# Validity of pseudo first order (PFO) approximation of binary adsorption kinetics

## Description

ADmix2isLin.m is a MATLAB function that gives the outcome 1 if modeling of binary adsorption kinetics by using the pseudo first order (PFO) approximation is appropriate, zero otherwise. Input parameters are parameters of reaction rate equation: ka1 ka2 kd1 kd2 No1 No2 M where ka refers to rate constant of adsorption, kd refers to rate constant of desorption No refers to the overall number of adsorbate molecules in the system M is the number of adsorption centers on the surface Reaction rate equations are N1'=ka1*No1*(M-N1-N2)-kd1*N1 N2'=ka2*No2*(M-N1-N2)-kd2*N2 The solutions to RRE are N1=Ne1+Nt11*exp(-t/tau1)+Nt12*exp(-t/tau2) N2=Ne2+Nt21*exp(-t/tau1)+Nt22*exp(-t/tau2) Steady state values Ne1 and Ne2 are outcome of the function STEADY_mix2lin.m Transient amplitudes Nt,ij are the outcome of the function TRANSmix2lin.m Time constants are the outcome of the function TAUmix2lin.m

## Files

## Steps to reproduce

All functions are independent. The function ADmix2isLin.m is obtained by training an artificial neural network to recognize if the solution to linear system of reaction rate equations (RRE) is in accord with the solution to matrix Riccati differential equations (MRDE). The underlined theory is explained in the linked paper. RRE set is N1'=ka1*No1*(M-N1-N2)-kd1*N1 N2'=ka2*No2*(M-N1-N2)-kd2*N2 MRDE set is N1'=ka1*(No1-N1)*(M-N1-N2)-kd1*N1 N2'=ka2*(No2-N2)*(M-N1-N2)-kd2*N2 The input for TAUmix2lin.m is ( ka,kd,No ) where ka, kd and No are columns of two elements, the first one being placed up and the second one down The input for TRANSmix2lin.m and for STEADY_mix2lin.m is ( ka,kd,No,M ) The input for ADmix2isLin(x1) is x1=[ka1 ka2 kd1 kd2 No1 No2 M]