Your fitting function is a horrible fit to your data. You must have something wrong. To visualize this do the following:

Manipulate[
 Show[ListLinePlot[data1, PlotStyle -> Orange], 
  Plot[2*Sqrt[diffusion]*x*(1/L)*(Pi^(-0.5) + 2*(\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 
           1\), \(100\)]\(\((\((\(-1\))\)^n)\)*
          Erfc[\((n*L)\)/\((Sqrt[diffusion]*x)\)]\)\))), {x, 0, 120}],
   PlotRange -> All], {diffusion, 0.0001, 1}]

You can sweep through values of diffusion and see it is a horrible fit. To get a "Best Fit" (which is equally horrible!) you need to constrain the value of diffusion to positive values to avoid imaginary numbers:

In[4]:= dataFitting = 
 FindFit[data1, {2*Sqrt[diffusion]*x*(1/L)*(Pi^(-0.5) + 2*(\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 
           1\), \(100\)]\(\((\((\(-1\))\)^n)\)*
          Erfc[\((n*L)\)/\((Sqrt[diffusion]*x)\)]\)\))), 
   diffusion > 0.0}, {diffusion}, x]

Out[4]= {diffusion -> 0.00911926}

Which gives you the "Best Fit" of:

function = 2*Sqrt[diffusion]*x*(1/L)*(Pi^(-0.5) + 2*(\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 
          1\), \(100\)]\(\((\((\(-1\))\)^n)\)*
         Erfc[\((n*L)\)/\((Sqrt[diffusion]*x)\)]\)\))) /. 
  dataFitting; 
Show[ListLinePlot[data1, PlotStyle -> Orange], Plot[function, {x, 0, 120}], 
     PlotRange -> All]

Which is not very good but "As good as you can get" with that function as your fitting function.

Regards,

Neil

Your first number is {1.*^-16, 0.} which is essentially two zeros. Maybe try to change it {0, 0}?