lecture - tu · pdf filedepartment of thermodynamics lecture ... 3 rd. ed., wiley – ......

1

Polymer Thermodynamics

Prof. Dr. rer. nat. habil. S. Enders

Faculty III for Process ScienceInstitute of Chemical EngineeringDepartment of Thermodynamics

Lecture

0331 L 337

1. Introduction and Basic Thermodynamics

2Polymer Thermodynamics

Lectures Friday 12.00 – 16.00 o‘clockRoom: TK 17

schedule

from 17. of April until 22. of May 2009

1. of May is official holiday


Contact Information:Tel.: 030 314 22755 Fax: 030 314 22406 E-Mail: [email protected] or [email protected]: TU Berlin, Sekr. TK 7, Straße des 17. Juni 135, 10623 Berlin

Consulting hours: Monday 14-15 o’clock, room TK 112

Office: Ms. Peters [email protected] hours: Wednesday 9.30-11.30 o’clock

Room TK 111



http://www.thermodynamik.tu-berlin.deactual information's:


Material: available as downloads

Newslecture presentations and exercisesinternet Links

Lehre → Polymer Thermodynamics

Downloads http://www.thermodynamik.tu-berlin.de/

6

Polymer ThermodynamicsRecommended literature

• J. Bicerano, Prediction of Polymer Properties, Marcel Dekker, 1993.• H.G. Elias, Makromoleküle; Band 2, Physikalische Strukturen und Eigenschaften,

Wiley-VCH Verlag, 2000.• K. Kamide, Thermodynamics of Polymer Solutions Phase Equilibria and Critical

Phenomena, Elsevier, 1990.• P.J. Flory, Principles of Polymer Chemistry, Cornell University Press 1953.• G. Astarita, S.I. Sandler, Kinetic and Thermodynamic Lumping of Multicomponent

Mixtures, Elsevier, 1991.• D.W. van Krevelen, Properties of Polymers, Elsevier, 1990.• R.P. Danner, M.S. High, Handbook of Polymer Solution Thermodynamics,

American Institute of Chemical Engineers, USA, 1993. • R. Koningsveld, W.H. Stockmayer, E. Nies

Polymer Phase Diagrams: A TextbookOxford University Press (2001) ISBN-13: 9780198556343.

• L.H. Sperling, Introduction to Physical Polymer Science, 3 rd. Ed., Wiley –Interscience (2001).


Attention: We have prepared all materials with great care. Nevertheless some errors can be involved.

3. Error Challenge

If you have found an error, please send my an E-Mail. [email protected]

The student, having found the most errors, will win a price.

Please use in the title: Error_Polymer

Invitation


Examination

oral, individual examinationduration 30 minutescontent: topics of the lecturePlease, bring along student ID and personal IDPlease, make a appointment in my office or via email

characteristic feature

Time: 25. of May until 29. of May 2009


„If you do not know thermodynamics youwould not get a bad design, you would get a wrong design!“

M. Parker, CEO Dow Chemical Company (2002)

Why do we need polymer thermodynamics ?



polystyrene

Which liquid can be put in cups made from polystyrene ?

Interaction of liquids (solvent) with polymers

solubility of polymersthermic stability of polymers



Polymer Production: based on Petrol (Petrol distillation)

Which polymers can be produced ? At which temperature ? Is the polymerization reaction an voluntary process ?Which solvent should be used ?

rubber productionplant

monomer



The most industrial polymer production processes take place in solutions.How it is possible to remove the solvent ?Which solvent should be used ?How we can avoid undesired phase separation in the production plant ?What are the thermodynamic properties (i.e. heat capacity, vapor pressure)

of polymer solutions?

13Polymer ThermodynamicsWhy do we need polymer thermodynamics ?

1. example: foam polystyrene = expanded polystyrene = EPS

Application of EPS

construction (heat, sound and tension insulation)

street buildinginsulating slab




construction (heat, sound and tension insulation)

Building by F. Hundertwasser (1928-2000) (Austrian artist) in Darmstadt (Germany)



Application of EPSpackaging

safety helmet for bikers

blister packaging material of any shape



1 2 3 4 5 6 7

Application of EPSlegendred: construction

(heat and sound insulation)

blue: packagingyellow: cupsgrey: others1 Europe2 North-America3 Africa/West-Asia4 Latin-America5 Japan6 Asia7 World

Caused by the great climatic differences the application depends strongly on the region.




polystyrene plant (Dow Chemical Company)

Thermodynamic task: Description of the involved phase equilibria during the whole production process.




Expansion: Polystyrene particle having a diameter of 1mm will be expanded using pentane.

first step: Heating of PS to 100-120°C(T>Tg) using hot water vapor

second step: Pentane will be evaporated and pressed into polymer particles. This leads to new particle (pearls) having a diameter of 3 mm.

Thermodynamic task: Can we predict the glass temperature

of polymers?What is the vapor pressure of pentane?Does the interfacial properties play an

important role?


1. example: foam polystyrene = expanded polystyrene = EPSExpansion: Polystyrene particle having a diameter of 1mm will be expanded using

pentane.Third step: Expanded polymer particle will be given in the desired forming.Fourth step: Little holes will be made on the polymer wall.Fifth step: Hot air will be pressed in the system in order to remove the pentane.Sixth step: Heating the polymer well above the glass transition temperature in

order to increase the volume by the factor 2 – 2.5.Seventh: Cooling down the whole system. The foam takes his final shape.Eight: The product will be stored several days in order to allow the completely remove

of pentane.

Thermodynamic task: At which conditions will the air be able to replace pentane ?How will the volume of the polymer be changed during heating and cooling procedures?Does a special interaction between the polymer and the fluid plays a role ?At which temperature the critical state of the gas can be found ?Is there a potential for simplification or improvement of the process ?What is the role of permeation in the procedure ?



Foaming of Polymers

Thermodynamic task:It is possible to use an alternative gas (hydrogen, nitrogen, carbon dioxide)?At which pressure can the foaming process be carried out ?





Application for heat insulation:Important property: heat conductivity

30

30

Polymer density [g/m3]

0.025air

0.019 to 0.024polyurethane-foam

0.032EPS

Heat conductivity[W/mK]

Material

Thermodynamic task: Why ? Which difference in layer thickness follows fromthe different heat conductivities, if the insulation power should be identical ?



2. example: polymers for medical applications

glasses, contact lenses, denture

valve, blood vessels, disc, artificial nervesdialysis membranes, dialysis tubes, artificial hip joint endoprosthesisimplant for skin

artificial knee joint

others 11%




Application: bags for blood, drug-formulations,safety gloves, tubes, blister-package

Advantage: suitable for thermic formability,high flexibility, excellent chemical resistance, very low potential for allergy

Disadvantage: phthalates is used as softener, but they can be toxic (teratogen and cancerogen) for humans

Challenge for thermodynamics:How can we produce ultra pure PVC with a negligible amount of softener ?How are the relation between polymer properties (i.e. molecular weight distribution ) and flexibility ?Can we use phase equilibria (demixing of polymer solution) to made tailor-made polymers?Which procedure can be applied for sterilization ?

PVC = poly(vinyl chloride)




PE – poly(ethylene)

Application: foil, packaging, containerstubes, bottles, implant (knee, hip)

Advantage: excellent chemical resistancehigh stiffness

Challenge for thermodynamics:How we can produce ultra pure PE ?What are the relations between polymer properties (i.e. molecular weight distribution )and other physical properties, like permeation, solubility?

Can we use phase equilibria (demixing of polymer solution) to made tailor-made polymers?Which procedure can be applied for sterilization ?LDPE is produced via high-pressure polymerization. What do we know about the influence of pressure on the phase equilibria ?




PS = polystyrene

Application: package, infusion equipment, tubes

Advantage: chemical resistanceexcellent deformability excellent transparence

Thermodynamic challengeHow can we produce tailor-made polymers basedon polystyrene, maybe copolymerization?Which copolymer should be applied for which purpose?What is the influence of chemical composition onthe properties of the copolymer ?




Application: artificial thread, artificial tissuemembranes for dialysisheart valve, syringe

Advantage: chemical resistanceexcellent deformability

Challenge for thermodynamics:How can we produce ultra pure PP ?What are the relations between polymer properties (i.e. molecular weight

distribution ) and other physical properties, like permeation, solubility chrystallinity?

Can we use phase equilibria (demixing of polymer solution) to made tailor-made polymers?

Which procedure can be applied for sterilization ?

PP = polypropylene




PLA = poly(lactic acid) O R C

O

O R1 O C

O

R2 C

O nI II

R = CH-CH3Advantage: biological degradation is possibletwo optical isomers poly( L-lactic acid) and poly( D-lactic acid)

Properties: partial crystallinemelting temperature 180°C

Properties: amorphousmelting temperature 75°C

copolymerization in order to tune the physical properties

Thermodynamic challenge: How is the influence of copolymer composition onphysical properties (chrystallinity, degradation, pH-stability)?

Application: tissue-engineering,artificial bone and articular



2. example: polymers for medical applicationsPLA = poly(lactic acid) as controlled drug delivery systems

encapsulation of drugs

Diseases: chemotherapy, hormone therapy

Advantage: long-term therapy over monthsis possible

Thermodynamic challenge: Can we predict the maximal amount of drug in the polymerparticles? Do we have any influence on this amount ?What do we know about the involved swelling equilibria ?How can we optimized the degradation behavior ?



Let us start to learn something about polymer thermodynamics !

The department of Thermodynamics und Thermic Engineering wishes you a lot of fun with thermodynamics and complete success.

Let us start to repeat the basics of thermodynamics, namely some basic terms, the first and second law of thermodynamics.


Basic terms of Thermodynamics

System and SurroundingSystem: certain sector of matter containing a large number of particles (≈1023) Examples: content of beaker, content of thermos bottle, chemical reactor, steam engine

system surrounding

material transfer energy transfer

open system closed system isolated systemFor heat and work holds the definition that heat or work put into the system has a positive sign. 0

0from surrounding to system dW or dQ endothermicfrom system to surrounding dW or dQ exothermic

→ > →→ < →


phase: Phase is a substance (pure phase) or a mixture of substances having spatial constant properties. The area, where the properties will bechanged is called interphase.

Liquid L

Vapor V

L

Vvapor density

ρV

liquid densityρL

interphase


Phase



Solid S

Liquid L

S

Lliquid density

ρL

solid densityρS

interphase


Phase



Liquid 2 L2

Liquid 1 L1L1liquid density

ρL1

liquid densityρL2

interphase


Phase

Example:oil + water

L2


state: Thermodynamic state of system is characterized by its state variables(i.e. temperature, pressure, density, composition, energy).


State

state functions (i.e h,u,f,g,s) depend on state variables (i.e. T,P,V, ni).

General: z=f(x,y)Change of state functions dz → exact differential

0 0

( , ) ( , ) ( , ) ( , ) ( , ) ( , )lim lim

( , ) ( , )( , ) ( , ) ( , ) (

( , ) ( , )( , )

, )

x yy x

y

y x

x

z x y z x x y z x y z x y z x y y z x yx x y y

z x y z x ydx z x dx y z x y

z x y z x ydz x y d

dy z x y dy z x yx y

x dyx y

Δ → Δ →

⎛ ⎞∂ + Δ − ∂ + Δ −⎛ ⎞ = =⎜ ⎟⎜ ⎟∂ Δ ∂ Δ⎝ ⎠ ⎝ ⎠

⎛ ⎞∂ ∂⎛ ⎞ = + − = + −⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠

⎛ ⎞∂ ∂⎛ ⎞= + ⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠exact differential


state: Thermodynamic state of system characterized by its state variables(i.e. temperature, pressure, density, composition, energy).


State

state functions (i.e h,u,f,g,s) depend on state variables (i.e. T,P,V, ni).

General: z=f(x,y)Change of state functions dz → exact differential

, ,, q s r qr s

z z zdz dq dr dsq r s

⎛ ⎞∂ ∂ ∂⎛ ⎞ ⎛ ⎞= + +⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂ ∂⎝ ⎠ ⎝ ⎠⎝ ⎠

partial differential coefficient related to experimental quantities

i.e. PP

P P T P

H S c H Vc V TT T T P T

∂ ∂ ∂ ∂⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= = = −⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠



Statestate functions: example

y

x

z(x1,y1)

z(x2,y2)

Y

Z dXX∂⎛ ⎞

⎜ ⎟∂⎝ ⎠

X

Z dYY∂⎛ ⎞

⎜ ⎟∂⎝ ⎠

2 23( , ) 3 22

z x y x xy y= + +

( ) ( )

6 2

2 3

6 2 2 3

y x

y

x

z zdz dx dyx y

z x yx

z x yy

dz x y dx x y dy

⎛ ⎞∂ ∂⎛ ⎞= + ⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠∂⎛ ⎞ = +⎜ ⎟∂⎝ ⎠

⎛ ⎞∂= +⎜ ⎟∂⎝ ⎠

= + + +



State



State

ΔZ = Zend - Zbeginning

state functions depend not from the route

0 5 10 15 20-100

-80

-60

-40

-20

0

20

40

60

80

state at end

state at beginning

route 1 route 2 route 3

f(X)

X

ΔZ = Δ1Z = Δ2Z=Δ3Z



State – Functions

Calculation of changes in state functions

2 23( , ) 3 22

z x y x xy y= + +

change in state = state at end – state at beginning

i.e. state at beginning: x=2, y=4state at end: x=5, y=1

(5,1) (2,4) 86.5 52 34.5z z zΔ = − = − =

Example:


Basic terms of ThermodynamicsState – Change

i.e. What is the change in volume, if the substance is transferred from state V(P,T,n) into state V(P+DP, T+DT,n) ?

2, , ,P n T n P T

V nR V nRT V RTT P P P n P∂ ∂ ∂⎛ ⎞ ⎛ ⎞ ⎛ ⎞= = − =⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂ ∂⎝ ⎠ ⎝ ⎠ ⎝ ⎠

, , ,

( , , )

P n T n T P

V f T P nV V VdV dT dP dnT P n

=

∂ ∂ ∂⎛ ⎞ ⎛ ⎞ ⎛ ⎞= + +⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂ ∂⎝ ⎠ ⎝ ⎠ ⎝ ⎠

nRTPV nRT VP

= → =

2

nR nRT RTdV dT dP dnP P P

= − +

Ideal gas law:



State – Functions

ΔZ = Zend - Zbeginning

Law of Schwarz: The sequence of differentiation can be interchanged.

qr

z zdz dq drq r

⎛ ⎞∂ ∂⎛ ⎞= +⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠⎝ ⎠for

2 2z zq r r q

⎛ ⎞ ⎛ ⎞∂ ∂=⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠

( , )z f q r= is valid

qr q r

z zr q q r

⎛ ⎞⎛ ⎞⎛ ⎞∂ ∂ ∂ ∂⎛ ⎞= ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠⎝ ⎠⎝ ⎠ ⎝ ⎠

state functions depend not from the route



State – Functions

ΔZ = ZEnd - ZBeginning

( , ) ( , ) ( , ) ' ' '

( , ) ( , )( , )

( ,

( , ) ( , ) ( , ) ( , )

) ( ,, )

,

(

)

)

(

y x

y x

z x y f x y g x y y uv vu

with

f x y f x ydf x y dx dyx y

g x y g x yd

dz x y g x y df x y f x y dg

g x y dx dy

x y

x y

= = +

⎛ ⎞∂ ∂⎛ ⎞= + ⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠

⎛ ⎞∂ ∂⎛ ⎞= + ⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠

= +

Rule for differentiation of products


Basic terms of ThermodynamicsState – Quantities

state quantities can be extensive or intensive.

Extensive state quantities will double their value if two equal systems will be united toone new system.

i.e. mass m, volume V, energy U

Intensive state quantities will keep their value if two equal systems will be united toone new system.

i.e. temperature T, pressure P, molar volume v, specific volume vsp

molar quantities

Vvn

=

n = amount of substance

specific quantities

spV vvm M

= =

m = mass, M = molar mass

density [g/l]concentration [mol/l]



Processes

The equilibrium state is the final state of the process. At equilibrium no changes can be observed, experimentally.

state 1 state 2 state 3process process



ProcessesProcesses: Transfer from initial (beginning) state to the final (end) state.

Process quantities: depend on the routethey are related to a process and not to a systemi.e. work and heat

extensive quantitiesi.e. work W, heat Q

intensive quantitiesi.e. molare enthalpies of chemical reactions

no heat exchangeconstantvolume

constanttemperature

constantpressure

adiabaticisochoreisothermisobar



Processes

heat and workfrom mechanics

dW Fds=

force route

i.e. to uplift of mass m from the height h1 to the height h2

2 2

1 1

2 1( )h h

HUBh h

W Gdh mg dh mg h h= = = −∫ ∫i.e. Acceleration of mass m from speed v=0 to speed v1

1 1 121

0 0 0

12

s v v

BedvW mads m vdt mvdv mvdt

= = = =∫ ∫ ∫

WHUB=mg(h2-h1)

h2h1

mg

h

WBe=mV12/2

V1

mV

V

dv dsa vdt dt

= =



Processes

V1

V2s2

s1

weight G area A

During expansion of an ideal gas against an outside acting force F caused be the weight, G, the work is given by:

2

1

2

1

2

1

S

VolS

V

Vol

V

VolVV

W Fds F PA dV Ads

dVW PAA

W PdV

= = =

= −

−

= −

∫

∫ ∫V2

V1

pV

dW Fds=

force routethermodynamics: mechanical work Wvol caused by themovement of the system limits via volume change

Mechanical work is always connected with a vectored movement of particles.

ds



Processes

V1

V2s2

s1

weight G area A

2 2

1 1

S V

VolS V

W Fds PdV= − = −∫ ∫

Thermodynamics: mechanical work, Wvol

The sign of mechanical work:

2 1

1 2

0 0

0 0

Vol

Vol

V V V W

V V V W

> → Δ > → <

> → Δ < → >→ work done by the system

→ work done on the system

ds

system

surrounding



Processesmechanical work at constant extern pressure (i.e. atmospheric pressure)

( )

2 2

1 1

2 1

2 1 0

S V

VolS V

Vol

Vol

W Fds PdV

W P V VV V W

= − = −

= − −

> → <

∫ ∫

V1

weight G

P

V2

weight G

P

state 1 state 2

The work is done by the system.



Processes

2

1

2 2

1 1

2

1

1 2

1

ln

0

V

VolV

V V

VolV V

Vol

Vol

W PdV mit PV nRT

nRTW dV nRT dVV V

VW nRTV

V V W

= − =

= − = −

⎛ ⎞= − ⎜ ⎟

⎝ ⎠> → >

∫

∫ ∫V2

weight G

P2

state 2

V1

weight G

P1

state 1

mechanical work at variable extern pressure

The work is done on the system.



Processes

21 2

1 1 2

lnVolV nRT nRTW nRT P PV V V

⎛ ⎞= − = =⎜ ⎟

⎝ ⎠

mechanical work at variable extern pressure

P1

P2

nRTPV

=

Isotherme

V2

V1

P

V



Processes

Two groups of hikers would like to go to mountain. The first group takes the direct way. The second group uses the serpentines.On the top of the mountains both groups have the same state (the same height), but the second group has done more work.

Change in state variables (i.e. height): depends not on the routeChange in process quantities (i.e. work): depends on the route



ProcessesHeat: is equal to the change of energy related to the energy of molecular motion.

- process quantity → depends on the way- is related to processes and not to systems

heat exchanges withchange of temperature

heat exchanges withoutchange of temperature

dQ TCd=heat capacity C

i.e. Heating of liquid in beakerlatent heat i.e. phase change,

chemical reactionsolution, adsorption

dQ qdζ=q molare heat of reactionζ reaction coordinate

dQ < 0 exothermicdQ > 0 endothermic

Ccn

=

specific heat capacity: spCcm

=



Processes

ice-20 0 20 40 60 80 100

Hea

t Q

T [°C]

water + ice

water

water + vapor

vapor



Processeswork heat



Equilibrium

a) thermic equilibrium: TI = TII = ... = T→ constant temperature

b) mechanical equilibrium: PI = PII = ... = P→ constant pressure

c) material equilibrium: μiI= μi

II= ... = μin

→ The chemical potential of the component, i, is equalin all present phases.



Equilibrium

PotE mgh=

stable

EPot→ global minimum

stable against all

perturbations

instable

EPot→ global maximum

instable against all

perturbations

metastable

EPot→ local minimum

stable against small

perturbations

lecture - tu · pdf filedepartment of thermodynamics lecture ... 3 rd. ed., wiley – ......

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