Chirality analysis of helical polymers

Helix or not

Chiroptical properties of a polymer may be based on a center of chirality and/or an axis of chirality (helix) and/or a plane of chirality with unequal populations of right- and left-handed enantiomeric structures.

If a polymer has no centers or planes of chirality, the observed chiroptical properties are reasonably ascribed to conformational chirality. While any conformation having no planes of symmetry can account for chiroptical properties, a helix may be proposed as the simplest one. As a typical example of a helical polymer having no centers or planes of chirality, optically active poly(9,9-dioctylfluorene-2,7-diyl) has been reported (Figure 3A) (Pietropaolo, Wang, & Nakano, 2015; Wang, Sakamoto, & Nakano, 2012; Wang, Harada, Phuong, Kanemitsu, & Nakano, 2018). Because axial chirality around the single bond’s connecting monomeric units is the only chiral element for this polymer, a preferred-handed twist is reasonably proposed to explain its chiroptical properties, and accumulated twists of the same hand in a chain means a preferred-handed helix. A helix can be thus deduced based only on chiroptical properties and simple, non-computational structural consideration for such a simple polymer. For this particular example, more accurate conclusions were obtained by theoretical calculations, as discussed later.

Figure 3:

Structures (top) and CD spectra (bottom) of typical helical polymers: poly(DOF) (A) and poly(TrMA) (B) [reproduced from references Wang et al. (2012) (A) and Okamoto et al. (1979) (B) with permissions].

If a polymer has centers of chirality, and, at the same time, they may have helical conformation, the helix needs to be established carefully. Considering (a) molar-mass effects, (b) temperature effects, (c) chemical transformation effects, and (d) chiroptical properties of the monomeric unit, model compounds may be important in confirming helix. When chiroptical properties do not remarkably change by these effects, they may arise mainly from centers of chirality because these effects can significantly affect the helix.

For example, the helix of stereoregular polyolefins bearing centers of chirality in the side chain was established considering molar-mass effects and temperature effects (Pino & Lorenzi, 1960). OR values of the polymers were higher for higher-molar-mass fractions (molar mass effects), and the OR of helical polymers changed to a greater extent than for small-molecular model compounds (temperature effects). The logic is that OR values based purely on centers of chirality in the side chain would not significantly change depending on molar-mass or temperature while OR values based on a helix could be because a longer chain would stabilize the helix and because the conformation may change depending on temperature. In addition, OR values of the polymers were much greater than those of the monomeric unit model compounds.

As another example, the helix of poly(triphenylmenthyl methacrylate) (poly[TrMA]), the first example of single-handed helical vinyl polymer having no centers of chirality in the side chain, was supported by molar-mass effects and chemical transformation effects (Figure 3B) (Nakano, Okamoto, & Hatada, 1992; Okamoto, Suzuki, Ohta, Hatada, & Yuki, 1979; Okamoto, Suzuki, & Yuki, 1980; Okamoto, Okamoto, & Yuki, 1981). Helical conformation of this polymer was proposed based on its almost entirely isotactic main-chain configuration, implying two aspects of stereochemistry; first, an isotactic chain has a plane of symmetry (mirror plane) orthogonal to it, and second, an isotactic chain can be reasonably folded into a helical shape, which may result in remarkable OR and CD spectra. Further, the remarkable chiroptical properties were only observed for higher-molar-mass chains and not for oligomers up to 8-mer (molar-mass effects). In addition, the proposed helical conformation was considered to be maintained by the steric repulsion between bulky triphenymethyl groups in the side chain. This was evidenced by solvolysis of the side chain leading to poly(methacrylic acid) and, following methylation, to poly(methyl methacrylate) (poly[MMA]) with a random conformation, showing only negligible OR (chemical transformation effects).

Helical-sense excess (h.e.)

As chromatographic chiral resolution of racemates is widely applicable for small molecules, determination of enantiomeric excess (e.e.) can be unambiguously conducted through such experiments. Chiral small molecules may be derived from natural compounds having 100% e.e. through reliable synthetic routes having no racemization. Relationships between e.e. and OR and CD spectra of many small molecules have been published, and e.e. of a sample can be determined based on observed chiroptical properties through comparison with literature information about specimens. In sharp contrast, resolution of a polymer helix can be extremely difficult and has not been attained except for very limited examples. This is why specimens of single-handed helical polymers are virtually unavailable so far, and h.e. has not been reported for most synthetic, helical polymers.

A renowned exception is poly(TrMA), whose single-handed helix (h.e. ∼100%) was established by a very careful open column chromatographic resolution using optically active poly(TrMA) itself as a chiral stationary phase (Figure 4) (Okamoto et al., 1981). A poly(TrMA) sample, which was a mixture of right- and left-handed helices, was resolved on (+)-poly(TrMA) into a number of fractions, among which, the first-eluted was (−)-poly(TrMA) showing the greatest absolute value of OR. This sample was again resolved under the same conditions, resulting in fractions showing almost the same OR as the (−)-poly(TrMA) obtained through the first resolution. These results indicate that the (−)-poly(TrMA) sample did not contain any (+)-fraction, which means that it had a single-handed helical conformation. This example is truly exceptional, and such a careful analysis has not been reported for most other helical polymers.

Figure 4:

Resolution of left- and right-handed helices of poly(TrMA) leading to a single-handed helical sample.

Determination of h.e. is therefore not possible for most helical polymers. Nevertheless, a single-handed helix is often concluded for new polymers simply because “large” OR or CD spectral intensity is observed. Because the intensity cannot be discussed without a specimen, “preferred-handed helix” is generally a more appropriate expression.

Absolute helical sense, left or right

X-ray analysis of single crystals can afford information of the absolute configuration of small molecules. This is the most general way of the determination of absolute configuration. Polymers, however, do not form single crystals mainly due to variation in chain lengths contained in the sample, leaving the left-handed or right-handed helix question still open for most helical polymers.

When CD spectra show clear Cotton splitting (a bisignate curve), considerations of exciton coupling effects may lead to absolute helical sense information (Figure 5) (Harada, Nakanishi, & Berova, 2012). Exciton coupling can occur between two or more identical, or very similar, chromophores located close enough in a molecule or a polymer in a twisted, chiral arrangement. If the dihedral angle related to the chromophore’s arrangement has a positive sign, positive Cotton splitting may be observed. Although this method itself has a solid theoretical background, it is often prone to errors due to insufficient structural information and spectral complexity with overlapping bands.

Figure 5:

CD/UV spectra and structures of cholest-5-ene-3β,4β-diol bis(p-bromobenzoate) showing negative exciton chirality [redrawn from reference Okamoto et al. (1979) with permission].

Computational methods

Chiroptical properties can be rationally interpreted based upon helical conformation including absolute helical sense using (theoretical) computational chemistry methods. Molecular simulations can predict most plausible conformations and their OR and CD spectra. The simulations can also accurately deduce signs of OR and CD for optimized structures if suitable conditions are chosen (Nakano, Tanikawa, Nakagawa, Yade, & Sakamoto, 2009; Pietropaolo & Nakano, 2013, 2020; Pietropaolo, Cozza, Zhang, & Nakano, 2018; Sakamoto, Fukuda, Sato, & Nakano, 2009). In the case of poly(9,9-dioctylfluroene-2,7-diyl) discussed earlier, the presence and the absolute helical sense of the helix were concluded by the following: (1) the most probable conformation was estimated, (2) theoretical CD spectra were calculated for the conformation, and (3) matching of the theoretical CD spectra with experimental CD spectra was confirmed (Figure 6) (Pietropaolo et al., 2015). The combination of experiments and theoretical calculations is thus a powerful method of chirality analysis of the helix. Other examples of helical conformational analyses combining experimental data and theoretical calculations include studies of polyacrylate (Pietropaolo & Nakano, 2013; Sakamoto et al., 2009) and poly(dibenzofulvene) (Nakano & Yade, 2003; Nakano, Takewaki, Yade, & Okamoto, 2001; Nakano et al., 2004; Pietropaolo et al., 2018).

Figure 6:

Structures (left) and CD spectra (right) of helical polymers: (A) poly(DOF) and (B) poly(DBF) (1) with a model unimer (2) and dimer (3) [reproduced from references Pietropaolo et al. (2015) (A) and Nakano et al. (2009) (B) with permissions].

However, it should be noted that real polymer systems are generally too large for calculations within a reasonable time. Proposing good, smaller models is therefore crucial in obtaining reliable results. In addition, calculation of accurate values of OR and CD intensity is still challenging, meaning that theoretical methods need to be improved to determine h.e.

GUI-based software packages are available, and some of them can run on Windows and Mac OS. The most representative software may be Gaussian (Frisch et al., 2016) or open-source ab-initio software such as OpenMolcas (Fdez. Galván et al., 2019), and QuantumEspresso (Giannozzi et al., 2009) featuring various types of calculation methods. Popular molecular dynamics software, such as GROMACS (Hess, Kutzner, van der Spoel, & Lindahl, 2008), NAMD (Phillips et al., 2005), LAMMPS (Plimpton, 1995), and open-source libraries like PLUMED (Bonomi et al., 2019), can be used to predict structural and molecular dynamical properties. Open source visualization packages, VMD (Humphrey, Dalke, & Schulten, 1996) and Avogadro (Hanwell et al., 2012), among others, can be useful to visualize and analyze the conformations of simulated molecules.

Other chiroptical spectroscopies

Vibrational CD (VCD) spectroscopy leads to chirality information on vibrational transitions; it is the IR version of CD spectroscopy. As most compounds are IR-active, VCD can give chirality information of a wide range of polymers including those containing no UV-active chromophores, such as polysaccharides, while overall sensitivity of measurements tends to be lower for VCD than CD. In addition, Raman optical activity (ROA) measurements can afford chirality information of polymers having no chromophores, while availability of ROA apparatus is not yet high at present.