GENERATION OF POLYNOMIAL EQUATION FOR THE DYNAMIC MECHANICAL ANALYSIS OF TERTIARY BUTYL ACRYLATE COMBINED WITH DIETHYLENE GLYCOL DIACRYLATE RESIN USING MATLAB

This is a project to provide a solvable equation for DMA analysis data for the loss modulus, storage modulus and tan_delta values obtained from the analysis. The Dynamic Mechanical Analysis was carried out in the research paper involving the 4D printing of Tertiary Butyl Acrylate combined Diethylene Gylcol Diacrylate, for which various characterizations were undergone. I have co-authored the paper, and we have performed the DMA characterization. There are no conflicts of interest for the authors regarding this mini-coded project.

The Dynamic Mechanical Analysis is a technique used to study and characterize materials. It is most useful for studying the viscoelastic behavior of polymers. A sinusoidal stress is applied and the strain in the material is measured, allowing one to determine the complex modulus (Storage Modulus and Loss Modulus). The temperature of the sample or the frequency of the stress are often varied, leading to variations in the complex modulus; this approach can be used to locate the Transition temperature of the material, as well as to identify transitions corresponding to other molecular motions.

Headers for the DMADATA file

FIRST COLUMN - Temperature

SECOND COLUMN - Storage Modulus

THIRD COLUMN - Loss Modulus

FOURTH COLUMN - Tan_delta

The DMADATA.txt file is attached to the project through a google drive link ( CLICK HERE TO VIEW THE DMA DATA FILE ) and the users are requested to see the data by placing the data on the same folder as that of the MATLAB directory to enable loading the data from the file. The data file is loaded into the MATLAB, and further is plotted over graphs in separate fashion. The code represents the plotting of the graphs, and overlapping these graphs with the curve fits generated with the 24th order polynomial that fits the curve, to the best accuracy. The curve fit data is generated and the coefficients of the 24th order polynomial are taken from the equation and are displayed.

Equations such as these could be generated in order to facilitate the authors with the intention to generate the data for Dynamic Mechanical Analysis, only in order to determine the Transition Glass temperature, which remains constant for a material, for other dynamic uses, it is required that they analyse their unique parts. By solving the equations, the approximate values of the data are to be used by the authors, who are unable to take data as in the case of COVID-19, whereas the accurate data sharing is not appreciated.

clear all
close all
clc
%loading the DMA data obtained for printing tBA-co-DEGDA material at print speed of 70 mm/sec and 70 print pulses/sec
data=load('DMADATA.txt')
%setting up the print parametes from the data containing 4 columns 
temperature=data(:,1);
storage_mod=data(:,2);
loss_mod=data(:,3);
tan_Delta=data(:,4);
% finding the coefficients and creating the curve fitting for the 24th order of polynomial, since it fits almost exactly
co_efficients1=polyfit(temperature,storage_mod, 24);
predicted_data1=polyval(co_efficients1, temperature);
%plot drawing for the storage modulus
figure
plot(temperature, storage_mod, 'linewidth', 3)
grid on
xlabel('temperature')
ylabel('storage_mod')
hold on
plot(temperature, predicted_data1, 'linewidth', 3, 'color', 'r')
co_efficients2=polyfit(temperature,loss_mod, 24);
predicted_data2=polyval(co_efficients2, temperature);
%plot drawing for the storage modulus
figure
plot(temperature, loss_mod, 'linewidth', 3)
grid on
xlabel('temperature')
ylabel('loss_mod')
hold on
plot(temperature, predicted_data2, 'linewidth', 3, 'color', 'r')
co_efficients3=polyfit(temperature,tan_Delta, 24);
predicted_data3=polyval(co_efficients3, temperature);
%plot drawing for the storage modulus
figure
plot(temperature, tan_Delta, 'linewidth', 3)
grid on
xlabel('temperature')
ylabel('tan_delta')
hold on
plot(temperature, predicted_data3, 'linewidth', 3, 'color', 'r')

disp('These are the coefficients of the 24th order polynomial equation for storage modulus.')
for j = 1:25
modified_storage_mod=disp(co_efficients1(1,j))
end
disp('These are the coefficients of the 24th order polynomial equation for loss modulus.')
for i =1:25
modified_loss_mod=disp(co_efficients2(1,i))
end
disp('These are the coefficients of the 24th order polynomial equation for the ration between moduli.')
for k=1:25
modified_tan_delta=disp(co_efficients3(1,k))
end
%solving the equation generated from the 24th order polynomial will aid in the solution of DMA, for the tertiary butyl acrylate - diethylene glycol diacrylate material
disp('solving the equation generated from the 24th order polynomial will aid in the solution of DMA, for the tertiary butyl acrylate - diethylene glycol diacrylate material')

The graphs obtained for the curve are provided as shown below:

The legend is as follows:

• RED PLOT - curve fit
• BLUE PLOT - actual curve

The frequency was maintained at 1 Hz throughout the variation of temperature range from 17 degrees to 68 degrees.