Effects of Odd–Even Side Chain Length of Alkyl-Substituted Diphenylbithiophenes on First Monolayer Thin Film Packing Structure

Because of their preferential two-dimensional layer-by-layer growth in thin films, 5,5'bis(4-alkylphenyl)-2,2'-bithiophenes (P2TPs) are model compounds for studying the effects of systematic chemical structure variations on thin-film structure and morphology, which in turn, impact the charge transport in organic field-effect transistors. For the first time, we observed, by grazing incidence X-ray diffraction (GIXD), a strong change in molecular tilt angle in a monolayer of P2TP, depending on whether the alkyl chain on the P2TP molecules was of odd or even length. The monolayers were deposited on densely packed ultrasmooth self-assembled alkane silane modified SiO2 surfaces. Our work shows that a subtle change in molecular structure can have a significant impact on the molecular packing structure in thin film, which in turn, will have a strong impact on charge transport of organic semiconductors. This was verified by quantum-chemical calculations that predict a corresponding odd-even effect in the strength of the intermolecular electronic coupling.


The influence of substrate temperature on the apparent grain size of P2TPs
The effect of substrate temperature on grain size was determined by thermally evaporating a half covered monolayer of C 8 -P2TP-C 8 on ODTS at substrate temperatures ranging from room temperature to 115 °C. A large increase in grain size is observed ( Figure S4), indicating substrate temperature as a large contributor to the increase in grain size. To see the effect of side chain length on the grain size, we evaporated the series of P2TP molecules on ODTS at 60 °C with a film thickness of 40 nm ( Figure S5). Towards longer side chain length, the grain size increases and becomes more irregular in shape. This indicates a stronger 2 dimensional growth mode due to a decrease in interaction of the conjugated core with the underlying layers. Although we did not investigate the grain size versus chain length for the first layer of molecules for the complete series of P2TP, we strongly suspect this will result in a similar trend. is observed for longer side chains due to a decreased interaction of the conjugated core with the underlying layers, or substrate.

Grazing incidence X-ray diffraction
The motif by which the molecules pack inside the C N -P2TP-C N unit cells was extracted by crystallographic refinement of the diffraction intensity obtained from the Bragg rods. This was achieved by fitting theoretically calculated diffraction intensities to the measured intensity data, assuming scattering from a smooth thin film is kinematical. Besides a correction for the beam polarization (95% inplane polarized), additional multiplicative corrections needed to be applied to the theoretical diffraction intensity values I hk (q z )~|F hk (q z )| 2 . Even though our GIXD setup involves no rotation of either detector or sample, a Lorentz correction, 1/cos(θ)sin(θ)cos(θ), is necessary because the film forms a 2D-powder in the substrate surface plane. For simplicity, we assumed an isotropic molecular mean square displacement U 2 , for the Debye Waller factor, exp(-U 2 q 2 ). It is important to realize that the correct total peak intensity is recorded in the uncorrected images. The angular dependence of the atomic scattering factors was calculated using a Cromer-Mann function and corresponding coefficients. The coefficients for the hydrogen factor were obtained by fitting literature data to a Cromer-Mann function. The energydependent real and complex corrections to the scattering factors were taken from literature.
The alignment of the two C N -P2TP-C N molecules in the determined monolayer unit cell was extracted from the GIXD peak intensities by numerical optimization of the crystallographic residual that fits the corrected theoretical diffraction intensities along the Bragg rods to the experimentally obtained intensity data. Integrated intensity values were measured at 40 different values of q z between q z =0.05…0.4 Å -1 along the first five Bragg Rods in GIXD images of a sub-monolayer C N -P2TP-C N films after background removal. In these GIXD images, the {01} and {10} rods are completely extinct which is indicative of p2gg symmetry (two glide-symmetry planes create systematic absences of peaks). Therefore, the respective experimental I 10 (q z ) and I 01 (q z ) values were set zero and included in the fit at five different q z values.

Configuration of the system
In the experimental set up, molecules that form surface coatings, like the ODTS Self-Assembled Monolayers (or SAMs), are deposited on an amorphous silicon dioxide substrate. The head group, consisting of three chlorine atoms, reacts with the -OH groups of the substrate, forming an -O-Si bond that tethers the molecule to the surface. To emulate this in the simulation, we tethered each SAM molecule to an x-y location in space. Since the ODTS ligands are relatively long (~2.3 nm), an explicitly modeled surface beneath the SAM is unnecessary. The ODTS SAM molecules were tethered to hexagonal lattice points in free space at the oxygen atom, i.e., the position of the oxygen atom was fixed throughout the simulation. This choice followed experimental evidence that suggests the oxygen atoms are attached to the substrate surface, thereby anchoring the SAM molecules at this point. It is possible that, on real surfaces, the SAM molecule could be tethered via more than one oxygen atom in the head group, which implies that the silicon atom of the head group is also essentially fixed in place [1]. To study the impact of this eventuality and better define an appropriate initial system configuration, we conducted simulations in which both the silicon and oxygen atoms were fixed in place. The energetics of the system differed by less than 5% in energy and with no observable structural difference in the system whether just oxygen was fixed, or both oxygen and silicon were fixed. Thus all the remaining simulations described in this paper assumed that the SAM molecule is tethered to the substrate by one oxygen atom.
The simulation set-up used ODTS's preferred hexagonal lattice; here, 98 SAM molecules, consisting of 7x7 unit cells with two molecules per unit cell. This involves the consideration of 5,928 atoms for the ODTS molecules alone. The characteristic lattice parameter of the hexagonal packing was chosen to match the packing density determined from X-ray diffraction measurements [2]. The oxygen atoms are fixed to simulate the binding of the ODTS with the substrate. After thermalizing at 300 K, the simulation shows that the tilt angle of ODTS is strongly correlated to the SAM density, as shown in Table S1. We determined that the ODTS molecules could be fixed in place during the simulation without loss of accuracy of the surface topography and subsequent morphology of P2TP molecules. This simplification is possible because the movement of individual SAM molecules is limited at this high density. The advantage of fixing the molecules is that it allows a very significant reduction in computational expenditure without loss of accuracy.
All the molecules used in the simulation (ODTS and P2TP) were created using the Molden software package [3] and an energy minimization of the initial guessed structures was performed using a standard minimization algorithm -the limited memory L-BFGS minimization using a modified version of the algorithm of Nocedal which is a part of the TINKER software package [4].
The next task is to determine the lowest energy configuration of a unit cell of two P2TP molecules, as a starting point for the simulations. Since the preferred P2TP orientation in the unit cell for the force field model chosen in this study is not known a priori, we had to investigate the effect of the angle between each molecule on the energy of the system, as shown in Figure S6. The maximum in energy corresponds to a completely eclipsed configuration (at ~270°). We observed two minima that are close in energy (-9 and -7.5 kcal/mole) at 240° and 300°, separated by a large energy barrier (of ~45 Kcal/mole). These minima are for two isolated molecules interacting with each other and do not necessarily represent the true global minima in energy for a bulk 2D lattice. This necessitated two separate sets of simulations,

S9
described below, to determine the configuration that gives rise to the lower energy in the bulk 2D lattice with periodic boundary conditions. Such a study found that the lower energy minimum for the bulk lattice occurred at an angle of 300°. Figure S6: Energy as function of the angle between two molecules.
The intermolecular distance at the energy minimum defines both the lattice parameters and the density of the monolayers. The first simulation runs performed a cursory fit allowing the energy to be minimized; this was determined by keeping one molecule fixed and moving the other molecule relative to the fixed molecule in the x and y directions. For example, for C3-P2TP-C3, the energy dependence on the distance is as shown in Figure S7. For each distance, the molecules were rotated and a minimum in the energy was found. The net results of minimizing both the distance and angle leads to the optimum configration of the molecles in the unit cell.

Intermolecular Potential Models
The choice of intermolecular potential model is a very important part of a molecular simulation. We chose to use the non-reactive semi-empirical MM3 potential to model all the SAM-SAM and P2TP-SAM interactions. The MM3 potential has been shown, by us and others [5][6][7][8], to describe, quite accurately, hydrocarbons [5], fluorinated hydrocarbons [7] and multiply ringed molecules of the type we studied here. MM3 incorporates stretching, bending, and torsional energies, as well as the van der Waals S12 interaction energies based on phenomenologically determined parameters. The total energy may be represented as follows: with where E b is the bond-stretch, E a is the angle-bend, E tor is the torsion, E aa is the bend-bend, E sb is the stretch-bend and E stor is the stretch-torsion potential. The potential does not involve electrostatic interactions. The intermolecular van der Waals interactions take the form of a Buckingham potential modified with tapering polynomials so that the energy may smoothly decrease to zero at a cut-off distance of 9Å.
We have used this model extensively to study the energetics and structural characteristics of an array of small organic semiconducting molecules including the acenes, rubrene, DIP, sexiphenyl and C 60 [9,10] and have confidence in its ability to model conjugated systems. For instance, we conducted an extensive survey of twelve Density Functional Theory models, as well as the MM3 and MM3-π models for biphenyl and eight models (four DFT and four semi-empirical models) for the sexiphenyl molecule. We found virtually all the models to give consistent energetically preferred structures [11]. Both MM3 models (with and without an additional term to represent pi-bonding) represented the behavior of sexiphenyl and biphenyl molecules with quantitative accuracy compared to the DFT models. Based on our studies and those of the Allinger group, we are confident in the ability of MM3 to be sufficiently accurate to describe P2TP molecules on a SAM surface without having to resort to using MM3-π, a variant of MM3 which is more accurate for molecules with an extensive π-electron system but which is about 20 to 100 times slower in execution time.

Simulation Details
The time evolution of the system was followed using a simulation approach using the Modified Beeman Algorithm as part of the TINKER software package. As mentioned above, optimized structures of the SAM molecules and the P2TP molecule were obtained from an energy minimization of an initial guess structures using a standard minimization algorithm, here, the limited memory L-BFGS minimization using a modified version of the algorithm of Nocedal [12]. The system consisted of the hexagonally packed ODTS layer underneath, and a P2TP layer arranged in a herringbone lattice on top of the ODTS.
The system was first thermalized at 300 K using a Nosé-Hoover thermostat in the canonical (NVT) ensemble for a period of ~100 ps with a time step of 1.0 fs (i.e., 100,000 time steps) in order to suppress significant fluctuations in temperature and equilibrate the system.
The bottom ODTS layer was now frozen and the top P2TP layer was subject to an isothermal-isobaric (NPT) ensemble in order to determine the optimum lattice constant. The system was run for about 100,000 time steps corresponding to ~100 ps. Once the system was equilibrated under NPT, the timeaveraged and spatially averaged lattice constant was calculated and, with this mean lattice constant fixed, the system was once again subjected to the NVT ensemble for another period of equilibration. The equilibration time was again around ~100 ps.
After equilibration was complete, the average tilt angle of the P2TP layer above the ODTS SAM layer was measured. The tilt angle was calculated as the angle made by the vector made by the backbone of the P2TP molecule with the normal to the surface of the film. This is in agreement with the manner in which the tilt angle was calculated experimentally. The tilt angle was then compared with experiment and observed to vary as a function of the side chain length of the P2TP molecule as described in the results section of the main article.

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To compare the optimized structure of the P2TP molecules in the presence or absence of the underlying SAM, we adopted a similar simulation procedure to that mentioned above, but without the presence of the SAM. The energy-minimized structure of the series of P2TP molecules with different alkane chain lengths were used as mentioned above: The simulation box was set up such that no SAM was present, and that sufficient vacuum existed above and below the 2D P2TP crystal so that periodic images would not interact and the system represented a thin film of the P2TP molecules. The initial 100 ps NVT step used above was omitted because there was no SAM layer that needed to be equilibrated. The following NPT step was extended to 400 ps because additional time was needed for the box to equilibrate with the SAM removed. This NPT step (in which the volume can vary) allowed the lattice parameters to change to further optimize the unit cell. The final 100 ps NVT step, as well as the angle measurements and equilibrated unit cell parameters, were carried out as described above.
The results for the preferred tilt in the absence of the SAM show that the odd-even effect persists in the absence of the SAM, but is diminished. This result shows that the odd-even effect is partially caused by the preferred packing of the P2TP molecule itself, but significantly enhanced by the interaction of the

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C D S16 Figure  The saturated field effect mobility was calculated by taking the slope of I ds 1/2 versus V g , as shown in Fig. S10. The intersection of the slope with the x-axis (I ds = 0) determines the threshold voltage V t . We used the following equation for calculating the mobility µ: where C d is the capacitance per unit area of the dielectric with a thickness d, W the width of the electrodes and L = the distance between source and drain electrode.