[?] Plot a graph for viscosity vs. molecular weight?

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1

Hi,
I just started learning mathematica.
I’m trying to plot this plot the graph for viscosity vs molecular weight (attached pictures Formula 1 and
books plot2 from Cosgrove book of colloidal sciences.)
I first try to sum functions (linear part EE(M) and non linear part EE(M)) but I don’t think it works like that (line 3).
So I used the “IF” command and it seems it is also wrong (line 5). I think I have problem with defining functions and parameters in mathematica.
My .nb file is attached and
I appreciate your help.

P.S: Also look at line7 why mathematica doesn’t plot when I use function’s name?

EE1[M1_] := a M1; 
EE2[M1_] := a M1^3.4;
Plot[{a M1 + a M1^3.4}, {M1, 1, 100}, PlotRange -> Automatic]
Mc = 54;
ee[M_] := If[M < Mc, M, M^3.4](*ee is viscosity [\eta]*)
Plot[If[M < Mc, M, M^3.4], {M, 1, 100}, PlotRange -> Automatic]

Also why this code doesn’t plot manipulate when i use function’s name

Manipulate[Plot[{EE1 + EE2}, {M1, 1, 100}, PlotRange -> Automatic], {a, 1, 3}]

formula.png
formula.png487×247 75 KB

plotofviscosity.png
plotofviscosity.png478×322 21.3 KB

2

Hold the expression using With and insert a value for a

With[{a = 1},
 Plot[{a M1 + a M1^3.4}, {M1, 1, 100}, PlotRange -> Automatic]
 ]

Same thing can be done, instead of setting the value for Mc

With[{Mc = 54},
 ee[M_] := If[M < Mc, M, M^3.4];(*ee is viscosity[\eta]*)
 Plot[ee[M], {M, 1, 100}, Filling -> Axis]
 ]

Make the EE functions of two arguments, then supply the value of a using the manipulator

EE1[M1_, a_] := a M1;
EE2[M1_, a_] := a M1^3.4;

Manipulate[
 Plot[EE1[M1, a] + EE2[M1, a], {M1, 1, 100}, PlotRange -> {0, 2*^7}],
 {a, 1, 3}]
1 Like
3

Thanks for the reply,
I see that manipulate expression that you sent works, thank you. However, the graph doesn’t look like what I see in book (figure attached). I think I have problem with PlotRange..?, maybe plotting conditional functions are different? \Eta is a function of M if M is less than Mc=600 M then \Eta is linear , if M is greater than Mc then plot is non linear.

4

The graph in the book uses logarithmic scales. Did you try LogLogPlot?

5

Yes I think you are right! Thank you,