GPC - Polymer solvent compatibility

[Oakwater]

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

 

[monodisperse]

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.