[논문]Diffusion of Probe Molecule in Small Liquid n-Alkanes: A Molecular Dynamics Simulation Study

Yoo, Choong-Do; Kim, Soon-Chul; Lee, Song-Hi

doi:10.5012/bkcs.2008.29.8.1554

Diffusion of Probe Molecule in Small Liquid n-Alkanes: A Molecular Dynamics Simulation Study 원문보기

Bulletin of the Korean chemical society, v.29 no.8, 2008년, pp.1554 - 1560

Yoo, Choong-Do (Department of Chemistry, Kyungsung University) , Kim, Soon-Chul (Department of Physics, Andong National UniversityKorea) , Lee, Song-Hi (Department of Chemistry, Kyungsung University)

Abstract ▼ AI-Helper

The probe diffusion and friction constants of methyl yellow (MY) in liquid n-alkanes of increasing chain length were calculated by equilibrium molecular dynamics (MD) simulations at temperatures of 318, 418, 518 and 618 K. Lennard-Jones particles with masses of 225 and 114 g/mol are modeled for MY. We observed that the diffusion constant of the probe molecule follows a power law dependence on the molecular weight of nalkanes, DMY${\sim}M^{-\gamma}$ well. As the molecular weight of n-alkanes increases, the exponent $\gamma$ shows sharp transitions near n-dotriacontane ($C_{32}$) for the large probe molecule (MY2) at low temperatures of 318 and 418 K. For the small probe molecule (MY1) $D_{MY1}$ in $C_{12}$ to C80 at all the temperatures are always larger than Dself of n-alkanes and longer chain n-alkanes offer a reduced friction relative to the shorter chain n-alkanes, but this reduction in the microscopic friction for MY1 is not large enough to cause a transition in the power law exponent in the log-log plot of DMY1 vs M of n-alkane. For the large probe molecule (MY2) at high temperatures, the situation is very similar to that for MY1. At low temperatures and at low molecular weights of n-alkanes, $D_{MY2}$ are smaller than $D_{self}$ of n-alkanes due to the relatively large molecular size of MY2, and MY2 experiences the full shear viscosity of the medium. As the molecular weight of n-alkane increases, $D_{self}$ of n-alkanes decreases much faster than $D_{MY2}$ and at the higher molecular weights of n-alkane, MY2 diffuses faster than the solvent fluctuations. Therefore there is a large reduction of friction in longer chains compared to the shorter chains, which enhances the diffusion of MY2. The calculated friction constants of MY1 and MY2 in liquid n-alkanes supported these observations. We deem that this is the origin of the so-called“solventoligomer”transition.

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This is the manifestation of the reduced friction in longer chains compared to the shorter chains for small solute molecules which diffuse faster than the solvent fluctuations. However, the reduction in the microscopic friction for the probe molecules is not large enough to cause a transition in the power law exponent in the log-log plot of Dmy1 vs M of n-alkane as shown in Figure 6. For the larger probe molecule, MY2, the calculated friction constants are much larger than those of MY1 at all the temperatures. At high temperatures of 518 and 618 K, the behavior ofthe slope in the log-log plot of Zmy2 vs M is very similar to that of MY1 except that the clear change of slope from the assumed linear dependence of the friction of MY2 on the chain length of n-alkane starts at C36 instead of C28 in the case of MY1 and that the initial slopes in the log-log plot of Zmy2 vs M at high temperatures are larger than those in the log-log plot of Zmy1 vs M at all the temperatures.
44 in various organic solvents.6 It is interesting to compare Dmy for both probe molecules in n-alkanes with Dself ofn-alkanes, denoted black and white symbols at each temperature in Figures 6 and 7. For MY1, Dmy1 are always larger than Dself at all the temperatures due to the relatively small molecular size of MY1. As the molecular weight of n-alkane increases, Dmy1 decreases much slower than Dself and two diffusion constants never cross each other.
We could obtain the friction constants by the time integral of the total FAC choosing the upper limit of tas the time which the FAC has the first negative value by assuming that the fast random force correlation ends at that time as proposed by Lagr'kov and Sergeev.34 The obtained friction constant (z) of center of mass of nalkane is plotted as function of molecular weight of liquid nalkane in the log-log plot as shown in Figure 8. The slopes are almost linear at given temperatures and this indicates that the behavior of Z vs M is well described by Z~MS. The obtained exponents are between 1.

제안 방법

For liquid n-alkanes, we have chosen 9 systems - ndodecane (C12H26), n-hexadecane (C16H34), n-eicosane (C20H42), n-tetracosane (C24H50), n-octacosane (C28H58), ndotriacontane (C32H66), n-hexatriacontane (C36H74), n-tetratetracontane (C44H90), and n-tetratetracontane (C80H162). Each simulation was carried out in the NpT ensemble with the probe molecule at the center of the simulation box to determine the volume of each system at given temperatures, and after the equilibrium density and hence the length of cubic simulation box were obtained, new NVT MD simulation was performed for each system to store the configurations of the probe molecule and n-alkanes for later analyses. The usual periodic boundary condition in the x-, y-, and z-directions and the minimum image convention for pair potential were applied.
6 kJ/mol (labeled as MY2). In order to study the size effect of the probe particle, we further carried out MD simulations for a smaller size of LJ particle of LJ potential parameters of c= 4.0 A and £ = 0.4 kJ/mol with molecular weight of 114 g/mol (labeled as MY1). For liquid n-alkanes, we have chosen 9 systems - ndodecane (C12H26), n-hexadecane (C16H34), n-eicosane (C20H42), n-tetracosane (C24H50), n-octacosane (C28H58), ndotriacontane (C32H66), n-hexatriacontane (C36H74), n-tetratetracontane (C44H90), and n-tetratetracontane (C80H162).
To calculate the diffusion constant of methyl yellow (MY) with molecular weight of225 g/mol in n-alkane matrices, we carried out MD simulations for the systems which consist of a Lennard-Jones (LJ) particle and N= 100 of n-alkane molecules with different carbon numbers. The LJ particle modeled for the probe interacts with all the interaction sites ofn-alkanes with LJ potential parameters of c= 6.

대상 데이터

We have extended equilibrium molecular dynamics (MD) simulations for the probe diffusion and friction dynamics of Lennard-Jones (LJ) particles modeled for methyl yellow (MY) in liquid n-alkanes at temperatures of 318, 418, 518, and 618 K to investigate the size effect of probe molecule and the temperature effect. Two LJ particles are chosen: MY1 with mass of 114 g/mol and LJ parameters of c= 4.0 A and £ = 0.4 kJ/mol, and MY2 of 225 g/mol and c= 6.0 A and £ = 0.6 kJ/mol. We observed that the diffusion constant of the probe molecule follows a power law dependence on the molecular weight of n-alkanes, Dmy 〜M^ well.

성능/효과

99 (C12) and 7.91 kcal/mol (C80) as shown in Figure 4. Our previous MD simulation study26 for liquid n-C12 〜C44 at T = 273-473 K gives the activation energies of 2.33, 3.29, 4.63, and 5.46 kcal/mol for C12, C20, C32, and C44, respectively. E” is also small for small n-alkanes.

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