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Sample records for kratkie soobshcheniya oiyai

  1. From small angle x-ray scattering to reflectivity: Instrumentation and sample study

    SciTech Connect

    Hua, D.W.; Beaucage, G.; Kent, M.S.

    1996-02-01

    In this study, we described the first results from an x-ray reflectometer which has been modified from an existing Kratky small angle x-ray scattering (SAXS) camera at the UNM/Sandia scattering center. Typically, seven orders of magnitude of reflectivity can be obtained over a range of 0.02 to 0.5 A{sup {minus}1} in {ital q}. This allows the resolution of surface features of 10 to 1000 A. The conversion to reflectometer is reversible and can be achieved in a short time, allowing for dual use of an existing Kratky camera. {copyright} {ital 1996 Materials Research Society.}

  2. Stretching semiflexible polymer chains: Evidence for the importance of excluded volume effects from Monte Carlo simulation

    NASA Astrophysics Data System (ADS)

    Hsu, Hsiao-Ping; Binder, Kurt

    2012-01-01

    Semiflexible macromolecules in dilute solution under very good solvent conditions are modeled by self-avoiding walks on the simple cubic lattice (d = 3 dimensions) and square lattice (d = 2 dimensions), varying chain stiffness by an energy penalty ɛb for chain bending. In the absence of excluded volume interactions, the persistence length ℓp of the polymers would then simply be ℓ _p=ℓ _b(2d-2)^{-1}q_b^{-1} with qb = exp (-ɛb/kBT), the bond length ℓb being the lattice spacing, and kBT is the thermal energy. Using Monte Carlo simulations applying the pruned-enriched Rosenbluth method (PERM), both qb and the chain length N are varied over a wide range (0.005 ⩽ qb ⩽ 1, N ⩽ 50 000), and also a stretching force f is applied to one chain end (fixing the other end at the origin). In the absence of this force, in d = 2 a single crossover from rod-like behavior (for contour lengths less than ℓp) to swollen coils occurs, invalidating the Kratky-Porod model, while in d = 3 a double crossover occurs, from rods to Gaussian coils (as implied by the Kratky-Porod model) and then to coils that are swollen due to the excluded volume interaction. If the stretching force is applied, excluded volume interactions matter for the force versus extension relation irrespective of chain stiffness in d = 2, while theories based on the Kratky-Porod model are found to work in d = 3 for stiff chains in an intermediate regime of chain extensions. While for qb ≪ 1 in this model a persistence length can be estimated from the initial decay of bond-orientational correlations, it is argued that this is not possible for more complex wormlike chains (e.g., bottle-brush polymers). Consequences for the proper interpretation of experiments are briefly discussed.

  3. Understanding the stiffness of macromolecules: From linear chains to bottle-brushes

    NASA Astrophysics Data System (ADS)

    Binder, K.; Hsu, H.-P.; Paul, W.

    2016-07-01

    The intrinsic local stiffness of a polymer is characterized by its persistence length. However, its traditional definition in terms of the exponential decay of bond orientational correlations along the chain backbone is accurate only for Gaussian phantom-chain-like polymers. Also care is needed to clarify the conditions when the Kratky-Porod wormlike chain model is applicable. These problems are elucidated by Monte Carlo simulations of simple lattice models for polymers in both d = 2 and d = 3 dimensions. While the asymptotic decay of the bond orientational correlations for real polymers always is of power law form, the Kratky-Porod model is found to be applicable for rather stiff (but not too long) thin polymers in d = 3 (but not in d = 2). However, it does not describe thick chains, e.g., bottle-brush polymers, where stiffness is due to grafted flexible side-chains, and the persistence length grows proportional to the effective thickness of the bottle-brush. A scaling description of bottle-brushes is validated by simulations using the bond fluctuation model.

  4. Solution X-ray scattering analysis of cold- heat-, and urea-denatured states in a protein, Streptomyces subtilisin inhibitor.

    PubMed

    Konno, T; Kataoka, M; Kamatari, Y; Kanaori, K; Nosaka, A; Akasaka, K

    1995-08-01

    Streptomyces subtilisin inhibitor (SSI), a homo-dimeric protein with a subunit of 113 residues with two disulfide bonds, is known to exist at low pH in at least three distinct thermodynamic states namely, the native (N), cold-denatured (D') and heat-denatured (D). Small-angle X-ray scattering was used to analyze and to compare overall chain conformations of SSI in typical, N, D', D and urea-denatured states (Durea). Molecular masses were determined from scattering intensities extrapolated to a scattering angle of zero, which showed that SSI exists as a homo-dimer in the N state, but as dissociated monomers in the D', D and Durea states. From Guinier plots of the scattering intensities, radii of gyration (Rg) were determined to be 20.1(+/- 1.8) A for N, and 20.7(+/- 1.3), 25.8(+/- 1.5) and 32 to 35 A for D', D and Durea, respectively. Kratky plots for both N and D' exhibited a bell-shape indicating that the polypeptide chain has a globular part not only in N but also in D', while Kratky plots for D and Durea showed that the polypeptide chain has no globular part either in Durea or D. Combined with the results from circular dichroism and 1H NMR spectra, a picture emerges for the polypeptide chain conformation of SSI such that in N it is a globular dimer close to that in the crystal, in Durea it is totally disordered and expanded nearly to a fully random chain with restrictions only from the disulfide bridges, in D the entire chain is disordered and expanded but with considerable local intra-chain interactions, and in D' the chain consists of a part with a unique tertiary structure and a part disordered and expanded to a degree comparable to D. PMID:7643393

  5. Single chain structure in thin polymer films: corrections to Flory's and Silberberg's hypotheses

    NASA Astrophysics Data System (ADS)

    Cavallo, A.; Müller, M.; Wittmer, J. P.; Johner, A.; Binder, K.

    2005-05-01

    Conformational properties of polymer melts confined between two hard structureless walls are investigated by Monte Carlo simulation of the bond fluctuation model. Parallel and perpendicular components of chain extension, bond-bond correlation function and structure factor are computed and compared with recent theoretical approaches attempting to go beyond Flory's and Silberberg's hypotheses. We demonstrate that for ultrathin films where the thickness, H, is smaller than the excluded volume screening length (blob size), ξ, the chain size parallel to the walls diverges logarithmically, R2/2Napb2+clog(N) with c~1/H. The corresponding bond-bond correlation function decreases like a power law, C(s) = d/sω with s being the curvilinear distance between bonds and ω = 1. Upon increasing the film thickness, H, we find—in contrast to Flory's hypothesis—the bulk exponent ω = 3/2 and, more importantly, a decreasing d(H) that gives direct evidence for an enhanced self-interaction of chain segments reflected at the walls. Systematic deviations from the Kratky plateau as a function of H are found for the single chain form factor parallel to the walls in agreement with the non-monotonic behaviour predicted by theory. This structure in the Kratky plateau might give rise to an erroneous estimation of the chain extension from scattering experiments. For large H the deviations are linear with the wavevector, q, but are very weak. In contrast, for ultrathin films, H<ξ, very strong corrections (albeit logarithmic in q) are found suggesting a possible experimental verification of our results.

  6. The size distribution of 'gold standard' nanoparticles.

    PubMed

    Bienert, Ralf; Emmerling, Franziska; Thünemann, Andreas F

    2009-11-01

    The spherical gold nanoparticle reference materials RM 8011, RM 8012, and RM 8013, with a nominal radius of 5, 15, and 30 nm, respectively, have been available since 2008 from NIST. These materials are recommended as standards for nanoparticle size measurements and for the study of the biological effects of nanoparticles, e.g., in pre-clinical biomedical research. We report on determination of the size distributions of these gold nanoparticles using different small-angle X-ray scattering (SAXS) instruments. Measurements with a classical Kratky type SAXS instrument are compared with a synchrotron SAXS technique. Samples were investigated in situ, positioned in capillaries and in levitated droplets. The number-weighted size distributions were determined applying model scattering functions based on (a) Gaussian, (b) log-normal, and (c) Schulz distributions. The mean radii are 4.36 +/- 0.04 nm (RM 8011), 12.20 +/- 0.03 nm (RM 8012), and 25.74 +/- 0.27 nm (RM 8013). Low polydispersities, defined as relative width of the distributions, were detected with values of 0.067 +/- 0.006 (RM 8011), 0.103 +/- 0.003, (RM 8012), and 0.10 +/- 0.01 (RM 8013). The results are in agreement with integral values determined from classical evaluation procedures, such as the radius of gyration (Guinier) and particle volume (Kratky). No indications of particle aggregation and particle interactions--repulsive or attractive--were found. We recommend SAXS as a standard method for a fast and precise determination of size distributions of nanoparticles.

  7. Nonlinear Behavior of Gelatin Networks Reveals a Hierarchical Structure.

    PubMed

    Yang, Zhi; Hemar, Yacine; Hilliou, Loic; Gilbert, Elliot P; McGillivray, Duncan J; Williams, Martin A K; Chaieb, Sahraoui

    2016-02-01

    We investigate the strain hardening behavior of various gelatin networks-namely physical gelatin gel, chemically cross-linked gelatin gel, and a hybrid gel made of a combination of the former two-under large shear deformations using the pre-stress, strain ramp, and large amplitude oscillations shear protocols. Further, the internal structures of physical gelatin gels and chemically cross-linked gelatin gels were characterized by small angle neutron scattering (SANS) to enable their internal structures to be correlated with their nonlinear rheology. The Kratky plots of SANS data demonstrate the presence of small cross-linked aggregates within the chemically cross-linked network whereas, in the physical gelatin gels, a relatively homogeneous structure is observed. Through model fitting to the scattering data, we were able to obtain structural parameters, such as the correlation length (ξ), the cross-sectional polymer chain radius (R(c)) and the fractal dimension (d(f)) of the gel networks. The fractal dimension d(f) obtained from the SANS data of the physical and chemically cross-linked gels is 1.31 and 1.53, respectively. These values are in excellent agreement with the ones obtained from a generalized nonlinear elastic theory that has been used to fit the stress-strain curves. The chemical cross-linking that generates coils and aggregates hinders the free stretching of the triple helix bundles in the physical gels. PMID:26667303

  8. Synthesis, solution and crystal structure of the coenzyme B(12) analogue Co(β)-2'-fluoro-2',5'-dideoxyadenosylcobalamin.

    PubMed

    Hunger, Miriam; Wurst, Klaus; Kräutler, Bernhard

    2015-07-01

    Crystal structure analyses have helped to decipher the mode of binding of coenzyme B12 (AdoCbl) in the active site of AdoCbl-dependent enzymes. However, the question of how such enzymes perform their radical reactions is still incompletely answered. A pioneering study by Gruber and Kratky of AdoCbl-dependent glutamate mutase (GLM) laid out a path for the movement of the catalytically active 5'-deoxyadenosyl radical, in which H-bonds between the protein and the 2'- and 3'-OH groups of the protein bound AdoCbl would play a decisive role. Studies with correspondingly modified coenzyme B12-analogues are of interest to gain insights into cofactor binding and enzyme mechanism. Here we report the preparation of Coβ-2'-fluoro-2',5'-dideoxyadenosylcobalamin (2'FAdoCbl), which lacks the 2'-OH group critical for the interaction in enzymes. 2'FAdoCbl was prepared by alkylation of cob(I)alamin, obtained from the electrochemical reduction of aquocobalamin. Spectroscopic data and a single crystal X-ray analysis of 2'FAdoCbl established its structure, which was very similar to that one of coenzyme B12. 2'FAdoCbl is a (19)F NMR active mimic of coenzyme B12 that may help to gain insights into binding interactions of coenzyme B12 with AdoCbl-dependent enzymes, proteins of B12 transport and of AdoCbl-biosynthesis, as well as with B12-riboswitches. PMID:25726330

  9. Rouse-Bueche Theory and The Calculation of The Monomeric Friction Coefficient in a Filled System

    NASA Astrophysics Data System (ADS)

    Martinetti, Luca; Macosko, Christopher; Bates, Frank

    According to flexible chain theories of viscoelasticity, all relaxation and retardation times of a polymer melt (hence, any dynamic property such as the diffusion coefficient) depend on the monomeric friction coefficient, ζ0, i.e. the average drag force per monomer per unit velocity encountered by a Gaussian submolecule moving through its free-draining surroundings. Direct experimental access to ζ0 relies on the availability of a suitable polymer dynamics model. Thus far, no method has been suggested that is applicable to filled systems, such as filled rubbers or microphase-segregated A-B-A thermoplastic elastomers at temperatures where one of the blocks is glassy. Building upon the procedure proposed by Ferry for entangled and unfilled polymer melts, the Rouse-Bueche theory is applied to an undiluted triblock copolymer to extract ζ0 from the linear viscoelastic behavior in the rubber-glass transition region, and to estimate the size of Gaussian submolecules. At iso-free volume conditions, the so-obtained matrix monomeric friction factor is consistent with the corresponding value for the homopolymer melt. In addition, the characteristic Rouse dimensions are in good agreement with independent estimates based on the Kratky-Porod worm-like chain model. These results seem to validate the proposed approach for estimating ζ0 in a filled system. Although preliminary tested on a thermoplastic elastomer of the A-B-A type, the method may be extended and applied to filled homopolymers as well.

  10. Conformational Statistics of Semi-Flexible Macromolecular Chains with Internal Joints

    PubMed Central

    Zhou, Yu

    2010-01-01

    Fluctuations in the bending angles at internal irregularities of DNA and RNA (such as symmetric loops, bulges, and nicks/gaps) have been observed from various experiments. However, little effort has been made to computationally predict and explain the statistical behavior of semi-flexible chains with internal defects. In this paper, we describe the general structure of these macromolecular chains as inextensible elastic chains with one or more internal joints which have limited ranges of rotation, and propose a method to compute the probability density functions of the end-to-end pose of these macromolecular chains. Our method takes advantage of the operational properties of the non-commutative Fourier transform for the group of rigid-body motions in three-dimensional space, SE(3). Two representative types of joints, the hinge for planar rotation and the ball joint for spatial rotation, are discussed in detail. The proposed method applies to various stiffness models of semi-flexible chain-like macromolecules. Examples are calculated using the Kratky-Porod model with specified stiffness, angular fluctuation, and joint locations. Entropic effects associated with internal angular fluctuations of semi-flexible macromolecular chains with internal joints can be computed using this formulation. Our method also provides a potential tool to detect the existence of internal irregularities. PMID:21243113

  11. Synthesis, solution and crystal structure of the coenzyme B(12) analogue Co(β)-2'-fluoro-2',5'-dideoxyadenosylcobalamin.

    PubMed

    Hunger, Miriam; Wurst, Klaus; Kräutler, Bernhard

    2015-07-01

    Crystal structure analyses have helped to decipher the mode of binding of coenzyme B12 (AdoCbl) in the active site of AdoCbl-dependent enzymes. However, the question of how such enzymes perform their radical reactions is still incompletely answered. A pioneering study by Gruber and Kratky of AdoCbl-dependent glutamate mutase (GLM) laid out a path for the movement of the catalytically active 5'-deoxyadenosyl radical, in which H-bonds between the protein and the 2'- and 3'-OH groups of the protein bound AdoCbl would play a decisive role. Studies with correspondingly modified coenzyme B12-analogues are of interest to gain insights into cofactor binding and enzyme mechanism. Here we report the preparation of Coβ-2'-fluoro-2',5'-dideoxyadenosylcobalamin (2'FAdoCbl), which lacks the 2'-OH group critical for the interaction in enzymes. 2'FAdoCbl was prepared by alkylation of cob(I)alamin, obtained from the electrochemical reduction of aquocobalamin. Spectroscopic data and a single crystal X-ray analysis of 2'FAdoCbl established its structure, which was very similar to that one of coenzyme B12. 2'FAdoCbl is a (19)F NMR active mimic of coenzyme B12 that may help to gain insights into binding interactions of coenzyme B12 with AdoCbl-dependent enzymes, proteins of B12 transport and of AdoCbl-biosynthesis, as well as with B12-riboswitches.

  12. Nonlinear Behavior of Gelatin Networks Reveals a Hierarchical Structure.

    PubMed

    Yang, Zhi; Hemar, Yacine; Hilliou, Loic; Gilbert, Elliot P; McGillivray, Duncan J; Williams, Martin A K; Chaieb, Sahraoui

    2016-02-01

    We investigate the strain hardening behavior of various gelatin networks-namely physical gelatin gel, chemically cross-linked gelatin gel, and a hybrid gel made of a combination of the former two-under large shear deformations using the pre-stress, strain ramp, and large amplitude oscillations shear protocols. Further, the internal structures of physical gelatin gels and chemically cross-linked gelatin gels were characterized by small angle neutron scattering (SANS) to enable their internal structures to be correlated with their nonlinear rheology. The Kratky plots of SANS data demonstrate the presence of small cross-linked aggregates within the chemically cross-linked network whereas, in the physical gelatin gels, a relatively homogeneous structure is observed. Through model fitting to the scattering data, we were able to obtain structural parameters, such as the correlation length (ξ), the cross-sectional polymer chain radius (R(c)) and the fractal dimension (d(f)) of the gel networks. The fractal dimension d(f) obtained from the SANS data of the physical and chemically cross-linked gels is 1.31 and 1.53, respectively. These values are in excellent agreement with the ones obtained from a generalized nonlinear elastic theory that has been used to fit the stress-strain curves. The chemical cross-linking that generates coils and aggregates hinders the free stretching of the triple helix bundles in the physical gels.

  13. A Combined Small-Angle X-ray and Neutron Scattering Study of the Structure of Purified Soluble Gastrointestinal Mucins

    PubMed Central

    Georgiades, Pantelis; di Cola, Emanuela; Heenan, Richard K; Pudney, Paul D A; Thornton, David J; Waigh, Thomas A

    2014-01-01

    The structures of purified soluble porcine gastric (Muc5ac) and duodenal (Muc2) mucin solutions at neutral and acidic pH were examined using small-angle X-ray scattering and small-angle neutron scattering experiments. We provide evidence for the morphology of the network above the semidilute overlap concentration and above the entanglement concentration. Furthermore, we investigated the gelation of both types of mucin solutions in response to a reduction in pH, where we observed the formation of large-scale heterogeneities within the polymer solutions, typical of microphase-separated gels. The concentration dependence of the inhomogeneity length scale (Ξ) and the amplitude of the excess scattering intensity [Iex(0)] are consistent with previously studied gelled synthetic polymeric systems. The persistence lengths of the chains were found to be similar for both Muc5ac and Muc2 from Kratky plots of the neutron data (8 ± 2 nm). © 2014 Wiley Periodicals, Inc. Biopolymers 101: 1154–1164, 2014. PMID:25041765

  14. Structural characterization of intramolecular Hg(2+) transfer between flexibly linked domains of mercuric ion reductase.

    PubMed

    Johs, Alexander; Harwood, Ian M; Parks, Jerry M; Nauss, Rachel E; Smith, Jeremy C; Liang, Liyuan; Miller, Susan M

    2011-10-28

    The enzyme mercuric ion reductase MerA is the central component of bacterial mercury resistance encoded by the mer operon. Many MerA proteins possess metallochaperone-like N-terminal domains (NmerA) that can transfer Hg(2+) to the catalytic core domain (Core) for reduction to Hg(0). These domains are tethered to the homodimeric Core by ~30-residue linkers that are susceptible to proteolysis, the latter of which has prevented characterization of the interactions of NmerA and the Core in the full-length protein. Here, we report purification of homogeneous full-length MerA from the Tn21 mer operon using a fusion protein construct and combine small-angle X-ray scattering and small-angle neutron scattering with molecular dynamics simulation to characterize the structures of full-length wild-type and mutant MerA proteins that mimic the system before and during handoff of Hg(2+) from NmerA to the Core. The radii of gyration, distance distribution functions, and Kratky plots derived from the small-angle X-ray scattering data are consistent with full-length MerA adopting elongated conformations as a result of flexibility in the linkers to the NmerA domains. The scattering profiles are best reproduced using an ensemble of linker conformations. This flexible attachment of NmerA may facilitate fast and efficient removal of Hg(2+) from diverse protein substrates. Using a specific mutant of MerA allowed the formation of a metal-mediated interaction between NmerA and the Core and the determination of the position and relative orientation of NmerA to the Core during Hg(2+) handoff.

  15. The Snakelike Chain Character of Unstructured RNA

    PubMed Central

    Jacobson, David R.; McIntosh, Dustin B.; Saleh, Omar A.

    2013-01-01

    In the absence of base-pairing and tertiary structure, ribonucleic acid (RNA) assumes a random-walk conformation, modulated by the electrostatic self-repulsion of the charged, flexible backbone. This behavior is often modeled as a Kratky-Porod “wormlike chain” (WLC) with a Barrat-Joanny scale-dependent persistence length. In this study we report measurements of the end-to-end extension of poly(U) RNA under 0.1 to 10 pN applied force and observe two distinct elastic-response regimes: a low-force, power-law regime characteristic of a chain of swollen blobs on long length scales and a high-force, salt-valence-dependent regime consistent with ion-stabilized crumpling on short length scales. This short-scale structure is additionally supported by force- and salt-dependent quantification of the RNA ion atmosphere composition, which shows that ions are liberated under stretching; the number of ions liberated increases with increasing bulk salt concentration. Both this result and the observation of two elastic-response regimes directly contradict the WLC model, which predicts a single elastic regime across all forces and, when accounting for scale-dependent persistence length, the opposite trend in ion release with salt concentration. We conclude that RNA is better described as a “snakelike chain,” characterized by smooth bending on long length scales and ion-stabilized crumpling on short length scales. In monovalent salt, these two regimes are separated by a characteristic length that scales with the Debye screening length, highlighting the determining importance of electrostatics in RNA conformation. PMID:24314087

  16. Structural characterization of intramolecular Hg2+ transfer between flexibly-linked domains of mercuric ion reductase

    SciTech Connect

    Johs, Alexander; Harwood, Ian M; Parks, Jerry M; Nauss, Rachel; Smith, Jeremy C; Liang, Liyuan; Miller, Susan M

    2011-01-01

    The enzyme mercuric ion reductase, MerA, is the central component of bacterial mercury resistance encoded by the mer operon. Many MerA proteins possess a metallochaperone-like N-terminal domain, NmerA, that can transfer Hg2+ to the catalytic core (Core) for reduction to Hg0. These domains are tethered to the homodimeric Core by ~30-residue linkers that are subject to proteolysis, which has limited structural and functional characterization of the interactions of these domains. Here, we report purification of homogeneous full-length MerA using a fusion protein construct and combine small-angle X-ray and neutron scattering with molecular dynamics simulation to characterize the structure of constructs that mimic the system before and during handoff of Hg2+ from NmerA to the Core. The radii of gyration, distance distribution functions and Kratky plots derived from the small-angle X-ray scattering data are consistent with full-length MerA adopting elongated conformations resulting from flexibility in the linkers to the NmerA domains. The scattering profiles are best reproduced using an ensemble of linker conformations. This flexible attachment of NmerA may facilitate fast and efficient removal of Hg2+ from diverse protein substrates. Using a specific mutant of MerA allowed determination of the position and relative orientation of NmerA to the Core during Hg2+ handoff. The small buried surface area at the site of interaction suggests molecular recognition may be of less importance for the integrity of metal ion transfers between tethered domains than for transfers between separate proteins in metal trafficking pathways.

  17. SAXSANA: an interactive program for the analysis and monitoring of static and time-resolved small-angle X-ray solution scattering measurements.

    PubMed

    Hiragi, Yuzuru; Sano, Yoh; Matsumoto, Tomoharu

    2003-03-01

    An interactive analytical program, SAXSANA, for small-angle X-ray scattering measurements of solutions is described. The program processes scattered data without disciplined knowledge of small-angle scattering. SAXSANA also assists in finding the best experimental conditions, thus avoiding blind runs of experiments. SAXSANA consists of the following procedures: (i) determination of the centre of scattered X-rays and moment transfer Q (Q = 4pisintheta/lambda, where 2theta is the scattering angle and lambda is the wavelength) for each measured channel; (ii) conversion of the data format to the format of Q versus scattered intensities J(Q); (iii) truncation of unnecessary data and smoothing of scattering curves by cubic-spline function; (iv) correction of the absorption effect and subtraction of the scattered intensity of the buffer (solvent) solution from that of the sample solution; (v) creation of a data file for a three-dimensional representation of time-resolved scattering curves; (vi) determination of radii of gyration by Guinier plots; (vii) determination of persistent lengths by Kratky plots; (viii) extrapolation of the small-angle part by Guinier plots; (ix) extrapolation of the wide-angle part by Porod's & Luzzati's laws for the Hankel transformation in order to obtain the distance distribution function p(r); (x) calculation of p(r) and computation of the invariant, the chord length, the Volume, the spherical radius, the maximum dimension D(max) and the radius of gyration (Rg). SAXSANA also serves as an on-site monitor for the validity of an experimental result during the measurements.

  18. Problems at the Nexus of Geometry and Soft Matter: Rings, Ribbons and Shells

    NASA Astrophysics Data System (ADS)

    Yong, Ee Hou

    There has been an increasing appreciation of the role in which elasticity plays in soft matter. The understanding of many shapes and conformations of complex systems during equilibrium or non-equilibrium processes, ranging from the macroscopic to the microscopic, can be explained to a large extend by the theory of elasticity. We are motivated by older studies on how topology and shape couple in different novel systems and in this thesis, we present novel systems and tools for gaining fundamental insights into the wonderful world of geometry and soft matter. We first look at how defects, topology and geometry come together in the physics of thin membranes. Topological constraint plays a fundamental role on the morphology of crumpling membranes of genus zero and suggest how different fundamental shapes, such as platonic solids, can arise through a crumpling process. We present a way of classifying disclinations using a generalized "Casper-Klug" coordination number. We show that there exist symmetry breaking during the crumpling process, which can be described using Landau theory and that thin membranes preserve the memory of their defects. Next we consider the problem of the shapes of Bacillus spores and show how one can understand the folding patterns seen in bacterial coats by looking at the simplified problem of two concentric rings connected via springs. We show that when the two rings loses contact, rucks spontaneous formed leading to the complex folding patterns. We also develop a simple system of an extensible elastic on a spring support to study bifurcation in system that has adhesion. We explain the bifurcation diagram and show how it differs from the classical results. Lastly, we investigate the statistical mechanics of the Sadowsky ribbon in a similar spirit to the famous Kratky-Porod model. We present a detail theoretical and numerical calculations of the Sadowsky ribbon under the effect of external force and torsion. This model may be able to explain new