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Homework Help: GPC - Polymer solvent compatibility

  1. Nov 29, 2013 #1
    1. The problem statement, all variables and given/known data

    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).

    2. Relevant equations

    [η]= KM[itex]\stackrel{a}{v}[/itex]

    [η][itex]_{x}[/itex] M[itex]_{x}[/itex] = [η][itex]_{PS}[/itex] M[itex]_{PS}[/itex]

    K[itex]_{x}[/itex] M[itex]\stackrel{ax +1}{x}[/itex] = K[itex]_{PS}[/itex] M[itex]\stackrel{aps +1}{PS}[/itex]

    3. 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.

  2. jcsd
  3. Dec 9, 2013 #2
    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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