The compatibility characteristics of TPS-based polymer blends were computed with the help of the Blends module. The screening of monomers, facilitated by the Blends module, provides a simplified yet effective approach, as the interactions between monomers serve as indicators of full polymer chain compatibility within this computational framework, allowing efficient prediction of polymer blend behavior [11] . The principle behind the Blends module calculations is expressed by a combination of the Flory-Huggins model and methods of simulations applied to molecules [12] . The ultimate aim is to calculate the compatibility of binary mixtures. These binary systems are evaluated in all sizes, ranging from small systems to relatively huge molecular models. Blends module algorithms establish the distinction between the two constituents of the system by assigning individual roles: one component is assigned the base (b) role, and the screen (s) role is assigned to the second [13] .

When two molecules are in relative spatial proximity, a phenomenon of intermolecular interaction will take place. The quantity of interaction energy between the two chemicals is termed binding energy. Blends algorithms combine binding energy parameters with coordination numbers during the compatibility investigation to generate the mixing energy (E_mix) and chi parameter [14] . Estimation of binding energies requires careful consideration and judgment of the high molecular orientation applied to the two constituents during screening [15] . An extensive number of molecular orientations is provided by the module, which subsequently estimates the energies of interaction related to every configuration. After screening for the binding energy, the Blends algorithm executes the sampling of those configurations considered to be energetically satisfactory [16] . The sampling method utilized here is an altered version of the molecular Silverware algorithm [17] : it is called excluded volume constraints. Excluded volume constraint sampling methods are employed to prevent spatial overlap between particles or molecules [18] . In this approach, a proposed configuration is generated and checked for particle overlap; configurations exhibiting overlaps are rejected, and new ones are sampled [19] . Here, the constraint is applied based on the excluded volume associated with each molecular configuration. In this sampling technique, the two molecules are joined together in order to establish a proximity of their van der Waals surfaces. Four distinct possible pairs will be generated after any base-screen combination. The binding energy value of each individual pair is expressed as:

Let us consider a binary mixture made of component A and component B. The binding energy of the interaction between those molecules is calculated using the excluded-volume constraint method. In this method, the calculation of the binding energy is initiated with two chemical compounds that are a representation of the condensed state [20] . After the estimation of binding energies is completed, the module automatically establishes the coordination numbers as well [21] . Once those parameters have been generated, the Blends algorithm performs the calculations of the mixing energy (E_mix) based on the equations derived from the Flory-Huggins model.

The efforts to understand the thermodynamics of polymeric solutions are represented by the Flory-Huggins theory. The theory provides a more precise investigation compared to the ideal solution theory. The ideal solution theory presents various conditions of limited ability [22] . Two of the most important limitations of the theory are the large size of polymeric systems compared to solvents, as well as the possibility of chemical interaction between different molecules. The Flory-Huggins model stands out as, without a doubt, the best and least complicated theory for the assessment of binary mixtures thermodynamics of phase separation and mixing [23] .

According to the model, the free energy of mixing of the binary system is expressed by the general equation:

$\Delta G/RT={\Phi }_b/n_b\ln {\Phi }_b+{\Phi }_s/n_s+\chi {\Phi }_b{\Phi }_s$ (1)

where: ΔG = free energy of mixing per mole;

Φ_b = volume fraction of component A;

Φ_s = volume fraction of component B;

Χ = interaction parameter;

T = absolute temperature;

R = gas constant.

The combinatorial entropy is expressed by the first two elements. Due to their negative mathematical contribution, they provide favorable conditions for a mixed state, which is preferred over the pure components [24] . The term at the end expresses the free energy generated due to interaction. A reliable sign of the attainment of a mixed state is the negative value of the chi interaction parameter.

If the parameter of interaction is positive, a mixed state is inferred to be disfavored [25] . Moreover, when there is equilibrium between both conditions, the algorithm will generate different phase diagrams. The following equation represents the χ interaction parameter:

$\chi =E_{\text{mix}}/RT$ (2)

where E_mix = mixing energy.

Mixing energy is defined as the free energy difference due to interactivity occurring between the pure state and blended state. The classical Flory-Huggins model suggests that each constituent molecule occupies a geometric arrangement of the points in space at which the atoms or ions of a crystal occur, i.e., a lattice site. Supposing that a lattice site has a coordination number Z, the mixing energy is defined by:

$E_{\text{mix}}=\frac{1}{2}z\left(E_{bs}+E_{sb}-E_{bb}-E_{ss}\right)$. [26] (3)

where, E_bb = Binding energy of Base-base pair;

E_ss = Binding energy of Screen-screen pair;

E_bs = Binding energy of Base-screen pair;

Z = Coordination number for each pair (which is the number of molecules of component B that can be packed around a single molecule of component A within the excluded-volume constraints).

A positive sign of the attainment of a mixed state is the negative value of the chi interaction parameter. If the parameter of interaction is positive, the mixed state is inferred to be disfavored. Moreover, when there is an equilibrium between both conditions, the algorithm will generate different phase diagrams. The combinatorial entropy is expressed by the first two elements. Due to their negative mathematical contribution, they provide favorable conditions for a mixed state, which is preferred over the pure components. The term at the end expresses the free energy generated due to interaction.

Three TPS-based polymer mixtures were selected for the compatibility analysis: TPS/NR and TPS/PCL. To begin, the individual structures of the constituting monomers were manually sketched on atomistic 3D windows. Subsequently, energy minimization of sketched structures was carried out through geometry optimization with 500 iteration cycles utilizing the COMPASS force field [27] and SMART algorithm. Energy minimization was conducted using the Forcite module, producing new 3D molecular structures with optimized geometries illustrated in Figures 1(a)-(c) , where hydrogen, oxygen, and carbon atoms are depicted as white, red, and grey spheres, respectively.

Calculations were executed with the help of the “blends” module. The blends module allows the screening of interaction energy between polymer and polymer, between polymer and solvent, as well as between solvent and solvent. The selection of the monomer to be studied was performed by specifying its head and tail atoms, followed by structure optimization before submission to the calculation tab.

The selected monomers were entered in the first row, and their roles—screen or base—were specified in the second. An overview of the calculation tab layout is provided in Figure 2 . In this work, TPS served as the base in every blend investigation. The reference temperature was kept at 298 K. Calculation outputs of the mixing task include mixing energy (E_mix), binding energies (for the base-base, base-screen, and screen-screen combinations), and χ chi values. The module task of mixing provides the user with an accurate sampling of the mixing characteristics of the selected binary blends. Blends allow the screening for interaction energy between polymer and polymer, between polymer and solvent, as well as between solvent and solvent. For further extrapolations, the blending characteristics of TPS/Natural rubber (NR) and TPS/Polycaprolactone (PCL) binary mixtures of monomers were recorded.

For the data analysis of mixing effectiveness of TPS blends, the following parameters have captured our attention: binding energies distributions (E_bs, E_bb, E_ss), Chi parameter χ, and energy of mixing (E_mix).

A strong indicator of structural compatibility between the input monomer pair is the similarity among the binding energy distribution curves for base-base (E_bb), base-screen (E_bs), and screen-screen (E_ss) interactions [29] .

From the plots in Figure 3 , a stronger overlap of binding energy distribution curves is observed for the TPS/PCL mixture ( Figure 3(b) ) relative to the TPS/NR system ( Figure 3(a) ). This suggests that TPS/PCL possesses better structural compatibility, whereas TPS/NR shows the least. This is justified by the fact that TPS/PCL forms compatible blends because of the hydrogen bonding interaction between the ester carbonyl of PCL and the OH groups on starch [30] . Furthermore, it has been observed that the addition of NR to TPS is restricted by phase separation due to poor compatibility between both constituents [31] .

The χ interaction parameter is a unitless property expressing the difference in energy between solvent-polymer interaction and a polymer-free solvent. Its value can be positive or negative [32] . A χ (chi) value close to zero indicates miscibility, as does an E_mix value that is close to zero [33] . Lower χ (chi) and mixing energy values for the TPS/PCL system ( Table 1 ) reflect higher compatibility. These results further confirm what has been implied from the binding energies distribution analysis.

Configurations with the lowest interaction energies

Through the Blends module, pair configurations (base-screen, base-base, and screen-screen) can be organized based on energy to inspect the characteristic binding and non-binding (non-contact) sites. This is demonstrated in Figure 4(a) and Figure 4(b) , where non-binding sites are denoted as NON-CONTACT.