Schematic representation of the inverse hexagonal (HII) mesophase of monoolein and its crystal lattice parameters (left), and the structural formulas of GMO and tricaprylin (right).
(a) Structure of the GMO molecule used throughout the process of building the GMO tubes. Axis (x) is the longest axis of rotation. Axes (y) and (z) are presented for completeness; (b) Graphical representation of a generated GMO ring with notations of the radius of the internal empty circle and the pivotal radius R w and R p; (c) Skewed side view of a constructed GMO tube (see Sec. III A for detailed explanations).
(a) Pivotal surface, A p, as a criterion for determination of the distance between GMO rings – 2R p (for parameter definitions, see Sec. III A and Eqs. (10) and (11); (b) Explanation of the process of GMO ring sectorization using the sector angle θ. (see Sec. III A for details).
Initial distribution of water molecules obtained by the Monte Carlo rejection sampling routine (see Sec. III B for details). The cylindrical volume of the distribution is rotated about the y-axis for a better view.
The effective part of a single GMO ring, which is initially hydrated; the same structural unit is used for calculation of the positions of the GMO molecules along the ring.
The pivotal area and the pivotal volume estimation by fitting an appropriate dataset with Eq. (11). The values of R w and A w are taken from Table I.
(a) Probability mass function and (b) cumulative distribution function of the distances between 1514 oxygen atoms of water molecules inside the water cylinder of a GMO/water structure. The oxygen lattice forms a cylindrical volume with no submerged GMO heads within (R w = 12 Å, h = 100 Å) (see Sec. III B for explanations).
Front (a) and side (b) visualization of the coordinate set of the initial structure of a GMO/water system. The first GMO ring of the structure is removed to satisfy the PBC requirements.
An illustrative example of the GMO/water structure obtained after the MD simulation of system with N l = 17 (Table I): (a) radial view; (b) side view with periodic boundary conditions applied. Due to the careful initial arrangement of water molecules and their quantity (fitting of water density), there is no depletion or significant excess of molecules.
Probability mass function of hydrogen bond distances between the GMO and the water molecules (G/W) and between the water molecules themselves (W/W).
Distribution of water density across the three cylinders with different radii: (a), (c), and (e) – radial distribution (xy-coordinates); (b), (d), and (f) – longitudinal distribution (z-coordinate). All z-positions of the planes of the GMO circles are marked with arrows.
Radial distribution function, , of the distance between the hydroxyl oxygen of GMO, , directed towards the water cylinder, and oxygen atoms of the water molecules. Only the xy-component of the distance is used.
Parameters of the studied systems at various water weight fractions and GMO/tricaprylin weight ratios26 (dilution line) at t = 25 °C: the hexagonal lattice parameter of the inverse hexagonal phase, α (Eq. (1)); the lipid volume ratio, ϕ l; the radius of the water cylinder, R w (Eq. (2)); area at the Luzatti interface, A 0 (Eq. (3)); the number of lipid molecules in a GMO ring, N l (Eq. (8)); the effective sector angle, θ eff (Eq. (9)), and the radius of the pivotal area, R p.
List of rejection sampling rules used to determine the coordinates of oxygen atoms in a randomized water lattice and to fix the positions of the hydrogen atoms of water molecules. See Sec. III B for details.
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