GPC - Polymer solvent compatibility

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SUMMARY

The discussion centers on the compatibility of polystyrene (PS) and polyvinyl chloride (PVC) with tetrahydrofuran (THF) using the Mark-Houwink equation, [η] = K.Mv^a. Given the constants K and a for PS (K = 1.6x10^5, a = 0.71) and PVC (K = 1.5x10^5, a = 0.77), PVC demonstrates greater compatibility with THF due to its higher 'a' value, indicating better polymer-solvent interaction. The relationship between molar mass and compatibility is highlighted, where a lower molar mass at a given elution volume suggests reduced compatibility. The discussion confirms that PVC's extended chain structure contributes to its superior solubility in THF compared to PS.

PREREQUISITES
  • Understanding of the Mark-Houwink equation
  • Knowledge of polymer chemistry, specifically polymer-solvent interactions
  • Familiarity with viscosity average molecular weight (Mv)
  • Basic concepts of elution volume in polymer characterization
NEXT STEPS
  • Research the Mark-Houwink parameters for other polymers in THF
  • Explore the effects of molecular weight on polymer-solvent compatibility
  • Investigate experimental methods for determining polymer solubility in solvents
  • Learn about the implications of polymer chain structure on solubility
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Chemists, polymer scientists, and materials engineers interested in polymer-solvent interactions and compatibility studies.

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Homework Statement



Given for polystyrene K = 1.6x10^5 and a = 0.71
and for PVC K = 1.5x10^5 and a = 0.77

a universal calibration curve has been created from PS and the molar mass of PVC at a certain elution volume has been calculated.

The part I'm not sure on is the question:

Show which of the two polymers is more compatible with tetrahydrofuran (THF).

Homework Equations



[η]= KM\stackrel{a}{v}

[η]_{x} M_{x} = [η]_{PS} M_{PS}

K_{x} M\stackrel{ax +1}{x} = K_{PS} M\stackrel{aps +1}{PS}

The Attempt at a Solution



From my understanding the constant "a" in the equation is related to the polymer - solvent interaction, in that the higher the value of a, the more compatible with the solvent the polymer is.
Also for the molar mass of PVC compared to PS at a given elution volume the molar mass is lower than that of PS, is this relevant? as a increases the molar mass continues to drop and at lower a values the molar mass rises. Am I correct in thinking that a greater molar mass at a given elution volume means that there is less compatibility between the polymer and the solvent?
Essentially, am I on the right lines here as I have done considerable searching but cannot find anywhere that explicitly links the constant "a" with compatibility or a study on a link between molar mass at elution volumes to compatibility.

I apologise if my equations are not completely clear.

Thanks
 
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The Mark-Houwink equation, [η]= K.Mv^a is what you want. http://en.wikipedia.org/wiki/Mark–Houwink_equation

When a = 0.5 the polymer solvent interaction is theta, higher is good, lower is bad. PVC is more soluble in THF than PS because a is higher. This means its hydrodynamic volume will be different for the same molecular weight, and the PVC is a more extended chain than PS.

The remaining given equations can be used to determine a conversion, and gives a constant when resolved for converting the observed viscosity average MW (Mv) of PVC into the actual Mv.
 

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