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I prepared 3 different polymer solutions with varying concentration of 100, 50 and 25 ppm in order to measure their viscosity . When I plot concentration vs viscosity graph in the excel, I have a perfect line that is the average viscosity is directly proportional to the concentration. However, when I plot a graph of reduced viscosity vs concentration, in this case I find that the points are not in a line but are scattered. In short, the values for reduced viscosities are not directly proportional to the concentration as was in the case of viscosity. To calculate the reduced viscosity, I used following relation : $$ \eta_{\text{red}}=\frac{\eta_0-\nu_s}{\eta_s\cdot c} $$ where $\eta_0$ is the average viscosity of the solution, $\eta_s$ the average viscosity of the solvent and $c$ the concentration of the solution.

My professor asked me to prepare another solution as according to him this is not normal and that reduced viscosity should also vary more or less directly with the concentration.

My question is - as I have my viscosity vs concentration graph a straight line, how will dividing each viscosities again by their respective concentration give another straight line as the quotient is different in this case? Or did I calculate the reduced viscosity incorrectly ( the formula I provided above).

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The reduced viscosity is normally defined as:

$$ \eta_r = \frac{\eta - \eta_0}{\eta_0\phi} $$

where $\eta$ is the viscosity of the solution, $\eta_0$ is the viscosity of the solvent and $\phi$ is the volume fraction of the polymer. However it's fine to use the concentration of the polymer $c$ as this just multiplies everything by a constant.

If you graph the reduced viscosity against concentration you would expect the graph to look like:

Viscosity

So it will be a straight line but it won't go through the origin. The $y$-intercept, shown as $[\eta]$, is called the intrinsic viscosity and gives you information about the size and shape of the polymer molecules.

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