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Membranes 2021, 11, 940 the convergence tolerance quality was set as ultrafine. A typical simulation box consiste of the polyelectrolyte chain with a degree of polymerization 20, 20 cations (Li+, Na+, Ca2 or Mg2+), a balanced charge of chloride ions (1:1 ratio for the monovalent ions and 1:2 fo the divalent ions), and 500 molecules of water. The constructed simulation box was geo 4 of 12 metrically optimized using the Forcite module and the system maintained electrical neu trality, as presented in Figure 2 for the PE-CaCl2-H2O system. Figure2..Mooddeellooffpoployleylecltercotlryotely-Ctea-Cla-Cwla2-tewramteorlemcuolelescautl2e9s8aKt.2T9h8eKp.uTrphlepreugriponlerreepgreiosennrtsepthresentsth 2 polyellecctrtroolylytetebabcakcbkobnoen. Ae.llAoltlhoetrhaetormatsormemsarienmthaeinsatmhesaasmdepaicsteddepinicFtiegdurien1F.igure 1. 2.3. Molecular Dynamics Simulations 2.3. Molecular Dynamics Simulations Molecular dynamics simulations were conducted using the Forcite module. The Molecular dynamics simulations were conducted using the Forcite module. The ini initial systems were structurally optimized using the congruent gradient, followed by tial systems were structurally optimized using the congruent gradient, followed by a dy a dynamics simulation on the constant pressure-constant temperature (NPT) ensemble −4 n(Pam=1ic0s siGmPual,aTti=on29o8nKt)hteocsotanbsitlaiznettphreesyssutreem-cwonitshtanstimteumlapteiornattuimree(oNfP5T00)penssaenmdble (P −4 1a0timGePsate,pTo=f 02.90801Kp)st. oTshteabmiloilzeecuthlees soyf sttheempowlyitehlecatrsoilmytuelachtiaoin ftriomme tohfe5l0a0st pfrsamaned a tim generated from the NPT simulation were fixed using the constraints toolbar, and the cations step of 0.001 ps. The molecules of the polyelectrolyte chain from the last frame generate were indicated as set. The system was subjected to the dynamics simulation under the from the NPT simulation were fixed using the constraints toolbar, and the cations wer constant volume-constant temperature (NVT) ensemble with a total simulation time of indicated as set. The system was subjected to the dynamics simulation under the constan 1.5 ns, and the trace file recording was output at every 5000 steps (5 ps). The starting volume-constant temperature (NVT) ensemble with a total simulation time of 1.5 ns, an velocity of the atoms at a given temperature was designated randomly by the Boltzmann the trace file recording was output at every 5000 steps (5 ps). The starting velocity of th distribution, the summation method was atom-based, and a truncation radius of 18.5 Å atoms at a given temperature was designated randomly by the Boltzmann distribution was chosen for the non-bonded interaction energy. The Particle–Particle Particle–Mesh t(hPPePsMum) meatthiodnomf esuthmomdiwngauspattohme c-obualsoemd,baicnedleacttrrousntactaictipoonternatdiaiul esnoefrg1y8.w5aÅswchaosecnh,osen fo tahned nthoenB-beorenndesdenincotenrsatacntitotnemenperagtyu.reThtheerPmaratlibclaet–hPaanrdtitchle cPoanrsttiacnlet–pMreesshur(ePsPyPstMem) metho was selected for temperature and pressure control. The total energy of the system under of summing up the coulombic electrostatic potential energy was chosen, and the Berend the NVT ensemble was determined to confirm the attainment of equilibrium. The total sen constant temperature thermal bath and the constant pressure system was selected fo energies of the CaCl2, LiCl, NaCl, and the MgCl2 systems fluctuated around 27,000, 21,700, temperature and pressure control. The total energy of the system under the NVT ensembl 21,000, and 30,000 kCal/mol, respectively, as presented in Figure 3. was determined to confirm the attainment of equilibrium. The total energies of the CaCl2 The diffusion properties of the ions within the polyelectrolytes were determined by LiCl, NaCl, and the MgCl2 systems fluctuated around 27,000, 21,700, 21,000, and 30,00 estimating the mean square displacement (MSD). The MSD indicates the average separation kCal/mol, respectively, as presented in Figure 3. of all particles from their corresponding initial positions at time t into the motion. The greater the MSD value, the higher the diffusivity of the ions within the system. The MSD at time t in a given ensemble is expressed by the Equation: 1N2 MSD = N ∑i=1|xi(t) − xi(0)| (1) where N represents the number of particles to be averaged, and xi(0) and xi(t) are the initial positions of the i ion and the position of the ion at time t, respectively. d r - - e - - = e d e t d e r d - r e 0PDF Image | Diffusion of Monovalent Ions in Polyelectrolyte
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