The collapse transition of a single polymer chain in two and three dimensions was studied using the bond-fluctuation model. The obtained exponents ν of the scaling law 〈S2N〉∼N2ν agree with values proposed in the literature as well as above, at and below the Θ-temperature TΘ. Transition curves and scaling analysis plots are presented. The scaling function α3SτN1/2 vs τN1/2 has a pronounced maximum before leveling off in the fully collapsed regime in accordance with the theory [α2S=〈S2N〉/〈S2N〉Θ, τ=‖(T−TΘ)/TΘ‖]. An analyzing of the subchain distances leads to disagreements with the blob model. The subchains are locally swollen for T≳TΘ and shrunken for T<TΘ. The probability distribution function of internal distances for T≥TΘ can be described by scaling functions of the form fs(x)∼xκs exp(−Dsxδs) for large x, x being the scaled distance. In contrast for T<TΘ none of these functions describe the data. The dynamic properties above TΘ are in agreement with the Rouse model, but below TΘ differences occur; the center of mass diffusion becomes anomalous and the relaxation times rise with a power law in N of the form τi(N)∼N2+3/d (d being the dimension of space).
The probability distribution functions P s ͑r͒ of the distance r between the end points of subchains of a single excluded volume chain in two and three dimensions were studied using the bond-fluctuation model. The index s refers to three principle cases. Case sϭ0: the subchain is identical to the whole chain. Case sϭ1: the subchain constitutes one extremity of the whole chain. Case sϭ2: the subchain belongs to the central part of the whole chain. It is shown that the data can be described by the functions f s (x) ϳ x s for small x and f s (x) ϳ x s exp( Ϫ D s x ␦ s ) for large x, x being the scaled distance. All exponents s , s , and ␦ s were calculated and compared with existing values in the literature. In two dimensions a crossover between s and s was detected whereas in three dimensions s Ӎ s within statistical errors.
The deformation behavior of a single polymer chain subjected to an external force was studied by Computer simulations. Both random walks and self-avoiding walks were investigated. The simulations were performed in two and three dimensions using the bond fluctuation model. The projection of the end-to-end vector in the force direction as a function of the applied force was compared to the scaling function obtained from renormalization group studies, covering the füll interesting force regime. The differences in the crossover between the linear force and Pincus-scaling regime were studied.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.