core.ac.uk · 271 mirror symmetry breaking of silicon polymers—from weak bosons to artiﬁ cial...

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Mirror Symmetry Breaking of Silicon Polymers—From Weak Bosons to Artifi cial Helix

MICHIYA FUJIKIGraduate School of Materials Science, Nara Institute of Science and Technology, 8916-5 Takayama, Ikoma, Nara 630-0036, Japanemail: [email protected]

Received 15 August 2009

ABSTRACT: From elemental particles to human beings, matter and living worlds in our universe are dissymmetric with respect to mirror symmetry. Since the early 19th century, the origin of bio-molecular handedness has been puzzling scientists. Nature’s elegant bottom-up preference, however, sheds light on new concepts of generating, amplifying, and switching artifi cial polymers, supramol-ecules, liquid crystals, and organic crystals that can exhibit ambidextrous circular dichroism in the UV/Visible region with effi ciency in production under milder ambient conditions. In the 1920s, Kipping, who fi rst synthesized polysilanes with phenyl groups, had much interest in the handedness of inorganic and organic substances from 1898 to 1909 in his early research life. Polysilanes—which are soluble Si-Si bonded chain-like near-UV chromophores that carry a rich variety of organic groups—may become a bridge between animate and inanimate polymer systems. The present account focuses on several mirror symmetry breaking phenomena exemplifi ed in polysilanes carrying chiral and/or achiral side groups, which are in isotropic dilute solution, as polymer particles dispersed in solution, and in a double layer fi lm immobilized at the solid surface, and subtle differences in the helix, by dictating ultimately ultraweak chiral forces at subatomic, atomic, and molecular levels. © 2009 The Japan Chemical Journal Forum and Wiley Periodicals, Inc. Chem Rec 9: 271–298; 2009: Published online in Wiley InterScience (www.interscience.wiley.com) DOI 10.1002/tcr.200900018

Key words: polysilane; helix; symmetry breaking; homochirality; parity violation

The Chemical Record, Vol. 9, 271–298 (2009) © 2009 The Japan Chemical Journal Forum and Wiley Periodicals, Inc.

T H E C H E M I C A L

R E C O R D

Introduction—Historical Background Leading to Mirror Symmetry Breaking

Since the time of Pasteur, the scenario of mirror symmetry breaking of biomolecules on the blue planet—homochirality—is one of the most encompassing and debated topics of science, attracting inter alia biologists, chemists, physicists, and astronomers. They argue possible answers to the homochirality question, which can be seen in many monographs and reviews.1–24 The issue is recognized as one of the remaining issues of the 21st century.17

DNA and polypeptide consist of D-ribose and l-amino acid as building blocks, respectively. Because these biopoly-

mers are derived from the same handedness of building blocks by selecting one-handed molecules from mirror-image mole-cules, they can adopt inherent helical structures in water. This handedness is responsible for emerging biological functions such as enzymatic catalysts, heritable characters, and pharma-ceutical and toxicological activities. However, a recent study revealed that d-amino acids have specifi c functions in living organisms, exemplifi ed in valinomicine.25 Nature’s elegant bottom–up approach has inspired material scientists to new interdisciplinary approaches of generating, amplifying, and switching handedness of artifi cial polymers, supramolecules, and organic crystals. Nevertheless, the mechanisms—whether matter of chance or necessity and/or intrinsic or extrinsic—


T H E C H E M I C A L R E C O R D

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have been much debated, despite the fact that homochirality is de facto.

As a fi rst glance, the historical background of chirality in chemistry and physics will be very briefl y discussed, looking back to the days of the European science community in the 19th century. The history inspired the author to philosophi-cally promote a series of studies on optically active polymers and supramolecules through his whole research life. In the present account, the author wishes to summarize several mirror symmetry breaking phenomena that have emerged in several polysilane systems by chemical and physical origins: (1) poly-mers dissolved in solution, (2) polymer particles dispersed in solution, (3) binary fi lm at the surface, and (4) helix-helix transition by signifi cantly amplifying a subtle left–right energy difference by chemical and physical origins, by means of UV, CD, and FL spectroscopic experiments.

Chirality and Optical Activity3,4,11,20,22,26

In 1811, Arago invented the polarimeter to support Fresnel’s wave theory and found the phenomena of chromatic and rota-tory polarizations of quartz. Subsequently, Häuy recognized a pair of hemihedral faces in left-handed and right-handed inor-ganic crystals. In 1815, Biot found optical activity from solu-tions of tartaric acid and several organic liquids. Biot noticed ambidextrous rotation from quartz crystals and inferred ambi-dextrous rotation from solution if individual molecules were chiral. In 1820, Herschel reported that hemihedral quartz crystals may be connected to ambidextrous rotation. In 1848, inspired by Biot’s and Häuy’s implications, Pasteur, with his mind prepared, successfully isolated a pair of hemihedral crys-tals manually from a racemic mixture of sodium ammonium tartrates by a mirror symmetry breaking crystallization process. He observed uniquely levorotatory and dextrorotatory polar-izations when each of the chiral crystals were dissolved in

water. All his fi ndings were verifi ed by agreement with Biot. In 1874, van’t Hoff accounted for the phenomenon of optical activity by assuming that the chemical bonds between carbon atoms and their neighbors are directed towards the corners of a regular tetrahedron. He shared his credit with Le Bel, who independently came up with the same idea. This hypothesis was the beginning of modern stereochemistry, meaning a paradigm shift from two dimensional to three dimensional chemistry.

In 1860, Pasteur conjectured that biomolecular homochi-rality arises from an inherent universal dissymmetry force. This indicated the concept of broken mirror symmetry by intrinsic physical origins, although there was no theoretical or experi-mental evidence. However, most chemists, including van’t Hoff, and most physicists believed that the laws of nature cannot distinguish between left and right and, therefore, are conserved in all physical properties and chemical processes.

In 1896, Kipping—a pioneer of organosilicon and orga-nopolysilane chemistry—with Pope investigated handedness of inorganic crystals with D- and L-forms, in which thousands of crystals were produced from achiral NaClO3 (molecular symmetry, C3v) by mirror symmetry breaking crystallization with/without seeding sugars in several runs.27 They did not reach the conclusion that the mirror symmetry breaking crystallization occurs by an inherent physical origin because the events were a statistical distribution—a matter of chance. However, they found a marked imbalanced population between D- and L-crystals with the help of sugar chirality as an external chemical bias. This led to several important approaches that chiral chemical biases as seeds facilitate generating the desired chiral compounds and materials with a preference, using chiral catalysts, chiral auxiliaries, and chiral separation chromatography.

Moreover, Kipping and Pope reported an interesting result that sodium ammonium tartrates preferentially crystal-

� Michiya Fujiki was born in Fukuoka, Japan, in 1954. He received B.S. and M.S. degrees in Chemistry of Organic Synthesis from Kyushu University, Fukuoka, Japan, in 1976 and 1978, respectively, and received a PhD. degree from Kyushu University in Fukuoka, Japan, in 1993. Since 1978, he has worked for Nippon Telegraph and Telephone Cooperation (NTT). He studied low-loss optical plastic fi bers from 1978 to 1982 and semiconducting phthalocyanine thin fi lms from 1983 to 1987. He investigated a structure-property-functionality relationship of σ-conjugated polysilanes and π-conjugated polymers since 1987 and moved to NAIST as a full Professor in 2002. His research interests are to design hierarchical polymers made of the 14 group elements and phthalocyanine supramolecular polymers and to seek molecular/polymer systems suitable for answering the homochirality question. �

M i r r o r S y m m e t r y B r e a k i n g o f S i l i c o n P o l y m e r s

www.tcr.wiley-vch.de 273The Chemical Record, Vol. 9, 271–298 (2009) © 2009 The Japan Chemical Journal Forum and Wiley Periodicals, Inc.

lize in the d-form without any additives, even under carefully controlled experiments in several runs, and ascribed this obser-vation to certain chiral dusts acting as chiral seeds and/or to d-tartrate in slight excess included in a racemic mixture.28

These mirror-symmetry breaking crystallization ap-proaches, which were without any chiral chemical origins, were often utilized by many workers to macroscopically choose between the molecular parity violation hypothesis (necessity) and mirror symmetry breaking (by-chance).29–38 The main problem, however, appears to be a diffi culty validating that the results are absolutely not infl uenced by chiral dusts, enan-tiopurity of substance, chemical purity, and mechanically twisting motion arising from inherently inhomogeneous experiments.

Seven Fundamental Symmetries

With respect to a relationship between symmetry (invariance) and conservation laws, four fundamental physical forces—gravity, electromagnetic force, strong nuclear force, and weak nuclear force—should be considered fi rst.5,9,10,14,15,18,21,22,39,40 When a system converts under one or more symmetry opera-tions, the four forces should obey the invariance of symmetry operations. The most important symmetry operations are P (parity, switching between r and −r), C (charge conjugation, switching between matter and anti-matter) and T (time rever-sal, switching between future and past). The combinational symmetries are CP, PT, CT, and CPT, though most physicists believe in invariance of CPT. Mirror symmetry is equivalent to P-operation with rotation by 180° within a mirror plane. Before 1955, most scientists believed in invariance of all P, C, T, CP, PT, CT, and CPT operations.3,11,21,22

Parity Violation at Subatomic and Atomic Levels

In 1956—a century later than Pasteur’s conjecture –, Lee and Yang theoretically pointed out that, in certain nuclear events governed by the weak force, parity may not be conserved.41 Although one can fi nd parity violation and parity non-conser-vation, which have the same meaning in many papers, parity violation (PV) became popularly used rather than parity non-conservation (PNC) in recent papers. Inspired by this hypoth-esis, Wu et al. experimentally confi rmed in 1957 that parity in the 60Co → 60Ni + e− + υ nuclear reaction is, indeed, not conserved from the observation of the highly asymmetric emis-sion of β-particles (high energy left-handed spinning electrons) and γ –rays (photons) between north- and south-poles of 60Co at 0.1 K oriented by an external magnetic fi eld.42 Rodberg and Weisskopf in 1957 experimentally verifi ed that parity in the 58Co → 58Fe + e+ + anti-υ nuclear reaction is not conserved from the observation of the highly asymmetric emission of positrons (e+).43

The weak nuclear force caused mirror symmetry breaking processes at certain subatomic levels. At the end of the 1960s, Glashow, Salam, and Weinberg theoretically succeeded in unifying parity-conserving (PC ) electromagnetic and parity-violating (PV ) weak nuclear forces into an electroweak force, known as the Standard model.44–46 This model was verifi ed experimentally by detecting massive charged W + (∼80 GeV)/W − (∼80 GeV) and massive neutral Z 0 (∼91 GeV) bosons at CERN in 1983.47

The Standard model gave rise to another prediction that even atoms, consisting of electrons, protons, and neutrons, may be chiral as a consequence of the PV effect. The effect mediated by neutral Z 0 bosons should cause weak neutral current (WNC) to all atoms, including hydrogen,48 leading to the observation of tiny optical activity as a result of an ultra-short range interaction between the electron and the nucleus. From the viewpoint of chemistry, WNC is a persistent torus current fl ow with a handedness in the absence of an external fi eld.8,48 This would be in contrast to a diamagnetic ring current of aromatic molecules induced by an external magnetic fi eld. This hypothesis was proven by detecting small values of optical rotation, on the order of µ radian or sub-milli degrees of ellipticity, and the Stark effect from Bi, Tl, and Pb vapors, circularly polarized luminescence from Cs vapor,49–53 neutron-spin rotation of 124Sn and 117Sn atoms,54–56 and polarized neutron-scattering from MnSi.57

With respect to CP symmetry, in 1964, Cronin and Fitch discovered the violation of CP symmetry in K-mesons (K 0) with the observation of fast and slow decays of KL and KS.58

The K 0-meson is composed of down (d ) and anti-strange (anti-s) quarks, and the anti-K-meson (anti-K 0) is composed of anti-down (anti-d) and strange (s) quarks. However, they can mix with each other in the equations, KL =1/√2 ⋅ (K 0 + anti-K 0) and KS = 1/√2 ⋅ (K 0 − anti-K 0). Under CP-symmetry conservation, the KL- and KS-mesons decay into π0 particles with a long lifetime of 50 psec and π+/π− pairs with a short lifetime of 70 fsec. However, due to subtle CP-symmetry violations, KL-mesons decay to π+/π− pairs with the probability of 1/500 compared to KS-meson decay events. However, the degree of CP violation from K-mesons was not very remarkable.39

On the basis of the Kobayashi and Maskawa theory, the so-called 6-plet model, composed of six quarks and six leptons in three generations,59 Carter and Sanda theoretically devel-oped this model and predicted that the CP symmetry breaking might occur signifi cantly in the decay of B0-mesons rather than K 0-mesons.60 They showed that B0- and anti-B0-mesons can be effi ciently mixed together compared to the K 0-/anti-K 0-pair and decay into J/ψ and KS-mesons in an oscillating manner with time. The estimated degree of CP violation from B-mesons ranged from ∼10% up to nearly 100%.61 This led Sanda and his colleagues to promote a construction of the




so-called B-factory in Tsukuba, a well-designed high-energy collider featuring asymmetric accelerators, in order to observe the predicted large CP-violation of B0-mesons. In 2001, a research team at KEK in Japan62 and a research team at the SLAC team in USA63 independently detected the predicted large CP-violation of B0-mesons. The weak nuclear force medi-ated by the charged W + and W − bosons was also responsible for the CP-symmetry violation of B0-mesons.61

Parity Violation at the Molecular Level

The PV-related theoretical and experimental outlets mediated by W +, W −, and Z 0 bosons at elemental particles, subatomic, and atomic levels gave rise to a further hypothesis that WNC-induced PV effects mediated by the neutral Z 0 boson may distinguish between neutral mirror image molecules in the realm of chemistry.3,4,6,7,9,10,11,14,16,17,18,19,21 This means that the fundamental concept of mirror image molecules given by Van’t Hoff and La Bel could be necessary to revise that all enantiomers existing in the matter world may not be true enantiomers but diastereomers owing to energetic inequal-ity.64–82 However, most theoretical predictions on molecular PV effects showed that the difference in energy between mirror image molecules, called parity violating energy difference (PVED) or parity violating energy shift (PVES), is on the order of 10−12–10−17 eV (cf. 0.026 eV equivalent to 300 K), hence, PV-related researchers have been seeking well-designed molecules including heavier atoms and high-precision appara-tus.68, 76–82 This ultrasmall PVED does not produce any observ-able effects in physical and chemical properties between enantiomers, hence, PC-electromagnetic forces mediated by massless photons nonspecifi cally govern all chiral chemical reactions and processes equally. This does not confl ict with the most fundamental principle of stereochemistry that an equal amount of mirror image molecules are generated if enantio-specifi c catalysts and entities are not used. Therefore, any noticeable differences in physical properties (m.p., b.p., NMR, IR, UV/Vis, optical rotation, CD, and so on) between mirror image molecules cannot be detected by ordinary measuring apparatus.76–82 Theorists are looking for more suitable mole-cules to prove the molecular PV hypothesis.

Mirror Symmetry Breaking by Amplifi cation

In 1991, Goldanskii et al. summarized, in their review, the magnitude of mirror symmetry breaking called the advantage factor (g*) by the physical origins:7 circularly polarized light (PC electromagnetic force) , 10−4–10−2; static magnetic fi elds and linearly polarized light, <10−4; longitudinally polarized β–particles, 10−9–10−11; WNC, 10−17 (up to 10−10 by recent work78). To greatly amplify these tiny molecular PVED, several possible amplifi cation mechanisms were postulated.

In 1953, Frank proposed an autocatalytic kinetic model to generate chiral species with a preference from achiral species without any initial chiral fi eld.83 Owing to the matter of chance events, the handedness is statistical between levo and dextro forms. Later, Condepudi and Nelson,84 Goldanskii et al.,7 Tranter,85 and other workers developed new autocatalytic and amplifi cation models by taking PVED and thermal fl uctuation into consideration, predicting that mirror symmetry breaking may occur in a fi nite time. The key of these autocatalysis models is the possibility to commonly share with several coop-erative phenomena, known as sergeant soldier and majority rule of polymers,86 supramolecular assemblies,87,88 and chiral synthetic chemistry.89–91 The sergeant soldier and majority rule experiments are regarded as a controlled seeding by chemical chirality origin.

In 1966, Yamagata proposed that PVED linearly adds up in proportion to the degree of polymerization exemplifi ed as DNA and to the number of molecules involved in a crystal, called the linear amplifi cation model.92 Also, most PV-related theorists assumed that it is possible for PVED to amplify by the 5th power arising from spin-orbital coupling (Z 2) and relativistic (Z 3) effects, when the atomic number, Z, of the constituents increases.3

Another fascinating theoretical model is second-order phase transition systems. In 1991, Salam predicted that in amino acids as a model of biomolecules, mirror symmetry breaking occurs around 270 K as a consequence of Bose–Einstein condensation between electron–neutron interactions in analogy with superconductivity—the most established second-order phase transition in condensed matter.93 Helix-helix transition phenomena may be a consequence of the second-order phase transition, while helix-coil transitions may be a fi rst-order phase transition.

As an electromagnetic force driven by the interaction between polar and axial vectors, circularly polarized excita-tion in a system can induce circular dichroism (CD) at the ground state and circularly polarized luminescence at the excited state as observable quantities if chiral molecules and helical polymers exist unequally in systems. This parity-even interaction—a pseudoscalar quantity—changes the sign of the chiroptical signal from positive to negative or vice versa, depending on molecular chirality. However, in parity-odd interactions induced by WNC for a pair of chiral molecules, one enantiomer destabilizes with an energy bias and, con-versely, the other enantiomer stabilizes with the same energy bias. Similarly, for a pair of helical polymers, a left-handed-screw (M) helix stabilizes with an amplifi ed PV bias in a cooperative manner of repeating units and a right-handed-screw (P) helix destabilizes with the same PV bias or vice versa. As a consequence, the WNC–induced mirror-symmetry breaking with differences in physical and chemical properties could be detectable by chiroptical signals and



even achiral signals with great care of precision measure-ments and analysis.

Several research groups are experimentally attempting to test the molecular PV hypothesis. Based on Salam’s hypothesis, Wang et al. examined a pair of amino acid single crystals by means of Raman, NMR, neutron scattering, magnetic suscep-tivity, calorimeter measurements, and so on.94–97 In a series of works, she claimed the appearance of subtle differences in physical properties between d- and l-alanine single crystals connecting to WNC below 270 K. Although these results were re-examined by other research groups independently, Compton, Schwerdtfeger et al.,98 and Wilson et al.99 could not agree with her claim owing to the lack of either reproducibility or mean-ingful detection signals. These researchers thought that Wang’s results originated from certain impurities incorporated in non-naturally occurring alanine and crystal imperfection. Recently, Shinitzky et al. reported positive experimental results support-ing subtle differences in helix-coil transition behavior between a pair of synthetic D- and L-oligopeptides with 24 residues in water characterized by CD and isothermal titration calorim-etry experiments.100 They ascribed the subtle difference to ortho (triplet, ↑↑) and para (singlet, ↑↓) spin states of methy-lene protons of amino acid residues.101 However, Lahav, Schurig, and co-workers failed to trace Shinitzky’s results and suggested Shinitzky’s observations were a result of certain impurities of the samples.102 More recently, Schwerdtfeger et al. described that several PV-related experimental results reported so far,94–98,103–106 including the author’s PV test,107 are based on a weak theoretical basis and, hence, are optimistic.108 Indeed, these experimental tests, classifi ed to so-called macroscopic PV experiments, are, in practice, diffi cult to verify by other independent researchers owing to the specifi city of both samples and instruments. To achieve discrete molecular systems existing in a diluted gas phase, enabling avoidance of molecular collisions, several research teams attempted to observe PV differences using ultrahigh-resolution spectroscopy in mid-IR and far-IR region as the best detection system. At the moment, conclusive results using common, easily available, chemical substances, that are testable by anyone at any time at any place, do not appear to be available yet.109–111

Chirality and Dynamics—Hund’s Paradox

In 1927, Hund gave rise to the most fundamental question on molecular chirality dynamics.112 This meant a paradigm shift that changes from space-oriented three dimensional to space-temporal–oriented four dimensional chiral chemistry. He questioned what is the essential role in a relationship between observable optical activity and mirror-image molecu-lar energy equality. Although classical thermodynamics showed exactly the same Gibbs free energy between a pair of enantio-

mers, quantum mechanics disagreed with this energy equality in what is called Hund’s paradox.

To answer this question, he fi rst introduced quantum tunneling to chiral chemistry. The idea, originally written in German, can now be seen in several papers and books written in English.6,11,21,113,114 In the stationary state of achiral systems, being ψL = 1/√2 ⋅ (ψ+ + ψ−), ψR = 1/√2 ⋅ (ψ+ − ψ−), or vice versa, positive (ψ+) and negative (ψ−) wavefunctions generate a small splitting energy (∆E±) depending on the ratio V/�υ in the temperature independent formulae, ∆E± = 1/(2√π) ⋅ √�υ Vb ⋅ exp(−Vb/�υ), where Vb is the tunneling barrier height, and υ is the frequency of the vibration modes in a single well potential. The racemization time Trac, based on the resonance tunneling mechanism, is Trac = �/∆E±. Achiral substances in a double well potential can possibly oscillate between enantiomers without any external bias. If ∆E± is suf-fi ciently large, one enantiomer cannot be isolated and optical activity as ensemble average of chiral states is not observed, leading to CD–silent chirality and dynamic chirality. Even if ∆E± is suffi ciently small, chiral substances will be isolatable and, eventually, racemize in a fi nite time. This is because the wavefunction of a L-isomer partly or fully mixes with that of a D-isomer.

In 1976, Harris, following a series of studies, theoretically demonstrated that, in a hypothetical chiral substance in a double-well potential, one can observe asymmetric oscillation—a quantum beat—in optical activity with time, arising from interference between PC-driven quantum tunneling and PV-driven energy bias.115–117 Baron also discussed the time-dependent optical activity of hypothetical chiral molecules in which energy splitting varies with a change from single-well to double-well potentials.118 Quack, who introduced the Hund’s paradox to us in his comprehensive review, proposed possible molecular PV detection approaches including ro-vibration modes.6,119 The double-well potential, followed by resonant quantum tunneling, may have a similarity of stochastic reso-nance in biology by thermal noise origins.120

Forces and Interactions in Chemistry

In chemistry, recent knowledge and understanding on a broad range of chemical forces and interactions led to the new idea that weak CH/π (and CH/X, X = F, O, N, and Cl) interac-tions with weak directionality may play key roles in stabilizing secondary, tertiary, and higher order structures of proteins and DNA because of the ubiquitous existence of C–H bonds and π-containing groups in biopolymers.121–123 These forces and interactions by chemical origins are consequences of PC-electromagnetic physical forces. Nishio pointed out the importance of CH/π and CH/X interactions among small molecules in crystals.121 Desiraju and Steiner classifi ed several types of hydrogen bonds into very strong, strong, and weak




C CCH3

C OOC

H

H

n

poly(triphenylmethylmethacrylate)

CN

n

poly(t-butyl isocyanide)

t-Bu

Thermally stable helix with achiral side groups at room temperature

n

poly(phenylenevinylene)

S n

N n

R

R2R2R1

Nn

SiR1

R2n

polythiophene

polypyrrole polyaniline

polyacetylene

polysilane

R1

R2

poly(diacetylene)

nn

poly(p-phenylene)

Helix induced by chiral side groups and/or chiral chemical influence

C

O

NR

polyisocyanate

n

CN

NR

polycarbodiimide

n

n

polyfluorene

R2R1

R2

R1

n

R1 R2 R1R

H

forces and/or into conventional and nonconventional interac-tions.122 Strong forces in chemistry refer to hydrogen bonding, coordination bonding, dipole-dipole, electrostatic, and π-π stacking forces. Although the CH/π interaction is one of the weakest forces (down to ∼0.2 kcal/mol), this weakness is responsible for increased structural adaptability.

However, the power of these forces, even with their weak-ness and weak directionality, can greatly add-up by cumulating attractive intramolecular and intermolecular interactions in a cooperative manner. Indeed, ultraweak CF/Si interactions (∼0.001 kcal/mol) underwent helix–coil transitions of polysi-lane carrying fl uoroalkyl groups.124 This CF/Si amplifi cation comes from the intramolecular proximity effect between the backbone and side groups. It is possible to tune the degree of the power by the choice of side-chains, solvents, molecular weight, chemical additives, and solution temperature. These weak and ultraweak forces permit unlimited opportunities for designing optically active helical polymers from CD–silent polymers with intra- and inter-molecular chirality transfer by dictating weak chiral forces. (Chart 1).

Mirror Symmetry Breaking by Chemical Bias

Thus far, much effort in asymmetric synthetic chemistry has been devoted to effi ciently producing chiral molecules with a

high ee value. The use of chiral auxiliaries and catalysts with high ee purity are usually required, leading to the product purity linearly responding to the ee of the auxiliary and catalyst used. Several theoretical models have suggested that autocata-lytic processes by chemical origins may result in kinetically controlled asymmetric amplifi cation. These predictions that a nonlinear relationship in ee values between the products and chiral catalysts occurs in many asymmetric chemical reactions are experimentally known.

On the other hand, polymers should essentially show this kind of cooperativity in single- and multiple-strand helical structures.86 Polymers, that are molecularly dissolved in solu-tion, aggregates in solution, on the surfaces, and in the solid fi lm state, become ideal molecular systems to reproducibly elucidate cooperative phenomena, including amplifi cation, switching, and memory of chirality, helicity, and, hence, chiroptical properties.125

Mirror Symmetry Breaking at the Polymer Level

In the early stage of helical polymer stereochemistry, a few polymers were known to adopt a helical main chain with a predominantly screw sense in solution at room tem-perature. Helical structures of poly(t-butyl isocyanides),126

poly(triphenylmethyl methacrylate),127 polyisocyanate,128 and

Chart 1. Optically active chromophoric helical polymers.



poly-α-olefi ns129 are maintained through proximity effects between side chains. These pioneering works prompted to create many artifi cial, optically active polymers with chromophoric main chains bearing chiral and/or bulky side groups or chiral additives. Polyisocyanide,130–135 polyisocya-nate,135,136 polyacetylene,137–139 polythiophene,140,141,142 poly(p-phenylenevinylene),143 polycarbodiimides,144,145 polydiacet-ylenes,146,147 polypyrroles,148 polyanilines,149,150 poly(para-phenylene),151 polyfl uorenes,152,153 and polysilanes125,154 are typical polymers.

In the review by Goldanskii et al, they demonstrated how it is possible for tiny left-right energy differences by extrinsic and intrinsic physical origins to attain homochirality on Earth at four hierarchical stages.7 The idea is applicable to material science and polymer science. Artifi cial helical polymers made of chromophoric main chains appear to be much simpler than biological polymers to test several cooperativity effects. Weak and ultraweak intra– and intermolecular interactions effi ciently add up to a strong force, enabling a system to overcome a thermal fl uctuation energy of ∼0.6 kcal/mol.124,125 This coop-erativity is detectable by ordinary circular dichroism (CD) and other physicochemical measurements.

Any minute chiral forces caused by intra– and intermo-lecular interactions can be detectable when proper chromo-phoric polymers were chosen to elucidate the cooperativity of amplifi cation, switching, and memory. In polyisocyanate bearing chiral H/D side groups in solution, a tiny energy on the order of several cal per mol (not kcal!) can distinguish the right-handed (P-, plus) and left-handed (M-, minus) screw senses and lead to a helical structure with a preferential screw-sense.135,136,155–158 The sergeant-soldier named by Green et al. features a preferential screw-sense helix amplifi cation in copo-lymers.135,136,159,160,161,162,163 A small portion of enantiopure chiral side groups determines the overall screw sense (P or M) of helical main chains bearing a majority of achiral side groups, and a population of helicity with one preferential screw-sense is nonlinearly amplifi ed as a function of the chiral impurity. Pino et al. fi rst reported this phenomenon in poly-α-olefi n copolymers,161 and this sergeant-soldier experiment has been demonstrated in polyisocyanate,159,160 polyacetylenes,162 and supramolecular assemblies.163 The majority rule named by Green et al. is another signifi cant helical amplifi cation in opti-cally active copolymers with a preferential screw-sense.135,136,164 The screw sense of helical main chain bearing, nonracemic chiral side groups is controlled by the %ee only and a popula-tion of preferential screw-sense helicity and optical activity were nonlinearly amplifi ed by the %ee of chiral side groups. Pino et al. fi rst reported this phenomenon in poly-α-olefi ns made of vinyl co-monomers bearing non-racemic chiral moi-eties,165 this majority rule has been demonstrated in polyisocya-nates bearing non-racemic chiral side chains164,166,167 and supramolecular assemblies.168,169

Circularly Polarization Light by Helix Origin

With respect to the chiroptical characterization of fl oppy polymer chains in solution at a given temperature, a major question will be whether an optically active polymer made of an enantiopure monomer adopts a helix with purely P- or M-screw sense or is composed of a diastereomerical mixture containing P- and its diastereomeric M (M′)-screw senses. Further questions are the chain dimensionality of polymers and degree of chain coiling. To obtain information of the main chain helicity, FL studies combined with CD and UV/Vis measurements from the main chain may be useful. The idea is based on the fact that photoexcited energy above the optical band gap should relax to segments in the lowest energy state incorporated in the same main chain and then be emitted from the segments.

A family of helical polysilanes containing only stereogenic bonds in the main chain are state-of-the-art polymers for elu-cidating the inherent nature of polymer helixes because they embody a fl uorophoric chromophore in the main chain, exhib-iting intense UV, CD, and FL bands arising from the Siσ-Siσ* transition around 300–400 nm.170,171 The uniqueness of helical polysilanes is to facilitate the characterization of helix coopera-tivity such as chiroptical amplifi cation, switching, and memory. Additionally, photophysical characteristics of polysilane—intensity, spectral width, peak position, Stokes’s shift, and spectral width—are very susceptible to main chain stiffness, population of P- and M-helices, degree of polymerization, temperature, and solvent polarity. These spectroscopic proper-ties can be straightforwardly connected to other achiral visco-metric measurements, NMR, and AFM observations.

In chromophoric polymers, the intuitive meaning of Cotton CD signal intensity is very similar to that of a UV/Vis signal, with the additional dimension of the subtracted absorp-tion between left and right circularly polarized light.18 Phenomenologically, absorption of light obeys the Beer-Lambert law and thus CD intensity is defi ned as ∆ε = εL − εR = (AL − AR) / cl, where ∆ε is the molar circular dichro-ism intensity, εL and εR are the molar absorptivity for L and R circularly polarized light, respectively, AL and AR are the absor-bance of L and R light, c is the molar concentration per repeat unit and l is the path length. CD bands are commonly referred to as either positive or negative Cotton effects and the peaks as extrema. The ratio of the absorption strength of unpolarized UV-vis signals over the magnitude of CD (polarized) absorp-tion is a useful characteristic. This is formalized in the dimen-sionless parameter, Kuhn’s dissymmetry ratio, gCD = 2 ⋅ ∆ε / (εL + εR) = ∆ε / ε = 2 ⋅ (AL − AR) / AL + AR), where ε is the molar absorptivity per repeat unit. The dissymmetry ratio is also a function of the magnetic and electric transition dipole moments (m and µ, respectively) and the angle θ between them, such that gCD = 4 ⋅ R/D = 4|m||µ| cos θ (m2 + µ2)−1, where




R and D are the rotatory strength and the dipole strength, respectively.172 For chromophoric helical polymers, this gCD value gives information on the helical characteristics (screw pitch, screw sense, and diastereomeric and/or chiroptical purities).

For discrete polysilane chains in isotropic media, the observed CD signal indicates chirality in the main chain helix with the preferential screw sense at the ground state. The ideal-ized CD and UV spectra for single P and M-screw sense poly-mers are illustrated in Figure 1 (a). Particular attention should be paid to the interpretation of gCD owing to an equal amount of the opposite screw sense helical segments with helix rever-sals. If absorption of P and M occurs at the same wavelength, the magnitude of gCD results in CD–silent signals, as illustrated in Figure 1 (b).

In 1994, two research groups independently reported the synthesis and chiroptical properties of dialkylpolysilanes bearing (S)-2-methylbutyl groups. Möller, Matyjaszewski et al. fi rst reported the optical activity from two copolymer systems.173 The author elucidated the most fundamental features of poly(n-decyl-(S)-2-methylbutylsilane) (1), poly(methyl-(S)-2-methylbutylsilane) (2), and homologues,174–176 followed by a series of related works by the author and his co-workers.

Polymer 1 showed the fi rst UV, CD, and FL spectral characteristics of an ideal rod-like P-helix with embodying chromophore and fl uorophore induced by preferential side group interactions in dilute isooctane at 20 °C. Although the P-helix is originally assumed to be the positive Cotton CD signal, this notation can now be verifi ed by a recent Gauss-ian03 TD-DFT program.

As evident in Figure 2 (a) and (b), 1 exhibits a very intense, narrow UV absorption at 323 nm, with ε ∼55,000 (repeat-unit)−1⋅dm3⋅cm−1 and an FWHM (full-width-at-half-maximum) of ∼8 nm. The value of ε is ca. six times greater and the FWHM and narrower by one-sixth than conventional random coiled dialkylpolysilanes. The CD spectral profi le at

323 nm completely fi ts within the UV spectrum. The FL spectral profi le at 328 nm is the mirror image of the UV and CD band profi les. The FL anisotropy (FLA) value around the 323 nm UV-CD bands reaches a theoretical limit of 0.4, when a rigid rod chromophoric fl uorophore is randomly distributed, being collinear in a rigid medium. Note that 1 was the fi rst example of ideal UV-CD-FL characteristics in the realms of polysilanes and optically active polymers.174,176 Several optically active chromophoric polymers in which a single CD signal profi le coinciding to the corresponding visible absorption band profi le have been discovered recently, for example, polyacety-lenes bearing chiral alkyl amides and chiral alkyl esters.177–179

The dipole strength of the UV absorption band appears to be independent of the n-alkyl side group length and main chain repeat numbers. Integration of the 323 nm UV absorp-tion band of the poly(n-alkyl-(S)-2-methylbutylsilane) deriva-tives depends only very weakly on the repeat number. These results led to the important idea that in the case of optically active polysilanes, the gcd value can be used to characterize helical parameters such as the population of P- and M-motifs and their regularity, rather than the values of ∆ε or optical rotation. From the Mark-Houwink-Sakurada plot of 1,174 the viscosity index (α) value of 1.35 in THF at 30 °C is typical of a rod-like global conformation. From precise experiments of dimensionality, the persistence length (q) of 1 was as long as 70 nm in isooctane at 20 °C elucidated by Sato et al180 and the high q value is almost identical to polyisocyanate (q = 76 nm) bearing β-branched (R)-2,6-dimethylheptyl groups.181

Bisignate Cotton CD signals have two possible origins. First, in a polymer containing both P- and M-screw senses with slightly different absorption wavelengths, the positive and negative Cotton effects will be slightly offset with respect to each other, resulting in an apparent bisignate signal.174,175 Second, for two adjacent chromophores, coupling between the stronger electronic transition dipole moments will occur to give bisignate split-type CD signals—the exciton couplet

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/ (re

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t-u

nit

) -1d

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/ (re

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) -1d

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UV

P

P(a)

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-0.5

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Wavelength / nm

CD

UV

P

M M

P

P

M

(b)

Fig. 1. Illustrations of coincident CD and UV absorption profi les for chromophoric main chain with (a) P-screw sense, (b) equal proportion of P- and M-screw senses.



signal.182 This is classifi ed as either an intramolecular interac-tion in the same molecule at a kink upon chain folding, or an intermolecular interaction in aggregate phases. The sign of the bisignate signal in the exciton couplet affords a simpler method for determining the absolute confi guration (right- or left-handed confi guration) between two intimately interacting chromophores.

In a series of poly(alkyl-(S)-2-methylbutylsilane)s, only 2 exhibited a very different CD spectrum around the UV absorp-tion at 300 nm.174,175 As seen in Figure 2 (c) and 2 (d), 2 exhibits a very broad, weak UV absorption around 300 nm, with ε ∼5,500 (Si-repeat-unit)−1⋅dm3⋅cm−1 and an FWHM ∼50 nm. An apparent bisignate CD signal with positive and negative bands was observed. The FLA value around the 300 nm UV and the bisignate CD band changed from 0.4 at 310 nm to almost 0.0 at 250 nm, probably with bent chromo-phores with different screw pitch and the opposite screw sense in the same chain in a coiled shape. Note that these UV-CD-FL characteristics of 2 are very typical for those of ordinary

fl oppy polysilanes. The α value of 2 of 0.59 in THF at 30 °C is typical of a coiled shape. This idea was supported from screw-sense-selective, cut-and-paste experiments, by producing a recombined 2 consisting of an almost pure P-screw sense.

Global Shape and Optical Property

The conformational mobility of a chromophoric polymer is often connected to its electronic structure. Therefore, changes in the UV/Vis absorption spectra and/or (chir)optical pro-perties are spectroscopically observable as thermo-, solvato-, piezo-, and electrochromisms. Although polysilanes exhibit these phenomena remarkably,183 their structural origins were controversial until relatively recently, since limited informa-tion was available on the correlation between the conforma-tional properties of the main chain, electronic state, and chiroptical characteristics. In 1996, the author found that, in various polysilanes in THF at 30 °C, the main chain

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ore

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ce (

a. u

.)

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ore

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y

Wavelength / nm

(b)

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ore

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.)

Wavelength / nm

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Flu

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Wavelength / nm

(d)

Fig. 2. (a) UV absorption and FL spectra and (b) Cotton CD spectra with FL anisotropy of poly(n-decyl-(S)-2-methylbutylsilane) (1, Mw = 5.3 × 106, Mn = 4.1 × 106, α = 1.35 in THF at 30 °C) in isooctane at 20 °C. (c) UV absorption and FL spectra and (d) Cotton CD spectra with FL anisotropy of poly(methyl-(S)-2-methylbutylsilane) (2, Mw = 5.1 × 104, Mn = 1.6 × 104, α = 0.59 in THF at 30 °C) in isooctane at 20 °C.




peak intensity per repeat unit, ε (Si-repeat-unit)−1⋅dm3⋅cm−1, increases exponentially as the value of α increases.184 Although conventional viscometric measurements require a wide range of narrow polydispersity polymer samples, a size exclusion chromatography instrument equipped with a viscometric detector provides the intrinsic viscosity, [η], as a function of the molecular weight of the polymer, M, in a real time, from the Mark-Houwink-Sakurada plot.

Figure 3 shows the UV absorption spectra of fi ve optically active dialkylpolysilanes bearing different chiral side groups (Chart 2) in THF at 30 °C.174,184 Evidently, as the value of α increases from 0.59 to 1.25, the UV absorption intensity

increases, whereas the full width at half maximum (FWHM) decreases. These results led to the fi nding of a semi-empirical relationship between the main chain absorption characteristics and the global shape of various polysilanes in solution. Suggested from extremely narrow, intense peaks at 316 nm, poly(6,9,12-trioxatetradecyl-(S)-2-methylpropylsilane) (3) is assumed to ideally adopt a perfectly extended rod (correspond-ing to α ∼ 1.7–2.0) in EtOH at −104 °C.182

Figure 4 shows a correlation between the values of ε, FWHM, and α of various poly(dialkylsilane)s and poly(alkylarylsilane)s in THF at 30 °C.171,184 The polymers include seven optically active helical dialkylpolysilanes with

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60,000

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200 250 300 350 400

e / (

Si-

rep

eat-

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it)-1

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Wavelength / nm

4

52

3 (-104 °C)

6

Fig. 3. UV absorption spectra of four optically active polysilanes in THF at 30 °C and one optically active polysilane in EtOH at −104 °C: Poly{methyl-(S)-2-methylbutylsilane} (2, α ∼0.59), poly{n-hexyl-(S)-4-methylpentylsilane} (6, α ∼0.75), poly{n-hexyl-(S)-3-methylpentylsilane} (5, α ∼0.92, poly{n-hexyl-(S)-2-methyl-butylsilane} (4S, α ∼1.25), and poly{6,9,12-trioxatetra-decyl-(S)-2-methyl-butylsilane} (3, expecting a very high α).

Si

(S)

H3C

CH3n

1

CH3

Si

CH3

(S)

H3C

CH3

n

2

H (S)

Si

O

O

O

CH3

H3C

CH3n

3

H

Si

(S)

CH3

H3CCH3

n

5

H

Si

(S)

CH3

CH3

H3C

n

6

H

Si

(S)

H3C

CH3n

4S

CH3

Si

(R)

H3C

Hn

4R

CH3

H CH3

1,000

10,000

100,000

100

1,000

10,000

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

e / (

Si-

rep

eat-

un

it)-1

dm

3 cm-1

FW

HM

/ cm

-1

Viscosity index (a )

200,000

rodlikestiffcoilglobule

20,000

Fig. 4. Correlation between near-UV intensity (ε) peaking from 300 to 350 nm, full width at half maximum (FWHM), and α value of various dialkylpolysilanes and alkylarylpolysilanes in THF at 30 °C.

Chart 2. Optically active polysilanes bearing enantiopure chiral side group.



four different types of chiral β–, γ –, and δ–branched pendants, eleven optically inactive dialkylpolysilanes with six different types of achiral β–, γ –, and δ–branched pendants, a CD-silent helical dialkylpolysilane with racemic chiral pendants, and two CD-silent helical alkylphenylpolysilanes. Although the value of λmax for these polysilanes ranges from 290 to 352 nm, the value of ε increases exponentially with an increase in the α value, and the value of the FWHM decreases exponentially. The degree of σ–conjugation, global conformation, and UV absorption characteristics are thus controllable by the choice of side groups, regardless of chirality and non-chirality in the side groups.

Polymer 2 has the most shrunken shape with α ∼0.59, whereas longer n-alkyl chain derivative, poly{n-hexyl-(S)-2-methylbutylsilane} (4S) is rod-like with α ∼1.25. Poly{n-hexyl-(S)-4-methylpentylsilane} (6) with α ∼0.75 is a random coil similar to conventional fl exible polysilanes. Poly{n-hexyl-(S)-3-methylpentylsilane} (5) with α ∼0.92 is stiff (semi-fl exible, semi-rigid), revealing an intermediate manner between 4S and 6.

From the ε–α –FWHM relationship of polysilanes, both the values of ε and FWHM provide information on the degree of chain coiling in solution at a given condition and, hence, are important in discussing the global shape in any condition. From the extrapolation of the ε-α relationship, the relationship predicted the upper limit of the ε value of an ideal polysilane rod. The upper limit of the ε value for an ideal polysilane rod will be ∼150,000 (Si-repeat-unit)−1⋅dm3⋅cm−1 because the maximum value of α for an ideal polymer rod may be 1.7–1.8.182,184 It was proven that 3 in ethanol progressively changed from an ε of 42,000 with an FWHM of 800 cm−1 (8 nm) at 323 nm to the ε value of 102,000 with an FWHM of 400 cm−1 (4 nm) at 318 nm when the solution temperature was cooled from 25 to −104 °C.182 This ε value, being the highest among all polysilanes tested, might be responsible for an ideal, perfect rod in an isotropic solution.

Mirror Symmetry Breaking by Chemical Origins

The Effective Side-Chain Proximity Effect in Solution—Sergeants-and-Soldiers

The most striking cooperativity in helix amplifi cation might be the sergeants-and-soldiers in copolymers, in relation to the homochirality question. The idea of cooperativity can be seen in Salam’s paper to plainly explain the origin of the phase transition.93 A minority of enantiopure chiral side groups effec-tively drives screw sense (P or M) of CD-silent helixes bearing a majority of achiral pendants, leading to a purely P- or M-helix. Although Möller, Matyjaszewski et al. fi rst reported two optical active copolymers, poly([bis{(S)-2-methylbutyl}silane)-co-(di-n-pentylsilane)) and poly[{(S)-2-methylbutyl-n-pentylsilane}-co-(di-n-pentylsilane)],173 the copolymers did not clearly show nonlinear enhancement of CD intensity around 320 nm in cyclohexane. This is attributable to the inclusion of fl oppy di-n-pentylsilane comonomer units.

Noticeable helix amplifi cation—sergeants-and-soldiers—was found in rod-like polysilane copolymers in isooctane by the author (8), which were prepared by Wurtz co-condensation of n-hexyl-2-methylpropyldichlorosilane (a-7), n-hexyl-(S)-2-methylbutyldichlorosilane ((S)-4), and n-hexyl-(R)-2-methylbutyldichlorosilane ((R)-4) (Chart 3).154,185 Although the UV–CD spectral features of the copolymers are almost identical with the UV spectral features of CD-silent poly(n-hexyl-2-methylpropylsilane) (7, α ∼1.21), the λmax of 8 varies sensitively with changes in the mole fraction of chiral substituents and temperature.154,185 Copolymer 8 is suitable for testing the sergeants-and-soldiers experiment by their inherent CD-UV characteristics. This arose from effective proximate effects between (S)-4, (R)-4, and a-7 comonomer repeating units. Both the corepeating units have commonly β-branched side chains, regardless of chiral and achiral side chains, afford-ing a rod-like nature. This combination is important to effec-tively afford several cooperativity phenomena.

Si

H3C

CH3

Si

CH3

CH3CH3

x 1-x n

H3C

Copolymer 9 with (S)-4 and (R)-4majority rule experiments

Si

H3C

CH3

CH3

n

Host polymer 7 for sergeants and soldiers experiments

(S) (R)

Si

H3C

CH3

Si

H3C

CH3

CH3CH3(S) or (R)

x 1-x n

Copolymers 8 with (S)-4 and (R)-4sergeants and soldiers experiments

Chart 3. Chemical structure of polysilane homopolymer (7) and copolymers (8 and 9) bearing chiral and achiral groups for mirror symmetry breaking experiment by internal chiral origins.




Figure 5 (a) compares the UV and CD spectra of 4S and copolymer 8 containing 0.1 mole fraction of (S)-4 and 0.9 mole fraction of a-7 in isooctane at −5 °C. The UV-CD spectra of 8 are almost identical to those of 4S, with the CD profi le matching the corresponding UV band except for their

λmax values. The UV and CD spectra of 8 bearing (R)-4 groups reveal almost identical features to those in 4R, the correspond-ing antipode of 4S, except for the sign of the CD band, as shown in Figure 5 (b). For comparison, UV and CD spectra of 7 in isooctane at −5 °C are displayed in Figure 5 (c). UV

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(R)-form (S)-formMole fraction of (R)- and (S)- groups in copolymer 8

(d)

318

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Wav

elen

gth

/ n

m

Mole fraction of (R)- and (S)- groups in copolymer 8(R)-form (S)-form

(e)

Fig. 5. (a) UV and CD spectra of 4S (solid lines) and copolymer 8 (dotted lines) consisting of 0.1 mole fraction of (S)-4 and 0.9 mole fraction of a-7 (by nominal feed) in isooctane at −5 °C and and 80 °C. (b) UV and CD spectra of 4R (solid lines) and copolymer 8 (dotted lines) containing of 0.1 mole fraction of (R)-4 and 0.9 mole fraction of a-7 in isooctane at −5 °C. (c) UV and CD spectra of 7 in isooctane at −5 °C. Plots of (d) the gCD value and (e) λmax value of copolymers 8 as functions of comonomer fraction of (S)-4 and (R)-4 in these copolymers in isooctane at −5 °C and 80 °C.



spectral characteristics (λmax, ε, and FWHM) between 4S, 4R, 7, and 8 are almost identical, although 7 shows an almost CD-silent signal at 320 nm, indicating an almost equal popu-lation of P- and M-73 helical motifs in the main chain.

Figure 5 (d) plots the gCD values of 8 as a function of the comonomer fraction of (R)-4 and (S)-4 in the copolymers at −5 °C and +80 °C. Evidently, 0.05–0.10 mole fraction of the chiral units in 8 effectively induces purely P- and M-helices at −5 °C. However, this cooperativity at +80 °C considerably diminishes and 0.20 mole fraction of the chiral units is neces-sary to induce a helix with a preferential screw sense, possibly owing to an increase in fl uctuation acting as thermal noise to the polymer systems.

Figure 5 (e) plots the λmax values of 8 as a function of the mole comonomer fractions of (R)-4 and (S)-4 in the copoly-mers at −5 °C and +80 °C. Evidently, the value of λmax redshifts nonlinearly at −5 °C and +80 °C as the chiral fraction increases.

The values of λmax at +80 °C tend to redshift compared to those at −5 °C at any chiral mole fraction when the solution tem-perature increases. These features are associated with a change in screw-pitch of the main chain because ab initio calculations of polysilane suggest that Siσ-Siσ* absorption blueshifts pro-gressively with a change in the main chain dihedral angle from planar all-anti to 41 helix.186

The Effective Side-Chain Proximity Effect in Solution—Majority Rule

The other noticeable helix amplifi cation—majority rule—was found in rod-like polysilane copolymers (9) bearing (S)-4 and (R)-4 units in isooctane by the author (Chart 3).154,185 This effect is important in relation to the homochirality question. Figure 6 (a) compares the UV and CD spectra between 4S and 9 with 0.60 mole fraction of (S)-4 and 0.40 mole fraction of

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Mole fraction of 2-methylbutyl groups

(S)-form

(R)-form

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

(C)

320

322

324

326

328

330

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-5 °C80 °C

0.00.10.20.30.40.50.60.70.80.91.0

Wav

elen

gth

/ n

m

(S)-form

(R)-form

Mole fraction of 2-methylbutyl groups

(d)

Fig. 6. (a) UV and CD spectra of 4S (solid lines) and 9 (dotted lines) containing 0.60 mole fraction of (S)-4 and 0.40 mole fraction of (R)-4 in isooctane at −5 °C. (b) UV and CD spectra of 4R (solid lines) and 9 (dotted lines) containing 0.60 mole fraction of (R)-4 and 0.40 mole fraction of (S)-4 in isooctane at −5 °C. The values of (c) gCD and (d) λmax in 9 as functions of the mole comonomer fraction of (R)-4 and (S)-4 in isooctane at −5 °C and 80 °C.




(R)-4 units (20 % (S)-ee) in isooctane at −5 °C. Figure 6 (b) compares the UV and CD spectra between 4R and 9 with 0.40 mole fraction of (S)-4 and 0.60 mole fraction of (R)-4 units (0.20 mole fraction (R)-ee) in isooctane at −5 °C.

The UV and CD spectra of 9 with 20% (S)-ee are almost identical to those of 4S and 4R. The CD peak profi le almost completely matches the corresponding UV absorption profi le, including peak intensity and λmax values. The UV and CD spectra of 9 with 20% (R)-ee exhibit almost identical features to those in the (S)-rich 9 with an inversion of the CD sign, as shown in Figure 6 (b).

As shown in Figure 6 (c), from the plot of the gCD values of 9 as functions of the mole fraction of (R)-4 and (S)-4 units, 20 %ee of (R)-unit over (S)-unit in 9 can effi ciently induce an almost purely M-helix and vice versa. Even only 6 %ee of 4S and 4R units can signifi cantly induce a preferential screw sense helix. The structural identity between 4S and 4R units in copolymers with stiffer main chains appear essential to induce an effective majority rule. As shown in Figure 6 (d), from the plot of the λmax value of 9 as a function of the mole comonomer fraction of (R)-4 and (S)-4 units, the value of λmax blueshifts very slightly, when the %ee of (R)-4 and (S)-4 units changes from 100 to zero, indicating minimal change in the screw-pitch of the main chain, in line with the ab initio calculation.186

Mirror Symmetry Breaking by Chemical and Physical Origins

Switching Helicity by Temperature Origin

Designing and controlling helical polymers with dynamic pro-perties are current issues. Polyisocyanate135,136,155,156,159,166,167,191 and polyacetylenes137,138,139,176,177,179,190,192,193 are the most suc-cessful polymer systems. However, the most striking helix ampli-fi cation phenomenon of a helical polymer might be preferential screw sense inversion by physical and/or chemical biases, as a

consequence of the opposite directions in helix amplifi cation. This phenomenon called helix-helix (PM) transition is classifi ed to mirror symmetry breaking by chemical and physical origins because the polymer should adopt CD-silent helix and/or CD-silent achiral states under given conditions. Biochemists originally found this intriguing phenomenon in synthetic DNA,187 known as the B-Z transition driven by a change in salt concentration, in 1972, and poly(l-aspartic acid ester)s driven by a change in temperature, in 1968.188 Subsequently, several syn-thetic polymers were found to undergo a PM-transition and this phenomenon became popular.189–195 The author and co-workers found that certain dialkypolysilane homopolymers and copolymers196–200 and a diarylpolysilane copolymer201 are able to undergo a PM-transition by temperature origin in solution. This section highlights dialkylpolysilane homopolymers for quanti-tatively discussing PM transition characteristics.202

Poly{(S)-3,7-dimethyloctyl-3-methylbutylsilane} (10) is classifi ed as a rod-like helical main chain polymer (Chart 4). Polymer 10 and its (R)-isomer (11) afford an intense, narrow CD band, completely matching the corresponding UV band and FL band mirror image profi les, characteristic of the rigid rod-like helical polysilanes described above. The occurrence of the PM transition is chiroptically detected as an inversion of the CD profi le. Figure 7 (a) and (b) compare the CD and UV absorption spectra of 10 at −40 °C and −5 °C, and, for comparison, poly{(S)-3,7-dimethyloctyl-2-methylpropylsilane} (12) at −82 and +80 °C in isooctane. The positive-sign CD spectrum of 10 with λext of 320 nm at −40 °C is almost the inverse of the negative-sign CD spectrum with λext of 322 nm at −5°C. Polymer 10 undergoes a PM transition between the two temperatures though helical motifs at −40 and −5 °C that are inequivalent energetically and spectroscopically. On the other hand, neither poly{(S)-3,7-dimethyloctyl-2-methylpropylsilane} (12) nor its (R)-isomer, poly{(R)-3,7-dimethyloctyl-2-methylpropylsilane} (13) undergo any such PM-transition detectable as inversion of the CD spectra in isooctane between −90 and +80 °C. The difference between

14

(S)

Si

H3C CH3

H

n

(S)

H3C

CH3

15

(R)

Si

H3C CH3

H

CH3

n

(S)

H3C

H

CH3

Si

H3C CH3

H3C CH3

(S)

Si

CH3

H3C CH3

(S)

CH3

2101

nn

13

Si

CH3

H3C CH3

(R)

CH3

n

CH3

Si

H3C CH3

H3C CH3

(R)

n

CH3

11

CH3 H H CH3

H

CH3

HH

Chart 4. Chemical structure of six polysilanes (10–15) bearing (S)- and (R)-3,7-dimethyloctyl chiral groups.



10/11 and 12/13 is only the number of methylene spacers between branched achiral side chains and the main chain.

The temperature dependent gCD values of 10 are directly connected to PM-populations of 10. To evaluate the PM-populations, the chiroptical analysis was carried out based on the assumption of weak temperature dependent gCD

values of 12, maintaining a purely P-73 helix at any temperature. Figure 8(a) and (b) show plots of the temperature dependency of gCD

values and the PM-populations of 10 in isooctane based on the above analysis. A steep PM transition clearly occurs at coalescence temperature, Tc, ∼ −20 °C. Polymer 10 with the highest Mw contains 12% P- and 88% M-motifs at −90 °C, while these values are 84% P- and 16% M-motifs at 25 °C. The medium and lower Mw specimens contain 15% P- and

85% M-motifs at −90 °C, while at 25 °C these values are inverted to 76% P- and 24% M-motifs. The transition tem-perature width (∆Tc) tends to slightly broaden as Mw decreases (not shown here). These PM transition characteristics, includ-ing Tc, ∆Tc, and PM-populations, very weakly depend on Mw, possibly arising from the two end termini inducing structural fl uctuations in the main chain.

Note that 10 became CD-silent owing to an almost equal population of P- and M-helices at Tc, regardless of the presence of chiral centers in the side chain. This contrasts to CD-silent 7 at any temperatures arising from a lack of chiral centers. Hence, below and above Tc, the PM-transitioned 10 is regarded as a consequence of mirror symmetry breaking by physical (temperature) origin.

0

50,000

100,000

150,000

-30

-20

-10

0

10

200 250 300 350 400

e / (

Si-

rep

eat-

un

it)-1

dm

3 cm-1

De /

(Si-

rep

eat-

un

it)-1

dm

3 cm-1

Wavelength / nm

-40°C

-40°C

-5°C

-5°CCD

UV

(a)

0

50,000

100,000

150,000

-30

-20

-10

0

10

20

200 250 300 350 400

e / (

Si-

rep

eat-

un

it)-1

dm

3 cm-1

De /

(Si-

rep

eat-

un

it)-1

dm

3 cm-1

Wavelength / nm

CD

UV

80°C

-82°C

80°C

-82°C

(b)

Fig. 7. CD and UV absorption spectra in isooctane of (a) poly{(S)-3,7-dimethyloctyl-3- methylbutylsilane} (10, Mw = 1.6 × 106, Mw/Mn = 1.53) at −40 °C (solid line) and −5 °C (dotted line), for comparison, (b) poly{(S)-3,7-dimethyloctyl-2-methylpropylsilane} (12, Mw = 4.2 × 104, Mw/Mn = 1.51) at −82 °C (solid line) and 80 °C (dotted line).

-3

-2

-1

0

1

2

3

-100 -50 0 50 100

gC

D /

10-4

Temperature / °C

Tc

10

12

(a)

0

20

40

60

80

100 0

20

40

60

80

100-100 -50 0 50 100

Po

pu

lati

on

of P

-hel

ix (

%)

Po

pu

lati

on

of M

-hel

ix (

%)

Temperature / °C

(b)

Fig. 8. (a) Temperature dependent dissymmetry ratios of poly{(S)-3,7-dimethyloctyl-3- methylbutylsilane} (10) (Mw = 1.6 × 106) and poly{(S)-3,7-dimethyloctyl-2-methylpropylsilane} (12) (assumed to a purely P-helix) in isooc-tane. (b) Temperature dependent P- and M-populations of 10 in isooctane evaluated by reference of the regression gCD –T curve in 12 (Fig. 8(a)).




Although the intrinsic origin of the PM-transition remains obscure, the subtle differences in potential energy between oligo-10 and oligo-12 may be critical. Calculations were made for thirty-one repeat units with hydrogen termini. Figure 9 (a) and (b) compare the potential energy of oligo-10 and oligo-12 for it- and st-sequences, respectively. Evidently, it-oligo-10 clearly is in a double-well, that is, two local minima with almost enantiomeric helices at dihedral angles of P-157° and M-210°. The global minimum M is slightly more stable than that of P by approximately 0.67 kcal per repeat unit and the barrier heights of the P- and M-states are only 1.7 and 2.3 kcal per repeat unit, respectively. Also, st-oligo-10 is in a similar double-well at P-160° and M-200° and the global minimum M-state is slightly more stable than the corresponding P by ∼1.3 kcal per repeat unit. The barrier heights for the respective P- and M-screws are only 3.4 and 4.6 kcal per repeat unit. The calculation of oligo-10s suggests that both pseudo-enantiomeric P- and M-motifs are likely to stably coexist in the same main chain at any temperature, regardless of tacticity and molecular weight. The M-motifs of 11 as an antipode of 10 may be more stable than P-motifs below Tc, as expected.

Contrarily, it-oligo-12 is in an unclear, but very asym-metric double well with a minima at P-160° and M-200°. The P-helix is very stable compared to the M-helix by approxi-mately 2.3 kcal per repeat unit. The barrier heights from the respective P and M are 3.9 and 1.4 kcal per repeat unit, indi-cating that P-helix might be stable. On the other hand, st-oligo-12 is in an almost single well potential with P-160°. These calculations assume that the P-motif of 12 is likely to adopt an M-motif at lower temperatures, regardless of tacticity, and conversely, the M-motif of 13 is more stable than the P-motif.

Simple energy parameters of the P- and M-states of oligo-10 (and oligo-11, not shown here) allowed discussion of the origin of the PM transition. Here, ∆G is the difference in free energy between the P- and M-states of 10, which are character-ized by the sign and intensity of the gcd value. Similarly, ∆H and ∆S are the differences in enthalpy and entropy between P- and M-states, respectively.

∆ ∆ ∆G G G H T S H H T S S= − = − = − − −P M P M P M( ), (1)

where P M P M∆ ∆H H H S S S= − = −, (2)

at thenT G T H Sc c, , /∆ ∆ ∆= =0 (3)

From Tc = 253 K and ∆H = −0.67 kcal per repeat unit for 10, it was assumed that ∆S = −2.6 cal⋅K−1 at Tc. The small negative ∆S value and small ∆H value are indicative that the PM-transition is the entropy driven event, arising from an order–disorder transition in the packing of the side chains and T acts as an external physical energy bias as well as electric and magnetic fi elds.

Quantized and Superposed Helicity

Hund’s answer inspired several quantum physicists and chem-ists to discuss quantum tunneling, oscillation, and quantum beating for chirality. Harris et al. theoretically demonstrated the preparation and detection of superposed optical activity for a hypothetical chiral molecule in a double-well potential using femtosecond circularly polarized light pulses,114 although they did not extend the ideas to the possibility of chirality quantum computing. These outlets and understanding on the PM-

-50

-40

-30

-20

-50

-40

-30

-20

90 120 150 180 210 240 270

it-10

st-10

En

erg

y fo

r is

ota

ctic

/ kc

al•m

ol-1

En

erg

y fo

r sy

nd

iota

ctic

/ kca

l•m

ol-1

Dihedral angle / degree

(a)

-50

-40

-30

-20

-50

-40

-30

-20

90 120 150 180 210 240 270

it-12

st-12

En

erg

y fo

r is

ota

ctic

/ kc

al•m

ol-1

En

erg

y fo

r sy

nd

iota

ctic

/ kca

l•m

ol-1


(b)

Fig. 9. Potential energy of (a) it- and st-(S)-3,7-dimethyloctyl-3-methylbutylsilane (10) thirty-one repeat units (oligo-10), and (b) it- and st-(S)-3,7-dimethyloctyl-2- methylpropylsilane (12) thirty-one repeat units (oligo-12) as a function of main chain dihedral angle (Discover 3, PCFF).



transition ability of 10–13 stimulated us to design more sophisticated PM-transitioned poly{(R)-3,7-dimethyloctyl-(S)-3-methylpentylsilane} (14) and non-PM-transitioned poly{(S)-3,7-dimethyloctyl-(S)-3-methylpentylsilane} (15) for comparison.

By referring to the regression curve with the gCD values of 12, being in a purely P-motif over the temperature range, it is possible to quantitatively evaluate the PM-population of 14 and 15 in solution. Figure 10 (a) plots variable temperature gCD values of 12, 14, and 15. Figure 10 (b) displays the evalu-ated portion of the PM-motifs of 14 and 15 in isooctane between −80 and +80 °C. It is evident that 14 features three

distinct switching regions; 1 (−80 to −10 °C), 2 (−10 to +10 °C), and 3 (+10 to +80 °C). Region 1 in 14 contains a constant 80% P and 20% M (60% P excess over M), but, contrarily, region 3 has 80% M and 20% P (60% M excess over P). However, 15 invariably contains temperature–independent, 80% P and 20% M (60% P excess) over the entire temperature range. This behavior arises from a greater difference in the potential energy between 14 and 15 (Fig. 11). This led to an idea that step-like switching between regions 1 and 3 may be the consequence of superposed helicity, as pre-dicted by Hund, but not from a simple PM-transition between pure P- and pure M-states.

-3

-2

-1

0

1

2

3

-100 -50 0 50 100

gC

D /

10-4

Temperature / °C

(a)

15

12

14

0

20

40

60

80

100 0

20

40

60

80

100-100 -50 0 50 100

Pro

po

rtio

n o

f P

-hel

ix (

%)

Pro

po

rtio

n o

f M

-hel

ix (

%)

Temperature / °C

region 1 region 3region 2

(b)

14

15

Fig. 10. (a) Variable temperature gCD of 14 (Mw = 5.8 × 106, Mn = 3.4 × 106, fi lled circles), 15 (Mw = 4.7 × 106, Mn = 2.1 × 106, open circles), and 12 (crosses) in isooctane in the range of −80 and +80 ˚C. (b) Evaluated proportion of P- and M-motifs of 14 (fi lled circles) and 15 (open circles) as a function of solution temperature.

-50

-45

-40

-35

-30

90 120 150 180 210 240 270

it-oligo-15it-oligo-14

En

erg

y / k

cal•

(Si r

epea

t u

nit

)-1


(a)

-48

-46

-44

-42

-40

120 140 160 180 200 220 240

En

erg

y / k

cal•

(Si r

epea

t u

nit

)-1


P-helix M-helix

below Tc

at Tc

above Tc

helixreversal

(b)

Fig. 11. (a) Dihedral angle dependency of potential energy for it-14 and it-15 model molecules with thirty-one repeating units and hydrogen termini (oligo-14 and oligo-15). (b) Schematic resonant tunneling picture between P- and M-states. Potential energy as a function of dihedral angles of it-oligo-14 with three switching regions. Below Tc (bottom trace with fi lled circles), at Tc (middle trace, hypothetical curve), and above Tc (upper trace, hypothetical curve). Dotted arrows indicate tunneling processes between wavefunctions of P- and M-motifs coexisting in the same main chain.




The most signifi cant feature of 14 exists in region 2 because the superposed state varies almost linearly with thermal energy bias as an external physical origin, ranging from 60% M- to 60% P-excess. The PM-switching characteristics can sensitively recognize the topology of small solvent molecules with the help of the two branched side chains. The superposed helicity linked by twisting motions is regarded as dynamic memory, since if the solvent molecules (external chemical bias) are taken away, the superposed state may modify the PM population. This led to a change in the Tc value with a range of hydrocarbon solvent molecules with different degrees of branching. This solvent effect was demonstrated in the emerg-ing optical activity from CD–silent polyisocyanate with the help of solvent chirality.203,204 Mirror symmetry breaking by this chiral solvation energy is as minute as 40 µcal per repeat unit.203

The present results of 10, 14, and other PM-transitioned polysilanes are attributed to the fi rst chiroptical detection of quantized and superposed helicity operating at almost ambient temperature, which could be a possible answer to the long-standing issue known as Hund’s paradox. A remaining chal-lenging issue is the chiroptical detection of quantum oscillation as a function of temperature and studies are now on-going.

Mirror Symmetry Breaking as a Polymer Particle by Solvent Chirality Transfer

By inspiring Hund’s paradox and PM-transitioned polysilanes, the essence of helix induction ability by internal and external chemical origins should be connected to the degree of barrier height in a double well. When the barrier is suffi ciently small,

helical motifs rapidly oscillate between one helix and the other helix with time. This led to the idea that, if polysilane without stereogenic centers in a symmetric double well had a low barrier height between P- and M-helices in a fl uid solution, helicity may oscillate dynamically, leading to CD-silent poly-silane. However, if the polysilane abruptly switched to a high barrier height by external chiral chemical bias, the oscillating helicity might quit according to Hund’s paradox. In this case, the sign and magnitude of CD signals from the polysilane should be connected to the solvent chirality added. To verify this hypothesis, in a homogeneous solution of CD-silent poly-mers without stereogenic centers in a double well, poly[n-hexyl-(p-n-propoxyphenylsilane] (16) as a model of a CD-silent polymer (Fig. 12) was tested with the help of a family of poorer chiral alcohols as external chiral chemical bias.203,204

Prior to this test, the potential curve of it-16 model oligo-mer with thirty-one repeating units and hydrogen termini (it-oligo-16) was calculated (Fig. 12). An it-oligo-16 clearly is in an almost symmetric double well, which has two energy minima at P-150° and M-210°. The barrier heights of the M- and P-screws are 3.0 kcal per repeat unit, equivalent to fi ve times RT. This small barrier height is enough to undergo an oscillation with time by quantum tunneling.

Indeed, 16-based particles produced in this way clearly showed CD-activity in the Siσ–Siσ* transition region (Fig. 13(a)).205 The 16 particles by chiral alcohol bias exhibit uniquely bisignate induce circular dichroism (ICD) based on amplifi ed chiral ordering as shown in Figure 14. The sign of the ICD depends on the absolute confi guration of the chiral alcohol used. This indicates that 16 forms chirally oriented particles with the help of the weak OH/O interaction between ether moieties and the OH group of the chiral alcohols.

-10

-5

0

5

90 120 150 180 210 240 270

En

erg

y / k

cal•

(Si-

rep

eat-

un

it)-1


P M

16

CH3

CH3

n

O

Si

Fig. 12. (a) Dihedral angle dependence of the potential energy for it-16 with thirty-one repeating units and hydrogen termini (it-oligo-16).



In a series of (S)-chiral primary alkyl alcohols with a monotonically increasing number of methylene spacers, the ICD sign of the polysilane aggregates oscillated according to the number of methylene carbons from the OH group to the chiral center, as shown in Figure 13 (b). Such CD phenomena have been referred to as the odd-even effect and have been observed in certain helical superstructures.206,207 Exciton couplet theory using models, empirically suggested that the odd-even effect originates from the transition between P- and M-handed supramolecular helicity. These results mean that the position of the chiral center might affect the preferred twisting direction of the main chain packing chirality in the polysilane aggregates.

Mirror Symmetry Breaking by Polymer Chirality Transfer at the Surface

According to Oparlin, the abiotic synthesis of organic mole-cules is the early stage in the origin of life.208 Several workers assumed that it is possible for mineral surfaces to provide an opportunity of generation, amplifi cation, transcription, and immobilization of molecular chirality. In 1971, Jackson reported a preferential polymerization, following a preferential adsorption of l-aspartic acids relative to d-aspartic acids on chiral surfaces (enantiomorphous edge) of Kaolinite.209 Otroshchenko et al. assumed that a mineral surface acts as the most probable adsorbent to promote DNA synthesis.210

Fig. 13. (a) UV and CD spectra of 16 (Mw = 7.7 × 105, Mw/Mn = 2.9) particles in a mixture of toluene/(S)- (a; solid line) or (R)-2-butanol (b; dotted line)/methanol at 20 °C. (b) The CD signal intensity of 16 particles as a function of methylene spacer in a series of (S)-alkyl alcohols with toluene/methanol cosolvent at 20 °C. The CD intensity with (S)-2-butanol was inserted for comparison.

0

10,000

20,000

30,000

40,000

-4

-3

-2

-1

0

1

2

3

250 300 350 400 450 500

e / (

Si r

epea

t u

nit

)-1d

m3 cm

-1

De /

(Si r

epea

t u

nit

)-1d

m3 cm

-1Wavelength / nm

CD

UV

a (S-form)

b (R-form)

CD

(a)

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

0

1

2

3

4

5

CD amplitude at 354 nm ( De / (Si repeat unit)-1dm3cm-1)

Nu

mb

er o

f m

eth

ylen

e sp

acer

bet

wee

n

OH

gro

up

an

d c

hir

al c

ente

r

CH3

OH*

H3C

OH*H3C

H3C

OH*

H3C

CH3

OH*

H3C

H3CH3C

CH3

OH*

H3COH*

H3C

(b)

Fig. 14. Schematic view of chiral orientation of polysilanes aggregates in a preferred helicity.




Cairns-Smith developed the genetic takeover concept, in which chiral mineral surfaces may be the fi rst replication system of the genetic code.212,212 This fascinating hypothesis led us to another sergeant-soldier experiment operated by the use of CD-active and CD-silent polysilane binary thin fi lms on quartz substrates.

Discrete helical polymers are typically induced by stereo-genic centers, either in the main chain or in the side chains. As demonstrated, in the case of chromophoric polymers con-sisting of only stereogenic centers in the main chain, helical polymers with a preferential screw sense can be produced by sergeants-and-soldiers amplifi cation by the proper choice of comonomers, shown earlier. This is regarded as the intrachain proximity effect occurring within a main chain, being a con-sequence of a side-chain chirality transcription process involv-ing improper helix error correction. For polysilanes, rod-like helical copolymers required comonomers bearing β-branched achiral and/or β-branched chiral side groups.

Inspired by the hypothesis of abiotic chiral synthesis, the sergeants-and-soldiers helix command surface experiment was carried out. The thermo-driven chiroptical transfer and ampli-fi cation occurring in CD-silent helical polysilane fi lms were induced by chirality from CD-active helical polysilane ultra-thin layers on quartz glass.213 This is the fi rst mirror symmetry breaking experiment by polymer chirality transcription to neighboring polymers occurring at the surface, recognized as the interchain proximity effect.

Although sergeants-and-soldiers for discrete polymers and supramolecular assemblies in solution are well-known, this concept was yet to be applied to polymer fi lms. The command surface principle was already established in photochemical material and surface science by Ichimura et al.214 To my knowledge, both sergeants-and-soldiers and command surface seem to be developed independently. The former is intrachain

amplifi cation in side chain chirality occurring in the same chain, while the latter is intermolecular amplifi cation of molec-ular shape and orientation at the surface occurring in binary fi lms, though chirality and helicity were not included.

CD-active 1 with a purely P-73 helix, CD-silent 73-helical poly(n-decyl-2-methylpropylsilane) (17), and CD-silent 73-helical poly(n-decyl-3-methylbutylsilane) (18) were chosen for this study (Chart 5). Polymers 17 and 18 have an equal popu-lation of P-73 and M-73 helices as a result of no CD signals near 320 nm. Polymers 1 and 17 carrying β-branching alkyl groups adopt rigid rod-like conformation with a persistent length of 60–70 nm, while 18 is semi-fl exible with a persistent length of ∼6 nm in solution at 20 °C.180 Although the 18 solid sample showed a clear m.p. at ∼40 °C,213 1 had no such m.p. in the range from −50 to 150 °C owing to very limited main chain mobility.

The double layer fi lm sample was prepared by either chemically grafting215 or by spin-coating of 1 (Mw = 2.1 × 105) onto the quartz substrate. The initial UV absorbance of 1 itself at 320 nm was ca. 0.04, followed by spin-coating of 18 (Mw = 1.1 × 105) or 17 (Mw = 3.4 × 104) onto the 1 surface. Total UV absorbance at 320 nm was adjusted between 0.39 and 1.50. The terms g and sc mean chemically grafted at the surface and a spin-coated fi lm onto the surface, respectively.

Figure 15 (a) compares the changes in UV-CD spectra of the 1(g)/18(sc) fi lm before and after the annealing process. The specimens were annealed in a vacuum at +80 °C for 1 h and were cooled down slowly to room temperature. Evidently, 1(g)-18(sc) showed a bisignate CD band with a positive at 309 nm and a negative at 324 nm, characteristic of exciton couplets arising from helically organized polysilane chains.

Moreover, the absolute magnitude of the couplet was greatly amplifi ed by the annealing. This enhancement is a conse-quence of CD-active 1 chirality transfer to CD-silent 18, arising from main chain and/or side chain helicity of 1. However, UV absorbance of 1(g)-18(sc) decreased after the annealing treatment (Fig. 15(a), bottom). Although most poly-silane chains lie down before annealing in the substrate plane by the spin-coating technique, thermal annealing permits

Fig. 15. Schematic presentation of thermo-driven chiroptical transfer and amplifi cation in CD–silent helical 18 (soldier) from CD-active helical 1 (sergeant) on quartz glass.

n

17

Si Si

CH3

CH3

CH3 CH3H3C

n

CH3

18

Chart 5. CD-silent rigid rod-like helical polysilane (17) and CD-silent semi-fl exible helical polysilane (18) used for the sergeants-and-soldiers—helix command surface experiments.



semi-fl exible 18 oriented partly perpendicular and/or tilted to the substrate plane, leading to a decrease in apparent UV absorbance at 321 nm, as illustrated in Figure 16.

In contrast, the optical activity transfer in the 1(g)-17(sc) fi lm was not observed. The CD signals of the 1(g)-17(sc) fi lm were markedly infl uenced by linear dichroism (LD) signals, which often causes an artifact CD signal. Even after prolonged annealing overnight and an increased annealing temperature as high as 150 °C, the LD infl uence was not eliminated. This is attributable to very limited main chain mobility and disen-tanglement of 17 during the spin coating process.

Although a weak van der Waals interaction exists among polysilane chains, this weakness in condensed fi lms may be responsible for effective mirror symmetry breaking with long-distance interactions up to 40 nm (Fig. 16(b)).

Mirror Symmetry Breaking by Intrinsic Physical Origin

It is possible for the electroweak force unifying PC electromag-netic and PV weak forces to distinguish mirror image mole-cules, which could be detectable as subtle differences. Although many attempts have long been undertaken in several laborato-ries, little was known about a discrete polymer system in an isotropic fl uid solution susceptible to subtle PVED bias, which was suitable for testing the parity question.

In 2001, the author reported the experimental test of whether chiroptical and achiral physicochemical experiments between a pair of enantiomeric polysilanes are identical.107

Enantiomeric polysilanes used in this test were poly

[bis{(S)-3,7-dimethyloctyl}silane] (19) and poly[bis{(R)-3,7-dimethyloctyl}silane] (20) (Chart 6). The pairs carry two iden-tical chiral side groups with 96 %ee. Prior to this test, molecular mechanics suggested that they are in a nearly degenerate double-well with P-73 and M-73 motifs. Indeed, they under-went a PM-transition at −65 °C in isooctane.

The author described subtle differences in CD/UV/29Si-NMR spectra and viscomeric data for the enantiomeric pair in solution, inferred by the PV hypothesis.64–82 The author assumed that 19 and 20 are advantageous to test the parity question at the chemistry level for the following reasons.

1. The polymers constitute a bridge between inanimate and biomolecular worlds because (S and R)-3,7-dimethyloctyl

-150

-100

-50

0

50

100

150

0.0

0.5

1.0

1.5

2.0

2.5

250 300 350 400

Wavelength / nm

After annealing

Before annealing

Elli

pti

city

(m

deg

)

Ab

sorb

ance

CD

UVAfter annealing

Before annealing

(a)

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50

Thickness / nm

Rel

ativ

e ch

ang

e in

gC

D =

gA

A/g

BA

Fig. 16. (a) CD and UV spectra of the grafted-1 and spin-coated-18 in binary fi lm onto quartz glass before (dotted lines) and after (solid lines) annealing, the initial UV absorbance of 1 itself was 0.04, and total UV absorbance of grafted-1/spin-coated-18 double layer was 0.39. (b) Change in the gCD ratios of the grafted-1 / the spin-coated-18 (fi lled square) on quartz surface before annealing (gBA) and after annealing (gAA) as a function of total fi lm thickness.

19 (Tc: -65°C)

(S)

Si

H3C CH3

CH3

H

n

(S)

H3C CH3

HCH3

(R)

Si

H3C CH3

n

(R)

H3C CH3

20 (Tc: -65°C)

HCH3

CH3

H

Chart 6. An enantiomeric pair of polysilanes (19 and 20) undergoing PM-transition at −65 °C in isooctane used for the PV question experiments.




groups, 95.74 and 95.88 % ee with an experimental error of ±0.2 %, respectively, from β-citronellol are highly enan-tiopure biomolecules available commercially (Fluka, now Aldrich). The l-β-citronellol is a constituent of rose and geranium oils, and the d-β-citronellol occurs in Ceylon and Java citronella oils. The use of β-citronellols enable one to reproducibly trace the present results in any laboratory regardless of time, hemispheres, radioactive sources, circu-larly polarized light, magnetic fi eld, cold interstellar uni-verse, and long travel from nebula and meteorites.

2. The intense, narrow CD/UV spectral characteristics of 19 and 20 facilitate chiroptical detection of macroscopic PV effects excluding chiral chemical auxiliary and seeding effects. This uniqueness enables us to directly compare the absolute apparent gCD values between the enantiomeric pair

in an isotropic solution because the gCD values are directly connected to the sum of the gPV and the gPC terms. Here, PVED will act as an additive force to the P-motif and, conversely, a subtractive force to the M-motif (or vice versa) with an equal absolute magnitude, regardless of side chain chirality. These effects should be connected to the gPV values. On the other hand, the PC term contributes to the gPC value with a change in sign and an equal magnitude when side chain chirality was inverted.

3. In the case of molecules, PVED ∼ <S|VPV|T> <T|VSO|S>/∆EST, where VPV is WNC proportional to Z3, VSO is the spin-orbit interaction proportional to Z2, |S> and the |T> singlet and triplet states are separated by ∆EST, respec-tively.3 For a certain polysilane, the value of ∆EST is 3.4 eV.216 Moreover, the heavier silicon atoms and the large effective conjugating numbers (Neff) of ∼103 may linearly enhance PVED.92 Therefore, the preliminary expected advantage ratio, gPV = PVED/kT ∼ 10−12 at 300 K, may exceed the detectable limit of ∼10−17.3,84

4. Moreover, 4.7% of natural abundant 29Si with −1/2 spin sate may enhance this PVED by several times analogous to

neutron optical rotation enhancement, as observed in the 117Sn isotope.55,56

Figure 17 gives a comparison of the UV and CD spectra between 19 and 20 with high molecular weight in isooctane below and above Tc. The positive-sign CD band of 19 with an extremum of 322 nm at 252 K is almost the inverse of the negative-sign CD band with an extremum of 318 nm at 205 K, over the whole 220 to 350 nm range. Conversely, the nega-tive-sign CD spectrum of 20 with an extremum of 322 nm at 243 K is almost the inverse of the positive-sign CD spectrum with an extremum of 319 nm at 197 K. Evidently, 19 and 20 undergo a PM-transition between the two temperatures.

Figure 18(a) and 18(b) compare the apparent gCD values around 320nm for 19 and 20 in isooctane as a function of solution temperature. When paired polymers with higher molecular weights were used, the PM-transition temperature of around 208 K was slightly different (Fig. 18(a)). It is noted that the absolute magnitude in the gCD values of 19 are greater than those of 20 in the range of 190 to 353 K. When the paired polymers with almost identical lower molecular weight (for 19, Mw = 31,400, Mn = 17,400, and for 20, Mw = 30,100, Mn = 20,000) were used, the differences between 19 and 20 were further pronounced (Fig. 18(b)). The absolute magnitudes in the negative gCD region are thus greater than those in the positive gCD region, regardless of side chain chiral-ity, temperature, and molecular weights of the polysilanes tested.

It is possible to that the differences in the apparent gCD value are connected to the gPV value for the P- and M-motifs doubly, in which the (|gPC| + |gPV|) term contributes to the negative gCD region and the (|gPC| − |gPV|) term contributes to the positive gCD region. The sign of gPV is negative and the preferential screw-sense is M rather than P in the range of 190 to 353 K regardless of side chain chirality. These tests led the author to an optimistic idea that the differences between

0

50,000

100,000

150,000

200,000

250,000

-30

-20

-10

0

10

200 250 300 350 400

e / (

Si-

rep

eat-

un

it)-1

dm

3 cm-1

De /

(Si-

rpea

t-u

nit

)-1d

m3 cm

-1

Wavelength / nm

205 K

205 K

252 K

252 K

(a)

0

50,000

100,000

150,000

200,000

250,000

-40

-30

-20

-10

0

10

20

200 250 300 350 400

e / (

Si-

rep

eat-

un

it)-1

dm

3 cm-1

De /

(Si-

rpea

t-u

nit

)-1d

m3 cm

-1

Wavelength / nm

243 K

197 K

197 K

243 K

(b)

Fig. 17. The UV and CD spectra of (a) 19 (Mw = 8.6 × 105, Mn = 1.5 × 105) and (b) 20 (Mw = 3.9 × 105, Mn = 8.6 × 104) in isooctane below and above PM-transition temperature (−65 °C).



mirror image polymers are not so subtle owing to a cooperative amplifi cation in the phase-transition behavior.

Subtle differences were observed in the 29Si-NMR spectra of 19 and 20, as seen in Figure 19 (a). Although the absolute gCD value in chloroform at 30 °C is nearly identical for 19 (gCD = +1.58 × 10−4) and 20 (gCD = −1.56 × 10−4), the twisting mobility of 19 and 20 is mediated by handed inner-shell electrons close to the nucleus and may be connected to the difference in linewidth (∆υ1/2) and a small difference in chemi-cal shift may be connected to the differences in paramagnetic and diamagnetic tensors, as predicted theoretically.81 For the 19–20 pairs, the main chain of 19 appears to be less mobile than that of 20; for 19, ∆υ1/2 = 19 Hz at −25.62 ppm and for 20,∆υ1/2 = 13 Hz at −25.68 ppm. Also, when compared in the

13C-NMR spectra of 19 and 20 pairs, subtle, detectable differ-ences in signal intensities at 22, 25, and 28 ppm arising from side chain mobility were seen, as shown in Figure 19 (b).

These subtle differences in the absolute gCD values of the 19–20 pair may be explained by slightly modifying the poten-tial energy of the 19 and 20 model oligomers. As shown in Figure 20 (a) and (b), the author hypothetically introduced a small PV bias of +0.5 kcal per Si atom for the P-motif and of −0.5 kcal per Si atom for the M-motif for clarity, regardless of the side chain chirality. PVED is, hence, assumed to be 1.0 kcal per Si atom. Without the PVED term, 19 and 20 are mirror image polymers because the preferential screw-sense in the double-well potential is determined by side chain chirality only. However, the pseudo-scalar PVED bias permits an

-3 -2 -1 0 1 2 3150

200

250

300

350

40019 (High Mw) 20(High Mw)

Dissymmetry ratio, gCD

/ 10-4

Tem

per

atu

re /

K

(a)

-3 -2 -1 0 1 2 3150

200

250

300

350

40019 (Low Mw) 20 (Low Mw)

Dissymmetry ratio, gCD

/ 10-4

Tem

per

atu

re /

K

(b)

Fig. 18. Comparisons of the apparent values of (a) gCD, between 19 (Mw = 8.6 × 105, Mn = 1.5 × 105) (fi lled circles) and 20 (Mw = 3.9 × 105, Mn = 8.6 × 104) (open circles), (b) gCD between 19 (Mw = 3.1 × 104, Mn = 1.7 × 104) (fi lled circles) and 20 (Mw = 3.0 × 104, Mn = 2.0 × 104) (open circles) in isooctane as a function of temperature.

-100 -50 0 50 100-28

-27

-26

-25

-24

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-25

-24

Intensity (19)

29S

i-N

MR

Ch

emic

al S

hif

t (p

pm

)

Intensity (20)

1/2

= 13 Hzn 1/2

= 19 Hz

19 (Low Mw) 20 (Low Mw)

(a)

29S

i-N

MR

Ch

emic

al S

hif

t (p

pm

)

-150 -100 -50 0 50 100 150

20

22

24

26

28

30

20

22

24

26

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30

Intensity (19)

13C

-NM

R C

hem

ical

Sh

ift

(pp

m)

Intensity (20)

13C

-NM

R C

hem

ical

Sh

ift

(pp

m)

(b)

Fig. 19. Comparisons of (a) 29Si-NMR spectra and (b) 13C-NMR spectra of 19 (Mw = 3.1 × 104, Mn = 1.7 × 104) and 20 (Mw = 3.9 × 105, Mn = 8.6 × 104) dissolved in CDCl3 (50 mg in CDCl3 0.6 mL at 40°C).




inequality in the mirror image double-well potentials. Hence, it is possible for the PV term to destabilize for the P-screw and, conversely, to stabilize for the M-screw-sense, respectively, regardless of the side chain chirality.

If the results were neither as a result of impurities nor to imperfection of instruments, the experimental results of 19 and 20 in an isotropic solution could infer the consequence of a great amplifi cation mechanism and could provide a possible answer to the long-standing question at the molecular level. In line with the CP-symmetry violation at the elemental particle level, a real enantiomer of M-screw polysilane with (S)-chiral side groups in the matter world may be a P-screw polysilane with (R)-chiral side groups in the anti-matter world.21,22,40 Although this idea is absolutely nonpractical, one can test T-variance in the framework of CPT-conservation. If CP-symmetry were broken at the molecular level, T-variance would not be conserved.

The experimental tests of the 19/20 pair could infer the possibility of detecting PT-violation from the temperature dependent gCD data, because increasing temperature means increasing the entropy of a system. Since the beginning of our universe, entropy in the matter world increases macroscopi-cally with the irreversible arrow of time.217 The T-variance issue may be a concern of the subtle differences in the rest mass of hydrogen atoms with two spin states. Although the zero-spin state with p (↑) and e− (↓) has 0.9 GeV, one-spin state with p (↑) and e− (↑) is slightly heavier by 6 × 10−15 GeV.218 The author has an optimistic belief that the hypotheses of P-, T-, and PT-violations in the realm of chemistry could be test-able, if, beyond the 19/20 pair, more well-defi ned polysilanes with a narrow polydispersity were isolated in the future. The author and co-workers are currently looking for such ideal

systems, which are reproducibly testable by anyone, any place, any time, and on any instruments. The expected outlets may be extended to electroweak chemistry and may lead to a paradigm shift from stereochemistry to temporal space chemistry.

Acknowledgements

Professors M. M. Green, J. Michl, R. West, K. Tamao, R. G. Jones, Y. Inoue, T. Sato, K. Takeda, H. Teramae, N. Matsu-moto, A. Teramoto, K. Terao, M. Hasegawa, H. Sakurai, T. Kunitake, J. R. Koe, J. Watanabe, Y. Kawakami, K. Okoshi, M. Kunitake, Z.-B. Zhang, Y.-G. Yang, E. Yashima, Y. Okamoto, K. Akagi, W. Zhang, B.-Z. Zhang, and K. Nomura are gratefully acknowledged for their intuitive insights on helical polysilanes, entropy driven transitions, and chiroptical analysis from the early stage of this work to the present time. MF is also thankful to Drs. H. Nakashima, O. Niwa, H.-Z. Tang, A. Saxena, S.-Y. Kim, A. Ohira, G.-Q. Guo, M. Ishikawa, M. Morita, M. Naito, H. Onouchi for fruitful discussions and contribution to the present work. MF wishes to thank H. Takigawa-Tamoto. M. Motonaga, Y. Kimura, F. Ichiyanagi, Y. Nakano, T. Mori, and Y. Kawagoe very much for stimulating discussions with much contribution to the present work and many unpublished outlets. MF acknowl-edges grants from CREST-JST (FY1998–FT2003), CREST-JST (FY2003–FT2006), Scientifi c Research of Priority Areas (446, FY2006–FY2009), Grant-in-Aid for Scientifi c Research from JSPS (16655046, FY2009–2010). Finally, MF acknowl-edges Professors E. Yashima and K. Nakanishi for cordially inviting the author to submit this account paper.

-20

-18

-16

-14

-12

90 120 150 180 210 240 270

PC originwith PV originE

ner

gy

/ kca

l (S

i-re

pea

t-u

nit

)-1


19(P) 19 (M)

EPV

EPV

(a)-20

-18

-16

-14

-12

90 120 150 180 210 240 270

PC originwith PV originE

ner

gy

/ kca

l (S

i-re

pea

t-u

nit

)-1


20 (P) 20 (M)

EPV

EPV

(b)

Fig. 20. Comparisons of the potential energy between (a) 19 and (b) 20 with uncorrected and corrected PV terms. For demonstration purpose only, PV energy bias was assumed to 0.5 kcal per Si repeating unit, hence, PVED was 1 kcal per repeating unit. All calculations were carried out for oligomers with fi fty silicon repeating units and hydrogen termini.



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