To perform quantum chemical simulations using Gaussian, it is first necessary to construct the molecule of interest on GaussView, a pre-post program for Gaussian that enables a series of Gaussian calculations and analyses, including modelling the molecule, performing quantum chemical calculations in Gaussian and visualising the calculation results. GaussView is a pre-post program for Gaussian that enables a series of Gaussian calculations and analyses, including modelling of molecules, execution of quantum chemical calculations in Gaussian and visualisation of calculation results. In this study, cWA molecules were constructed, calculated and analysed in a window on GaussView. The construction of the cWA molecule is described below.

The amino acids Ala and Trp, which constitute the cWA, were selected in Biological Fragments and placed in the window. These amino acids were then combined to form the CDP. Subsequently, the following molecules were obtained by paying attention to optical isomers and adjusting dihedral angles, etc. (Fig. 1.1).

Fig. 1.1 Molecular structure of cWA created using GaussView

After constructing the molecules for the calculations, the solvation free energies were calculated. In order to reduce the calculation time, the calculations were carried out using the semi-empirical method PM7. The calculations yielded a model of the solvation cavity.

In order to create cavities with solvent molecules, the solute molecules need to pull some of the solvent molecules that are attracted to each other apart. This requires energy, which is referred to as the cavity cost. The stronger the attraction between solvent molecules, the greater the energy required to pull them apart, and therefore the greater the cavity cost. The larger the solute molecules, the larger the cavity and the more energy is required to pull them apart. Therefore, the strong interaction between solvent molecules and the large size of the solute molecules act in the direction of reduced solubility.

The solvation free energy calculated in this study is expressed by subtracting the cavity cost from the intermolecular interaction energy between solute and solvent. The higher this energy is, the higher the solubility. Therefore, although the present study analysed the cavity of one type of molecule in one solvent, it is possible to consider the solubility of the target CDP molecule in biological membranes and water by conducting additional analyses using phospholipids, which constitute biological membranes, as well as water, as solvents and by analysing cavity size and solvation free energy using similar CDPs and comparing the results. The results of this analysis are also compared with the analysis of cavity size and free energy of solvation using similar CDPs.

Our modeling shows that cWA is highly hydrophobic and that cWA is a very suitable material to be mixed into paints, which shows strong promise for social implementation.

Fig.1.2 Calculation of solvation free energy of cWA in water

Resistance that obstructs ship propulsion includes shape resistance caused by the shape of the ship, wave-making resistance consumed by the waves generated by the ship, frictional resistance created by friction with seawater, air resistance, and others. At the 62nd session of the International Maritime Organization's Commission for the Protection of the Marine Environment held in July 2011, the Convention on the Prevention of Marine Pollution (CMP) established standards to control greenhouse gas emissions from ships' fuel consumption. The Convention sets standards for the control of greenhouse gas emissions from ships' fuel consumption. The Convention defined the Energy Efficiency Design Index (EEDI) (Equation 2.1). When barnacles are attached to the loaded weight, the denominator value increases and the EEDI value decreases, as shown in Equation 2.2. From this, it can be said that barnacle adhesion affects the propulsion of a vessel in an energy efficient manner.

In fluid dynamics, frictional resistance is considered as follows. The water flow around the ship has a sufficiently high Reynolds number, and the frictional stress  near a smooth wall surface is expressed by Equation 2.3. where  is the viscosity coefficient, u and v are the velocity components in the flow direction and perpendicular to the wall, u' and v' are their variation components, y is the vertical distance from the wall, and  is the density. The second term is called Reynolds stress, which is unique to turbulent flows and is considered the main component of turbulent drag. When barnacle encrustation requires the vessel to generate more velocity than apparent in order to make the apparent velocity of the vessel the same as before barnacle encrustation, u and v increase, and the Reynolds number increases accordingly.

In Chapter 2, it was shown that the bottom area of a vessel has been shown to play a role in the resistance to the vessel. Therefore, modelling was carried out to determine the extent to which the surface area increases when barnacles are attached. This time, the complex shape of the barnacles was simplified and modelled by approximating them as cones. l is the length of one side of the unit square, h is the height of the cone and m is the length of the generatrix of a cone with a base that just fits in this square, and the mathematical model was created. This was organised into the following model (Equation 3.1).

Substituting 3 cm, the average size of barnacles, into this equation yields l = 4, m = √13, and S ≈ 26.09, approximately 1.6 times the area of the square l^2 = 16 without barnacles attached. This result suggests that as the area increases, the resistance increases.

The barnacles' attachment was plotted on the coordinate plane using python (Fig. 3.1). Future work will involve modelling the increased surface area of the vessel caused by barnacles with this complex geometry.