Molecular orientations

After discussing the thermodynamic aspects of the thiol self-assembly on the surface of liquid mercury let us now take a detailed view on the structure of the crystalline islands of the standing thiol molecules. A sketch of a thiol molecules in the standing-up configuration on liquid Hg surface is shown in Fig. 4.15. The tilt angle, θ, is defined

as the angle between the z-axis and vector connecting the sulfur headgroup with the CH₃endgroup of the same thiol (i.e. thiol molecular axis). I chose the x-axis to point along the S–Hg–S bond of the R–S–Hg–R–S molecule under consideration. Then the azimuthal tilt direction angle, ϕ, is defined as the angle between the x-axis and the projection of the thiol molecular axis onto the xy-plane. Further, three vectors R_nn1, R_nn2andR_nn3are defined as the vectors pointing from the bound Hg atom of the chosen R–S–Hg–R–S molecule to the 1st, 2nd and 3rd nearest bound Hg atoms. Consequently, I define three anglesα1,α2andα3as the angles between thex-axis and vectorsR_nn1, R_nn2,R_nn3, respectively. The probability distribution of the tilt angles is given by

P(θ) = 1 N_th

*_N

th

∑

k

δ(θ−θ_k) +

, withθ_k= 180^◦

π arccos|l_kz|

|l_k|, (4.20) wherel_k is the molecular axis vector of thek-th thiol andl_kz is its projection onto the z-axis, and it is treatedh ias average over molecular configurations. Additionally, the

Figure 4.15: (a) Schematic view of an alkylthiol molecule in the standing phase on liquid Hg;x-axis is aligned along the S–Hg–S bond of a selected molecule;R_nn1,R_nn2 andR_nn3are 2D vectors connecting the selected bound Hg atom with its 1st , 2nd and 3rd nearest neighbors, respectively;α₁, α₂ andα₃ (not shown) are the angles between the x-axis and R_nn1, R_nn2 and R_nn3 vectors, respectively. The tilt angleθ is defined as an angle between the molecular axis (the vector connecting S and CH₃ groups of the same thiol) and its projection onto thez-axis. The azimuthal tilt direction angleϕ is defined as an angle between the projection of the molecular axis onto the xy-plane and thex-axis. (b) The xy-projection of the thiol molecule. The correct aspect ratio is preserved.

surfactant conformations on top and bottom sides of the Hg film are treated as indepen-dent ones, thus, the total number of the molecular configurations used for the averaging equals two times the number of time steps. The distributions of the tilt angles for the dodecanethiol and octadecanethiol systems forσ=1.6114 nm⁻²andA_cs=903.5 nm² are represented in Fig. 4.16a. The observed tilt angles range from 35^◦to 39^◦ for dode-canethiols and octadedode-canethiols, respectively. The broad peaks at 90^◦in the distributions of the tilt angles are due to the laying-down molecules. The broadness of these peaks is caused by the surface corrugations due to the capillary waves, the amplitude of which may reach several Angströms for such system cross-section and room temperature, as well as by occasional folding of the laying-down molecules over each other.

To proceed with the further analysis the following criteria is introduced. A R–S–Hg–

R–S molecule will be considered to be a standing one, if the tilt angle of its both thiol tails is lesser than 45^◦. ThenN_m^isl is defined as the total number of standing molecules (R–S–Hg–S–R) for an instant molecular configuration, i.e. N_m^isl varies with time. Now to check the mutual azimuthal tilt orientation of thiols the distribution of the mutual azimuthal tilt direction of the two thiols belonging to the same R–S–Hg–S–R complex is calculated as wherel_1xy andl_2xy are thexy-projections of the molecular axes of two thiols of the same R–S–Hg–S–R molecule. Additionally, the mutual orientation of the S–Hg–S bonds for the surfactants lying within 10 Å (corresponds to three coordination spheres of bound Hg atoms) from each other is calculated as

P(ξ) =

whereh_mis the two-dimensional (2D) vector of the S–Hg–S bond belonging to them-th R–S–Hg–S–R molecule,r_mn is the distance (in thexy-plane) between them-th andn-th bound Hg atoms, andNN_tot is the total number of bound Hg atom pairs that lie within the sphere of the radius of 10 Å for a given instant molecular configuration. The P(ω)

0

Figure 4.16: Molecular orientations in the islands of standing octadecanethiol (SC18) and dodecanethiol (SC12) molecules.σ =1.6114 nm⁻²andA_cs=903.5 nm². (a) Dis-tribution of the tilt angles,P(θ)(Eq. 4.20); (b) distribution of the mutual azimuthal tilt direction of the thiols of the same R–S–Hg–S–R surfactant complex,P(ω)(Eq. 4.21);

(c) distribution of the mutual orientation of the S–Hg–S bonds of the neighboring sur-factants,P(ξ)(Eq. 4.22); (d) distribution of the azimuthal tilt directions relative to the S–Hg–S bonds,P(ϕ)(Eq. 4.23).

andP(ξ) distributions (for both, SC18 and SC12 molecules) are shown in Fig. 4.16b and 4.16c, respectively. From these distributions one can see that in the SC18 as well as SC12 islands of the standing thiols are tilted in the same direction and the S–Hg–S bonds of the neighboring surfactants are aligned. From broader peaks of the SC12 systems one can infer that the SC12 islands possess larger degree of orientational disorder. In order to find out the azimuthal tilt direction of thiols relative to the S–Hg–S bonds, I compute the respective distribution

where l_ixy is the xy-projection of the molecular axis of the i-th thiol belonging to the m-th R–S–Hg–S–R surfactant. The P(ϕ) distribution is shown in Fig. 4.16d. This distribution reveals that the thiols tilt direction creates an angle of∼75^◦and 81−83^◦ with the S–Hg–S bonds in the case of SC18 and SC12 systems. The pronounced tail of theP(ϕ)distribution of the SC12 systems confirms the above suggestion of the larger degree of orientational disorder for these systems.