Study of collective radial breathing-like modes in double-walled carbon nanotubes: Combination of continuous two-dimensional membrane theory and Raman spectroscopy

Radial breathing modes (RBMs) are widely used for the atomic structure characterization and index assignment of single-walled carbon nanotubes (SWNTs) from resonant Raman spectroscopy. However, for double-walled carbon nanotubes (DWNTs), the use of conventional ¿RBM(d) formulas is complicated due to the van der Waals interaction between the layers, which strongly affects the frequencies of radial modes and leads to new collective vibrations. This paper presents an alternative way to theoretically study the collective radial breathing-like modes (RBLMs) of DWNTs and to account for interlayer interaction, namely the continuous two-dimensional membrane theory. We obtain an analytical ¿RBLM(do, di) relation, being the equivalent of the conventional ¿RBM(d) expressions, established for SWNTs. We compare our theoretical predictions with Raman data, measured on individual index-identified suspended DWNTs, and find a good agreement between experiment and theory. Moreover, we show that the interlayer coupling in individual DWNTs strongly depends on the interlayer distance, which is manifested in the frequency shifts of the RBLMs with respect to the RBMs of the individual inner and outer tubes. In terms of characterization, this means that the combination of Raman spectroscopy data and predictions of continuous membrane theory may give additional criteria for the index identification of DWNTs, namely the interlayer distance

Photoluminescence from an individual double-walled carbon nanotube

We report direct and unambiguous evidence of the existence of inner semiconducting tube (ISCT) photoluminescence (PL) from measurements performed on four individual freestanding index-identified double-walled carbon nanotubes (DWNTs). Based on thorough Rayleigh scattering, Raman scattering, and PL experiments, we are able to demonstrate that the ISCT PL is observed with a quantum yield estimated to be a few 10-6 independent of the semiconducting or metallic nature of the outer tube. This result is mainly attributed to ultrafast exciton transfer from the inner to outer tube. Furthermore, by carrying out PL excitation experiments on the (14, 1)@(15, 12) DWNT, we show that the ISCT PL can be detected through the optical excitation of the outer tube, indicating that the exciton transfer can also occur in the opposite way

Landau theory of crystallization and the capsid structures of small icosahedral viruses

International audienceA new approach to the capsid structures of small viruses with spherical topology and icosahedral symmetry is proposed. It generalizes Landau theory of crystallization to describe icosahedral viral shells self-assembled from identical asymmetric proteins. An explicit method which predicts the positions of centers of mass for the proteins constituting the shell is discussed in detail. The method is based on irreducible density distribution function which generates the protein positions. The universal form of the density distribution function which contains no fitting parameter permits to classify the capsids structures of small viruses. The theory describes in a uniform way both the structures satisfying the well-known Caspar and Klug geometrical model for capsid construction and those violating it. A group theory analysis of the Caspar and Klug model and of the “quasiequivalence” principle for protein environments in viral capsids is given. The molecular basis of difference in protein environments and peculiarities in the assembly thermodynamics are also discussed

Physics Approach to Protein Arrangements in Icosahedral Viral Capsids: beyond the Caspar and Klug Model

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Theory of a Reconstructive Structural Transformation in Capsides of Icosahedral Viruses

6 pagesInternational audienceA theory of a reconstructive structural transformation in icosahedral capsid shells is developed for a whole family of virulent human viruses. It is shown that the reversible rearrangement of proteins during the virus maturation transformation is driven by the variation in the wave number l associated with the protein density distribution function. The collective displacement field of protein centers from their positions in the initial (procapsid) and the final (capsid) two-dimensional icosahderal structures is derived. The amplitude of the displacement field is shown to be small and it minimizes the calculated free energy of the transformation. The theory allows us to propose a continuous thermodynamical mechanism of the reconstructive procapsid-to-capsid transformation. In the frame of the density-wave approach, we also propose to take an equivalent plane-wave vector as a common structural feature for different icosahedral capsid shells formed by the same proteins. Using these characteristics, we explain the relation between the radii of the procapsid and capsid shells and generalize it to the case of the viral capsid polymorphism

Capsid Structure and Self-assembly in Small Icosahedral Viruses

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Structural Transformation during Maturation Process

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Capsid Structures of Small Icosahedral Viruses

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Physics of Icosahedral Viruses: Capsid Structure, Self-assembly and Maturation

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Viscoelastic dynamics of spherical composite vesicles

A micromechanical model for the low-frequency dynamics of spherical composite vesicles (CVs) is proposed. Solidlike viscoelastic properties of the CVs are taken into account. The equations of motion of a CV surrounded by a viscous liquid are derived. They have discrete solutions which describe linearly coupled stretching and bending relaxation modes and an independent shear mode. The qualitative difference between the bending modes excited in a spherical vesicle and that in a flat membrane is demonstrated. The shear elasticity of the CVs gives an essential contribution to the relaxation rate of the bending mode at small wave numbers. It is also shown that even in an incompressible spherical vesicle with a finite shear modulus, the bending mode involves both radial and tangent displacements. These reasons make both in-plane and out-of-plane low-frequency responses of the CV quite different with respect to those of the flat membrane. To compare our theoretical results with published experimental data, the power spectra of the actin-coated CV are calculated