Processos de polimerização e transição de colapso em polímeros ramificados. / Polymerization processes and collapse transition of branched polymers.

AUTOR(ES)

Ubiraci Pereira da Costa Neves

DATA DE PUBLICAÇÃO

1997

RESUMO

The phase diagram and the tricritical point of a collapsing lattice animal are studied through an extended series expansion of the isothermal compressibility KT on a square lattice. As a function of the variables x (fugacity) and y = e1/T (T is the reduced temperature), this series KT is investigated using the partial differential approximants technique. The characteristic flow pattern of partial differential approximant trajectories is determined for a typical stable fixed point. We obtain satisfactory estimates for the tricritical fugacity Xt = 0.024 ± 0.005and temperature Tt = 0.54 ± 0.04.Taking into account only linear scaling fields we are also able to get the scaling exponent γ = 1.4 ± 0.2 and the crossover exponent Φ = 0.66 ± 0.08. Our results are in good agreement with previous estimates from other methods. We also study ramified polymerization through computational simulations on the square lattice of a kinetic growth model generalized to incorporate branching and impurities. The polymer configuration is identified with a bond tree in order to examine its topology. The fractal dimensions of clusters are obtained at criticality. Simulations also allow the study of time evolution of clusters as well as the determination of time autocorrelations and dynamical critical exponents. In regard to finite size effects, a fourth-order cumulant technique is employed to estimate the critical branching probability be and the critical exponents v and β. In the absence of impurities, the surface roughness is described in terms of the Hurst exponents. Finally we simulate this kinetic growth model on the square lattice using a Monte Carlo approach in order to study ramified polymerization with short distance attractive interactions between monomers. The phase boundary separating finite from infinite growth regimes is obtained in the (T,b) space (T is the reduced temperature and b is the branching probability). In the thermodynamic limit, we extrapolate the temperature T = 0.102 ± 0.005 below which the phase is found to be always infinite. We also observe the occurrence of a roughening transition at the polymer surface.

ASSUNTO(S)

cumulantes kinetic growth model lattice animal aproximantes diferenciais parciais simulações monte carlo tricritical point animal na rede modelo de crescimento cinético monte carlo simulations cumulants partial differential approximants polímeros ramificados series expansion collapse transition transição de colapso branched polymers ponto tricrítico expansão em série

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