Although the $\sigma $-conjugated polysilanes have not attracted as much attention as $\pi $-conjugated polymers, it is, first and foremost, the nature of the structure/property relationships that is the focus of this article (and not the origin of conjugation nor the specific potential for applications[71]). From this perspective these polymers may be viewed as exceptional because they exhibit an extraordinarily diverse phase behavior. Many PSils are well known for highly crystalline phases and, additionally, there is a remarkable sensitivity in the structural phase behavior to even very minor differences in the choice of dialkyl substituent or to the specific physiochemical processing procedures. In a few polymers it is even possible to, under some circumstances, partially decouple molecular level processes that lead to bulk crystallization from those that induce a high degree of main chain conformational order. Because the monomer unit repeat is relatively small, the dense intramolecular spacing of alkyl chains increases the relative contribution of intramolecular alkyl-alkyl interactions and so these materials should reflect the limiting case of materials dominated by strong intrachain interactions.

The origin of $\sigma $-conjugation is slightly more difficult to summarize than for $\pi $-conjugation because it involves contributions from two different types of orbital overlap. This is shown in Fig. 7. The first component, termed a geminal interaction, relates to electron orbital overlap between the two neighboring Si-Si $\sigma $-bonding orbitals on each individual Si atom. The second contribution comes from a vicinal interaction between sigma-bonding orbitals of nearest-neighbor and next-nearest neighbor Si atoms. The vicinal term carries virtually all of the torsion angle dependent $\sigma $-conjugation and, in this instance, theoretical studies[72,73] identify behavior approximating a $\cos \phi$ dependence on Si-Si torsion angles.

Figure 7: Top: Chemical structures of poly(dialkylfluorene) and poly(dialkylsilane). Bottom: Sketches of the $p_z$ orbitals responsible for $\pi $-conjugation, the $sp^3$ orbitals necessary for $\sigma $-conjugation, and the torsion angles affecting conjugation length.

The sensitivity of the optical and structural properties with respect to alkyl chain length is truly striking. Unsubstituted polysilane has a backbone torsion potential which gives rise to both anti and gauche conformations[74,75] in close analogy to saturated hydrocarbons. Dimethyl substitution creates significant steric packing constraints along the polymer backbone and so there are 10 to 15$^\circ $ deviations from planarity[76,77] which induces a hypsochromic shift in the optical interband absorption. Structure factor calculations, using the known monoclinic unit cell[78], are shown for room temperature in Fig. 8 and indicate that torsional deviations closer to 15$^\circ $ are more likely. The actual differences between the planar and non-planar model, as indicated by vertical arrows, are quite small but statistically significant. For longer alkyl side chains it becomes progressively more difficult to employ structural refinement to analyze backbone torsion angles unless large torsional deviations are present. Poly(diethylsilane) and poly(di-$n$-propylsilane) still exist in a near planar form[79,80] but both poly(di-$n$-butylsilane) and poly(di-$n$-pentylsilane) are best known for adopting structures identified with 7/3 helices[81,82,83] although other structural phases are possible[84,85]. Poly(di-$n$-hexylsilane) is almost always observed in a near planar crystalline phase[86,87,88] but both di-$n$-octyl and di-$n$-decyl substituted polysilanes are given to multiple phases, many of which are metastable, and the overall structural evolution is extremely sensitive to the physiochemical processing history[89,90,91] (even by polysilane standards).

Figure 8: Comparison of calculated structure factors and experimental powder X-ray diffraction profiles for poly(dimethylsilane) using a planar anti model and a representative non-planar model.

A basic molecular level understanding of the underlying principles governing this diverse behavior has been established. Much of this complexity stems from the convergence of at least two fundamentally important structure/property relationships operating at subnanometer length scales. Acting at the smallest length scales are repulsive interactions between the two inner most methylene hydrogen atoms on each of the two alkyl side chains. In saturated hydrocarbons this hydrogen repulsion leads to the well-known eclipsed and staggered skeletal geometry marked by three torsional equilibrium conformations identified as anti and gauche with C-C-C-C dihedral angles of 180$^\circ $ and $\pm60^\circ$ respectively. In the poly(dialkylsilanes) there are two adjacent and comparable dihedral angles, one for each Si-C linkage ($\phi _1$-$\phi _2$ in Fig. 9), which nominally correspond to nine distinct conformational minima (i.e., $3\times3$) in a simple 2D $\phi _1$-$\phi _2$ mapping of the conformational energies for these two torsion angles.

Figure 9: Left: Cross-sectional sketch of poly(di-$n$-butylsilane) showing the two Si-C torsion angles ($\phi _1$ and $\phi _2$) Right: Schematic model depicting the cross-over of side chain packing from splayed tetraradial to biradial construction as the alkyl side chain length increases.

The local structure of the neighboring Si atoms and their attached side chains strongly alter the actual topology of the side chain $\phi _1$-$\phi _2$ minimum energy surface. After extending this simple geometrical construct to include all other pair interactions one finds almost equally strong but secondary interactions between alkyl side chains on next-nearest neighbor Si atoms which are situated approximately 4 Å distant (if the Si skeletal backbone is assumed to lie close to an all anti conformation). The lowest energy minimum of the nine ``starting'' minima is extremely sensitive to the explicit Si-Si-Si-Si torsion angles (or $\phi_\tau$). Specifying the local conformational unit therefore requires three parameters, $\phi_\tau$, $\phi _1$ and $\phi _2$ or a family and two clans using nomenclature suggested in oligosilane studies[92] by Michl and coworkers.

The simplest case, assuming a periodic repeat of this family/two clan structure, allows for assessment of the relative energies of these nine distinct minima and an example isoenergy surface contour map relative to $\phi _1$ and $\phi _2$ in a single large dibutylsilane oligomer is shown in Fig. 10 at a fixed Si-Si $\theta_\tau$ dihedral angle of $170^\circ$. In this instance only two of the nine potential minima are very deep. After allowing for Si backbone relaxations as well, these two minima and that of a third are nearly degenerate in energy. Thus there are a trio of energetically favorable conformers and these most closely correspond to 15/7, 9/4 and 7/3 helices with Si $\phi_\tau$ torsion angles near 150$^\circ $, 160$^\circ $ and 170$^\circ $ degrees respectively. The structural phase behavior is therefore dominated by three basic types of conformational isomers. One can easily imagine that if this conformational energy topology is reflected in the real materials then frustration and trapping in various local minima are likely. Depending on the specific intrachain and interchain interactions some of these minima may be expected to incorporate repeating sequences of two or, possibly, more of these three conformational isomers.

For helical poly(di-$n$-butylsilane) a more extensive analysis identifies a low energy repeat sequence comprised of two base conformers (a dyad construction) and also the possibility of conjugation disrupting gauche type conformers. The net effect is to produce long sequences of a single helical pitch that is dominated by a complex 14/6 helix [or more accurately an s(2$*$7/6) helix] punctuated by isolated gauche defects[93]. This yields relatively broad optical absorption and emission spectra. For hexyl side chains the balance is shifted towards the 15/7 helix and, additionally, appearance of a stable planar anti type conformer[94]. These polymers exhibit sharper and more red shifted spectroscopic features.

Figure 10: Topographic and isoenergy contour map of di-$n$-butyl silane oligomer energies [H(SiBu$_2$)$_{14}$H in units of kcal/mol per two (di-$n$-butylsilane) monomers] as the two Si-C dihedral torsional angles are varied (and assuming a uniform family/clan pair construction). In this case the Si-Si-Si-Si torsion angle is fixed at 170$^\circ $.

At the heart of molecular level engineering are better design strategies for systematically tailoring the conjugation length[95,48]. Fujuki[96] has shown a direct relationship between the optical absorption band width and the oscillator strength in a large number of polysilane derivatives. In at least one instance[97] it is possible to identify an atactic and asymmetric chiral substituted polydialkylsilane, poly[$n$-decyl-((S)-2-methyl-butyl)silane], which exhibits an extremely sharp optical absorption band, a very small Stokes shift in the PL and virtually no inhomogeneous broadening. Molecular simulations[98] show similar Si torsion angle vs. energy curves for isotactic and syndiotactic isomers. This polymer includes only a single additional methyl group at the C2 carbon position and so it is straightforward to test the impact of this substitution on a smaller structural analog, poly[$n$-pentyl-(2-methyl-butyl)silane]. In atactic poly[$n$-pentyl-((S)-2-methyl-butyl)silane] the conformer identified with the ``7/3 helix'' is lower in energy than the other two candidate conformers and, more significantly, exhibits very minimal variations in the backbone dihedral angles (averaging approximately $154^\circ\pm1^\circ$). For atactic poly[$n$-pentyl-((R)-2-methyl-butyl)silane] this same conformer is, employing MM3 empirical force fields, over 1.5 kcal/mol/monomer higher in energy and conformationally disordered. The second test conformation is actually unphysical because the lowest energy structure has the opposite helical handedness. Most striking in the first isomer is the overwhelming preference for a single helix and its ``fault'' tolerant nature with respect to tacticity. Identifying similar mechanisms in $\pi $-conjugated materials, possibly through core mesogen containing side chains, would validate a bottom up approach to enhanced structural order of the skeletal backbone as opposed to an ordering imposed by side chain components at the far ends (which more resembles a ``top-down'' strategy).

This leads to the next important issue, that structural behavior associated with packing of the side chains in their entirety will also have a major impact. In poly(dialkylsilanes) the second key nanoscale structure/property relationship relates to an abrupt change in the alkyl orientation and packing as the side chain length is increased. Already it has been noted that in P3ATs there is a strong tendency for alkyl chains to adopt a packing motif which reflects that of bulk hydrocarbons. All three of the aforementioned low energy poly(di-$n$-alkylsilane) conformational isomers include a splayed and open packing of the alkyl chains. Thus there is a fundamental incompatibility with respect to the tightly nested herringbone packing of alkanes onto a pseudohexagonal lattice. For alkyl side chains, at or beyond octyl in length, analysis of X-ray diffraction data identifies[91] a crossover from the splayed ``tetraradial'' construction to a zippered ``biradial'' type packing (see Fig. 9 on right). Analogous behavior has been reported for non-conjugated organic molecules[99]. In the poly(di-$n$-alkylsilanes) this behavior has a very strong temperature component and so at higher temperatures, typically associated with a hexagonal columnar LCP mesophase (HCM), the tetraradial construction may be more favorable but at low temperatures the biradial packing is preferred.

The combination of these two molecular level processes results in polymers that are highly polymorphic. Poly(di-$n$-octylsilane) and poly(di-$n$-decylsilane) films exhibit upwards of five distinct ordered phases. These differing phases strongly impact the backbone conformation but there is, in general, no direct one-to-one correspondence between a single backbone conformation and one specific structural phase. In some instances thermal quenching, which suppresses side crystallization, leads to thin films with sharper optical absorption and emission features. The impact of this complexity on even very basic optical properties is quite extensive because singlet excitons, the progenitor of the predominant radiative process, may decay luminescently at trapped metastable conformers or, alternatively, pass through these regions while on their way to chain segments with smaller interband transition energies.

Figure 11 displays a series of alternately recorded UV absorption and PL spectra from a poly(di-$n$-decylsilane) thin film which has been thermally quenched[91] (to ca. 220 K) from the conformationally disordered high temperature HCM. Even this limited data set reveals some of the disconcerting complexities associated with this polymorphic phase behavior. At the lowest temperature shown, 175 K, the absorption includes at a minimum a superposition of both sharp and broad components. Slowly cooled samples generally display only broader lineshapes. The PL is unusual as well because the wavelength of the maximum PL intensity does not correspond well to the leading edge of the long wavelength absorption band. This implies that either singlet exciton recombination is less efficient in chain segments having the longest conjugation lengths or, more likely, exciton migration and energy transfer are impaired. In fact there are two discernible peaks in the 175 K PL spectra. Modest warming, which allows first for local structural relaxation followed by cold crystallization, gives rise to multiple changes in both sets of spectra.

In the UV absorption there is first an increase in the proportion of the long wavelength component followed by a resurgence and narrowing of the intermediate wavelength feature and ending with the gradual increase in the short wavelength HCM absorption. On warming the long wavelength PL feature undergoes a 10 nm red shift to 380 nm and also increases in intensity (well in excess of the gradual rise of the 305 nm absorption). Thereafter it diminishes and is superseded by emission of an intermediate wavelength PL band and then is finally replaced by PL from the high temperature mesophase. Surprisingly the intermediate wavelength ca. 350 nm peak dominates the absorption at both 175 K and in the vicinity of 295 K but, in terms of PL signal, only at the higher temperature range does this emission feature dominate the spectra. A molecular level description is not yet available but there can be no doubt as to the complexity of this process in terms of exciton formation, intrachain migration and interchain energy transfer. Devices which employ these or structurally related materials will likely exhibit diverse properties as well.

Figure 11: A series of steady-state UV absorption and PL spectra on heating from the identical spot of a poly(di-$n$-decylsilane) thin film cast onto a sapphire substrate after thermal quenching from the disordered hexagonal columnar mesophase.

In a more general sense this structural evolution directly impacts energy flow at both the molecular level and over much larger distances. In order to better resolve the nature of energy migration and transfer between different structural phases a more illustrative approach is to simultaneously monitor both absorption and PL in a polysilane which has a far simpler phase diagram. Of the many poly(dialkylsilanes) studied poly(di-$n$-hexylsilane) (pdHexSi) has perhaps the simplest and most widely investigated phase behavior. At low temperatures pdHexSi adopts a well-ordered crystal phase [Abs.( $\lambda_{\mbox{\small max}}$)$= 368\pm 1$ nm; PL( $\lambda_{\mbox{\small max}}$)$=380\pm 1$ nm ] and, in the vicinity of 45 $^\circ $C undergoes an ODT to a LCP mesophase with broader emission and absorption peaks appearing at shorter wavelengths[100,101]. Ultra-thins films exhibit this ODT but it occurs with very much slowed kinetics[102] that can span seconds, minutes or even days. Monitoring of this transition is easily accomplished although exposure to the PL excitation line (in this case 305 nm) must be kept to a minimum to lessen the incidence of photodegradation (especially of the high temperature mesophase). Figure 12 displays data recorded at intermediate times for three different temperatures of undercooling. Small changes in the temperature lead to enormous variations in the kinetics. More important is the observation that PL from the ordered phase always precedes its appearance in the absorption and its onset is characterized by a more rapid rise. As a result the ordered phase PL saturates relatively quickly. The disparity would be even more pronounced if these data included a correction factor for the monotonically decreasing absorption at the excitation wavelength. If this phase transition is viewed as a simple two-phase coexistence then these results imply large scale and efficient energy flow of neutral excitations (i.e., singlet excitons) over distances well in excess of 20 nm (a typical coherence length) or more to ordered phase regions of the film. In another conjugated polymer material, solid-state polymerized crystals of polydiacetylene, exciton migration over micron distances has been observed[103].

Figure 12: Left: Time evolution of the relative UV absorption and PL from the order phase of a pdHexSi thin film ($\sim $20 nm thick, cast from 0.2% w/w polymer in toluene) after cooling from thermotropic mesophase. Right: PL and UV absorption spectra from this sample when cooled to 300 K at selected times. The PL data do not include corrections for self-absorption but the effects are generally small.

Addition of dialkyl substituents produces structural and photophysical behavior which initially appears, if anything, more complicated than that seen in the P3ATs (and related polymers). Still a basic molecular level understanding can be established from fairly simple constructs. The next section demonstrates that this facile side chain substitution yields strong parallels among $\pi $-conjugated materials although, not surprisingly, there are indications of significant polymer specific differences.

Winokur 2004-01-28