I have 4 sets of values of equilibrium partial pressure of the solute and loading on bed for 4 different temperatures (each set with 6 data points). After drawing the isotherms, how should I find the equilibrium partial pressures for a chosen loading, using MS-Excel or Matlab, so that an Isostere can be plotted, without fitting the drawn isotherms to any known isotherms like BET, Langmuir etc.
Similar que. in my mind if any knowledgeable person share your expertise
"Isostere plot usefulness? where it lies in gas adsorption studies??"
As I get you right, you have 4 "Isotherms", each described with 6 data points, but you do not fit these 6 points to get a whole isotherm.
If you want to get the partial pressure for a choosen loading you need a mathematical model to interpolate between your data points above and below your choosen loading. Of course you must not use Lagmuir, BET, etc. you can also choose a linear interpolation. No matter what you might want to do: from my point of view you need a mathematical model to interpolation between your measured points.
I prefer to use a spline function to interpolate between points, rather than an isotherm model, but I always have many more data points than you (more like 60 than 6). With only 6 points a spline may not be reliable. Free add-ins for Excel which allow splines to be fitted to data are available on the web, and I'm sure Matlab will do this also.
@Mihir, Isostere is drawn generally using ln(p) in y axis and 1/T in x axis and the slope that we get, gives d(lnp)/d(1/T).This term also appears in calculation of isosteric heat of adsorption.And as you know,we have a concept that if an adsorbent bed is energetically homogeneous, then the Isosteric heat will be independent of the value of loading. Hence if we plot isosteres for 3 or 4 loadings and see that the slopes of the lines (generally we get st.lines) are nearly same we may verify the above fact. This can be one use of Isosteres
Thanks a lot,Thomas and Peter for sharing your approaches to solve the problem.
You can just plot isotherms in one figure, and draw horizon lines for a certain adsorption amount, then draw vertical lines from the intersection points of the horizon line and the isotherms. In this way, you can determine the p values for a certain adsorbate uptake at different temperatures. And at last plot d(lnp)/d(1/T).
However, this method may not be accurate if you start with a 6-point isotherm.
@ Ayoup can the vertical and horizontal lines as stated by Xin be drawn with any direct command or option in excel ?
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