Chrysene

During the third trimester of pregnancy, personal monitoring was carried
out as previously described (Perera et al. 2003 (link)). Vapors and particles ≥2.5 μg in diameter were collected
on a precleaned quartz microfiber filter and a pre-cleaned polyurethane
foam cartridge backup. The samples were analyzed at Southwest Research
Institute (San Antonio, TX) for benz[a]anthracene, chrysene, benzo[b]fluroanthene, benzo[k]fluroanthene, BaP, indeno-[1,2,3-cd]pyrene, disbenz[a,h]anthracene, and benzo[g,h,i]perylene as described by Tonne et al. (2004) (link). For quality control, each personal monitoring result was assessed as
to accuracy in flow rate, time, and completeness of documentation. All
of the 183 subjects had samples of acceptable quality.

To explore the formation of metal-organic precursors comprising chrysene tectons, we used the coarse-grained MC model developed previously [24 (link),25 (link),26 (link),27 (link)]. Specifically, the chrysene molecules, abbreviated here as ch, were represented by flat rigid collections of four interconnected segments, each corresponding to one benzene ring, as shown in Figure 1. These monomers were equipped with two differently distributed active interaction centers imitating the halogen substituents (red arrows therein). The molecules were placed on a triangular lattice of equivalent adsorption sites mimicking the catalytically active (111) metallic surface (e.g., gold, silver, copper). For convenience, the lattice constant of the adsorbing surface a was assumed to be equal to 1. A single segment of ch was allowed to occupy one adsorption site (lattice vertex), and the consecutive segments of ch were centered at the next neighbor sites of the lattice (i.e., they were separated by a distance of $a\sqrt{3}$ ). The active centers of chrysene tectons provided directional interactions with the coadsorbed metal atoms modeled as single segments. The range of these metal–organic interactions was limited to nearest neighbor sites, measuring from the vertices 1–12 of the polyhexagonal contour shaded in Figure 7. The formation of metal–organic links sustaining the precursors was possible only when the interaction directions of the contributing molecules were collinear, as illustrated in the figure. In this case, the energy of interaction assumed for a single link was equal to 2ε, where ε stands for the energy of elementary metal–monomer interaction. Nonlinear 120° linker-metal-linker configurations contributed with energy ε, reflecting the effect of repulsive interactions between active molecular segments located too close to each other. Figure S4 in the Supporting Information section shows the possible one- and bi-molecular metal-linker configurations along with their corresponding energies.
In the calculations, the conventional canonical MC method with Metropolis sampling was used, where the total number of species N, temperature T, and system size A (here area of the adsorbing surface) were fixed [38 ]. To eliminate edge effects, periodic boundary conditions in both planar directions were imposed. The simulations started with a mixture of N_l molecules of a given isomer and N_m metal atoms distributed randomly on a rhombic fragment of a triangular lattice with side L equal to 200a (i.e., 200 by 200 adsorption sites); $N=N_l+N_m$ . Next, the adsorbed overlayer was equilibrated in a series of trial moves, each of which corresponded to a single MC step. During one MC step, a molecule or metal atom was picked up at random, and its potential energy in the current position, U_o, was calculated by reckoning the elementary directional interactions (ε) and taking into account the geometric conditions discussed previously (preferred linear →•← links). Next, the selected component was translated to a new random position on the lattice. In the case of chrysene isomers, these units were additionally rotated in-plane by a multiple of 60 degrees. If in the new position, there was enough space (sufficient number of unoccupied adsorption sites), the selected component was inserted therein; otherwise, it was returned to its original site, and the calculation started again. The potential energy of the new configuration, U_n, was determined using the same procedure as for U_o. To accept this configuration, the Metropolis criterion was used with the acceptance probability $p=\mathrm{m}\mathrm{i}\mathrm{n}[1,\exp \left(-\frac{∆U}{kT}\right)]$ , where $∆U=U_n-U_o$ and k stands for the Boltzmann constant. The calculated value of p was compared with a uniformly distributed random number $r\in \left(\mathrm{0,1}\right)$ . If $r<p$ , the new configuration was accepted; in the opposite case, the selected atom or molecule was moved back to the initial (old) position on the lattice and the next MC step was performed. In the simulation, typically, $N\times {10}^5$ steps were made at a given T, the last 10% of which were used for the calculation of average values. Moreover, to minimize the risk of trapping the modeled systems in metastable states, gradual cooling of the adsorbed overlayer was implemented. During this procedure, the temperature was linearly decreased from 0.51 to 0.01 using 500 steps of equal length.
Surface coverage θ was defined as the average number of adsorbed segments per lattice site, that is, $(4N_l+N_m)/L^2$ . Quantitative descriptors of the simulated systems presented here, including coordination functions, cluster size distributions, and order parameters, are averages over ten independent replicas.
Energies and temperatures of our model were expressed in the units of ε and $\left|\mathsf{\epsilon }\right|/k$ , respectively. Precisely, the values of system energy and temperature are dimensionless and have no physical units. Instead, they are real numbers that specify how many times the elementary portion of energy, ε, and the temperature, |ε|/k, fit into the simulated values of energy and temperature, T, respectively. Note that ε can be given in any energy units (J, cal, eV), so that the units of temperature |ε|/k are automatically adjusted. To maintain the broad applicability of the model, we decided to use only numerical values for the parameters and leave the choice of units to the reader, depending on the specific system. For that reason, our model is dependent on just one working parameter, ε, which describes the single metal–linker interaction and whose numerical value was assumed to be −1. Accordingly, the reduced Boltzmann constant, k, was set to 1 to make temperature, T, dimensionless.
In summary, the input parameters in our model are L, ε, N, and T, with the first two being fixed in all of the calculations, that is $L=200$ and $\epsilon =-1$ . The targeted parameters include the orientational parameters δ_a and δ_c, the fractions of homochiral (S-S and R-R) and heterochiral (R-S) metal-mediated links, and the statistics of aggregate size. The parameters δ_a and δ_c were determined by counting the number of molecules with their arms (a) and cores (c) oriented in the three primary directions of the triangular lattice. Figure S5 in the Supporting Information section illustrates the definitions of the core- and arm-based orientation directions. The determined numbers of molecules with distinct orientations were inserted into Equation (S1) in that section. The fraction of homo- and heterochiral links was calculated by accounting for metal atoms coordinated with two enantiomers of the same type for homochiral links and of opposite types for heterochiral links. These numbers were divided by the total number of metal atoms in the system (N_m) to yield the corresponding fractions. Examples of bimolecular configuration of the aforementioned types are presented in Figure S4 in the Supporting Information Section. The statistics of aggregate size were determined based on the number of clusters consisting of a specific number of molecules (ranging from 1 to N_l), which were calculated using a suitably modified Hoshen–Kopelman algorithm for cluster identification [39 (link)].
The algorithm employed in our calculations implemented the conventional Metropolis sampling in the canonical ensemble [39 (link)]. The lattice of adsorption sites was represented as a square L × L table, with each cell being characterized by the occupation variable s, which could take on values of 0 (representing an unoccupied site), 1 (indicating occupancy by a molecular segment), or 2 (denoting occupancy by a metal atom). The nearest neighbors of a specific cell in the table were redefined to include six cell sites, corresponding to the topology of a triangular lattice. The simulation began with a collection of randomly distributed molecules (collections of cells with $s=1$ ) and metal atoms (single cells with $s=2$ ) in quantities N_l and N_m, respectively. To adsorb a molecule, a cluster of four sites matching the shape of a given chrysene tecton was selected, as illustrated in Figure 7. The distance between any pair of neighboring segments of the molecule was equal to $a\sqrt{3}$ , corresponding to the next-nearest-neighbor distance on a triangular lattice. The occupation variables s of the cells corresponding to these sites were all set to 1. In the case of a metal atom, a single cell was chosen, and the associated value of s was updated to 2. To determine if there exists an effective interaction between an adsorbed molecule and a metal atom, the active molecular segments were probed. To that end, the next-nearest-neighbor site of a selected active segment was searched out in the direction determined by the specific position of the halogen substituent. If the occupation variable s of this site was equal to 2, then a further search in the same direction was made at the next step of $a\sqrt{3}$ , aiming to determine if a second molecule could be linked with the metal atom. If for that site s was zero, then the first molecule interacted with the metal atom with energy $\epsilon$ , providing single metal coordination. If s was equal to one, the match between the interaction directions (halogen substituents) of the first and second molecule was checked. If the interaction directions were collinear (→←), the second molecule contributed with an additional input of ε, resulting in double coordination of the metal atom with energy 2ε. If the interaction directions were not collinear, the energy of this configuration was reduced and equal to ε. For all other situations in which the occupation variables associated with neighboring segments were not equal to 1 (linker) and 2 (metal), the interaction energy was zero. An analogous scheme was used for a metal atom if this component was selected in the equilibration procedure. In this case, a single lattice site was considered, so the occupation variable for an adsorbed metal atom was set to 2.
To account for the interactions with neighboring molecules, six next-nearest-neighbor sites of the metal atom were checked (at a distance of $a\sqrt{3}$ each). If any of these sites were occupied by an active molecular segment, the directionality of the interaction provided by this molecular segment (halogen position) was inspected. If the interaction direction assigned to the segment pointed towards the metal atom, a single link was formed with energy ε. Then, the second site of the six surrounding the metal atoms was examined, and if this site was occupied by an active molecular segment, the same procedure was used to determine the corresponding interaction direction. If this interaction direction was collinear with that of the first molecule, the second link was formed, contributing to ε. For the 120° alignment of interaction directions, the energy was equal to ε. No more than two linkers were allowed to link with a single metal atom, and this condition was always checked when updating the coordination of a metal atom. The energy of a selected molecule or a metal atom was determined using the method described above, and it served as the input $U_o$ (old configuration) or $U_n$ (new configuration) for the previously mentioned Metropolis acceptance criterion.
All computer programs utilized in this study were developed from scratch using the FORTRAN programming language. The calculations were carried out on a computer cluster running the Linux operating system. Executable files were generated using the gfortran GNU compiler.