Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices

Polymers in highly confined geometries can display complex morphologies including ordered phases. A basic component of a theoretical analysis of their phase behavior in confined geometries is the knowledge of the number of possible single-chain conformations compatible with the geometrical restrictions and the established crystalline morphology. While the statistical properties of unrestricted self-avoiding random walks (SAWs) both on and off-lattice are very well known, the same is not true for SAWs in confined geometries. The purpose of this contribution is (a) to enumerate the number of SAWs on the simple cubic (SC) and face-centered cubic (FCC) lattices under confinement for moderate SAW lengths, and (b) to obtain an approximate expression for their behavior as a function of chain length, type of lattice, and degree of confinement. This information is an essential requirement for the understanding and prediction of entropy-driven phase transitions of model polymer chains under confinement. In addition, a simple geometric argument is presented that explains, to first order, the dependence of the number of restricted SAWs on the type of SAW origin.

Download Full-text

Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices

10.20944/preprints201811.0112.v1 ◽

2018 ◽

Author(s):

Javier Benito ◽

Nikos Ch. Karayiannis ◽

Manuel Laso

Keyword(s):

Random Walks ◽

Approximate Expression ◽

Polymer Chains ◽

Face Centered Cubic ◽

Single Chain ◽

Confined Geometries ◽

Confined Polymers ◽

Ordered Phases ◽

Face Centered ◽

Chain Conformations

Polymers in highly confined geometries can display complex morphologies including ordered phases. A basic component of a theoretical analysis of their phase behavior in confined geometries is the knowledge of the number of possible single-chain conformations compatible with the geometrical restrictions and the established crystalline morphology. While the statistical properties of unrestricted self-avoiding random walks (SAWs) both on and off-lattice are very well known, the same is not true for SAWs in confined geometries. The purpose of this contribution is a) to enumerate the number of SAWs on the simple cubic (SC) and face-centered cubic (FCC) lattices under confinement for moderate SAW lengths, and b) to obtain an approximate expression for their behavior as a function of chain length, type of lattice, and degree of confinement. This information is an essential requirement for the understanding and prediction of entropy-driven phase transitions of model polymer chains under confinement. In addition, a simple geometric argument is presented that explains, to first order, the dependence of the number of restricted SAWs on the type of SAW origin.

Download Full-text

Self-Avoiding Random Walks as a Model to Study Athermal Linear Polymers under Extreme Plate Confinement

Polymers ◽

10.3390/polym12040799 ◽

2020 ◽

Vol 12 (4) ◽

pp. 799

Author(s):

Oscar Parreño ◽

Pablo Miguel Ramos ◽

Nikos Ch. Karayiannis ◽

Manuel Laso

Keyword(s):

Random Walks ◽

Hard Spheres ◽

Configurational Entropy ◽

Polymer Chains ◽

Crystal Nucleation ◽

Face Centered Cubic ◽

Linear Polymers ◽

Parallel Plates ◽

Uniform Size ◽

Chain Conformations

Monte Carlo (MC) simulations, built around chain-connectivity-altering moves and a wall-displacement algorithm, allow us to simulate freely-jointed chains of tangent hard spheres of uniform size under extreme confinement. The latter is realized through the presence of two impenetrable, flat, and parallel plates. Extreme conditions correspond to the case where the distance between the plates approaches the monomer size. An analysis of the local structure, based on the characteristic crystallographic element (CCE) norm, detects crystal nucleation and growth at packing densities well below the ones observed in bulk analogs. In a second step, we map the confined polymer chains into self-avoiding random walks (SAWs) on restricted lattices. We study all realizations of the cubic crystal system: simple, body centered, and face centered cubic crystals. For a given chain size (SAW length), lattice type, origin of SAW, and level of confinement, we enumerate all possible SAWs (equivalently all chain conformations) and calculate the size distribution. Results for intermediate SAW lengths are used to predict the behavior of long, fully entangled chains through growth formulas. The SAW analysis will allow us to determine the corresponding configurational entropy, as it is the driving force for the observed phase transition and the determining factor for the thermodynamic stability of the corresponding crystal morphologies.

Download Full-text

Zufallswege und Reaktionen atomarer Gitterfehler in Modellkristallen

Zeitschrift für Naturforschung A ◽

10.1515/zna-1969-0311 ◽

1969 ◽

Vol 24 (3) ◽

pp. 367-376 ◽

Cited By ~ 1

Author(s):

Helmut Mehrer

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

Random Walks ◽

Point Defects ◽

Preceding Paper ◽

Initial Distribution ◽

Face Centered Cubic ◽

Cubic Lattices ◽

Face Centered

AbstractRandom walks and reactions of point defects in face-centered cubic lattices have been simulated by means of a Monte-Carlo method described in the preceding paper (I) . In this paper the method is applied to the recombination of vacancies and interstitials. Equal or different numbers as well as random or correlated initial distribution of vacancies and interstitials are considered. The inter action between the defects is taken into account by a model for the pair volume surrounding a vacancy.

Download Full-text

Dynamics of a face-centered cubic lattice model for polymer chains

Macromolecules ◽

10.1021/ma00162a017 ◽

1986 ◽

Vol 19 (8) ◽

pp. 2202-2206 ◽

Cited By ~ 22

Author(s):

James Patton Downey ◽

Charles C. Crabb ◽

Jeffrey Kovac

Keyword(s):

Lattice Model ◽

Polymer Chains ◽

Face Centered Cubic ◽

Cubic Lattice ◽

Face Centered

Download Full-text

Voids in Irradiated Tungsten and Molybdenum

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100062865 ◽

1969 ◽

Vol 27 ◽

pp. 190-191

Author(s):

Robert C. Rau ◽

Robert L. Ladd

Keyword(s):

Melting Point ◽

Fast Neutron ◽

Neutron Irradiation ◽

Elevated Temperatures ◽

Irradiation Temperature ◽

The Body ◽

Face Centered Cubic ◽

Body Centered Cubic ◽

Cubic Metals ◽

Face Centered

Recent studies have shown the presence of voids in several face-centered cubic metals after neutron irradiation at elevated temperatures. These voids were found when the irradiation temperature was above 0.3 Tm where Tm is the absolute melting point, and were ascribed to the agglomeration of lattice vacancies resulting from fast neutron generated displacement cascades. The present paper reports the existence of similar voids in the body-centered cubic metals tungsten and molybdenum.

Download Full-text

A study of interface sliding at F.C.C.-B.C.C. boundaries in a Cu-Zn alloy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100109252 ◽

1978 ◽

Vol 36 (1) ◽

pp. 422-423

Author(s):

F. Monchoux ◽

A. Rocher ◽

J.L. Martin

Keyword(s):

Face Centered Cubic ◽

Creep Tests ◽

High Voltage Electron Microscopy ◽

Diffusion Treatment ◽

Voltage Electron ◽

The Face ◽

Face Centered ◽

Interface Sliding ◽

Zn Alloy ◽

Made In

Interphase sliding is an important phenomenon of high temperature plasticity. In order to study the microstructural changes associated with it, as well as its influence on the strain rate dependence on stress and temperature, plane boundaries were obtained by welding together two polycrystals of Cu-Zn alloys having the face centered cubic and body centered cubic structures respectively following the procedure described in (1). These specimens were then deformed in shear along the interface on a creep machine (2) at the same temperature as that of the diffusion treatment so as to avoid any precipitation. The present paper reports observations by conventional and high voltage electron microscopy of the microstructure of both phases, in the vicinity of the phase boundary, after different creep tests corresponding to various deformation conditions.Foils were cut by spark machining out of the bulk samples, 0.2 mm thick. They were then electropolished down to 0.1 mm, after which a hole with thin edges was made in an area including the boundary

Download Full-text

Microstructure of Electro-Eroded Cemented Carbide Surfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100101165 ◽

1968 ◽

Vol 26 ◽

pp. 284-285

Author(s):

V. N. Filimonenko ◽

M. H. Richman ◽

J. Gurland

Keyword(s):

Surface Layer ◽

Cobalt Content ◽

Cemented Carbides ◽

Face Centered Cubic ◽

X Ray Diffraction ◽

Metallographic Examination ◽

Standard Procedures ◽

Face Centered ◽

Diamond Paste ◽

Plastic Carbon

The high temperatures and pressures that are found in a spark gap during electrical discharging lead to a sharp phase transition and structural transformation in the surface layer of cemented carbides containing WC and cobalt. By means of X-ray diffraction both W2C and a high-temperature monocarbide of tungsten (face-centered cubic) were detected after electro-erosion. The W2C forms as a result of the peritectic reaction, WC → W2C+C. The existence and amount of the phases depend on both the energy of the electro-spark discharge and the cobalt content. In the case of a low-energy discharge (i.e. C=0.01μF, V = 300v), WC(f.c.c.) is generally formed in the surface layer. However, at high energies, (e.g. C=30μF, V = 300v), W2C is formed at the surface in preference to the monocarbide. The phase transformations in the surface layer are retarded by the presence of larger percentages of cobalt.Metallographic examination of the electro-eroded surfaces of cemented carbides was carried out on samples with 5-30% cobalt content. The specimens were first metallographically polished using diamond paste and standard procedures and then subjected to various electrical discharges on a Servomet spark machining device. The samples were then repolished and etched in a 3% NH4OH electrolyte at -0.5 amp/cm2. Two stage plastic-carbon replicas were then made and shadowed with chromium at 27°.

Download Full-text

Faceted antiphase boundaries in GaAs grown on Ge

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010012638x ◽

1987 ◽

Vol 45 ◽

pp. 314-315

Author(s):

N.-H. Cho ◽

S. McKernan ◽

C.B. Carter ◽

K. Wagner

Keyword(s):

Cross Section ◽

Atomic Resolution ◽

Face Centered Cubic ◽

Electrical Behavior ◽

Sphalerite Structure ◽

Antiphase Boundaries ◽

Transmission Electron ◽

Face Centered ◽

Quality Material ◽

Simulated Images

Interest has recently increased in the possibility of growing III-V compounds epitactically on non-polar substrates to produce device quality material. Antiphase boundaries (APBs) may then develop in the GaAs epilayer because it has sphalerite structure (face-centered cubic with a two-atom basis). This planar defect may then influence the electrical behavior of the GaAs epilayer. The orientation of APBs and their propagation into GaAs epilayers have been investigated experimentally using both flat-on and cross-section transmission electron microscope techniques. APBs parallel to (110) plane have been viewed at the atomic resolution and compared to simulated images.Antiphase boundaries were observed in GaAs epilayers grown on (001) Ge substrates. In the image shown in Fig.1, which was obtained from a flat-on sample, the (110) APB planes can be seen end-on; the faceted APB is visible because of the stacking fault-like fringes arising from a lattice translation at this interface.

Download Full-text

Electron diffraction detection of ordliking in annealed PbTe thin film

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100178227 ◽

1990 ◽

Vol 48 (4) ◽

pp. 1018-1019

Author(s):

Karimat El-Sayed

Keyword(s):

Thin Film ◽

Electron Diffraction ◽

Lead Telluride ◽

Structural Basis ◽

Face Centered Cubic ◽

X Ray ◽

Polycrystalline Thin Films ◽

Stage Process ◽

Diffraction Patterns ◽

Face Centered

Lead telluride is an important semiconductor of many applications. Many Investigators showed that there are anamolous descripancies in most of the electrophysical properties of PbTe polycrystalline thin films on annealing. X-Ray and electron diffraction studies are being undertaken in the present work in order to explain the cause of this anamolous behaviour.Figures 1-3 show the electron diffraction of the unheated, heated in air at 100°C and heated in air at 250°C respectively of a 300°A polycrystalline PbTe thin film. It can be seen that Fig. 1 is a typical [100] projection of a face centered cubic with unmixed (hkl) indices. Fig. 2 shows the appearance of faint superlattice reflections having mixed (hkl) indices. Fig. 3 shows the disappearance of thf superlattice reflections and the appearance of polycrystalline PbO phase superimposed on the [l00] PbTe diffraction patterns. The mechanism of this three stage process can be explained on structural basis as follows :

Download Full-text