CN105653766A - Method for calculating molecular diffusion coefficients through non-equilibrium molecular dynamics simulation - Google Patents
Method for calculating molecular diffusion coefficients through non-equilibrium molecular dynamics simulation Download PDFInfo
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Abstract
The invention provides a method for calculating molecular diffusion coefficients through non-equilibrium molecular dynamics simulation. According to the method, the molecular dynamics simulation is purely adopted to directly calculate the concentration gradients and diffusion fluxes of components in mixtures along the diffusion direction, so that the molecular diffusion coefficients of the components can be accurately calculated. Compared with a double-control volume grand canonical molecular dynamics (DCV-GCMD) simulation method, the method provided by the invention is capable of effectively improving the simulation efficiency and remarkably reducing the simulation program compiling difficulty.
Description
Technical field
The invention belongs to micro/nano-scale Molecular Simulation Technique field, relate to a kind of method that non-equlibrium molecular dynamics simulation calculates coefficient of molecular diffusion.
Background technology
Absorption and the important means that absorption is chemical separating, be widely used in CO2Recovery, waste gas and field of waste water treatment. And molecule diffusion is absorption and the important factor in order absorbed. Adopt molecular simulation means can inquire into the mechanism of molecule diffusion process from microcosmic angle.
Adopt molecular simulation to calculate coefficient of molecular diffusion at present and mainly adopt double control volume huge canonical molecular dynamics (DCV-GCMD) method. But, the method also exists following defect:
1) huge canonical Monte Carlo (GCMC) method is inserted the ratio of deletion big not compared with molecular dynamics (MD) step time, will lead to errors result;
2) owing to DCV-GCMD simulation relates to two processes of GCMC and MD simultaneously, when simulation process can consume substantial amounts of computer, while program to write difficulty also bigger.
In consideration of it, it is contemplated that explore a kind of non-equlibrium molecular dynamics simulation to calculate the new method of coefficient of molecular diffusion, to make up the deficiency of DCV-GCMD method, improve computational efficiency.
Summary of the invention
It is an object of the invention to provide a kind of method that non-equlibrium molecular dynamics simulation calculates coefficient of molecular diffusion, the method can adopt merely molecular dynamics simulation directly to calculate each component in mixture along the Concentraton gradient of dispersal direction and diffusion flux such that it is able to calculates the coefficient of molecular diffusion of each component accurately.
For reaching object above, the present invention provides following technical scheme:
A kind of non-equlibrium molecular dynamics simulation calculates the method for coefficient of molecular diffusion, and the method comprises the following steps:
S1: in calculating mixture (containing component 1 and 2 two kinds of components of component), component 1 is in the molar concentration of high concentration end Yu low concentration endc h Withc l ;
S2: calculate component 1 in the timetThe interior clean molecule amount by a certain cross section EN;
S3: calculated the diffusion coefficient of component 1 by below equationD,
In formula,NFor by the clean molecule amount of cross section E;LFor the distance between high concentration end and low concentration end;N AFor Avogadro's number;ACross-sectional area for cross section E;tFor timing statistics;c h Withc l Represent the component 1 molar concentration in high concentration region Yu low concentration region respectively.
Further, described S1 calculates the component 1 molar concentration at high concentration end Yu low concentration endc h Withc l , specifically comprise the following steps that
The volume that system is in turn divided into Di Nong district, diffusion region, highly concentrated district, diffusion region, Di Nong district totally 5 regions, highly concentrated district and Di Nong district along dispersal direction is expressed asV h WithV l ;Described cross section E is positioned at diffusion region (due to symmetry system having symmetry, only consider the cross section in a certain diffusion region). At simulation initial time, being positioned over of the quantity such as component 1 and component 2 is simulated in box;
Simulation process implements the steps of:
1) every t1Interval, randomly selects the molecule of a component 2 in high concentration region, randomly selects the molecule of a component 1 in low concentration region, exchanges two molecular position, and each self-sustaining speed is constant;
2) reaching after stable state until system, in the statistics t time, component 1 is at the mean molecule number in highly concentrated district Yu Di Nong districtN h WithN l , then component 1 can be calculated by following two formulas with the concentration in Di Nong district in highly concentrated district:
Described S2 calculates component 1 in the timetThe interior clean molecule amount by a certain cross section EN, specifically comprise the following steps that
After system reaches stable state, in the statistics t time, the times N that component 1 exchanges with component 2 molecular positionc, then in time t, by the clean molecule amount of a certain cross section EN=N c /2��
It is an advantage of the current invention that:
The present invention adopts merely non-equlibrium molecular dynamics simulation to calculate coefficient of molecular diffusion, compared with double control volume huge canonical molecular dynamics (DCV-GCMD) analogy method, this invention can be effectively improved simulation precision, and significantly reduces the difficulty during simulation program is write.
Accompanying drawing explanation
Fig. 1 is the flow chart of the method for the invention;
Fig. 2 is the statistics component 1 molecule amount by a certain cross section E and the schematic diagram in highly concentrated district and Di Nong district concentration thereof.
Detailed description of the invention
In order to make the object, technical solutions and advantages of the present invention clearly, below in conjunction with accompanying drawing, the present invention is described in further detail.
Simple non-equlibrium molecular dynamics simulation provided by the invention calculates the method for coefficient of molecular diffusion, as it is shown in figure 1, in simulations for convenience of processing, system is disposed as periodic boundary condition along tri-directions of x, y, z; System is in turn divided in the x-direction Di Nong district, diffusion region, highly concentrated district, diffusion region, Di Nong district totally 5 regions, as in figure 2 it is shown, the volume in highly concentrated district and Di Nong district is expressed asV hWithV l. At simulation initial time, being positioned over of the quantity such as component 1 and component 2 is simulated in box, in simulation process, performs following steps:
1) every t1Interval, randomly selects the molecule of a component 2 in high concentration region, randomly selects the molecule of a component 1 in low concentration region, exchanges two molecular position, and keeps respective speed constant;
2) reach after stable state until system, a stable Concentraton gradient will be formed along dispersal direction. Component 1 will be spread to Di Nong district by highly concentrated district. StatisticstIn time, component 1 is at the mean molecule number in highly concentrated district Yu Di Nong districtN h WithN l , then component 1 can be calculated by following two formulas with the concentration in Di Nong district in highly concentrated district:
;
3) in the statistics t time, the exchange times N of component 1 and component 2 molecular positionc, then in the t time, the component 1 clean molecule amount by a certain cross section EN=N c / 2;
4) the coefficient of molecular diffusion D of component 1 is calculated by below equation,
In formula,NFor by the clean molecule amount of cross section E;LFor the distance between high concentration end and low concentration end;N AFor Avogadro's number;ACross-sectional area for cross section E;tFor timing statistics;c h Withc l Represent the component 1 molar concentration in high concentration region Yu low concentration region respectively.
What finally illustrate is, above example is only in order to illustrate technical scheme and unrestricted, although the present invention being described in detail with reference to preferred embodiment, it will be understood by those within the art that, technical scheme can be modified or equivalent replacement, without deviating from objective and the scope of technical solution of the present invention, it all should be encompassed in the middle of scope of the presently claimed invention.
Claims (2)
1. the method that a non-equlibrium molecular dynamics simulation calculates coefficient of molecular diffusion, it is characterised in that: comprise the following steps:
Step 1, calculates the molar concentration comprising component 1 and component 1 in the mixture of 2 two kinds of components of component at high concentration end Yu low concentration endc h Withc l ;
Step 2, calculates component 1 in the timetThe interior clean molecule amount by a certain cross section EN;
Step 3, calculates the diffusion coefficient of component 1 by below equationD,
In formula,NFor by the clean molecule amount of cross section E;LFor the distance between high concentration end and low concentration end;N AFor Avogadro's number;ACross-sectional area for cross section E;tFor timing statistics;c h Withc l Represent the component 1 molar concentration in high concentration region Yu low concentration region respectively.
2. the method that a kind of non-equlibrium molecular dynamics simulation according to claim 1 calculates coefficient of molecular diffusion, it is characterised in that: specifically comprising the following steps that of described step 1
The volume that system is in turn divided into Di Nong district, diffusion region, highly concentrated district, diffusion region, Di Nong district totally 5 regions, highly concentrated district and Di Nong district along dispersal direction is expressed asV hWithV l,
Described cross section E is positioned at diffusion region, at simulation initial time, simulates in box by being positioned over of the quantity such as component 1 and component 2;
Simulation process is implemented to comprise the following steps:
1) every t1Interval, randomly selects the molecule of a component 2 in high concentration region, randomly selects the molecule of a component 1 in low concentration region, exchanges two molecular position, and each self-sustaining speed is constant;
2) reaching after stable state until system, in statistics t interval, component 1 is at the mean molecule number in highly concentrated district Yu Di Nong districtN h WithN l , then component 1 can be calculated by following two formulas with the concentration in Di Nong district in highly concentrated district:
Specifically comprising the following steps that of described step 2
After system reaches stable state, in statistics t interval, the times N that component 1 exchanges with component 2 molecular positionc, then in time t, by the clean molecule amount of a certain cross section EN=Nc/2��
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Cited By (2)
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| CN105760598A (en) * | 2016-02-15 | 2016-07-13 | 哈尔滨理工大学 | Nanometer material plasticity modulus calculating method based on molecular dynamics simulation |
| CN108491569A (en) * | 2018-02-07 | 2018-09-04 | 北京工业大学 | A method of nano-multilayer film self-propagating reaction process diffusion coefficient is predicted according to molecular dynamics simulation |
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| CN103150477A (en) * | 2013-03-14 | 2013-06-12 | 复旦大学 | Monte carlo simulation method for forecasting free radical polymerization in microtube reactor |
| CN103926173A (en) * | 2014-04-25 | 2014-07-16 | 西北核技术研究所 | Device and method for measuring molecular diffusion coefficient in gas medium |
| CN104237079A (en) * | 2014-10-10 | 2014-12-24 | 中国石油大学 | Experimental method and device for measuring diffusion coefficient of carbon dioxide in water |
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| CN103150477A (en) * | 2013-03-14 | 2013-06-12 | 复旦大学 | Monte carlo simulation method for forecasting free radical polymerization in microtube reactor |
| CN103926173A (en) * | 2014-04-25 | 2014-07-16 | 西北核技术研究所 | Device and method for measuring molecular diffusion coefficient in gas medium |
| CN104237079A (en) * | 2014-10-10 | 2014-12-24 | 中国石油大学 | Experimental method and device for measuring diffusion coefficient of carbon dioxide in water |
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| HIDENORI HIGASHI ETAL.: "Calculation of diffusion coefficients for carbon dioxide + solute system near the critical conditions by non-equilibrium molecular dynamics simulation", 《FLUID PHASE EQUILIBRIA》 * |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN105760598A (en) * | 2016-02-15 | 2016-07-13 | 哈尔滨理工大学 | Nanometer material plasticity modulus calculating method based on molecular dynamics simulation |
| CN108491569A (en) * | 2018-02-07 | 2018-09-04 | 北京工业大学 | A method of nano-multilayer film self-propagating reaction process diffusion coefficient is predicted according to molecular dynamics simulation |
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