Conformations of Crumpled Sheet Polymers

1992 ◽  
Vol 272 ◽  
Author(s):  
David R. Nelson
Keyword(s):  
Orientational Order ◽  
Polymer Chains ◽  
Linear Polymer ◽  
Three Dimensions ◽  
Linear Polymers ◽  
Two Dimensional ◽  
Geometric Concepts ◽  
Bond Orientational Order ◽  
Important Possibility ◽  
Planar Membranes

Flexible sheet polymers or “membranes” can be regarded as two-dimensional generalizations of linear polymer chains, for which there is a vigorous theoretical and experimental literature. Flexible membranes should exhibit even more richness and complexity, for two basic reasons. The first is that important geometric concepts like intrinsic curvature, orientability and genus, which have no direct analogue in linear polymers, appear naturally in discussions of two-dimensional macromolecules. Our understanding of the interplay between these concepts and the statistical mechanics of surfaces is still in its infancy. [1] The second reason is that surfaces can exist in a variety of different phases. The possibility of a two-dimensional shear modulus in planar membranes shows that we must distinguish between solids and liquids when these objects are allowed to crumple into three dimensions. Hexatic membranes, with extended six-fold bond orientational order, provide yet another important possibility. All three phases have quite distinctive properties. [2, 3] There are no such sharp distinctions for linear polymer chains.

Crystal to Glass Transition and Melting in Two Dimensions

1993 ◽  
Vol 321 ◽  
Author(s):  
M. Li ◽  
W. L. Johnson ◽  
W. A. Goddard
Keyword(s):  
Glass Transition ◽  
Intermediate Phase ◽  
Orientational Order ◽  
Finite Size ◽  
Two Dimensions ◽  
Size Difference ◽  
Two Dimensional ◽  
Atomic Size ◽  
Bond Orientational Order ◽  
Dynamics Simulations

ABSTRACTThermodynamic properties, structures, defects and their configurations of a two-dimensional Lennard-Jones (LJ) system are investigated close to crystal to glass transition (CGT) via molecular dynamics simulations. The CGT is achieved by saturating the LJ binary arrays below glass transition temperature with one type of the atoms which has different atomic size from that of the host atoms. It was found that for a given atomic size difference larger than a critical value, the CGT proceeds with increasing solute concentrations in three stages, each of which is characterized by distinct behaviors of translational and bond-orientational order correlation functions. An intermediate phase which has a quasi-long range orientational order but short range translational order has been found to exist prior to the formation of the amorphous phase. The destabilization of crystallinity is observed to be directly related to defects. We examine these results in the context of two dimensional (2D) melting theory. Finite size effects on these results, in particular on the intermediate phase formation, are discussed.

Adsorption of linear polymers

1990 ◽  
Vol 68 (9) ◽  
pp. 1089-1093 ◽  
Author(s):  
M. Daoud ◽  
B. Farnoux ◽  
G. Jannink ◽  
A. Johner
Keyword(s):  
Neutron Scattering ◽  
Monomer Concentration ◽  
Polymer Chains ◽  
Linear Polymer ◽  
Linear Polymers ◽  
Fixed End ◽  
Scaling Arguments

Linear polymer chains usually interact strongly with surfaces. Various regimes are obtained when one varies the bulk monomer concentration C or the interaction δ of a monomer with the surface. We discuss the recent results that were obtained theoretically by scaling arguments and compare them with hydrodynamic, neutron-scattering, and reflectivity measurements. Although the agreement is satisfactory in some cases, no general agreement has been reached so far. We also discuss the relaxation of the streched chain when the fixed end constraint is released. Possible experimental realizations are given.

scholarly journals Bond-orientational order and Frank’s constant in two-dimensional colloidal hard spheres

2018 ◽  
Vol 30 (10) ◽  
pp. 104003 ◽  
Author(s):  
Alice L Thorneywork ◽  
Joshua L Abbott ◽  
Dirk G A L Aarts ◽  
Peter Keim ◽  
Roel P A Dullens
Keyword(s):  
Hard Spheres ◽  
Orientational Order ◽  
Two Dimensional ◽  
Bond Orientational Order ◽  
Colloidal Hard Spheres

scholarly journals Circuit topology of linear polymers: a statistical mechanical treatment

RSC Advances ◽  
2015 ◽  
Vol 5 (64) ◽  
pp. 51682-51689 ◽  
Author(s):  
Alireza Mashaghi ◽  
Abolfazl Ramezanpour
Keyword(s):  
Mechanical Treatment ◽  
Polymer Chains ◽  
Linear Polymer ◽  
Linear Polymers ◽  
Circuit Topology ◽  
Statistical Mechanical

Circuit topology landscapes of linear polymer chains with intra-chain contacts are defined and studied for their properties.

The theta condition for linear polymer chains in continuous space and three dimensions

1996 ◽  
Vol 105 (21) ◽  
pp. 9666-9673 ◽  
Author(s):  
C. W. Yong ◽  
Julian H. R. Clarke ◽  
Juan J. Freire ◽  
Marvin Bishop
Keyword(s):  
Polymer Chains ◽  
Linear Polymer ◽  
Three Dimensions ◽  
Continuous Space

Dimensionality of hexatic melting in liquid crystals by in situ electron diffraction

1992 ◽  
Vol 50 (1) ◽  
pp. 270-271
Author(s):  
S.W. Hui ◽  
M. Cheng ◽  
J.T. Ho ◽  
R. Pindak
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Electron Diffraction ◽  
Long Range ◽  
Organic Liquid ◽  
Orientational Order ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Free Standing

The theory of melting in two dimensions indicates that it is very different from the melting in three dimensions. An intermediate hexatic phase, with long range orientational but short range translational order, is proposed to exist between two dimensional solid and fluid phases. Because the long range order is limited experimentally by the domain or “grain” size, which is expected to be of sub-millimeter size, selected area electron diffraction is the method of choice for observing orientational order. Free-standing smectic liquid crystal films prove to be a most attractive system in which to verify this theory. However, multilayered liquid crystal samples are not strictly two dimensional systems because of interlayer interaction, their melting characteristics are expected to deviate from that of two dimensional systems. Furthermore, the outer layers may behave differently from the inner ones due to interfacial tension. We have applied low dose electron diffraction to study the effect of dimensionality, or number of layers, on the melting of multilayer organic liquid crystals.

Chemistry of Self-Assembling Bilayers and Related Molecular Layers

MRS Bulletin ◽  
1995 ◽  
Vol 20 (6) ◽  
pp. 22-25 ◽  
Author(s):  
Toyoki Kunitake
Keyword(s):  
Inorganic Nanoparticles ◽  
Water Soluble ◽  
Polymer Chains ◽  
Scanning Tunneling ◽  
Linear Polymers ◽  
Two Dimensional ◽  
Tunneling Microscopy ◽  
Solid Supports ◽  
Polymer Layers ◽  
Self Assembling

The two-dimensional packing of organic molecules (small and large) produces ultimately thin organic films. Several possibilities exist for achieving this result from linear polymers, taking advantage of surfaces and interfaces as spatial templates. Monomolecular polymer layers can be prepared on the surface of water by polymerization of monolayers. They can be transferred onto solid supports by the Langmuir-Blodgett-Kuhn technique. Polyion complexation at the air-water interface provides a second method of two-dimensional arrangements of linear polymers. More recent approaches include polymerization-induced epitaxy (PIE) and alternate polyion adsorption. In the case of PIE, growing polymer chains in solution are adsorbed onto immersed graphite plates, most probably as single polymer layers (Figure la). Chain alignment is commensurate with the graphite lattice, as confirmed by scanning tunneling microscopy (STM). This epitaxial adsorption is independent of polymerization mechanisms. On the other hand, the alternate adsorption consists of sequential dipping of charged solid supports in aqueous solutions of oppositely charged linear polyions (Figure 1b). The regularity of the layer thickness is remarkable and, under appropriate conditions, the deposition is repeatable without limit. This method is applicable not only to pairs of linear polyions but also to combinations of linear polyions with water-soluble proteins or inorganic nanoparticles.

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