We analytically calculate the gas-liquid critical endpoint (cep) for hard spheres with a Yukawa attraction. This cep is a boundary condition for the existence of a liquid. We use an analytical Helmholtz energy expression for the attractive Yukawa (hard) spheres based on the first-order mean spherical approximation to the attractive Yukawa potential by Tang and Lu (J. Chem. Phys. 1993, 99, 9828). This theory and our analytical simplification of it predict the gas-liquid and fluid-solid phase behavior, as found from computer simulations, very accurately as long as the range 1/kappa of attraction is not too short. We find that the cep is situated at kappasigma approximately 6 and at a contact potential around 2 kT. It follows that a liquid state is only possible when the attraction range is longer than (1/6) of the particle diameter sigma, and the attraction strength is smaller than 2 kT. The liquid region does not span more than 0.6 kT in strength, and there is also a relatively narrow window for the attraction range.
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http://dx.doi.org/10.1021/jp063650j | DOI Listing |
J Gastroenterol
January 2025
Department of Gastroenterology and Hepatology, Kyorin University School of Medicine, Mitaka, Japan.
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BMJ Open
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Cardiometabolic Medicine Center, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, China
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January 2025
School of Medicine, Nankai University, Tianjin, China.
Oxidative balance score (OBS) is a composite measures that assess the balance between pro-oxidant and antioxidant factors in an individual's diet and lifestyle, with higher scores indicating greater antioxidant exposure. Despite its potential significance, there is a limited body of research exploring the relationship between OBS and all-cause and cardiovascular disease (CVD) mortality specifically in younger patients with diabetes. We aimed to investigate the possible relationship between OBS and all-cause and CVD mortality in younger patients with diabetes.
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