Introductionto“polymers” ArchimatAutrans2014 ...€¦ · Introductionto“polymers” ArchimatAutrans2014 2ndInternationalSchoolonArchitectured Materials LEPMIUMR5279-LMOPS/[email protected]

Introduction to “polymers”Archimat Autrans 2014

2nd International School on ArchitecturedMaterials

LEPMI UMR 5279 - LMOPS / [email protected]

June 3rd 2014

LEPMI UMR 5279 - LMOPS / [email protected] Introduction to “polymers” Archimat Autrans 2014 2nd International School on Architectured Materials

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1. What is a “Polymer”

Coming up ...

1 What is a “Polymer”



Definition: PolymerA Polymer is a collection of “mer” units often arranged in a linear fashion,however this can be largely altered by chemist to change the propertiesof the resulting materials !



A polymer can also be viewed as a combination of strong (covalent) andweak (secondary) bonds :

Note: This lectureIn this lecture, this second definition will be prefered.


2. Structural features / classification

Coming up ...

2 Structural features / classificationChain architectureInter chain interactionsorganization


2. Structural features / classification2.1 Chain architecture

Definition: OrganizationLinear Polymers exist where the polymer chains are arranged in a linearfashion. These can be tangled (like “spaghettis” a) or they can be ordered(crystallized form).

a. I am not very fond of this picture, and you will let me know why.



Linear branched polymers exist where side reaction during polymerizationcause branches to form reducing the density of the polymer (e.g. LDPE)



Thanks to organic chemsitry :

Definition: CopolymersPolymers composed of two or more different “mer” units

Warning: The best is yet to comeEndless kinds of materials ... and properties !



Definition: Molecular weight in polymerThe molecular weight in a polymer represents the number of monomersper molecules.

Polymer molecular weight is important because it determines manyphysical properties. Some examples include the temperatures for transitionsfrom liquids to waxes to rubbers to solids and mechanical properties suchas stiffness, strength, viscoelasticity, toughness, and viscosity.



The molecular weight in a given polymer varies from one molecule to thenext. One needs to “average” this number.



Number average molecular weight (first order) :

Mn =∑

i

niMi

ni= 20 + 16 + 10

3 Mmonomer = 15.3Mmonomer

Number average molecular weight : (second order)

Mw =∑

i

niM 2i

niMi= 202 + 162 + 102

20 + 16 + 10 Mmonomer = 16.4Mmonomer

Polydispersity index : IP (Fr : « indice de polymolécularité »)

Ip = Mw

Mn = 1.1



Higher average molecular weights : MzMz =

∑i

niMn+1i

niMni

One average molecular weight which does not fit into the mold of Mk isthe viscosity average molecular weight or Mv. It is defined by

Mv =(∑

i

niMa+1i

niMni

)(1/a)



K - Homework - K # 1Determine the molecular weight in the two following configurations :

9 mol, molecular weight ( Mw ) = 30,000g/mol , and 5 mol,molecular weight ( Mw ) = 50,000g/mol9 grams, molecular weight ( Mw ) = 30,000g/mol , 5 grams,molecular weight ( Mw ) = 50,000g/molAnswer 1 : Mn = 37kg/mol and Mw = 40kg/molAnswer 2 : Mn = 35kg/mol and Mw = 37kg/mol



K - Homework - K # 2Use “excel” or any other tool, to easily determine the different molecularweights from a given distribution.


2. Structural features / classification2.2 Inter chain interactions

Polymers may be placed into three main distinct areas :Thermoplastics Rubbers

Thermosets

From left to right : Increasing amount of irreversible links


2. Structural features / classification2.3 organization

K - Homework - K # 3

How many atoms would you count in 1 cm3 of solid matter ?

Note: Hint ...The distance between two of them is of about 1Å.

Note: AnswerThe answer is the the largest physical constant you know.



In ceramics or metals, a crystalline solid comprises repeating unit cells thatcontain each of the component atoms in the material.

In a polymer this is not possible :the molecules are chainscontaining potentially millions offormula units.

There is, however a repeating unit in a polymer - the monomer from whichit was made. This is the basis of both long and short-range order in apolymeric material.Some strong local organization in the form of crystallized structure may befound.



How to place ≈ 1024 atoms in 1cm3 solid ?Two extreme cases are possible :In the right order, crystalline solids : - metals - ceramics - polymersWith no order, amorphous solids : - polymers - ceramics - glasses - carbon- some metals

SOLIDE CRISTALLIN

Solide

amorphe

(ou liquide)

Figure : Cristallin vs amorphous



K - Homework - K # 4Draw the diffraction spectra and the pair correlation function (Defined asthe probability of finding the center of a particle at a given distance fromthe center of another particle.) for these two extreme cases



Here is a free hint :

Figure : Quartz versus Silica



Polymer Crystallinity :

Definition: Polymer Crystallinity :The fraction of the ordered molecules in polymer is characterized by thedegree of crystallinity, which typically ranges between 0% and 80 vol%

Crystallite





Crystallite





Crystallite


3. Characteristic temperatures

Coming up ...

3 Characteristic temperaturesTgMelting temperature : Tm


3. Characteristic temperatures3.1 Tg

Definition: TgThe glass transition temperature is hard to define properly. It is usuallydefined with its consequences :

Tg does not alter the chain organization (S = cte, almost a secondorder phase transition)Below Tg : Combination of strong (covalent) and weak (secondary)bonds.Above Tg : Only strong (covalent) bonds remain : flexibility



Despite the massive change in the physical properties of a materialthrough its glass transition, the transition is not quite a phase transition. Itis defined by one of several conventions. Such conventions include aconstant cooling rate (10K/min) 1 and a viscosity threshold of 1012Pa.s.Upon cooling or heating through this glass transition range, the materialalso exhibits a smooth step in the thermal expansion coefficient and in thespecific heat, with the location of these effects again being dependent onthe history of the material. 2 However, the question of whether some phasetransition underlies the glass transition is a matter of continuing research. 3

1. 11357-2 : Plastics Differential scanning calorimetry (DSC) Part 2 : Determinationof glass transition temperature (1999).

2. Angell, C. A. ; Ngai, K. L. ; McKenna, G. B. ; McMillan, P. F. ; Martin, S. W.(2000). “Relaxation in glassforming liquids and amorphous solids”. App. Phys. Rev. 88(6) : 3113 ?3157.

3. Zarzycki, J. (1991). Glasses and the Vitreous State. Cambridge University Press.ISBN 0521355826



K - Homework - K # 5Can you find in the materials around you :

a polymer that is above its Tg,a polymer that is below its Tg

Why are they so different ?Which one is the most surprising as compared to the other type ofmaterials ?



Tg may also be defined from the microstructural changes it induces.

Bellow Tg : Combination between strong (covalent) and weak (secondary)bonds. The entropy of the system is constant.

Above Tg : Only strong (covalent) bonds remain allowing large flexibilityTg does not alter (much) the chain organization



Meaning in terms of Spec. Vol.

The Enthalpy (H) is the internalenergy.The specific volume Vs is the ratioof the substance’s volume to itsmass.

Note: Like a second-order phase transitions : discontinuity in asecond derivative of the free energy

K - Homework - K # 6

You know this curve ! No ? Find its first derivative ? (smooth-it)


3. Characteristic temperatures3.2 Melting temperature : Tm

Polymer “Crystals” ?Similar to small molecules/metallic crystals

1 Three dimensional positional order2 First-order transition

Different from small molecules/metallic crystals1 Degree of crystallinity (T < Tm) is less than 100%2 Unit cell never contains the whole chain3 Bonding differs greatly in different directions (covalent vs secondary)



Definition:The term melting point, when applied to polymers, does not suggests asolid-liquid phase transition but a transition from a semi-crystallinephase to a solid amorphous phase. Simply abbreviated as Tm, isshould be more properly called the “crystalline melting temperature”.

Warning: Tm is not uniqueUnlike what is commonly measured with metals, the melting temperatureof polymers is broadly distributed in a bell curve. This temperaturedistribution reflects a distribution in crystal stability and sizes.



Tm may also be defined from the microstructural changes it induces.

Below Tm : Combination between strong (covalent) and weak (secondary)bonds

Above Tm : Only strong (covalent) bonds remainflexibility Tm induces disorderLarge change in the entropy (S = kB ln Ω).



Meaning in terms of Spec. Vol.

Note:Like a first-order phase transitions : discontinuity in the first derivative ofthe free energy

K - Homework - K # 7You know this curve ! No ? Find its first derivative ? (smooth-it)



Note:Tg and Tm seem very similar in polymers : both describe a change in thesecondary bounds whilst the covalent ones remain unchanged.

QuestionAre they really ?



Note:Tg and Tm seem very similar in polymers : both describe a change in thesecondary bounds whilst the covalent ones remain unchanged.

QuestionAre they really ?



K - Homework - K # 8Think about the Boyer relations

symmetrical molecules :TgTm

= 12

asymmetrical molecules :TgTm

= 23

Aout 80% of the data 4 of symmetrical and asymmetrical polymers arewithin the Tg/Tm limits 0.5-0.8.

K - Homework - K # 9A patent claims the invention of a new polymer in which the meltingtemperature is lower than Tg. Is this useful ? Is this possible ?

4. Boyer RF. The relation of transition temperatures to chemical structure in highpolymers. Rub Chem Technol (Rub Rev) 1963 ;36(5) :1303-421.



Determination by measurement of specific volume

Tg also depends on cooling or heating rate, not Tm.



Some polymers “cold crystallize” when heated



Some polymers “cold crystallize” : example of PET

When quenched Below Tg PET chains have a lot of mobility. Upon thenext they eventually reach the right temperature ( Tg + 20OC ), and gainenergy by moving into crystalline arrangements. Further on the curve,melting occurs again.



DMA is commonly used to characterize the behavior in polymers :



Warning:Warning : “room temperature” strongly varies from one to the next !

K - Homework - K # 10Try to find for each kind of materials where would room temperature beplaced as compared to the characteristic temperatures. This can be largelyextended to any polymer including the ones within complex structures,composites, etc.


4. Elasticity in polymer

Coming up ...

4 Elasticity in polymerIntroductionNature of elasticityThermodynamicsOverview


4. Elasticity in polymer4.1 Introduction

Example:You all know this example of mechanical properties :

Warning: Is it always true ?Do you know materials with a different qualitative behavior ?



Example:You all know this example of mechanical properties :

Warning: Is it always true ?Do you know materials with a different qualitative behavior ?



Definition: Hooke lawBack in 1676 Hooke published “the true theory of elasticity or springiness”in which is proposed the famous :“ut tensio sic vis”

- “as the extension, so is the force”.F = K ∗ δlF [N] K [N .mm−1]δl [mm]

You all know :- the slope in the F(δl) depends on the nature and geometry of the sample.- this law is virtually always true ( ?)



Definition: Hooke lawBack in 1676 Hooke published “the true theory of elasticity or springiness”in which is proposed the famous :“ut tensio sic vis” - “as the extension, so is the force”.

F = K ∗ δlF [N] K [N .mm−1]δl [mm]




Definition: Hooke lawBack in 1676 Hooke published “the true theory of elasticity or springiness”in which is proposed the famous :“ut tensio sic vis” - “as the extension, so is the force”.F = K ∗ δlF [N] K [N .mm−1]δl [mm]




Warning: Hooke’s lawWhere does this law come from ?Is it really true for all materials ?What is its domain of validity ?


4. Elasticity in polymer4.2 Nature of elasticity

On atomic level :

1D crystal

Interaction energyUU

dd

Between two atoms Three atoms

f = K’∆∆∆∆L + K’’∆∆∆∆L2 + …

This is true for almost all materials (metals, vitreous polymers, crystal,ceramics, etc)



In the case of elastomers, things are a “little different”

S = k ln Ω

5

Relaxed chains

called «Gaussian state »

Large number of configurations

Large entropy

Mechanically stretched chain

Much less configurations

Lower entropy

S

The “spring” comes from the changes in intramolecular arrangement andnot from the intermolecular .Can one prove this ?



Can one understand this ?



Ludwig Boltzmann (1844 - 1906)


4. Elasticity in polymer4.3 Thermodynamics

Definition: Free energyThe thermodynamic free energy is the amount of work that athermodynamic system can perform. The concept is useful in thethermodynamics of chemical or thermal processes in engineering andscience. The free energy is the internal energy of a system minus theamount of energy that cannot be used to perform work. This unusableenergy is given by the entropy of a system multiplied by the temperatureof the system.

Gibbs free energy : for systems at constant pressure and temperature.

Definition:F = U − TSF [J] U [J ] T [K] S [J/K]



Two extreme cases :

For low temperatures : For high temperatures :



F = U –TS

(Free energy at T and V cst)

TVTVTV l

ST

l

U

l

Ff

,,,

∂∂−

∂∂=

∂∂=

7

Entropy

(configuration

Of the chains)

Internal energy

(distance between

neighbors)

TVTVTV lll ,,, ∂ ∂ ∂


4. Elasticity in polymer4.4 Overview

f =[∂U∂l

]V ,T

− T[∂S∂l

]V ,T

Two distinct cases :For low temperatures :

Crystalline phases andvitreous polymersNo change in chainarrangementsEntropic term is negligible

f ≈[∂U∂l

]V ,T

For high temperatures :Elastomer, rubbery materialsLoss of short rangeinteractionsEnthalpic term is negligible

f ≈ T[∂S∂l

]V ,T



f =[∂U∂l

]V ,T

− T[∂S∂l

]V ,T

Two distinct cases :

For low temperatures :Crystalline phases andvitreous polymersNo change in chainarrangementsEntropic term is negligible

f ≈[∂U∂l

]V ,T


f ≈ T[∂S∂l

]V ,T



f =[∂U∂l

]V ,T

− T[∂S∂l

]V ,T



f ≈[∂U∂l

]V ,T


f ≈ T[∂S∂l

]V ,T



f =[∂U∂l

]V ,T

− T[∂S∂l

]V ,T



f ≈[∂U∂l

]V ,T


f ≈ T[∂S∂l

]V ,T



Note: Macroscopic properties (elastomers) :No neckingSimilar stress/curve with changing dε/dtNo strain set even after 300% strain or more



The stress strain curve is intrinsically non linear :f = NkT (λ− 1/λ2)This law should be preferred to the “Young modulus” for elastomers.At high strain an additive strain hardening should be added, thephenomenological Mooney-Rivlin works well :σ = 2 ∗ (C1 + C2/λ) ∗ (λ− 1/λ2)


5. Viscoelasticity :

Coming up ...

5 Viscoelasticity :Influence of •

ε (T=cte)Effect of temperatureDefinition


5. Viscoelasticity :5.1 Influence of

•ε (T=cte)

Conclusion :Mechanical properties of polymeric materials depend on strain rate.. Only the elastomers do not follow this trend


5. Viscoelasticity :5.2 Effect of temperature

Warning:Tg characterization by DMTA is not well suited. The •

ε dependance is marked at temperatures close to Tα


5. Viscoelasticity :5.3 Definition

Definition:Viscoelastic properties correspond to a mixture between elastic andviscous properties.. If stress follows the strain, the material is elastic (spring). If stress follows the times derivative of strain, the material is viscous(dash-pot)

The mechanical properties of polymers at low strains may be easilymodeled with series and parallel functions of a spring and a dash-pot.Examples may be found here :http://www.sgm.univ-savoie.fr/cours/Cours_Master_PTA.html


http://www.sgm.univ-savoie.fr/cours/Cours_Master_PTA.html

http://www.sgm.univ-savoie.fr/cours/Cours_Master_PTA.html

6. DMTA :

Coming up ...

6 DMTA :


6. DMTA :

On the practical stand point :

Note:Three different zones :

Glassy state : secondary bonds are strong, polymer is brittle, elasticityis enthalpicTransistion : large dissipationRubbery : the secondary bounds are lost, entropic elasticity


6. DMTA :

Sometimes, only a small part of the polymer may undergo a transition :

Dynamic mechanical analysis data for atatctic polystyrene

Note:The exact nature of the relaxation may usually be determined by varyingthe chemistry of the materials.Relaxtions below Tg are very important (PC is very ductile).


6. DMTA :

Influence of the structural features on glass transition temperature :


7. Large strain

Coming up ...

7 Large strain


7. Large strain

Influence of the type of polymer on the stress strain curves :

K - Homework - K # 11Try and relate the stress-strain curves to the chemistry of the samples.


7. Large strain

Note:Brittle : thermoset or thermoplastics below Tg (some)Transitory : thermoplastics amorphous below Tg (some) or semicrystallize (Tg<RT<Tm)Elastomers : above Tg

Polymers can experience elongations up to 1000% and more !


7. Large strain

Mechanical Characteristics of Polymers v.sensitive toTemperatureStrain rateEnvironment (RH, solvent, O2)


7. Large strain

Case of Semicrystalline Polymers, or glassy but ductile polymers 5

Warning:Neck gets stronger since deformation aligns the chains (covalent)This increases local strength in the neck region (2-5 times) => neckdoes not failDifferent from ductile metals where the deformation is confined in theinitial neck region and induce failure

5. Ashby Jones “Matériaux”LEPMI UMR 5279 - LMOPS / [email protected] Introduction to “polymers” Archimat Autrans 2014 2nd International School on Architectured Materials

8. Conclusions

Coming up ...

8 Conclusions


8. Conclusions

You have probably notice that polymers are everywhere (see, for instance,the Polymer Science Learning Center : http://www.pslc.ws ).Today’s challenges concern functional polymers

Semiconducting Conjugated Polymers (OPV, LED, electronics)Stimuli-Responsive Polymers (artificial muscles)Drug delivery systems (PLA)Controlled gradient index for optics ...

Polymer in Architectured Multimaterials !


http://www.pslc.ws/macrog.htm

8. Conclusions

You have probably notice that polymers are everywhere (see, for instance,the Polymer Science Learning Center : http://www.pslc.ws ).Today’s challenges concern functional polymers

Semiconducting Conjugated Polymers (OPV, LED, electronics)Stimuli-Responsive Polymers (artificial muscles)Drug delivery systems (PLA)Controlled gradient index for optics ...Polymer in Architectured Multimaterials !


http://www.pslc.ws/macrog.htm

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Introductionto“polymers” ArchimatAutrans2014 ...€¦ · Introductionto“polymers” ArchimatAutrans2014 2ndInternationalSchoolonArchitectured Materials LEPMIUMR5279-LMOPS/[email protected]