Kinetics of polymer crystallization - II. Growth régimes

1988 ◽  
Vol 416 (1851) ◽  
pp. 463-476 ◽  
Keyword(s):  
Growth Rate ◽  
Continuum Model ◽  
Continuum Limit ◽  
Polymer Chains ◽  
Lamellar Crystal ◽  
Folding Rate ◽  
Edge Roughness ◽  
State Growth ◽  
Kinetics Of ◽  
The Continuum

From the models of paper I, exact expressions are found for the steady-state growth rate of a portion of the edge of a lamellar crystal in terms of the number of polymer segments M in the portion, the nucleation rate α on the edge and the folding rate v of polymer chains. Both hexagonal and square crystal structures are analysed. Simpler expressions are given in various limiting cases or régimes. One such régime is the continuum model of Bennett et al. (J. statist. Phys . 24, 419 (1981)). We find that the growth rates in our models differ substantially from this continuum limit when edge roughness is significant. The continuum growth rate provides an exact upper bound on the growth rate in Frank’s model (Frank, F. C. J. Cryst. Growth 22, 233 (1974)), which is sometimes exceeded by Frank’s approximation.

Microkinetics of lamellar crystallization in a long chain polymer

1971 ◽  
Vol 324 (1556) ◽  
pp. 79-97 ◽  
Keyword(s):  
Growth Rate ◽  
Chemical Composition ◽  
Crystallization Rate ◽  
Lamellar Thickness ◽  
Lamellar Crystal ◽  
Chain Polymer ◽  
Secondary Nucleus ◽  
Independent Estimate ◽  
Chemical Crosslinks ◽  
Kinetics Of

The growth kinetics of single crystal lamellae grown from polyisoprene melts have been determined by thin film electron microscopy which also reveals the relevant microstructure. The growth rate of a continuous lamellar crystal is independent of the length of the crystal and (in the absence of crosslinks) depends only upon temperature and the chemical composition of the polymer. The temperature dependence is closely similar to that observed for bulk crystallization and spherulite growth, with a maximum crystallization rate around — 24 °C. The growth rate at a given temperature is extremely sensitive to the chemical composition of the polyisoprene, being for a polymer containing 10% trans -polyisoprene one thousandth of that for pure cis -polyisoprene. Between these extremes the logarithm of the growth rate decreases linearly with increasing trans content. A similar effect is produced by the introduction of chemical crosslinks instead of trans units. These effects are attributed to a reduction in the probability of formation of the ‘secondary nucleus’, whose size can be calculated from the experimental data. The secondary nucleus is found to correspond to three molecular folds and this agrees well with an independent estimate obtained, by using thermodynamic theory, from the dependence of lamellar thickness on temperature.

Microkinetics of Lamellar Crystallization in a Long Chain Polymer

1972 ◽  
Vol 45 (5) ◽  
pp. 1315-1333 ◽  
Author(s):  
E. H. Andrews ◽  
P. J. Owen ◽  
A. Singh
Keyword(s):  
Growth Rate ◽  
Chemical Composition ◽  
Crystallization Rate ◽  
Lamellar Thickness ◽  
Trans Content ◽  
Lamellar Crystal ◽  
Chain Polymer ◽  
Secondary Nucleus ◽  
Chemical Crosslinks ◽  
Kinetics Of

Abstract The growth kinetics of single crystal lamellae grown from poly(isoprene) melts have been determined by thin film electron microscopy which also reveals the relevant microstructure. The growth rate of a continuous lamellar crystal is independent of the length of the crystal and (in the absence of crosslinks) depends only upon temperature and the chemical composition of the polymer. The temperature dependence is closely similar to that observed for bulk crystallization and spherulite growth, with a maximum crystallization rate around —24° C. The growth rate at a given temperature is extremely sensitive to the chemical composition of the poly(isoprene), being for a polymer containing 10 per cent trans-poly(isoprene) one thousandth of that for pure cis-poly(isoprene). Between these extremes the logarithm of the growth rate decreases linearly with increasing trans content. A similar effect is produced by the introduction of chemical crosslinks instead of trans units. These effects are attributed to a reduction in the probability of formation of the ‘secondary nucleus’, whose size can be calculated from the experimental data. The secondary nucleus is found to correspond to three molecular folds and this agrees well with an independent estimate obtained, by using thermodynamical theory, from the dependence of lamellar thickness on temperature.

Instability and Collapse in Discrete Wave Equations

2005 ◽  
Vol 5 (3) ◽  
pp. 223-241
Author(s):  
A. Carpio ◽  
G. Duro
Keyword(s):  
Continuum Limit ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Blow Up ◽  
Theoretical Predictions ◽  
Initial States ◽  
The Impact ◽  
The Continuum

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.

Diffusion model for deposition of epitaxial GaAs layers prepared by the MOCVD method

1991 ◽  
Vol 56 (10) ◽  
pp. 2020-2029
Author(s):  
Jindřich Leitner ◽  
Petr Voňka ◽  
Josef Stejskal ◽  
Přemysl Klíma ◽  
Rudolf Hladina
Keyword(s):  
Experimental Data ◽  
Growth Rate ◽  
Kinetic Model ◽  
Gas Phase ◽  
Substrate Surface ◽  
Deposition Process ◽  
Hydrogen Atmosphere ◽  
Epitaxial Gaas ◽  
Kinetics Of ◽  
Good Agreement

The authors proposed and treated quantitatively a kinetic model for deposition of epitaxial GaAs layers prepared by reaction of trimethylgallium with arsine in hydrogen atmosphere. The transport of gallium to the surface of the substrate is considered as the controlling process. The influence of the rate of chemical reactions in the gas phase and on the substrate surface on the kinetics of the deposition process is neglected. The calculated dependence of the growth rate of the layers on the conditions of the deposition is in a good agreement with experimental data in the temperature range from 600 to 800°C.

scholarly journals Hierarchical modeling of mechano-chemical dynamics of epithelial sheets across cells and tissue

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yoshifumi Asakura ◽  
Yohei Kondo ◽  
Kazuhiro Aoki ◽  
Honda Naoki
Keyword(s):  
Wound Healing ◽  
Cell Migration ◽  
Continuum Model ◽  
Tissue Level ◽  
Chemical Signals ◽  
Cellular Level ◽  
Mathematical Framework ◽  
Collective Cell Migration ◽  
The Continuum ◽  
Cell Cell

AbstractCollective cell migration is a fundamental process in embryonic development and tissue homeostasis. This is a macroscopic population-level phenomenon that emerges across hierarchy from microscopic cell-cell interactions; however, the underlying mechanism remains unclear. Here, we addressed this issue by focusing on epithelial collective cell migration, driven by the mechanical force regulated by chemical signals of traveling ERK activation waves, observed in wound healing. We propose a hierarchical mathematical framework for understanding how cells are orchestrated through mechanochemical cell-cell interaction. In this framework, we mathematically transformed a particle-based model at the cellular level into a continuum model at the tissue level. The continuum model described relationships between cell migration and mechanochemical variables, namely, ERK activity gradients, cell density, and velocity field, which could be compared with live-cell imaging data. Through numerical simulations, the continuum model recapitulated the ERK wave-induced collective cell migration in wound healing. We also numerically confirmed a consistency between these two models. Thus, our hierarchical approach offers a new theoretical platform to reveal a causality between macroscopic tissue-level and microscopic cellular-level phenomena. Furthermore, our model is also capable of deriving a theoretical insight on both of mechanical and chemical signals, in the causality of tissue and cellular dynamics.

Crystal-growth kinetics of protein single crystals along capillary tubes in the gel-acupuncture technique

1999 ◽  
Vol 55 (2) ◽  
pp. 577-580 ◽  
Author(s):  
Abel Moreno ◽  
Manuel Soriano-García
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Capillary Tube ◽  
Crystal Growth Rate ◽  
Equilibrium Studies ◽  
Acta Cryst ◽  
Average Growth ◽  
X Ray Crystallography ◽  
Growing Cell ◽  
Kinetics Of

In attempts to obtain protein crystals of a sufficient size for structural studies, lack of knowledge of the physicochemical properties of protein solutions and of their crystal-growth behaviour lead to a bottleneck for drug design as well as for X-ray crystallography. Most formal investigations on crystal-growth phenomena have been focused on equilibrium studies, where the protein is soluble, and on the kinetics of crystal growth, which is related to both nucleation and crystal-growth phenomena. The aim of this work is to measure the crystal-growth rate along a capillary tube used as a growing cell. These experiments were carried out using the gel-acupuncture technique [García-Ruiz et al. (1993). Mater. Res. Bull. 28, 541–546; García-Ruiz & Moreno (1994). Acta Cryst. D50, 484–490; García-Ruiz & Moreno (1997). J. Cryst. Growth, 178, 393–401]. Crystal-growth investigations took place using lysozyme and thaumatin I as standard proteins. The maximum average growth rate obtained in the lower part of the capillary tube was about 35 Å s−1 and the minimum average growing rate in the upper part of the capillary tube was about 8 Å s−1. The crystal-growth rate as a function of the supersaturation was experimentally estimated at a constant height along the capillary tube.

Correlations for Interaction Layer Growth in U-Mo/Al Dispersion Fuels

2017 ◽  
Vol 375 ◽  
pp. 29-39
Author(s):  
Boris A. Tarasov ◽  
Stepan N. Nikitin ◽  
Dmitry P. Shornikov ◽  
Maria S. Tarasova ◽  
Igor I. Konovalov
Keyword(s):  
Growth Rate ◽  
Growth Process ◽  
Aluminum Matrix ◽  
Layer Growth ◽  
Radiation Diffusion ◽  
Fission Rate ◽  
Interaction Layer ◽  
The Matrix ◽  
Mechanism And Kinetics ◽  
Kinetics Of

Paper presents the results of the growth rate of the interaction layer of uranium-molybdenum dispersed fuel in aluminum matrix and influence of silicon alloying on it. The growth process of amorphous interaction layer depends on the radiation diffusion which is proportional to the fission rate in the power of 1⁄4. The alloying of the matrix by silicon does not lead to a change in the mechanism and kinetics of the interaction layer growth, but only slows it down.

Supercritical Fluid Deposition of Ruthenium Thin Films: A Kinetic Study

2007 ◽  
Vol 992 ◽  
Author(s):  
Christos F. Karanikas ◽  
James J. Watkins
Keyword(s):  
Thin Films ◽  
Growth Rate ◽  
Deposition Temperature ◽  
Zero Order ◽  
Measurable Effect ◽  
Deposition Rates ◽  
Reaction Pressure ◽  
Deposition Kinetics ◽  
First Order ◽  
Kinetics Of

AbstractThe kinetics of the deposition of ruthenium thin films from the hydrogen assisted reduction of bis(2,2,6,6-tetramethyl-3,5-heptanedionato)(1,5-cyclooctadiene)ruthenium(II), [Ru(tmhd)2cod], in supercritical carbon dioxide was studied in order to develop a rate expression for the growth rate as well as to determine a mechanism for the process. The deposition temperature was varied from 240°C to 280°C and the apparent activation energy was 45.3 kJ/mol. Deposition rates up to 30 nm/min were attained. The deposition rate dependence on precursor concentrations between 0 and 0.2 wt. % was studied at 260°C with excess hydrogen and revealed first order deposition kinetics with respect to precursor at concentrations lower then 0.06 wt. % and zero order dependence at concentrations above 0.06 wt. %. The effect of reaction pressure on the growth rate was studied at a constant reaction temperature of 260°C and pressures between 159 bar to 200 bar and found to have no measurable effect on the growth rate.

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