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  • Articles  (17)
  • Polymer and Materials Science  (14)
  • 02.70.L9  (1)
  • Bead spring model  (1)
  • Finite-size scaling  (1)
  • 1
    ISSN: 1434-6036
    Keywords: 05.50.+9 ; 02.70.L9
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A qualitative model for solid mixtures of diatomic molecules, where one species (called CO, to be specific) carries both a dipole moment and a quadrupole moment, while the other species (calledN 2) has only a quadrupole moment, is studied by Monte Carlo methods. We use spinsS i =±1 to represent the orientations of the CO electric dipole moment, if the lattice sitei is taken by a CO molecule, whileS i =0 if the site is taken by anN 2 molecule. Assuming nearest-neighbor antiferroelectric interactions between CO molecules, and a bilinear dipole-quadrupole coupling between CO andN 2, the randomly quenchedN 2 molecules act like random fields do in the random field Ising model. In previous work it was already shown that this crude model is in very good agreement with experimental data in two dimensions (adsorbed layers), where the random fields induces a rounding of the transition. Here Monte Carlo simulations of the three-dimensional version of this model are presented and analyzed with finite size scaling concepts. As expected from the theory, a behaviour qualitatively different from the two-dimensional case is detected. The Monte Carlo data provide qualitative evidence that the random field induces crossover to an universality class with critical exponents distinct from the pure Ising model, but it is not feasible to us to study large enough systems that would allow a reliable estimation of these exponents. But the results show that dilution without dipole-quadrupole coupling has much less drastic effects on the critical behavior, and that in the presence of this coupling very small impurity concentrations do indeed change the critical behavior.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of computer-aided materials design 2 (1996), S. 167-181 
    ISSN: 1573-4900
    Keywords: Polymer adsorption ; Monte Carlo methods ; Bead spring model ; Theta solvent ; Diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Using a bead spring model of flexible polymer chains, the density profiles and chain configurational properties of polymer solutions confined between parallel plates were studied. A wide range of density ϕ, chain length N, and strength ε of a short-range attractive wall potential was investigated. Both a temperature T in the good solvent regime (T 〉 θ, θ being the Theta temperature where a chain in unconfined bulk three-dimensional solution would behave ideally) and a temperature in the bad solvent regime (T 〈 θ) were considered. It is shown that phase separation in a polymer-rich and polymer-poor solution in the slit competes with polymer adsorption at the walls. A qualitative connection to the wetting behavior of semi-infinite polymer solutions is drawn. The acceptance rate for monomer motions was studied for various conditions, and profiles of monomer mobility across the slit were recorded. Also, average chain relaxation times were extracted from the time dependence of mean-square displacements. Although with increasing density the chain radii (at T 〉 θ) show a crossover from two-dimensional excluded volume behavior (Rg ∝ N2ν with ν = 3/4) to ideal random walk behavior (ν = 1/2), the relaxation times show effective exponents Zeff (τ ∝ NZ eff) that clearly deviate from the Rouse prediction in concentrated confined solutions.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 55 (1989), S. 87-126 
    ISSN: 1572-9613
    Keywords: Finite-size scaling ; anisotropic systems ; Lifshitz points ; driven Kawasaki model ; nonequilibrium phase transitions ; Monte Carlo simulations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Various thermal equilibrium and nonequilibrium phase transitions exist where the correlation lengths in different lattice directions diverge with different exponentsv ‖,v ⊥: uniaxial Lifshitz points, the Kawasaki spin exchange model driven by an electric field, etc. An extension of finite-size scaling concepts to such anisotropic situations is proposed, including a discussion of (generalized) rectangular geometries, with linear dimensionL ‖ in the special direction and linear dimensionsL ⊥ in all other directions. The related shape effects forL ‖≠L ⊥ but isotropic critical points are also discussed. Particular attention is paid to the case where the generalized hyperscaling relationv ‖+(d−1)v ⊥=γ+2β does not hold. As a test of these ideas, a Monte Carlo simulation study for shape effects at isotropic critical point in the two-dimensional Ising model is presented, considering subsystems of a 1024x1024 square lattice at criticality.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Die Makromolekulare Chemie 189 (1988), S. 2357-2365 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Monte Carlo simulations are presented for binary (AB) symmetric polymer mixtures (chain lengths NA=NB=N) for the case that an attractive interaction ∊ exists between monomers of the same kind, and the limiting case that one species (B) is very diluted. It is shown that with increasing interaction strength ∊/(kB · T), T being the absolute temperature, the minority chains collapse to a very dense configuration, while the majority chains stay nearly Gaussian. Both chain radii, structure factors and numbers of nearest neighbour contacts are discussed.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 4 (1995), S. 119-136 
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: We present results of computer simulations by the method of Brownian dynamics of polymeric brushes attached to impenetrable planes. For testing both model and method we have used one polymer brush attached to a repulsive plane and compare some results with Monte Carlo results of Lai and Binder on the bond fluctuation model. We have also studied two polymeric brushes attached to two parallel planes at different distances between planes, and investigate the interplay between the interpenetration of the brushes and the configurational properties of the grafted chains.
    Additional Material: 19 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 7 (1998), S. 649-658 
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Short block copolymers in selective solvents (bad for A-block, good for B-block) are modeled by flexible bead-spring chains, where beads interact with short range Morse potentials of variable strength. It is shown that already very short chains (NA = NB = 2) exhibit a rather well-defined critical micelle concentration (cmc). The mass distribution of the micelles and their gyration tensor components as well as their internal structure are studied. It is shown that the relaxation time increases exponentially with the strength EAA of the attractive energy between the A-monomers, and thus frozen-in micelles of medium size are obtained when EAA is chosen too large. Our results are compared to studies of related but somewhat different models.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 4 (1995), S. 1063-1084 
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Results of computer simulations of polymer layers consisting of chains grafted by one end on an unpenetrable plane are presented. Characteristics of translational and rotational motion of different chain segments and correlation functions of chain radii were calculated both for single layers at different grafting densities s and for two interacting layers at different distances D between parallel grafting planes. Two values of grafting density were used in the latter case. The behavior of different correlation times as function of s and D and the interplay between the interpenetration of the brushes and rotational and translational motion are discussed. Both relaxation functions and mean square displacements are discussed in terms of stretched exponentials, and the behavior of the resulting “Kohlrausch exponents” γ is presented in detail.
    Additional Material: 20 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 3 (1994), S. 305-323 
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A bead-spring off-lattice model of a polymer chain with repulsive interactions among repeating units confined into straight tubes of various cross sections, DT2, is studied by Monte Carlo simulation. We are also varying the chain length from N = 16 to 128 and the strength of a short-range attractive interaction between the repeating units and the walls of the tube. Longitudinal and perpendicular static linear dimensions of the chains are analyzed, as well as the density profile of repeating units across the tube. These data are interpreted in terms of scaling concepts describing the crossover between three-dimensional and quasi-one-dimensional chain conformations and the adsorption transition of chains at flat infinite walls, respectively. We also study the time-dependent mean-square displacements of repeating units and obtain various relaxation times. It is shown that both relaxation times scaling proportional to N2 and to N3 play a role in the reptative motion of the chain in the tubes.
    Additional Material: 17 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 7 (1998), S. 141-156 
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: We present results of computer simulations of polymer brushes (layers of polymer chains attached at one end onto an impermeable planar surface) under shear deformation at constant shear rate. As the first stage of calculations the behavior of a single brush was studied. The monomer density profile, the distribution of the chain ends, the positions and orientations of different monomers along the chain were calculated. Dimensions of the polymer chains as functions of the shear rate were obtained for different grafting densities. An increase in the brush thickness over the grafting plane with an increase in the shear rate as predicted by the theory of Barrat was observed. However, the magnitude of the effect appears to be small. We explain this by finite extensibility of the grafted chains.
    Additional Material: 16 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 3 (1994), S. 915-929 
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A recently introduced coarse-grained model of polymer chains is studied analyzing various contributions to the pressure as obtained from the virial theorem as a function of chain length N, temperature T and density φ. The off-lattice model of the polymer chains has anharmonic springs between the beads, but of finite extensibility, and the Morse-type interaction between beads is repulsive at very short distances and attractive at intermediate distances. Solvent molecules are not explicitly included. It is found that the covalent forces along the chain (modelled by the spring potentials) contribute a negative term to the pressure, irrespective of temperature, which vanishes linearly in φ as φ → 0. In contrast, both contributions to the pressure due to intrachain nonbonded forces and due to forces between different chains change sign from high temperatures (T ≫ θ, θ the theta-temperature) where they are positive, to low temperature where both parts of the pressure become negative. It is shown that the total pressure has the expected behavior with temperature near the θ-temperature, i.e., Δp ≡ ptot - kB · Tp ∼ (T - θ). We study also the concentration and chainlength dependence of the various contributions to the pressure in the good solvent regime and interpret them with scaling predictions.
    Additional Material: 9 Ill.
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