CN101256132A - Steady ultra-hydrophobic surface controllable design method based on geometric analysis - Google Patents

Abstract

The invention provides a stabilizing ultra-hydrophobic surface controllable design method based on geometric analysis, relating to the fields of material research modeling and simulating material (compute) design, which is characterized in that firstly establishing parallel grating shaped or circular pit and other regular shaped microstructure surface model, according to the established microstructure feature, deriving the apparent contact angle theory predictor formula of the liquid droplet on the microstructure surface based on Wenzel theory and Cassie theory; at the same time, analyzing the C/W converting process on the microstructure surface from the geometric angle; then, pre-designing the geometric parameter of the established microstructure surface model, calculating the apparent contact angle of the liquid droplet on the microstructure surface by the apparent contact angle theory predictor formula derived above, determining whether the designed microstructure surface has ultra-hydrophobicity; at last, calculating h<SUB>0</SUB> of pre-designed microstructure geometric parameter and the corresponding apparent contact angle derived from calculation, judging whether the designed microstructure surface has ultra-hydrophobic stability. The invention is direct viewing, and is easy to operate, which has strong controllability.

Description

Stable ultra-hydrophobic surface controllable design method based on geometric analysis

Technical field

The present invention relates to investigation of materials modelling and simulation, material (calculating) design field, refer in particular to by the wetting mode switch process of micro-structure surface is carried out a kind of method that theoretical analysis is realized the controlled design of stable super hydrophobic surface from geometric angle, applicable to surface with regular pattern microstructures such as parallel grating shape, circular pit shapes.

Background technology

Wetting state is one of key character of solid surface, and it is by the chemical constitution on surface and micromechanism is common determines.In research, it is found that about biological surface " lotus leaf effect ", many biological surfaces have the hierarchical structure that micron combines with nanophase, and the many just biological surfaces of the bilayer of this micro-nano-scale combination or MULTILAYER COMPOSITE coarse structure have the basic reason of ultra-hydrophobicity.The knowledge nature, realize the ultra-hydrophobicity of material surface by the compound coarse structure of making the micro-nano-scale combination at material surface, just can make material have the self-cleaning characteristic that is unsurpassed in excellence, thereby can in industrial and agricultural production and daily life, be widely used.

Surface with super-hydrophobicity generally is meant the surface greater than 150 ° with the contact angle θ of water, wherein contact angle can be according to the Wenzel in the wetting theory of classics theoretical and Cassie theory carry out theoretical prediction.About the contact form of drop on the rough surface, R.N.Wenzel thinks that the groove that liquid can fill up on the rough surface all the time forms wetting contact.At this moment, the apparent contact angle θ of wetting surface _r ^WAnd intrinsic contact angle (being the Young contact angle) θ _eThe pass be:

$\cos {\mathrm{\&theta;}}_r^w=r\cos {\mathrm{\&theta;}}_e---\left(1\right)$

Wherein r is a roughness factor, the real area (being the solid-liquid contact area) of expression rough surface and the ratio of its horizontally-projected area.A.B.D.Cassie thinks then that with S.Baxter drop contacting on rough surface is a kind of compound contact, and drop is not filled in the pit on the rough surface and is positioned at the top of coarse projection, so the apparent contact angle θ of composite surface _r ^CBe expressed as:

$\cos {\mathrm{\&theta;}}_r^C=-1+f_1(\cos {\mathrm{\&theta;}}_e+1)---\left(2\right)$

Its f ₁The shared area fraction of projection on the expression solid surface.

More than two formulas promptly be the formula description of the theoretical and Cassie theory of Wenzel.In practical study, often make up the microstructure of the comparison rule that is easy to process, comprising how much microstructures such as parallel grating shape, circular pit shape on the surface.

Point out in the research of N.A.Patankar, on same rough surface, can have two kinds of super-hydrophobicity states simultaneously, correspond respectively to Wenzel pattern and Cassie pattern.Under the self gravitation or external interference effect of drop, can take place between these two kinds of wetting patterns by of the irreversible conversion (the following C/W that all is called changes) of Cassie pattern to the Wenzel pattern.By making up the problem that to consider wetting mode switch when surface micro-structure prepares desirable stable ultra-hydrophobic surface, make drop can be in stable Cassie pattern thereon as far as possible, and do not enter the groove between the microstructure structure.As seen, accurately passing judgment on drop, can C/W conversion take place at micro-structure surface be the key that can micro-structure surface obtain super-hydrophobic stability.

The research of carrying out micro-structure surface C/W conversion from geometric angle is less at present, W.Li and A.Amirfazli etc. have done the work of some this respects in recent years, they have provided critical altitude (h first when inquiring into the lip-deep square column height of square column array microstructure to the influencing of wetting mode switch _c) notion, and to have proposed the comprehensive criterion that wetting mode switch takes place drop from geometric point of view (be h＞h _c), but they do not further investigate the computing method of critical altitude, also not with the judgment criteria of this criterion as super-hydrophobic stability.As seen, its result of study exists certain limitation.

Summary of the invention

The purpose of this invention is to provide the method that a kind of design has the regular morphology micro-structure surface of stable ultra-hydrophobic, it is the theoretical criterion that proposes the wetting mode switch of micro-structure surface from geometric point of view, and the possibility of micro-structure surface C/W conversion is carried out theoretical prediction, thereby realize the controlled design of stable ultra-hydrophobic surface by calculating.

The present invention realizes according to following technical scheme:

At first, set up the micro-structure surface model of rule such as parallel grating shape or circular pit shape, promptly determine geometrical parameters a, b, h, as for grating shape, a, b, h are respectively raster width, spacing and depth of groove; For circular pit shape, a, b, h are respectively circular pit diameter a, pit spacing b and pit depth h.At the microstructure appearance of setting up, serve as that the theoretical prediction formula of drop at the apparent contact angle of this micro-structure surface derived on the basis with Wenzel theory and Cassie theory (formula (1) and (2)); Simultaneously, the process of micro-structure surface C/W conversion is analyzed from geometric angle, proposed " moistening height (h ₀) " notion and derive its computing formula, be the theoretical criterion of geometric angle that crucial geometric parameter is established the C/W conversion with it; Then, the micro-structure surface model of having set up is carried out geometric parameter to be designed in advance, the apparent contact angle theoretical prediction formula of deriving more than the utilization calculates the apparent contact angle of drop at micro-structure surface, determines whether the micro-structure surface of design may have super-hydrophobicity (apparent contact angle then may have super-hydrophobicity greater than 150 °); At last, with the microstructure geometric parameter of design in advance and the corresponding apparent contact angle substitution moistening height h that calculates ₀Computing formula in calculate h ₀Size, thereby realize theoretical prediction in the theoretical criterion of geometric angle of substitution specific microstructure surface C/W conversion to its C/W conversion, whether the micro-structure surface of determining design according to predicting the outcome may have super-hydrophobic stability (if the C/W conversion can not take place, then may have super-hydrophobic stability; Otherwise need carry out geometric parameter again designs in advance and carries out corresponding subsequent operation).

In the technical scheme, the derivation method of the apparent contact angle theoretical prediction of micro-structure surface formula: according to designed concrete microstructure appearance, according to the definition of r and f1 in formula (1) and the formula (2), with the apparent contact angle θ of corresponding micro-structure surface under Wenzel pattern and the Cassie pattern _r ^WAnd θ _r ^CRepresent to get final product with the microstructure geometric parameter respectively.Apparent contact angle theoretical prediction formula is the main foundation of micro-structure surface super-hydrophobicity design.

" moistening height (h ₀) " proposition and the calculating formula thereof of notion: when geometric point of view is analyzed the wetting regime of micro-structure surface drop, drop is entered into the degree of depth h of the groove between the surface micro-structure ₀The moistening height that is called drop.As the crucial geometric parameter in the C/W replacement theory criterion, moistening height h ₀Must predict by the microstructure geometric parameter of pre-design, thereby can embody the controllability of design.In view of the above, first analytic liquid drops in residing wetting regime on the specific microstructure surface of foundation, analyzes microstructure geometric parameter, apparent contact angle and the moistening height h of drop under this state from the different directions and the different angles of microstructure ₀Etc. the relation that may exist between the parameter, thereby draw moistening height h through mathematics manipulation ₀Computing formula.

The establishment of the theoretical criterion of C/W conversion geometric angle: the vertical height of establishing the surface micro-structure projection is h, by research drop moistening height h ₀And the relation between the h is established the theoretical criterion of C/W conversion.Based on this thought, the comprehensive theory criterion that the C/W conversion can earlier can the surface with various different microstructures be taken place is expressed as: if h ₀The C/W conversion does not then take place in＜h, and drop is in the Cassie pattern; If h ₀The C/W conversion has then taken place in 〉=h, and the drop that is in the Cassie pattern originally will be to the Wenzel mode switch.This comprehensive criterion is the foothold and the foundation of the super-hydrophobic stability Design of micro-structure surface, the h that will derive at the specific microstructure surface ₀Computing formula be incorporated into above comprehensive criterion, promptly obtain the theoretical criterion of geometric angle of specific microstructure surface C/W conversion.

Advantage of the present invention: purely the wettability (super-hydrophobicity and wetting mode switch) of micro-structure surface is carried out theoretical prediction from geometric angle, relatively more directly perceived, and operation easily; Proposed the notion of moistening height, for the comprehensive theory criterion that crucial geometric parameter is established various micro-structure surface C/W conversions, had practicality widely with it; Pre-design by the surface micro-structure geometric parameter, utilize the apparent contact angle theoretical prediction formula of derivation and the theoretical criterion of C/W conversion geometric angle of foundation to realize that the regulation and control of the super-hydrophobicity and the super-hydrophobic stability of micro-structure surface are had stronger controllability.

Description of drawings

Fig. 1 parallel grating shape microstructure model and parameter designing synoptic diagram thereof

Fig. 2 is along the profile synoptic diagram of the groove direction drop of parallel grating shape microstructure

Fig. 3 is perpendicular to the profile synoptic diagram of the groove direction drop of parallel grating shape microstructure

The profile synoptic diagram of drop in the single groove of Fig. 4 parallel grating shape microstructure

Fig. 5 circular pit shape microstructure model and parameter designing synoptic diagram thereof

Fig. 6 is along the profile sectional view of circular pit diametric(al) drop

The profile synoptic diagram of drop in the single circular pit of Fig. 7

Embodiment

Be the details that example illustrates the technical scheme that the present invention proposes respectively with parallel grating shape micro-structure surface and circular pit shape micro-structure surface below.

(1) parallel grating shape micro-structure surface

The theoretical prediction formula of the apparent contact angle of elder generation's derivation.Fig. 1 is parallel grating shape microstructure model and parameter designing synoptic diagram thereof, and its geometric parameter that relates to has raster width a, spacing (being recess width) b and depth of groove h.The zone of choosing in the right frame of broken lines of figure is that one-period is analyzed, and the length of optional grating orientation is l, according to r and f ₁Definition have: r=[(a+b) l+2hl]/[(a+b) l]=1+2h/ (a+b), f ₁=(al)/[(a+b) l]=a/ (a+b).Substitution formula (1) and formula (2) obtain respectively:

$\cos {\mathrm{\&theta;}}_r^W=[1+\frac{2h}{a+b}]\cos {\mathrm{\&theta;}}_e---\left(3\right)$

$\cos {\mathrm{\&theta;}}_r^C=-1+\frac{a}{a+b}(\cos {\mathrm{\&theta;}}_e+1)---\left(4\right)$

Moistening height h again derives ₀Computing formula.Suppose that the drop on the parallel grating shape micro-structure surface may be by the Cassie mode switch to the Wenzel pattern, get the critical conditions that the C/W conversion takes place drop and analyze that the contact angle of establishing drop under this state is θ _r, common θ _r ^C＞θ _r＞θ _r ^W, and θ _rApproach very much θ _r ^W(can be calculated by formula (3)) can be similar to when analyzing and get θ _r=θ _r ^WFig. 2 is the profile synoptic diagram along the groove direction drop of parallel grating shape microstructure, and the radius of drop is R, and it is L with the line length that contacts on surface.The gravity of ignoring drop, then the profile with top can be approximately spherical crown to drop on the surface; Equally, the profile that drop enters single groove part also can be approximately little spherical crown, then moistening height h ₀Be the height of little spherical crown, the radius of establishing little spherical crown is r.Fig. 3 is the profile synoptic diagram perpendicular to the groove direction drop of parallel grating shape microstructure, drop on the surface with the large ball prefix appearance profile line on top and drop the bead hat appearance profile line in groove, bead hat appearance profile line and the drop of drop in groove all should be tangent along the minimum outline line of level of groove direction, could form rounding off thus, so the centre of sphere of big or small spherical crown and both points of tangency should be on same straight lines, wherein l ' is the width of bead crown gear profile, little spherical crown is identical in the profile live width of all directions, obviously l '=b/2 should be arranged.Fig. 4 is the profile synoptic diagram of the interior drop of single groove of parallel grating shape microstructure, and the central angle of establishing bead hat profile is α.Based on above hypothesis and explanation, the geometric relationship of analyzing between each parameter can obtain:

2. $\sin \frac{\mathrm{\&alpha;}}{2}=\frac{b}{2r};$ ③ $\cos \frac{\mathrm{\&alpha;}}{2}=\frac{r-h_0}{r}.$ Three equatioies can get thus:

$h_0=\frac{b}{2}\&CenterDot;\frac{1+\cos {\mathrm{\&theta;}}_r^W}{\sin {\mathrm{\&theta;}}_r^W}=\frac{b}{2}\&CenterDot;\cot \frac{{\mathrm{\&theta;}}_r^W}{2}---\left(5\right)$

Establish the theoretical criterion of C/W conversion geometric angle at last.Can predict moistening height h theoretically according to (5) formula ₀Value, the theoretical criterion of geometric angle that the comprehensive theory criterion of substitution C/W conversion can obtain parallel grating shape micro-structure surface C/W conversion is as follows: if $h_0=\frac{b}{2}\&CenterDot;\cot \frac{{\mathrm{\&theta;}}_r^W}{2}<h,$ Then drop is in stable Cassie pattern, and the C/W conversion can not take place; If $h_0=\frac{b}{2}\&CenterDot;\cot \frac{{\mathrm{\&theta;}}_r^W}{2}\&GreaterEqual;h,$ Then drop will be the Wenzel pattern by original C assie mode switch.

(2) circular pit shape micro-structure surface

The theoretical prediction formula of the apparent contact angle of elder generation's derivation.Fig. 5 is circular pit shape microstructure model and parameter designing synoptic diagram thereof, and its geometric parameter that relates to has circular pit diameter a, pit spacing b and pit depth h.Figure is right to have indicated the one-period of this kind microstructure by frame of broken lines, it is analyzed know equally: r=[(a+b) ²+ π ah]/(a+b) ²=1+ π ah/ (a+b) ², f ₁=[(a+b) ²-π a ²/ 4]/(a+b) ²=1-π a ²/ [4 (a+b) ²].Substitution formula (1) and formula (2) obtain respectively:

$\cos {\mathrm{\&theta;}}_r^W=[1+\frac{\mathrm{\&pi;ah}}{{(a+b)}^2}]{\cos \mathrm{\&theta;}}_e---\left(6\right)$

$\cos {\mathrm{\&theta;}}_r^C=\cos {\mathrm{\&theta;}}_e-\frac{\mathrm{\&pi;}{a}^2}{4{(a+b)}^2}(\cos {\mathrm{\&theta;}}_e+1)---\left(7\right)$

Moistening height h again derives ₀Computing formula.Drop on the same supposition circular pit shape micro-structure surface may be by the Cassie mode switch to the Wenzel pattern, and the contact angle θ of the critical conditions of C/W conversion takes place drop _rThe approximate θ that is taken as _r ^W(can calculate) by formula (3).Fig. 6 is the profile sectional view along circular pit diametric(al) drop, and the radius of drop is R, and it is L with the line length that contacts on surface.The gravity of ignoring drop, then the profile with top can be approximated to be spherical crown to drop equally on the surface.Fig. 7 is the profile synoptic diagram of drop in the single circular pit, and the profile that drop enters single pit also can be approximately little spherical crown, then moistening height h ₀Be the height of little spherical crown also, the radius of establishing little spherical crown is r, and central angle is β; Drop also is in the critical conditions that the C/W conversion takes place with contacting of pit sidewall, so the contact angle of drop and sidewall also is θ _r(≈ θ _r ^W).Based on above hypothesis and explanation, can obtain by geometric relationship: 2. $\sin \frac{\mathrm{\&beta;}}{2}=\frac{b}{2r},$ ③ $\cos \frac{\mathrm{\&beta;}}{2}=\frac{r-h_0}{r}.$ Three equatioies can get thus:

$h_0=\frac{b}{2}\&CenterDot;\frac{1-{\sin \mathrm{\&theta;}}_r^W}{-\cos {\mathrm{\&theta;}}_r^W}=\frac{b}{2}\&CenterDot;\frac{\tan \frac{{\mathrm{\&theta;}}_r^W}{2}-1}{\tan \frac{{\mathrm{\&theta;}}_r^W}{2}+1}---\left(8\right)$

Establish the theoretical criterion of C/W conversion geometric angle at last.Can predict moistening height h theoretically according to (8) formula ₀Value, the theoretical criterion of geometric angle that the comprehensive theory criterion of substitution C/W conversion can obtain circular pit shape micro-structure surface C/W conversion is as follows:

If $h_0=\frac{b}{2}\&CenterDot;\frac{\tan \frac{{\mathrm{\&theta;}}_r^W}{2}-1}{\tan \frac{{\mathrm{\&theta;}}_r^W}{2}+1}<h,$ Then drop is in stable Cassie pattern, and the C/W conversion can not take place; If $h_0=\frac{b}{2}\&CenterDot;\frac{\tan \frac{{\mathrm{\&theta;}}_r^W}{2}-1}{\tan \frac{{\mathrm{\&theta;}}_r^W}{2}+1}\&GreaterEqual;h,$ Then drop will be the Wenzel pattern by original C assie mode switch.

After finishing at the above theoretical analysis of parallel grating shape micro-structure surface and circular pit shape micro-structure surface etc., just can carry out geometric parameter to concrete micro-structure surface model designs in advance, utilize the theoretical prediction formula of apparent contact angle to calculate the apparent contact angle of drop on the one hand, if apparent contact angle θ at this micro-structure surface _r ^CMicro-structure surface greater than 150 ° of explanation designs may have super-hydrophobicity (otherwise designing in advance again); Utilize moistening height h on the other hand ₀Computing formula calculate h ₀Size, the theoretical criterion of substitution corresponding C/W conversion geometric angle is predicted, if the C/W conversion can not take place, illustrate that the micro-structure surface that designs may have super-hydrophobic stability (otherwise designing in advance again).

Above embodiment proposed by the invention only describes technical scheme, and does not limit.

Claims (2)

1. based on the stable ultra-hydrophobic surface controllable design method of geometric analysis, it is characterized in that: at first, set up the micro-structure surface model of rules such as parallel grating shape or circular pit shape, promptly determine geometrical parameters a, b, h, as for grating shape, a, b, h are respectively raster width, spacing and depth of groove; For circular pit shape, a, b, h are respectively circular pit diameter a, pit spacing b and pit depth h, at the microstructure appearance of setting up, be that the theoretical prediction formula of drop at the apparent contact angle of this micro-structure surface derived on the basis with Wenzel theory and Cassie theory; Simultaneously, the process of micro-structure surface C/W conversion is analyzed from geometric angle, with moistening height h ₀Establish the theoretical criterion of geometric angle of C/W conversion for crucial geometric parameter; Then, the micro-structure surface model of having set up is carried out geometric parameter to be designed in advance, the apparent contact angle theoretical prediction formula of deriving more than the utilization calculates the apparent contact angle of drop at micro-structure surface, determines whether the micro-structure surface of design may have super-hydrophobicity; At last, with the microstructure geometric parameter of design in advance and the corresponding apparent contact angle substitution moistening height h that calculates ₀Computing formula in calculate h ₀Size, thereby realize theoretical prediction in the theoretical criterion of geometric angle of substitution specific microstructure surface C/W conversion to its C/W conversion, whether may have super-hydrophobic stability according to the micro-structure surface of determining design that predicts the outcome, if the C/W conversion can not take place, then may have super-hydrophobic stability; Otherwise carrying out geometric parameter again designs in advance and carries out corresponding subsequent operation;

The derivation method of the apparent contact angle theoretical prediction of micro-structure surface formula: according to designed concrete microstructure appearance, with the apparent contact angle θ of corresponding micro-structure surface under Wenzel pattern and the Cassie pattern _r ^WAnd θ _r ^CRepresent to get final product with the microstructure geometric parameter respectively.

2. the stable ultra-hydrophobic surface controllable design method based on geometric analysis according to claim 1, it is characterized in that: the establishment of the theoretical criterion of described C/W conversion geometric angle: the vertical height of establishing the surface micro-structure projection is h, and the comprehensive theory criterion that can the surface that will have various different microstructures earlier the C/W conversion take place is expressed as: if h ₀The C/W conversion does not then take place in＜h, and drop is in the Cassie pattern; If h ₀The C/W conversion has then taken place in 〉=h, and the drop that is in the Cassie pattern originally will be to the Wenzel mode switch.

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