Hanyang Univ. Spring 2007 Unlike small molecules, polymers are typically a mixture of differently...

Hanyang Univ.Hanyang Univ.

Spring 2007

Unlike small molecules, polymers are typically a mixture of differently sized molecules. Only an average molecular weight can be defined.

Chap 5. Characterization of MW

In case of Low MWsamplein moles ofnumber

wtsample total

N

W M Wt.Molecular


Spring 2007

Measurements of average molecular weight (M.W.)

mer-fraction mole:N

N

M

mer- samplein moles of # total

W

N

WMn

1

1

1

1

1samplemer - total

xn

n

n

n

n

w

x

x

x

x

xx

xxx

xx

xx

x

Weight Average Molecular Weight ,Mw

Number average molecular weight Mn

considers the number of molecules of each size, Mi, in the sample

The weight average, Mw, considers the mass of molecules of each size within the sample

samplein mer - offraction wt :W

M

MM

W

MMM

samplesmer - of wt total

samples of wt totalM

2211

xw

n

nw

w

w

w

w

w

w

xw

x

xx

xxx

x

xxx

xx

Viscosity average M.W. ,Mv Average determined by viscosity measurements. Closer to Mw than Mn


Spring 2007

WN

lengthchainorDPAv.wtM

lengthchainorDPAv.#Mn

r.u of mwM

Mnthan alwaysM M

2x

x

xw

x

x

xn

ww

nn

x

w

xn

xnxx

n

n

xnx

xxmw

xxm

mxm

ww moreincreases rialsheavy mate of

For further details,

CLICK the following link.

http://www.pslc.ws/mactest/weight.htm

RELATED LINK:

High MW sensitive Low MW sensitive

seMonodisper1MnM

sePolydisper1MnM

=

>

w

w

:Mn:Mw

Polydispersity : Polydispersity = Mw/ Mn


Spring 2007

Influence of Increasing Molar Mass on Properties


Spring 2007Influence of Molecular

Weight on Mechanical Properties.


Spring 2007Methods of Molecular Weight Determination

Number Average Molecular WeightEnd-group analysisdetermine the number of end-groups in a sample of known massColligative Propertiesmost commonly osmotic pressure, but includes boiling point elevation and

freezing point depression

Weight Average Molecular WeightLight scatteringtranslate the distribution of scattered light intensity created by a dissolved polymer sample into an absolute measure of weight-average MW

Viscosity Average Molecular WeightViscometrythe viscosity of an infinitely dilute polymer solution relative to the solvent relates to molecular dimension and weight.

Molecular Weight DistributionGel permeation chromatographyfractionation on the basis of chain aggregate dimension in solution


Spring 2007

Weight Average Molecular Weight

Light scattering

Determination of Molecular Weight

• Large particles in solution/suspension scatter light.

• Responsible for phenomena such as refraction, Tyndall effect.

• Extent of scattering is a function of the size and shape of the particles.

• Consequently yields information about Mw.

Measuring Light scattering

• Ar or He/Ne laser source• Photometer/goniometer measures light intensity at various angles (θ)


Spring 2007Determination of Molecular Weight

• The concentration dependence is observed to follow this functional dependence:

• Neglect higher order term in c.

• Plot of hsp/c vs c will yield [h] as y-intercept.

sp

c k 2c k c2

k = Huggins constantk=2 for rigid uncharged spheresk=0.35 for flexible polymers

y-intercept

Viscosity Average Molecular Weight

Viscometry


Spring 2007

Virtual Experiment

Case Western Reserve Univ.Polymer and Liquid Crystals

Viscosity Measurements

Click the next homepage, experiment part

http://plc.cwru.edu/tutorial/enhanced/lab/visco/visco.htm

If you have the trouble viewing this site,

See this page http://plc.cwru.edu/tutorial/enhanced/software.html

http://www.macromedia.com/shockwave/download/triggerpages_mmcom/default.html

KMa

• K and a are empirical parameters characteristic of a polymer and a solvent

- a=0.5 for a well-coiled polymer in a poor solvent

- a=1.7 for rigid rod-like polymer


Spring 2007

•Solvent flow carries molecules from left to right; big ones come out first

while small ones get caught in the pores.•It is thought that particle volume controls the order of elution.•But what about shape?

For further details

CLICK the following link,

http://www.pslc.ws/mactest/sec.htm

Surfing to the internet

Size Exclusion Principle

Molecular Weight Distribution

Gel permeation chromatography

Determination of Molecular Weight


Spring 2007

Simple GPC

degas

pump

injector

DRIVe

log 10

M

c

c

log 10

M

c

log10M


Spring 2007

Three factors are of general interest1. What Solvents will dissolve what polymer?

2. How does the polymer-solvent interaction influence the solution properties/

3. To what applications do the interesting properties of polymer solutions lead?

General rules foe polymer solubility1. Like dissolve like; Polar polymers- polar solvents Nonpolar polymer-nonpolar s

olvent. ex) PVA in water, PS in toluene

2. Solubility will decrease with increasing molecular weight at const. temp.

3. Crystallinity decreases solubility.

4. Crosslinking eliminates solubility.

5. The rate of solubility increases with short branches, allowing the solvent

molecules to penetrate more easily.

6. The rate of solubility decreases with longer branches, because the

entanglement makes it harder for individual molecules to separate.

Chap 6. Polymer Solubility and Solutions


Spring 2007

ΔGm=ΔHm-TΔSm < 0Where, ΔGm = the change in Gibbs free energy in the process ΔHm = the change in enthalpy in the process ΔSm = the change in entropy in the processOnly if ΔGm is negative will the solution process be feasible.

A positive ΔH solvent and polymer “prefer their own company”, the purematerials are in a lower energy state.A negative ΔH the solution is in the lower energy state, specific interactionsare formed between the solvents and polymer molecules.

Thermodynamics Basics

Gmix < 0

Gmix > 0

A B

Immicible

AB solution

+

[Ref : H.Tompa; polymer solutions, Butterworths,London, 1956,chapter 7]


Spring 2007

The solubility parameter is defined as:

H E = 12(1 2)2 (cal/cm3soln)

1, 2 : vol. frac. 1 : polymer solubility parameter. 2 : solvent solubility parameter. = (CED)1/2 = (Ev/v)1/2 = (cal/cm3)1/2

Ev/v : molar vol. of liq. rule of thumb1 2 0.5 for solubility.

Solubility Parameter

lumev:molar voction , x:mole fra

vxvxδvxδvx

ixturesolvent mδ

2211

222111

For further details,

Click next homepage.

http://palimpsest.stanford.edu/byauth/burke/solpar/


Likely crosslinked polymer

Uncrosslinked polymer

: Polymer solvent solubility parameter

Swel

ling

Fig. Determination of (polymer ) by swelling


Spring 2007

Lattice model of solubility

Filled circles : SoluteOpen circles : Solvent

(a) Low-molecular-weight solute (b) polymeric solute.


Spring 2007

internal energy on vaporization

21

2222

vE

where

v

E

vE

vE

vE

ii

hdp

pdhv

Ev = Eh + Ed + Ep

Hansen’s 3-D Solubility Parameter

The cohesive energy, δ 2 , is divided into three parts:

1) Dispersion forces (δd )

2) Polar forces ( δp )

3) Hydrogen bonding ( δH )

d P H


Spring 2007

SOLVENT

Chloroform 808 1.5 2.8 9.36

THF 802 2.8 3.9 9.50

MEK 7.77 4.4 2.5 9.27

m-cresol 8.8 2.5 6.3 11.1

Methanol 7.4 6.0 10.9 14.5

Toluene 8.82 0.7 1.0 8.91

H2O 6.0 15.3 16.7 23.5

PS 8.6 3.0 2.0 9.33

Styrene 9.09 0.49 2.0 9.32

d

P

H

Hansen’s 3-D Solubility Parameter


Spring 2007

Properties of dilute solutions

-Good solvent : Solubility parameter closely matches that of the polymer.

The secondary forces between polymer segments and solvent

molecules are strong, and the polymer molecules are strong, and the

polymer molecules will assume a spread-out conformation in solution.

-Poor solvent : the attractive forces between the segments of the polymer chain are

greater than those between the chain segments and the solvent.

Ex) polystyrene (δ = 9.0 ~ 9.3 )

Chloroform (δ = 9.2 )

Then non-solvent is added , methanol( δ = 14.5 ),the mixed solvent(Chloroform + methanol)

becomes too”poor” to sustain solution, and the polymer precipitates out.

When ΔG = 0 and ΔH = TΔS (θ condition)


Spring 2007

Glass Transition

PolybutadienePolyethylacrylate rubbery at RT, when cooled in Liq. N2

Polyisoprene become rigid and glassy, shatters when break

• At low temperatures, all amorphous polymers are stiff and glassy, sometimescalled as the Vitreous State, especially for inorganic polymers.

• On Warming, polymers soften in a characteristic temperature range known as theglass-rubber transition region.

• The glass transition temperature (Tg), is the temperature at which the amorphousphase of the polymer is converted between rubbery and glassy states.

• Tg constitutes the most important mechanical property for all polymers. In fact,upon synthesis of a new polymer, the glass transition temperature is among thefirst properties measured.

Chap 7. Transitions in Polymers

PMMA, PS hard, rigid glassy plastics at RT when heated to 125C, become rubbery


Spring 2007

•Amorphous regions of the material begin to exhibit long-range, cooperative segmental motion

•Molecular motion available to polymer chains below their Tg are restricted primarily to vibrational modes.

•Above Tg there is sufficient thermal energy for the chains, through cooperative rotational motion about the backbone bonds, to flow under an applied stress.

•The presence of this large-scale segmental motion (20–50 atoms moving in concert) above Tg produces an increase in the free volume of the polymer.

Molecular Motions in an Amorphous Polymer


Spring 2007Differential Thermal Analysis (DTA)

Principal components of the experiment include:

• an oven for the controlled heating of the samples• separate temperature sensing transducers for both the analysis and reference samples

DTA Design


Spring 2007Differential Scanning Calorimeter (DSC)

For further details, Click next homepage.

http://www.pslc.ws/mactest/dsc.htm


Two samples, each heated independently. Temperature difference is monitored. Control heat flow into analysis sample (adjusting heater power) to keep the temperature difference ∆T = 0. This is a null experiment with feedback.


Spring 2007DTA & DSC Images and Sample data

DTA

DTA sample data DSC sample data


Spring 2007

0.00048b0.025aTg)-b(TaEq. WLFsf

f vv

v

1.Free volume of the polymer vf.

Free volume vf = v vs

v: specific volume of polymer mass vs: volume of solidly packed molecules

2. Attractive forces between molecules. Tg

Main factor of Tg


Spring 2007

3. Internal mobility of chains (= freedom to rotate about bond)

Tg Eo

Silicone 7.3 -120 ~ 0

PE 7.9 -85 3.3

PTFE 6.2 >20 4.7

Example (1)


Spring 2007

TgTg500forTgTg xx

c

4. Stiffness of the materials

Young’s Modulus E may be written as: σ = Eε σ = Tensile stress; ε = Tensile strain

Young’s modulus is a fundamental measure of the stiffness of the material. The higher its value, the more resistant the material is to being stretched.Unit of E: dynes/cm2 (10 dynes/cm2 = 1 Pascal)

5. Chain Length.


Spring 2007

copolymerin monomers offraction wt.:TgTgTg

1

2

2

1

1 www

T : Kelvin temperature1, 2 : polymer 1 and 2

Tg of Copolymer

For further details about Tg,

Click next homepage.

http://www.pslc.ws/mactest/tg.htm

&

http://plc.cwru.edu/tutorial/enhanced/files/polymers/therm/therm.htm



Spring 2007

Tm (C) (g/cm3) TS (psi) Water cont (%)

Nylon 6 216 1.14 12,000 1.7

Nylon 11 185 1.04 8,000 0.3

Nylon 12 177 1.02 7,500 0.25

PE 135 0.97 5,500 Nil.

Nylon n Tm TS water contExample (2)

Tg Comparision

PU O C

O

NH ( CH 2 ) n

x PA NH C

O

Purea NH CO NH

T m T m T m

Example (3)

H-bonding Hm

PU : O (Swivel) flexibility

Extra NH in polyurea more extensive H-bond. Hm


Spring 2007

300 C , PET rapidly cooled to RT

rigid and transparent

heated to 100 C maintained at

that temp

and becomes translucent

then cooled down to RT again

now, it is translucent rather

than transparent.

Example (4)


Spring 2007

•Homogeneous, amorphous

•Amorphous and glassy, rigid

Influence of Copolymerization on Properties

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