Critique of the Theory of Optical Activity of Helical Polymers

Moffitt, W.; Fitts, Donald D.; Kirkwood, John G.

doi:10.1073/pnas.43.8.723

Cited by 194 publications

(35 citation statements)

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“…Their shape and size resemble natural light-harvesting systems in green sulphur bacteria, 1,[13][14][15][16][17][18] while these systems also have a comparable geometry to previously studied helical polymers. [19][20][21] Because of this and the strong intermolecular excitation transfer interactions, these synthetic J-aggregates are considered excellent candidates for artificial light-harvesting systems. 22 This perspective motivates many of the recent studies of the optical absorption and luminescence properties of the collective exciton states in these systems, as well as the energy transport and relaxation caused by these states.…”

Section: Introductionmentioning

confidence: 99%

Disorder-induced exciton localization and violation of optical selection rules in supramolecular nanotubes

Vlaming

Bloemsma

Nietiadi

et al. 2011

The Journal of Chemical Physics

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Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Using numerical simulations, we study the effect of disorder on the optical properties of cylindrical aggregates of molecules with strong excitation transfer interactions. The exciton states and the energy transport properties of such molecular nanotubes attract considerable interest for application in artificial light-harvesting systems and energy transport wires. In the absence of disorder, such nanotubes exhibit two optical absorption peaks, resulting from three super-radiant exciton states, one polarized along the axis of the cylinder, the other two (degenerate) polarized perpendicular to this axis. These selection rules, imposed by the cylindrical symmetry, break down in the presence of disorder in the molecular transition energies, due to the fact that the exciton states localize and no longer wrap completely around the tube. We show that the important parameter is the ratio of the exciton localization length and the tube's circumference. When this ratio decreases, the distribution of polarization angles of the exciton states changes from a two-peak structure (at zero and ninety degrees) to a single peak determined by the orientation of individual molecules within the tube. This is also reflected in a qualitative change of the absorption spectrum. The latter agrees with recent experimental findings. I. INTRODUCTIONDuring the past decade, there has been a growing interest in molecular J-aggregates of cylindrical geometry. 1-14 Examples of molecules that in solution self-assemble into aggregates of a tubular shape are carbocyanine molecules with hydrophobic and hydrophilic side groups 2-7 and porphyrin derivatives. [8][9][10][11][12] Both these molecules yield aggregates with a diameter of the order of 10 nm and a length of up to microns, which explains why they are often referred to as molecular nanotubes. Their shape and size resemble natural light-harvesting systems in green sulphur bacteria, 1, 13-18 while these systems also have a comparable geometry to previously studied helical polymers. [19][20][21] Because of this and the strong intermolecular excitation transfer interactions, these synthetic J-aggregates are considered excellent candidates for artificial light-harvesting systems. 22 This perspective motivates many of the recent studies of the optical absorption and luminescence properties of the collective exciton states in these systems, as well as the energy tran...

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Section: Introductionmentioning

confidence: 99%

Disorder-induced exciton localization and violation of optical selection rules in supramolecular nanotubes

Vlaming

Bloemsma

Nietiadi

et al. 2011

The Journal of Chemical Physics

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“…Hence, methods were developed to synthesize homopolymers and copolymers of amino acids as simple models (19,20,130) in order to elucidate the interactions present in proteins, and various physical chemical techniques [such as optical rotation and circular dichroism (204,205,298,375,377), infrared (203), Raman (381), and nuclear magnetic resonance (127,406) spectroscopies, kinetics of deuterium-hydrogen exchange (122,176), and immunochemical measures of folding equilibria (291)] were developed to investigate these interactions. At the same time, the development of thermodynamic and statistical mechanical methods began to emerge (150-152, 296, 297) to treat the interactions that determine conformation, conformational changes, and intramolecular structure in polypeptides and proteins.…”

Section: Transition To a Molecularmentioning

confidence: 99%

“…With the aid of these synthetic materials, the spectroscopic and deuterium-hydrogen-exchange characteristics of the various conformational elements of proteins (~t-helix, 13-sheet, 13-bend, and disulfide bonds) were elucidated (9,122,127,176,189,203,204,205,298,375,(377)(378)(379)(380)(381)(382)(383)(384)(385)406), and used empirically to investigate protein structure in solution.…”

Section: Synthetic Polypeptides Asmentioning

confidence: 99%

Protein structure and function, from a colloidal to a molecular view

Scheraga

1984

Carlsberg Res. Commun.

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“…We start with the familiar semi-empirical Moffitt equation (3)(4)(5)(6)(7) for the long wavelength region (A >> Ao) and adapt it for the case of DL-copolymers. The […”

Section: Moff1tt's Equationmentioning

confidence: 99%

“…There are three types of urns; in the zeroth urn Do, the probabilities of drawing the residues L1 and Di Are ap exp (#,CDDL) and aq exp (flcIDD), respectively; in the urn Lj (j = 1 -z -1), the probabilities of drawing the residues Lj+j and Dj+j are bp exp (APLL) and bq exp (FtLD), respectively; in the urn L k (k = z -m), the probabilities of drawing the residues LH*k+ [7] In the same way, a similar expression for the probability Since the value nPL m is equal to the mean number of the sequences of m L-residues in the D,L-copolymer of DPn, using the following approximate relation [10] E nPLm + E nPD m p"-i + qz-1 ( m=z m~z It should be noticed that c and c' disappear in Eq. [11].…”

Section: Moff1tt's Equationmentioning

confidence: 99%

A Statistical Study of Optical Rotation for Synthetic D,L-Copolypeptide Solutions

Gotoh

Lin

Eyring

1974

Proc. Natl. Acad. Sci. U.S.A.

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The right-handed helical fraction HL in a D,L-copolypeptide chain is evaluated by a simple probability theory for each L-fraction, p. The curves of optical rotation at a single wavelength against p for poly(-ybenzyl-D,L-glutamate) and D,L-copolyleucine of a series of different D: L ratios in several positive helix-solvents are calculated with a modified semi-empirical Moffitt equation. From the comparison between the rotations calculated by us and observed by Downie et al., it is shown that to reproduce the observed rotations, the minimum number of right-handed helical nuclei or sequences of L-residues appropriate to the Moffitt equation are eight and four for degrees of polymerization 320 and 1860, respectively. . We shall show that the right-(or left)-handed helical fraction HL (or HD, HL + HD = 1) obtained by counting with a probability theory and the number of sequences having z (a parameter) or more L-or D-residues occurring in a chain are obtainable from the results of using the Moffit equation to calculate the rotation curves. The calculation will be carried out for the case where the total fractional helix content or the concentration of residues in all helices in a chain fa is approximately unity for the DL-copolypeptides in the positive helix solvents. In a subsequent paper, a more sophisticated probabilistic model of polymer statistics will be discussed. MOFF1TT'S EQUATIONWe start with the familiar semi-empirical Moffitt equation (3-7)

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Critique of the Theory of Optical Activity of Helical Polymers

Cited by 194 publications

References 4 publications

Disorder-induced exciton localization and violation of optical selection rules in supramolecular nanotubes

Disorder-induced exciton localization and violation of optical selection rules in supramolecular nanotubes

Protein structure and function, from a colloidal to a molecular view

A Statistical Study of Optical Rotation for Synthetic D,L-Copolypeptide Solutions

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