Download Sucrose hydrolysis

Problem 1
Sucrose hydrolysis
Catalytic reaction of sucrose hydrolysis is a first rate reaction, hence is governed by the following
equation:
𝑑𝑐
= −𝑘𝑐(𝑡)
𝑑𝑡
1. Using analytical or numerical techniques compute the evolution of c in time.
2. Transform the equation into linear form.
3. Import data to MATLAB from given Excell file. It contains a sequence of measured concentration
of sucrose in the experiment .
4. Plot data.
5. Confirm linear correlation by computing 𝑅 2.
6. Compute linear regression model using matrix method.
7. Compare results with the ones computed using built-in MATLAB functions.
8. Analyze residuals, plot its histogram.
Problem 2
Controlled drug release systems
Mesoporous silica structures are often considered as a future system for controlled release of the drugs.
On of the methods is to functionalize its inner surface with polar groups and thus create stopping
mechanism for the drug diffusion. The state-of-the-art technique to design and analyze such constructs
are Molecular Dynamics computations performed on High Power Computing grids. In order to calculate
self-diffusion coefficient one has compute so called MSD (Mean Square Displacement) of the drug
molecule. The MSD is the average square distance of the molecule from its original position. What is
interesting the MSD is related with self-diffusion coefficient by so called Einstein’s relationship:
𝐷=
1
𝑑𝑀𝑆𝐷
lim
6 Δ𝑡→∞ 𝑑(Δ𝑡)
Thus by measuring MSD vs. time and calculating its slope one can compute D. The csv file contains
already computed (approx. 4000 hours of CPU time) MSD vs. time of galactose molecule in a 𝑁𝐻3+
functionalized SBA-15 system. Your task is to compute the D of galactose.
1.
2.
3.
4.
Download csv file containing MSD of galactose in SBA-15 vs time.
Choose appropriate regime (time interval) where the MSD is linear.
Perform linear regression.
Compute self-diffusion coefficient in 𝑐𝑚2 /𝑠.