I have used in this qe=qm*exp(-KE*(R*T*ln(1+1/Ce))^2) form, but it failed to work. Also, we can fix the value of R, but T has different values at different temperatures, so will we change the value of T in the equation if we want to apply the equation to data obtained at different temperatures?
Generally, the DR equation is applied to isothermal data so the temperature should be constant. Depending on what you want to determine, the linear form is usually the most useful as you can then relate the gradient to the temperature, gas constant and the potential of the gas phase molecule. The equation relates uptakes to different pressures along an adsorption profile, so unless you have data at different pressures, you would not be able to keep the other factors constant (including T), in order to determine the micropore filling.
Generally, the DR equation is applied to isothermal data so the temperature should be constant. Depending on what you want to determine, the linear form is usually the most useful as you can then relate the gradient to the temperature, gas constant and the potential of the gas phase molecule. The equation relates uptakes to different pressures along an adsorption profile, so unless you have data at different pressures, you would not be able to keep the other factors constant (including T), in order to determine the micropore filling.
What software are you using for nonlinear regression?
This expression worked fine for me (the fit was not good, but worked)
You should change the temperature for each isotherm obtained.
I used this equation: qeq =q*exp(-Ke*(R*T*ln(1+1/Ceq))^2).
I used OriginPro8.5 and a rotine that I'm developing for adsorption in Matlab. For both the results were the same for qm and Ke.
What error does Origin report?? Maybe changing the value of the initial parameter value will solve the problem.
First try reducing the K value to 0.001 or lower if you have not tried it yet.
I do not recommend that you substitute Ke=K*(R^2)*(T^2) for K, since you will estimate the error of the constants T and R (which are constants) along with the error of K.
I already have tried the equation you suggested [qeq =q*exp(-Ke*(R*T*ln(1+1/Ceq))^2)], but if you take R and T as constants, it will give the same results as qe=qm*exp(-Ke*ln(1+1/Ce)^2) this equation gives. however, 1) if you give values to R=8.314 and T=298...then it does not give any results. 2) if we fix the values of R and T still it doesn't give any results, and 3) by changing the initial value of Ke, and fixing the values of R to 8.314 and T to, for example, 298 it gives the same results as qe=qm*exp(-Ke*ln(1+1/Ce)^2) this one, where the value of K was determined as mentioned in the previous ans. Try it.
It seems to me that you are setting the T and R as parameter when you create the function. If you are doing this, try to set T and R as constant when you create the equation.
Using qeq =q*exp(-Ke*(R*T*ln(1+1/Ceq))^2) and qe=qm*exp(-Ke*ln(1+1/Ce)^2),
and recalculating using Ke=K*R^2*T^2, results in 3% deviation for Ke and Ke deviation (for all data sets that i have). I checked this sometime ago. For all adsorption isotherms models that has an constant in the model i got this results. Thats why i recommended you to use the first expression.
Changing the initial value of a parameter will not change the values of the regression if the regression is considered satisfactory...
But if the regression was NOT considered satisfactory (you saidit failed to work" ), I recommended you to change the value of the initial kick. Doing this, mabe the program will fit the model to the data set.
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