CN110010207A - Molecular dynamics method for measuring bending stiffness of monolayer molybdenum disulfide - Google Patents
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- 239000002356 single layer Substances 0.000 title claims abstract description 59
- CWQXQMHSOZUFJS-UHFFFAOYSA-N molybdenum disulfide Chemical compound S=[Mo]=S CWQXQMHSOZUFJS-UHFFFAOYSA-N 0.000 title claims abstract description 57
- 229910052982 molybdenum disulfide Inorganic materials 0.000 title claims abstract description 55
- 238000005452 bending Methods 0.000 title claims abstract description 53
- 238000000034 method Methods 0.000 title claims abstract description 40
- 238000000329 molecular dynamics simulation Methods 0.000 title claims abstract description 27
- 238000013507 mapping Methods 0.000 claims abstract description 12
- 239000010410 layer Substances 0.000 claims description 20
- 229910052750 molybdenum Inorganic materials 0.000 claims description 14
- 238000005381 potential energy Methods 0.000 claims description 13
- ZOKXTWBITQBERF-UHFFFAOYSA-N Molybdenum Chemical group [Mo] ZOKXTWBITQBERF-UHFFFAOYSA-N 0.000 claims description 12
- NINIDFKCEFEMDL-UHFFFAOYSA-N Sulfur Chemical group [S] NINIDFKCEFEMDL-UHFFFAOYSA-N 0.000 claims description 9
- 230000008569 process Effects 0.000 claims description 9
- 238000005259 measurement Methods 0.000 claims description 5
- 239000011733 molybdenum Substances 0.000 claims description 5
- 238000005457 optimization Methods 0.000 claims description 4
- 230000003993 interaction Effects 0.000 claims description 3
- 125000004122 cyclic group Chemical group 0.000 claims description 2
- 230000000694 effects Effects 0.000 abstract description 17
- 230000008859 change Effects 0.000 abstract description 7
- 239000002086 nanomaterial Substances 0.000 abstract description 3
- 230000005476 size effect Effects 0.000 abstract 1
- 239000000463 material Substances 0.000 description 7
- 239000005864 Sulphur Substances 0.000 description 4
- 238000004364 calculation method Methods 0.000 description 3
- 238000010276 construction Methods 0.000 description 3
- 238000011161 development Methods 0.000 description 3
- 230000018109 developmental process Effects 0.000 description 3
- 238000002474 experimental method Methods 0.000 description 3
- 238000011160 research Methods 0.000 description 3
- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 description 2
- 238000013461 design Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 230000004323 axial length Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000008901 benefit Effects 0.000 description 1
- 239000002041 carbon nanotube Substances 0.000 description 1
- 229910021393 carbon nanotube Inorganic materials 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 239000003814 drug Substances 0.000 description 1
- 229910021389 graphene Inorganic materials 0.000 description 1
- 238000012067 mathematical method Methods 0.000 description 1
- 238000000324 molecular mechanic Methods 0.000 description 1
- 238000012805 post-processing Methods 0.000 description 1
- 230000005610 quantum mechanics Effects 0.000 description 1
- 239000000523 sample Substances 0.000 description 1
- 239000004065 semiconductor Substances 0.000 description 1
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Abstract
The invention provides a method for measuring single-layer molybdenum disulfide elbowA molecular dynamics method of bending rigidity belongs to the technical field of calculating two-dimensional nano materials. Firstly establishing a flat plate structure model of a single-layer molybdenum disulfide molecule with required size, then mapping the flat plate structure with the size into tubular structure models with different curvatures by a coordinate mapping method, then applying circumferential constraint on the tubular structure models to ensure that the configuration constraint of the tubular structure models is under the inherent curvature after mapping, counting the strain energy density of the models under the different curvatures by molecular dynamics simulation, making a strain energy density and curvature square curve graph, and taking the curvature of the tubular structure model less than 0.1nm‑1The bending stiffness is obtained by fitting the small deformation region. Through calculating several groups of models with different characteristic sizes bending at different boundaries, the results show that the boundary effect of different bending rigidity change trends of the single-layer molybdenum disulfide when bending along different boundaries and the size effect of gradually consistent bending rigidity along with the increase of the characteristic sizes.
Description
Technical field
The invention belongs to calculate two-dimension nano materials technical field, it is related to a kind of with molecular dynamics simulation measurement single layer
The numerical method of molybdenum disulfide bending stiffness.
Background technique
So-called generation material, generation equipment.The development of material science is basis and the driving force of Development of Modern Science, is had
Particularly important meaning.Carbon nanotube and graphene are as revolutionary super material, with its excellent mechanical property etc. in life
Object medicine, the fields such as space flight and aviation are widely used.But, due to lacking corresponding bandgap structure, this limits them in integrated circuit for it
Application in equal devices.Single layer molybdenum disulfide (MoS2) with its special bandgap structure and characteristic of semiconductor, in integrated circuit
There are huge potentiality for application with photoelectric device.And the safety military service of equipment and material is close with its mechanical property and deformational behavior
Cut phase is closed.
Wherein, effectively the bending property of measurement single layer molybdenum disulfide is designed and is applied in two-dimensional nano flexible device to it
It plays a key effect, and the research currently for the bending property of single layer molybdenum disulfide is less, therefore to its mechanics of bending
Quality Research is particularly important.In addition, being caused for nanometer sized materials due to boundary effect and dimensional effect etc.
It shows the characteristic different from macroscopic material performance, equally largely affects the design and preparation of material.And it is big
Amount data shows that single layer molybdenum disulfide has difference in its armchair and the borderline property of sawtooth pattern
(Nanotechnology, 2015,26 (18): 185705), therefore the spy to single layer molybdenum disulfide boundary effect and dimensional effect
Study carefully also particularly important.
Currently, the method for studying nano material includes experimental method, quantum mechanics method, Molecular mechanics method and molecule
Dynamic method.Experimental method due to experimental facilities limitation, it is and complicated for operation, therefore carry out test at the nanoscale and remain
Greatly challenging.Based on quantum-mechanical calculation method, it is similarly subjected to the limitation of scale, computable molecule amount has
The systems such as macromolecular are difficult to calculate by limit.Molecular dynamics simulation as a kind of effectively means of research " microcosmos " with
Method is widely used.Based on the studies above background and method, the present invention is based on Molecular Dynamics methods effectively to measure
The bending stiffness of single layer curing, and calculated result shows the boundary effect of single layer molybdenum disulfide molecular curvature property
It with dimensional effect, carries out being bent its bending stiffness difference along different boundary, and with the increase of characteristic size, bending stiffness
Gradually reach unanimity.
Summary of the invention
The present invention provides a kind of method based on molecular dynamics simulation measurement single layer molybdenum disulfide bending property, Ke Yiyou
Effect accurately measures its bending stiffness.Furthermore the method for the present invention calculated result illustrates the boundary of single layer molybdenum disulfide bending property
Effect and dimensional effect, this is under micro/nano-scale, and design electronic component provides important theoretical reference.
Technical solution of the present invention:
A kind of Molecular Dynamics method measuring single layer molybdenum disulfide bending stiffness, steps are as follows:
(1) single layer molybdenum disulfide is by the plate molecular model of the class sandwich structure of three layers of atomic building upper and lower two
Layer is sulphur (S) atomic layer, and centre is molybdenum (Mo) atomic layer；Plate molecular model is divided into armchair boundary according to its boundary characteristic
With sawtooth pattern boundary；Initially set up the single layer molybdenum disulfide (MoS of required size2) plate molecular model, then reflected by coordinate
The single layer molybdenum disulfide plate molecular model established is mapped to 5 kinds of different songs by shooting method (mathematical method of coordinate conversion)
The tubular structure model of rate；It is divided into large scale plate molecular model and small according to the size of single layer molybdenum disulfide plate molecular model
Size flat-panel molecular model, large scale plate molecular model are the plate molecular model that the size of curved edges is 30nm-50nm, point
90,180,270,360 degree of tubular structure Ying She not become；Small size plate molecular model is that the size of curved edges is 5nm-
The plate molecular model of 25nm is mapped to 15,30,45,60 degree of tubular structures respectively；It is counted respectively by Molecular Dynamics method
Out under different size flat-panel molecular models and corresponding 5 kinds of different curvatures tubulose structural molecule model total potential energy, and calculate
Potential energy difference under same size between tubular model and flat plate model out；
(2) it is based on theory of continuous medium mechanics, the bending stiffness D of single layer molybdenum disulfide is obtained by its strain energy Δ U, this is answered
Change can be the potential energy difference that above-mentioned Molecular Dynamics method counts, and specific equation form is as follows:
Wherein, κ is the curvature of tubular model after bending；A is the true area of the plate molecular model of single layer molybdenum disulfide,
Assuming that the surface area of mapping front and back plate molecular model is constant, using the surface area of plate molecular model as area herein；It is logical
Cross the curve that above-mentioned relation formula makes plate the molecular model strain energy density under each curvature and curvature square, and benefit
It is less than 0.1nm with curvature-1The calculated result in small deformation region carry out linear fit, fitting 2 times of line slope are current
The bending stiffness of dimension model；
Above-mentioned molecular dynamics simulation is specific as follows:
Using open source software LAMMPS, described between single layer molybdenum disulfide atom using Stillinger-Weber (SW) potential energy
Interaction；
Boundary condition is applied to computation model first: (1) single layer two of tubulose will be mapped to by the way of hoop constraint
Each molybdenum atom of molybdenum sulfide middle layer constrains in the cyclic annular curvature after its mapping inherently, and in tubulose single layer molybdenum disulfide
The axial direction of interbed is similar to apply centripetal force without constraint；(2) the bilevel sulphur atom of single layer molybdenum disulfide of tubulose
Without constraint, sulphur atom freely carries out structural adjustment；(3) above-mentioned constraint is applied using spring, one end of spring
In the center point of tubular structure model, the spring other end connects molybdenum atom, molybdenum atom is made to be only capable of carrying out in its intrinsic curvature
Adjustment；(4) in addition, boundary atom for un-flexed side (tube axial direction), is constrained in its axial direction, make its configuration
Do not twist deformation in optimization process；
Then, the computation model for applying boundary condition is subjected to energy minimum, then carries out dynamics relaxation process, moved
Mechanical relaxation uses NVT assemblage, and temperature is controlled in 0.01K；And every 500 step exports the total of a computation model in relaxation process
Potential energy；The above results are counted and are post-processed, relationship between energy density and curvature is obtained, final fitting is bent just
Degree.
Beneficial effects of the present invention: the present invention is primarily based on Molecular Dynamics method and has obtained single layer molybdenum disulfide molecule
Bending stiffness avoids experiment measurement bring difficulty and cost.Then by calculate different characteristic size different boundary into
The curved several group models of row give the boundary effect and dimensional effect curve of single layer molybdenum disulfide molecular curvature behavior.As a result
It shows and carries out being bent the different boundary effect of its bending stiffness along different boundary, and with the increase of characteristic size, it is curved
The dimensional effect that stiffness gradually reaches unanimity.
Detailed description of the invention
Fig. 1 is computation model and schematic illustration.Scheming (a) is single layer molybdenum disulfide planar structure schematic diagram；Scheming (b) is
Different curvature tubular structure single layer molybdenum disulfide stereoscopic schematic diagram after coordinate mapping；(c) is schemed for the signal of tubular model boundary condition
Figure.
Fig. 2 different characteristic dimension model bending stiffness approximating method figure.Scheming (b) is strain energy density and curvature relationship figure；
Scheming (a) is strain energy density and curvature linear fitted figure.
Fig. 3 is the trend chart that bending stiffness increases simultaneously with each edge circle characteristic size.
Fig. 4 is the trend chart that bending stiffness increases with curved boundaries characteristic size.
Fig. 5 is the trend chart that bending stiffness increases with un-flexed boundary characteristic size.
Specific embodiment
With reference to the accompanying drawing with technical solution, a specific embodiment of the invention is further illustrated.
The present invention uses Molecular Dynamics method, to measure single layer molybdenum disulfide bending stiffness as specific embodiment, with this
Verify the validity and feasibility of the method for the present invention.Specific step is as follows:
As shown in Fig. 1 (a), single layer molybdenum disulfide is by the plate molecule mould of the similar sandwich structure of three layers of atomic building
Type, upper layer and lower layer are sulphur (S) atom, and centre is molybdenum (Mo) atomic layer.Armchair side can be classified as according to its boundary characteristic
Boundary and sawtooth pattern boundary.Single layer molybdenum disulfide (the MoS of size needed for being established first using Matlab2) plate molecular model, so
The size single layer molybdenum disulfide slab construction, is mapped to the tubular structure of 5 kinds of different curvatures by the method mapped afterwards by coordinate
Model (large scale (size of curved edges is 30nm-50nm) model is mapped to as shown in Fig. 1 (b) respectively as 90,180,270,
360 degree of tubular structure, small size (the size 5nm-25nm of curved edges) model are mapped to 15,30,45,60 degree of tubular structures).
It counts total potential energy of tubular structure and slab construction under this 5 kinds of different curvatures respectively by Molecular Dynamics method, and calculates
Potential energy difference between the tubular structure and slab construction of different curvature out.
Then, it is based on theory of continuous medium mechanics, the bending stiffness D of single layer molybdenum disulfide obtains (this by its strain energy Δ U
The strain energy at place is the potential energy difference that Molecular Dynamics Calculation counts).Specific equation is as follows:
Wherein, κ is the curvature of tubular model after bending；A is the true area of the plate molecular model of single layer molybdenum disulfide.
This is that deformation of the present invention is small deformation, it is assumed that the surface area of mapping front and back plate molecular model is constant, using plate
The surface area of molecular model is as area herein；The plate molecular model is made under each curvature by above-mentioned relation formula
The curve of strain energy density and curvature square, and it is less than 0.1nm using curvature-1Small deformation region calculated result carry out it is linear
Fitting, 2 times of fitting line slope are the bending stiffness of current size model；
Molecular dynamics simulation details of the present invention is as follows: molecular dynamics simulation uses open source software LAMMPS.And it uses
Stillinger-Weber (SW) potential energy describes the interatomic interaction of single layer molybdenum disulfide.Molecular dynamics simulation is right first
Computation model applies boundary condition and will be mapped to the every of the single layer molybdenum disulfide middle layer of tubulose by the way of hoop constraint
In one molybdenum (Mo) atom bound curvature intrinsic after its mapping, and upper layer and lower layer sulphur (S) atom is without constraint, Ke Yijin
Row structural adjustment.In LAMMPS, using Spring (spring) order after secondary development of the present invention to two sulphur of single layer of tubulose
Changing molybdenum molecule progress hoop constraint, (shown in such as Fig. 1 (c), which can be to Mo atoms all in computation model in circumference
Direction (x and z directions) is constrained, and axial direction (direction y) is without constraint.It is similar to apply centripetal force), one end of spring
In the center point of tubular model structure, the spring other end connects Mo atom, Mo atom is made to be only capable of carrying out in its intrinsic curvature
Adjustment.In addition, the outermost layer boundary atom (such as Fig. 1 (b) outlines part with rectangle in (c)) for un-flexed side is axially square
It is constrained upwards, its structure is made not twist in optimization process, recenter order is specifically used in LAMMPS.Its
It is secondary, energy minimum (geometry optimization) is carried out to the computation model for being applied with boundary condition, then carries out dynamics relaxation process,
Dynamics relaxation uses NVT assemblage, and temperature is controlled in 0.01K.The calculated result of molecular dynamics is exported again, the present invention
Every 500 step exports total potential energy of a computation model.Statistics finally is carried out to the above results and is bent rigidity with post-processing.
The present invention is divided into following to probe into the dimensional effect and boundary effect of single layer molybdenum disulfide molecular curvature property
6 big groups are simulated, and are bent respectively with sawtooth pattern boundary as curved edges using armchair, characteristic size is same along two boundaries
(size keeps large scale 50nm constant and other a line circle feature to Shi Bianhua by the model and a line circle of 5nm to 50nm)
Change in size (size by 5nm to 50nm) model.All group model characteristic sizes change every time as 5nm.Specific Modeling Calculation
It is as follows with analysis process:
As shown in Fig. 2, to be bent on armchair boundary, and along a group model of curved boundaries feature size variations it is
Example is established armchair boundary dimensions using Matlab first respectively and is increased by 5nm to 50nm, serrated boundary (un-flexed side) ruler
The very little model for remaining 50nm amounts to 10 kinds, then distinguishes the plate molecular model of the single layer molybdenum disulfide of each size
It is mapped to the tubular model of 5 kinds of different curvatures, by molecular dynamics simulation, respectively obtains the lower 5 kinds of differences of different characteristic size
The strain energy density of the plate molecular model of bending angle (curvature) single layer molybdenum disulfide, and curvature is taken to be less than 0.1nm-1Small change
It draws out shown in relational graph such as Fig. 2 (a) of strain energy density and curvature in shape region.Then to square of strain energy density and curvature
The scatter plot of relationship carries out linear fit, and 2 times of fitting line slope are the bending of current size single layer molybdenum disulfide model
Rigidity.Therefore, bending stiffness of this group of single layer molybdenum disulfide model under each characteristic size shown in Fig. 2 (b) by being fitted
It arrives.
By calculating above and statistical method, above-mentioned 6 group model calculated result is obtained as shown in Fig. 3,4,5.Wherein Fig. 3 is
Respectively using sawtooth pattern and armchair boundary as curved edges, increase (two simultaneously along bending and un-flexed two boundary characteristic sizes
Boundary is changed as 5nm to 50nm) obtained from bending stiffness trend chart.With single layer it can be seen from trend in figure
The increase of two boundary characteristic sizes of molybdenum disulfide, bending stiffness is also gradually increased and the value that tends towards stability.
Fig. 4 is to be bent respectively in sawtooth pattern and armchair boundary, in un-flexed boundary (tubulose single layer molybdenum disulfide
Axial (direction y in figure)) large scale of 50nm is kept, and become along the bending stiffness variation that curved boundaries characteristic size increases
Gesture figure, variation tendency is similar with Fig. 3 trend, and with the increase of curved boundaries characteristic size, bending stiffness is gradually increased simultaneously
Tend towards stability value.Fig. 5 is to be bent respectively with sawtooth pattern and armchair boundary, keeps the big ruler of 50nm in curved boundaries
It is very little, the trend chart of the bending stiffness obtained from the increase of un-flexed boundary (direction y) characteristic size, as seen from the figure,
Its variation tendency is different from former group models, when being bent on armchair boundary, with the increasing of the characteristic size on un-flexed side
Add, bending stiffness gradually increases and the value that tends towards stability, but amplitude of variation is smaller (8.52eV to 8.62eV variation).When in sawtooth
When type boundary is bent, with the increase of the characteristic size on un-flexed side, bending stiffness is but gradually reduced, and is finally tended towards stability
Value.It is available to draw a conclusion by above 6 groups of examples: 1. with single layer molybdenum disulfide characteristic size increase, bending is rigid
Degree gradually reaches unanimity, about 8.65eV.2. changing its bending stiffness of characteristic size compared to along un-flexed boundary (tube axial direction)
Variation, change characteristic size in curved boundaries, the amplitude of variation of bending stiffness is bigger, and (changing caliber size has caused bending rigid
The variation of degree is bigger than changing amplitude caused by axial length).3. it is general to carry out curved its bending stiffness of model on sawtooth pattern boundary
Curved model is carried out on armchair boundary all over being greater than.
In conclusion only a specific embodiment of the invention, but the protection scope invented is not limited thereto, and it is any ripe
Within the technical scope of the present invention, some transformation that can be done such as change computation model to the engineers and technicians for knowing the art
Size, molecular dynamics ensemble etc., all should be as invading protection scope of the present invention.Because the protection scope of the invention should
Subject to the scope of protection of the claims.
Claims (2)
1. a kind of Molecular Dynamics method for measuring single layer molybdenum disulfide bending stiffness, which is characterized in that steps are as follows:
(1) single layer molybdenum disulfide is by the plate molecular model of the class sandwich structure of three layers of atomic building, and upper layer and lower layer are
Sulphur atom layer, centre are molybdenum atom layer；Plate molecular model is divided into armchair boundary and sawtooth pattern side according to its boundary characteristic
Boundary；The single layer molybdenum disulfide plate molecular model of required size is initially set up, then by coordinate mapping method, by what is established
Single layer molybdenum disulfide plate molecular model is mapped to the tubular structure model of 5 kinds of different curvatures；According to single layer molybdenum disulfide plate
The size of molecular model is divided into large scale plate molecular model and small size plate molecular model, and large scale plate molecular model is
The size of curved edges is the plate molecular model of 30nm-50nm, and mapping becomes 90,180,270,360 degree of tubular structure respectively；
Small size plate molecular model is the plate molecular model that the size of curved edges is 5nm-25nm, be mapped to 15 respectively, 30,45,
60 degree of tubular structures；Counted respectively by Molecular Dynamics method different size flat-panel molecular models and it is corresponding 5 kinds not
With total potential energy of tubulose structural molecule model under curvature, and calculate the gesture under same size between tubular model and flat plate model
It can be poor；
(2) it is based on theory of continuous medium mechanics, the bending stiffness D of single layer molybdenum disulfide is obtained by its strain energy Δ U, the strain energy
The potential energy difference that as above-mentioned Molecular Dynamics method counts, specific equation form are as follows:
Wherein, κ is the curvature of tubular model after bending；A is the true area of the plate molecular model of single layer molybdenum disulfide, it is assumed that
The surface area of mapping front and back plate molecular model is constant, using the surface area of plate molecular model as area herein；By upper
The curve that relational expression makes plate the molecular model strain energy density under each curvature and curvature square is stated, and utilizes song
Rate is less than 0.1nm-1The calculated result in small deformation region carry out linear fit, fitting 2 times of line slope are current size
The bending stiffness of model.
2. the Molecular Dynamics method of measurement single layer molybdenum disulfide bending stiffness according to claim 1, which is characterized in that
The molecular dynamics simulation is specific as follows:
Using open source software LAMMPS, the interatomic phase interaction of single layer molybdenum disulfide is described using Stillinger-Weber potential energy
With；
Boundary condition is applied to computation model first: (1) the single layer curing of tubulose will be mapped to by the way of hoop constraint
Each molybdenum atom of molybdenum middle layer constrains in the cyclic annular curvature after its mapping inherently, and tubulose single layer molybdenum disulfide middle layer
Axial direction without constraint, it is similar to apply centripetal force；(2) the bilevel sulphur atom of single layer molybdenum disulfide of tubulose not into
Row constraint, sulphur atom freely carry out structural adjustment；(3) above-mentioned constraint is applied using spring, one end of spring is in pipe
The center point of shape structural model, the spring other end connect molybdenum atom, molybdenum atom are made to be only capable of being adjusted in its intrinsic curvature；
(4) in addition, boundary atom for un-flexed side, is constrained in its axial direction, make its configuration in optimization process not
Twist deformation；
Then, the computation model for applying boundary condition is subjected to energy minimum, then carries out dynamics relaxation process, dynamics
Relaxation uses NVT assemblage, and temperature is controlled in 0.01K；And every 500 step exports total gesture of a computation model in relaxation process
Energy；The above results are counted and are post-processed, relationship between energy density and curvature is obtained, final fitting is bent just
Degree.
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| CN112798822A (en) * | 2021-01-13 | 2021-05-14 | 国家纳米科学中心 | Method for testing bending stiffness of two-dimensional nano material and interface adhesion performance between two-dimensional nano material and substrate |
| CN113486561A (en) * | 2021-07-20 | 2021-10-08 | 中国科学院工程热物理研究所 | Engine rotor dynamic characteristic improving method based on strain energy distribution |
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| CN113486561A (en) * | 2021-07-20 | 2021-10-08 | 中国科学院工程热物理研究所 | Engine rotor dynamic characteristic improving method based on strain energy distribution |
| CN113486561B (en) * | 2021-07-20 | 2022-06-28 | 中国科学院工程热物理研究所 | Engine rotor dynamic characteristic improving method based on strain energy distribution |
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