Partition function zeros and finite size scaling for polymer adsorption

Luettmer-Strathmann, Jutta

doi:10.1063/1.4902252

Title: Partition function zeros and finite size scaling for polymer adsorption

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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 bond-fluctuation model for the polymer and obtain the density of states for the tethered chain by Wang-Landau 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 root-free zone about the positive real axis and follows Yang-Lee theory. As the chain length increases, the base of each tail moves toward the real axis, converging on the phase-transition point in the thermodynamic limit. We apply finite-size scaling theory of partition-function 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 »« less

Authors:

Luettmer-Strathmann, Jutta ^[1]

Department of Physics and Department of Chemistry, University of Akron, Akron, Ohio 44325 (United States)

Publication Date:: Fri Nov 28 00:00:00 EST 2014

OSTI Identifier:: 22413254

Resource Type:: Journal Article

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 141; Journal Issue: 20; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

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., E-mail: taylormp@hiram.edu, and Luettmer-Strathmann, Jutta. Partition function zeros and finite size scaling for polymer adsorption.  United States: N. p., 2014. 
        Web.  doi:10.1063/1.4902252.

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                    Taylor, Mark P., E-mail: taylormp@hiram.edu, & Luettmer-Strathmann, Jutta. Partition function zeros and finite size scaling for polymer adsorption.  United States.  https://doi.org/10.1063/1.4902252

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                    Taylor, Mark P., E-mail: taylormp@hiram.edu, and Luettmer-Strathmann, Jutta. 2014.  
        "Partition function zeros and finite size scaling for polymer adsorption".  United States.  https://doi.org/10.1063/1.4902252.

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@article{osti_22413254,

  title        = {Partition function zeros and finite size scaling for polymer adsorption},

  author       = {Taylor, Mark P., E-mail: taylormp@hiram.edu and Luettmer-Strathmann, Jutta},

  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 bond-fluctuation model for the polymer and obtain the density of states for the tethered chain by Wang-Landau 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 root-free zone about the positive real axis and follows Yang-Lee theory. As the chain length increases, the base of each tail moves toward the real axis, converging on the phase-transition point in the thermodynamic limit. We apply finite-size scaling theory of partition-function 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},

  url          = {https://www.osti.gov/biblio/22413254},
  journal      = {Journal of Chemical Physics},

  issn         = {0021-9606},

  number       = 20,

  volume       = 141,

  place        = {United States},

  year         = {Fri Nov 28 00:00:00 EST 2014},

  month        = {Fri Nov 28 00:00:00 EST 2014}

}

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