 29.0 18.0 8.4 21.1

2-Butanol 22.2 15.8 5.7 14.5

Isobutanol 22.7 15.1 5.7 16.0

Benzyl alcohol 23.8 18.4 6.3 13.7

m-Cresol 22.7 18.0 5.1 12.9

Methyl salicylate 21.7 16.0 8.0 12.3

Polyhydric Alcohols

Cyclohexanol 22.4 17.4 4.1 13.5 Ethylene glycol 32.9 17.0 11.0 26.0


The real power of the Hansen system stems from the fact that a simple mixing rule can be applied according to the following equations to derive the solubility parameters of a solvent blend:to derive the solubility parameters of a solvent blend:

...3,32,31,1 +++= dddd δφδφδφδ

∑∑= ipip ,δφδ

∑= ihih δφδwhere φi = volume fraction of the ith solvent in the mixture.

∑ ihih ,φ

For a 50:50 vol:vol mixture of toluene and ethanol:9.168.155.00.185.0 =⋅+⋅=dδ

1588504150δ 1.58.85.04.15.0 =⋅+⋅=pδ

7.104.195.00.25.0 =⋅+⋅=hδ



A polymer is probably soluble in a solvent (or solvent blend) if the Hansen parameters for the solvent lie within the solubility sphere for the polymerthe polymer.

Calculate whether the distance of the solvent from the center of the polymer solubility sphere is less than the radius of interaction for the polymer:interaction for the polymer:

D(S-P) = [4(∂ds - ∂dp)2 + (∂ps - ∂pp)2 + (∂hs - ∂hp)2]½where

D Di t b t l t d t f lD(S-P) = Distance between solvent and center of polymer solubility sphere

∂xs=Hansen component parameter for solvent∂xp=Hansen component parameter for polymer (The figure "4" in the first term doubles the dispersion component scale to create a nearly spherical volume of solubility.)

If the distance (D(s-p)) is less than the radius of interaction for the polymer, the-solvent would be expected to dissolve the polymer.



Since the dispersive component parameters are similar for most solvents, two-dimensional plots of δH versus δp are commonly used for psolvent selection purposes.

Component parameters for a Co po e t pa a ete s o apolymer of interest can be compared to potential solvents, with the likelihood of solubilitywith the likelihood of solubility increasing with improved matching of individual component parameterscomponent parameters.


Dilute Solution Viscosity

The “strength” of a solvent for a given polymer not only effects solubility, but the conformation of chains in solution.

A polymer dissolved in a “poor” solvent tends to aggregateA polymer dissolved in a poor solvent tends to aggregate while a “good” solvent interacts with the polymer chain to create an expanded conformation.Increasing temperature has a similar effect to solventIncreasing temperature has a similar effect to solvent strength.

Th i it f lThe viscosity of a polymersolution is therefore dependenton solvent strength.

Consider Einstein’s equation:η=ηs(1+2.5φ)η ηs( φ)

where η is the viscosityηs is the solvent viscosityand φ is the volume fraction of


and φ is the volume fraction of dispersed spheres.

Determining the Solubility Parameter

Shown below is the intrinsic viscosity of A: Poly(isobutylene) and B: Poly(styrene)B: Poly(styrene)as a function of solubility parameter.

When δ for the solvent matchesthat of the polymer, the chain

f ti i t d dconformation is most expanded,resulting in a maximum viscosity.

This is another method ofdetermining the solubilityg yparameter of a given polymer.


Concentrated Solutions - Plasticizers

Important commercial products are solutions where the polymer is the principal component.

Poly(vinyl chloride) is a rigid material (pipes house siding)Poly(vinyl chloride) is a rigid material (pipes, house siding), but is transformed into a leathery material upon addition of a few percent of dioctylphthate, a common plasticizer.

Plasticizers are small molecules that dissolve within a polymeric matrix to greatly alter the material’s viscosity.

Sh ld th b “ d” l t i th d iShould they be “good” solvents in a thermodynamic sense or relatively “poor” solvents?On what basis would you choose a plasticizing agent?What process would you use to mix the agent with the polymer?


Test your knowledge

Polymers can be purified by dissolution/precipitiation. In this method the material is dissolved in a minimum amount of a good solvent (solvent 1) to produce a homogeneous solution Thesolvent (solvent 1) to produce a homogeneous solution. The resulting solution is added dropwise to an excess of a second solvent (solvent 2). Solvent 2 is chosen for its inability to dissolve the polymer and its ability to maintains a miscible condition withthe polymer, and its ability to maintains a miscible condition with solvent 1. Therefore, the polymer precipitates from the solvent 1 / solvent 2 mixture.

U k l d f l bilit t tUse your knowledge of solubility parameters to propose solvent 1 / solvent 2 combinations to purify polyisobutylene, polymethyl methacrylate, polystyrene and cellulose acetate.


Permeability in Polymer Systems

The transport of small molecules through polymeric materials is relevant to a wide range of engineering applications.

Food packaging – oxygen and water transportFood packaging oxygen and water transportCoatings and adhesives – drying of polymer filmsPolymer synthesis – gas-phase polymerizations, solvent removal from polymer cementsremoval from polymer cementsMembrane separations – desalination, gas purificationControlled drug delivery – transdermal patches for morphine, i ti d linicotine delivery

Home brewing of high quality bitter ales – carbon dioxide flux through plastic bottles

We will discuss the definition and measurement of permeability, the solution-diffusion model commonly used to describe the yphenomenon, and the differences in rubber, glassy, and semi-crystalline polymers.

We will start with an inflated balloonWe will start with an inflated balloon

Diffusion in Polymer Systems CHEE 490 6.1

PermeabilityThe permeability coefficient of a permeant / polymer system, P, is the molar flux of permeant through the polymer (NA) normalized by the film thickness (L) and the difference between upstream (p2) and downstream (p1) partial pressures:

12

A

ppLNP−

=

The units used in the permeability literature vary with the nature of the permeant (gas phase, liquid) and the source of data.

12 pp


PermeabilityHere is a table of permeability values for oxygen and water vapour through a range of polymeric materials.

Why do oxygen permeabilities vary by seven orders of magnitude on going from PVA to PDMS?

Why is the water permeability of PVA hi h hil it bilitso high, while its oxygen permeability

is very low?

Which material is best suited for foodWhich material is best suited for food packaging, and which may be useful for contact lens applications?


Solution Diffusion Model of Permeability

Small molecule transport through nonporous polymers is generally believed to proceed by the solution diffusion mechanism, in which penetrant molecules:penetrant molecules:

1. Sorb into the polymer from a high activity external gas or liquid phase,2. Diffuse across the polymer driven by a chemical potential gradient, 3. Desorb from the polymer to a low activity gas or liquid external phase. 3 p y y g q p

While these three generalWhile these three general steps of the solution-diffusion mechanism are agreed upon, th ifi f ti i tthe specifics of sorption into and out of the polymer phase and diffusion across it are still active areas of research.


Solute Transport in Amorphous Rubbery Polymers

Polymer molecules do not occupy the entire volume of a sample. Because of packing inefficiencies andof packing inefficiencies and molecular motion, some of the volume in the polymer matrix is empty

“f ” d thi ll d for “free” and this so-called free volume is redistributed continuously.

The rate-limiting step for penetrantdiffusion is the creation of transient “gaps” in the polymer matrix via random, thermally-stimulated motion of polymer segments.of polymer segments.


Permeant Diffusivity

The diffusion coefficient is a kinetic parameter that measures the overall mobility of thethe overall mobility of the penetrant molecules through the polymer matrix.

The diffusivity depends on various factors, including (1) th i d h f(1) the size and shape of

molecules, (2) the mobility of the polymer

chains, and (3) the free-volume size and

distribution of the polymerp y

Diffusion coefficients for penetrants in natural rubber and rigid poly(vinyl chloride) at 30°C.


Permeant Solubility

On the basis of the solution-diffusion model, the permeability (P) of a component across the membrane is a product of diffusivity (D) and solubility coefficient (S):and solubility coefficient (S):

Permeability = Diffusivity * Solubility Coefficient

Consider the diffusion of an equimolar mixture of two gasesConsider the diffusion of an equimolar mixture of two gases through a rubbery membrane, one being much more soluble than the other.

c

0

cA,1 Which component will experience the higher concentration gradient?pA,1 = pB,1 pA,2 = pB,2 = 0

cB 1

concentration gradient?

Can you tell which component will have thecB,1

cA,2 = cB,2 = 0component will have the higher permeability?


X=0 X=L

Permeant Solubility

The solubility or partition coefficient (S) is a thermodynamic parameter that relates penetrant concentration in the polymer to that in the contacting gas/liquid phasein the contacting gas/liquid phase.

A,fluid

polymerA,

CC

S =

The concentration of gases in rubbery polymers (above Tg) relative to their partial pressures in the contacting gas phase can be using H ’ LHenry’s Law,

in which case:AC

AHenryA pkC =

HenryA

A kpCS ==

Simple equations describing the partitioning of liquid phase permeants are not available, but Flory-Huggins treatments of this problem have been developed.problem have been developed.


Rubbery Polymers: Plasticization Effects

Transport plasticization is defined as a significant increase in the diff i it f t t bdiffusivity of a penetrant because polymer segmental motion is enhanced by another penetrant

l l i it i i itmolecule in its vicinity .

These higher concentrations can i h f bloccur in cases where favorable

polymer–penetrant interactions promote solubility. This is common for organic vapors and even for molecules such as CO2, H2S and SO2.

Permeabilities of various gases in silicone rubber at 35°C.


Influence of Temperature

The temperature dependence of permeability is usually modeled by an Arrhenius expression:an Arrhenius expression:

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

RTE

expPP po

As evident from the log plot id d t th i ht i ifi t

⎠⎝

provided to the right, significant increases in permeability are observed for amporphous polymers on either side of Tg.

Heightened molecular mobility improves diffusivity, Effect of temperature on oxygen permeability at y p ythereby increasing permeability

Solubility is also affected, albeit to a smaller extent.

75% RH. PET is poly(ethylene terephthalate), AN is an acrylonitrile–styrene copolymer, PVDC is vinylidene chloride–vinyl chloride copolymer, and EVOH 27 is ethylene vinyl alcohol copolymer albeit to a smaller extent.


containing 27 mol% ethylene.

Solute Transport in Amorphous Glassy Polymers

In the glassy state, molecular mobility is limited to severely hindered torsional motionshindered torsional motions.

Natural rubber has a Tg of -73°C, while rigid PVC has a Tg of 81°Cwhile rigid PVC has a Tg of 81 C. The impact of polymer chain mobility on the diffusion coefficient i d ti ill t t d his dramatic, as illustrated here.

Note that the selectivity of permeation for different penetrants is greater for glassy polymers, a fact that is exploited in some pmembrane applications.

Diffusion coefficients for penetrants in natural rubber and rigid poly(vinyl chloride) at 30°C.


Semi-Crystalline Polymers: Solubility Coefficient

Crystalline domains are impenetrable by even tiny gas molecules, resulting in a drop in solubility coefficient for semi-crystalline materials such as polyethylenematerials such as polyethylene.

Polyethylene at 25°CThe proportional relationship between S and the volume fraction

ent C

A/p

A

between S and the volume fraction of the amorphous phase supports a simple scaling expression:

lity

coef

ficie

where Samorph is the solubility

amorphamorphSS Φ=

Sol

ubicoefficient of the amorphous

phase, and Φamorph is the amorphous phase volume fraction.

Volume fraction of amorphous phase

0.0 0.2 0.4 0.6 0.8 1.0

p p


Semi-Crystalline Polymers: Diffusion CoefficientImpermeable crystallites act as physical barriers to diffusion, increasing the path length for transport and restricting chain mobility, both of which reduce permeant diffusivity.

This twofold effect has been treated in terms of a tortuosity factor τ , and

h i i bili ti f t b th

p y

a chain immobilization factor β, both of which increase with increasing crystalline fraction.

βτaDD =

The parameters D and Da are the diffusion coefficients in the actual sample and in a totally amorphoussample and in a totally amorphous sample, respectively.


Test Your Knowledge

You are given a spherical balloon with a radius of 1 cm, and inflate it to a radius of 10 cm. Derive an equation for the balloon radius as a function of time.

Relevant data:P bilit 2E 11 3 / 2 h PPermeability = 2E-11 m3 m /m2 hour PaModulus of cured rubber = 350 PaUnstretched balloon thickness = 2.5E-4 m

0.100 9 0E‐0235 000

0.075

0.100

m) 6.0E‐02

7.0E‐02

8.0E‐02

9.0E 02

25,000

30,000

35,000

kness (m)

e (Pa)

0.050

oon Ra

dius (m

3.0E‐02

4.0E‐02

5.0E‐02

10 000

15,000

20,000

Ballo

on Thick

loon

Pressure

0.000

0.025

Ballo

0.0E+00

1.0E‐02

2.0E‐02

0

5,000

10,000 B

Ball


0 10 20 30Hours

0 10 20 30Hours

Test Your Knowledge

Isostatic methods of measuring permeability use a continuous flow on both sides of the polymer film toboth sides of the polymer film to provide constant penetrantconcentrations.

Consider this typical test cell. Derive an equation for the steady-state flux of penetrant through the film, and develop an equation that can be used to calculate the film’s permeability coefficient.


Weeks1-2

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