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  • 1
    Electronic Resource
    Electronic Resource
    Scattering function and the dynamics of phase separation in polymer mixtures under shear flow (1988)
    Springer
    Colloid & polymer science 266 (1988), S. 132-140 
    Details
    ISSN: 1435-1536
    Keywords: Polymermixtures ; shear flow ; concentration fluctuations ; scattering function ; spinodal decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The phenomenological mean-field theory describing concentration fluctuations and spinodal decomposition of binary mixtures of long flexible macromolecules is generalized to mixtures under steady shear flow. This shear flow leads to a partial orientation and stretching of the coils, as well as to an anisotropic deformation of concentration fluctuations. Generalizing the approach of Onuki and Kawasaki, we obtain the collective scattering function describing these concentration fluctuations in the mixture under shear flow. Both the steady-state situation in the one-phase region and the initial stages of spinodal decomposition for concentrations inside of the spinodal curve are considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01452810
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  • 2
    Electronic Resource
    Electronic Resource
    Scattering from concentration fluctuations in polymer blends: A monte carlo investigation (1989)
    Springer
    Colloid & polymer science 267 (1989), S. 469-479 
    Details
    ISSN: 1435-1536
    Keywords: Polymermixtures ; self-avoidingwalk ; MonteCarlosimulation ; spinodalcurves ; collectivescatteringfunction ; effectiveχ-parameter
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The collective scattering function Scoll( $$\vec q$$ ), which describes light (neutron-, x-ray) scattering under wavevector $$\vec q$$ , is obtained from Monte Carlo simulations for a symmetrical polymer mixture. The polymers are modelled by self-avoiding walks ofN A=NB=N steps on a simple cubic lattice, where a fractionφ V of sites is left vacant, and an attractive energyε occurs if two neighboring sites are taken by the same kind of monomer. Spinodal curves are estimated from linear extrapolation of S coll −1 (0) vs.ε/k B T, whereT is the temperature. Also the single chain structure factor is obtained and the de Gennes random phase approximation (RPA) can thus be tested. Unexpectedly, strong deviations are found if one species is very dilute. The estimation of an effective Flory-Hugginsχ-parameter from scattering data is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01416052
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  • 3
    Electronic Resource
    Electronic Resource
    Dynamics of phase separation and critical phenomena in polymer mixtures (1987)
    Springer
    Colloid & polymer science 265 (1987), S. 273-288 
    Details
    ISSN: 1435-1536
    Keywords: Polymermixtures ; spinodaldecomposition ; Flory-Huggins model ; critical point ; computer simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The phenomenological mean-field theory for statics and dynamics of polymer mixtures is described, generalizing the approaches of Flory-Huggins, Cahn-Hilliard and de Gennes. Predictions are made for critical behavior, spinodal decomposition and homogeneous nucleation. The validity of the mean-field approximations is discussed with Ginzburg criteria. The results of the theory are compared to computer simulations and recent experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01417926
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  • 4
    Electronic Resource
    Electronic Resource
    Static and dynamic critical phenomena of the two-dimensionalq-state Potts model (1981)
    Springer
    Journal of statistical physics 24 (1981), S. 69-86 
    Details
    ISSN: 1572-9613
    Keywords: Potts model ; first-order transition ; second-order transition ; Monte Carlo ; critical slowing down ; critical exponents ; dynamic scaling ; nonlinear relaxation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Theq-state Potts model on the square lattice is studied by Monte Carlo simulation forq=3, 4, 5, 6. Very good agreement is obtained with exact results of Kiharaet al. and Baxter for energy and free energy at the critical point. Critical exponent estimates forq=3 areα≈0.4,β≈0.1,γ≈1.45, in rough agreement with high-temperature series extrapolation and real space renormalization-group methods. The transition forq=5, 6 is found to be a very weakly first-order transition, i.e., pronounced “pseudocritical” phenomena occur, specific heat, susceptibility, etc. (nearly) diverge at the first-order transition temperature. Dynamics is associated to the model in the same way as for the kinetic Ising model, and the nonlinear slowing down of the order parameter and of the energy is studied. The dynamic exponent is estimated to be Δ (=zv)≈1.9. Within our accuracy noq dependence is detected. The relaxation is found to be consistent with dynamic scaling predictions, and dynamic scaling functions associated with the nonlinear relaxation are estimated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01007636
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  • 5
    Electronic Resource
    Electronic Resource
    Finite-size scaling analysis of the Φ4 field theory on the square lattice (1986)
    Springer
    Journal of statistical physics 44 (1986), S. 749-784 
    Details
    ISSN: 1572-9613
    Keywords: Continuous Ising model ; order-disorder ; displacive ; Monte-Carlo simulation ; finite-size scaling ; critical exponents
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Monte-Carlo calculations are performed for the model Hamiltonian ℋ = ∑i[(r/2)Φ 2(i)+(u/4)/gF4(i)]+∑〈ij〉 (C/2)[Φ (i)−Φ(j)]2 for various values of the parametersr, u, C in the crossover region from the Ising limit (r→-∞,u+∞) to the displacive limit (r=0). The variableφ(i) is a scalar continuous spin variable which can lie in the range-∞〈φ(i)〈+∞, for each lattice site (i).φ(i) is a priori selected proportional to the single-site probability in our Monte Carlo algorithm. The critical line is obtained in very good agreement with other previous approaches. A decrease of apparent critical exponents, deduced from a finite-size scaling analysis, is attributed to a crossover toward mean-field values at the displacive limit. The relation of this model to the coarse-grained Landau-Ginzburg-Wilson free-energy functional of Ising models is discussed in detail, and, by matching local moments 〈Φ 2(i)〉, 〈Φ 4(i)〉 to corresponding averages of subsystem blocks of Ising systems with linear dimensionsl=5 tol=15, an explicit construction of this coarse-grained free energy is attempted; self-consistency checks applied to this matching procedure show qualitatively reasonable behavior, but quantitative difficulties remain, indicating that higher-order terms are needed for a quantitatively satisfactory description.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01011906
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