The Boyle temperature, TB, for an n-segment polymer in solution is the temperature where the second osmotic virial coefficient, A2, is zero. This characteristic is of interest for its connection to the polymer condensation critical temperature, particularly for n → ∞. TB can be measured experimentally or computed for a given model macromolecule. For the latter, we present and examine two approaches, both based on the Mayer-sampling Monte Carlo (MSMC) method, to calculate Boyle temperatures as a function of model parameters. In one approach, we use MSMC calculations to search for TB, as guided by the evaluation of temperature derivatives of A2. The second approach involves numerical integration of an ordinary differential equation describing how TB varies with a model parameter, starting from a known TB. Unlike general MSMC calculations, these adaptations are appealing because they neither invoke a reference for the calculation nor use special averages needed to avoid bias when computing A2 directly. We demonstrate these methods by computing TB lines for off-lattice linear Lennard-Jones polymers as a function of chain stiffness, considering chains of length n ranging from 2 to 512 monomers. We additionally perform calculations of single-molecule radius of gyration Rg and determine the temperatures Tθ, where linear scaling of with n is observed, as if the polymers were long random-walk chains. We find that Tθ and TB seem to differ by 6% in the n → ∞ limit, which is beyond the statistical uncertainties of our computational methodology. However, we cannot rule out systematic error relating to our extrapolation procedure as being the source of this discrepancy.
Skip Nav Destination
Article navigation
21 October 2024
Research Article|
October 18 2024
Methodical evaluation of Boyle temperatures using Mayer sampling Monte Carlo with application to polymers in implicit solvent
Special Collection:
Monte Carlo methods, 70 years after Metropolis et al. (1953)
Andrew J. Schultz
;
Andrew J. Schultz
(Conceptualization, Formal analysis, Funding acquisition, Methodology, Software, Visualization, Writing – review & editing)
Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York
, Buffalo, New York 14260-4200, USA
Search for other works by this author on:
David A. Kofke
David A. Kofke
a)
(Conceptualization, Formal analysis, Funding acquisition, Methodology, Visualization, Writing – original draft, Writing – review & editing)
Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York
, Buffalo, New York 14260-4200, USA
a)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
a)Author to whom correspondence should be addressed: [email protected]
J. Chem. Phys. 161, 154108 (2024)
Article history
Received:
July 09 2024
Accepted:
October 03 2024
Citation
Andrew J. Schultz, David A. Kofke; Methodical evaluation of Boyle temperatures using Mayer sampling Monte Carlo with application to polymers in implicit solvent. J. Chem. Phys. 21 October 2024; 161 (15): 154108. https://doi.org/10.1063/5.0227411
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
DeePMD-kit v2: A software package for deep potential models
Jinzhe Zeng, Duo Zhang, et al.
CREST—A program for the exploration of low-energy molecular chemical space
Philipp Pracht, Stefan Grimme, et al.
Freezing point depression of salt aqueous solutions using the Madrid-2019 model
Cintia P. Lamas, Carlos Vega, et al.
Related Content
Path-integral Mayer-sampling calculations of the quantum Boltzmann contribution to virial coefficients of helium-4
J. Chem. Phys. (November 2012)
Virial coefficients of model alkanes
J. Chem. Phys. (September 2010)
Mayer-sampling Monte Carlo calculations of uniquely flexible contributions to virial coefficients
J. Chem. Phys. (September 2011)
Two complementary molecular energy decomposition schemes: The Mayer and Ziegler–Rauk methods in comparison
J. Chem. Phys. (October 2008)
Anisotropic coarse-grain Monte Carlo simulations of lysozyme, lactoferrin, and NISTmAb by precomputing atomistic models
J. Chem. Phys. (September 2024)