Partition function zeros and finite size scaling for polymer adsorption
Abstract
The zeros of the canonical partition functions for a flexible polymer chain tethered to an attractive flat surface are computed for chains up to length N = 1536. We use a bondfluctuation model for the polymer and obtain the density of states for the tethered chain by WangLandau sampling. The partition function zeros in the complex e{sup β}plane are symmetric about the real axis and densest in a boundary region that has the shape of a nearly closed circle, centered at the origin, terminated by two flaring tails. This structure defines a rootfree zone about the positive real axis and follows YangLee theory. As the chain length increases, the base of each tail moves toward the real axis, converging on the phasetransition point in the thermodynamic limit. We apply finitesize scaling theory of partitionfunction zeros and show that the crossover exponent defined through the leading zero is identical to the standard polymer adsorption crossover exponent ϕ. Scaling analysis of the leading zeros locates the polymer adsorption transition in the thermodynamic (N → ∞) limit at reduced temperature T{sub c}{sup *}=1.027(3) [β{sub c}=1/T{sub c}{sup *}=0.974(3)] with crossover exponent ϕ = 0.515(25). Critical exponents for the order parameter and specific heat aremore »
 Authors:
 Department of Physics, Hiram College, Hiram, Ohio 44234 (United States)
 Department of Physics and Department of Chemistry, University of Akron, Akron, Ohio 44325 (United States)
 Publication Date:
 OSTI Identifier:
 22413254
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 20; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ADSORPTION; DENSITY OF STATES; FLUCTUATIONS; ORDER PARAMETERS; PARTITION FUNCTIONS; PHASE TRANSFORMATIONS; POLYMERS; SPECIFIC HEAT; SURFACES
Citation Formats
Taylor, Mark P., Email: taylormp@hiram.edu, and LuettmerStrathmann, Jutta, Email: jutta@uakron.edu. Partition function zeros and finite size scaling for polymer adsorption. United States: N. p., 2014.
Web. doi:10.1063/1.4902252.
Taylor, Mark P., Email: taylormp@hiram.edu, & LuettmerStrathmann, Jutta, Email: jutta@uakron.edu. Partition function zeros and finite size scaling for polymer adsorption. United States. doi:10.1063/1.4902252.
Taylor, Mark P., Email: taylormp@hiram.edu, and LuettmerStrathmann, Jutta, Email: jutta@uakron.edu. 2014.
"Partition function zeros and finite size scaling for polymer adsorption". United States.
doi:10.1063/1.4902252.
@article{osti_22413254,
title = {Partition function zeros and finite size scaling for polymer adsorption},
author = {Taylor, Mark P., Email: taylormp@hiram.edu and LuettmerStrathmann, Jutta, Email: jutta@uakron.edu},
abstractNote = {The zeros of the canonical partition functions for a flexible polymer chain tethered to an attractive flat surface are computed for chains up to length N = 1536. We use a bondfluctuation model for the polymer and obtain the density of states for the tethered chain by WangLandau sampling. The partition function zeros in the complex e{sup β}plane are symmetric about the real axis and densest in a boundary region that has the shape of a nearly closed circle, centered at the origin, terminated by two flaring tails. This structure defines a rootfree zone about the positive real axis and follows YangLee theory. As the chain length increases, the base of each tail moves toward the real axis, converging on the phasetransition point in the thermodynamic limit. We apply finitesize scaling theory of partitionfunction zeros and show that the crossover exponent defined through the leading zero is identical to the standard polymer adsorption crossover exponent ϕ. Scaling analysis of the leading zeros locates the polymer adsorption transition in the thermodynamic (N → ∞) limit at reduced temperature T{sub c}{sup *}=1.027(3) [β{sub c}=1/T{sub c}{sup *}=0.974(3)] with crossover exponent ϕ = 0.515(25). Critical exponents for the order parameter and specific heat are determined to be β{sup ~}=0.97(5) and α = 0.03(4), respectively. A universal scaling function for the average number of surface contacts is also constructed.},
doi = {10.1063/1.4902252},
journal = {Journal of Chemical Physics},
number = 20,
volume = 141,
place = {United States},
year = 2014,
month =
}

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