Experimental Method: Determination of : Osmotic Pressure
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Experimental Method: Determination of : Osmotic Pressure Polymer Solubility 1 1 0 1 1 V Solven the of Volume Molar 1 V 2 2 2 2 1 0 1 1 ) 1 1 ( ) 1 ln( ) ( v x v v RT V 2 / ) 1 ln( 2 2 2 2 v v v x v v RT V / 1 2 1 2 2 1
description
Experimental Method: Determination of : Osmotic Pressure. 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. Is temperature dependent. - PowerPoint PPT Presentation
Transcript of Experimental Method: Determination of : Osmotic Pressure
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
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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
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An Example
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Applications of
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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
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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
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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
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MixMixMix STHG
Solubility Parameters:
Thermodynamics of Mixing
21vkTNH Mix
Summary
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Free Energy of Mixing:
2,,1
011
nPT
Mix
nG
2222
011 )11()1ln()( vxvvRT
Summary
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Chemical Potential and Osmotic Pressure:
1011 V
xvvRTV /1
21
221
...1 232
0lim
cAcAMRTc nc
)1)(21( 2
212
V
A
Summary
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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.
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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.
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Properties of The polymer–solvent interaction
parameter is only slightly sensitive to the molecular weight.
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Molecular Weight Averages
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Molecular Weight Distribution
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Determination of Number Average Mw
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a) End-group Analysis
b) Colligative Properties
Osmotic Pressure
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Flory q-Temperature
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Intrinsic Viscosity
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Some Definitions
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The Mark-Houwink Relationship
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Experimental Techniques
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Example
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Example (cont.)
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Gel Permiation Chromatography
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Size Exclusion Chromatography
Schematic View
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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.
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Calibration Method
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Molecular Weight of a Suspension Polymerized PS
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GPC of a Blend
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End of Chapter 2
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