Experimental Method:Determination of : Osmotic Pressure

Polymer Solubility 1

1011 V Solvent theof VolumeMolar 1 V

22221

011 )11()1ln()( vxvvRTV

2/)1ln( 2222 vvv

xvvRTV /1

21

221

Polymer Solubility 2

22122

1 VA

The osmotic pressure data for cellulose tricaproate in dimethylformamide at three temperatures. The Flory -temperature was determined to be 41 ± 1°C

Modified Flory-Huggins theory

Polymer Solubility 3

Is temperature dependent

TTvvvnvnR

NS

vvT

RTN

Hmix

Mix

212211

212

lnln

Therefore, any temperature which causes =1/2 will be the Flory temperature

Flory-Huggins Parameters

Polymer Solubility 4

An Example

Polymer Solubility 5

Applications of

Polymer Solubility 6

The Chain Expansion Ratio and -Temperature

The Expansion Ratio, r

o

r r

r2

22

Applications of

Polymer Solubility 7

r depends on balance between i) polymer-solvent and ii) polymer-polymer interactions

If (ii) are more favourable than (i) r < 1 Chains contract Solvent is poor

If (ii) are less favourable than (i) r > 1 Chains expand Solvent is good

If these interactions are equivalent, we have theta condition r = 1 Same as in amorphous melt

Applications of

Polymer Solubility 8

For most polymer solutions r depends on temperature, and increases with increasing temperature

At temperatures above some theta temperature, the solvent is good, whereas below the solvent is poor, i.e.,

T > q r > 1

T = q r = 1

T < q r < 1

Often polymers will precipitate out of solution, rather than contracting

Applications of

Polymer Solubility 9

The Solvent Goodness:

)1)(21( 2

212

V

A

• A Positive A2 indicates a good solvent, i.e. a solvent that gives rise to an exothermic enthalpy of mixing. This arise when <1/2.

• When A2=0 the solvent is nearly Ideal. This is important for use of osmotic pressure to measure molar mass.

• A negative A2 indicates a poor solvent (>1/2). The entalpy of mixing is positive here.

• The goodness of solvent can be adjusted by changing the temperature.

Applications of

Polymer Solubility 10

211 vNRTHmix

RTwz /121

2/122

2/1112211

21

121112 )()()(2 wwwwwww

Recall:

Note that the energy terms w11, w22 and w12 are attractiveterms and are usually negative .When Hmix =0 for a solvent -polymer system, thus w11=w22 and the cohesive energy density.

Summary

Polymer Solubility 11

MixMixMix STHG

Solubility Parameters:

Thermodynamics of Mixing

21vkTNH Mix

Summary

Polymer Solubility 12

Free Energy of Mixing:

2,,1

011

nPT

Mix

nG

2222

011 )11()1ln()( vxvvRT

Summary

Polymer Solubility 13

Chemical Potential and Osmotic Pressure:

1011 V

xvvRTV /1

21

221

...1 232

0lim

cAcAMRTc nc

)1)(21( 2

212

V

A

Summary

Polymer Solubility 14

Other Forms of Flory-Huggins Eqs:

0.35 (in older literature), or zero

Properties of If the value of is below 0.5, the polymer

should be soluble if amorphous and linear. When equals 0.5, as in the case of the

polystyrene–cyclohexane system at 34°C, then the Flory conditions exist.

If the polymer is crystalline, as in the case of polyethylene, it must be heated to near its melting temperature, so that the total free energy of melting plus dissolving is negative.

For very many nonpolar polymer–solvent systems, is in the range of 0.3 to 0.4.

Polymer Solubility 15

Properties of For many systems, has been found to

increase with polymer concentration and decrease with temperature with a dependence that is approximately linear with, but in general not proportional to, 1/T.

For a given volume fraction 2 of polymer, the smaller the value of , the greater the rate at which the free energy of the solution decreases with the addition of solvent.

Negative values of often indicate strong polar attractions between polymer and solvent.

Polymer Solubility 16

Properties of The polymer–solvent interaction

parameter is only slightly sensitive to the molecular weight.

Polymer Solubility 17

Molecular Weight Averages

Polymer Solubility 18

Molecular Weight Distribution

Polymer Solubility 19

Determination of Number Average Mw

Polymer Solubility 20

a) End-group Analysis

b) Colligative Properties

Osmotic Pressure

Polymer Solubility 21

Flory q-Temperature

Polymer Solubility 22

Intrinsic Viscosity

Polymer Solubility 23

Some Definitions

Polymer Solubility 24

The Mark-Houwink Relationship

Polymer Solubility 25

Experimental Techniques

Polymer Solubility 26

Example

Polymer Solubility 27

Example (cont.)

Polymer Solubility 28

Gel Permiation Chromatography

Polymer Solubility 29

Size Exclusion Chromatography

Schematic View

Polymer Solubility 30

CalibrationGPC is a relative Molecular

Weight MethodNarrow molecular weight

distribution, anionically polymerized polystyrenes are used most often.

Other Polymers: PMMA, Polyisoprene, polybutadiene, Poly(ethylene oxide) and sodium salts of PMA.

Polymer Solubility 31

Calibration Method

Polymer Solubility 32

Molecular Weight of a Suspension Polymerized PS

Polymer Solubility 33

GPC of a Blend

Polymer Solubility 34

End of Chapter 2

Polymer Solubility 35