CN102509009A - Simulation method based on random walking in limited space - Google Patents
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Abstract
The invention discloses a simulation method based on random walking in a limited space. The simulation method is used for simulating chemical separation and analysis problems of chromatograph, electrophoresis, capillary electrophoresis, micro flow control and the like and comprises the steps that: a periodic limited space is built, particles to be separated do random movement in a free space in the periodic unit, the adsorption phenomenon is generated when particles to be separated are collided with barriers, the stay time of the particles on the barrier wall is determined according to the adsorption energy dimension, the movement of multiple particles in the limited space is simulated in a serial or parallel mode, one directed movement is overlapped during the random movement of the separation particles, the direction of the movement is the same as the flow rate direction of the separation particles, and the speed the movement is relevant to the driving force received by the particles to be separated; and the movement of multiple particles in the limited space is simulated by the serial or parallel mode. The method has the advantages that the redundant process detail in the dynamic simulation is omited, so the calculation is greatly simplified, the operation speed is high, the efficiency is high, and greater step numbers or longer time can be simulated in the unit time.
Description
Technical field
The invention belongs to analytical chemistry, chemistry, Computer Simulation and computational science field, be specifically related to a kind of emulation mode based on random walk in the restricted clearance.
Background technology
Compartment analysis is that the compounding substances with several kinds of components is separated from each other, and from separating behavior, reaches the technology to each component testing goal, all has important use in each side such as petrochemical complex, organic synthesis, Physiology and biochemistry, medical and health, Food Sciences.Method for separating and analyzing comprises chromatogram, electrophoresis, Capillary Electrophoresis, microflow control technique and micro-total analysis system etc.
Because compartment analysis has important use and is worth, above-mentioned various analytical approachs are just founded from being born and have been developed various research theories.With the chromatogram is example; Before surplus this method for separating and analyzing is born in 100 year; And the peak type prediction theory that constantly developed the separation theorem that is the basis with chromatographic process thermodynamics and be the basis of application stage afterwards with the diffusion process (Lu Peizhang wears the affairs of state, and Zhang Xiangmin compiles.Chromatographic theory basis (second edition).Beijing: Science Press).These can set forth the generation and the shape of signal peak in the chromatography separating method well based on the thermodynamics of macroscopic view and the theory of kinetics of diffusion; But these theories belong to macroscopic theory; Do not consider the influence of the shape, size, packed density, surface physicochemical property of discrete device inner stuffing, and these microscopic properties there is fundamental influence to separating effect to compartment analysis.
Set forth the development that various detachment processes are subject to computational science and technology from microcosmic.The molecular dynamics method once was considered and was applied to the description of detachment process; But there is the problem that computing time is long, can't consider solvation in it; This method shortcoming such as can't correctly describe to restricted clearance internal barrier and tube wall to the interaction of particle simultaneously, thereby has limited its application in daily compartment analysis is described.
The proposition of random walk notion is (Pearson, K. for some time; Nature, 1905,72,294), on the books for being applied in some documents of random walk model itself, like (Niehaus, A. M. S. such as Niehaus; Vlachos, D. G.; Edwards, J. S.; Plechac, P.; Tribe; R. Biophysical Journal 2008; 5,1551-1564) adopt following random walk model that particle movement is simulated: particle time interval of each unit equiprobably up and down, one of left and right four direction moves a unit; Hinder the potential barrier of particle movement and simulate with the border of ad-hoc location, when particle movement was wanted crossing the boundary to unit in border in view of the above and next step, certain Probability p was crossed over potential barrier, and probability (1-p) is mobile by potential barrier bounce-back and opposite direction.(Zachary D. Pozuna, Graeme Henkelma such as Zachary in addition; Journal of Membrane Science 2010,364 9-16) also adopts similar model that the infiltration and the diffusion of gas in the film are studied.Before this; Software engineering researchers invent has been arranged based on simple program (STP Random Walk 2D Program) (Harvey Gould, Jan Tobochnik, the Wolfgang Christan of above-mentioned model; And Anne Cox; STP Random Walk 2D Program, http://www.compadre.org/stp/items/detail.cfm ID=8163), but the problem that above program and model exist is mainly:
(1) direction of motion of particle has only four in the above model, can't be on 360 ° of directions completely random, this does not meet the real motion track of particle;
(2) particle can only move a motor unit at every turn in the above model, and this just means that also the particle's velocity size is certain and the residing position of particle is that coarse usefulness " lattice " is described, and can not describe Brownian movement or thermal motion;
(3) potential barrier in the above model is to use the part on the border of " lattice " to simulate, and its form is single, can not change arbitrary shape and position;
(4) effect of particle and potential barrier is pure probability problem in the above model, can not describe to interact and absorption.
So the previous random walk model that proposes can't be applied in the simulation of compartment analysis system.
Summary of the invention
Goal of the invention: to the deficiency that exists in the prior art; The purpose of this invention is to provide a kind of emulation mode based on random walk in the restricted clearance; This method has been omitted the process details of redundancy in the dynamics simulation, and calculating is greatly simplified, and travelling speed is fast; Efficient is high, can in the unit interval, simulate more step number or longer time.
Technical scheme: in order to realize the foregoing invention purpose, the technical scheme that the present invention adopts is:
A kind of emulation mode based on random walk in the restricted clearance is used for analog chromatogram, electrophoresis, Capillary Electrophoresis, Chemical Decomposition and problem analysis such as micro-fluidic, may further comprise the steps:
(1) the Chemical Decomposition device is reduced to the unit with periodic structure, comprises in the unit and treat that separating particles can free-movingly have the space on border, also comprises or do not comprise the potential barrier that particle can not get into; Wherein, the length of side of structural unit and origin position indefinite scope can be provided with as required voluntarily;
(2) treat random motion in the free space of separating particles in periodic unit, its movement velocity has distribution characteristics; Wherein, velocity magnitude indefinite scope can be provided with as required voluntarily;
Produce adsorption phenomena when (3) treating the collision of separating particles and potential barrier, by the Frenkel expression formula
T=t
0Exp (Q/RT) can confirm to treat the residence time of separating particles on the potential barrier wall, and wherein Q is an energy of adsorption, and R is a gas law constant, t
0Be the time of vibration of vertical surface, t is the residence time; Mostly this absorption is physisorption, and its energy size is generally 0 ~ 40KJ/mol;
(4) treat in random motion, the superpose motion of an orientation of separating particles, its direction is consistent with the flow velocity direction of separating particles, its speed with treat that the suffered driving force of separating particles is relevant; For example, in gas chromatography, treat that the direction of the directed movement that separating particles superposes is identical with the flow rate of carrier gas direction, size is flow rate of carrier gas;
(5) mode that adopts serial or parallel to a plurality of particles the motion in restricted clearance simulate, the statistical distribution of the move distance of these particles in preset time is the CONCENTRATION DISTRIBUTION in the discrete device; Particle is covered the signal to the required time statistical distribution simulation separation detection of set a distance.
In the step (1), the Chemical Decomposition device comprises chromatogram, electrophoresis and micro-fluidic, i.e. the micro-fluidic chip technology.
In the step (1), the unit of periodic structure possesses the restricted clearance of the general architectural feature of various discrete devices.
In the step (2), utilize the random walk motion to describe the random motion of particle.
In the step (3), utilize the residence time, stop promptly that step number characterizes particle and potential barrier is the interaction between the filling material in the discrete device.
In the step (4), utilize the directional movement speed simulation to treat the suffered driving force of separating particles, for example pressure, electric field force etc.
In the step (5), utilize the CONCENTRATION DISTRIBUTION of a plurality of particles in the range distribution simulation discrete device of preset time; Utilize a plurality of particles to pass through detection to the time distribution simulation separation signal of set a distance.
In Chemical Decomposition and analytic process, optimized Separation operating conditions, evaluation separating effect, improving discrete device is complicacy and difficult task.The generally employing experience of optimization of separation operation condition in the past adds the way of trial, has wasted a lot of samples and time.Traditional separation simulation method is not considered the characterization of molecules of the details and the material to be separated matter of filling material in the discrete device based on macroscopical diffusion theory, and being difficult to provides valuable reference to the optimization of separation operation condition and discrete device.The random walk method that the present invention will have the microcosmic characteristics is applied in the simulation of compartment analysis process, has promoted to the optimization of separation condition with to the improvement of discrete device.
Among the present invention that discrete device is abstract in having periodic structural unit, the length of its directions X simulation discrete device, the width of Y direction simulation discrete device.Contain in the periodic structure and remain free-moving space of separating particles and the inaccessiable potential barrier of particle, be used to simulate the filling material of discrete device.This processing can the various discrete devices of true reappearance micromechanism, and adopted random walk method in the simulation of particle spread apart with microscopic feature.This scheme has not only been taken the general features of particle movement and the various micromechanisms in the discrete device into account; Therefore omitted a large amount of redundant information in the particle movement process simultaneously, can realize economical to the detachment process of the multicomponent system that contains a large amount of particles and microcosmic Simulation fast.In demonstration to analog result, can be dynamically, the CONCENTRATION DISTRIBUTION in the display separation device in real time, also can distribute the detection signal of analog chromatogram through the time of flowing out to particle under the set a distance.
Beneficial effect: compare with method of the prior art; Emulation mode method based on random walk in the restricted clearance of the present invention has following outstanding advantage: the emulation mode based on random walk in the restricted clearance of the present invention; This method has been omitted the process details of redundancy in the dynamics simulation, and calculating is greatly simplified, and travelling speed is fast; Efficient is high, can in the unit interval, simulate more step number or longer time.Simulation than macroscopic theory; This method can be simulated particle movement in the detachment process, collision and filling material character micro details such as (shape, size, packed density, surface physicochemical properties); The simulation that makes compartment analysis also can be played predicting function to the separation of unknown material simultaneously more accurately and reliably.Because the scale of simulation is enough big, the time long enough, can contrast with general macroscopic measurement signal, also can do contrast with the simulation based on macroscopic theory.In a word, the random walk emulation mode has found the equilibrium point between calculated amount and the counting system in the restricted clearance of the present invention, has promoted the compartment analysis the reach of science, quickens the speed of compartment analysis condition optimizing.
Description of drawings
The packed column chromatogram of Fig. 1 normal hexane and normal heptane;
The capillary column chromatography figure of Fig. 2 normal hexane and normal heptane;
Fig. 3 utilizes the inventive method to simulate single particle carries out random walk in the cycle space that positive ten hexagon potential barriers constitute trajectory diagram, and this structure can be simulated the detachment process in the packing chromatography;
Fig. 4 utilizes the inventive method to simulate single particle carries out random walk in the space of no potential barrier trajectory diagram, and this structure can be simulated Capillary Electrophoresis, not have to fill and analyze chromatogram etc.;
Fig. 5 utilizes the inventive method to simulate the concentration profile in the discrete device in Fig. 3 structure;
Fig. 6 utilizes the inventive method to simulate the concentration profile in the discrete device in Fig. 4 structure;
Fig. 7 utilizes the inventive method to simulate the detection signal of Fig. 3 structure discrete device;
Fig. 8 utilizes the inventive method to simulate the detection signal of Fig. 4 structure discrete device.
Embodiment
Below in conjunction with specific embodiment the present invention is done further explanation.
Embodiment 1 packed column chromatogram is carried out the separation simulation of normal hexane and normal heptane
The sample that preparation contains 1g normal hexane and 2g normal heptane uses nitrogen to be carrier gas, and FID is a detecting device.Flow rate of carrier gas is 10mL/min; Air velocity is 300mL/min; Hydrogen flow rate is 30mL/min; Column temperature is 60 ℃; Detector temperature is 160 ℃; Temperature of vaporization chamber is 160 ℃; Adopt area normalization method to calculate each component concentration.Detection signal is as shown in Figure 1.
Normal hexane and normal heptane (following represent with A, B respectively), population is made as 50 and 100 respectively, in the space that positive ten hexagon potential barriers are filled, carries out the random walk simulation of these 150 particles.Temperature is made as 333K, and the simulation number of times is respectively 50 and 100, and the length of side of periodic structure unit is 5mm.The center of each periodic structure unit (2,2) is made as true origin, the coordinate that particle begins random walk is set simultaneously is (0,0).If the Delta distribution characteristics is followed in the thermal motion of band separating particles, promptly all speed constantly are definite value.Its velocity amplitude is made as 3200mm/s and 3000mm/s respectively.The velocity magnitude that is caused by driving force is 111210mm/s, and direction is identical with the X axle, and per time in step is made as 0.001 s.Energy of adsorption between particle and the potential barrier (filling material) is respectively 29.5kJ/mol and 33.8kJ/mol.The track of particle random walk is as shown in Figure 3.In order to simulate the CONCENTRATION DISTRIBUTION of two kinds of particles of A and B in separating pipe, be made as 600s preset time.The CONCENTRATION DISTRIBUTION of two kinds of ions to be separated is as shown in Figure 5.In order to simulate the separation detection signal, setting separating pipe length is 150mm, and the simulation of its detection signal is as shown in Figure 7.
With comparing between retention time value of simulating and the actual measured value, concrete outcome is as shown in table 1.
The comparison of table 1 simulation retention time and actual value
| Component | Simulation t R/min | Actual t R/min | ⊿t R/min | Error/% |
| Normal hexane | 5.397 | 5.037 | 0.360 | 7.2 |
| Normal heptane | 5.893 | 5.654 | 0.239 | 4.2 |
From the result; Retention time value and the error between the actual measured value of simulation be less than 8%, analog result comparatively accurately and reliably, hence one can see that; This analogy method can effectively reduce the workload of optimized Separation condition, also can play predicting function to the separation of unknown material simultaneously.
The sample that preparation contains 1g normal hexane and 2g normal heptane uses nitrogen to be carrier gas, and FID is a detecting device.Flow rate of carrier gas is 10ml/min; Air velocity is 300ml/min; Hydrogen flow rate is 30ml/min; Column temperature is 60 ℃; Detector temperature is 160 ℃; Temperature of vaporization chamber is 160 ℃; Adopt area normalization method to calculate each component concentration.Detection signal is as shown in Figure 2.
Normal hexane and normal heptane (following represent with A, B respectively), it is 50 and 100 that population is made as respectively, in the space of no potential barrier, carries out the random walk simulation of these 150 particles.Temperature is made as 333K, and the simulation number of times is respectively 50 and 100, and pipe diameter is 0.25mm.The length of side a of periodic structure unit is 3200mm, and b is 319.75mm.The initial cell centre coordinate is that (1600,100) are made as true origin, the coordinate that particle begins random walk is set simultaneously is (2,0).If molecular thermalmotion has the Delta distribution characteristics, the Delta distribution characteristics is followed in the thermal motion of band separating particles, and promptly all speed constantly are definite value.Its velocity amplitude is made as 3200mm/s and 3000mm/s respectively, and the velocity magnitude that is caused by driving force is 346520mm/s, and direction is identical with the X axle, and per time in step is made as 0.001 s.Energy of adsorption between two kinds of material to be separated matter of A and B and the tube wall is respectively 29.5 kJ/mol and 33.8 kJ/mol.The track of particle random walk is as shown in Figure 4.In order to simulate the CONCENTRATION DISTRIBUTION of two kinds of particles of A and B in separating pipe, be made as 350 s preset time.The CONCENTRATION DISTRIBUTION of two kinds of ions to be separated is as shown in Figure 6.In order to simulate the separation detection signal, setting separating pipe length is 30m, and the simulation of its detection signal is as shown in Figure 8.
With comparing between retention time value of simulating and the actual measured value, see table 2.
The comparison of table 2 simulation retention time and actual value
| Component | Simulation t R/min | Actual t R/min | ⊿t R/min | Error/% |
| Normal hexane | 2.391 | 2.225 | 0.166 | 7.5 |
| Normal heptane | 2.876 | 2.737 | 0.139 | 5.1 |
From the retention time value of result's simulation and the error between the actual measured value less than 8%; Analog result comparatively accurately and reliably; Hence one can see that, and this analogy method can effectively reduce the workload of optimized Separation condition, also can play predicting function to the separation of unknown material simultaneously.
Claims (5)
1. emulation mode based on random walk in the restricted clearance is used for analog chromatogram, electrophoresis, Capillary Electrophoresis, Chemical Decomposition and problem analysis such as micro-fluidic, it is characterized in that, may further comprise the steps:
(1) the Chemical Decomposition device is reduced to the unit with periodic structure, comprises in the unit and treat that separating particles can free-movingly have the space on border, also comprises or do not comprise the potential barrier that particle can not get into;
(2) treat random motion in the free space of separating particles in periodic unit, its movement velocity has distribution characteristics;
Produce adsorption phenomena when (3) treating the collision of separating particles and potential barrier, by the Frenkel expression formula
T=t
0Exp (Q/RT) confirms to treat the residence time of separating particles on the potential barrier wall, and wherein, Q is an energy of adsorption, and R is a gas law constant, t
0Be the time of vibration of vertical surface, t is the residence time;
(4) treat in random motion, the superpose motion of an orientation of separating particles, its direction is consistent with the flow velocity direction of separating particles, its speed with treat that the suffered driving force of separating particles is relevant;
(5) mode that adopts serial or parallel to a plurality of particles the motion in restricted clearance simulate, the statistical distribution of the move distance of these particles in preset time is the CONCENTRATION DISTRIBUTION in the discrete device; Particle is covered the signal to the required time statistical distribution simulation separation detection of set a distance.
2. the emulation mode based on random walk in the restricted clearance according to claim 1 is characterized in that: in the step (1), the Chemical Decomposition device comprises chromatogram, electrophoresis and micro-fluidic.
3. the emulation mode based on random walk in the restricted clearance according to claim 1 is characterized in that: in the step (2), distribution characteristics is that Delta distributes, Gaussian distributes, Maxwell-Boltzmann distributes and/or Cauchy-Lorentz distributes.
4. the emulation mode based on random walk in the restricted clearance according to claim 1 is characterized in that: in the step (3), utilize the residence time, stop promptly that step number characterizes particle and potential barrier is the interaction between the filling material in the discrete device.
5. the emulation mode based on random walk in the restricted clearance according to claim 1 is characterized in that: in the step (4), said driving force is pressure or electric field force.
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Cited By (4)
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| CN106599596A (en) * | 2016-12-22 | 2017-04-26 | 嘉兴学院 | Method for simulating chemical catalytic reaction process optimization by combining with random walk and statistical distribution |
| CN108875284A (en) * | 2018-08-13 | 2018-11-23 | 辽宁大学 | A kind of gas-chromatography separation emulation mode based on STOCHASTIC DIFFUSION theory |
| CN111483976A (en) * | 2020-04-26 | 2020-08-04 | 南通大学 | Preparation method of novel patterned nanostructure based on special-shaped double-cylinder array |
| CN111498798A (en) * | 2020-04-26 | 2020-08-07 | 南通大学 | Preparation method of ordered microstructure based on array-limited self-assembly |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106599596A (en) * | 2016-12-22 | 2017-04-26 | 嘉兴学院 | Method for simulating chemical catalytic reaction process optimization by combining with random walk and statistical distribution |
| CN108875284A (en) * | 2018-08-13 | 2018-11-23 | 辽宁大学 | A kind of gas-chromatography separation emulation mode based on STOCHASTIC DIFFUSION theory |
| CN108875284B (en) * | 2018-08-13 | 2022-07-19 | 辽宁大学 | Gas chromatography separation simulation method based on random diffusion theory |
| CN111483976A (en) * | 2020-04-26 | 2020-08-04 | 南通大学 | Preparation method of novel patterned nanostructure based on special-shaped double-cylinder array |
| CN111498798A (en) * | 2020-04-26 | 2020-08-07 | 南通大学 | Preparation method of ordered microstructure based on array-limited self-assembly |
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