u[r_,ϵ_,σ_]:=4 ϵ((σ/r)^12-(σ/r)^6);

Manipulate[
Plot[u[r,e,s],{r,0,4},PlotStyle->Directive[Red,Thick],PlotRange->{-1.2e,e},Frame->True,FrameLabel->{"r","u"}],
{e,0.1,10},
{s,0.5,2}]

v2=Integrate[4π r^2 (1-Exp[-β u[r,ϵ,σ]]),{r,0,Infinity},Assumptions->{β>0, ϵ>0,σ>0}]

LogLinearPlot[Evaluate[v2/.{σ->1,β ϵ->1/T}],{T,0.5,100},PlotStyle->Blue,Frame->True,FrameLabel->{"(SuperStar[T])","(B^2)"}]