CN111028892A - Method for determining nano-droplet wettability based on molecular dynamics - Google Patents
Method for determining nano-droplet wettability based on molecular dynamics Download PDFInfo
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Abstract
The invention discloses a method for determining the wettability of a nano liquid drop based on molecular dynamics, which comprises the following steps of generating a graph of substrate curvature and static contact angle of the liquid drop, wherein the graph comprises the following steps: acquiring each substrate curvature and a corresponding liquid drop static contact angle, wherein the liquid drop static contact angle corresponding to each substrate curvature is acquired, and a curve graph is drawn based on each substrate curvature and the corresponding liquid drop static contact angle; the static contact angle of the drop corresponding to the current substrate curvature is determined in the generated graph. The method realizes the prediction of the static contact angle of the liquid drop corresponding to the curvature of the current substrate according to the wetting process of the nano liquid drop on the solid substrate.
Description
Technical Field
The invention relates to the field of molecular dynamics, in particular to a method for determining the wettability of a nano liquid drop based on molecular dynamics.
Background
The research on the wettability of the nano liquid drop on the micro-nano surface is an important research direction in the field of surface and interface mechanics, such as the self-transportation of the liquid drop under the curvature gradient, the super-wettability of the surface liquid enhanced by the surface roughness, the directional jumping behavior of the liquid and the like. In the past, the shape design of a flat material substrate is mainly aimed at realizing wetting conversion, and the influence of the substrate curvature on the wetting performance is ignored, so that the wetting behavior of nano droplets cannot be well understood, and even if the influence is not ignored, the influence of the substrate curvature cannot be clarified due to the small size of the nano droplets.
For the wetting process of the nano liquid drop on the solid substrate, experimental equipment observation is not a good choice, because the time and space of the observation process are limited, and the time from the impact of the nano liquid drop to the relaxation is about 1ns, so that the dynamic process of the nano liquid drop cannot be displayed by an instrument.
Disclosure of Invention
The invention aims to provide a method for determining the wettability of a nano liquid drop based on molecular dynamics, which realizes the prediction of a liquid drop static contact angle corresponding to the current substrate curvature according to the wetting process of the nano liquid drop on a solid substrate.
In order to achieve the above object, the present invention provides a method for determining wetting property of nano liquid drop based on molecular dynamics, generating a graph of substrate curvature and static contact angle of liquid drop, comprising: acquiring each substrate curvature and the corresponding static contact angle of the liquid drop, wherein the acquiring of the static contact angle of the liquid drop corresponding to each substrate curvature comprises the following steps: for each base, performing: acquiring position information and density information of the nano liquid drop on the current substrate in relaxation preset time based on a preset trained numerical model; determining a first curve of the nano liquid drop on a liquid-gas interface and a first data point corresponding to the first curve, and a second curve of the nano liquid drop on the solid-liquid interface and a second data point corresponding to the second curve according to the position information and the density information; respectively fitting the first curve and the second curve by using a preset numerical order polynomial to obtain a first fitting curve corresponding to the first curve and a second fitting curve corresponding to the second curve, determining a coefficient of the first fitting curve based on a least square method and a first data point, and determining a coefficient of the second fitting curve based on the least square method and a second data point; acquiring an intersection point of the first fitted curve and the second fitted curve and an angle difference between a tangent of the first fitted curve and a tangent of the second fitted curve at the intersection point as a static contact angle of the liquid drop corresponding to the current substrate; plotting a curve based on the curvature of each substrate and its corresponding static contact angle of the droplet; the static contact angle of the drop corresponding to the current substrate curvature is determined in the generated graph.
Preferably, the acquiring the position information and the density information of the nano-droplets on the current substrate for the relaxation preset time based on the preset trained numerical model comprises: determining the molecular number and the interatomic first potential function of the nano liquid drop according to the density, the viscosity and the surface tension of the nano liquid drop; acquiring a second potential function between atoms of the current substrate; determining a third potential function between atoms of the current substrate and atoms of the nano liquid drop according to the first potential function and the second potential function, and acquiring the curvature of the current substrate; initializing a nano-droplet velocity, a nano-droplet temperature, and a nano-droplet first location, and a second location of the substrate; maintaining the number of particles, the volume and the temperature of the nano-droplets in the wetting process unchanged to meet the NVT ensemble; updating the position and the speed of atoms of the nano liquid drops by utilizing a Velocity-Verlet algorithm and a Langevin hot bath method, and keeping the temperature of the NVT ensemble oscillating within a preset range; controlling the nano liquid drop to relax on the current substrate for a preset time; slicing the nano-droplets in layers, including at equal intervals
Respectively cutting a preset X axis and a Y axis perpendicular to the X axis to obtain a plurality of concentric hollow thin columns, wherein the Y axis is configured as a symmetry axis of the nano-droplets, and counting the volume and the number of atoms of each hollow thin column to determine density information of each hollow thin column; and outputting updated position and density information of atoms of the nano-droplets.
Preferably, the determining the first fitted curve coefficient based on the least square method and the first data point or the determining the second fitted curve coefficient based on the least square method and the second data pointThe second fitted curve coefficients include: for a given n +1 data points (x)i,yi) Assume that the m-th order fitting polynomial L (x) is taken such that the sum of squares I (a)0,a1,...,am) At a minimum, wherein a0,a1,...,amIs the unknown number of the coefficient to be solved; determining a first fitted curve coefficient or a second fitted curve coefficient by the following formula;
according to the technical scheme, the static contact angles of the liquid drops on the substrates with different curvatures are measured by using a data analysis means, so that the contact angles of the nano liquid drops can be more accurately judged, and a reliable numerical prediction and technical means are provided for nano wetting.
Additional features and advantages of the invention will be set forth in the detailed description which follows.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
FIG. 1 is a flow chart of a molecular dynamics simulation;
FIG. 2a is an initial modeling of the impact of nano-water droplets on a curved copper wall;
FIG. 2b is a schematic illustration of static contact angle measurement;
FIG. 3 is the evolution process of the nano-water droplet with impact velocity of 300m/s on the curved copper wall surface;
FIG. 4 is a schematic view of a layered slice of a droplet (denoted by the letter a) and a hollow thin column (denoted by the letter b);
FIG. 5a is a contact angle of a single drop on a curved copper wall;
FIG. 5b contact angle measurement on a curved copper wall;
fig. 6 is a number density distribution of droplets at different curvatures: k ═ 1.333 (denoted by the letter a); k ═ 1 (denoted by letter b); k ═ 0.5 (denoted by the letter c); k ═ 0.375 (denoted by the letter d) and K ═ 0.3 (denoted by the letter e);
FIG. 7a is the contact angle of a single drop on a flat copper wall;
FIG. 7b is a contact angle measurement on a flat copper wall;
FIG. 8 is a graph of substrate curvature K versus static contact angle θ of a droplet; and
FIG. 9 is a flow chart of a method for determining the wettability of a nanodroplet based on molecular dynamics according to the present invention.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating the invention, are intended for purposes of illustration and explanation only and are not intended to limit the scope of the invention.
FIG. 9 is a flow chart of a method of determining the wettability of a nanodroplet based on molecular dynamics, the method comprising: a, generating a graph of substrate curvature and static contact angle of a liquid drop, wherein the graph comprises the following steps: obtaining each substrate curvature and the corresponding static contact angle of the liquid drop, wherein the obtaining of the corresponding static contact angle of the liquid drop of each substrate curvature comprises: for each base, performing: acquiring position information and density information of nano liquid drops on a current substrate in relaxation preset time based on a preset trained numerical model; determining a first curve of the nano liquid drop on a liquid-gas interface and a first data point corresponding to the first curve, and a second curve of the nano liquid drop on the solid-liquid interface and a second data point corresponding to the second curve according to the position information and the density information; respectively fitting the first curve and the second curve by utilizing a preset numerical order polynomial to obtain a first fitting curve corresponding to the first curve and a second fitting curve corresponding to the second curve, determining a coefficient of the first fitting curve based on a least square method and a first data point, and determining a coefficient of the second fitting curve based on the least square method and a second data point; acquiring an intersection point of the first fitted curve and the second fitted curve and an angle difference between a tangent of the first fitted curve and a tangent of the second fitted curve at the intersection point as a static contact angle of the liquid drop corresponding to the current substrate; plotting a graph based on the curvature of each base and its corresponding static contact angle of the droplet; and B, determining the static contact angle of the liquid drop corresponding to the current substrate curvature in the generated graph.
Preferably, the acquiring the position information and the density information of the nano-droplets on the current substrate for the relaxation preset time based on the preset trained numerical model comprises: determining the molecular number and the interatomic first potential function of the nano liquid drop according to the density, the viscosity and the surface tension of the nano liquid drop; acquiring a second potential function between atoms of the current substrate; determining a third potential function between atoms of the current substrate and atoms of the nano liquid drop according to the first potential function and the second potential function, and acquiring the curvature of the current substrate; initializing a nano-droplet velocity, a nano-droplet temperature, and a nano-droplet first location, and a second location of the substrate; maintaining the number of particles, the volume and the temperature of the nano-droplets in the wetting process unchanged to meet the NVT ensemble; updating the position and the speed of atoms of the nano liquid drops by utilizing a Velocity-Verlet algorithm and a Langevin hot bath method, and keeping the temperature of the NVT ensemble oscillating within a preset range; controlling the nano liquid drop to relax on the current substrate for a preset time; slicing the nano-droplets in layers, including at equal intervals
Respectively cutting a preset X axis and a Y axis perpendicular to the X axis to obtain a plurality of concentric hollow thin columns, wherein the Y axis is configured as a symmetry axis of the nano-droplets, and counting the volume and the number of atoms of each hollow thin column to determine density information of each hollow thin column; and outputting updated position and density information of atoms of the nano-droplets.
Preferably, the determining the first fitted curve coefficient based on the least square method and the first data point or the determining the second fitted curve coefficient based on the least square method and the second data point comprises: for a given n +1 data points (x)i,yi) Assume that the m-th order fitting polynomial L (x) is taken such that the sum of squares I (a)0,a1,...,am) At a minimum, wherein a0,a1,...,amFor coefficients to be foundKnowing; determining a first fitted curve coefficient or a second fitted curve coefficient by the following formula;
the invention is further described below with reference to the accompanying drawings.
FIG. 1 is a flow chart of a molecular dynamics simulation. Fig. 2 is a schematic diagram of initial modeling (denoted by letter a) and static contact angle measurement (denoted by letter b) of the impact of a nano-water droplet on a curved copper wall. FIG. 3 is the evolution process of the nano water drop with impact velocity of 300m/s on the curved copper wall surface. The detection method of the static contact angle measurement mentioned in fig. 2 comprises the following steps:
And 2, determining two curves of a liquid-gas interface and a solid-liquid interface of the liquid drop according to the position and number density information output in the step 1 to obtain corresponding data points. The two curves are fitted with a sixth order polynomial, respectively, and coefficients of the sixth order polynomial are determined by a least square method. What is important is that the intersection of the two fitted curves is considered to be the point of three-phase contact. Then, calculating the included angle between the two fitting curves and the horizontal axis at the point, and calculating the difference between the included angle of the liquid-gas fitting curve and the included angle of the solid-gas interface, namely the static contact angle of the liquid drop;
and 3, selecting the substrates with different curvatures according to the step 1 and the step 2, drawing a graph of the substrate curvature and the static contact angle of the liquid drop, and judging the influence of the substrate curvature on the wettability of the liquid drop.
The numerical calculation method adopted in the step 1 and the output of the position and density information comprise the following steps:
step 101: determining molecular number and interatomic Lennard-Jones potential function parameter values of the liquid drop according to the density, viscosity and surface tension of the liquid drop;
step 102: looking up related data and determining potential functions among substrate atoms;
step 103: looking up the relevant data, determining the parameter value of the Lennard-Jones potential function between the substrate atoms and the atoms in the liquid drop, and giving the curvature of the substrate;
step 104: initializing the velocity, temperature and position of the droplet, and the position of the substrate;
step 105: the number of particles, volume and temperature of the droplets during wetting are maintained constant, i.e., the NVT ensemble is satisfied. Updating the position and the speed of atoms by utilizing a Velocity-Verlet algorithm and a Langevin hot bath method, and keeping the ensemble temperature oscillating within a small range;
step 106: allowing the droplet to relax on the substrate for more than 100 ps;
step 107: slicing the liquid drop in layers, i.e. with equal distance between the symmetrical axis of the liquid drop as Y axis and the certain direction perpendicular to the axis as X axis
And cutting the X axis and the Y axis respectively, so that the liquid drop is divided into concentric hollow thin columns, the inner diameter and the outer diameter of each hollow thin column are larger along with the increase of the X equal distance, and the slicing of the bottommost layer is repeated along with the increase of the Y equal distance. Then, counting the volume and the number of the atoms of each hollow thin column to obtain the number density of the hollow thin column;
FIG. 4 is a schematic diagram of a layered slice of a droplet (indicated by the letter a) and a hollow thin column (indicated by the letter b);
step 108: and selecting proper time to output the position and the number density information of the droplet atoms.
In step 2, the two curves are respectively fitted by utilizing a sixth-order polynomial, and the coefficients of the sixth-order polynomial are determined by a least square method, which specifically comprises the following steps:
step 201: for a given n +1 data points (x)i,yi) Assume that a fitting polynomial L (x) of order m (usually 6) is taken such that the sum of squares I (a)0,a1,...,am) At minimum, wherein L (x) and I (a)0,a1,...,am) Specific table ofThe following are achieved:
wherein a is0,a1,...,amIs the unknown number of coefficients to be solved.
Step 202: to square the sum I (a)0,a1,...,am) At minimum, the extremum problem is solved according to the multivariate function, and then the problem is expressed as the following expression:
further comprising:
expressed in a matrix as follows:
the abbreviated matrix is Aa ═ B, wherein A is an m × n-order matrix, and a and B are n-dimensional column vectors;
step 203: as long as data points (x) are giveni,yi) And the highest order m (namely 6) of the fitting polynomial, and corresponding fitting polynomial coefficient vectors can be obtained by processing data.
A processing method for acquiring influence of substrate curvature on nano-droplet wettability based on molecular dynamics obtains the number density distribution of droplets under different curvatures:
FIG. 5 is a graph of contact angle of a single drop on a curved copper wall (denoted by letter a) and contact angle measurement on a curved copper wall (denoted by letter b);
fig. 6 is a number density distribution of droplets at different curvatures: k ═ 1.333 (denoted by the letter a), K ═ 1 (denoted by the letter b), K ═ 0.5 (denoted by the letter c), K ═ 0.375 (denoted by the letter d), and K ═ 0.3 (denoted by the letter e), where K is defined as the quotient of the curvature of the substrate and the curvature of the droplet, and characterizes a dimensionless value;
FIG. 7 is a contact angle of a single drop on a flat copper wall (denoted by letter a) and a contact angle measurement on a flat copper wall (denoted by letter b);
therefore, the following steps are carried out: the smaller theta is along with the increase of the dimensionless curvature K;
FIG. 8 is a graph of substrate curvature K versus static contact angle θ of a droplet;
therefore, the following steps are carried out: k1.333 corresponds to θ 94 °, K1 to θ 96 °, K0.5 to θ 98 °, K0.375 to θ 100 °, K0.3 to 102 °, K0 to θ 105 °.
And (4) conclusion: decreasing the curvature of the substrate increases the tendency to be hydrophilic and less hydrophobic.
The preferred embodiments of the present invention have been described in detail with reference to the accompanying drawings, however, the present invention is not limited to the specific details of the above embodiments, and various simple modifications can be made to the technical solution of the present invention within the technical idea of the present invention, and these simple modifications are within the protective scope of the present invention.
It should be noted that, in the foregoing embodiments, various technical features described in the above embodiments may be combined in any suitable manner, and in order to avoid unnecessary repetition, various combinations that are possible in the present invention are not described separately.
In addition, any combination of the various embodiments of the present invention is also possible, and the same should be considered as the disclosure of the present invention as long as it does not depart from the spirit of the present invention.
Claims (3)
1. A method for determining the wettability of nano-droplets based on molecular dynamics is characterized in that,
generating a substrate curvature versus droplet static contact angle graph comprising:
obtaining each substrate curvature and the corresponding static contact angle of the liquid drop, wherein the obtaining of the corresponding static contact angle of the liquid drop of each substrate curvature comprises:
for each base, performing:
acquiring position information and density information of nano liquid drops on a current substrate in relaxation preset time based on a preset trained numerical model;
determining a first curve of the nano liquid drop on a liquid-gas interface and a first data point corresponding to the first curve, and a second curve of the nano liquid drop on the solid-liquid interface and a second data point corresponding to the second curve according to the position information and the density information;
respectively fitting the first curve and the second curve by using a preset numerical order polynomial to obtain a first fitting curve corresponding to the first curve and a second fitting curve corresponding to the second curve, determining a first fitting curve coefficient based on a least square method and a first data point, and determining a second fitting curve coefficient based on the least square method and a second data point;
acquiring an intersection point of the first fitted curve and the second fitted curve and an angle difference between a tangent of the first fitted curve and a tangent of the second fitted curve at the intersection point as a static contact angle of the liquid drop corresponding to the current substrate;
plotting a graph based on the curvature of each substrate and its corresponding static contact angle of the droplet;
the static contact angle of the drop corresponding to the current substrate curvature is determined in the generated graph.
2. The method for determining wettability of nano-droplets based on molecular dynamics according to claim 1, wherein said obtaining the position information and the density information of the nano-droplets on the current substrate at a relaxation preset time based on a preset trained numerical model comprises:
determining the molecular number and the interatomic first potential function of the nano-droplet according to the density, the viscosity and the surface tension of the nano-droplet;
acquiring a second potential function between atoms of the current substrate;
determining a third potential function between atoms of the current substrate and atoms of the nano liquid drop according to the first potential function and the second potential function, and acquiring the curvature of the current substrate;
initializing a nano-droplet velocity, a nano-droplet temperature, and a nano-droplet first location, and a second location of the substrate;
maintaining the number of particles, the volume and the temperature of the nano-droplets in the wetting process unchanged to meet the NVT ensemble;
updating the position and the speed of atoms of the nano liquid drop by utilizing a Velocity-Verlet algorithm and a Langevin hot bath method, and keeping the temperature of the NVT ensemble oscillating within a preset range;
controlling the nano liquid drop to relax on the current substrate for a preset time;
slicing the nano droplets in layers, including at equal intervals
Respectively cutting a preset X axis and a Y axis perpendicular to the X axis to obtain a plurality of concentric hollow thin columns, wherein the Y axis is configured as a symmetry axis of the nano-droplets, and counting the volume and the number of atoms of each hollow thin column to determine density information of each hollow thin column; and
outputting updated position and density information of atoms of the nano-droplets.
3. The method of determining a wetting property of a nano-droplet based on molecular dynamics of claim 1, wherein the determining the first fitted curve coefficient based on a least squares method and a first data point or the determining the second fitted curve coefficient based on a least squares method and a second data point comprises:
for a given n +1 data points (x)i,yi) Assume that the m-th order fitting polynomial L (x) is taken such that the sum of squares I (a)0,a1,...,am) At a minimum, wherein a0,a1,...,amIs the unknown number of the coefficient to be solved;
determining a first fitted curve coefficient or a second fitted curve coefficient by the following formula;
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114741885A (en) * | 2022-04-18 | 2022-07-12 | 大连理工大学 | Method for accurately regulating and controlling wettability of double-layer two-dimensional material based on interlayer spacing |
| CN115101134A (en) * | 2022-07-06 | 2022-09-23 | 四川大学 | Method for evaluating anti-wetting property of material surface |
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2019
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114741885A (en) * | 2022-04-18 | 2022-07-12 | 大连理工大学 | Method for accurately regulating and controlling wettability of double-layer two-dimensional material based on interlayer spacing |
| CN114741885B (en) * | 2022-04-18 | 2022-10-14 | 大连理工大学 | Method for accurately regulating and controlling wettability of double-layer two-dimensional material based on interlayer spacing |
| CN115101134A (en) * | 2022-07-06 | 2022-09-23 | 四川大学 | Method for evaluating anti-wetting property of material surface |
| CN115101134B (en) * | 2022-07-06 | 2024-04-19 | 四川大学 | Evaluation method for anti-wetting performance of material surface |
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