DOI: 10.5281/zenodo.18372403
title: Exact enumeration results and figure data for "Unified origin of negative energetic elasticity in a lattice polymer chain: soft self-repulsion and bending stiffness"

description: This record contains the data files and plotting scripts used to generate (and/or directly provide the numerical content of) the figures in:



Shirai, N. C. “Unified origin of negative energetic elasticity in a lattice polymer chain: soft self-repulsion and bending stiffness”


Overview

This study investigates the elastic response of a single lattice polymer chain with fixed end-to-end distance, incorporating both Domb–Joyce (DJ) soft-core self-repulsion and local bending-energy cost. The total energy is defined as:

$$E(\omega) = \varepsilon m(\omega) + \varepsilon_b b(\omega)$$

where:



$\varepsilon$ is the DJ self-repulsion strength

$\varepsilon_b$ is the bending-energy cost

$m(\omega)$ is the DJ overlap count

$b(\omega)$ is the bend count


Data Files

Input Data




File
Description
Format




W_data.csv
Enumeration data of random walks on a cubic lattice
n,r,m,b,W




Columns:



n: Chain length (number of steps)

r: End-to-end distance

m: DJ overlap count (number of site overlaps)

b: Bend count (number of direction changes)

W: Number of configurations with given $(n, r, m, b)$, i.e., $W_{n,m,b}(r)$


Figure 1 data




File
Description
Format




Fig1_coordinate_data.csv
Coordinates of a representative 20-step configuration
i,x,y,z




This file contains the coordinates of the configuration shown in Figure 1, demonstrating a 20-step random walk with endpoints fixed at the origin and $(10,0,0)$.

Figure 2 data




File
Description
Format




Fig2_beta_k.csv
Stiffness decomposition data
beta_eps,beta_eps_b,beta_k,beta_kU,beta_kS




Columns:



beta_eps: Dimensionless DJ parameter $\beta\varepsilon$

beta_eps_b: Dimensionless bending parameter $\beta\varepsilon_b$

beta_k: Dimensionless total stiffness $\beta k$

beta_kU: Dimensionless energetic stiffness $\beta k_U$

beta_kS: Dimensionless entropic stiffness $\beta k_S$


Parameters: $(n, r) = (20, 10)$

Figure 3 data




File
Description
Format




Fig3_U_S.csv
Internal energy and entropy vs end-to-end distance
r,U,S




Columns:



r: End-to-end distance

U: Internal energy $U/\varepsilon_b$ (in units of bending energy)

S: Entropy $S/k_B$ (dimensionless)


Parameters: $n=20$, $\varepsilon=0$, $\beta\varepsilon_b=1$ (bending-only limit)

Figure 4 data




File
Description
Format




Fig4_U.csv
Internal energy for various chain lengths and bending strengths
n,r,beta_eps_b,U




Columns:



n: Chain length

r: End-to-end distance

beta_eps_b: Dimensionless bending parameter $\beta\varepsilon_b$

U: Internal energy $U/\varepsilon$ (in units of self-repulsion energy)


Parameters: $\beta\varepsilon=1$, $\beta\varepsilon_b \in \lbrace 0, 2^{-6}, 2^{-4}, 2^{-2}\rbrace$, $n \in \lbrace 10, 11, \ldots, 20\rbrace$

Plotting scripts (Gnuplot, Figure 4)

These scripts generate the Figure 4 plots from Fig4_U.csv.




Script
Description
Output




plot_Fig4_U_vs_n.plt
Internal energy $U/\varepsilon$ vs $n$
Fig4_U_vs_n.pdf


plot_Fig4_U_vs_slack.plt
Internal energy $U/\varepsilon$ vs $(n-r)^{7/4}/n$
Fig4_U_vs_slack.pdf




Shared configuration:



config_plot_Fig4.plt (common settings and analytic fitting functions)


Usage (Gnuplot)

From the directory containing these files:



gnuplot plot_Fig4_U_vs_n.plt
gnuplot plot_Fig4_U_vs_slack.plt


Dependencies

Gnuplot



Gnuplot 5.x or later (for .plt scripts)


Tested environment



Gnuplot 6.0 patchlevel 3


Citation

If you use this data, please cite:



Shirai, N. C. “Unified origin of negative energetic elasticity in a lattice polymer chain: soft self-repulsion and bending stiffness”